12590001 173civil Engineering Management

ISSN 1392-3730

Vilnius Gediminas Technical University

Lithuanian Academy of Sciences

Journal of Civil Engineering and Management 2004, Vol X, Supplement 1

Vilnius „Technika“ 2004

EDITORIAL BOARD Editor-in-Chief Prof Edmundas K. ZAVADSKAS, Lithuanian Academy of Sciences, Vilnius Gediminas Technical University, Saulëtekio al. 11, LT-10223 Vilnius-40, Lithuania Editors Building Materials and Structures

Structural Mechanics and Physics, Information Technologies

Construction Technology and Management

Prof Audronis K. KVEDARAS, Vilnius Gediminas Technical University, Saulëtekio al. 11, LT-10223 Vilnius-40, Lithuania

Prof Romualdas BAUÐYS, Vilnius Gediminas Technical University, Saulëtekio al. 11, LT-10223 Vilnius-40, Lithuania

Prof Artûras KAKLAUSKAS, Vilnius Gediminas Technical University, Saulëtekio al. 11, LT-10223 Vilnius-40, Lithuania

Managing editor Assoc Prof Darius BAÈINSKAS, Vilnius Gediminas Technical University, Saulëtekio al. 11, LT-10223 Vilnius-40, Lithuania International Editorial Board Dr Rogerio BAIRRAO, Portuguese National Laboratory for Civil Engineering, Av. Brasil, 101, 1700-066 Lisboa, Portugal Prof György L. BALÁZS, Budapest University of Technology and Economics, Mûegyetem rkp.3, H-1111 Budapest, Hungary Assoc Prof Erik BEJDER, Aalborg University, Fibigerstraede 16, 9220 Aalborg, Denmark Prof Adam BORKOWSKI, Institute of Fundamental Technological Research, Swiætokrzyska 21, 00-049 Warsaw, Poland Prof Michaù BOLTRYK, Biaùystok Technical University, Wiejska 45A, 15-351 Biaùystok, Poland Prof Patrick J. DOWLING, Felow Royal Society, University of Surrey, Guildford GU25XH, UK Prof Aleksandr A. GUSAKOV, Moscow State University of Civil Engineering, Dorogomilevskaja, 5/114, 121059 Moscow, Russia Prof Boris V. GUSEV, International and Russian Engineering Academies, Tverskaja 11, 103905 Moscow, Russia Assoc Prof Edward J. JASELSKIS, Iowa State University, Ames, IA 50011, USA Prof Oleg KAPLIÑSKI, Poznan University of Technology, Piotrovo 5, 60-965 Poznan, Poland Prof Herbert A. MANG, Austrian Academy of Sciences, Vienna University of Technology, Karlsplatz 13, A-1040 Vienna, Austria

Prof Rene MAQUOI, University of Liege, Building B52/3, Chemin des Chevreuils 1, B 4000 Liege, Belgium Prof Yoshihiko OHAMA, Nihon University, Koriyama, Fukushima-Ken, 963-8642, Japan Prof Friedel PELDSCHUS, Leipzig University of Applied Science, 132 Karl Liebknecht St, 04227 Leipzig, Germany Prof Karlis ROCENS, Latvian Academy of Sciences, Riga Technical University, Âzenes str. 16, Riga, LV-1048 Latvia Prof Les RUDDOCK, University of Salford, Salford, Greater Manchester M5 4WT, UK Prof Miroslaw J. SKIBNIEWSKI, Purdue University, West Lafayette, Indiana 47907-1294, USA Prof Martin SKITMORE, Queensland University of Technology, Brisbane QLD 4001, Australia Prof Zenon WASZCZYSZYN, Cracow University of Technology, Warszawska 24, 31-155 Krakow, Poland Prof Frank WERNER, Bauhaus University, Marienstrasse 5, 99423, Weimar, Germany Prof Nils-Erik WIBERG, Chalmers University of Technology, SE - 412 96 Göteborg, Sweden Prof Jiøí WITZANY, Czech Technical University, Prague, Thákurova 7, CZ 166 29 Praha 6, Czech Republic

Prof Antanas ALIKONIS, Vilnius Gediminas Technical University, Saulëtekio al. 11, LT-10223 Vilnius-40, Lithuania Prof Juozas ATKOÈIÛNAS, Vilnius Gediminas Technical University, Saulëtekio al. 11, LT-10223 Vilnius-40, Lithuania Prof Algirdas E. ÈIÞAS, Vilnius Gediminas Technical University, Saulëtekio al. 11, LT-10223 Vilnius-40, Lithuania Assoc Prof Juozas DELTUVA, Kaunas University of Technology, Studentø g. 48, LT-3028 Kaunas, Lithuania Prof Romualdas GINEVIÈIUS, Vilnius Gediminas Technical University, Saulëtekio al. 11, LT-10223 Vilnius-40, Lithuania Prof Arvydas JUODIS, Kaunas University of Technology, Studentø g. 48, LT-3028 Kaunas, Lithuania Prof Pranciðkus JUÐKEVIÈIUS, Vilnius Gediminas Technical University, Saulëtekio al. 11, LT-10223 Vilnius-40, Lithuania Prof Rimantas KAÈIANAUSKAS, Lithuanian Academy of Sciences, Vilnius Gediminas Technical University, Saulëtekio al. 11, LT-10223 Vilnius-40, Lithuania Prof Gintaris KAKLAUSKAS, Vilnius Gediminas Technical University, Saulëtekio al. 11, LT-10223 Vilnius-40, Lithuania

Prof Stanislovas KALANTA, Vilnius Gediminas Technical University, Saulëtekio al. 11, LT-10223 Vilnius-40, Lithuania Prof Ipolitas Z. KAMAITIS, Lithuanian Academy of Sciences, Vilnius Gediminas Technical University, Saulëtekio al. 11, LT-10223 Vilnius-40, Lithuania Prof Romualdas MAÈIULAITIS, Vilnius Gediminas Technical University, Saulëtekio al. 11, LT-10223 Vilnius-40, Lithuania Prof Gediminas J. MARÈIUKAITIS, Vilnius Gediminas Technical University, Saulëtekio al. 11, LT-10223 Vilnius-40, Lithuania Prof Josifas PARASONIS, Vilnius Gediminas Technical University, Saulëtekio al. 11, LT-10223 Vilnius-40, Lithuania Prof Vytautas STANKEVIÈIUS, Lithuanian Academy of Sciences, Lithuanian Institute of Architecture and Building Construction, Tunelio g. 60, LT-3035 Kaunas, Lithuania Prof Vytautas J. STAUSKIS, Vilnius Gediminas Technical University, Saulëtekio al. 11, LT-10223 Vilnius-40, Lithuania

Local Editorial Board

3 ISSN 1392–3730

JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT http:/www.vtu.lt/english/editions

2004, Vol X, Suppl 1, 3–9

RESISTANCE OF MASONRY WALL PANELS TO IN-PLANE SHEAR AND COMPRESSION Piotr Aliawdin1, Valery Simbirkin2, Vassili Toropov3 2Belarussian

1University

of Zielona Góra, Poland. E-mail: [email protected] Research Institute for Construction (BelNIIS), Minsk, Belarus. E-mail: [email protected] 3Altair Engineering, Coventry, UK. E-mail: [email protected] Received 30 Apr 2004; accepted 7 June 2004

Abstract. The paper presents results of large-scale tests carried out on masonry wall panels made of perforated bricks. The specimens were subjected to in-plane: lateral loading combined with different levels of axial compression; concentrated compressive load applied to the wall top at different distances from the wall edge. Relationships between shear strength and deformability of masonry and compressive stresses perpendicular to the shear plane have been found. An evaluation of strength of masonry under local compression is given depending on the position of the concentrated load relative to the wall edge. Analysis of test results and comparison of calculation techniques adopted in different design codes is performed. Behaviour of the test specimens is modelled using the finite element method. Keywords: masonry structures, full-scale tests, shear, compression, strength, deformations.

1. Introduction

2. Properties of masonry and masonry materials

By the present time, an extensive theoretical and experimental research has been carried out on the behaviour of masonry structures made of solid clay bricks, for instance [1–5]. However, there are a few test results for masonry structures made of perforated bricks that are widely used in practice and have a number of advantages. This study presents an experimental and analytical research into the behaviour of masonry wall panels made of perforated clay bricks. The test specimens were subjected to in-plane 1) local compressive force, and 2) racking shear force combined with vertical compression. For each loading type, two test series have been devised. In the local compression tests, position of the applied force was changed. In the shear tests, lateral force was combined with different levels of axial compression. In the first case, vertical kinematic restraints were installed on the wall top to prevent in-plane rotation of the walls. The vertical pressure arising in this case varied during the loading process and had the minimum value. In the second case, the lateral load was combined with the given vertical compression. The loading of the specimens was increased monotonically up to the total failure of the specimens. The resistance of the masonry walls to the predominant action was evaluated with reference to the strength and deformability.

The following materials were used for producing the test specimens: • Clay bricks (length 250 mm, width 120 mm, height 88 mm) with vertical holes. Each brick had 21 holes whose cross-sections were square-shaped, 20x20 cm (volume of holes is 28 % of the gross volume). Brick grade M150. • Dry pre-packed mortar mix, grade M100: Portland cement of grade 500ÄÎ – 180 kg/t, lime – 50 kg/t, sand – 770 kg/t, water-retaining agent Valotsel 45000 – 0,3 κg/t. The strength properties of the brick and mortar were determined experimentally. Their mean values are presented in Table 1. Table 1. Brick and mortar strengths

Brick strength, MPa Compressive (b y British Standard BS 3921 [6], appendix D)

Tensile (b y testing b ricks for b ending)

31,6

2,3 Mortar strength, MPa

3

Compressive (b y testing cub es of side 70,7 mm)

Shear (b y testing a masonry fragment of three b ricks)

9,9…12,7

0,23

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The initial modulus of elasticity of the masonry is computed according to [7] using the following logarithmic stress-strain relation proposed by L. I. Onistchik:

Strength and deformative properties of the masonry under short-term compression were determined by tests of five prismatic specimens having dimensions lxhxt = 380×490×250 mm. On all four vertical sides of each specimen, displacement transducers were installed over a gauge length of 200 mm. They measured longitudinal (vertical) and lateral (horizontal) deformations of the masonry. The strains measured in this way were used to calculate the deformation modulus and the Poisson’s ratio of the masonry. While testing the specimens, the mortar compressive strength was checked. Its mean value was 9,9 MPa. The tests showed that the masonry compressive strength ranged between 8,4 and 11,1 MPa, and its value averaged over strengths obtained for five specimens was equal to σult = 9,3 MPa. Averaged curves for strains, secant deformation modulus, and Poisson’s ratio of the masonry are presented in Fig 1.

ε=−

Shear tests were performed on six wall panels that were produced of the masonry with the chain bond. The overall dimensions of the specimens were as follows: length 1500 mm, height 1500 mm, thickness 120 mm, with the thickness of mortar joints of 10 to 12 mm. After manufacture the specimens were stored under polyethylene until the mortar has hardened (not less than 3 days). The tests were carried out at an age of the specimens 19 to 25 days (after the mortar achieved the compressive strength of 10 MPa). The test specimens were divided into two series (Fig 2). The specimens of the first series (series 1A) were tested for incremental lateral load P, applied to the top of the panel in its plane, combined with minimal vertical pressure that was necessary to prevent in-plane rotation of the wall. The vertical pressure was produced by spring kinematic restraints on the wall top and varied during loading so that detachment of the wall bottom from the floor was not greater than 5 cm. Displacement transducers (LVDTs) were installed along the wall height to measure lateral deflections during loading (Fig 2). In addition, displacement transducers were used to measure translation of the horizontal support and detachment caused by a compliantly restrained rotation of the wall in its plane. Their readings were taken into account for calculation of the “clear” lateral deflections by correcting the values obtained by LVDTs Th1…Th5. Unlike the first type specimens, specimens of the series 1B were loaded, in addition to the lateral load P, with a vertical uniformly distributed load q equal to 0,2Fk = 225 kN/m, where Fk is the ultimate failure load in the pure compression case. This load did not vary during the testing. The load P was applied to four top rows of bricks, and displacements were measured only at one level (at a height of 1450 mm from the wall bottom). The test showed that specimens of the series 1A collapsed immediately after a zigzag crack has appeared

s/s ult

0,8 0,6

longitudinal strain lateral strain elongation

0 –50

b)

–25

shortening 0

25

50

75

100

125

ε×105

0,6

s/s ult

0,5 0,4 0,3 0,2 0,1 0 7500

10000

12500

15000

17500

E sec , MPa

c) 0,6

s/sult

0,5 0,4 0,3 0,2 0,1 0 0,00

0,05

0,10

0,15

0,20

(1)

3. Response to shear

1

0,2

  , 

where: σ is the mean compressive stress in the test specimens; ∑ is the mean experimental value of strains obtained under stress σ; µ is the plasticity coefficient depending on the masonry type. The value of the masonry initial modulus of elasticity computed in this way is equal to 11 290 MPa.

à)

0,4

µσult  σ ln 1 − E0  µσult

0,25

Poisson's ratio Fig 1. Dependences of strains ∑, secant deformation modulus Esec, and Poisson’s ratio upon stress level for masonry under axial short-term compression

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a) Series 1A (Pult=104,6 kN)

a) Test series 1A (three specimens)

b) Series 1B (Pult=192,6 kN)

b) Test series 1B (three specimens)

– LVDTs

Fig 2. Shear test setup

along the wall diagonal connecting the lateral loading point and the horizontal support (Fig 3, a). The failure lateral load was equal to: 120,0 kN for the first specimen, 113,8 kN for the second specimen, and 80,0 kN for the third one. Therefore, the failure lateral load averaged over three these values was Pult = 104,6 kN. At the ultimate stage, average total value of the compressive load q was equal to 118 kN. Experimental graphs showing the deforming process of the series 1A specimens are presented in Fig 4. The walls of the series 1B having been tested for combined shear and compression failed also with an inclined crack connecting the lateral loading point and the horizontal support. However, in this case some vertical

Fig 3. Crack patterns after testing (general views and local failure at horizontal support)

cracks were observed, and a local failure at the horizontal support was clearer (Fig 3, b). The ultimate failure lateral load was equal to: 200,0 kN for the first specimen, 207,7 kN for the second specimen, and 170,0 kN for the third one. The failure lateral load averaged over three the values was Pult = 192,6 kN.

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Wall height, cm

a)

over, the compressive action on the masonry walls resulted in 84 % increase of the load-carrying capacity of the walls under lateral loading. Therefore, the effect of vertical compression leads to a higher resistance of the masonry walls to shear loads, making their rigidity and load-carrying capacity higher. Behaviour of the test specimens is modelled on the finite element basis using Software Stark_Es of the MicroFE family. The wall panels are modelled with highly accurate hybrid plane stress elements (mesh 30x30) derived using a Reissner functional [8]. Second order geometrical effects and unilateral elastic supports are taken into account. As an example, Fig 6 shows some analysis results for the specimens of series 1A.

150 100 P/Pult=0,10 P/Pult=0,29 P/Pult=0,48 P/Pult=0,67

50 0 0

5

10

15 20 25 Lateral displacement, mm

b) 0,8

P/ P ult

0,6

a) Deformed scheme

0,4 h=850 mm h=1150 mm h=1450 mm

0,2 0 0

5

10

15 20 25 Lateral displacement, mm

Fig 4. Lateral deflections for the series 1A specimens: a) distribution of displacements along the wall height; b) load–displacement relationships

The lateral load-displacement relationship averaged over results of three tests of the series 1B is shown in Fig 5. b) Distribution of vertical normal stresses σz along the wall length at a level of a half of the wall height

P/P ult

1 0,8 0,6

0

0,4

-0,40

0,2

-0,80 0

0,5

1

1,5

2

óz, MPa

0 2,5

Lateral displacement, mm (h=1450 mm)

-1,20 -1,60 -2,00 -2,40

Fig 5. Lateral deflections for the series 1B specimens

-2,80 -3,20

Comparing the graphs presented in Figs 4 and 5 we can notice that in-plane shear behaviour of the series 1B specimens was more plastic than the behaviour of the series 1A specimens which deformed almost elastically up to the failure (excepting a displacement leap observed at the second loading stage) and collapsed in a brittle mode. Indeed, in the series 1A specimens the cracks were not observed up to the failure, but cracks in the series 1B specimens appeared under the lateral load equal to 0,3 to 0,4 of the ultimate load. However, the specimens of the series 1A had a much lower rigidity than those of the other test series. Their failure occurred at lateral deflections that were an order of magnitude higher than ultimate deflections of the series 1B specimens. More-

-3,60 -4,00

0,00 0,15 0,30 0,45 0,60 0,75 0,90 1,05 1,20 1,35 1,50

Wall length, m Fig 6. Finite element analysis results for wall panels of series 1A (under P = 104,6 kN)

The test results presented above enable to draw an experimental relationship between the shear strength and compressive stress rate in masonry. This relationship is presented in Fig 7. As we can see in Fig 6, the masonry shear strength depends almost linearly upon the compressive stress level.

6

Shear strength, MPa

P. Aliawdin, et al / JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT – 2004, Vol X, Suppl 1, 3–9 a) Test series 2A (three specimens)

1,4 1,2

test EC6, eq. 3.3a EC6, eq. 3.3c Ðÿä4

1 0,8 0,6 0,4

masonry strength

0,2

mortar strength

0 0

0,5

1

1,5

2

2,5

3

Compressive stress, MPa

Fig 7. Relationships between masonry shear strength and compressive stress level

Hence we can propose the following empirical formula for approximate evaluation of the shear strength of masonry in a plane stress state for different levels of the compressive stresses: τult = τult ,0 + 0,28σ z ,

(2) b) Test series 2B (three specimens)

where: τult is the masonry shear strength; σ z is the mean compressive stress perpendicular to the shear plane; τult ,0 is the initial masonry shear strength, under zero compressive stress. In equation (2), all magnitudes are in MPa. Equation (2) is valid for only the cases where the compressive stress ⌠ does not exceed 0,2 of the ultimate compressive strength. A similar relationship is given in Eurocode 6 [9] to compute the masonry shear strength depending on the compressive stress value. In our case, this strength should be determined using equation 3.3a [9] but its value must be not higher than a value computed by equation 3.3c [9]. A graphical representation of the values calculated by these equations for our cases is given in Fig 7. As can be seen, equation 3.3a overestimates the shear strength of masonry, but equation 3.3c provides a rather high safety margin for the masonry shear strength.

Fig 8. Local compression test setup

4. Response to local compression For local compression tests of masonry walls, six specimens were produced and stored analogously as described in the previous section. The test specimens were tested to collapse for concentrated vertical load P applied incrementally at a distance 650 mm (series 2A) and 350 mm (series 2B) from the wall edge, as shown in Fig 8. The bearing area was 10×12 = 120 cm2. Along the loading line on both sides of the specimens, displacement transducers (Tv, Fig 8) were installed at the middle height over a gauge length of 800 mm to measure mean vertical strains. The tests showed that the specimens of both series had the same failure mode – the failure was practically brittle with formation of a local failure zone under the bearing and a vertical crack along the loading line (Fig 9).

Fig 9. Failure pattern

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7

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2 , kN

Until the load reached the value P = 150 kN, the mean vertical strains increased with loading almost identically for specimens of both series and had a slightly non-linear kind (Fig 10). However, further loading caused a deviation of the “load-strain” curve for series 2B from the direct line and from the curve shown by the series 2A specimens. After that, under the load 188 to 200 kN the failure of the series 2B specimens occurred. The mean value of the failure load for these specimens was 192,7 kN. The series 2A specimens showed a higher loadbearing capacity equal to 220 to 256 kN with the mean value of 234,7 kN.

Software Stark_Es. Results of the analysis are given in Fig 11. The analysis shows that for specimens of the different series under the ultimate failure load the maximum compressive stresses below the loaded area (óz) have the same ratio as the loads applied. However, calculated tensile stresses in the orthogonal direction (óx), which have caused the vertical crack formation in the test specimens, in the series 2B specimens are 1,25 times greater than in the series 2A specimens even under a smaller load. This indicates that in the series 2B specimens local compression (casing-type) effect is not so significant than in the other series specimens. This fact is affirmed by the kind of deformation distribution in the vicinity of the loaded area – in the series 2A specimens the effective area is greater than in the other specimens. From the deformed shape presented in Fig 11 we can assume that the effec-

200 150 100

series 2A series 2B

50

a) Series 2A

0 0

5

10

15

20

25

5

εx10

30

Fig 10. Experimental “load-strain” curves

At the failure moment, the mean value of the mid height vertical strain was 50 ⋅ 10 5 and 35 ⋅ 10 5 for specimens of the series 2A and 2B respectively. As can be seen from Fig 1a, such strains correspond to compressive stresses not exceeding a half of the ultimate strength of masonry in pure axial compression. Thus the failure of the specimens was local below the loaded area. The results presented enable to evaluate the effect of increase of the masonry resistance to concentrated compressive loads as compared with overall axial compression case. Table 2 presents values of the enhancement factor for concentrated loads obtained experimentally and calculated according to different building codes.

b) Series 2B

Table 2. Local compression effect

Test series 2A 2B

Enhancement factor for concentrated compressive loads EC6 [9], test SNiP [10] PN [11] 2,1 1,5 1,45 1,7 1,5 1,35

As we can see from Table 2, all design codes provide a rather high safety margin for the compressive strength of masonry subjected to concentrated loads. In addition, Russian code [10] defines the same enhancement factor for both the test series and, in contrast to Eurocode 6 [9] and Polish code [11], does not take into account changes of the masonry local compressive strength depending on the wall height. The ultimate stage of the wall behaviour is modelled on the basis of the finite element method using

Fig 11. Results of finite element analysis (displacement scale 200:1)

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tive area includes wall parts of 250 mm length for the series 2A specimens and 200 mm for the series 2B specimens to both sides from the loaded area (but not 120 mm as adopted in code [10] for both our cases). In this case, the enhancement factor calculated by Eq (19) given in [10] would be equal to 1,82 and 1,71 for specimens of the first and the second series respectively. These values are much closer to the experimental ones than those calculated according to [10]. Therefore, the masonry resistance to concentrated compressive loads can be evaluated sufficiently accurate by the finite element analysis.

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Acknowledgement. The authors are pleased to acknowledge the support of INTAS under international project 00-0600. References

5. Conclusions 1. Large-scale tests carried out on masonry wall panels subjected to in-plane lateral (shear) loading combined with different levels of axial compression show that: • Behaviour of masonry wall panels subjected to pure shear is almost perfectly elastic, the failure occurs in a brittle mode. Compressive load affects the shear behaviour of the masonry making it plastic. • Shear capacity of masonry walls increases by about 80 % due to the action of axial compressive load equal to 20 % of the ultimate compressive strength; the lateral rigidity of such walls can be of an order of magnitude higher as compared with the walls under pure shear. 2. Local compression tests of masonry walls show that resistance of masonry to concentrated compressive load depends significantly on the distance from the wall edge to the load position even if this distance 2,5 times greater than the wall thickness. This fact is not taken into account in SNiP II-22-81 [10]. A finite element analysis can be used for strength evaluation for masonry subjected to concentrated loads.

1.

Bull, J. W. Computational modelling of masonry, brickwork and blockwork structures. Saxee-Coburg Publications, 2001. 346 p.

2.

Hendry, A. W. Structural masonry. London: Mac-Millan Education Ltd, 1990. 284 p.

3.

Majewski, S.; Szojda, L. Numerical analysis of a masonry structure. Engineering and construction, 2002, No 10, p. 578–581 (in Polish).

4.

Orùowicz, R.; Maùyszko, L. Masonry structures. Cracks and their elimination. Olsztyn: Wydawnictwo Uniwersytetu Warmiñsko-Mazurskiego, 2000. 152 p. (in Polish).

5.

Kubica, J.; Drobiec, Ù.; Jasiñski, R. Study of secant deformation modulus of masonry. In: Proceedings of XLV Scientific Conference KILiW PAN i KN PZITB. WrocùawKrynica, 1999, p. 133–140 (in Polish).

6.

BRITISH STANDARD BS 3921: Specifications for clay bricks. London: British Standards Institution, 2001. 22 p.

7.

Sementsov, S. A. On the method of selection of logarithmic stress-strain relation using test data. In: Strength and stability of large-panel structures, Vol 15. Moscow: Gosstroyizdat, 1962, p. 303–309 (in Russian).

8.

Semenov, V. A.; Semenov, P. J. Highly accurate finite elements and their use in software MicroFE. Residential Construction, 1998, No 8, p. 18–22 (in Russian).

9.

prEN 1996-1-1: Redraft 9A. Eurocode 6: Design of masonry structures – Part 1-1: Common rules for reinforced and unreinforced masonry structures. – European Committee for Standardization, 2001. 123 p.

10. SNiP II-22-81. Masonry and reinforced masonry structures. Design Code. (ÑÍèÏ II-22-81. Moscow: Gosstroi USSR, 1983. 39 p. (in Russian). 11. PN-B-03002:1999. Masonry structures. Design and analysis. PKN, 1999. 67 p. (in Polish).

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11 ISSN 1392–3730

JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT http:/www.vtu.lt/english/editions

2004, Vol X, Suppl 1, 11–18

FE SOFTWARE ATENA APPLICATIONS TO NON-LINEAR ANALYSIS OF RC BEAMS SUBJECTED TO HIGH TEMPERATURES Darius Bacinskas1, Gintaris Kaklauskas2, Edgaras Geda3 Dept of Bridges and Special Structures, Vilnius Gediminas Technical University, Saulëtekio al 11, LT-10233 Vilnius-40, Lithuania. E-mail: [email protected], [email protected], [email protected] Received 15 Apr 2004; accepted 23 Feb 2004 Abstract. Reinforced concrete structures subjected to fire will generally experience complex behaviour. This paper presents a strategy of numerical simulation of reinforced concrete members exposed to high temperatures and subjected to external loading. Finite element modelling of full load – deflection behaviour of experimental reinforced concrete beams reported in the literature has been carried out by the FE software ATENA. A constitutive model based on Eurocode 2 specifications has been used in the analysis. Comparison of numerical simulation and test results have shown reasonable accuracy. Keywords: reinforced concrete fire design, non-linear finite element analysis, fire tests, fire resistance, constitutive models of concrete and steel.

behaviour of a member under elevated temperature conditions can be simulated using the finite element method [6, 7]. Because of increasing interest in the field of structural fire protection, the number of existing software capable to analysing the thermal response of materials under transient heating conditions is quite large [8, 9]. The majority of these programmes was developed in professional software houses, such as DIANA [10], ATENA [11], ABAQUS, MSC.MARC, etc. Such programmes have many advantages including documentation, sophisticated non-linear material models, pre/postprocessing facilities, etc. This paper presents a strategy of numerical simulation of reinforced concrete members exposed to high temperatures and subjected to external loading. Finite element modelling of full load – deflection behaviour of experimental reinforced concrete beams reported in [12] has been carried out by the FE software ATENA. A constitutive model based on Eurocode 2 specifications for fire design [13] has been used in the analysis. Comparison of numerical simulation and test results has been carried out.

1. Introduction There are many buildings and civil engineering structures (tunnels, high-rise buildings, bridges and viaducts, containment shells, offshore platforms, airport runways etc.) under construction which are at risk of fire. A few dramatic accidents in recent years have prompted investigations in the field of safety of reinforced concrete structures subjected to fire. Fires in railway Channel Tunnel (autumn 1996), in the road tunnels of Mont Blanc (France/Italy 1999), in the television tower of Ostankino (Moscow, 2000), in the Twin Towers (New York, 2001) should be mentioned [1]. In all cases, the load-bearing capacity of structure in the actual fire conditions is of primary importance for evacuation of persons and things, as well as for safety of rescue teams. The analysis of the behaviour of load-bearing members under high temperature conditions is very complicated [2, 3]. Various factors influencing the behaviour of members need to be taken into account, including: variation of member temperature with time, variation of temperature over the cross-section and along the member, temperature effects on material properties (expansion, creep, reduction in strength and stiffness, spalling, etc), material non-linearity, external restrains, section shape, etc. A parametric study of the influence of different factors on the behaviour of RC beams and frames is presented in [4]. Because of the no-linear nature of the problem, closed-form solutions usually cannot be found and an iterative approach is required [5]. The non-linear

2. Reported fire tests of RC beams employed in the numerical analysis The present analysis employs experimental data [12] of reinforced concrete beams subjected to external loading and elevated temperatures. A total of 13 specimens were cast and tested. Except for TSB2-1, the other specimens were heated on three surfaces (the bottom and two

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The present report includes results of modelling three beams of the TF series, namely TSB2-1, TSB2-4 and TSB2-6, first exposed to temperatures of 20°, 400° and 600 °C, respectively, and then subjected to external loading. The experimental temperature distribution throughout the section of the beams TSB2-4 and TSB2-6 is shown in Fig 2. The experimental load-deflection diagrams are presented in Fig 3 with the failure load specified in Table 1. 180 Depth of section, mm

lateral surfaces) according to the same heating curve. Specimens TSB1-(0-6) were tested in the FT (force-temperature) path to obtain failure temperatures under different applied load levels. These specimens were first loaded to a predetermined value, and then heated until the specimens failed. Specimens TSB2-(1-6) were tested in the TF (temperature-force) path to obtain ultimate bending moment resistances. These specimens were first heated up to a predetermined temperature, and then loaded at a quicker rate until the specimens failed. As the loading time was very short compared to its heating time, the thermal duration effect during loading can be neglected. Thus, the duration of thermal exposure between the FT and TF paths can be considered to be the same. The specimens were 1300 mm long, 100 mm wide, and 180 mm deep, with a 10 mm concrete cover all round the section. The specimens were cast in two batches of normal Portland cement (Standard grade China cement), natural river sand and crushed limestone with 15 mm maximum size. The mean compressive cube strength of TSB2 series is 29,45 MPa. Low-carbon plain steel bars with diameter 10 mm and yield stress 270 MPa at room temperature were used as tensile and compressive reinforcement, while those with diameter 3,5 mm and yield stress 289 MPa at room temperature were used as stirrups. The specimen tensile steel ratio was 0,95 % and the stirrup spacing was 80 mm. The specimen dimensions, detailing and loading positions are shown in Fig 1. The specimens were compacted using a vibrating rod and cured in a moist environment at 20 °C and 100 % relative humidity for a period of 7 days after casting, and then placed in a natural environment. To reduce the difference of the water content between specimens arising from a long test period, all specimens were tested after 60 days.

400 C temperature 400 ºC 600 C temperature 600 ºC

150 120 90 60 30 0 0

100

200

300

400

500

600

700

T emperature, C

Fig 2. Experimental temperature distribution within the section depth

0.024

20 °C

400 °C

600 °C

0.02 0.016

P, MN

12

0.012 0.008 0.004 0

D10

0

D3,5@80

1

0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05

f, m

Fig 3. Experimental load-deflection diagrams of beams TSB2-1, TSB2-4 and TSB2-6

D10

1300 mm 1

1-1

D10

10

Table 1. Failure loads of test beams 180

D3,5@80

10

D10 400

400

400

1200 10

10 100

Fig 1. Dimensions, cross-section and loading of test specimens

12

Beam

Temperature, oC

Failure load, kN

TSB2-1

20

19,46

TSB2-4

400

14,99

TSB2-6

600

5,49

D. Bacinskas, et al / JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT – 2004, Vol X, Suppl 1, 11–18

13

3. A Constitutive model applied in the analysis The reliability of a fire analysis results is strongly affected by the choice of the constitutive laws of materials and the values of theirs parameters. In the present FE model the material properties are considered to be temperature-dependent. This section describes constitutive models for concrete and steel assumed in the numerical analysis. The constitutive relationships are based on Eurocode 2 specifications [13, 14]. 3.1. Concrete The constitutive model (material model) describes the behaviour of heated and loaded concrete in mathematical terms. It is based on the stress-strain relationships of heated concrete. The strain components can be modelled using the superposition theory whereby the total strain is considered to be the sum of various strain components [3]:

Fig 4. Stress-strain relationship of concrete at different temperatures

εtot = ε σ (σ, σ, θ) + εth (θ) + ε cr (σ, θ, t ) + εtr (σ, θ) , (1) where ε tot is the total strain, εσ the stress-related strain, εth the thermal strain, εcr the creep strain, ε tr the transient strain, θ the temperature, t the time, σ a stress, σ the stress history. The superposition theory has been particularly useful in the analysis of the strain components at high temperature and has been found to be applicable experimentally [3]. Each of the terms of Eq 1 is briefly described below. The EC2 model implicitly takes account of the effect of high-temperature creep. Both the physical loss of moisture and shrinkage at high temperature cause a decrease in the coefficient of expansion, but these effects have not been considered in the present model. The model also does not attempt to model spalling, the concrete cross-section being assumed to remain intact.

εcu(θ)

fct(θ)

εc0 (θ)

Ec (θ)

εc(θ)

εcr(θ) εcu(θ)

fc (θ)

Fig 5. Theoretical model of the stress-strain relationship of concrete

Stress-strain behaviour of compressive concrete under normal conditions ( θ = 20 o C ) in ATENA is modelled by the EC2 [14] relationship the ascending branch of which has the form

3.1.1. Stress-strain relationships in compression and tension

(

)

(

σc 20 o C = f c 20 o C

The stress-strain relationships of compressed concrete for different temperature levels are shown in Fig 4. The theoretical model of these relationships is given in Fig 5. On the compression side, the curve consists of a parabolic branch followed by a descending curve until crushing occurs. On the tension side, the curve consists of a bilinear diagram. An initial stiffness of concrete in tension is equal to that in compression. At tensile strains greater than this value of εcr the concrete is assumed to follow the descending branch of the stress-strain curve. Once tensile strains exceed εcu , the concrete in tension is ignored, although it is still assumed to be capable of carrying compression. Once the concrete has crushed, it is assumed to have no residual strength in either compression or tension.

(

where σc 20 oC

)

)1 +kη(k−−η2)η 2

(2)

is the stress of concrete at room

(

) (

)

( ) strain of concrete at room temperature, ε c 0 (20 o C ) is the

temperature, η = ε c 20 oC ε c 0 20 oC , ε c 20 oC is the

concrete strain at peak stress at the same condition,

(

f c 20 o C

strength

)

(

is the characteristic value of compressive of

) (

concrete

) (

)

at

(

t = 20 oC ,

)

k = 1,1Ec 20 oC ε c 0 20 o C / f c 20 oC , Ec 20 o C is the elastic modulus of concrete. It should be noted that the stress-strain relationship for compressive concrete presented in Eurocode 2 for fire design of concrete structures [13] is different from formula 2. The former relationship is not available on

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14

the ATENA 2D user interface. However, the shape of the stress-strain relationship of the compressive concrete does not have significant influence on the results of the analysis. Therefore, Eq (2) has been modified in order to model temperature effects. Thus the parameters

Ec (θ) = βc (θ)Ec (20 º C ) ,

where βc (θ ) is an empirical factor, for normal strength concrete taken as:

βc (θ) = 1− 0,0017θ .

( ) fc (20 oC) , εc (20 oC) , εc0 (20 oC) and Ec (20 oC ) from formula (2) corresponding to normal con-

σc 20 oC ,

)

f c (θ) f c 20 oC of concrete with siliceous and calcareous aggregates under increasing temperatures is shown in Fig 6. Similar relationship for strain ε c 0 (θ) is presented in Fig 7. 1

f ct (θ) = kt (θ) f ct (20 º C ) .

kt (θ) = 1,0

) (

f c (θ ) f c 20 o C

0.2 0 400

600

800

1000

1200

1400

Temperature, °C

Fig 6. Relative compressive strength of concrete with siliceous and calcareous aggregates at elevated temperatures

for

  100 º C < θ ≤ 600 º C  (8)  600 º C < θ 

G f (θ) = 0,000025 f t (θ) , [MN/m].

0.03

(9)

It should be noted that a sudden drop in tensile strength with increasing temperatures takes place, leading to degradation of tension softening.

0.025

ε c 0 (θ)

for

20 º C ≤ θ ≤ 100 º C

To the authors' knowledge, investigations regarding the limit strain ε cu (θ ) of tensile concrete are practically absent. In reference [16] it is taken as 15ε cr (θ ) , where ε cr (θ) = f ct (θ) / Ec (θ) is the cracking strain of concrete. The same source also notes that the analysis of RC beams at ambient temperature is very sensitive to the assumed tensile behaviour of concrete. In ATENA 2D post-peak behaviour of tensile concrete is modelled using principles of fracture mechanics [17]. Fracture energy G f was assumed by modifying a formula from [11] given for θ = 20 º C :

0.4

200

for

θ − 100 kt (θ) = 1 − 500 kt (θ) = 0

0.6

0

(7)

In absence of a more accurate information the following kt (θ) values should be used [13]:

Siliceous t Calcareous t

0.8

(6)

The behaviour of concrete in tension under fire conditions is not fully investigated. So far few investigations have been carried out, mainly aimed at the overall and stress-strain behaviour of structures. As mentioned above, the behaviour of tensile concrete was modelled by a bilinear diagram. The current model of tensile concrete is characterised by two main factors: tensile strength and the ultimate cracking strain. The reduction of tensile strength of concrete at high temperatures is accounted for by the coefficient kt (θ) , taken as [13]:

ditions ( θ = 20 o C ) were replaced by respective parameters σc (θ) , f c (θ ) , ε c (θ) , ε c 0 (θ) and Ec (θ) taken for given temperature θ . Further the relationships for f c (θ ) , ε c 0 (θ) and Ec (θ) are briefly discussed. The variation of the relative compressive strength

(

(5)

0.02 0.015

3.1.2. Thermal strain

0.01 0.005 0 0

200

400

600

800

1000

1200

Temperature, °C

Fig 7. Variation of strain ε c 0 (θ ) corresponding to maximum stress f c (θ ) under increasing temperature

Thermal strain of concrete during heating is a simple function of temperature and its theoretical curve is plotted in Fig 8. The theoretical curve also includes drying shrinkage, but despite this, the curve is justified for rapid heating during fire. 3.1.3. Creep strain The creep strain depends on concrete, the load, the temperature and the time. The following expression is used to describe the creep of ordinary concrete:

A relationship for Ec (θ) is absent in Eurocode 2, therefore it was taken from [15]:

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D. Bacinskas, et al / JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT – 2004, Vol X, Suppl 1, 11–18

15

ing. It is an irreversible process and occurs only during the first heating. The transient stress is found to be proportional to the thermal expansion and to the ratio between the compressive stress and strength at 20 °C: εtr (σ, θ ) = −2,35 ×

σ(θ )

(

f c 20o C

)× εth

(11)

(

)

where εtr (σ, θ) is the transient strain, σ(θ) f c 20 o C is the ratio between the compressive stress and compressive strength of the concrete at 20 °C, εth the thermal expansion. Fig 8. Thermal strain of concrete

3.2. Reinforcement

ε cr (σ, θ, t ) = − 530 ⋅ 10

−6

σ(θ) ∆t × × ×e σcu (θ) 3

3,04(θ− 20 ) 1000

The constitutive model describes the behaviour of heated and loaded steel in mathematical terms. Since transient strain does not exist for steel, the model is simpler than for concrete and is described as the sum of three terms [13]:

(10)

where ε cr (σ,θ, t ) is the creep strain, σ(θ) a stress of concrete, σcu (θ) the ultimate compressive stress of concrete (Fig 5), θ is the temperature of concrete, ∆t the time interval.

εtot = ε cr (σ, θ) + εth (θ) + ε cr (σ, θ, t ) (12) where ε tot is total strain, ε cr (σ, θ) the stress related strain, εth (θ) the thermal strain, ε tot the total strain. The strength and deformation properties of reinforcing steel at elevated temperatures shall be obtained from the stress-strain relationships [13] specified in Fig 9 and Table 2.

3.1.4. Transient strain Transient stress is the hindered part of thermal expansion for loaded concrete structures exposed to heat-

Table 2. Stress-strain relationships for steel under a high temperature Range Elastic

Stress

Tangent modulus

E s (θ)

ε < ε sp (θ)

σ s (θ) = E s (θ)ε s ,

Non-linear

σ s (θ) = f sp (θ) − c + (b / a ) a 2 − ε sy (θ) − ε s (θ) 2

ε sp (θ) ≤ ε s ≤ ε sy (θ) Plastic

ε sy (θ) ≤ ε s ≤ ε st (θ) Descending branch

ε st (θ) ≤ ε s ≤ ε su (θ) Failure

ε s = ε su (θ)

(

)

E s (θ) =

(

(

E s (θ) = 0

 ε (θ) − ε st (θ) σ s (θ) = f sy (θ)1 − s   ε u (θ) − ε st (θ)

–

0

–

Parameters

ε sp (θ) = f sp (θ) / E s (θ) , ε sy (θ) = 0,02 , ε st (θ) = 0,15 , ε sy (θ) = 0,2

Functions

a 2 = ε sy (θ) − ε sp (θ) ε sy (θ) − ε sp (θ) + c / E s (θ)

)(

(

),

)

b 2 = c ε sy (θ) − ε sp (θ) E s (θ) + c 2 ,

( f sy (θ)− f sp (θ))2 c= (ε sy (θ)− ε sp (θ))E s (θ)− 2( f sy (θ)− f sp (θ)) 15

)

a a 2 − ε s (θ) − ε sp (θ) 2

σ s (θ) = f sy (θ)

(

)

b ε sy (θ) − ε s (θ)

D. Bacinskas, et al / JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT – 2004, Vol X, Suppl 1, 11–18

16

Es (θ) / Es (20 º C )

1

hot rolled cold worked

0.8

0.6

0.4

0.2 0 0

200

400

600

800

1000

1200

1400

Temperature, °C

Fig 12. Relative elastic modulus of hot-rolled and coldworked steel at elevated temperatures

Fig 9. Stress-strain relationship of steel

For a given steel temperature, the stress-strain curves in Fig 9 are defined by three parameters: – the slope of the linear elastic range Es (θ) for reinforcement, – the proportional limit f sp (θ) , – the maximum stress level f sy (θ) . Values for each of the three parameters for hot rolled and cold worked steel are given in Fig 10–12 [13].

f sy (θ) / f yk (20 º C)

1.2

4. Numerical modelling of experimental beams 4.1. FE package ATENA ATENA is a commercial finite element software package developed for non-linear simulation of concrete and reinforced concrete structures. Based on advanced material models it can be used for realistic modelling the structural response and behaviour. ATENA programme consists of solution core and the user interface. The solution core has got capabilities for the 2D and 3D analysis of continuum structures. It has libraries of finite elements, material models and solution methods. ATENA User Graphic Interface for 2D analysis is a programme, which enables access to the ATENA solution core. It is limited to 2D graphical modelling and covers the state of plane stress, plain strain and rational symmetry. A smeared approach is used to model the material properties, such as cracks. This means that material properties defined for a material point are valid within a certain material volume, which is in this case associated with the entire finite element. The constitutive model is based on the stiffness and is described by the equation of equilibrium in a material point. The concrete models can include the following effects of concrete behaviour: non-linear behaviour in compression including hardening and softening, fracture of concrete in tension based on the non-linear fracture mechanics, biaxial strength failure criterion, reduction of compressive strength after cracking, tension stiffening effect, reduction of the shear stiffness after cracking (variable shear retention), fixed direction crack model. The discrete reinforcement is in the uniaxial stress state and its constitutive law is a bilinear stress-strain diagram. The material matrix is derived using the non-linear elastic approach. In this approach the elastic constants are derived from a stress-strain function. ATENA enables loading of the structure with various actions: body forces, nodal or linear forces, supports, prescribed deformations, temperature, shrinkage, pre-

hot rolled cold worked

1 0.8 0.6 0.4 0.2 0 0

200

400

600

800

1000

1200

1400

Temperature, °C

Fig 10. Relative maximum stress of hot-rolled and coldworked steel at elevated temperatures 1.2

hot rolled cold worked

f sp (θ) / f yk (20 º C)

1 0.8 0.6 0.4 0.2 0 0

200

400

600

800

1000

1200

1400

Temperature, °C

Fig 11. Relative proportional limit of hot-rolled and coldworked steel at elevated temperatures

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D. Bacinskas, et al / JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT – 2004, Vol X, Suppl 1, 11–18

stressing. These loading cases are combined into load steps, which are solved utilising advanced solution methods: Newton–Raphson, modified Newton–Raphson or arclength. Secant, tangential or elastic material stiffness can be employed in particular models. Line-search method with optional parameters accelerates the convergence of solution, which is controlled by residual-based and energy-based criteria. This is only a concise survey of ATENA features. All the described features support the user by engineering analysis of connections between steel and concrete and computer simulation of its behaviour.

17

400 and 600 °C, respectively. As the temperatures were increasing from the bottom to the top, the beams have deflected downwards. The calculated deflections due to temperature effects only (no loading) are in a good agreement with the tests for the beam TSB2-6, but some discrepancies can be noted for the beam TSB2-4. With increasing load the experimental load-deflection diagrams (Figs 2, 14) can be roughly approximated by a bilinear diagram consisting of two lines: the first one describing pre-yielding and the second post-yielding behaviour. It can be seen from Fig 14 that the shape of experimental load-deflection diagrams has been qualitatively captured in the finite element analysis. Pre-yielding deflections were accurately modelled for the beam TSB2-1 (t = 20 ºC), but were underestimated for the beam TSB24 and overestimated for the beam TSB2-6. Agreement of the ultimate load is within reasonable limits. Deflection fields and cracking pattern of TSB2-4 beam at load P = 16 kN are shown in Fig 15.

4.2. FE model of experimental beams Load-deflection behaviour of the experimental beams described in Section 2 have been analysed by the finite element package ATENA. The present report includes results of modelling the three beams of the TF series, ie TSB2-1, TSB2-4 and TSB2-6, first exposed to temperatures 20, 400 and 600 °C, respectively, and then subjected to external loading till failure. SBETA material model with parameters given in Section 3 was applied for simulating the concrete behaviour. Reinforcement is modelled by a single straight line in a discrete way („bar reinforcement“). Material of reinforcement is represented by the bilinear model. The experimental temperature distribution throughout the section of the beams TSB2-4 and TSB2-6 is shown in Fig 2. In order to assess degrading material properties due to high temperature effects, the beams within the depth were divided into six macroelements. These macroelements were discretised by CCIsoQuad type quadraliteral elements with rigid connections between the macroelements. The temperatures and respective material properties in different macroelements were assessed according to the experimental temperature diagrams from Fig 2. Standard Newton-Raphson solution method was applied for non-linear analysis of experimental beams. FE model of TSB2 series experimental beams is presented in Fig 13.

20 C temperature

400 C temperature

600 C temperature

20 C ºCAtena 20

400 400 C ºCAtena

600 600 C ºCAtena

0,025

P , MN

0,02

0,015

0,01

0,005

0 0

0,005

0,01

0,015

0,02

0,025

0,03

0,035

0,04

0,045

0,05

f, m

Fig 14. Calculated and experimental load-deflection diagrams

Fig 13. FE model of TSB2 series experimental beams Fig 15. Deflection fields and cracking pattern of TSB2-4 beam at load P = 16 kN

4.3. Analysis results In this section, comparison of numerical modelling with test data has been carried out. The modelled loaddeflection diagrams are presented in Fig 8 along with the experimental curves. The modelling has included all the stages of temperature and loading. First, the beams TSB2-4 and TSB2-6 were subjected to temperature of

5. Concluding remarks Load-deflection behaviour of reinforced concrete beams subjected to high temperatures (up to 600 °C) has been modelled by the finite element package ATENA.

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18

A constitutive model based on specifications of Eurocode 2 has been used in the analysis. Comparison of the experimental and modelling results has shown that ATENA has satisfactorily captured the load-deflection behaviour of the beams.

7.

Bratina, S.; Planinc, I.; Saje, M. and Turk, G. Non-Linear Fire-Resistance Analysis of Reinforced Concrete Beams. Structural Engineering and Mechanics, Vol 16, No 6, 2003, p. 695–712.

8.

Sullivan, P. J. E.; Terro, M. J. and Morris, W. A. Critical Review of Fire-Dedicated Thermal Structural Computer Programs. In: Applied Fire Science in Transition Series, Vol III Computer Applications in Fire Protection Engineering. Paul R. DeCicco ed Baywood Publishing Company, Inc., 2001. p. 5–27.

9.

Wang, Y. C. Steel and Composite Structures. Behaviour and Design for Fire Safety. EF & N Spon, 2002. 264 p.

6. Acknowledgment The financial support under Framework 5 project “Cost-effective, sustainable and innovative upgrading methods for fire safety in existing tunnels” (UPTUN, project No GRD1-2001-40739/UPTUN) provided by the European Community is gratefully acknowledged.

10. de Witte, F. C. and Wijtze, P. K. DIANA – Finite Element Analysis. Users Manual Release 8.1. Analysis Procedures. TNO Building and Construction Research, Delft, 2002. 580 p.

References 1.

2.

11. Cervenka, V. and Cervenka, J. ATENA Program Documentation. Part 2. ATENA 2D User Manual. Prague, 2002. 138 p.

Felicetti, R.; Gambarova, P. G. and Meda, A. Expertise and Assesment of Structures after Fire. In: Report in the Meeting of fib Task Group 4.3.2 Guidelines for the Structural Design of Concrete Buildings Exposed to Fire, Brussels, Nov 2002. 15 p.

12. Shi, X.; Tan T.-H.; Tan, K.-H. and Guo, Z. Effect of Force– Temperature Paths on Behaviour of Reinforced Concrete Flexural Members. Journal of Structural Engineering, Vol 128, No 3, March 2002, p. 365–373.

Khoury, G. A.; Anderberg, Y.; Both, K.; Felinger, J.; Majorana, C. E. and Hoj, N. P. Fire Design of Concrete: Materials, Structures and Modelling. In: Proc. of the 1st fib Congress Concrete Structures in 21st Century, Osaka, 2002, p. 99–118.

3.

Khoury G. A., Majorana C. E., Pesavento F. and Schrefler B. A. Modelling of Heated Concrete. Magazine of Concrete Research, Vol 54, No 2, 2002, p. 77–101.

4.

Riva, P. Parametric Study on the Behaviour of RC Beams and Frames under Fire Conditions. In: Report in the Meeting of fib Task Group 4.3.2 Guidelines for the Structural Design of Concrete Buildings Exposed to Fire, Brussels, Nov 2002. 61 p.

5.

Bazant, Z. P and Kaplan, M. F. Concrete at High Temperatures: Material Properties and Mathematical Models. Longman Group Lt., 1996. 412 p.

6.

Mutoh, A. and Yamazaki, N. Non-linear Analysis of Reinforced Concrete Members under High Temperature. In: Proc. of Conf. DIANA Computational Mechanics ’94. Kluwer Academic Publishers, 1994, p. 45–55.

13. prEN 1992-1-2. Eurocode2: Design of Concrete Structures - Part 1.2: General Rules – Structural Fire Design. European Committee for Standartisation, Brussels, July 2001. 102 p. 14. prEN 1992-1. Eurocode2: Design of Concrete Structures Part 1: General Rules and Rules for Buildings. European Committee for Standartisation, Brussels, Oct 2001. 230 p. 15. Iljin, N. A. Outcomes of fire effect on reinforced

concrete structures (Ïîñëåäñòâèÿ îãíåâîãî âîçäåéñòâèÿ íà æåëåçîáåòîííûå êîíñòðóêöèè). Moscow: Stroizdat, 1979. 128 p. (in Russian).

16. Cai, J.; Burgess, I. and Plank, R. A Generalised Steel/Reinforced Concrete Beam-Column Element Model for Fire Conditions. Engineering Structures, Vol 25, No 6, 2003, p. 817–833. 17. Karihaloo, B. L. Fracture Mechanics and Structural Concrete. Longman Scientific and Technical, England, 1995. 330 p.

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19 ISSN 1392–3730

JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT http:/www.vtu.lt/english/editions

2004, Vol X, Suppl 1,19–22

ANALYSIS OF THERMAL STRAIN OF STRUCTURAL STEELS IN VARIABLE THERMAL FIELD Zoja Bednarek, Renata Kamocka The Main School of Fire Service (MSFS) in Warsaw, Str. J. Sùowackiego 52/54, 01-629 Warsaw, Poland. E-mail: sgsp@ sgsp.edu.pl Received 3 Nov 2003; accepted 8 Apr 2004 Abstract. The strain analysis of steels subjected to a thermal field with a high temperature increase rate is presented. The results of tests of thermal strain caused by thermal expansion and the coefficient of linear thermal expansion are presented for the structural steel, class AIII, grade 34GS, tested in a linearly variable temperature field at various heating rates. The impact of heating rate on thermal strain εT = α(T) · ∆T and coefficient of linear thermal expansion α(T) is discussed. Keywords: thermal expansion, thermal strain, coefficient of linear thermal expansion, structual steel.

Structural strength under fire conditions and fire resistance are calculated on the basis of well established mechanical and strength characteristics of building materials. The nature of structural steels strain, being a result of simultaneous impact of stresses and time-dependent thermal field during a fire, is still under examination. According to a proposal made by RILEMCOMMITEE 44-PHT, an international committee, total strain at elevated temperatures can be described by the following constitutive equation for the material (steel):

1. Introduction The impact of elevated temperatures on structural materials (including structural steels) results in a change of their elastic and plastic behaviour. The intensity of such phenomena as creep and relaxation also increases with temperature. As results of our previous studies, such phenomena have a considerable impact on structural strength at fire temperatures. Furthermore, not only an absolute value of temperature is essential but also temperature distribution with time and rate of temperature increase are of vital importance. Our previous studies [1] concerning the impact of rapid-heating conditions, like fire, on the properties of reinforcing steel, also including its thermal strain, have shown that: • Such properties and the type of rupture are influenced by temperature distribution during the test, and in particular, by temperature increase rate dT/dτ, what was found while testing steels at both relatively slight and significant temperature increase rates; • Different grades of steels (including structural steels) show some kind of inertia, which consists in a partial or full inhibition of some processes leading to the material rupture due to heating at a significant rate as compared to the same processes at constant temperatures or at a slight rate of temperature increase; • Thermal fields characterised by higher temperature increase rates undoubtedly produce more favourable effects in terms of the material strength, eg result in higher critical temperatures (causing rupture).

ε = εT (T ) + ε e− p (σ, T ) + ε τ (σ, T , τ) ,

(1)

where εT is thermal strain εT = α(T ) ⋅ ∆T caused by thermal expansion of steel, ε e− p mechanical strain computed ignoring creep strain as described by Ramberg-Osgood equation as follows: εe− p = εe + ε p =

σ 1 µ (T ) µ (T ) −1 σ σ ,(2) ] + 0,002[ σ y (T ) E (T )

ε τ is creep strain (dependent on time τ) as described by Dorn’s theory and Harmothy’s studies; also being the subject of our earlier studies conducted at the Applied Mechanics Department (MSFS) under Z. Bednarek’s guidance. The total strain of steel at elevated temperatures can be calculated by summing up the thermal strain, the strain calculated from the Ramberg-Osgood equation and the creep strain. This paper presents the results of studies of the first component of the steel strain model based on equation (1), ie the thermal strain caused by linear expansion of steel.

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There is the following relation between the linear expansion coefficient α and the anharmonicity coefficient:

2. Model of thermal expansion of solid bodies According to the microscopic description, the thermal expansion of solid bodies can account for an increase of the crystal lattice parameter (interatomic distances in a crystal). Some of these phenomena can also account for defects in the crystal lattice – mainly vacancies (the lack of atom in the place, which is assigned to such atom). As temperature rises, the amplitude of atoms oscillations from their average equilibrium positions increases (Fig 1).

α=

< x > b⋅k 1 . = 2 ⋅ r0 ⋅ T K r0

(4)

The higher the curve asymmetry, the greater the thermal expansion coefficient. 3. Testing the impact of temperature on steel strain due to linear thermal expansion Steel is a homogenous and isotropic continuous medium, which is subject to thermally activated strain. A body length at a given temperature can be determined by means of the following formula: (5) l(T) = l0 (1 + αT + βT2). For isotropic changes (a steel specimen), when approximating linearity of changes in length, we can write: ∆l = l(T) – l0 = α(T) l T

.

Ho H

or

(6)

ε = ∆l/l = α(T) × T. According to Harmothy [3–6] (ENV 1993-1-2), the strain of heated steel with temperature can be expressed by the following formulae:

7(H)

Ho

Ho H1 H2

∆l = 1,2 · 10–5T + 0,4 · 10–8T2 – 2,416 · 10–4 l 20 °C < T < 750 °C,

H -1

-2

∆l = 1,1 · 10–2 l

62>61

The interatomic distance at temperature 0 °K is constant and equal to r0. As temperature rises up to T1, the energy of atoms in the crystal lattice increases resulting in their oscillations from their average equilibrium position r1 [2]. It can be shown that the average displacement of the equilibrium position can be expressed as

b ⋅ k ⋅T , K2

750 °C < T < 860 °C, (7b)

∆l = 2 ⋅ 10–5T + 6,2 ⋅ 10–3 860 °C < T < 1200 °C. (7c) l The linear expansion coefficient can be precisely defined as:

Fig 1. Relation between force, potential energy and interatomic distance r: r0, r1, r2 – average interatomic distances at increasingly elevated temperatures

< x >=

(7a)

α=

1 dl ( p, T ) ( )p, l0 dT

(8)

where p – constant pressure. At constant pressure, coefficient α is a temperaturedependant function. For practical purposes of making structural analysis, the average based on the reference value of 1,2 · 10–5(1/deg) for low-carbon steels is frequently assumed instead of an actual value of linear expansion coefficient α at a given temperature. There is no available precise data on the linear expansion coefficient for structural steels for the needs of a more detailed steel strain analysis at elevated temperatures, including fire conditions characterised by a rapid increase in temperature. When searching through the publications available to us we have only found the data on American steel ASTM A36 [7], austenitic steels S350GD, S355 and S460 [8] and formulae describing the relation between coefficient α and temperature as follows:

(3)

where <x> – average distance from r0 , eg <x> = r1 – r0; b – anharmonicity coefficient (determines the deviation of atom oscillations from harmonicity); K – coefficient of quasi-elastic force acting between atoms in the crystal lattice (Fx = –Kx + bx2); T – temperature; k – Boltzman constant. Thus, as temperature rises, the average interatomic distance increases and the solid body expands.

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α = (0,004T + 12) · 10–6 (1/K) [9, 6],

(9)

α = (6,1 + 0,0019T) · 10–6 inch/inch per degree [10].(10) For the needs of further studies on individual components of formula (1), which describes the strain of structural steels at fire temperatures, the behaviour of linear expansion coefficient for the steel, class AIII, grade 34GS, was examined in a linearly variable temperature field at different heating rates. The tests were conducted under anisothermic conditions (T ≠ const) for 4 different temperature increase rates. Fig 2 shows temperature-time distributions. Under fire conditions, the rate of temperature increase is 5 °C/min for a steel element covered by a good quality fire insulation. For uncovered structures, the rate of temperature increase can reach 50 °C/min. The results of tests are shown on Figs 3 and 4, below.

21

b–

∆l = 1,32 · 10–5T + 0,256 · 10–8T2 – 5,95 · 10–4, l (11a)

c–

∆l = 1,27 · 10–5T + 0,322 · 10–8T2 – 6,65 · 10–4, l (11b)

d–

∆l = 1,28 · 10–5T + 0,298 · 10–8T2 – 7,79 · 10–4, l (11c)

∆l = 1,28 · 10–5T + 0,244 · 10–8T2 – 7,85 · 10–4. l (11d) The points marked in Fig 3 to determine curves "b, c, d and e" are measuring points obtained by the authors from their own tests, whereas points on curve "a" were calculated according to the formula 7a taken from the references. Below, we present a comparison of the curve taken from the references (curve “a”) with our curves (curves “b, c, d, e” in Fig 4) describing the relation between Thermal expansion coefficient á [1/deg]

e –

Fig 2. Relation between temperature and time for specimens heated at various temperature increase rates

1,6E-05 1,4E-05

a

1,2E-05 1,0E-05

a – wg Lie,T.T. [3] b – dT/dτ = 5 °C/min c – dT/dτ = 10 °C/min d – dT/dτ = 15 °C/min e – dT/dτ = 20 °C/min

b c d

8,0E-06 6,0E-06

e

4,0E-06 2,0E-06

0,0E+00 0

100

200

300

400

500

600

Temperature [°C]

Fig 4. Relation between thermal expansion coefficient and temperature for specimens heated at various temperature increase rates

thermal expansion coefficient a and temperature that we obtained by experiments: a – α = 4 · 10–9T + 1,2 · 10–5,

b – α = – 2,51 · 10–11T2 + 2,78 · 10–8T + 5,87 · 10–6, (12a)

Fig 3. Relation between strain and temperature for specimens heated at various temperature increase rates

c – α = – 2,81 · 10–11T2 + 3,04 · 10–8T + 5,3 · 10–6, (12b) d – α = – 3,08 · 10–11T2 + 3,39 · 10–8T + 3,9 · 10–6, (12c)

Below, we present a comparison of the curve taken from ENV 1992-1-2/1995/ (curve a) with our curves (curves b, c, d, e in Fig 3) describing the relation between strain and temperature that we obtained from experiments: a–

(formula 9)

e – α = – 3,89 · 10–11T2 + 4,09 · 10–8T + 1,95 · 10–6. (12d) The points marked in Fig 4 to determine curves “b, c, d and e” are measuring points obtained by the authors in their own tests, whereas points on curve “a” were calculated according to formula (9) taken from the references.

∆l = 1,2 · 10–5T + 0,4 · 10–8T2 – 2,416 · 10–4, l (formula 7a)

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4. Conclusions

References

The objective of investigations was to determine and conduct a comparative analysis of thermal strain and thermal expansion coefficient for structural steels at different temperature increase rates. As the results of the tests conducted at different heating rates on specimens made of structural steel, class AIII, grade 34GS show, the thermal strain of specimens is affected by the temperature increase rate. The higher the temperature increase rate, the lower the thermal strain of specimen. The thermal expansion coefficient also changes in a similar way. The reason for such a behaviour of steel is its material inertia which consists in a partial or full inhibition of some processes leading to the material rupture and taking place in steel due to a significant heating rate, as we have also shown in our papers [1] and [11]. Linear expansion coefficient α(T) rises with temperature. As the regression analysis of the results, obtained by the tests on linear expansion coefficient α at a given heating rate shows, the best correlation degree was obtained when approximating experimental data with quadratic polynomials. This paper includes the functions that describe the relation between coefficient a and temperature at different heating rates (formulae 12a, b, c, and d).

1.

Bednarek, Z. Influence of thermal conditions on strength parameters of reinforcing steel exposed to fire. Inýynieria i Budownictwo, 12/93, p. 526–528.

2.

Staub, F. Metal Science, WNT Katowice 1994.

3.

Lewis, K. R. Fire design of steel members, fire engineering research report 2000/07 ISSN 1173–5996.

4. Böðvar, T. High performance concrete. Design guide lines, Department of fire safety engineering, Report 5008, Lund, 1998. 5.

Burgon, B. Elevated temperature and high strain rate properties of offshore steels, Steel Construction Institute, Offshore Technology Report 2001, 020, Norwich.

6.

Alfawakhiri, F.; Sultan, M. A.; MacKinnon, D. H. Fire Resistance of Loadbearing Steel-Stud Walls Protected with Gypsum Board: A Review, Fire Technology, Vol 35, No 4, 1999.

7.

Skowroñski, W. Theory of fire safety of steel structures, PWN 2001.

8.

Outinen, J.; Kaitila, O.; Mäkeläinen, P. High-temperature testing of structural steel and modelling of structures at fire temperatures. Research report TKK-TER-23. Helsinki University of Technology, 2001.

9.

Guy C. Gosselin. Structural fire protection- predictive methods, Building science inside 1987, Institute for Research in Construction, National Research Council Canada.

10. R.H.R. Tide: Integrity of structural steel after exposure to fire, Engineering Journal /First Quarter, 1998. 11. Bednarek, Z. Effects of increase of temperature on structural steel strength parameters as applied to the estimation of fire safety of concrete construction. Doctor Habilitatis thesis. Vilnius: Technika, 1996, p. 1–208.

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23 ISSN 1392–3730

JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT http:/www.vtu.lt/english/editions

2004, Vol X, Suppl 1, 23–29

SLIP OF “BULLDOG”-TYPE TOOTHED-PLATE CONNECTORS IN STEEL-TIMBER JOINTS OF OPEN-WEB GIRDERS Rimantas Èechavièius Dept of Metal and Timber Structures, Vilnius Gediminas Technical University, Saulëtekio al. 11, LT-10223 Vilnius-40, Lithuania. E-mail: [email protected] Received 4 June 2003; accepted 3 May 2004 Abstract. Composite steel-timber open-web girders invented by Truss Joint MacMillan company (Canada) provide some technological and structural advantages. Timber chords and steel diagonals of triangular open-web are connected by "Bulldog" type single-sided toothed-plate connectors. The article presents the results of research on four real-size (span – 3 m) open-web trussed purlin with "Bulldog"-type connectors. From carried out tests next parameters are determined: resistance of "Bulldog"-type connectors, slip modulus and statical slip values depending on the angle between the force and wood fibres directions. It is also received numerical values of the slip modulus and statical slip, which are substantically greater than given in experimental Eurocode 5. The tests also let to find that redistribution of forces in steel diagonals of the trussed purlin starts when slip of "Bulldog"-type connectors in steel-to-timber joints approaches to the limit (2 mm) value. Keywords: composite structure, steel-timber joint "Bulldog"-type connector, slip, resistance test.

The majority of these results is obtained by investigating separate joints. But there is a lack of data concerning the slip of such joints in real steel-timber structures where the redestribution of stresses among individual truss elements becomes clear. The article presents the results of research on four open-web trusses with “Bulldog”-type connectors [10– 12]. Not only the strength of such joints and their slip but also the stress redestribution among elements of the truss were determined.

1. Introduction Toothed “Bulldog”-type plate connectors (DS “Bulldog”) are means of mechanical ties used in timber structures. The main purpose of them is to increase the timber bearing area in structural joints and to diminish the slip of feathered joints. They could also allow to increase considerably the bearing capacity of such joints and to tie light steel-timber open-web girders (trusses) and frames. This is characteristic of “OPEN-WEB” trusses having been produced since 1960 by the joint-stock company ”MacMillan”; these trusses can be used for spanning both small openings (l ≈ 4,5–9 m) and large (12– 120 m) ones (Fig 1). The main advantages of such trusses are their small weight and rational joint work of timber chords and the network of metal tubes. The main research on the bearing capacity of toothed “Bulldog”-type connectors was performed at Stevin-Laboratorium (Delft University of Techology, Netherlands), Dannish Construction Research Institute, Otto-Graf Institute (Stuttgart University, Germany) [1–5]. During these investigations the strength of joints was analysed by J.H. Blass, etc [6–7]. The model of calculating such joints presented in his work is recommended by the project of new Eurocode standards [8]. The slip of “Bulldog”-type plate connectors was investigated by Y. Hirashima [9]. The results are presented in Fig 2, where slipping of different joining means is compared.

Fig 1. Composite steel-timber open-web truss of Truss Joist MacMillan

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Fig 2. Experimental load-slip curves for joints in tension parallel to the grain: a – glued joints (12, 5·10³ mm²), b – split ring (100 mm), c – double-sided toothed plate (¸ 62 mm) [15], d – dowel (¸ 14 mm), e – bolt (¸ 14 mm), f – punched plate (0,1E5 mm²), nail (¸ 4,4 mm) 4. A

4. B 3. A

Joint M6

Fig 4. Truss testing scheme: a – general view of truss testing (SN-1-3); b – truss SN-1-1 testing diagram: 1 – truss SN-1-1; 2 – traverse; 3 – hinge; 4 – stiff support; 5 – jack; 6 – dynamometer; 7 steel spreader; 8 – timber pad; X – traverse braces; T1-T16 – electric strain resistance gauges; II.1 – II.7 – 0,01 mm accuracy dial gauges (deflection indicators); In.1–In. 6 – displacement of ends of pipe indicators with precision of 0,01 mm

=

3. B

Joint M1

2. The structure of trusses and test scheme Four steel-timber (3 m span) trusses SN-1-1, SN-12, SN-1-3, SN-1-4 have been tested and some joints of them strengthened by DS “Bulldog” [13]: all joints in SN-1 and SN-2; mostly loaded were the joints M1, M5, M6, M7, M10 and M11 in trusses SN-1-3, SN-4. In the latter trusses, the less loaded joints M2, M3, M4, M8, M9 were connected only by bolts M16. All the network

3. C

Fig 3. Structure of SN-1 trusses: a – diagram for analysis; b – structure of M6 joint; c – structure of M1 joint

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25

Table 1. Schedule of materials for a SN-1 truss

No

Materials and details

1

Wooden element (upper chord)

2 3 4 5 6 7 8

Wooden element (lower chord) Tube (truss network) Toothed connector Pin Plate (insertion) Washer Nut

Characteristic 50×120 Fig 4. Test of girder diagram:mm, 1 = 3280 mm 50×120 mm, 1 = 2680 mm d = 45,0 mm, t = 4,0 mm, 1 = 680 mm E75M16 M16,1 = 200 mm a = 68 mm, t = 8 mm, hole 16,5 mm a = 68 mm, t = 6 mm, hole 16,5 mm M16

Remarks, standards Pinewood, 2nd sort W = 12%+/-2% Pinewood, 2nd sort W = 12%+/-2% C235, GOST 10704-76 DIN 1052 Bulldog [19] C235, GOST 1759-70 C235, GOST 27772-88 C235, GOST 27772-88 C235, GOST 1759-70

Fig 5. General view of testing the open-web truss: a – test of truss SN-1-2; b – arrangement of test devices in the truss SN 1–4

elements of metal tubes are connected at 60° angle with the upper and lower chords. The tubes at connecting points are flattened and a hole of 16,2 mm was drilled. In joints with one network element (M6 and M11), an insertion was put. The structure of these trusses and the testing scheme are shown in Figs 3, 4 and Table 1. The trusses were tested at the laboratory of building structures of the VGTU. The source of loading was a hydraulic jack based on a rigid metal frame. The scheme of truss testing is shown in Fig 4. Strain gauges (20 mm on metal and 50 mm on wooden basis) were used only when testing SN-1-1 truss. The vertical strains of truss supports and lower chords joints as well as slip strains of joints M1, M5, M6, M11 were measured by indicators of 0,01 mm precision. For stability of experimental equipment in the plane of bending moment, hinge supported horizontal wooden squared beam connections were provided. It was observed during testing that the horizontal ties are free and they do not hinder transferring vertical forces.

to 38,61 MPa and characteristic volume weight rk = 434 kg/m². Testing trusses lasted for 2–3 h. During this time span the strains of on average 21 devices were determined at every stage of 15 loadings. Loading duration in separate stages was in the interval of 10–20 min depending on the necessity to rearrange either the devices (when strains were larger than the size of limit strains) or the equipment of horizontal braces. Testing trusses is shown in Fig 5. The unit deformations of the truss SN-1-1 are shown in Fig 6. The average strains in compressive truss bars 1–7 and 5–10 under the loading of 80 kN (σc = 86,64 MPa) and in the members in tension 1–6 and 5–11 under the loading of 110 kN (σc = 121,46 MPa) were close to those calculated theoretically according to the experimentally defined pipe compressive (Et) and tensioned bars elasticity models: E c  = 2,10·10 5  MPa, and Et = 2,12·105 MPa. But from F = 85–90 kN loading the growth of strains of compressed pipes and from F = 110 kN the strains of tensioned pipes decreased considerably and later have stopped almost entirely. Thus at the increase of loading the stresses in these bars have not changed, ie the stresses were redestributed among the truss elements. This phenomenon can be explained by the data of Table 2: exactly at this time M-11 ir M-6 joints slip deformations were larger than the allowable 2

3. Test results It has been determined by testing steel-timber connections [14, 15] that the characteristic value Rck  of truss chord timber compressive strength along fibres is equal

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Table 2. Characteristics for serviceability limit state of “Bulldog”-type connectors in steel-to-timber joints Impact kN No of girder No of joint α °, connections connections

Connections B-2 Connections B-1

SN-1-1 SN-1-2 SN-1-3 SN-1-4

M1 M2 M3 Vid.: M4 M5 M6 Vid.: M6 M11 M6 M11 M6 M11 M6 M11 Average

90 90 90 90 0 0 0 0 60 60 60 60 60 60 60 60 60

Slip modulus according to LST EN 26891 [19], kN/mm

Fmax

F2

Ks

K0,6

K0,7

K0,8

Keu

Keser

36,2 32,2 31,8 33,4 34,0 38,0 39,5 37,1 36,4 36,4 34,2 34,2 37,0 37,0 37,0 37,0 36,2

23,0 21,6 21,0 21,9 26,2 30,0 25,7 27,3 29,3 24,5 29,2 20,7 19,2 19,5 26,2 29,2 24,7

21,0 22,9 20,3 21,4 24,0 24,6 25,9 24,8 41,8 38,4 39,2 17,7 14,2 10,2 44,0 48,3 31,7

12,0 13,8 11,8 12,6 18,6 21,6 16,2 18,8 21,7 15,3 19,4 10,7 7,6 9,2 19,1 19,3 15,3

11,0 9,6 9,2 10,0 15,3 17,9 – 16,6 – – – – – – – –

– – –

2,8 3,9 5,8 4,2 5,7 5,4 4,4 5,2 7,7 6,6 11,8 5,4 6,2 2,8 2,5 9,7 6,6

11,5 10,8 10,5 10,9 13,1 15,0 12,8 13,6 14,7 12,2 14,6 10,4 9,6 9,8 13,1 14,6 12,4

– – – 16,0 9,6 15,4 7,3 5,7 8,5 11,2 15,7 11,2

Keser Ktser

Keu Ktu

1,18 1,11 1,08 1,12 1,34 1,54 1,31 1,40 1,51 1,25 1,50 1,07 0,98 1,00 1,34 1,50 1,27

0,43 0,60 0,89 0,64 0,93 0,83 0,68 0,81 1,18 1,01 1,81 0,83 0,95 0,43 0,38 1,49 1,01

Slip according [14]

Uy, mm

Uu, mm

1,07 0,85 0,85 0,92 0,97 1,17 0,92 1,02 0,7 0,5 0,4 1,1 1,0 0,4 0,4 0,4 0,6

13,0 8,2 5,5 8,9 6,0 7,1 9,0 7,4 4,7 5,5 2,9 6,3 6,0 5,3 5,9 3,8 4,9

µs 12,15 9,65 6,47 9,42 6,19 6,07 9,80 7,35 6,7 11,0 7,3 5,7 6,0 13,2 14,8 9,5 7,4

Fig 7. End displacements of web members of SN-1-2 truss (Figs 3, 4): dial gauges In.1 and In.4 for tensile member 1 – 6; In.2 and In.5 – for tensile member 5 – 11; In.3 and In.6 – for compressive struts 1 – 7 and 5 – 10, respectively

Fig 6. Kinetics of strain in steel web members of SN-1-1 (Figs 3, 4). Tension members: 1 – 6 (T-9, T-10) and 5–11 (T-15, T-16); compression members: 1 – 7 (T-11, T-12) and 5–10 (T-13, T-14); 1, 2 – strain of compression and tension members, respectively

Fig 8. Views of joints M6 (In.1) (a) and M1 (In.3 and In.4) (b) of SN-1-4 truss after failure

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mm limit (the total loading F reached 86,6 kN and 103,3 kN, and F2 for one DS was equal to 24,5 kN and 29,3 kN, respectively. It is clearly shown in Fig 7: the joint M6 (In.1) slip strains were very similar to those of the joint M1 (In. 3 and In. 4). In Fig 8, deformations after failure of joints M6 (In. 1) and M1 (In. 3 and In. 4) are seen. Maximal bearing deformations of steel bolts M16 (dv = 15,9 mm) reached 0,3 – 0,4 mm, and their bend 8,5 mm (SN-1-4) and 14,8 mm (SN-1-3). In this picture the character of bolt hole deformations is seen too. The determined after the failure measurements of bolt holes in upper and bottom chords are presented in Table 3. It shows that the direction (a) of hole maximal dimensions correlates well with the force direction: in the girder SN-1-4 the maximal dimension of 19,0 mm of joint M6 is of a = 60° direction, and M-1 is a maximal dimension (19,35 mm) of a = 0° direction.

27

Fig 9. Variation of slip modulus of “Bulldog”-type steeltimber connectors with relative force (F/Fmax) and angle (α) between force and timber grain directions

4. The characteristic of DS “Bulldog” serviceability limit state This characteristic is presented in Figs 9, 10 and Table 2. Here also the results of tests B-1 and B-2 of metal-wood joints with “Bulldog”-type connectors are shown. In this Table the theoretical moduli of the slip of such joints were calculated according to European experimental standards [14]: Ktser = 0,3 ds r k = 9,76 kN/mm, Ktu =  2·Ktser /3 = 6,51 kN/mm. K, kN/mm F/Fmax . In these formulas, due to a shortage of tests concerning the humidity of timber, the influence of the connection elements thickness and the number of connectors in a joint has not been evaluated, as well as the influence of the angle between the force and wood fibres. It was noted by H. J. Blass [16], too. Our investigations have disclosed that the bearing capacity of DS “Bulldog” at the states of security and serviceability (failure loading Fmax; force F2, when the strain of the slip connector equals 2,0 mm; magnitude of slip modulus at reaching the serviceability limits state Keser, connection static slip ms) depends on the angle (a) between the force and wood fibres. In Fig 9 we can see that the dependence of slip modulus size on the impact angle (a) is valid for the whole time span of the connector strain: from the initial impetus up to failure. Table 2 includes the DS “Bulldog” static slip average characteristics determined according to DAN-ENV 1995-1-1 [14]; in many cases they are larger (a/v µs = 7,35 – 9,42 depending on a) than in these norms: 3 < µs < 6. It has been determined that the slip modulus Keser is by 1,12–1,4 times larger than that defined by [14] depending on the angle between the force and wood fibres.

Fig 10. Relationship between carrying capacity of “Bulldog”-type connector in steel-to-timber joints and angle α between force F and grain direction: 1 – Ktser – theoretical value of slip modulus [14]; 2 – slip modulus at serviceability limit state (Keser); 3 – force (F2) when connector slip equals 2 mm; 4 – maximum force (Fmax); 5 – statical slip in steel-to-timber joints µes [14]

5. Conclusions 1. The bearing capacity of steel-timber connections with “Bulldog”-type connectors depends, according to the state of serviceability limits, on the angle between the force and wood fibres. 2. Experimental slip modulus Keser is by 1,12–1,4 times larger than that theoretically determined by experimental European standards. Its value depends on the angle between the force and wood fibres. 3. The static slip value µs with “Bulldog”-type connectors in steel-timber connections is much larger than

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Table 3. Dimensions of holes in chords of open-web girders after testing

Joint No

α,° *2

M-11

0 60 90 120 0 60 90 120 0 60 90 120 0 60 90 120 0 60 90 120 0 60 90 120 0 60 90 120 0 60 90 120 0 60 90 120 0 60 90 120 0 60 90 120

M-10

M-9

M-8

M-7

M-6

M-5

M-4

M-3

M-2

M-1

Dimensions of bolt holes in girder upper chords, mm *1 SN-1-1 SN-1-2 SN-1-3 SN-1-4 front side front side inner side front side inner side front side inner side

17,9 16,1 16,0 16,7 16,4 16,0 16,4 16,0 16,0 16,0 16,0 16,0 16,5 16,2 16,0 16,1 17,7 16,8 16,6 16,0

Average dimensions

16,1

16,1

16,4

16,2

16,1

15,9

16,2

18,3 16,8 16,9 15,8 16,4 16,1 16,2 16,5 16,1 16,0 16,1 16,1 16,6 16,7 16,0 16,2 16,7

18,8 17,4 16,7 16,1 16,3 16,3 17,1 16,8 16,7 16,3 16,3 16,4 16,4 17,4 16,2 16,4 16,5

19,0 17,2 16,5 16,3 16,4 16,8 18,5 18,5 17,8 17,2 17,4 18,0 18,5 17,1 16,0 16,3 17,5

17,5 16,8 16,1 16,2 15,9 16,3 17,7 17,8 17,3 16,6 16,6 17,5 17,8 16,8 15,9 16,0 16,8

18,5 16,8 16,8 16,4 16,5 17,7 17,7 18,2 17,5 17,0 16,8 17,4 18,0 17,1 16,1 16,4 16,8

17,4 16,7 16,5 16,1 16,1 16,7 17,3 17,5 17,0

17,4 17,1 16,3 16,0 16,4

18,2 17,0 16,6 16,2 16,3 16,6 17,4 17,6 17,1 16,6 16,6 17,1 17,4 17,0 16,1 16,2 16,8

17,8

18,0

20,1

19,4

20,2

17,8

18,9

16,0 18,4 16,6 16,4 17,7 16,2 16,4 16,1 16,1 16,3 15,9 16,0 16,0 16,2 16,2 16,1 16,2 19,1 17,1 16,5 16,5

16,5 18,5 17,1 16,0 16,0 16,8 17,2 16,0 16,0 16,0 16,1 15,9 15,8 16,5 16,3 16,0 16,1 18,8 17,2 16,2 16,1

16,6 19,1 16,7 16,1 16,8 17,3 16,6 16,2 16,5 16,6 16,4 16,4 16,4 17,5 16,4 16,4 16,8 18,2 16,9 16,7 16,4

16,4 18,8 16,1 15,9 16,2 17,4 16,4 16,3 16,3 16,7 16,5 16,5 16,4 17,8 16,6 16,7 16,8 17,9 16,9 16,0 16,5

16,2 17,7 16,5 16,3 17,5 17,7 16,6 16,6 16,6 16,9 16,9 16,8 16,9 18,0 16,2 16,3 17,8 19,7 17,2 16,8 17,9

16,7 19,6 17,8 16,6 17,0 17,3 16,8 16,5 16,5 17,3 16,3 16,5 16,4 19,5 16,8 16,3 17,3 20,0 17,1 16,3 16,9

16,4 18,7 16,8 16,2 16,9 17,1 16,7 16,3 16,3 16,6 16,4 16,4 16,3 17,6 16,4 16,3 16,8 19,0 17,1 16,4 16,7

*1

dimensions were taken from the inner side of joint

*2

clockwise in the front side

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that given in experimental European standards (Eurocode 5). Its magnitude also depends on the angle between the force and wood fibres. 4. Redistribution of stresses between the girder webmembers starts when the slip strains in steel-timber connections with “Bulldog”-type connectors are near the limit value (2 mm).

9.

References

11. Ðliþys, M. Application of ring-toothed connectors in metaltimber girders (Dantytøjø sprausteliø panaudojimas). Vilnius, 1999. 81 p. (in Lithuanian).

1.

10. Èechavièius, R. Investigation of ring-toothed connectors in metal-timber girders. Research report of Technical Centre for Timber Structures (Mokslo tiriamojo darbo ataskaita. Dantytøjø sprausteliø tyrimai). Vilnius, 1999. 93 p. (in Lithuanian).

Kuipers, J. and Kurstjens, P. B. J.: Creep and damage research on timber joints. Part one. Rapport 4-86-15-HD23. Stevin-Laboratorium. Delft University of Technology, Netherlands, 1986.

2.

Kurstjens, P. B. J. Creep and damage research on timber joints. Part two. Rapport 25.4-89-15 C HD-24, StevinLaboratorium, Delft University of Technology, Netherlands, 1989.

3.

Kurstjens, P. B. J. Creep and damage research on timber joints. Part three. Rapport 25.4-90-12 C HD-26, StevinLaboratorium, Delft University of Technology, Netherlands, 1990.

4.

Kurstjens, P. B. J. and Stolle, P. Creep and damage research on timber joints. Part four. Rapport 25.4-91-06/ C HD-28, Stevin-Laboratorium, Delft University of Technology, Netherlands, 1991.

5.

Frech, P. and Kolb, H. Test of Bulldog-type connectors. Test results H 30471 (Prüfung von Bulldog-Holzverbindern Prüfzeugnis H 30471). Otto–Graf Institute of Stuttgart University, 1971 (in German).

6.

Blass, J. H.; Ehlbeck, J. and Schlager, M. Characteristic strength of toothed-plate connector joints. Holz als Rohund Werkstoff, 51, 1993, p. 395–399.

7.

Blass, H. J.; Aune, P.; Choo, B. S.; Görlacher, R.; Griffiths, D. R.; Hilson, B. O.; Racher, P. and Steck, G. Timber Engineering. Netherlands: Centrum Hout, 1995.

8.

Eurocode 5. Design of timber structures. Part: General rules and rules for buildings. ENV 1995–1–1. Brussels: CEN, 1993. 133 p.

Hirashima, Y. (1990). Lateral resistance of timber connector joints parallel to grain direction. In: Proceedings of the International Engineering Conference, Vol 1: 254–261, Tokyo.

12. Narmontas, D.; Èechavièius, R.; Kudzys, A. Behaviour of composite open-web trusses with toothed-plate connectors. In: Proceedings of the International PhD Symposium in Civil Engineering, Institute of Structural Engineering University of Agricultural Sciences, Vienna, Oct 5–7, 2000, p. 431–434. 13. Standard of Germany. DIN 1052, Part 2: Timber structures design and construction (Deutsche Norm. Holzbauwerke-Berechnung und Ausführung). Beuth Berlin, 1988. 27 p. (in German). 14. Standard of Lithuania. LST EN 28970. Timber structures. Testing of joints made with mechanical fasteners (Medinës konstrukcijos. Sujungimø mechaninëms tvirtinimo detalëms bandymas). Requirements for wood density, 2000. 4 p. (in Lithuanian). 15. Standard of Lithuania. LST EN 26891. Timber structures. Joints made with mechanical fasteners (Medinës konstrukcijos. Sujungimai mechaninëmis tvirtinimo detalëmis). General principles for the determination of strength and deformation characteristics, 2000. 6 p. (in Lithuanian). 16. Blass, J. H. Joints of toothed-plate connectors. In: Timber structures in limit state. Introduction of Eurocode 5. Buildings materials and dimensioning basis (Assemblages par crampons. À: Structures en bois aux états limites). STEP1. Introduction à l’Eurocode 5. Matériaux et bases de calcul, Sedibois, Paris, 1996. 517 p.

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2004, Vol X, Suppl 1, 31–37

OPTIMUM DESIGN OF COLD-FORMED STEEL SHEETING USING GENETIC ALGORITHMS Wei Lu1, Pentti Mäkeläinen2, Jyrki Kesti3, Jukka Lindborg 4 1Steel

Structures, Helsinki University of Technology, FIN-02015, Espoo, Finland. E-mail: [email protected] Structures, Helsinki University of Technology, FIN-02015, Espoo, Finland. E-mail: [email protected] 3Rautaruukki Oyj, Construction Solutions / R &D, Helsinki, Finland. E-mail: [email protected] 4Rautaruukki Oyj, Construction Solutions / R &D, Helsinki, Finland. E-mail: [email protected]

2Steel

Received 1 March 2004; accepted 18 May 2004 Abstract. Cold-formed steel profiled sheeting is widely used for roof, floor system and wall cladding. Due to the variety of profiles available on the market, finding the optimum shapes is necessary. In this paper, genetic algorithms are applied to optimise dimensions of cold-formed steel profiled sheeting. The objective of the optimization is to obtain the optimum dimensions of profiled sheeting that has the minimum weight subjected to the given constraints. Sheathings are designed in accordance with Eurocode 3, Part 1.3. With this optimization process, a set of easily accessed optimum sections may be provided for structural steel designers and steel manufacturers. Keywords: cold-formed steel, profiled sheeting, optimization, genetic algorithm.

the weight of sheathing [11, 12]. In this paper, GA-based optimization method is used to obtain the optimum shape and dimension of roof sheathing that minimise the weight under the given constraints, such as the geometric, stress and fabrication constraints. Sheathings are designed in accordance with Eurocode 3, Part 1.3 [5]. Because of the many types of sheeting available and the diverse functional requirements and loading conditions that apply, design is generally based on experimental investigation. The analytical method can be used mostly for trapezoidal sheeting. The GA-based design procedure is demonstrated with four design examples. With this optimization process, a set of easily accessed optimum sections may be provided for structural steel designers and steel manufacturers.

1. Introduction Because of the high strength to weight ratio and ease of assembly, the profiled sheeting has been widely used for roofing, cladding and extended to floor systems in building constructions. Due to the variety of profiles available on the market, finding the optimum shapes is necessary. Genetic Algorithm (GA) is a general-purpose, derivative-free, stochastic search algorithm [3, 6, 10] and starts by randomly choosing an initial population that consists of candidate solutions to the problem at hand. Each individual in the population is characterised by a fixed length binary bit string, which is called chromosome. These chromosomes are evaluated by means of a fitness function. Combining the fittest individuals from the previous population, a new generation of chromosomes is created. Evolutionary operators such as selection, crossover, and mutation are used to create this new population. Besides, Elitism, which is a method that copies the best chromosome or a few better chromosomes to the new population, might be incorporated into the algorithm to avoid losing the best individual. This process continues until the specified level of fitness is reached. Normally, the objective for optimization is to achieve maximum use of material by using appropriating profiles, for instance, to maximize the resistance of sheeting subjected to bending stress [7] or to minimise

2. Description of optimum design problem The minimum weight design can be expressed as:

Minimise

W = ρ ⋅ ( Ag / bd ) ⋅ L ,

(1)

where W is the sheeting weight; L is the span of the sheeting; and bd is the notation width of the pitch as shown in Fig 1. Fig 1 also shows the dimensions of the sheeting for one fold, in which, bu and bp are notation widths of the plane elements; hw is the height of the web; Sw is the slant height of the web; and θ is the inclination of the web. Except for Sw and bd, all other dimensions shown in the figure are design variables.

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top flange. Similarly to the top flange, the dimensions of the bottom flange are shown in Fig 6. The design variables are the width and the height f the stiffeners, x9 and x10, the position of the stiffeners, x8; the inclination of the stiffener, θsp, and the number of the stiffeners.

Fig 1. Dimension of the cross-section for one fold

The shapes of the stiffeners on the flanges are shown in Fig 2. The number of the stiffeners on the flange can be zero, one or two. The stiffeners are assumed to be symmetric on the top of the flange. When two stiffeners appear, the sizes of them are the same. Fig 4. Type of web stiffeners

Fig 2. Types of flange stiffener

The dimensions of the upper flanges are shown in Fig 3. The design variables are width and depth of the stiffeners, x2 and x3, the position of the stiffeners, x1; the inclination of the stiffener, θsu, and the number of the stiffeners.

Fig 5. Dimension of web with two stiffeners Fig 3. Dimensions of the upper flange

According to the number of stiffeners on the web, three cases can be classified: case (a) without stiffener, case (b) with one stiffener and case (c) with two stiffeners as shown in Fig 4. In case (c), the size of the stiffeners is assumed to be the same. The dimensions of the stiffeners on the web are shown in Fig 5, in which the design variables are height and width of stiffeners bsw and ssw1; positions of stiffeners, sw1 and sw2, and the number of the stiffeners. The numbers and the dimensions of stiffeners on the bottom flange may be different from those on the

Fig 6. Dimensions of the bottom flange

The constraints can be classified into three categories: the geometrical constraints, the strength constraints and the fabrication constraints. The geometrical limits that should be satisfied are taken from Eurocode 3,

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where αi is the normalised geometrical and strength constraint and β is the normalised fabrication constraint and is defined as (Ls / LStrip – 1). Since the number of the fold is calculated as dividing the required width of the strip, Lstrip, by length of sheeting of each fold calculated from the current combination of design variables, thus, the value of |Ls / Lstrip| is less than one. And the value of  ισ ϖαριεδ µορε ρεγυλαρλψ ωηεν χοµπαρινγ το ϖαλυε 〈. Τηερεφορε, τηε πεναλτψ ισ διϖιδεδ ιντο τωο τερµσ, ιε 〈 ανδ . In the above formula, nn1 is the coefficient that

Part 1.3. These limits are listed in Table 1 as G1 and G2. When designing sheeting, the following checks should be carried out: bending resistance, shear resistance, concentrated load resistance (crippling resistance), interaction of bending and shear and/or crippling, and stiffness of the sheeting. Thus, the strength constraints are given in Table 2 as SM1, SM2, SF3, SF4, SF5, SV6 and SMV7. Table 1. Geometrical constraints Symbols G1 G2

Constraints descriptions Sw/t ≤ 200/sinθ bp/t ≤ 500 or bu/t ≤ 500

  makes the values of W and  (max( 0 ,α i )) 2  at the    i  same order and nn2 makes the values of W and β 2 at the same order so as to avoid one value dominating the other. KKi ≥ 0 are coefficients and the solution of the penalty problem can be made arbitrarily close to the solution of the original problem by choosing KKi sufficiently large [2]. Since GA is suitable to find the maximum value of an optimization problem, thus, the above-mentioned unconstrained minimisation problem should be transformed into maximisation problem by using the following formula [1]:

∑

Table 2. Strength constraints Symbols SM1, SM2 SF3, SF4 SMF5 SV6 SMV7

Constraints descriptions Moment resistance, positive and negative Web crippling, end and internal support Combined bending and crippling Web shear Combined bending and shear

The fabrication constraint in this analysis is defined as to manufacture the profiled sheeting with actual provided strip width, ie

Ls = Lstrip ,

F = Φ max − Φ ifΦ < Φ max , F =0

(2)

where Ls is the total length of sheeting calculated by using the cross-section dimensioned with the current combination of design variables; and Lstrip is the length of the provided strip width. For the purpose of the practical application, the overlap length has been taken into account in the calculation of Ls (Fig 7).

3. GA-based design Since GA is suitable for an unconstrained optimization problem, the constrained problem can be transformed to an unconstrained problem through a penalty function. A suitable penalty function must incur a positive for infeasible points and no penalty for feasible points. In this analysis, the quadratic penalty function is used, and the corresponding unconstrained problem becomes:

Minimise Φ = W + KK1 ⋅ nn1 ⋅ ∑ (max(0, α i )) 2 + KK 2 ⋅ nn2 ⋅ β ,

ifΦ ≥ Φ max ,

(4)

where Φmax is average fitness, ie Φmax = ave(Φ) so that the individuals with fitness greater than or equal to this value are discarded and with no chance to enter the mating pool. In GA terminology, F is called fitness function, which is used in the reproduction stage. Fig 8 shows how the sheeting design is integrated into the GA optimization process. GA-based design starts from randomly generating an initial population that is composed of candidate solutions to the current problem. Each individual in the population is a bit string of fixed length. After decoding, these individuals that represent the dimensions of the sheeting are sent to the sheet design programme, by which the resistances of the sheeting are calculated. After that, the constraints are checked and if the constraints are violated, the penalty is applied and the fitness function is calculated. After the evaluation of the fitness for each individual, a new generation is created using such operators as selection, crossover and mutation. In order to keep the best individuals in each generation, the elitism may also be used. This process is continued until the specified stopping criteria are satisfied. Compared to other search and optimization algorithms, GA has the following features: GAs search a set of points in parallel, not only at a single point; GAs do not require derivative information or other auxiliary knowledge. Only the objective function and corresponding fitness affect the search direction; GAs use probability rules; and GAs provide a number of potential

Fig 7. Overlap of two sheathings

i 2

33

(3)

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Start

Initialising the parameters

Randomly generating the initial population

Sheeting design: Gross section properties Effective section properties Moment resistance Shear resistance Buckling resistance

Checking the constraints and calculating the normalised constraints

Applying the penalty for the violated constraints

Output the results and stop

Decoding

Fitness evaluation

Yes

Check if the max generation is reached No Apply the GA operators: selection, crossover and mutation

Fig 8. GA-based sheeting design

stiffener from the nearest corner is set to 10 mm and the minimum distance between stiffeners is set to 10 mm.

solutions to a given problem. The final solution is left to user. 4. Examples Fig 9 shows two-span roof sheathing with applied loading. The loading includes the permanent load such as the self-weight of sheeting and insulations, which are represented as g, and variable loads, in this case, snow load, which is represented as s. The inclination of the whole sheeting is assumed to be zero. The load combination for the ultimate state design according to Eurcode 1[4] can be calculated as:

q = 1,35 × (Gk + w) + 1,5 × Qk

(5)

in which 1,35 and 1,5 are partial safety factors for dead load and variable load, respectively, under unfavorable effects; Gk and Qk are characteristic values of dead load and variable load; and w is the self-weight of the sheeting. The yield strength of the steel is 350 N/mm2, the elastic modulus is 210 000 N/mm2 and the density is 7850 kg/m3. The characteristic value of permanent load is assumed to be 0,5 kN/m2 and that of variable load is 1,8 kN/m2. The thickness of the profile is 0,6 mm. The support length is assumed to be 100 mm. The length of span is 4 m. In addition, the minimum distance of the

Fig 9. Loads applied to sheathing

Four design examples are demonstrated in this section according to the GA-based design procedure mentioned above. The first example is to find the optimum dimensions of the profiled sheeting without any stiffeners. The other three examples are with stiffeners on the flanges, with stiffeners on the webs and with no limitations, ie the stiffeners can be either on the flanges or on the webs, or both or no stiffeners at all.

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W. Lu, et al / JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT – 2004, Vol X, Suppl 1, 31–37 L −L

The GA, which is based on bit representation, twopoint crossover, bit-flip mutation, and tournament selection with elitism, is used to perform the optimization. The population size is set to at least twice of the length of individual string. Such parameters as the crossover rate and the mutation rate in genetic algorithms are set to 0,8 and 0,001, respectively. The selection of these parameters is based on previous research [8].

L

35 −L

2: 10 f cave , and case 3: 10 fave cave , in which Lf is the order of weight of each individual; Lc is the order of

   ∑ (max(0, αi )) 2  or β 2 ; L is the order of average ave  i  weight of individuals in a population and Lcave is the

 2 order of average value of  ∑ (max(0, αi ))  or β 2 in  i  a population. The effects of these three cases on finding the optimum profile are shown in Table 3. Due to the fixed size of population, the behaviour of GA may be different from run to run due to the error of finite sampling [9]. (One run is terminated when the given generation is reached). Thus, the optimization for each case is performed in 20 runs and minimum weight in 20 runs is taken as the optimum value. Table 3 also shows the length of sheathing and the percentage value of the dominant constraints, ie the combination of bending and local crippling. In addition, the average values of weight in 20 runs are also provided in the Table.

4.1. Profiles without stiffeners The dimensions of the profile are shown in Fig 10. The design variables are the width of the top flange bu, which is varied from 20 mm to 200 mm; the width of the bottom flange bp, which is varied from 20 mm to 200 mm; the height of the profile hw, which is varied from 20 to 170 mm and the inclination of the web θ, which is varied between 45° to 90°.

Table 3. Comparison of case 2 and case 3 Case 2 (kk1 = 1000, kk2 = 100) SMF5 Ls W1 [mm] [kg/m2] 98,64 1500,54 12,87 99,12 1500,36 14,21 99,40 1500,19 13,19 99,44 1500,43 13,54 99,99 1499,98 13,37 100,18 1499,86 13,58 90,03 1500,43 15,64 99,07 1500,50 12,77 99,30 1500,14 13,82 95,49 1500,23 14,46 91,74 1500,35 14,68 98,43 1500,27 13,67 99,95 1500,15 13,75 98,77 1500,02 14,30 99,48 1499,73 13,18 99,36 1499,77 13,48 97,80 1500,26 13,58 98,82 1499,71 13,97 98,61 1499,94 13,33 99,31 1500,41 13,94 Min 12,77 Ave 13,77

Fig 10. Dimensions of the profile without stiffeners

Each individual in the initial population can be formed as concatenating the design variables end by end and presenting them as a single string. For each design variable, the binary encoding method is used. The general formula for decoding design variable is [1]:

X = X min +

Xd 2L

( X max − X min ) ,

(6)

where X is the decoded value of design variable; Xmax and Xmin are the maximum and minimum value for the given design variables; Xd is the decimal integer value of the binary string; L is the string length corresponding to each design variable. In the process of calculating the fitness function, the values of KK1 and KK2 are set in the following way: perform the optimization with initial value of KK1 = 10 and KK2 = 10; check the violation constraints afterwards. If constraints for the profile with minimum weight are violated, the values of KK1 and KK2 are increased, for instance, KK1 to 100 and KK2 to 100, until there is no constraint violation for the profile of minimum weight. In this analysis, the value of KK1 is found as 1000 and that of KK2 is as 100. The role of nn1 and nn2 in equation (3) is to make the weight at the same order as penalty. Three formulas L −L are used to define value of nni, ie case 1: 10 f c , case

Case 3 (kk1 = 1000, kk2 = 100) SMF5 Ls W1 [mm] [kg/m2] 99,33 1500,44 14,10 97,89 1500,44 13,37 99,09 1499,70 12,97 95,28 1500,32 15,11 100,16 1500,58 13,97 99,73 1500,01 13,85 99,20 1499,61 13,75 95,93 1500,17 14,47 95,76 1499,68 13,47 99,99 1500,11 13,55 97,31 1500,20 14,32 98,64 1500,27 13,51 99,67 1499,78 13,39 97,50 1500,20 14,08 98,53 1500,14 13,82 99,70 1500,13 13,73 97,32 1500,04 13,58 96,17 1499,61 13,55 99,44 1499,88 14,19 95,45 1499,68 14,61 12,97 13,87

By running the program based on case 1, we found out that the profile of minimum weight with no violations of the inequality constraints can be found via increasing the value of KK1 gradually. However, we cannot find the profiles that have the acceptable values of strip length via varying the value of KK2. This is due to the fact the formula of defining nni in case 1 does not include the effect of the order of each individual. Only the integer part is taken into account. According to the definition of penalty for inequality constraints, the feasible individuals are kept with α = 0. Therefore, as the

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optimization is preceded, the optimization is concentrated to find the minimum weight among the individuals with no constraints violation even the effect of the order is not considered. However, the value of β always appeared in the formula for calculating fitness function. As the optimization proceeds, those individuals with lower value of integer part rather than those with small constraints violations are kept. When comparing the optimization results based on case 2 and case 3, it can be seen from the Table that both case 2 and case 3 give reasonable results. However, the case 2 provides the least weight comparing to case 3. As far as case 3 is concerned, it is only necessary to calculate the order of the average weight and the order of the average constraint. Thus, the calculation speed is improved when more design variables are involved. The analysis in this paper is based on case 2. The final optimum dimensions for the profile without any stiffeners in 20 runs are shown in Fig 11. In the figure, “n4-W1337” represents that the number of the fold is 4 and the minimum weight is 13,37 kg/m2. The weight of the best profile is 12,77 kg/m2 and the number of fold is 6. The constraints for the optimum profiles are shown in Table 4. 160 140 120 100 80 60 40 20 0

(mm)

n4-W1337 n6-W1277

4.2. Profiles with stiffeners The calculation is classified into three cases: profiles with flange stiffeners, profiles with web stiffeners and profiles without any limitation. Besides the design variables provided in the profiles without stiffeners in the previous section, the range of the following variables are given before running the programme: the heights of the flange stiffeners are varied from 0 mm to 15 mm; the widths of the flange stiffeners are varied from 5 mm to 15 mm; the inclinations of the flange stiffeners are varied from 45° to 90° and the length of the web stiffeners are varied from 0 mm to 30 mm. The optimum dimensions for the above-mentioned three cases are shown in Figs 12, 13, 14, respectively. Similarly, these figures also show the other possible profiles with different numbers of folds. The corresponding constraints for these three cases are shown in Table 4. (mm)

n4-W1125 n6-W1136

160 140 120 100 80 60 40 20 0

n5-W 1318 n7-W 1564

n5-W1104

(mm) 0

50

100

150

200

Fig 12. Optimum dimensions of profiles with flange stiffeners

(mm) 0

50

100

(mm) 160 140 120 100 80 60 40 20 0 0

150

Fig 11. Optimum dimensions of the profile without stiffeners

The results in 20 runs can be classified into several groups according to the numbers of folds. The profiles illustrated in Fig 11 are selected as the one with least weight in each group. By doing so, it is possible to provide more options for the manufacturers or designers when the manufacture facilities and practical application is taken into account. For instance, roof sheeting can be classified as “cold” roof, which has outer waterproof skin with internal insulation if required, and “warm” roof, which includes insulation and waterproofing. For “warm” roof, the main requirement of preventing penetration by rainwater leads to shallow profiles with a sequence of wide and narrow corrugations. For “warm” roof, it normally has the wider flanges on the top so as to provide sufficient support for the insulation.

n4-W1130 n6-W1166

n5-W 1081 n7-W 1188

(mm) 50

100

150

200

Fig 13. Optimum dimensions of profiles with web stiffeners

When comparing the optimum profiles shown in Fig 11 to those in Fig 12, it can be seen that the profile with stiffeners both on the flanges and on the webs has the minimum weight. However, the other cases provided here can give the alternatives when the cost, techniques of manufacturing, and the practical applications of the profiles are taken into account.

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Table 4. Values of constraints as percentage of the limits for the optimum profile for various cases

Cases NoS FS WS NL

(mm) 160 140 120 100 80 60 40 20 0 0

G1 28,3 42,6 37,4 38,9

G2 18,9 21,8 13,1 21,1

SM1 63,7 72,8 68,7 62,5

n4-W0972

SM2 90,6 65,8 79,5 69,8

SF3 21,7 38,6 28,1 35,6

SF4 33,2 59,2 43,1 54,5

n5-W1032

100

150

200

4.2. Comparison Fig 15 shows the comparison of the weight of optimized profiles for the case without any limitation for web and flange stiffeners to some commercial profiles. It also shows the ratio of calculated strip width using current dimensions to the provided strip width (1500 mm here). It can be seen that optimized profile using GA shows the lighter weight and more efficient use of materials. 0,83

Comercial profiles

0,68

SMV7 85,6 66,8 67,5 58,9

Ls [mm] 1500,5 1501,3 1500,0 1500,0

References

Fig 14. Optimum dimensions of the profiles with no limitations

0,82

SV6 18,5 48,4 21,0 32,0

The results of the numerical examples indicate that of four types of profiles studied, the profile with stiffeners both on the flanges and on the webs has the minimum weight. However, the other cases provided here can give the alternatives when the cost, techniques of manufacturing, and the practical applications of the profiles are taken into account. Besides, in order to provide the standard optimum dimensions under certain loads and for various span lengths for the practical applications, a large amount of calculations are required

(mm) 50

SMF5 99,1 100,0 98,0 99,4

1

1.

Adeli, H. and Cheng, N. T. Integrated genetic algorithm for optimization of space structures. Journal of Aerospace Engineering, 1993, Vol 6, No 4, p. 315–328.

2.

Bazaraa, M. S.; Sherali, H. D. and Shetty, C. M. Nonlinear programming: theory and algorithms. John Wiley & Sons, Inc., 1993, p. 360–372.

3.

Cogan, B. The evolution of genetic algorithms. Scientific Computing World, 2001, May/June, p. 28–31.

4.

ENV 1991-1 Eurocode 1: Basis of design and actions on structures, Part 1: Basis of design, 1994, p. 45–53.

5.

ENV 1993 Eurocode 3: Design of steel structures, Part 1.3: General rules. Supplementary rules for cold-formed thin gauge members and sheeting, 1996.

6.

Koumousis, V. K. and Georgion, P. G. Genetic algorithms in discrete optimization of steel truss roofs. Journal of Computing in Civil Engineering, 1994, Vol 8, p. 309–325.

7.

Lee, C. L; Mioduchowski, A. and Faulkner, M. G. Optimization of corrugated claddings. Journal of Structural Engineering, 1995, Vol 121, No 8, p. 1190–1196.

8.

Lu, W. Optimum design of cold-formed steel purlins using genetic algorithms, Publications, TKK-TER-25, Laboratory of steel structures, Helsinki University of Technology, 2003, p. 59–79.

9.

Michalewicz, Z. Genetic Algorithms + Data Structures = Evolution Programs, Third, revised and Extended Edition, Springer, 1999, p. 57–93.

10. Mitchell, M. An introduction to genetic algorithms. Cambridge (MA) MIT Press, 1998, p. 1–31.

Opt. profile (NL)

11. Nagy, Z. V. Evolution of optimum trapezoidal sheeting profile based on Eurocode, using finite strip method and genetic algorithm. Proceedings of the third international conference on coupled instabilities in metal structures, Lisbon, Portgual, 21–23 Sept, 2000, p. 643–650.

Fig 15. Comparisons with commercial profiles

5. Summary and future perspectives

12. Seaburg, P. A. and Salmon, C. G. Minimum weight design of light gage steel members. Journal of Structural Division, 1971, Vol 97, No ST1, p. 203–222.

As demonstrated in this paper, the Genetic Algorithm (GA) can be used as an optimization tool to obtain the optimum dimensions of the profiled sheeting.

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2004, Vol X, Suppl 1, 39–43

DEKORATYVINIO TANKAUS SILIKATINIO BETONO MIÐINIO SANDØ SAVYBIØ ÁTAKA DIRBINIØ KOKYBEI Algimantas Naujokaitis Statybiniø medþiagø katedra, Vilniaus Gedimino technikos universitetas, Saulëtekio al. 11, LT-10223 Vilnius-40, Lietuva. El. paðtas: [email protected] Áteikta 2003 08 28; priimta 2004 04 21 Santrauka. Iðnagrinëta dekoratyvinio tankaus silikatinio betono miðinio savybiø priklausomybë nuo miðinio sandø. Darbo tikslas buvo parodyti, kokios sandø savybës turi átakos tiksliø matmenø silikatiniø dekoratyviniø betonø savybëms. Nustatyta, jog miðinio sutankinimo vienodumui, suformuoto dirbinio matmenø tikslumui didþiausios átakos turi miðinio granuliometrinë sudëtis. Darbas atliktas naudojant naujo preso kompiuteryje tikslingai sukauptus duomenimis. Tyrimams gamybinëmis sàlygomis buvo naudoti praktiðkai neuþterðti priemaiðomis, vidutinio smulkumo ir smulkieji Giraitës telkinio kvarciniai smëliai. Parengta nauja miðiniø su daþomaisiais pigmentais sudëèiø parinkimo metodika, ávertinanti riðiklio su pigmentu savybes. Tyrimo duomenys naudojami tiksliø matmenø dekoratyviniø dirbiniø gamyboje. Raktaþodþiai: sandai, silikatinis betonas, betono sudëtis, smëlis, grûdinë sudëtis, pigmentai, smëlio smulkumas, tiksliø matmenø dirbiniai, sutankinimo koeficientas.

1. Ávadas

valios formos grûdeliø. Pusfabrikaèio stipris priklauso nuo slëgio vandens mikrokapiliaruose, kuriuos sudaro dispersinës dalelës, susikaupusios tarp ávairaus dydþio smëlio daleliø. Stiprio didinimas galimas didinant mikrokapiliarø kieká miðinio struktûroje. Tai pasiekiama, parenkant smëlio grûdinæ sudëtá, didinant dispersiniø ir riðamosios medþiagos daleliø kieká. Pusfabrikaèio stipris dar priklauso nuo tarpmolekuliniø traukos jëgø, atsirandanèiø ávairaus dydþio daleliø susilietimo vietose, kai atstumas tarp daleliø maþesnis uþ jø skersmená [1]. Labai keièiasi kalkiniø daleliø dydis ir kiekis masëje. Be to, á spalvotus dirbinius pridedama smulkiadispersinio pigmento, kuris chemiðkai veikia miðiná. Kaip teigiama [2], daleliø lyginamasis pavirðius yra 18 900 – 34 600 cm2/g. Kalkiø daleliø skersmuo: d = 6 · 103 / (ρ Sp), mkm, (1) ρ – Ca(OH)2 tankis; Sp – lyginamasis pavirðius, cm2/g. Dalelës skersmuo gali bûti nuo 1,5 mkm iki 210 mkm. Taigi gali susidaryti pakankamai daug kontaktø [2, 3]. Negalima pamirðti, kad dalelës linkusios koaguliuoti. Gesintøjø kalkiø masëje yra rezervø riðamajai medþiagai atsirasti [4]. Smëlio grûdeliai daþnai yra aðtriabriauniai, tokie yra ir nagrinëjamos technologijos atveju. Aðtrûs kampai padidina pusfabrikaèio stiprá, taèiau priklauso nuo dispersiðkumo ir elektrostatinës sankibos [4]. Diskutuojama dël tankiø plonø vandens plëveliø, presuojant suriðanèiø dispersines daleles [5, 6]. Taèiau tokios

Gaminant dekoratyviná silikatiná betonà visi jo sandai dalyvauja cheminëse reakcijose ir turi átakos visoms produkto savybëms. Pasikeitus vienam ið sandø, pasikeièia ir pagamintos medþiagos mechaninës bei fizikinës savybës. Tai privalu ávertinti, parenkant silikatinës masës sandø sudëtá, ypaè daþomojo pigmento rûðá ir kieká. Ðie klausimai buvo sprendþiami empiriðkai, analizuojant atskirus sandus dalimis, o vëliau sujungiant juos á sistemà. Akivaizdu, kad vienodomis gamybos sàlygomis, kai sandø savybës yra panaðios, silikatinio betono kokybiniai rodikliai pirmiausia priklauso nuo silikatinës cementuojanèios medþiagos sudëties. Autorius daro prielaidà, kad dekoratyvinis silikatinis betonas bûna geriausios kokybës, kai sunaudojamas minimalus kalcitiniø kalkiø kiekis, galintis, naudojant daþomuosius pigmentus, susijungti su kvarciniu smëliu. Idealiu atveju susidariusios cementuojanèios medþiagos kiekis priklausys nuo trijø veiksniø: naujadarø sluoksnio storio, kvarcinio smëlio lyginamojo pavirðiaus ir pigmento dispersiðkumo. Ávertinus tai parenkami smëlio, kalkiø ir pigmento kiekiai. Reikia ávertinti ir norimo suformuoti pusfabrikaèio stiprá, kuris priklauso nuo lyginamojo slëgio á formavimo masæ, slëgimo trukmës, riðiklio ir kvarcinio smëlio granuliometrinës sudëties, koloidiniø daleliø kiekio, drëgmës kiekio masëje. Apskaièiuojami miðinio sandø kiekiai ir gaminamas miðinys. Smëlio, kurio grûdeliai yra aðtriabriauniai, su nelygiu pavirðiumi, frakcijø sankiba yra didesnë, nei ap-

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Pilnutinës liekanos ant sietø, %

plëvelës daþniausiai yra tik intarpai tarp daleliø. Iðskirtinæ vietà, kaip manoma, turi koloidinës medþiagos, kuriø dalelës gali sudaryti tiltelius, jungianèius stambesnes daleles, esanèias didesniu atstumu nei molekuliniø jëgø veikimo laukas [7]. Sutankintas pusfabrikatis sudaro pakankamai akytà medþiagà, kurioje yra daug mikro- ir makrokapiliarø, nevisiðkai uþpildytø vandeniu. Susidaræ tarp daleliø vandens meniskai, turintys pakankamai laisvosios energijos, sukelia átempimus, taèiau kartu stiprina pusfabrikatá [7, 8]. Maþesnis pigmentø priedas turi teigiamos átakos kalcio hidrosilikatø susidarymui, pagerëja gaminiø stiprumas ir jø eksploatacinës savybës [9]. Nustatyta, kad pigmentø daþomàjà gebà lemia jø smulkumas ir juose esanèios daþomosios medþiagos kiekis. Esant didesnëms ðiø rodikliø reikðmëms intensyvesnë ir pigmentø daþomoji geba [10]. Paþymëtina iðskirtinë suodþiø átaka silikatinio akmens savybëms, ypaè vandens ágeriamumui. Ðie pigmentai yra hidrofobiðki, yra didelis lyginamasis pavirðius, taèiau vandens ágeriamumas taip pat didelis. Manoma, kad prie pigmento daleliø susidaro mikroporos dël didelio hidrofobiðko pavirðiaus blogo sàlyèio su silikatinio akmens hidrosilikatais [11]. Iðanalizavus minëtas teorijas, reikia pabrëþti, jog spalvotas silikatinis miðinys, ið kurio formuojami gaminiai, yra sudarytas ið gamtinio grûdinio smëlio, dispersiðkos riðamosios medþiagos, taip pat ir gesintøjø kalkiø bei pigmentø, susidedanèiø ið gausybës smulkiø daleliø, o smëlyje yra labai maþø kvarco grûdeliø bei molio mineralø. Miðinyje yra ir vandens bei oro burbulëliø, kuriø nepakanka uþpildyti formavimo metu susidariusioms tuðtumoms. Sutankinant silikatiná miðiná veikia ávairios jëgos, didinanèios jo stiprá: tai mechaninis grûdeliø sulipimas, molekuliniai sukibimo ryðiai vandens plëveliø kapiliaruose ir tarpkoloidiniø daleliø sàveika. Ypaè didelæ reikðmæ turi vanduo, sujungdamas koloidines maþàsias daleles su stambesniais smëlio grûdeliais. Sukibimo 0 10 20 30 40 50 60 70 80 90 100

jëgø dydis priklauso nuo sandø savybiø: smëlio granuliometrinës sudëties, grûdeliø formos ir dydþio, sumalto smëlio kiekio, kalkiø dispersiðkumo ir hidratacijos laipsnio, priemaiðø sudëties ir kiekio, pigmentø kiekio ir savybiø, vandens kiekio. Technologiniai preso ypatumai irgi svarbûs geram pusgaminio sutankinimui, nes privalu kuo geriau uþpildyti laisvà tûrá tarp smëlio grûdeliø, kad juos vienas nuo kito skirtø ploniausi riðamosios medþiagos sluoksniai. Toks sutankinimas leidþia gauti tankø ir stiprø silikatiná betonà. Darbo tikslas – iðtirti atskirø sandø átakà tiksliø matmenø dekoratyviniø silikatiniø betonø ir plytø gamybai. Atsiradus ðalyje naujai technologinei árangai, yra galimybë gaminti didesnio santykinio tankio tiksliø matmenø ávairios formos ir dydþio gaminius. Iki ðiol naudojamais technologiniais árenginiais negalima buvo tiksliau reguliuoti dirbiniø matmenø. Suformuoti pusfabrikaèiai deformuojasi dël ávairiø veiksniø, taèiau gaminant tiksliø matmenø dirbinius bûtina pagaminti kiek ámanoma stipresná pusgaminá, maþiausiai paþeidþiamà kitose technologinëse operacijose. Naujai iki ðiol ðalyje nenaudotai technologinei presavimo árangai, kai naudojami vietiniai sandai, technologiniø tyrimø nëra atlikta. Reikëjo iðnagrinëti ðiuos technologinius parametrus: formavimo miðinio sudëties átakà; dvipusá slëgimà á pusgaminá; smulkiosios sandø dalies kieká formavimo masëje, miðinio lyginamojo pavirðiaus átakà, vandens kieká. Pagrindinis tyrimo tikslas – parinkti miðiná, norint gauti kokybiðkus dirbinius. 2. Tyrimø metodika Tyrimams buvo naudotas dvipusio slëgio hidraulinis automatiðkai valdomas KSP 402 presas, kurio valdymo sistema leidþia fiksuoti atskirø operacijø atlikimà ir technologinius parametrus, áraðant juos á valdymo sistemos atmintá. Naudotas kvarcinis smëlis ið Giraitës telkinio. Cheminë jo sudëtis: SiO 2 82,6–91,48 %, Al 2O3 3,2– 4,19 %, CaO 2,8–4,5 %. Grûdinë sudëtis pateikiama 1 pav. Sijojimas atliekamas pagal standarto EN 1015-1 reikalavimus. Dalis smëlio buvo ápilta malant kalkes, já vadinsime maltu smëliu. Smëlio smulkumas buvo nustatomas AT-5 prietaisu. Kalcitinës negesintosios antros rûðies kalkës – „Naujojo kalcito“ gamybos, jø aktyvumas 65– 85 %, MgO – 1,2–1,5 %. Jø savybës tirtos pagal GOST 9179 metodikà. Spalvà suteikiantis pigmentas – Bayer firmos – 920, tankis 4,1 g/cm3, Fe2O3 yra 85–87 %. Silikatinio betono miðiniai buvo ruoðiami naudojant sausas medþiagas, dozuojami pagal masæ. Bandiniai formuoti natûralaus dydþio (25×12×8,8 cm). Miðinio sudëties, slëgio dydþiui presavimo formoje, dirbinio sutankinimui, granuliometrinës sudëties ir drëgnio átakai nustatyti bandiniai nebuvo kietinami. Tyrimai atlikti suformavus bandinius. Dalis jø buvo kietinami ir nustatomas galutinis gniuþdomasis bei lenkiamasis jø stipris, tankis ir vandens ágëris.

B A

0

0,075

0,125

0,25

0,5

1

2

4

Sietø akuèiø dydis, mm

1 pav. Smëlio grûdinë sudëtis: A – Giraitës telkinio smëlis; B – sijotas, geros grûdinës sudëties smëlis Fig 1. Sieve graphical analysis of sand: A – sand from the Giraitës deposit; B – sand riddle, granular structure of high quality

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P3= q1 S1 P4 / A + q2 S2 P1 / A,

(2)

P = P1+ P2+ P5,

(3)

P2 = P3+ P4,

(4)

0,008 0,007 0,006 0,005 0,004 0,003 0,002 0,001 0

q = f.S

10 0 20 0 20 0 35 0 45 0

Pagrindiniai dekoratyviniø silikatiniø dirbiniø tikslumo technologiniai parametrai yra presavimo bûdas, presavimo slëgio dydis ir formavimo miðinio sudëtis. Presavimo slëgio dydá tiriamoje technologijoje galima keisti nepriklausomai nuo kitø technologiniø parametrø: formavimo miðinio suslegiamumo, demferuojanèio veiksnio, miðinio sudëties. Miðinio granuliometrinë sudëtis buvo pasirinkta gera ir natûrali karjerinë. Ji yra svarbi dirbinio suformavimui, deformavimuisi nuo fizikiniø ir kitø veiksniø, todël buvo sudaryta naujos sudëties jo parinkimo principinë metodika. Siûlomas miðinio sudëties parinkimo metodas. Riðiklio kiekis P3 apskaièiuojamas taip:

20

Aktyvaus CaO kiekis (q), kg

3. Tyrimø rezultatai

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2

Smëlinio komponento lyginamasis pavirðius, m /kg

2 pav. Minimalus aktyvaus CaO kiekis miðinyje priklausomai nuo smëlio smulkumo Fig 2. Minimal amount of CaO in the mix depending on fine grained sand

Smëlio tuðtymëtumas ir lyginamasis pavirðius

P5 = [K11 (P1S1 + P4S2)+ K21 (P3 A S3)] / K5S4; (5)

Sand voids and specific surface

èia P – 1 m3 sutankinto sauso formavimo miðinio masë, kg; P1  – smëlio masë 1 m3 sutankintame sausame formavimo miðinyje, kg; P2  – riðiklio masë 1 m3 sutankintame sausame formavimo miðinyje, kg; P3  – kalkiø masë 1 m3 sutankintame sausame formavimo miðinyje, kg; P4  – malto smëlio masë 1 m3 sutankintame sausame formavimo miðinyje, kg; P5  – pigmentø masë 1 m 3 sutankintame sausame formavimo miðinyje, kg; q1  – optimali CaO masë, sunaudojama 1 m2 maltam smëliui padengti, kg; q2  – optimali CaO masë, sunaudojama 1 m2 nemaltam smëliui padengti, kg; S1  – malto smëlio lyginamasis pavirðius, m2/kg; S2  – nemalto smëlio lyginamasis pavirðius, m2/kg; S3  – kalkiø lyginamasis pavirðius, m2/kg; S4  – pigmentø lyginamasis pavirðius, m2/kg; A  – kalkiø aktyvumas, vieneto dalimis; K11  – koeficientas, ávertinantis nemalto smëlio daleliø pavirðiø; K21  – koeficientas, ávertinantis malto smëlio daleliø pavirðiø; K5  –  koeficientas, ávertinantis pigmentø savybes; q – reikðmës, nustatomos pagal 2 pav. reikðmes.

Grûdeliø skersmuo, mm

Smëlio tuðtymëtumas, %

Vidutinis grûdeliø skersmuo, mm

Lyginamasis pavirðius, m2/kg

2,0–1,0

35,7

1,4

4,65

1,0–0,5

38,7

0,82

7,95

0,5–0,25 0,25–0,125

39,5 40,6

0,15 0,26

10,75 27,6

0,125–0,075

45,5

0,11

154,6

0,075–0,038

49,5

0,04

223,0

Sudarant silikatinæ masæ kalkës sveriamos ne pagal bendrà masæ, o pagal aktyviosios dalies masæ, kuri dalyvaus cheminëje reakcijoje. Be to, ávertinama kvarcinio (malto ir nemalto) smëlio ir pigmento savybës. Esant tam paèiam kalkiø aktyvumui, pagal siûlomà sudëties parinkimo metodikà faktinis kalkiø kiekis priklauso nuo jø kokybës. Naudojant ðvieþiai iðdegtas didelio aktyvumo kalkes su minimaliu priemaiðø kiekiu, jø masë sumaþëja. Jei kalkës turi daug neiðdegusio kalkakmenio ir priemaiðø ir buvo ilgai laikytos ore, jø masë padidëja. Pakeitus nenutrûkstamai veikianèius dozatorius á periodinio-porcijinio svërimo dozatorius, buvo galima gerokai tiksliau pasverti kalkes ir silikatinæ riðamàjà medþiagà. Sumaþëjo kalkiø sànaudos 1000 vnt. spalvotøjø plytø reikiamai stiprumo markei gauti. Realiai tai pasiekiama tik naudojant elektroniná svërimo valdiklá. Slegiant tik preso puasonu ið vienos pusës, slëgis silikatinës masës pripildytoje presformoje pasiskirsto netolygiai [12]. Miðinys susitankina prie formos sieneliø, o vidinëje dalyje ir prieðingoje puasono pusëje masë susitankina maþiausiai.

1, 2 pav. ir lentelëje pateikiami duomenys silikatinio betono sudëèiai parinkti pagal kalkiø aktyviosios dalies masæ ir smëlinës dalies dispersiðkumà. Kiti duomenys apie sandus imami pagal savybiø tyrimo reikðmes. Pigmentø savybiø koeficientø (K11, K21) reikðmës ávertinamos pagal gamintojo deklaracijas.

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Slegiant ið abiejø dirbinio pusiø dviem slëgimo dydá reguliuojanèiais puasonais, dirbinio tankis skerspjûvyje suvienodëja (2 pav). 3 paveiksle pateiktas slëgio dydþio pasiskirstymas sutankintame silikatiniame betone. Hidraulinis presas slegia pradþioje apatinæ masës dalá, o po 0,5 s ásijungia ir virðutinis puasonas. 3 pav. a) pateikta geresnë smëlio grûdinë sudëtis, todël gaunamas tankiausias daleliø iðsidëstymas, o pusfabrikaèio stipris bûna vienodesnis negu 3 pav. b), kur smëlio grûdinë sudëtis artima natûraliai. Miðinio struktûrà sudaro visi sandai, ji priklauso nuo ðiø sandø iðsidëstymo ir uþimamo tûrio. Svarbiausi elementø parametrai yra tûris ir stambiøjø daleliø vidutinis skersmuo, turintis átakos riðamosios medþiagos kiekiui. Vienodø stambiøjø daleliø didesnis kiekis didina sistemos tuðtymëtumà, o ðioms tuðtymëms uþpildyti sunaudojama daugiau riðamosios medþiagos. a)

Pusfabrikaèio stipris, MPa

Miðinio aktyvumo didinimas ekonomiðkai yra nenaudingas, nes sunaudojami dideli riðamosios medþiagos kiekiai ir pablogëja galutinio produkto atsparumas atmosferiniams veiksniams. Todël praktiðkai pakanka 5,3– 6,2 % miðinio aktyvumo.

0,266

0,268

0,265

0,273

0,271

a= 250 mm

h = 88 mm

0,245

0,244

0,266

0,252

0,279

0,271

2

1

0

5

10 15 20 25

Miðinio aktyvumas, %

4 pav. Miðinio sudëties átaka pusfabrikaèio stipriui: 1 – apskaièiuotos pagal (3) ir (4) formules; 2 – apskaièiuota pagal nepakeistà silikatinës masës paruoðimo schemà

b) 0,265

0,35 0,3 0,25 0,2 0,15 0,1

Fig 4. Influence of mix composition on the strength of half-finished product: 1 – composition according to formulae 3 and 4; 2 – composition under the application of non-modified silica paste preparation scheme

Silikatinio dekoratyvinio miðinio sutankinimas tiesiogiai priklauso nuo smëlio grûdinës sudëties (5 pav).

a = 250 mm

3 pav. Silikatinio (nesukietinto) betono stipris gniuþdant, MPa (slëgis formoje 18,6 MPa): a) – geros grûdinës sudëties smëlis; b) – smëlio grûdinë sudëtis nëra pakankamai gera (Giraitës telkinio smëlis sijotas per 20 mm akutës sietà)

Sutankinimo koeficientas

2,3

Fig 3. Silicate concrete compressive strength: a – good granular structure sand; b – sand granular structure is not good enough (Giraitës bed sand sifted through the 20 mm stitch bolter)

Tuðtymëtumui sumaþinti reikia smulkesniø dispersiniø daleliø. Koloidinës dalelës, maþesnës kaip 0,1 mkm, yra labai svarbios [12]. Padidëja kontaktø tarp stambiø daleliø kiekis. Pigmentai dekoratyviniame silikatiniame miðinyje atlieka klijuojanèios medþiagos vaidmená ir padidina pusfabrikaèio stiprá. Buvo naudotas ávairios sudëties kalkiø ir smëlio miðinys. Ruoðiant toká miðiná imamas vienodas pigmento kiekis ir keièiamas tik kalkiø kieká permalant miðiná. Ruoðiamas miðinys, kurio aktyvumas – nuo 5 % iki 18 %. Dispersiðkumas apytikriai vienodas. Maiðyta permalimo ir trynimo bûdu, o antrajame variante pasverti komponentai sumaiðyti priverstiniame maiðytuve. 4 pav. matyti, jog sandø sudëtis pusfabrikaèio stipriui nëra labai svarbu, bet sumaiðymo bûdas yra reikðmingas. Sveriant sandus automatiðkai reguliuojamomis svarstyklëmis, gaunami pakankamai tikslûs jø kiekiai, todël praktikoje pasirenkami priverstinio tipo maiðytuvai, uþtikrinantys vienodà sandø pasiskirstymà miðinyje. Miðinio daliø permalimas gamybos sàlygomis yra sudëtingas, tam reikia dideliø energijos sànaudø.

2,1

1

1,9 2

1,7

3

1,5 1,3 0,5

1.0

1,5

2

2,5

Smëlio stambio modulis, Ms

5 pav. Smëlio grûdinës sudëties átaka silikatinës masës su pigmentu sutankinimui. Aktyvumas: 1 % – 7,40 %; 2 % –  5,30 %; 3 % – 2,50 % Fig 5. Influence of grain composition of sand on the compaction of silica paste with pigment. Activity: 1 % –  7,40 %; 2 % – 5,30 %; 3 % – 2,50 %

Kuo daugiau miðinyje yra ávairiø frakcijos daleliø, tuo lengviau jis sutankinamas, tuo didesnis gaunamas pusfabrikaèio stipris. Kalkiø ir pigmento smulkiadispersës dalelës kartu su vandeniu uþpildo poras tarp stambesniø grûdeliø, padidëja kontaktø kiekis tarp miðinio daleliø, susidaro mikrokapiliarai, iðnaudojamos vandens fizikinës savybës didesniam pusfabrikaèio gniuþdomajam stipriui gauti. Silikatinës masës formavimo drëgnis turi

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bûti proporcingas ðio miðinio lyginamajam pavirðiui. Jis nustatomas ne pagal smëlio frakcijos kieká, o pagal smulkiøjø daleliø masæ ir jø bendràjá lyginamàjá pavirðiø (5 pav). Miðinio drëgná charakterizuoja maksimalus jo drëgnio imlumas. Matome, kad kreivës 1, 2 ir 3 yra vienodo pobûdþio, didëjant miðinio drëgniui pusfabrikaèio stipris taip pat didëja. Reguliuojamas masës presavimo bûdas leidþia pasiekti pakankamà pusfabrikaèio mechaniná gniuþdomàjá stiprá, esant 4,5–5,3 % formavimo masës drëgniui. Visais atvejais pusgaminio stiprio pagrindas yra dispersinës dalies kiekis, kurio suriðimo procese dalyvauja vanduo, esantis mikrokapiliaruose. Sutankintas miðinys su daþomaisiais pigmentais yra stipresnis.

43

Literatûra

4. Iðvados 1. Bûtina suderinti dekoratyvinio tankaus silikatinio betono sudëtiniø daliø savybes, norint pagaminti geros kokybës dirbinius. 2. Parenkant miðinio sudëtá, riðamosios medþiagos ir kalkiø kiekis apskaièiuojamas ne pagal bendrà kalkiø masæ, o tik pagal aktyviosios dalies masæ, susiejant jà su kitø miðinio sandø savybëmis. 3. Optimalus pigmentø kiekis, su riðamàja medþiaga maiðant mineraliná pigmentà, kuris suteikia pageidaujamo intensyvumo spalvà, parenkamas pagal kalkiø ir kitø dispersiniø daleliø kieká. Tai sudaro galimybæ taupyti pigmentus (jø sunaudojama perpus arba net kelis kartus maþiau), pagerinti dirbiniø kokybæ. Pusfabrikaèio stiprio vienodumas dirbinio tûryje gaunamas slegiant paruoðtà silikatinæ masæ vienodu slëgiu pagrindinëms plokðtumoms prieðingomis kryptimis. 4. Silikatinio betono pusfabrikaèio matmenø tikslumui ir stipriui didþiausios átakos turi du pagrindiniai veiksniai: silikatinës masës suspaudimo bûdas ir dispersiðkosios dalies kiekis. 5. Gaminant didelio matmenø tikslumo spalvotus silikatinius dirbinius rekomenduojama naudoti minimalaus tuðtymëtumo aðtriabriaunius smëlius, jø kiekius apskaièiuojant pagal siûlomà metodikà, tankinant dvipusio slëgio presuose.

1.

Pohl, G. Lime burning and quality (Kalk brenen und Kalkqualitat). TJZ, 1993. No 9/10. 63 p. (in German).

2.

Durable concrete structures. Concrete Report, No 5, (S). Swedish Concrete Association, 1999. 56 p.

3.

Dvorkin, L. I. Projecting of concrete composition with given characteristics (Ïðîåêòèðîâàíèå ñîñòàâà áåòîíà ñ çàäàííûìè ñâîéñòâàìè). Rovno: PDTU, 1999, p. 121– 125 (in Russian).

4.

Chavkin, L. M. Production of silicate concrete with given characteristics of cementing substance. In: VNII Strom, No 66 (46). Ìoscow: VNIIStrom, 1998. 42 p. (in Russian).

5.

Walker, S.; Bloem, D. I. Effects of aggregate size on properties of concrete. Journal of American Concrete Institute, Vol 57, No 3, 1992, p. 215–221.

6.

Hiese, W.  Collection of works (Baustoffkentnis Düsseldorf), 1995, p. 452–462 (in German).

7.

Chavkin, L. M. Colouring of silica bricks. Building materials (Ñòðîèòåëüíûå ìàòåðèàëû), No 7. Moscow, 1998, p. 15–17 (in Russian).

8.

Weiss, R. Burnt lime production and characteristics (Physikalisch-chemische Untersuchung über den Zustand des Brannkalkes). Zement-Kalk-Gips, No 10, 1999. 86 p. (in German).

9.

Karsten, R. Constructional chemistry 9 (Bauchemie 9). Aufl., Verlag C. F. Müller. Karlsruhe, 1999. 16 p. (in German). 10. Rade, D. Research of inorganic pigments and their use for the production of coloured silica articles (Einige Untersuchungen über dieVerwendung von Anorganischen Baupigmenten zur Herschtellung von Farbkalksandstein). II JSD KB, Hannower, 1975. 62 p. (in German). 11. Hanssen, V. Inorganic pigments for the production of silica bricks, Areas of application (Anorganische Bayer-Pigmente zur Einfarbung on Kalksandsteinen). Sparte AC Anwendungstechnik 10/96. Leverkusen P, Bayer AG, 1999. 27 p. (in German). 12. Larrend, F. The Influence of aggregate on the compressive strength of normal and high-strength concrete. ACI Materials Journal, Vol 94, No 5, 1997, p. 417–426.

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JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT http:/www.vtu.lt/english/editions

2004, Vol X, Suppl 1, 45–50

THE APPLICATION OF THE MODERN METHOD OF EMBANKMENT COMPACTION CONTROL Maria Jolanta Sulewska Biaùystok Technical University, Faculty of Civil Engineering and Environmental Engineering, 15-351 Biaùystok, 45E Wiejska Str., Poland. E-mail: [email protected] Received 3 Sept 2003; accepted 17 May 2004 Abstract. Light drop-weight tester is a device for field tests and it is used for quick control of bearing capacity and compaction quality of built-in soils in different types of embankments. It is a modern device which is commonly used in Germany and now in Poland. The examples of calibration of the light drop-weight tester in laboratory and in-situ, and its application in real embankment are presented. Keywords: embankments, compaction control, light drop-weight tester, dynamic modulus of soil deformation.

1. Introduction

index Io= E2/E1 (where E1 and E2 – primary and secondary moduli of soil deformation tested with VSS plate) or secondary modulus of deformation E2 [8].

Increase of demands concerning the quality of different types of earth structures has been observed recently. Special stress is also put on the short duration of construction. That is why the interest in quick methods of control of ground compaction has increased recently. Application of quick and not complicated method of current control is especially important. Falling-weight deflectometers FWD of different structure and parameters are used in many countries for control tests of achieved compaction of subsoil and made ground [1– 4]. Falling-weight deflectometers mounted on automotive vehicles has been introduced recently in highway engineering. They are used for measurement of bearing capacity of road surface based on deflection bowl [3]. Force impulse in the range of 7 kN to 250 kN is transmitted on the surface of tested medium through thrust plate of radius 300 mm. A scheme of measurement of deflection bowl on road surface using FWD is presented in Fig 1. On the theoretical basis of considered problem [5, 6] it is assumed that loading of soil with the lightweight dynamic deflectometer can be treated as a problem of short duration quasi-statical pressure of the plate on the elastic half-space. This paper describes a light drop-weight tester used in Germany [4, 7] and Czech Republic [2]. There are also companies in Poland which apply this device. The measure of quality of controlled compaction of soil built in embankments is the value of soil degree of compaction Is= ρd/ρds (where ρd – dry density of solid particles, ρds – maximum dry density of solid particles tested with Proctor method) or the value of deformation

Fig 1. Scheme of measurement of bowl of deflections on road surface using FWD [3]

These types of tests are labour-consuming and longlasting and they cannot be conducted in all field conditions. Light drop-weight tester has many advantages comparing with traditional control tests. These are: • elimination of heavy equipment, which is used as counterweight in the method of tentative static loads with VSS plate,

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• possibility to conduct the tests in case of limited surface and difficult access, eg dykes, backfills of narrow excavations, • small dimensions (1,5 m high) and light weight (20 kg), • short time for a test (about 3 min) enables to make many tests and to densify tested points and find “weak” areas, • possibility to obtain results immediately shortens the duration of construction and does not cause shutdowns during earth works. The paper presents examples of calibrations of the light drop-weight tester which were made prior to its application in compaction control of real embankments. Correlations between dynamic modulus of soil deformation ED and other geotechnical parameters (IS, E1, E2), which are normally tested for evaluation of compaction quality, were determined on the basis of our own laboratory examinations of medium sand. Dependency ED = f(IS) was determined basing on examinations of allin aggregate on the test field.

The test is based on producing force impulse of short duration (amplitude 7,07 kN) through the weight impact dropping along guide bar from the height (h) on the shock absorber. The impulse is transmitted by the thrust plate to the surface of tested soil and it causes deformation of soil under the plate. The value of dynamic modulus of soil deformation is a result of this test [4]. It is calculated from the following equation:

E D = 1,5

rσ D uD

=

22.5 , uD

(1)

where r – diameter of the thrust plate, r = 300 mm; σ D – amplitude of dynamic stress under the thrust plate, σ D = 0,1 MPa; u D – average settlement of the thrust plate calculated from the results of 3 impacts made after three initial impacts, mm. 2.2. Application of light drop-weight tester This tester is used for quick examination of dynamic modulus of deformation. The modulus is used for evaluation of bearing capacity and indirectly - for control of compaction quality of subsoil, soil-surfaced roads, layers of embankments or backfills built from mineral soils, soils improved with lime or from waste materials. Light drop-weight tester can be used [4, 7] under the following conditions: • under the measurement range 15 ≤ ED ≤ 80 MPa, • for mineral coarse-grained soil with content of grains d ≥ 63 mm not exceeding 15 % (and soil with up to 30 % of crushed stone) and fine-grained non-cohesive and cohesive soil in semisolid or low plastic state, • when thickness of tested uniform soil layer is in the range of 0,3 to 0,5 m [9, 10].

2. The description of the test method 2.1. Light drop-weight tester The light drop-weight tester consists of steel thrust plate (1) diameter of 300 mm with holders (2) and the detector for settlement measurement (3). Guide bar (4) with shock absorber (5) and 10 kg weight (6) hanging in snap fastener (7) is placed on the thrust plate. Detector is connected with the electronic settlement meter (8). The settlement meter shows and registers deflection of subsoil under the thrust plate after each of three impacts and then the average deflection out of the three measurements, the value of dynamic modulus of soil deformation ED and the “time of acceleration” uD/v (where uD – deflection of soil under the thrust plate, v – the deflection rate). The diagram of the light drop-weight tester is presented in Fig 2.

2.3. The way of conducting the test The thrust plate is set up on the even surface and additionally it is adjusted by shifting and rotating. The surface of coarse grain soil can be even up with the layer of dry fine sand thickness of few millimeters. Then the guide bar is set up on the thrust plate and the deflection meter is connected. The weight is lifted to the height (h) and then dropped on the shock absorber and gripped when it rebounds. Three initial hits should be made in order to get a good contact between the plate and soil. Three test hits are made after turning on the meter. 2.4. Interpretation of test results Quality control of compaction of soil layers consists in comparison of tested value of degree of compaction Is (or Io or E2) with the minimum required standard value which for road embankments is Is ≥  0,92÷1,03 (Io = 2,5÷2,2 and E2 ≥ 30÷120 MPa) depending on category of traffic and the depth of the tested soil layer [8].

Fig 2. Diagram of light drop-weight tester with electronic settlement meter

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The tests of dynamic modulus of soil deformation were conducted using light drop-weight tester type ZFG 01 according to [4]. Primary and secondary moduli of soil deformation were determined by means of thrust plate with static load (VSS) according to [8]. The dynamic modulus of deformation was calculated by equation (1). The values of primary and secondary moduli of deformation were calculated by the equation:

The above parameters can be determined indirectly on the base of developed correlation with dynamic deformation modulus for the given soil built in embankment. The general correlations or dependencies determined for many types of soil or for particular groups of soil would be the most useful. 3. Example of calibration of light drop-weight tester The aim of the test was to determine the dependencies between dynamic modulus of deformation ED and degree of compaction Is or primary E1 and secondary E2 deformation modulus for medium-grained sand, according to [10]. The sieve-analysis curve is presented in Fig 3.

∆σ 22,5 , (4) = ∆u ∆u where ∆σ – the range of stress in which modulus E1 and E2 were calculated, ∆u – measured settlement of the thrust plate for σ 2 and σ1 , mm, correspondingly, ∆u = u2 − u1 , ∆σ = σ 2 − σ1 = 0,125 − 0,050 = 0,075MPa . A set of variables (Is, ED, E1, E2) was obtained as a result of examinations of modelled soil. The set consisted of n = 30 results: n1 = 14 for a1 = 0,3 m and n2 = 16 for a2 = 0,5 m. Statistical analysis of the set of variables (Table 1) was made with computer program Statgraphics [13]. Verification of hypothesis of equal average values in groups (using the method of variance analysis with singular classification based on the least significant differences) was conducted in order to determine whether the thickness of tested soil layer influences the value of dynamic modulus of deformation. The level of significance was α = 0,798. This conclusion confirmed also the test of homogenous groups. In order to justify the conclusion by the variance analysis, two assumptions were checked [13]: normality of characteristic distribution in groups using Kolmogorov – Smirnov’s test of goodness of fit and homogeneity of variance in groups using Chochran’s test and Bartlett’s test. The above analysis allowed formulating the following conclusion: the thickness of soil layer (in the range 0,3 m to 0,5 m) does not influence the value of dynamic modulus of soil deformation ED. Then correlations between variables in the set of all measurements were determined. The best fitted models of regression between two variables were chosen using simple regression analysis [13, 14]. Table 2 presents matrix of linear correlation coefficients for tested variables. Analysis of correlation matrix shows significant dependencies between dynamic modulus of deformation and statical moduli of deformation as well as the relationship between degree of compaction. The dependencies: ED=f(Is) and ED=f(E1), ED=f(E2) are presented in Figs 4 and 5. E1 or E2 = D

Fig 3. Medium sand sieve-analysis curve

The test was performed on laboratory setup on the model subsoil from medium-grained sand. Soil water content was in the range of 3,5 to 6,7 %. The investigated soil layer thickness a1 = 0,3 m or a2 = 0,5 m was placed on a sublayer thickness 0,3÷0,4 m of Is ≥ 1,0 and it was evenly compacted with plate compactor. Degree of compaction was calculated by the equation

Is =

ρd , ρ ds

47

(2)

where ρ d – dry density of solid particles, ρ ds – maximum dry density of solid particles, tested using method I (normal Proctor’s method) according to [11]. Dry density of solid particles was calculated by the equation:

100ρ , (3) 100 + w where ρ – bulk density of soil tested with sand volumeter according to [12], w – water content tested by drying according to [11]. ρd =

4. Control of soil compaction using light drop-weight tester according to German instructions In German recommendations regarding road earth works [15, 16] light drop-weight tester is allowed to be

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Table 1. Statistical parameters of variables (Is, ED, E1, E2)

Geotechnical parameter Is ED E1 E2

[–] [MPa] [MPa] [MPa]

Number of observations 15 30 15 15

Minimum value

Maximum value

Average value

0,907 11,0 11,2 38,1

0,993 38,8 39,5 112,5

0,962 29,0 28,0 91,8

Standard deviation

Coefficient of variation

0,024 7,1 8,1 22,9

2,5 24,6 29,1 25,0

Skewness ratio

Kurtosis

–1,02 –0,96 –0,72 –1,47

0,17 0,10 –0,21 1,03

Table 2. Matrix of linear correlation coefficients for tested variables

Is ED E1 E2

Is 1,000 0,920 0,951 0,954

ED 1,000 0,926 0,911

E1

E2

1,000 0,902

1,000

used for control of embankments compaction (as an independent or additional test to static plate load). It is recommended to determine limit values of moduli ED in comparison with secondary moduli of deformation E2 tested in the given soil condition. In the case of lack of own correlation dependencies, the values in Table 3 can be used for orientation [16]. Table 3. Values of secondary modulus of deformation E2 (according to [17]) and dynamic modulus of deformation ED [16]

Fig 4. Dependency ED = f(Is) for medium grained sand: ED = 270,51Is-231,34; r = 0,920; Syx = 2,85 MPa, r-correlation ratio; Syx – standard estimation error; (1), (2) – ranges of confidence limits for regression line and predicted values calculated for probability 95 %

E2 [MPa] ED [MPa]

120 60

100 50

80 40

45 25

Comparative examinations has been conducted for many years in order to develop correlation dependencies for different groups of mineral and anthropogenic soils and in order to determine obligatory limit values of modulus ED in comparison with minimum required values of modulus E2. Weingart [18] suggested to consider the following observations: a) the value of “time of acceleration” uD/v ratio, where uD – settlement of thrust under impact, v – speed of settlement, gives additional information on soil compaction, b) at proper compaction (when E2/E1 ≤ 2,5 [15]) the condition 2,2 ≤ E2 /E D ≤ 2,6 should be satisfied; at not sufficient compaction (when E2/E 1 > 2,5) it is observed that E2/ED< 2,2. On the base of examinations of road load-bearing layers Weingart proposed the following limit values and additional conditions (they do not refer to fine-grained soils sensitive to water) (Table 4).

Fig 5. Dependency ED = f(E1) and ED = f(E2) for medium grained sand: (1) ED = 6,32+0,81E1; r = –0,926; Syx= 2,74 MPa, (2) ED = 2,98+0,28E2; r = –0,911; Syx = 3,00 MPa

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Table 4. Values of secondary modulus of deformation E2 depending on the value of dynamic modulus of deformation ED [18]

E2 [MPa] ED [MPa]

150 120 100 80

60

45

70

30

25

55

45

40

Additional conditions: E2/E1<2,2, uD/v<3,5ms

5. Example of light drop-weight tester application on the building site Light drop-weight tester was used to control the quality of compaction of layers built in road embankments (parking platforms) of considerable area and the thickness up to 5 m. The embankments were built of glacial sand-gravel mix from local deposit. The embankments were formed with layers compacted using vibrating tamping rollers and smooth rollers. Control of soil compaction was conducted currently for each compacted layer of thickness of 0,30÷0,50 m. The test points were located in square grid, side length about 25 m. The tests of dynamic modulus of soil deformation were conducted using light drop-weight tester type ZFG 01 according to [4]. Comparative tests in 28 points were made in order to calibrate the light drop-weight tester for the most commonly built-in soils. The following geotechnical parameters were determined according to [11]: – maximum dry density of solid particles ρds and optimum water content wopt (using I Proctor’s method) (ρds= 1,922÷2,179 g/cm3, wopt= 6,7÷11,1 %), – bulk density of soil ρ, using sand volumeter (ρ = 1,995÷2,311 g/cm3), – water content w, using drying method (w = 2,4÷7,4 %), – degree of compaction Is (Is=0,90÷1,05). Soils were qualified as sand-gravel mix (Po) according to [11]. Chi-square test and Kolmogorov-Smirnov test (at significance level α = 0,05) were conducted at the beginning and it was accepted that tested variables had a distribution consistent with normal distribution. Then, based on analysis of matrix coefficients of linear correlation of variables and stepwise regression analysis, it was found that soil water content (in the tested range) did not influence significantly the value of modulus ED. The best fitted model was found based on the method of simple regression. The dependency ED=f(IS) and the confidence limits of regression line (1) and predicted values (2) for probability 95 % are shown in Fig 6. The values of dynamic modulus of deformation depend on soil compaction – they increase with increase of the value of compaction degree. The developed correlation curve was used to current control of compaction quality of built-in soil layers.

Fig 6. Dependency E D = f(I s ) for sand-gravel mix: 1/ED = 0,176–0,156Is; r = –0,778; Syx = 0,004

It was decided to accept the following limiting values of modulus ED: EDmin < 40 MPa, – when Is< 0,97 → – when 0,97 ≤ Is< 1,00 → 40 ≤EDmin< 50 MPa, – when 1,00 ≤ Is< 1,03 → 50 ≤EDmin< 65 MPa, – when Is ≥ 1,03 → EDmin ≥ 65 MPa. 6. Conclusions Preliminary examinations (calibration of the device) were made prior to application of the light drop-weight tester in field for compaction quality control of embankments. Correlations ED=f(IS) and ED=f(E1), ED=f(E2) were determined for medium sand, and correlation ED=f(IS) was determined for all-in aggregate. Examinations performed by the author showed that there exist dependencies between values of dynamic modulus of soil deformation and values of soil degree of compaction and values of moduli of deformation E1 or E2. These correlations can be used during compaction control of embankments under construction. The light drop-weight tester can be applied for quick current control of the quality and uniformity of compaction. This may considerably promote earth works. Acknowledgements This study was supported by State Committee for Scientific Research, project number W/IIB/9/01. References 1.

49

Benoist, I. and Schaeffner, M. Falling Weight Deflectometer. Bulletin of Laboratory of Bridges and Higways (Bulletin des Laboratoires de Ponts et Chaussees), No 122. Paris: Nov / Dec 1982, p. 61–72 (in French).

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2.

ÈSN 73 6192. Impact Load Tests for Road Surfaces and Subsurfaces (Rázové zate•ovací zkoušky vozovek a podlo•i). Czech Standardization Institute, Praha, 1996. 24 p. (in Czech).

3.

Horz, H. W. Falling Weight Deflectometer in Road Building in Germany. Streets and Highways (Strasse und Autobahn), No 3. Bonn, 1992, p. 170–172 (in German).

4.

Technical Specification for Soil and Rock in Road Construction TP BF-StB Part B 8.3 (Technische Prüfvorschriften für Boden und Fels im Straßenbau TP BF-StB Teil B 8.3: Dynamischer Platten-druckversuch mit Hilfe des Leichten Fallgewichts-gerätes). Road and Transportation Research Association, Köln, 1997. 18 p. (in German).

5.

Weingart, W. Problems of Dynamic Test Using Light DropWeight Tester. The Street (Die Strasse), No 11. Berlin, 1998, p. 369–373 (in German).

6.

Kudla, W.; Floss, R. and Trautmann, Ch. Dynamic Test with Plate – Quick Method of Quality Assurance of Road Layers without Binder (Dynamischer Plattendruckversuch – Schnellprüfvehrfahren für die Qualitätssicherung von ungebundenen Schichten). Streets and Highways (Strasse und Autobahn), No 2. Bonn, 1991, p. 66–71 (in German).

7.

Directions of Application of Light Drop-Weight Tester in Railways (Richtlinie für die Anwendung des Leichten Fallgewichtsgerätes im Eisenbahnbau). NGT 39, German Railways, 1997. 7 p. (in German).

8.

PN-S-02205 Roads – Earthwork – Specifications and Testing (Drogi samochodowe. Roboty ziemne. Wymagania i badania). Polish Standardization Committee, Warsaw, 1998. 25 p. (in Polish).

9.

Sulewska, M. J. New Control Method of Uniformity of Compaction of Non-cohesive Soils. Engineering and Building (Inýynieria i Budownictwo), No 4. Warsaw, 1999, p. 218–220 (in Polish).

odksztaùcenia gruntu niespoistego wyznaczone metodà dynamicznà). PhD thesis, Bialystok Technical University, Bialystok, 1993. 161p. (in Polish). 11. PN-88/B-04481 Building Soils. Laboratory Tests (Grunty budowlane. Badania laboratoryjne). Polish Standardization Committee, Warsaw, 1988. 63 p. (in Polish). 12. BN-77/8931-12 Determination of Soil Degree of Compaction (Oznaczanie wskaênika zagæszczenia). Polish Standardization Committee, Warsaw, 1977. 5 p. (in Polish). 13. Podgorski, J. Statistics with Computer. Statgraphics version 5&6 (Statystyka z komputerem. Statgraphics wersja 5&6). Warsaw, 1995. 300 p. (in Polish). 14. Draper, N. R. and Smith, H. Applied Regression Analysis (Analiza regresji stosowana). Warsaw: Polish Scientific Publishers, 1973. 459 p. (in Polish). 15. Additional Technical Requirements and Instructions for Earth Works in Road Constructions (Zusätzliche Technische Vertragsbedingungen und Richtlinien für Erdarbeiten im Straßenbau) ZTVE-StB 94, Road and Transportation Research Association, Köln, 1994/ 1997. 108 p. (in German). 16. Additional Technical Requirements and Instructions for Excavations in Road Constructions (Zusätzliche Technische Vetragsbedingungen und Richtlinien für Aufgrabungen in Verkehrsflächen) ZTVA-StB 97, Road and Transportation Research Association, Köln, 1997. 120 p. (in German). 17. DIN 18134 Building Ground. Tests and Test Methods. Load with plate (Baugrund. Versuche und Versuchsgeräte. Plattendruckversuch), German Standardization Institute, Berlin, 1993. 9 p. (in German). 18. Weingart, W. Controll of Road Layers without Binder Using Light Drop-Weight Tester. In: Transactions in Mineral Materials in Road Construction (Tagungsband Minerallstoffe in Strassenbau), No 6. Köln: 1993. p. 50–53 (in German).

10. Sulewska, M. J. Modulus of Deformation for Non-cohesive Soil Determined with Dynamic Method (Moduùy

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2004, Vol X, Suppl 1, 51–55

SAUGOS IR SVEIKATOS PROBLEMOS IR PERSPEKTYVOS STATYBVIETËSE Ritoldas Ðukys  Darbo ir gaisrinës saugos katedra, Vilniaus Gedimino technikos universitetas, Saulëtekio al. 11, LT-10223 Vilnius-40, Lietuva. El. paðtas: [email protected]  Áteikta 2004 04 26; priimta 2004 05 19 Santrauka. Lietuvai tapus Europos Sàjungos nare svarbu nustatyti integracijos pasekmes socialinëms, ekonominëms, ûkinëms ir kitoms sritims. Viena ið prioritetiniø srièiø yra darbuotojø sauga ir sveikata. Statyba pagal savo darbø specifikà (daþnai keièiasi darbo pobûdis ir vieta, atliekami su rizika susijæ darbai, dirbama ávairiomis klimato sàlygomis) yra viena ið pavojingiausiø ðiuo poþiûriu ûkio srièiø. Tyrimo tikslas – kaip galima tiksliau nustatyti kokybinius ir kiekybinius poveikius, kuriuos patiria Lietuvos statybos ámonës, ágyvendindamos ES Tarybos direktyvà 92/57/EEB „Dël minimaliø saugos ir sveikatos reikalavimø laikinosiose ir kilnojamosiose statybos aikðtelëse“. Tyrimui taikyti statistiniaianaliziniai, apklausos, analizës, analogijø, finansinis ataskaitø apibendrinimø ir kiti mokslinio tyrimo metodai. Nustatytos ámoniø iðlaidos, iðlaidos valstybiniame lygmenyje, teigiamas direktyvos poveikis, parengtos rekomendacijos.  Raktaþodþiai: integracija, darbuotojø sauga ir sveikata, ES Tarybos direktyva 92/57/EEB, finansinës iðlaidos, statyba.

1. Ávadas

tyrimø [5–14]. Juose nustatyti teigiami ir neigiami poveikiai Lietuvos ûkiui, pateiktos rekomendacijos darbuotojø saugai ir sveikatos apsaugai gerinti. ES Tarybos direktyvos 92/57/EEB „Dël minimaliø saugos ir sveikatos reikalavimø laikinosiose ir kilnojamosiose statybos aikðtelëse“ ágyvendinimo pasekmiø tyrimo rezultatai ir rekomendacijos padës statybos ámonëms ágyvendinti Lietuvos teisës aktø, reglamentuojanèiø saugà ir sveikatos apsaugà darbe, reikalavimus. Tai pagerins darbo sàlygas ámonëse, sumaþins profesiniø ligø skaièiø bei padës ámonëms laiku ir geriau pasirengti integracijai á Europos Sàjungos rinkà. Atliekant Direktyvos 92/57/EEB ágyvendinimo pasekmiø tyrimà dalyvavo Lietuvos statybininkø asociacijos bei jos ámoniø darbuotojai. Buvo bendradarbiaujama su suinteresuotomis ágyvendinti Direktyvà institucijomis – Socialinës apsaugos ir darbo ministerija, Valstybine darbo inspekcija, Valstybiniu visuomenës sveikatos centru, Statybos darbuotojø profsàjunga, aukðtøjø mokyklø profilinëmis katedromis.

 Lietuvai tapus Europos Sàjungos nare svarbu nustatyti integracijos pasekmes socialinëms, ekonominëms, ûkinëms ir kitoms sritims. Viena ið prioritetiniø srièiø yra darbuotojø sauga ir sveikata. Statyba pagal savo darbø specifikà (daþnai keièiasi darbo pobûdis ir vieta, atliekama daug su rizika susijusiø darbø, dirbama ávairiomis klimato sàlygomis) yra viena ið pavojingiausiø ðiuo poþiûriu ûkio srièiø [1–4]. Lietuvos statybos ámonës turi vadovautis ES Tarybos direktyvos 92/57/EEB „Dël minimaliø saugos ir sveikatos reikalavimø laikinosiose ir kilnojamosiose statybos aikðtelëse“ nuostatomis. Direktyva nustato minimalius saugos ir sveikatos laikinøjø ar kilnojamøjø statybos aikðteliø árengimo reikalavimus, susijusiø su darbuotojø sauga ir sveikata. Joje nustatyti minimalûs ir privalomi reikalavimai, kurie turi bûti ágyvendinti steigiamose ar esamose statybvietëse. Tai reikalavimai, keliami statybvieèiø pastatams, darbo ir buitinëms patalpoms, apðvietimui, durims ir vartams, këlimo mechanizmams, transporto priemonëms, þemës darbø maðinoms, kitiems árenginiams, keliams ir kt. Nagrinëjamos Direktyvos nuostatos yra svarbios ir reikalingos didinant statybos ámoniø konkurencingumà bei uþtikrinant darbuotojø saugà ir sveikatos apsaugà statybose. Svarbu þinoti visapusiðkà ðio teisës akto poveiká Lietuvos ûkiui. Lietuvoje atlikta nemaþa darbuotojø saugà ir sveikatos apsaugà reglamentuojanèiø teisës aktø, parengtø pagal ES direktyvø reikalavimus, pasekmiø

2. Tyrimo tikslas, uþdaviniai ir metodika  Tyrimo tikslas – kaip galima tiksliau nustatyti kokybinius ir kiekybinius poveikius, kuriuos patiria Lietuvos statybos ámonës ir valstybës institucijos, ágyvendindamos ES Tarybos direktyvà 92/57/EEB „Dël minimaliø saugos ir sveikatos reikalavimø laikinosiose ir kilnojamosiose statybos aikðtelëse“.

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veikianèiø statybos ámoniø padaugëjo apie 16 %. Respublikoje vyrauja smulkios ir vidutinës statybos ámonës, kurios sudaro daugiau kaip 99 % visø statybos ámoniø. Duomenys apie nelaimingus atsitikimus darbe statybose, kuriems 1997–2002 m. buvo suraðyti N-1 formos aktai, pateikiami lentelëje.  

Atliekant tyrimus siekta: • ávertinti dabartinæ situacijà (darbuotojø saugos ir sveikatos bûklæ statybos ámonëse); • nustatyti teigiamà Direktyvos poveiká; • nustatyti iðlaidas statybos ámonëms ir vieðajam (valstybiniam) sektoriui; • parengti rekomendacijas statybos ámonëms, valstybës ir visuomenës institucijoms. Tyrimas atliktas vadovaujantis Europos komiteto prie Lietuvos Respublikos Vyriausybës parengta „Reguliuojanèiø teisës aktø poveikio ávertinimo metodika“. Tyrimui buvo taikomi statistinis-analizinis, apklausos, analizës, analogijø, finansinis ataskaitø apibendrinimø moksliniai metodai. Vertinant ES Tarybos direktyvos 92/57/EEB reikalavimus bei jø ágyvendinimo poveiká statybos ámonëms ir valstybinëms institucijoms buvo atlikta anoniminë apklausa pagal parengtas apklausos anketas. Jos skirtos statybos ámonëms, valstybinëms bei visuomeninëms institucijoms ir savarankiðkiesiems darbuotojams. Anketose pateikti klausimai, siekiant iðsiaiðkinti Direktyvos nuostatø átakos, uþtikrinant darbuotojø saugà ir sveikatos apsaugà statybos ámonëse, vertinimus. Pagrindinis tikslas, atliekant apklausà, yra gauti tyrinëjamos visumos (generalinës aibës) charakteristikas. Tam pasirinktas atrankinis stebëjimas, kaip neiðtisinio stebëjimo dalinis variantas, t. y. kai tiriami tik analizuojamos dalies vienetai. Tyrimui taikytas vienas ið atsitiktinës atrankos metodø – blokinë atranka. Ði atranka leidþia su santykinai maþomis imtimis gauti prasmingus rezultatus. Tai aktualu esant didelëms generalinëms aibëms ir visiðkai tinka tyrimo tikslui. Atliekant ámoniø apklausà svarbu nustatyti atrankos imtá, kad apklausos rezultatai bûtø pakankamai patikimi. Reikiama imtis nustatyta remiantis ribinës paklaidos apskaièiavimu. Taikyta atranka be pasikartojimø ir reikiama apklausos imtis apskaièiuota pagal formulæ: n=

N t 2 σ 02 ∆ x N + t 2 σ 02

,

Nelaimingi atsitikimai darbe statybose Accidents at work in construction Metai 1997 1998 1999 2000 2001 2002

lengvi 429 486 401 302 291 343

Nelaimingi atsitikimai darbe sunkûs mirtini 34 13 36 13 27 19 26 14 34 23 35 23

ið viso 476 535 447 342 348 401

1997–2002 m. nelaimingø atsitikimø darbe skaièius (iðskyrus mirtinus ir sunkius atvejus) statybos ámonëse sumaþëjo. Taèiau 2003 m. statistika verèia nerimauti – nelaimingø atsitikimø darbe statybos ámonëse skaièius padidëjo.   3.2. Apklausos, atliktos ámonëse, rezultatai ir jø analizë Atlikus ámoniø apklausos rezultatø analizæ nustatyta: • Apie 68 % visø apklaustø statybos ámoniø Direktyvai ágyvendinti reikia finansinës, 59 % – konsultacinës (mokymo), 54 % – informacinës, 40 % – ástatyminës paramos (þr. 1 pav.).

70 60 50

(1)

40 30

n – atrankos imtis, N ámoniø skaièius, t patikimumo koeficientas, ∆ x ribinë atrankos paklaida, σ 2 variacinio poþymio dispersija. Þinant generalinæ aibæ (t. y. veikianèiø statybos ámoniø skaièiø Respublikoje) ir imant didþiausià atrankos paklaidà – 5 %, o variacinio poþymio maksimalià dispersijà – 0,5, kai patikimumo koeficientas t = 2,5, gauta ámoniø atrankos imtis (n) apklausai atlikti, pagal kurià gautos pakankamai tikslios visos tyrinëjamos visumos charakteristikos. Buvo atliktas gautø duomenø tyrimas ir analizë.

1 pav. Direktyvai ágyvendinti reikalingos paramos procentinis pasiskirstymas

3. Tyrimo rezultatai

 Fig 1. Percent distribution of support needed to implement the directive

20 10 0 Reikalinga parama Finansinë

3.1. Dabartinë situacija

Konsultacinë

Informacinë

Ástatyminë

• Apklausa parodë, kad dauguma statybos ámoniø susidurs su problemomis uþtikrinant darbuotojø saugà ir sveikatos apsaugà pagal ES reikalavimus.

Statistikos departamento duomenimis, 2003-01-01 buvo 2877 áregistruotos veikianèios statybos ámonës, ið jø 1126 individualios. Palyginti su 2001 m., áregistruotø

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Pagrindinës ið jø yra rizikos vertinimas, darbuotojø aprûpinimas asmeninëmis apsauginëmis priemonëmis, jø mokymas ir informavimas (þr. 2 pav.). • Apibendrinus apklausos rezultatus paaiðkëjo, kad 68 % statybos ámoniø ðios Direktyvos reikalavimø vykdymas sukels skirtingas problemas. Didelës problemos kils 9 %, vidutinës 27 % statybos ámoniø. 31 % statybos ámoniø problemø neturës.

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70 60 50 40 30 20

50

10

45

0 Teigiamas poveikis

40 35

Pagerës darbo sàlygos

30

Sumaþës profesiniø ligø skaièius

25

Sumaþës nelaimingø atsitikimø skaièius

20

Pagerës darbo rezultatai

15

Pagerës darbo kultûra

10

Pagerës darbø kokybë

5

3 pav. Direktyvos teigiamø poveikiø pasekmiø procentinë priklausomybë

0 Didelës problemos

Vidutinës problemos

Nedaug problemø

Nëra problemø

 Fig 3. Percent dependence of directive‘s positive consequences

Rizikos vertinimas

 

Darbuotojø aprûpinimas apsauginëmis priemonëmis Darbuotojø medicininë apþiûra

3.4. Direktyvos 92/57/EEB ágyvendinimo iðlaidos

Saugos instrukcijø rengimas

 Direktyvos ágyvendinimo iðlaidos nustatytos apklausos ir statistiniu-analiziniu metodais. Tyrimo rezultatai rodo, kad 86 % statybos ámoniø bendros iðlaidos Direktyvos reikalavimams ágyvendinti yra reikðmingos. Didelës jos yra 18 % ámoniø, vidutinës – 44 % ir 24 % – maþos. Bendras iðlaidø procentinis pasiskirstymas pateiktas 4 pav.

M okymas ir informavimas

2 pav. Svarbiausiø problemø, kylanèiø statybos ámonëms uþtikrinant darbuotojø saugà ir sveikatos apsaugà, procentinis pasiskirstymas pagal jø dydá Fig 2. Percent distribution by size of main problems, faced by construction companies while securing workers’ health and safety

 

3.3. Direktyvos ágyvendinimo nauda (teigiamas poveikis)  Visos ámonës Direktyvos ágyvendinimo pasekmes vertina teigiamai ir mano, kad tai pagerins darbuotojø saugà ir sveikatos apsaugà statybvietëse, turës teigiamos átakos darbo rezultatams ir darbo kultûrai. Teigiamø Direktyvos poveikio pasekmiø procentinë priklausomybë pateikta 3 pav. Ðio teisës akto ágyvendinimo pasekmiø tyrimas: • turi teigiamos átakos valstybës institucijø ir visuomenës bei verslo atstovø tarpusavio supratimui ir bendradarbiavimui sprendþiant strateginius klausimus; • suteikia visuomenei daugiau informacijos apie valstybës institucijø veiklà ir jos rezultatus; • padeda ámonëms prisitaikyti prie ES ir Lietuvos teisës aktø reikalavimø; • sudaro sàlygas saugos darbe gerinimui ir profesiniø ligø maþëjimui.

4 pav. Bendras iðlaidø procentinis pasiskirstymas Fig 4. Total percentage of expenser

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gumo nepagamintos produkcijos. Per metus bûtø sutaupoma apie 1 mln Lt. 3. Pagrindinës Direktyvos reikalavimø nevykdymo prieþastys yra nepatenkinamas rûpinimasis saugos ir sveikatos apsaugos darbe priemonëmis, rizikos veiksniø neávertinimas, didelës Direktyvos reikalavimø ágyvendinimo iðlaidos, sumaþëjusios statybos darbø apimtys, rekomendacijø ir metodikø, kaip taikyti Direktyvos nuostatas, stoka. 4. 68 % ámoniø Direktyvos reikalavimø vykdymas sukelia problemø. Daugiausia problemø kelia: § rizikos vertinimas – 91 %; § statybos organizavimo ir technologijos projektuose nurodyti saugos ir sveikatos apsaugos priemonës ir reikalavimai – 73 %; § saugiø darbovieèiø statybvietëse árengimas – 77 %. 5. Kad ágyvendintø direktyvos nuostatas, ámonëms reikalinga parama. Dauguma jø norëtø finansinës bei konsultacinës (mokymo) paramos. 6. Apie 27 % apklaustø ámoniø manoma, kad valstybës institucijos nepakankamai bendradarbiauja su ámonëmis, todël trûksta informacijos, kaip praktikoje ádiegti Direktyvos nuostatas. 36 % ámoniø manoma, kad kryptinga valstybës finansinë-ekonominë politika padëtø ágyvendinti Direktyvos nuostatas, ir siûlo statybos darbams sumaþinti pridëtinës vertës mokestá. 7. Pirmaisiais Direktyvos ágyvendinimo metais iðlaidos ðalies (ûkio) mastu yra apie 50 mln. Lt. 8. Ágyvendinant Direktyvà daugiausia problemø turi smulkios ámonës. Dauguma naujø ámoniø yra smulkios, darbdaviai neávertina saugaus darbo svarbos, átakos darbuotojø sveikatai, ekonominiams rodikliams ir produkcijos kokybei. Be to, jiems trûksta þiniø apie saugos ir sveikatos apsaugos reikalavimus teisës aktuose. 9. Smulkioms ámonëms trûksta lëðø, kad galëtø rûpintis darbo sàlygomis. Darbdaviai nepatenkinamai organizuoja darbuotojø saugos ir sveikatos apsaugos tarnybø, komitetø veiklà, neávertinami rizikos veiksniai. Norint LR statybos ámonëse ágyvendinti Direktyvos reikalavimus, reikia ágyvendinti ðias priemones: § sudaryti galimybes suinteresuotoms ámonëms susipaþinti su rengiamais saugà ir sveikatos apsaugà reglamentuojanèiø teisës aktø projektais, kad jos ið anksto galëtø tinkamai pasirengti teisës aktø nuostatø ágyvendinimui; § efektyvesnei Direktyvos ádiegimo kontrolei bûtina VDI biudþetà padidinti 2 %; § atsiþvelgdamos á savo finansines galimybes, rinkos bûklæ, konkurencijà, ámonës turi numatyti ekonomines priemones Direktyvai ágyvendinti. Tai galëtø bûti: • pelno sumaþinimas Direktyvos ádiegimo iðlaidø dydþiu; • iðlaidø priskyrimas savikainai ir statybos kainos didëjimas; • tarpinis variantas, t. y. pelno maþinimas ir savikainos didinimas;

Duomenø apie nelaimingus atsitikimus statybos ámonëse analizë rodo, kad pagrindinës jø prieþastys yra norminiø aktø reikalavimø nevykdymas. Direktyvos ágyvendinimo iðlaidos susideda ið vienkartiniø ir einamøjø iðlaidø. Visas Direktyvos ágyvendinimo iðlaidas priskyrus statybos savikainai, ji padidëja 1,21 % pirmaisiais Direktyvos nuostatø ágyvendinimo metais, o vëlesniais sumaþëja vienkartiniø iðlaidø dydþiu ir sudaro 1,01 %. Statybos darbø kaina ðiuo atveju iðauga atitinkamai 1,12 % ir 0,93 %. Visomis Direktyvos ágyvendinimo iðlaidomis sumaþinus statybos ámoniø pelnà, jis sumaþëja 14,76 % pirmaisiais Direktyvos nuostatø ágyvendinimo metais, o vëlesniais – 12,26 %. Direktyvos reikalavimø ágyvendinimo statybos ámonëse iðlaidos didþiausios átakos turi smulkiø statybos ámoniø prekiø savikainos didëjimui. Pirmaisiais Direktyvos nuostatø ágyvendinimo metais ji padidëja 2,12 %, vëlesniais – 2,01 %. Statybos investicijos pirmaisiais Direktyvos nuostatø ágyvendinimo metais padidëtø 8,5 %. Atsiþvelgdamos á savo finansines galimybes, rinkos bûklæ ir konkurencijà ámonës turi numatyti taikomas ekonomines priemones.   4. Pagrindinës tyrimo iðvados ir rekomendacijos  1. Parengiamiesiems darbams, kad pradëtø ágyvendinti Direktyvos reikalavimus, statybos ámonëms buvo skirta 18 mën. Taèiau daug statybos ámoniø ðiuos reikalavimus vykdo nepatenkinamai: § apie 15 % ámoniø vadovø nëra susipaþinæ su Direktyvos reikalavimais; § apie 65 % ámoniø neatliekamas rizikos vertinimas; § apie 30 % statybvieèiø dël sunkios statybos ámoniø ekonominës bûklës per lëtai pertvarkomos; § 87 % savarankiðkøjø darbuotojø nëra susipaþinæ su Direktyvos reikalavimais; § Valstybinë darbo inspekcija neinformuojama apie statybos darbø pradþià. Nepaskirti projekto ir saugos bei sveikatos apsaugos darbe priemoniø ágyvendinimo koordinatoriai, saugos ir sveikatos apsaugos priemoniø statybvietëse planai; § ne visose statybvietëse yra tinkamos buitinës sàlygos; § treèdalio statybos ámoniø darbuotojai neaprûpinti visomis reikalingomis asmeninëmis apsauginëmis priemonëmis. 2. Visos statybos ámonës, valstybinës ir visuomeninës institucijos bei ekspertai Direktyvos nuostatas vertina teigiamai: § ágyvendinus Direktyvos nuostatas statybvietëse, pagerës sauga ir sveikatos apsaugos darbe – statybos ámonës greièiau ir lengviau áeis á bendrà Europos rinkà; § ágyvendinus Direktyvos nuostatas statybos ámonëse, sumaþëtø nelaimingø atsitikimø darbe. Investicijos á saugos ir sveikatos apsaugos darbe gerinimà, laikantis Direktyvos nuostatø reikalavimø, sugráþtø, nes maþiau reikëtø iðmokø dël darbuotojø sveikatos paþeidimø ir maþiau bûtø dël darbuotojø nedarbin-

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§

§

§

§

§

• dalies sumos, sukauptos Socialinio draudimo fonde (tai yra nelaimingø atsitikimø darbe ir profesiniø ligø draudimo lëðos) skyrimas (proporcingai statybos daliai visame ûkyje) Direktyvai ágyvendinti, nes ðios lëðos taip pat skirtos nelaimingø atsitikimø ir profesiniø ligø prevencijai; Direktyvoje numatytiems socialiniams reikalavimams ágyvendinti statybos ámonës turi sudaryti priemoniø planus, numatyti jø ágyvendinimo terminus ir tam skirti reikiamø lëðø; statybos ámonëms daugiau dëmesio skirti bendradarbiavimui su mokslo institucijomis diegiant Direktyvos nuostatø taikymà. Tokio bendradarbiavimo formos galëtø bûti teminiai moksliniai-praktiniai seminarai, neakivaizdinës diskusijos, tiksliniai moksliniai tyrimai ir pan.; pagal mokymo, kvalifikacijos këlimo ir atestavimo nuostatus bei teorinio mokymo programas tikslinga ádiegti nuotoliná mokymà. Tai sumaþintø iðlaidas mokymo procesui organizuoti ir vykdyti; daugiau dëmesio skirti visuomenës informavimui apie darbuotojø saugos ir sveikatos apsaugos bûklæ. Televizija ir radijas tam turi skirti informacinæ valandëlæ; sukurti informacijos pateikimo sistemà apie darbuotojø saugà ir sveikatos apsaugà statybvietëse.  

reikalavimø“ ágyvendinimo pasekmiø http://osha.vdi.lt (in Lithuanian).

3.

Summary of investigation „Working conditions in European Union and in countries – candidates“ accomplished in year 2001 by European fond of living and working conditions development (Europos gyvenimo ir darbo sàlygø gerinimo fondo 2001 m. atlikto tyrimo „Darbo sàlygos Europos Sàjungoje ir ðalyse kandidatëse“ reziumë):

4.

Yearly report of Lithuanian national work safety inspectorate (Lietuvos valstybinës darbo inspekcijos metinë ataskaita 2001–2002): http://vdi.lt (in Lithuanian).

5.

Investigation of consequences of EU Directives 86/188/ EEC „About workers’ protection against risks, concerning noise influence at work“ implementation (ES Direktyvos 86/188/EEB „Dël darbuotojø apsaugos nuo rizikos, susijusios su triukðmo poveikiu darbe, reikalavimø“ ágyvendinimo pasekmiø tyrimas): http://osha.vdi.lt (in Lithuanian).

Investigation of consequences of EU Directives 98/24/EC „About workers health and safety protection at work, concerning chemical factors“ implementation (ES Direktyvos 98/24/EB „Dël darbuotojø saugos ir sveikatos apsaugos nuo pavojø darbe, susijusiø su cheminiais veiksniais“, ágyvendinimo pasekmiø tyrimas): http://osha.vdi.lt (in Lithuanian).

8.

Investigation of consequences of EU Directives 93/103/ EC establishing minimal health and safety requirements in fishing boats, implementation (EB Direktyvos 93/103/EB, nustatanèios minimalius saugos ir sveikatos reikalavimus þvejybos laivuose, ágyvendinimo poveikio ávertinimas): http://osha.vdi.lt (in Lithuanian).

9.

Investigation of consequences of EU Directives 92/57/EEC „About minimal health and safety requirements in temporary and transportable construction sites“ implementation (ES Direktyvos 92/57/EEB „Dël minimaliø saugos ir sveikatos reikalavimø laikinosiose ir kilnojamosiose statybvietëse“ ágyvendinimo pasekmiø tyrimas): http://osha.vdi.lt (in Lithuanian).

12. Regulating effects of implementation of workers’ health and safety law certificates „Rules of using health and safety signs at workplace“ partial evaluation (Darbuotojø saugos ir sveikatos teisës akto „Saugos ir sveikatos apsaugos þenklø naudojimo darbovietëse nuostatai“ reguliuojanèio poveikio dalinis ávertinimas): http://osha.vdi.lt (in Lithuanian).

http://osha.vdi.lt (in Lithuanian).

6.

7.

11. Regulating effects of implementation of law certificates „Rules of workers protection against biological materials“ partial evaluation (Teisës akto „Darbuotojø apsaugos nuo biologiniø medþiagø nuostatai“ ágyvendinimo reguliuojanèio poveikio dalinis ávertinimas): http://osha.vdi.lt (in Lithuanian).

 1. Facts 18. European Agency for Safety and Health at Work 2001: http://agency.osha.eu.int Didier Duper Accidents at work in the EU 1998–1999 EUROSTAT Statistics in Focus: http://agency.osha.eu.int

tyrimas):

10. Regulating effects of implementation of standard law certificates Lithuanian hygiene norm HN 32–1998 „Working with video terminals. Health and safety requirements“ partial evaluation (Norminio teisës akto Lietuvos higienos norma HN 32–1998 „Darbas su video terminalais. Saugos ir sveikatos reikalavimai“ ágyvendinimo dalinis reguliuojanèio poveikio ávertinimas): http://osha.vdi.lt (in Lithuanian).

Literatûra

2.

55

13. Regulating effects of implementation of law certificates „Safety rules for workers working in potentially explosive environment“ partial evaluation (Teisës akto „Darbuotojø, dirbanèiø potencialiai sprogioje aplinkoje, saugos nuostatai“ reguliuojanèio poveikio dalinis ávertinimas): http://osha.vdi.lt (in Lithuanian). 14. Investigation of consequences of EU Directives 89/655/ EEC „About health and safety minimal requirements for working equipment“ and replacing directives 95/63/EEC implementation (ES Direktyvos 89/655/EEB „Dël minimaliø darbo árengimams taikomø darbuotojø saugos ir sveikatos reikalavimø“ ir jà pakeièianèios Direktyvos 95/ 63/EEB ágyvendinimo pasekmiø tyrimas): http://osha.vdi.lt (in Lithuanian).

Investigation of consequences of EU Directives 89/654/ EEC „About minimal health and safety requirements for workplace“ implementation (ES Direktyvos 89/654/EEB „Dël minimaliø darbovietei taikomø saugos ir sveikatos

55

57 ISSN 1392–3730

JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT http:/www.vtu.lt/english/editions

2004, Vol X, Suppl 1, 57–63

TRAUMØ PREVENCIJOS IÐLAIDØ STATYBOJE OPTIMIZAVIMAS Sigutë Vakrinienë1, Petras Èyras2, Ritoldas Ðukys3 1

Matematinës statistikos katedra, Vilniaus Gedimino technikos universitetas, Saulëtekio al. 11, 10223 Vilnius-40, Lietuva. El. paðtas: [email protected] 2, 3 Darbo ir gaisrinës saugos katedra, Vilniaus Gedimino technikos universitetas, Saulëtekio al. 11, 10223 Vilnius-40, Lietuva. El. paðtas: [email protected], [email protected] Áteikta 2004 04 26; priimta 2004 05 26 Santrauka. Duomenø apie nelaimingus atsitikimus statybos ámonëse analizë rodo, kad pagrindinës jø prieþastys yra norminiø aktø reikalavimø nevykdymas, netinkamai organizuotas darbas, tai, kad nesinaudojama saugos priemonëmis, netinkamai organizuota darbo vieta, nepakankamai rûpinamasi darbuotojø apmokymu. Darbdaviui svarbu þinoti, kaip optimaliai paskirstyti lëðas, skirtas nelaimingø atsitikimø prevencijai. Tai leistø (vidutiniðkai arba su tam tikra tikimybe) sumaþinti nelaimingø atsitikimø skaièiø ir kartu sumaþinti socialinio draudimo iðmokas. Nagrinëjamas stochastinio programavimo uþdavinys, kuris modeliuoja lëðø, skirtø nelaimingø atsitikimø darbe statyboje prevencijai, optimalaus paskirstymo problemà. Kad su norimu patikimumu gautume optimalià lëðø, skirtø nelaimingø atsitikimø darbe statyboje prevencijai, paskirstymo strategijà, reikia iðspræsti separabelinio programavimo uþdaviná, kurio leistinø planø sritis nëra iðkilioji. Nustatyta ðio uþdavinio Lagranþo daugikliø prasmë nagrinëjamai problemai bei globaliojo ekstremumo iðskyrimo taisyklë. Sprendþiant pavyzdþius gautos gana tikslios ir patikimos funkcinës priklausomybës tarp uþdavinio sprendinio ir jo parametrø. Tai leidþia optimizuoti lëðø, skirtø nelaimingø atsitikimø darbe statyboje, panaudojimà ir parodo tikëtino iðvengtø traumø skaièiaus priklausomybæ nuo pasikliautinumo lygmens ir lëðø, skirtø nelaimingø atsitikimø darbe statyboje prevencijai, variacijos. Raktaþodþiai: nelaimingi atsitikimai, prevencija, optimalus lëðø paskirstymas, stochastinis programavimas, Lagranþo funkcija, Kuno-Takerio sàlygos, pasikliautinumo lygmuo, lëðø variacija.

Straipsnyje nagrinëjamas stochastinio programavimo uþdavinys, kuris modeliuoja lëðø, skirtø nelaimingø atsitikimø statyboje prevencijai, optimalaus paskirstymo problemà. Kad su norimu patikimumu gautume optimalià lëðø, skirtø nelaimingø atsitikimø darbe statyboje prevencijai, paskirstymo strategijà, reikia iðspræsti separabelinio programavimo uþdaviná, kurio leistinø planø sritis nëra iðkilioji. Straipsnyje nustatyta ðio uþdavinio Lagranþo daugikliø prasmë nagrinëjamai problemai bei globaliojo ekstremumo iðskyrimo taisyklë. Sprendþiant pavyzdþius gautos gana tikslios ir patikimos funkcinës priklausomybës tarp uþdavinio sprendinio ir jo parametrø. Tai leidþia optimizuoti lëðø, skirtø nelaimingø atsitikimø darbe statyboje, panaudojimà ir parodo tikëtino iðvengtø traumø skaièiaus priklausomybæ nuo pasikliautinumo lygmens ir lëðø, skirtø nelaimingø atsitikimø darbe statyboje prevencijai, variacijos. Skaièius traumø, kurios ávyks, jei vienos ar kitos traumø prevencijos priemonës nevykdysime, yra atsitiktinis dydis, kurio pasiskirstymo dësnis ir parametrai gali bûti ávertinti, remiantis duomenø apie jau ávykusias traumas ir jø prieþastis statistine analize. Ðiame darbe daroma prielaida, kad ðie dydþiai yra pasiskirstæ pagal Puasono dësná.

1. Ávadas Duomenø apie nelaimingus atsitikimus statybos ámonëse analizë rodo, kad pagrindinës jø prieþastys yra norminiø aktø reikalavimø nevykdymas, netinkamai organizuotas darbas, tai, kad nesinaudojama saugos priemonëmis, netinkamai organizuota darbo vieta, nepakankamai rûpinamasi mokymu. Darbdaviui svarbu þinoti, kaip optimaliai paskirstyti lëðas, skirtas nelaimingø atsitikimø prevencijai. Tai leistø (vidutiniðkai arba su tam tikra tikimybe) sumaþinti nelaimingø atsitikimø skaièiø ir kartu sumaþinti socialinio draudimo iðmokas [1–8]. Praktiðkai daþniausiai neámanoma visiðkai ágyvendinti visø traumø prevencijos priemoniø, siekiant visiðkai paðalinti traumatizmo prieþastis. Prevencijos priemoniø kainos daþnai labai didelës, o visø nelaimingo atsitikimo aplinkybiø numatyti ið anksto negalime, nes jo prieþastis kartais bûna pats darbuotojas. Darbdaviui svarbu þinoti, kurios traumø prevencijos priemonës yra efektyviausios, kaip optimaliai paskirstyti traumø prevencijai skirtas lëðas. Þinojimas, kiek traumø tokiu bûdu bus iðvengta (vidutiniðkai arba su tam tikra tikimybe) leistø palyginti iðlaidas traumø prevencijai su nelaimingø atsitikimø atvejais iðmokamø kompensacijø suma [9–12].

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Straipsnyje [13] optimalaus lëðø, skirtø darbø saugos priemonëms, paskirstymo problema sprendþiama taikant stochastiná programavimà. Optimaliajam kriterijui parinkti siûlomas matricinis loðimas su atsitiktiniais elementais, kurie rodo skaièiø traumø, ávykstanèiø dël vienokiø ar kitokiø saugos priemoniø nebuvimo ir darbuotojø klaidø. Lëðos, reikalingos kiekvienai traumø prieþasèiai visiðkai paðalinti, bendruoju atveju taip pat yra atsitiktiniai dydþiai. Todël modifikuotas tiesinio programavimo uþdavinys minëto matricinio loðimo optimaliai strategijai gauti, nagrinëjamas straipsnyje [14], tampa stochastinio programavimo uþdaviniu, kuriam surandamas ekvivalentinis separabelinio programavimo uþdavinys. Straipsnyje [15] nagrinëjamas stochastinio programavimo uþdavinio atvejis, kai traumø prevencijos priemoniø kainos determinuotos. Ðio darbo tikslas yra bendresnio stochastinio programavimo uþdavinio sprendinio savybiø tyrimas. Kadangi tenka spræsti separabelinio programavimo uþdaviná, kuris nëra iðkilojo programavimo uþdavinys, atsiranda globalinio ekstremumo atpaþinimo problema, nes artutiniais metodais gauti ekstremumai gali bûti lokalieji. Naudojant Lagranþo funkcijà ir Kuno-Takerio sàlygas darbe rastos bûtinosios ir pakankamosios sàlygos globaliajam ekstremumui nustatyti. Nagrinëjamo uþdavinio Lagranþo daugikliai turi labai konkreèià prasmæ – vieni ið jø yra piniginio vieneto arba konkreèios prevencinës priemonës „naudingumo“ áverèiai (iðvengtø traumø skaièiaus prasme), kiti – atsitiktiniø uþdavinio komponenèiø dispersijø „nenaudingumo“ áverèiai (ta paèia prasme). Gauti sàryðiai tarp optimalios lëðø traumø prevencijai skirtos skirstymo strategijos ir Lagranþo daugikliø, tikëtinai iðvengto traumø skaièiaus ir Lagranþo daugikliø bei jø priklausomybë nuo uþdavinio parametrø. Minëtieji sàryðiai sprendþiant pavyzdþius leido gauti gana tikslias ir pakankamai patikimas funkcines priklausomybes tarp optimaliø uþdavinio kintamøjø reikðmiø ir uþdavinio parametrø. Detaliau iðtirta optimalios traumø prevencijos strategijos ir tikëtino iðvengtø traumø skaièiaus (jei ðià strategijà taikysime) priklausomybë nuo pasikliautinumo lygmens ir traumø prevencijos kainø variacijos.

Tegul d ij yra j-tojo darbo drausmës paþeidimo nulemto vidutinio traumø, kuriø galima iðvengti visiðkai paðalinus i-tàjà prieþastá, priklausanèià nuo darbdavio, skaièiaus dalis. Pavyzdþiui, pakankama prieþiûra gali tam tikru dydþiu sumaþinti skaièiø traumø, susijusiø su technologinio proceso paþeidimais, arba saugos priemonëmis nesinaudojama daþnai dël to, kad jø trûksta. Dydþiai a ij = b i + d ij , i = 1,2, …, m, j = 1,2,…, n, yra matricinio loðimo matricos a ij

a11 a 21

a 12 a 22

... ... a m1 a m 2

elementai:

... a1n ... a 2n . ... ... ... a mn

(1)

Matricinio loðimo a ij pirmojo „loðëjo“ (t. y. darbdavio) optimali grynoji strategija (t. y. vienos konkreèios prevencijos priemonës pasirinkimas) arba miðri (t. y. dalinis keliø konkreèiø prevencijos priemoniø vykdymas) strategija garantuoja, kad nepriklausomai nuo darbuotojø padarytø paþeidimø bus iðvengta vidutiniðkai V0 traumø (per laiko vienetà). Èia V0 yra matricinio loðimo vertë. Tvirtinimas, kad bus iðvengta vidutiniðkai V0 traumø, remiasi prielaida, kad, sumaþinus dalá traumas nulëmusiø prieþasèiø, proporcingai sumaþës ðiø prieþasèiø sukeliamø traumø skaièius. Jeigu matricinis loðimas a ij turi balno taðkà, t. y. turi stulpelá j = k, atitinkantá atvejá, kai darbuotojai paþeidimø nedaro ( d ik = 0), paþymëkime a ik = a i = b i . Tada optimali grynoji strategija rodo efektyviausià traumø prevencijos priemonæ, taèiau ði priemonë gali bûti per daug brangi. Todël turime þinoti, kokia yra kiekvienos traumatizmo prieþasties paðalinimo kaina. Tarkime, c i yra vidutinis kiekis lëðø, reikalingø i-tajai traumø prieþasèiai visiðkai paðalinti (i = 1,2,…, m). Kai turima C lëðø, optimalø jø paskirstymà gautume iðsprendæ tiesinio programavimo uþdaviná: max W

2. Matricinis loðimas

m

∑ a i xi ≥ W,

Ávairiø traumatizmo veiksniø paðalinimà vadinsime 1-àja, 2-àja, ....., i-tàja, ....., m-tàja traumø prevencijos priemonëmis. Tarkime, kad b i yra vidutinis (per laiko vienetà) dël i-tosios prieþasties, priklausanèios nuo darbdaviø, ávykusiø traumø skaièius, kuriuo, visiðkai ágyvendinus i-tàjà prevencijos priemonæ, galima sumaþinti bendrà traumø skaièiø. Asmenines, nuo darbuotojø priklausanèias, traumø prieþastis, tokias kaip technologinio proceso reikalavimø nesilaikymas, nesinaudojimas saugos priemonëmis, neblaivumas ir kt., vadinsime 1-uoju, 2-uoju, ...., j-uoju, ..., n-uoju darbo drausmës paþeidimais.

i =1 m

∑ c i xi ≤ C,

i =1

(2)

0 ≤ xi ≤ 1, i = 1,2, ..., m. Jeigu ðio uþdavinio optimalus planas yra ( x10 , x20 ,…, 0 ) ir W 0 – optimali tikslo funkcijos reikðmë, kiekviexm nai prevencijos priemonei skirdami xi0 100 % visø jai visiðkai ávykdyti reikalingø lëðø nepriklausomai nuo darbuotojø elgesio galësime iðvengti vidutiniðkai ne maþiau kaip W 0 traumø.

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Þodis „vidutiniðkai“ reiðkia, kad iðvengtø traumø skaièius gali bûti ir maþesnis uþ skaièiø W 0 (didesnis

m

y 2 = ∑ a i xi2 ,

(4)

i =1

taip pat). Net jeigu dydþiai a ij (per laiko vienetà, pavyzdþiui, per metus, ávykstanèiø traumø, susijusiø su i-tàja prieþastimi ið darbdavio pusës, ir j-tuoju darbuotojo padarytu paþeidimu, vidutinis skaièius) gaunami remiantis daugelio metø statistiniais duomenimis apie traumas ir jø prieþastis, jø negalima laikyti visiðkai determinuotais. Todël toliau nagrinëjamas rekomenduojamø matematiniø metodø ir gautø rezultatø patikimumas.

m

2

z 2 = ∑ σi xi2 , i =1

y ≥ 0, z ≥ 0, 0 ≤ xi ≤ 1, i = 1, 2, ..., m. Jeigu vidutiniai kvadratiniai nuokrypiai σi , i = 1, 2, ..., m, nëra þinomi, ðá uþdaviná galima spræsti pasirenkant ávairias atsitiktiniø dydþiø ci variacijos σi reikðmes. koeficientø vi = ai Optimali tikslo funkcijos reikðmë W 1 yra skaièius 2 traumø, kuriø su tikimybe, ne maþesne kaip p , iðvengsime, jeigu turimas lëðas C traumø prevencijai paskirstysime pagal separabelinio uþdavinio sprendiná:

3. Stochastinio programavimo uþdavinys Tarkime, kad prevencijos priemonëms visiðkai ávykdyti reikalingi lëðø kiekiai ci , i = 1, 2, ..., m yra nepriklausomieji normuotieji atsitiktiniai dydþiai, kuriø vidurkiai c i , i = 1, 2, ..., m, ir vidutiniai kvadratiniai nuokrypiai σi , i = 1, 2, ..., m. 2 Kad su tam tikra tikimybe p galëtume teigti, jog, optimaliai pasirinkus prevencijos priemoniø finansavimo strategijà, iðvengtø traumø skaièius bus ne maþesnis uþ konkretø dydá ir kad lëðø sumos C pakaks ðiam prevencijos planui ávykdyti, reikia spræsti stochastinio programavimo uþdaviná:

(

)

X = x11, x12 , ..., x1m .

(5)

Sprendinio komponentë x1i rodo, koks procentas visø jai reikalingø lëðø turi bûti skiriamas i-tajai prevencijos priemonei. Ðiame darbe, tirdami optimalios traumø prevencijos priemoniø finansavimo strategijos priklausomybæ nuo patikimumo p ir prevencijos priemoniø kainø variacijos, laikysime, kad visi variacijos koeficientai vienodi: v1 = v2 = … = vm = v. Tuomet σi = vci .

max W

m  P ∑ ai xi ≥ W  ≥ p,  i =1 

59

(3)

m  P ∑ ci xi ≤ C  ≥ p,  i =1 

4. Lagranþo daugikliai Separabelinio programavimo uþdavinio leistinø planø sritis nëra iðkilioji, todël artutiniais metodais gautas sprendinys gali bûti lokaliojo maksimumo taðkas. Ði problema gali bûti iðspræsta naudojant Lagranþo funkcijà:

0 ≤ xi ≤ 1, i = 1, 2, ..., m. Èia ai yra atsitiktinis dydis – traumø, susijusiø su i-tàja prieþastimi ið darbdavio pusës, skaièius per laiko vienetà. Traumø skaièiø per laiko vienetà galima laikyti Puasono atsitiktiniu dydþiu, nes progø ávykti traumoms yra daug, taèiau jos (ypaè sunkios ir mirtinos) ávyksta gana retai. Taigi darome prielaidà, kad atsitiktiniai dydþiai ai , i = 1, 2, ..., m, yra nepriklausomi ir pasiskirstæ pagal Puasono dësná su vidurkiais a i . Straipsnyje [14] árodoma, jog tuomet stochastinio programavimo uþdaviniui bus ekvivalentiðkas ðis separabelinio programavimo uþdavinys, kuriame yra nauji neneigiami kintamieji y ir z:

m  L(W , x1, x2 , ..., x m , y, z ) = − W − λ1 ∑ a i xi − u p y − W  −  i =1  m m     λ 2  − ∑ c i xi − u p z + C  − µ1 y 2 − ∑ a i xi2  −  i =1    i =1 m   m µ 2  z 2 − v 2 ∑ ci2 xi2  − ∑ (1 − xi )αi ,   i =1 i −1

uþraðytà minimizavimo uþdaviniui:

max W ,

min(−W )

m

∑ a i xi – u p y ≥ W ,

m

∑ a i xi − u p y ≥ W ,

i =1

i =1

m

∑ c i xi + uq z ≤ C ,

m

− ∑ c i xi − u p z − C ≥ 0,

i =1

i =1

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60

W = λ 2 C + ∑ αi .

m

y 2 − ∑ a i xi2 = 0, i =1

(7)

xi =1

Gautos iðraiðkos bei sàryðiai tarp Lagranþo daugikliø

m

z 2 − v 2 ∑ ci2 xi2 = 0,

µ1 = −

i =1

1 − xi ≥ 0, i = 1, 2, ..., m,

xi ≥ 0, i = 1, 2, ..., m.

, λ2 = −

µ z 2 zµ 2 , λ2 = 2 µ1 y up

(9)

Taikant programinës árangos SAS/OR netiesinio optimizavimo procedûrà NLP buvo iðspræstas didelis skaièius pavyzdþiø, kuriuose parametrai p, v, ai, ci ir C buvo keièiami. Remiantis ðiø pavyzdþiø sprendiniais maþiausiøjø kvadratø metodu buvo gauti funkciniai sàryðiai:

§ µ1 rodo, kiek, optimaliai paskirsèius lëðas traumø prevencijai, sumaþës iðvengtø traumø skaièius, jei

m m m m   ∑ ai ci ; C p; p ∑ ai ; ∑ ci p; v 2 ∑ ci2 ;   i =1  i =1 i =1 i =1 W = F  m  ∑a C  i    i =1 

m

atsitiktinio dydþio ∑ ai xi dispersija padidës vienetu; i =1

§ µ 2 rodo, kiek, optimaliai paskirsèius lëðas traumø prevencijai, sumaþës iðvengtø traumø skaièius, jei

m m m m   ∑ ai ci ; C p ; p ∑ ai ; ∑ ci p; v 2 ∑ ci2;   i =1  i =1 i =1 i =1 xi = G  m  ∑ a C; a c , i = 1, 2 , ...,m  i i i    i =1 

m

atsitiktinio dydþio ∑ ci xi dispersija padidës vienetu; i =1

§ α I rodo, kokio traumø skaièiaus iðvengsime, jei i-toji traumø prevencijos priemonë bus pakankamai finansuojama, t. y. kai optimalus xi = 1. Naudodami Kuno-Takerio sàlygas ðiam netiesinio programavimo uþdaviniui su neneigiamais kintamaisiais gauname iðvadas: 1) sprendinyje Lagranþo daugikliai λ 1 ir λ 2 yra teigiami, o daugikliai µ1 ir µ 2 – neigiami; 2) globalusis ekstremumas gaunamas tada ir tik tada,

(10)

(11)

kurie leidþia kintamuosius W ir xi rasti su vidutinëmis paklaidomis 1,8 ir 0,17 bei determinacijos koeficientais – atitinkamai 0,83 ir 0,70. Konkreèiam uþdaviniui, kai ai ir ci fiksuoti, analogiðki funkciniai sàryðiai yra tikslesni (vidutinës paklaidos 1,09 ir 0,10) ir patikimesni (determinacijos koeficientai 0,98 ir 0,90).

kai λ1 = 1 (didþiausia galimoji reikðmë), o µ1 ir µ 2 reikðmës minimalios;

6. Rezultatø analizë Lentelëje ir grafikuose pateikti duomenys iliustruoja optimalios traumø prevencijos strategijos bei traumø skaièiaus, kurio iðvengsime (su tikimybe p) jà naudodami, priklausomybæ nuo prevencijos kainø variacijos v ir pasikliautinumo lygmens p. Jiems gauti buvo naudojami minëti funkciniai sàryðiai konkreèiam uþdaviniui tuo atveju, kai turime 50 % visø traumø prevencijai reikiamø lëðø. Analizuodami ðiuos grafikus galime padaryti keletà iðvadø. Lentelës, kurioje pateikta traumø prevencijos strategijos priklausomybë nuo pasikliautinumo lygmens p, duomenys rodo, kad, norëdami gauti didesná patikimumà p, traumø prevencijai turëtume tolygiai paskirstyti lëðas. Esant maþai prevencijos priemoniø kainos variacijai (1 %), ði tendencija iðryðkëja pradedant pasikliautinumo lygmeniu p = 0,7, o kai variacija v didelë – jau nuo p = 0,6. Kitø duomenø analizë pateikiama grafikuose.

3) optimalusis xi iðreiðkiamas formule: 2(µ1ai + µ 2 v 2ci2 )

2y

5. Stochastinio uþdavinio sprendinio priklausomybë nuo uþdavinio parametrø

Kiekvienas Lagranþo daugiklis turi konkreèià prasmæ: § λ1 rodo, kiek, optimaliai paskirsèius lëðas traumø prevencijai, padidës iðvengtø traumø skaièius, jei pirmojo apribojimo laisvasis narys padidës vienetu; § λ 2 rodo, kiek, optimaliai paskirsèius lëðas traumø prevencijai, padidës iðvengtø traumø skaièius, jei skirstoma suma C padidës vienu piniginiu vienetu;

λ 2 ci − ai

up

rodo, kokio pobûdþio priklausomybë galëtø bûti tarp iðvengtø traumø skaièiaus W ir variacijos v bei kvantilio u p (arba pasikliautinumo lygmens p).

y ≥ 0, z ≥ 0,

xi =

(8)

, kai 0 < xi < 1 ,

i = 1, 2, ..., m;

ai ≤ λ2 ; ci 5) kai optimalusis xi = 1, tai

4) optimalusis xi = 0, kai

αi = ai – λ 2 ci + 2( µ1 ai + µ 2 v 2 ci2 ; 6) optimali tikslo funkcijos reikðmë (didþiausias su pasikliautinumo lygmeniu p tikëtinas skaièius traumø, kuriø bus galima iðvengti) iðreiðkiama formule:

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Traumø prevencijos strategijos priklausomybë nuo pasikliautinumo lygmens p

Pasikliautinumo lygmuo p

Subjection of injury prevention strategy to confidence level p Kai prevencijos priemoniø kainø variacija V=0,01

X1

0,50 0,53 0,55 0,58 0,60 0,63 0,65 0,68 0,70 0,73 0,75 0,78 0,80 0,83 0,85 0,88 0,90 0,93 0,95 0,98

X2

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0,957 0,872 0,785

Kai prevencijos priemoniø kainø variacija V=0,4

X3

X4

X5

X1

X2

X3

X4

X5

0,468 0,454 0,442 0,431 0,422 0,413 0,407 0,401 0,396 0,391 0,388 0,385 0,383 0,381 0,380 0,379 0,379 0,379 0,379 0,379

1 1 1 1 1 1 1 1 1 1 1 1 1 0,966 0,922 0,876 0,828 0,778 0,726 0,672

0 0 0 0 0 0 0 0,005 0,033 0,060 0,086 0,111 0,136 0,159 0,183 0,205 0,227 0,249 0,270 0,291

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0,987 0,906 0,822 0,737 0,650

0 0 0 0 0 0 0 0 0 0,005 0,037 0,071 0,107 0,143 0,181 0,219 0,259 0,299 0,340 0,382

0,325 0,311 0,298 0,288 0,278 0,270 0,263 0,257 0,252 0,248 0,245 0,242 0,240 0,238 0,237 0,236 0,236 0,236 0,236 0,237

1 1 1 1 1 1 1 1 1 0,974 0,942 0,907 0,869 0,828 0,785 0,739 0,691 0,641 0,589 0,535

0 0 0 0 0 0,007 0,037 0,066 0,094 0,121 0,147 0,172 0,197 0,220 0,243 0,266 0,288 0,310 0,331 0,352

0 0 0 0 0 0 0 0 0 0 0 0 0 0,012 0,049 0,082 0,128 0,168 0,209 0,2508

xi

Xi

1,2

1,2

1

1

0,8

0,8

0,6

0,6

0,4

0,4

0,2

0,2

0

0,1 x1

0,2 x2

0,3 x3

0,4 x4

V

0

V

0

0

0,5

0,1 x1

x5

0,2 x2

0,3 x3

0,4 x4

0,5 x5

2 pav. Traumø prevencijos strategijos priklausomybë nuo prevencijos priemoniø kainos variacijos, kai p = 0,9

1 pav. Traumø prevencijos strategijos priklausomybë nuo prevencijos priemoniø kainos variacijos, kai p = 0,8

Fig 2. Subjection of injury prevention strategy to variation of prevention measures costs, if p = 0,9

Fig 1. Subjection of injury prevention strategy to variation of prevention measures costs, if p = 0,8

4 ir 5 pav. grafikai rodo, kad tikëtinas iðvengtø traumø skaièius maþëja tiek didëjant pasikliautinumo lygmeniui p, tiek ir didëjant prevencijos priemoniø kainos variacijai v, o juo labiau didëjant abiem ðiems parametrams. Priklausomybë nuo patikimumo p stipresnë; su tikimybe p = 0,99 galime tikëtis perpus maþesnio iðvengtø traumø skaièiaus negu su tikimybe p = 0,7 (tuo atveju,

1–3 pav. grafikai rodo, kad, didëjant prevencijos priemoniø kainø variacijai, optimalus lëðø traumø prevencijai paskirstymas tampa tolygesnis, ypaè kai norime gauti didelá pasikliautinumo lygmená p. Visais atvejais reikðminga tik tokia variacija, kuri yra ne maþesnë kaip 10 %.

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62

xi

W

0,8

16

0,7

14

0,6

12

0,5

10

0,4

8

0,3

6

0,2

4

0,1

2

V

0 0

0,1

x1

0,2

x2

0,3

0,4

x3

x4

0

0,5

0

x5

0,2

0,4

V=0,001

3 pav. Traumø prevencijos strategijos priklausomybë nuo prevencijos priemoniø kainos variacijos, kai p = 0,999

0,6

0,8 V=0,2

1

1,2

p

V=0,4

5 pav. Iðvengtø traumø skaièiaus priklausomybë nuo pasikliautinumo lygmens p, kai traumø prevencijos kainø variacija V skirtinga

Fig 3. Subjection of injury prevention strategy to variation of prevention measures costs, if p = 0,999

Fig 5. Subjection of number of avoided injury to confidence level p if variation of injury prevention costs V differs

W

16

Skaièiams ai padidëjus 10 ar net 100 kartø, tikimybës p ir variacijos v átaka optimaliai traumø prevencijos strategijai iðlieka. Taèiau tam, kad prioritetai pasikeistø, turi bûti vis didesnës p ir v reikðmës. Todël siûloma metodika ir optimalumo principas gerai tinka ne tik sunkiø ir mirtinø traumø (kuriø bûna nedaug), bet ir nesunkiø traumø (kuriø bûna daug) prevencijai planuoti.

14 12 10 8 6 4

Literatûra

2 V

0 0

0,1

p=0,6

0,2

0,3

p=0,8

0,4

0,5

1.

Èyras, P.; Ðukys, R.; Jakutis, A.; Nainys, V. Investigation of European Union directives, about workers’ health and safety protection at work, influence on Lithuanian economy. Health Sciences (Sveikatos mokslai), No 7 (30), 2002, p. 6– 10 (in Lithuanian).

2.

Ðukys, R.; Èyras, P.; Jakutis, A.; Paèësa, A. R. Investigating consequences of directives 92/57/EEC „Implementation of minimum safety and health requirements at temporary or mobile constructions sites“, implementation (Direktyvos 92/57/EEB „Dël minimaliø saugos ir sveikatos reikalavimø laikinosiose ir kilnojamosiose statybos aikðtelëse ágyvendinimo pasekmiø tyrimas“). In: National health council’s yearly report (Nacionalinës sveikatos tarybos metinis praneðimas), 2003, p. 29–32 (in Lithuanian).

3.

Èyras, P.; Juozulynas, A.; Nainys, V.; Ðukys, R. Strategy of occupational health and safety in years 2004–2006. Health Sciences (Sveikatos mokslai), No 8 (31), p. 18–23 (in Lithuanian).

4.

Èyras, P.; Jakutis, A.; Rutkauskas, A. V.; Ðukys, R. Implementing directives about health and safety at work in Lithuania: analysing expenses. Technological and economic development of economy (Ûkio technologinis ir ekonominis vystymas), 2003, Vol 9, No 2, p. 60–66 (in Lithuanian).

0,6

p=0,99

4 pav. Iðvengtø traumø skaièiaus priklausomybë nuo traumø prevencijos kainø variacijos, kai pasikliautinumo lygmuo p skirtingas Fig 4. Subjection of number of avoided injury to variation of injury prevention costs if the confidence level p differs

kai variacija didelë, t. y. v = 0,4). Variacijos koeficientas reikðmingas tiktai bûdamas didesnis kaip 20 %. Straipsnyje [15], kuriame analogiðkos problemos sprendþiamos esant determinuotoms traumø prevencijos kainoms, pastebëtas faktas, jog tuo atveju, kai skaièiai ai yra dideli, optimali traumø prevencijos strategija keièiasi tik esant labai dideliam patikimumui p (arti vieneto). Ðis teiginys nëra teisingas atsitiktiniø kainø atveju.

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6.

7.

8.

63

pagal Europos Bendrijø profesinës saugos ir sveikatos strategijà 2002–2006 m), 2003. 40 p. (in Lithuanian).

Èyras, P.; Rutkauskas, A.; Ðukys, R.; Jakutis, A.; Nainys, V. Investigating consequences of European Union directives „Concerning the minimum safety and health requirements for the workplace 89/654/EEC implementation (ES Tarybos direktyvos 89/654/EEB „Dël minimaliø darbovietei taikomø saugos ir sveikatos reikalavimø“ ágyvendinimo pasekmiø tyrimas), 2000. 44 p. (in Lithuanian).

9.

Charalambos, D. Stochastic nonlinear minimax dynamic games with noisy measurements. In: IEEE Transactions on Automatic Control, Vol 48, No 2, 2003, p. 261–267.

10. Qinru Qiu, Qing, Wu, Massoud Pedram. Stochastic modelling of a power-managed system - construction and optimization. In: IEEE Transactions on computer-aided design of integrated circuits and systems, Vol 20, No 10, 2003, p. 1200–1217.

Èyras, P.; Ðukys, R.; Jakutis, A.; Paèësa, A. R. Investigating consequences of EU Council Directives „Implementation of minimum safety and health requirements at temporary or mobile constructions sites“ (eight separate directive, as described and Directives 89/391/EEC 16 clause, 1 part) implementation (1992 m. birþelio 24 d. ES Tarybos Direktyvos 92/57/EEB „Dël minimaliø saugos ir sveikatos reikalavimø laikinosiose ir kilnojamosiose statybvietëse“ (aðtuntoji atskiroji direktyva, kaip apibrëþta Direktyvos 89/391/EEB 16 straipsnio 1 dalyje) ágyvendinimo pasekmiø tyrimas), 2001. 46 p. (in Lithuanian).

11. Dempster, M. A. H.; Pedron, N. H.; Medova, E. A., Scott, J. E.; Sembos, A. Planning logistics operations in the oil industry. Operational Research Society, Vol 51, No 11, 2000, p. 1271–1289. 12. McKnight, J. G. R. Why did employee health insurance contributions rise? Health Economics (Sveikatos ekonomika), 2003, Vol 22, No 6, p. 1085–1104.

Èyras, P.; Ðukys, R.; Jakutis, A. Estimating social and economical consequences of accidents and occupational diseases at work, and preparing prevention measures and recommendations for economical work areas (Profesiniø ligø ir nelaimingø atsitikimø darbe ekonominiø ir socialiniø pasekmiø nustatymas ir prevenciniø priemoniø bei rekomendacijø ekonominës veiklos sritims parengimas), 2003. 47 p. (in Lithuanian).

13. Vakrinienë, S.; Èyras, P. Optimal distribution of resources for work safety measures, using stochastic programming. (Lietuvos matematikos rinkinys), 2003, Vol 42, No 1–6, p. 591–596 (in Lithuanian).

Èyras, P.; Ðukys, R.; Nainys, V. Occupational health and safety programs for years 2004/2006-project preparation according to European Communitys occupational health and safety strategy for years 2002/2006 (Profesinës saugos ir sveikatos programos 2004–2006 m. projekto parengimas

15. Vakrinienë, S.; Èyras P. The solution of the financing problems of injury prevention by stochastic programming. Health Sciences (Sveikatos mokslas), 2003, No 8 (31), p. 68–71 (in Lithuanian).

14. Vakrinienë, S.; Èyras, P. Investigation of the efficiency of labour safety means by statistical games. Civil engineering and management (Statyba), 2002, Vol 8, No 3, p. 192– 196 (in Lithuanian).

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65 ISSN 1392–3730

JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT http:/www.vtu.lt/english/editions

2004, Vol X, Suppl 1, 65–70

IDENTIFICATION OF NON-LINEAR DYNAMIC SYSTEMS POLYHARMONIC OSCILLATIONS Viktorija Volkova Dnepropetrovsk National University of Railway Transport named after Academician Lazarjan, 2 Lazarjan St, Dnepropetrovsk, UA-49010 Ukraine. E-mail: [email protected] Received 2 Apr 2004; accepted 16 June 2004 Abstract. An analytical investigation of oscillations is a necessity of construction of mathematical model. The data of technical drawings, descriptions and other documentation about frame and values of parameters might be used for this purpose. However, in some cases this information can be insufficient. The methods of systems identification are effective. Keywords: identification, phase trajectories, polyharmonic oscillations, non-linear dynamic systems.

2. Application of the phase diagrams to investigation of oscillatory processes

1. Introduction The qualitative investigation of a dynamic system behaviour is reduced to the analysis of behaviour of trajectories in a phase space. Fundamentals of the qualitative theory of dynamic processes were built by Poincaré. The exclusive role in development of qualitative method of testing dynamic systems belongs to Andronov A. A. [1], Leontovich E. A., Gordon I. I. Primary goal of the classic theory of qualitative investigation is the definition of dynamic properties of systems without obtaining the precise analytical solution. The phase trajectories on a plane ( y, y& ) were widely used for this purpose. Let’s note that the phase space of dynamic systems is multidimensional. Other choice of phase plane parameters is also possible. For the first time, an attempt to apply phase trajectories on planes ( y, &y&) and ( y& , &y&) to the investigation of dynamic systems was made in the monograph [2]. As follows from the obtained results, the phase trajectories on a plane ( y, &y&) can be effectively used for identification of dynamic systems. In the monograph [3] the results of qualitative investigation of oscillations of conservative systems having non-linear dissipative and elastic characteristics of different types are shown. The purpose of this paper is the analysis of dynamic behaviour of asymmetrical systems with the piecewise linear elastic characteristic, obtained of time processes and phase trajectories ( y, &y&) and ( y& , &y&) for different oscillatory regimes.

The phase trajectories on a plane ( y, &y&) is of greatest interest. It is connected with the fact that the power relations on it are interpreted most visually. Besides, the relation &y&( y ) is back symmetrical relative an axis y to the diagrams of elastic properties change. For example, in Fig 1 the diagrams of change of the elastic characteristic and accelerations for a system with “backlash” are presented. The phase trajectories &y&( y ) allow to establish the type and level of system non-linearity. It is known that accelerations of points are more sensitive to deviations of oscillations from harmonic. We compare linear system to non-linear symmetric system with double-well potential (buckling). It should be noted that the oscillograms of these systems at some regimes of oscillations at the excitement frequency are similar, but accelelograms are different. So, accelelogram of linear system looks like a harmonic process, and asymmetrical system with double-well potential – like sawtooth type [2]. The major difficulty of formation of phase trajectories &y& ( y ) and &y& ( y& ) consists in the necessity to exclude parameter of time t from the appropriate dependencies. It is not always possible to perform this operation analytically. The majority of measuring devices register the changes of displacements, velocities and accelerations of investigated systems points in time. Sanitary and technological norms bring restrictions in values of these parameters. Accepting consistently appropriate pairs of parameter values y (t ) and y (t ) or y (t ) and y& (t ) , it is possible to obtain phase characteristic data (Fig 2).

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&y&

R (y)

y

y

Fig 1. Change of elastic properties and acceleration for system with “backlash”

&y&

t

y

&y&

y

t

Fig 2. Formation of phase trajectory

3. Differential equation of forced oscillations of systems with the asymmetrical piecewise linear characteristic

By values µ = 0 and µ = 1 the formula (2) describes a harmonic excitement with frequency ω and amplitudes F 1 and F1 + Fm respectively. Let's assume that the elastic characteristic is asymmetrical and changes under the law

The differential equation of forced oscillations has a view

y + ε y& + R ( y ) = F (t ) ,

α 1 y , y ≤ 0 ; R (y) =   α 2 y , y > 0.

(1)

where y is generalised co-ordinate, R ( y ) is elastic characteristic, ε is friction coefficient; F (t ) – function of an outer excitement. Let us focus our consideration on a case of an asymmetrical biharmonic excitement. We assume that the characteristic of an outer polyharmonic excitement has the following form

(3)

It is known [4, 5], that the natural frequency of dynamic systems with the bilinear elastic characteristic does not depend on initial conditions. It equals

ω0 =

F (t ) = F1 cos (ω1 t ) + Fm cos (ωm t ), m = 1, 2, 3K. (2)

2ω1 ω 2 , ω1 + ω 2

(4)

where ω 1 = α 1 and ω 2 = α 2 . Despite this fact, the installation of sub- and ultraharmonic is possible. These oscillations are reshaped on the basis of free oscillations of a system, which are supported by an outer driving force (Fig 3). As against symmetrical systems with piecewise linear elastic characteristics, stable conditions sub- (ω0 2 )

It is known that the characteristic of an outer excitement is a periodic function of time t only in case of multiple frequencies, ie ω m = µ ω 1 , µ = 0, 1, 2, 3, K . It should be noted that the appearance of stationary oscillations is possible only under a periodic excitation. Therefore we shall study the cases of multiple frequencies.

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67

ω

AMPLITUDE, M

3ω ω/ 2

ω/3

FREQUENCY, RAD/S

Fig 3. An amplitude-frequency characteristic of forced oscillations of an asymmetrical system with the piecewise linear elastic 2 −1 −2 characteristic. ε = 0,1 s , α 1 = 10,8 s −1, α 2 = 40,8 s −1 , F1 = 0,15 m s , F2 = 0,15 ms , µ = 3

and ultraharmonic (2 ω0 ; 4ω0 ) of oscillations on even harmonics here will be realised.

form. The spectral characteristics of the oscillating processes are obtained by means of the standard programme of the fast Fourier transformation. The standard graphic programme complex is used for the graphic formation of the dynamic processes. The usage of HCC is described further after the definite example.

4. Technique of hybrid modelling The hybrid computing complexes (HCC) present the synthesis of analog and numerical computers. They possess the speed of the analog and the precision of the numerical computers at the large volume of memory. HCC gives the posibility to observe visually the computing process during the investigations by means of oscillographs, self-recorders, etc [6]. Besides, it is possible to change the parameters of the investigated system in the process of computing. The investigation of the forced oscillation systems with buckling was carried out on the HCC produced on the base of the IBM PC and analog computer ACC-31 with the signal generator of special shape. The maximum output signal constitutes 10 V at the frequency range 0,001–10 KHz. The double-trace oscillograph C1-99 was used for visual observation of the computing process – electric signals from the major amplifier outputs. The results of the non-linear differential equation system integration were transmitted by means of the interface devices on IBM PC. The standard mathematical securing is used for the analog–to–digital converter functioning. The information, put into IBM PC, is stored in the hard disk in text file

5. Analysis of results As contrasted to the system with the linear elastic characteristic, the studied system has a large number of resonance frequency ranges. The oscillations on frequency of a excitement, and also oscillation on either higher or lower frequencies developed. The following parameters of a dynamic system (1) are adopted: ε = 0,1 s −1 ; α 1 = 10,8 s −1 ; α 2 = 40,8 s −1 ;

F1 = 0,15 m s 2 ; F2 = 0,15 ms −2 ; µ = 3 . Let us compare the dynamic behaviour of the system under study (1) with ones of the following systems &y& + ε y& + R ( y ) = F1 cos(ω1 t ),

(5.a)

&y& + ε y& + R ( y ) = Fm cos(ωm t ).

(5.b)

The amplitude-frequency characteristic of an equation (1) is shown in Fig 3. Here two resonance zones related to resonances for each of harmonics of an outer excitement are sharply expressed. The skeleton curve of

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the given system is a straight line on frequency ω0 = 4,33 rad s . Their comparison with amplitude-frequency characteristics for systems (4.a) and (4.b) in the range of a main resonance (Fig 3) demonstrates rather close coincidence of oscillation parameters with resonance-inducing harmonic. In the range of the second resonance an insignificant extension of frequency range and amplitude increase for the system (4.b) are observed. The characteristics of subharmonic resonance of the order ω 2 for systems (1) and (4.a) are similar, while insignificant expanding of frequency range of a subharmonic oscillation on frequency ω 3 for a case of a biharmonic excitement is observed (Fig 3). Thus it is possible to conclude that the amplitudefrequency characteristic can be obtained for some ranges with an adequate accuracy in analysis of systems with simpler structure of an outer excitement. The existence of two harmonics of an outer excitement results in changes in the structure of periodic regimes. These changes basically are inherent in the frequency range below the main resonance and lead, first of all, to the change of the orders of sub-ultraharmonic tones being manifested. In the interval between the main and the second frequency ranges of a system (1), the resonance oscillations of order (µ + 1)ω µ are sharply manifested. Let's note that in the given range the oscillations on frequency

become unstable, and here a pair of subharmonic oscillations of frequency of order ω µ appears. One of them is resonant and another is non-resonant. Oscillation amplitude on a harmonic (µ + 1)ω µ increases rapidly, and even exceeds oscillation amplitude of fundamental frequency ω . Despite the large steepness of the conforming segments of amplitude-frequency characteristics, the investigation of these types of oscillations by numerical methods is difficult [7]. Presence of isolated frequency ranges, manifestation of additional sub- and ultraharmonic oscillations are connected with the fact that the natural frequency of essentially non-linear systems depends on the parameters of a rather large number of harmonics which are parts of the solution [8]. The steady branches of an amplitude-frequency characteristic of a system (1) can be divided into five frequency ranges. The time processes, spectral characteristics and phase trajectories on planes ( y, y& ) , ( y, &y&) and ( y& , &y&) for each one have been obtained. Range I (ω = 0 ÷ 3 rad s ) is a domain of superposition of ultraharmonic oscillations of order µω on oscillations of a fundamental tone, both at increasing and decreasing the basic excitement frequencyv (Fig 4). Range II (ω = 3 ÷ 7rad s ) is characterised by the stall of resonant oscillations on the fundamental tone.

a)

b)

Fig 4. Time processes, spectral characteristics and phase trajectories of a symmetrical system with the piecewise linear elastic characteristic. Range I: a) monoharmonic excitement; b) biharmonic excitement

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Range III (ω = 7 ÷ 11rad s ) demonstrates subharmonic oscillations of orders ω 2 . It is worth noting that the oscillations on even harmonics are steady due to the asymmetrical system. The amplitudes of a resonant subharmonic oscillation are commensurable with the amplitudes of resonance oscillations of a fundamental tone. Range IV (ω = 11÷ 14 rad s ) is a domain of subharmonic oscillations of order ω 3 , both at increasing and decreasing frequency of an excitement (Fig 5). Range V (ω > 14 rad s ) is an after-resonance domain, where the only "small" oscillations are realizable. In Figs 4a, 5a and the time processes, spectral characteristics and related phase trajectories for a system (4a) for the same frequencies of the lowest harmonic are shown. The analysis of relations of dynamic parameters presented in Figs 4, 5 allows to mark the following. The influence of sub- and super-harmonic oscillations results in change of time processes (t , &y&) . It has poly-harmonic nature. Sub- and super-harmonics cause the appearance of additional closed loops on phase trajectories. The spectral content of the solution can vary in cardinal way with changing a frequency of an outer excitement. It follows from the analysis of given amplitudefrequency characteristics and spectral characteristics of a few time processes. The biharmonic outer excitement promotes such changes of the spectral content. By varying the dependencies of outer excitement change, it is possible either to achieve the required frequency ranges or to exclude the undesirable ones. It creates the basis

69

for designing structural elements, for which the regular dynamic regimes can be specified initially. 6. Conclusions The analysis of results obtained allows to make a conclusion that the systems with non-linear elastic characteristics are rather sensitive to the dependence on an outer excitement change. Therefore the widely used assumptions about the monoharmonic dependence of an outer excitement change in studies of actual mechanical systems are not always correct. Thus rather small deviations of the outer excitement form from monoharmonic does not make considerable effect within wide ranges of frequencies (resonances of frequencies ω and ω 3 ) but can result in qualitative changes in other ranges The development of qualitative methods of investigation of dynamic systems suggested by the authors is an effective means of analysis and identification of dynamic systems. Simultaneous use of all three types of signals. registered in time, namely displacement, velocity and acceleration allows to expand considerably the opportunities of traditional methods of investigation. Unlike the existing asymptotic and stochastic methods [9, 10] of identification of dynamic systems, the use of the suggested technique is not connected with the use of a significant amount of computing procedures, and also has a number of advantages when investigating the explosive oscillations.

a)

b)

Fig 5. Time processes, spectral characteristics and phase trajectories of a symmetrical system with the piecewise linear elastic characteristic. Range IV: a) monoharmonic excitement; b) biharmonic excitement

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References 1.

2.

3.

Andronov, A. A.; Leontovich, E. A.; Gordon, I. I.; Maier, A. G. Qualitative theory of second-order systems. New York: Halsted Press Book, 1973. 524 p. Kazakevich, M. I.; Volkova, V. E. Dynamics of systems with double-well potential. Dnepropetrovsk: Art-Press, 2000. 159 p. (in Russian). Kazakevitch, M. I.; Volkova, V. E. Identification of nonlinear dynamic systems. In: Proceedings of the 7-th International Conference on Modern Building Materials, Structures and Techniques, Vol 3. Vilnius: Technika, 2001, p. 145–150.

4.

Blehman, I. I. (ed). Oscillations in engineering: Reference book in 6 volumes, Vol 2. Moscow: Engineering, 1979. 315 p. (in Russian).

5.

Zakrzhevskij, N. M. Oscillations in essential non-linear mechanical systems. Riga: Zinatne, 1980. 190 p. (in Russian).

6.

Gorbatsevitch, E. D.; Levinzon, F. F. Analog modelling of the control systems. Moscow: Nauka, 1984. 304 p. (in Russian).

7.

Tompson, J. M. T. Instabilities and catastrophes in science and engineering. New York: John Willey & Sons, 1982. 254 p.

8.

Butenin, N. V. Introduction into the theory of non-linear oscillations. Moscow: Nauka. 1976. 286 p. (in Russian).

9.

Lichtenberg, A. J.; Lieberman, M. A. Regular and stochastic motion. Berlin: Springer-Verlag, 1984. 573 p.

10. Adams, E. D.; Allemang, R. J. Survey of non-linear detection and identification techniques for experimental vibrations. In: Proceedings of ISMA 23, Vol 1. Davenport: Pergamon, 1998, p. 269–281.

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DAUGIAKRITERINËS NEKILNOJAMOJO TURTO ELEKTRONINËS PREKYBOS SISTEMOS TAIKYMO YPATUMAI Edmundas Kazimieras Zavadskas, Artûras Kaklauskas, Saulius Raslanas, Mindaugas Krutinis Statybos technologijos ir vadybos katedra, Statybos ekonomikos ir nekilnojamojo turto vadybos katedra, Vilniaus Gedimino technikos universitetas, Saulëtekio al. 11, LT-10223 Vilnius-40, Lietuva. E-paðtas: [email protected] Áteikta 2003 11 27; priimta 2004 05 06 Santrauka. Viena ið pagrindiniø internetiniø informaciniø sistemø problemø yra ta, jog jose sunku rasti reikiamà gaminá ar paslaugà. Internete siûloma tûkstanèiai to paties gaminio ar paslaugos rûðiø. Juos vartotojas paprastai nori palyginti su kitais panaðiais gaminiais ar paslaugomis. Analogiðkø pasiûlymø palyginimà galima atlikti ðiais bûdais, tai gaminiø paieðka hipertekstiniuose dokumentuose pagal tarpininkus, alternatyviø gaminiø paieðka duomenø bazëse, alternatyviø gaminiø paieðka ir sugretinimas lentelëse, alternatyviø gaminiø ir paslaugø paieðka ávairiose elektroninës prekybos svetainëse, paieðka ir daugiakriteriniø sprendimø priëmimas. Autoriai sukûrë internetinæ daugiakriterinæ nekilnojamojo turto elektroninës prekybos (NTEP) sistemà. Pateikta NTEP sistema gali padidinti nekilnojamojo turto vertæ ðiais bûdais: ði sistema vartotojams gali padëti nustatyti savo poreikius, nustatyti jø poreikius atitinkantá nekilnojamàjá turtà, palyginti ir ávertinti ávairius siûlomus nekilnojamojo turto variantus, padëti vartotojams ávertinti nekilnojamojo turto naudingumà já ásigijus ir pan. Raktaþodþiai: internetinës informacinës sistemos, NTEP sistema, daugiakriterinë analizë.

aspektus (ekonominius, kokybinius, techninius, teisinius, socialinius, ekologinius ir pan.) apibûdinanti informacija [10]. Ji gali bûti pateikta skaitmenine, tekstine, grafine forma (schemos, grafikai, diagramos, brëþiniai), tai gali bûti formulës, nuotraukos, garso ar vaizdo áraðai. Remdamasi ðia informacija NTEP sistema gali ávertinti nekilnojamàjá turtà ávairiais aspektais (t. y. rinkos vertës, investicinës vertës, esamo naudojimo rinkos vertës ir kt. verèiø nustatymas); ji gali ávertinti atskirus kriterijus, turinèius átakos vertei (pavyzdþiui, nekilnojamojo turto vietos, nusidëvëjimo, pasiûlos, paklausos ir pan. ávertinimas), nustatyti optimalaus panaudojimo variantà (pavyzdþiui, pirkëjas bûstà renkasi maksimaliai tenkindamas gyvenimo bûtinumo, komfortiðkumo bei asmeninius poreikius) (http://193.219.145.99/PROJ2/TEORIJA/teorija1.htm). Kadangi nekilnojamàjá turtà racionalu vertinti ávairiais aspektais, todël tarp sprendimø paramos sistemos modeliø yra tokiø, kurie sprendimø priëmëjui padeda atlikti kompleksinæ alternatyvø analizæ ir priimti sprendimà. Pavyzdþiui, teigiamas ir neigiamas nagrinëjamø alternatyvø savybes galima detaliai iðanalizuoti remiantis apskaièiuotais kriterijø reikðmingumais, jø prioritetiðkumo, naudingumo laipsnio ir rinkos verèiø reikðmëmis. NTEP sistemos pagrindinis voratinklio svetainës tinklalapis (http://193.219.145.99) turi nuorodas á kitus tinklalapius:

1. Ávadas Dauguma elektroninës prekybos sistemø bando rasti ekonomiðkiausius sprendimus daugiausia siekdamos tik ekonominiø tikslø [1–4]. Todël daugelis elektroninës prekybos sistemø apdoroja ir teikia tik ekonominæ informacijà bei taiko ekonominius modelius. Taèiau nagrinëjamas alternatyvas daþnai reikia vertinti ne tik ekonominiu, bet taip pat ir kokybiniu, techniniu, teisiniu, socialiniu ir kitokiu atþvilgiu [5–7]. Kuriant siûlomà sistemà buvo stengiamasi iðvengti ðiø ir kitø sistemø trûkumø. 2. Daugiakriterinës nekilnojamojo turto elektroninës prekybos sistemos apraðymas Remiantis informaciniø, ekspertiniø, sprendimø paramos ir elektroninës prekybos sistemø analize buvo sukurta daugiakriterinë nekilnojamojo turto elektroninës prekybos (NTEP) sistema, kurios trumpas apraðymas pateiktas ðiame straipsnyje [8–9]. Ði sistema sudaryta ið duomenø bazës bei duomenø bazës valdymo sistemos, modeliø bazës bei modeliø bazës valdymo sistemos ir vartotojo interfeiso. Duomenø bazëje (http://193.219.145.99/PROJ2/ TEORIJA/teorija1.htm) nekilnojamàjá turtà apraðant kiekybine ir koncepcine formomis, pateikiama ávairius jo

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• Teorijos voratinklio tinklalapis (http:// 193.219.145.99/PROJ2/TEORIJA/teorija1.htm). Jame pateikta autoriø pasiûlyta teorija, kuria remiantis buvo sukurta NTEP sistema. • Darbo su sistema instrukcijos voratinklio tinklalapis (http://193.219.145.99/proj2/help2.pdf). Remiantis ðiomis instrukcijomis gana nesudëtinga praktiðkai naudotis NTEP sistema. • Sistemos galimybiø apraðymo voratinklio tinklalapis (http://193.219.145.99/proj2/help1.pdf). Ðiame voratinklio tinklalapyje trumpai apraðytos suinteresuotosios grupës, kurios savo praktinëje veikloje gali naudotis NTEP sistema ir sistemos galimybëmis. • Komerciniø pastatø voratinklio tinklalapis (http:// 193.219.145.99/PROJ2/PARDUOT/parduot.htm). • Vienbuèiø gyvenamøjø namø voratinklio tinklalapis (http://193.219.145.99/PROJ2/NAMAI/namai.htm). • Sodybø voratinklio tinklalapis (http://193.219.145.99/ PROJ2/SODYBOS2/sodybos2_1.htm). Ðios nuorodos iðryðkintos. Norint pasinaudoti nuoroda, reikia paspausti iðryðkintà vietà. Taip atsiranda daugybë Lietuvos nekilnojamojo turto rinkos dalyviø (pardavëjai, tarpininkai, agentai, investuotojai, ávairios organizacijos, ámonës, bankai, kitos finansø institucijos ir kt. kreditoriai, draudimo kompanijos, pirkëjai, vertintojai, teismai), kurie nori turëti iðsamià informacijà apie objektus, siûlomus rinkoje [11]. Ðios suinteresuotosios grupës savo praktinëje veikloje taikydamos NTEP sistemà savo tikslus ágyvendintø operatyviau ir profesionaliau. Ateityje tobulinant NTEP sistemà numatoma praplësti pagrindinës tikslinës naudojimo paskirties nekilnojamojo turto duomenø bazæ, sudaryti galimybæ atlikti jo perleidimo operacijas (nuomos, lizingo, dovanojimo, pirkimo ir pardavimo), sumokëti uþ já, patikrinti, ar sumokëta uþ já, gauti informacijos apie kliento asmeninæ sàskaità (patikrinti, ar joje yra reikiama pinigø suma), keistis informacija (skelbimø lenta, diskusijø forumai, reklama, laiðkø dëþutë, straipsniai, kita informacija). Kadangi informacija apie siûlomà nekilnojamàjá turtà nuolatos keièiasi, todël naujausios informacijos reikia ieðkoti agentûrø ir kitø suinteresuotø grupiø tinklalapiuose. Todël numatoma pateikti nuorodas ir á suinteresuotø grupiø Web mazgus. Be to, numatoma pateikti informacijà apie turto vertintojø, agentûrø ir kitø asociacijø veiklà, ádëti ávairius skelbimus, informacijà apie padëtá rinkoje, jos pokyèius ir prognozes ateièiai, apie leidþiamus periodinius informacinius biuletenius, kità naujausià vartotojams rûpimà informacijà.

ti vertinamojo objekto ir parduotø objektø (lyginamøjø objektø) konkurencingumà. 2003 m. balandþio mënesá nekilnojamojo turto rinkoje buvo siûloma parduoti þemës sklypà su pastatais poilsio sodybai ákurti. Kliento pageidavimu ðá nekilnojamàjá turtà reikëjo ávertinti rinkos verte. Tuo metu nekilnojamojo turto rinkos aktyvumas didëjo, parduotø lyginamøjø objektø netrûko, todël jie ðiam vertinimui buvo parinkti ið to paties rajono. Ðiuo atveju apskaièiuota lyginamoji vertë lygi rinkos vertei, be to, ávertinti visi kriterijai, darantys átakà ðios nekilnojamojo turto rûðies rinkos vertei. Kriterijø reikðmës ir pradiniai reikðmingumai buvo ávertinti padedant nekilnojamojo turto ekspertams ir atsiþvelgiant á turtu suinteresuotø asmenø nuomonæ. 3.1. Koncepcinis vertinamojo ir lyginamøjø nekilnojamojo turto objektø apraðymas 3.1.1. Pirmosios (vertinamosios) poilsio sodybos koncepcinis apraðymas Vietovës apraðymas. Sodyba yra Anomislio kaime, Toliejø seniûnijoje, Molëtø rajone (1 pav.). Artimiausias kaimynas – uþ 500 m á ðiauræ nuo sodybos. Uþ 600 m á rytus nuo sodybos yra graþus Jaurio eþeras. Iki miðko – 100 m. Privaþiuojamieji keliai geri: 4 km ilgio þvyrkelis, toliau eina asfaltuotas kelias. Artimiausia gyvenvietë Toliejai yra uþ 2 km. Molëtai – uþ 12 km. Vilnius – uþ 72 km.

1 pav. Vertinamoji poilsinë sodyba

Þemës sklypas. Þemës sklypo plotas – 1 ha. Uþstatyta pastatais – 0,20 ha, visa kita – þemës ûkio naudmenos ir sodas. Sklype yra gyvenamasis namas, ûkinis pastatas, pirtis, darþinë, nedidelis tvenkinys ir lapuoèiø miðkelis. Sodas – senas. Pastatø fizinës charakteristikos. Visi minëti pastatai yra ikikarinës statybos, iðskyrus ûkiná pastatà. Gyvenamasis namas – vieno aukðto, medinis, ið ràstø, apkaltas ðaliuote. Bendras plotas – 80 m2. Namas buvo gerai priþiûrimas, remontuojamas. Jam reikëtø rekonstrukcijos

3. Praktinis pavyzdys Kad bûtø lengviau suvokti daugiakriterinæ nekilnojamojo turto analizës esmæ, pateikiamas jos taikymo pavyzdys [12]. Uþdavinys – nustatyti poilsio sodybos rinkos vertæ, esant lyginamøjø ir vertinamojo objekto kiekybiniams, kokybiniams skirtumams, taip pat nustaty-

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arba nedidelio remonto. Darþinë taip pat statyta ið ràstø. Jo bûklë patenkinama (reikëtø kapitalinio remonto arba rekonstrukcijos). Ûkinis pastatas iðsilaikæs gerai, todël jam reikëtø nedidelio remonto. Pirties bûklë gera. Ji buvo rekonstruota 1992 m. Patogumai. Elektra yra tik gyvenamajame pastate. Ðildoma krosnimi. Vandentiekio ir telefono nëra. Kieme stovi ðulinys. Apribojimai. Servitutø þemës sklype nëra. Yra apribojimø pagal LR Vyriausybës nutarimo Nr. 343 XXIX skyriø dël vandens telkiniø pakrantës apsaugos juostos, apribojamas plotas – 0,05 ha. Þemës sklypo padëties elementai. Atstumas iki Molëtø (rajono centro) – 12 km. Iki artimiausios gyvenvietës – 3 km. Privaþiuojama prie þemës sklypo nuo gyvenvietës þvyrkeliu – 3 km. Sklypas yra graþioje vietoje. Galima uþsiimti ûkine veikla (ðalia yra laisvos valstybinës þemës), kaimo turizmu. Aplinka neuþterðta, vieta rami.

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nis pastatas, pirtis, darþinë ir du garaþai buvo nugriauti ir perstatyti ið plytø 1994 m. Todël ðiø pastatø bûklë gera (remonto nereikia). Patogumai. Elektra yra visuose pastatuose. Gyvenamasis namas ðildomas krosnimi. Vandentiekio ir telefono nëra. Kieme stovi ðulinys. Apribojimai. Servitutø þemës sklype nëra. Yra apribojimø pagal LR Vyriausybës nutarimo Nr. 343 XXIX skyriø dël vandens telkiniø pakrantës apsaugos juostos, apribojamas plotas – 0,04 ha. Þemës sklypo padëties elementai. Atstumas iki Molëtø (rajono centro) – 16 km. Iki artimiausios gyvenvietës – 5 km. Prie þemës sklypo nuo gyvenvietës privaþiuojama asfaltu – 4,5 km ir þvyrkeliu – 0,5 km. Sklypas yra graþioje vietoje. Galima vystyti ûkinæ veiklà (ðalia yra laisvos valstybinës þemës), kaimo turizmà. Aplinka neuþterðta, vieta rami. Sodybos pardavimo kaina – 44 000Lt. 3.1.3. Treèiosios poilsio sodybos (lyginamojo objekto) koncepcinis apraðymas

3.1.2. Antrosios poilsio sodybos (lyginamojo objekto) koncepcinis apraðymas

Vietovës apraðymas. Sodyba yra Juodënø kaime, Èiulënø seniûnijoje, Molëtø rajone (3 pav.). Artimiausias kaimynas – uþ 100 m á vakarus nuo sodybos. Uþ 500 m á pietvakarius nuo sodybos yra Virintø eþeras. Iki miðko – 300 m. Privaþiuojamieji keliai geri: 1 km ilgio þvyrkelis, toliau eina asfaltuotas kelias. Artimiausia gyvenvietë Toliejai yra uþ 4 km. Rajono centras – Molëtai yra uþ 10 km, Vilnius – uþ 70 km. Þemës sklypas. Þemës sklypo plotas – 2 ha. Uþstatyta pastatais – 0,20 ha, visa kita – þemës ûkio naudmenos ir sodas. Þemës sklype yra gyvenamasis namas, ûkinis pastatas, darþinë, sodas.

Vietovës apraðymas. Sodyba yra Migiðkiø kaime, Balninkø seniûnijoje, Molëtø rajone (2 pav.). Artimiausias kaimynas – uþ 100 m nuo sodybos. Uþ 500 m á pietryèius nuo sodybos yra Sabalos eþeras. Iki miðko – 300 m. Privaþiuojamieji keliai geri: 0,5 km ilgio þvyrkelis, toliau eina asfaltuotas kelias. Artimiausia gyvenvietë Girsteitiðkis yra uþ 5 km, Molëtai – uþ 18 km, Vilnius – uþ 78 km.

2 pav. Antroji (lyginamoji) poilsio sodyba

Þemës sklypas. Þemës sklypo plotas – 0,7 ha. Uþstatyta pastatais – 0,30 ha. Visa kita – þemës ûkio naudmenos ir sodas. Þemës sklype yra gyvenamasis namas, ûkinis pastatas, darþinë, pirtis. Sodas – senas. Pastatø fizinës charakteristikos. Gyvenamasis namas – ikikarinës statybos, vieno aukðto, medinis, ið ràstø, apkaltas ðaliuote. Bendras plotas – 80 m2. Namas buvo gerai priþiûrimas ir remontuojamas. Jam reikëtø nedidelës rekonstrukcijos arba nedidelio remonto. Ûki-

3 pav. Treèioji (lyginamoji) poilsio sodyba

Pastatø fizinës charakteristikos. Gyvenamasis namas – ikikarinës statybos, vieno aukðto, medinis, ið ràstø, apkaltas ðaliuote. Bendras plotas 80 m2. Jam reikëtø rekonstrukcijos arba remonto. Ûkinis pastatas mûrinis. Remonto nereikia. Darþinë taip pat mûrinë, geros bûklës, jai reikëtø nedidelio remonto.

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Patogumai. Elektra yra visuose pastatuose. Gyvenamasis namas ðildomas krosnimi. Yra telefonas. Vandentiekio nëra. Kieme stovi ðulinys. Apribojimai. Servitutø þemës sklype nëra. Yra apribojimø pagal LR Vyriausybës nutarimo Nr. 343 XXIX skyriø dël vandens telkiniø pakrantës apsaugos juostos, apribojamas plotas – 0,07 ha. Þemës sklypo padëties elementai. Privaþiuojama prie sklypo nuo Molëtø á Utenos pusæ asfaltu (9 km) ir þvyrkeliu á Juodënus (1 km). Atstumas iki Molëtø (rajono centro) – 10 km. Sklypas graþioje vietoje. Galima vystyti ûkinæ veiklà (ðalia yra laisvos valstybinës þemës), kaimo turizmà. Aplinka neuþterðta, vieta rami. Sodybos pardavimo kaina – 40 000 Lt.

Apribojimai. Servitutø þemës sklype nëra. Yra apribojimø pagal LR Vyriausybës nutarimo Nr. 343 XXIX skyriø dël vandens telkiniø pakrantës apsaugos juostos, apribojamas plotas – 0,07 ha. Þemës sklypo padëties elementai. Atstumas iki Molëtø (rajono centro) – 20 km. Iki artimiausios gyvenvietës – 3 km. Privaþiuojama prie þemës sklypo nuo Molëtø asfaltu (17 km) ir þvyrkeliu (3 km). Sklypas yra graþioje vietoje. Galima vystyti ûkinæ veiklà (ðalia yra laisvos valstybinës þemës), kaimo turizmà. Aplinka neuþterðta ir rami. Sodybos pardavimo kaina – 36 000 Lt. 3.1.5. Penktosios poilsio sodybos (lyginamojo objekto) koncepcinis apraðymas

3.1.4. Ketvirtosios poilsio sodybos (lyginamojo objekto) koncepcinis apraðymas

Vietovës apraðymas. Sodyba yra Anomisliø kaime, Èiulënø seniûnijoje, Molëtø rajone (5 pav.). Artimiausias kaimynas – uþ 500 m á pietus nuo sodybos. Uþ 300 m á vakarus nuo sodybos yra graþus Susiedo eþeras. Iki miðko – 100 m. Privaþiuojamieji keliai geri: 2 km ilgio þvyrkelis, toliau eina asfaltuotas kelias. Artimiausia gyvenvietë Juodënai yra uþ 2 km, Molëtai – uþ 10 km, Vilnius – uþ 70 km.

Vietovës apraðymas. Sodyba yra Antamakiø kaime, Balninkø seniûnijoje, Molëtø rajone (4 pav.). Artimiausias kaimynas – uþ 300 m á pietus nuo sodybos. Uþ 700 m á vakarus nuo sodybos yra Makio eþeras. Iki miðko – 300 m. Privaþiuojamieji keliai geri: 3 km ilgio þvyrkelis, toliau eina asfaltuotas kelias. Artimiausia gyvenvietë Balninkai yra uþ 3 km, Molëtai – uþ 20 km, Vilnius – uþ 80 km.

5 pav. Penktoji (lyginamoji) poilsio sodyba

Þemës sklypas. Þemës sklypo plotas – 0,6 ha. Uþstatyta pastatais – 0,20 ha, kita þemë – naudmenos ir sodas. Sklype yra gyvenamasis namas, ûkinis pastatas, sodas. Pastatø fizinës charakteristikos. Visi pastatai yra ikikarinës statybos. Gyvenamasis namas – vieno aukðto, medinis, ið ràstø. Bendras plotas 65 m2. Pastato bûklë gera (jam reikëtø rekonstrukcijos arba nedidelio remonto). Ûkinis pastatas taip pat medinis. Jo bûklë patenkinama (reikëtø kapitalinio remonto arba rekonstrukcijos). Patogumai. Elektra yra tik gyvenamajame name. Jis ðildomas krosnimi. Vandentiekio ir telefono nëra. Kieme stovi ðulinys. Apribojimai. Servitutø þemës sklype nëra. Yra apribojimø pagal LR Vyriausybës nutarimo Nr. 343 XXIX skyriø dël vandens telkiniø pakrantës apsaugos juostos, apribojamas plotas – 0,05 ha.

4 pav. Ketvirtoji (lyginamoji) poilsio sodyba

Þemës sklypas. Þemës sklypo plotas – 0,5 ha. Uþstatyta pastatais – 0,10 ha. Visa kita – þemës ûkio naudmenos ir sodas. Sklype yra gyvenamasis namas, ûkinis pastatas, darþinë. Sodas – senas. Pastatø fizinës charakteristikos. Visi pastatai yra ikikarinës statybos. Gyvenamasis namas – vieno aukðto, medinis, ið ràstø. Bendras plotas 70 m2. Pastato bûklë patenkinama (jam reikëtø rekonstrukcijos arba remonto). Ûkinis pastatas ir darþinë taip pat mediniai. Jø bûklë patenkinama (reikëtø kapitalinio remonto arba rekonstrukcijos). Patogumai. Elektra yra tik gyvenamajame name. Ðildoma krosnimi. Vandentiekio ir telefono nëra. Kieme stovi ðulinys.

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Þemës sklypo padëties elementai. Atstumas iki Molëtø (rajono centro) – 10 km. Iki artimiausios gyvenvietës – 3 km. Privaþiuojame prie sklypo nuo Molëtø asfaltu (8 km) ir þvyrkeliu (2 km). Sklypas yra graþioje vietoje. Galima vystyti ûkinæ veiklà (ðalia yra laisvos valstybinës þemës), kaimo turizmà. Aplinka neuþterðta, vieta rami. Sodybos pardavimo kaina – 38 000 Lt.

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d11 = 39,500 ⋅ 1,00 /(39,50 + 44,0 + 40,0 + 36,0 + 38,0) = 0, 2; d12 = 44,00 ⋅ 1,00 /(39,50 + 44,0 + 40,0 + 36,0 + 38,0) = 0, 2228; d13 = 40,00 ⋅ 1,00 /(39,50 + 44,0 + 40,0 + 36,0 + 38,0) = 0, 2025; d14 = 36,00 ⋅ 1,00 /(39,50 + 44,0 + 40,0 + 36,0 + 38,0) = 0,1823; d15 = 38,00 ⋅ 1,00 /(39,50 + 44,0 + 40,0 + 36,0 + 38,0) = 0,1924.

Kiekvieno kriterijaus gautø bedimensiø ávertintø reikðmiø d ij suma visada lygi ðio kriterijaus reikðmingumui, pavyzdþiui, poilsio sodybos atstumo iki eþero kriterijus apskaièiuojamas taip:

3.2. Pateikto uþdavinio sprendimas 3.2.1. Sprendimo priëmimo matricos sudarymas

n

Skaièiavimai atlikti pagal apraðytà [12] metodà. Remiantis pateiktu poilsio sodybø koncepciniu apraðymu 2.1 poskyryje buvo sudaryta sprendimo priëmimo matrica (1 lent.). Ðioje matricoje reikëjo nustatyti poilsio sodybos, esanèios Anomislio kaime, Toliejø seniûnijoje, Molëtø rajone, rinkos vertæ ir kompleksiðkai ávertinti vertinamojo ir lyginamøjø objektø teigiamas ir neigiamas savybes. Lyginamieji objektai, esantys tame paèiame Molëtø rajone, buvo parduoti 2003 m., ir jø pardavimo kainos buvo þinomos (1 lent.). Kriterijø sistema sudaryta, atsiþvelgiant á visus galimus kriterijus, apibûdinanèius vertinamojo ir lyginamøjø objektø kokybines ir kiekybines savybes. Kokybiniø kriterijø reikðmës ir reikðmingumai nustatyti ekspertiniu bûdu, apklausiant rinkos dalyvius, t. y. vertintojus-ekspertus, pirkëjus ir pardavëjus [9–10]. Lyginamøjø objektø pardavimo kainos yra nepadidintos ir nesumaþintos dël rinkos dalyviø asmeniniø prieþasèiø ir kitø nenumatytø aplinkybiø. Galima teigti, kad visi kriterijai, turintys átakos tiriamo turto rûðies rinkos vertei, yra numatyti. Lyginamøjø objektø pardavimo laikas artimas objekto vertinimo momentui, todël á laiko pataisos koeficientà nebuvo atsiþvelgta. Pardavimo kainos kriterijaus reikðmingumas buvo imtas lygus visø kitø rinkos vertei turinèiø átakos kriterijø reikðmingumø sumai. Sprendimo priëmimo matricoje kiekybiniø kriterijø, pavyzdþiui, lyginamøjø objektø pardavimo kaina, atstumai iki vertinamojo objekto, pagalbiniø pastatø skaièius, gyvenamojo pastato bendrasis plotas, matavimo vienetai buvo nustatyti kiekybiniais dydþiais: litais, kilometrais, hektarais, vienetais, kvadratiniais metrais, o kokybiniai kriterijai buvo matuojami balais, kurie nustatyti iðrenkant konkretaus objekto geriausià reikðmæ, o kitiems objektams suteikiant santykines reikðmes.

q3 = ∑ d 3 j =0,0341 + 0,0284 + 0,0284 + j =1

0,0398 + 0,0170 = 0,1477.

Vertinant buvo nustatyta, kad didþiausios átakos poilsio sodybos rinkos vertei turi ðie veiksniai: jos nuotolis iki Vilniaus (q2 = 0,1358), atstumas iki eþero (q3 = 0,1477), miðko (q4 = 0,1238), gyvenamojo namo bûklë (q9 = 0,1065), vietovës kraðtovaizdis (q12 = 0,1106). Vëliau buvo apskaièiuotos lyginamuosius ir vertinamàjá objektus apibûdinanèiø minimizuojanèiø S− j ir maksimizuojanèiø S+ j ávertintø normalizuotø rodikliø sumos: S −1 = 0,2000 + 0,0264 + 0,0341 + 0,0113 + 0,0317 + 0,0044 + 0,0049 = 0,3127; S +1 = 0,0990; S − 2 = 0,3409; S + 2 = 0,0941; S −3 = 0,3098;

S + 3 = 0,0970;

S − 4 = 0,3148;

S + 4 = 0,0710;

S −5 = 0,0284;

S + 5 = 0,0760.

Ðiuo atveju S+ j ir S− j dydþiai iðreiðkia lyginamaisiais objektais pasiektø tikslø lygá. Bet kuriuo atveju visø lyginamøjø objektø pliusø S+ j ir minusø S− j sumos visada yra atitinkamai lygios visoms maksimizuojanèiø ir minimizuojanèiø kriterijø reikðmingumø sumoms: S − = 0,3127 + 0,34091 + 0,3098 + 0,3148 + 0,0284 = 1,3066; S + = 0,4371.

Nustatomas kiekvieno lyginamojo ir vertinamojo objekto santykinis reikðmingumas: Q1 =0,4104; Q2 =0,3798; Q3 =0,4113; Q4 =0,3803; Q5 =0,4182.

Pirmame artëjimo cikle naudingiausiu pagal naudojimo paskirtá buvo pripaþintas lyginamasis objektas, esantis Anomisliø kaime N5 = 100 %, antrasis pagal naudingumà – lyginamasis objektas, esantis Juodënø kaime N3= 98,37 %, ir treèiasis – vertinamasis objektas, esantis Anomisliø kaime (2 lent.). Vëliau buvo nustatytas lyginamøjø ir vertinamojo objektø efektyvumo lygis E xj . Jis rodo, kiek procentø yra geresnis (blogesnis) vertinamasis objektas, palyginti su lyginamaisiais objektais, ir jie lyginami tarpusavyje.

3.2.2. Pirmo artëjimo skaièiavimo rezultatai Pirmame artëjimo cikle vertinamojo objekto pradinë vertë buvo prilyginta lyginamøjø objektø pardavimo kainø vidurkiui, t. y. 39 500 Lt (1 lent.). Sudarius kriterijø sistemà ir nustaèius jø reikðmes bei reikðmingumus, buvo parengta sugrupuota sprendimø priëmimo matrica (1 lent.). Remiantis ðia matrica buvo suskaièiuoti kriterijø reikðmingumai (2 lent.):

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1 lentelë. Pradiniai duomenys poilsio sodybos daugiakriterinei analizei atlikti *

Kriterijaus matavimo vienetas

Kriterijaus reikðmingumas

Vertinamoji sodyba

Pardavimo kaina (pradinë vertë)

–

Lt(t)

1,0

1 X

2 44,0

3 40,0

4 36,0

5 38,0

Atstumas nuo poilsio sodybos iki Vilniaus

–

km

0,1358

72

78

70

80

70

Atstumas nuo poilsio sodybos iki eþero

–

km

0,1477

0,60

0,50

0,50

0,70

0,30

Atstumas nuo poilsio sodybos iki miðko

–

km

0,1238

0,10

0,30

0,30

0,30

0,10

Atstumas nuo poilsio sodybos iki kaimyno

–

km

0,0951

0,50

0,10

0,10

0,30

0,50

Atstumas nuo poilsio sodybos iki plento

–

km

0,0215

4,00

8,00

3,00

3,00

1,50

Atstumas nuo poilsio sodybos iki gyvenvietës

–

km

0,0389

2,00

5,00

4,00

3,00

2,00

Gyvenamojo namo bendrasis plotas

+

m2

0,0461

80,00

80,00

80,00

70,00

65,00

Gyvenamojo namo bûklë

+

balai

0,1065

0,80

0,80

0,70

0,60

0,70

Pagalbiniø pastatø skaièius

+

vnt.

0,0179

3

3

2

2

1

Þemës sklypo plotas

+

ha

0,0789

1,00

0,70

2,00

0,50

0,60

Nagrinëjami kriterijai

Lyginamosios poilsio sodybos

Vietovës kraðtovaizdis

+

balai

0,1106

1,00

1,00

0,60

0,60

0,80

Rajono prestiþas

+

balai

0,0120

1,00

1,00

1,00

1,00

1,00

Oro, aplinkos uþterðtumo ir triukðmo lygis

+

balai

0,0652

1,00

1,00

0,80

1,00

0,80

* + (-) rodo, kad atitinkamai didesnë (maþesnë) kriterijaus reikðmë labiau atitinka suinteresuotos þmoniø grupës interesus.

Pavyzdþiui:

3.2.3. Galutiniai rezultatai Kaip matome ið 2 lentelës, pirmame artëjimo cikle naudingiausias pagal naudojimo paskirtá yra lyginamasis objektas, esantis Anomisliø kaime N5 =100 %, antrasis pagal naudingumà – lyginamasis objektas, esantis Juodënø kaime N3 = 98,37 %, ir treèiasis – vertinamasis objektas, esantis Anomisliø kaime (N1 = 98,14 %). Kaip matome ið apskaièiuotø objektø naudingumo procento, vertinamosios poilsio sodybos pradinë vertë x = 39 500 Lt yra per maþa, dël to ðis objektas nëra vienodai konkurencingas rinkoje, palyginti su kitomis sodybomis, kompleksiðkai ávertinus jø teigiamas ir neigiamas savybes. Tà patvirtina ir nelygybë kax =6,22>1 %. Remiantis ðia nelygybe buvo nustatyta, kad dar nepakankamai tiksliai apskaièiuota vertinamosios poilsio sodybos vertë. Todël, remiantis vertinamojo nekilnojamojo turto objekto rinkos vertës skaièiavimo struktûrine schema (pateikta adresu http://193.219.145.99/PROJ2/TEORIJA/ teorija1.htm), skaièiavimø ciklai buvo tæsiami tol, kol vertinamojo objekto naudingumo procento vidutinis nukrypimas atitiko nelygybæ  kax < 1 %.

E11 = 98,14 % − 98,14 % = 0,000 %; E12 = 98,14 % − 90,81 % = 7,33 %; E13 = 98,14 % − 98,37 % = −0,23 %; E14 = 98,14 % − 90,95 % = 7,19 %; E 21 = −7,33 %; E 22 = 0,000 %; E 23 = −7,56 %; E 24 = −0,14 %; E 25 = −9,19 %.

Vëliau buvo apskaièiuotas vertinamojo objekto naudingumo procento vidutinis nukrypimas k x , nuo kurio ir priklauso, ar kitu etapu iðkart bus nustatoma vertinamojo objekto rinkos vertë, ar bus tik patikslinta pradinë vertë ir kartojamas artëjimo ciklas. Po pirmojo artëjimo vertinamojo objekto naudingumo procento vidutinis nukrypimas k x neatitiko metodo nelygybës  kax < 1 %, gautas toks rezultatas:

kax =6,22>1. Tuomet buvo patikslinta vertinamojo objekto vertë:

V1 = 39 500 (1+6,22/100) = 41 956,48 Lt. Patikslinus vertinamojo objekto vertæ, pagal metodo struktûrinæ schemà toliau eina metodo artëjimo ciklas.

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2 lentelë. Poilsio sodybø daugiakriterinës analizës rezultatai (1 artëjimo ciklas, X = 39 500) *

Poilsio sodybos (normalizuotø ávertintø kriterijø skaitmeninës reikðmës dij)

Nagrinëjami kriterijai Pardavimo kaina (pradinë vertë)

1 0,2000

-

2 0,2228

3 0,2025

4 0,1823

5 0,1924

Atstumas nuo poilsio sodybos iki Vilniaus

-

0,0264

0,0286

0,0257

0,0294

0,0257

Atstumas nuo poilsio sodybos iki eþero

-

0,0341

0,0284

0,0284

0,0398

0,0170

Atstumas nuo poilsio sodybos iki miðko

-

0,0113

0,0338

0,0338

0,0338

0,0113

Atstumas nuo poilsio sodybos iki kaimyno

-

0,0317

0,0063

0,0063

0,0190

0,0317

Atstumas nuo poilsio sodybos iki plento

-

0,0044

0,0088

0,0033

0,0033

0,0017

Atstumas nuo poilsio sodybos iki gyvenvietës

-

0,0049

0,0122

0,0097

0,0073

0,0049

Gyvenamojo namo bendras plotas

+

0,0098

0,0098

0,0098

0,0086

0,0080

Gyvenamojo namo bûklë

+

0,0237

0,0237

0,0207

0,0178

0,0207

Pagalbiniø pastatø skaièius

+

0,0049

0,0049

0,0033

0,0033

0,0016

Þemës sklypo plotas

+

0,0164

0,0115

0,0329

0,0082

0,0099

Vietovës kraðtovaizdis

+

0,0277

0,0277

0,0166

0,0166

0,0221

Rajono prestiþas

+

0,0024

0,0024

0,0024

0,0024

0,0024

Oro, aplinkos uþterðtumo ir triukðmo lygis

+

0,0142

0,0142

0,0113

0,0142

0,0113

Maksimizuojanèiø normalizuotø ávertinimø rodikliø suma S+j

0,0990

0,0941

0,0970

0,0710

0,0760

Minimizuojanèiø normalizuotø ávertinimø rodikliø suma S-j

0,3127

0,3409

0,3098

0,3148

0,0284

Nekilnojamojo turto objektø reikðmingumas Qj

0,4104

0,3798

0,4113

0,3803

0,4182

3

5

2

4

1

98,14%

90,81%

98,37%

90,95%

100%

6,22%

–12,10%

6,78%

–11,77%

10,87%

Nekilnojamojo turto objektø prioritetas Nekilnojamojo turto objektø naudingumo procentas Nj Nekilnojamojo turto objektø konkurencingumas kx Vertinamojo objekto patikslinta vertë Vxp

41956,48

• + (-) rodo, kad atitinkamai didesnë (maþesnë) kriterijaus reikðmë labiau atitinka suinteresuotos þmoniø grupës reikalavimus.

Ðiø skaièiavimø ciklø rezultatas – vertinamosios poilsio sodybos Anomisliø kaime patikslintos vertës kitimas ir rinkos vertës nustatymas – pateiktas 3 lentelëje.

Kaip matome, pirmame cikle vertinamojo objekto naudingumo procento vidutinis nukrypimas neatitiko nelygybës  kax < 1 %, bet jau antrajame cikle ði nelygybë buvo patenkinta, o tai reiðkia, kad vertinamosios sodybos rinkos vertë buvo nustatyta teisingai. Paskutiniame – antrajame artëjimo cikle nustatyta, kad vertinamojo objekto naudingumas lyginamøjø objektø atþvilgiu yra N1= 95,22 %, lyginamojo objekto, esanèio Anomisliø kaime, N5 = 100 %, o kito lyginamojo objekto, esanèio Juodënø kaime, jis liko nepakitæs per visus artëjimo ciklus – N3 = 98,30 %. Apskaièiuoti objektø naudingumo laipsniai rodo, kad vertinamas objektas yra naudingesnis 10,70 % uþ lyginamàjá objektà, esantá Magiðkiø kaime, ir 12,44 % maþiau naudingas uþ lyginamàjá objektà, esantá Anomisliø kaime. Ðie skaièiai taip pat rodo, á kurá objektà labiau apsimoka investuoti pinigus.

3 lentelë. Vertinamojo objekto naudingumo lygio vidutinio nukrypimo ir patikslintos vertës kitimas bei rinkos vertës nustatymas

Artëjimo Vertinamojo ciklas objekto patikslinta vertë Vxp (Lt)

Vertinamojo Vertinamojo objekto objekto rinkos naudingumo vertë lygio vidutinis V (Lt) x nukrypimas kx (%)

1 2

½6,22½>1 ½0,49½<1

39 500 41 956,48

41956,48 (1+0,49:100)= 42 162,95 » 42 000 Lt

4. Iðvados Daugelis elektroninës prekybos sistemø apdoroja ir teikia tik ekonominæ informacijà, taiko ekonominius modelius. Taèiau nagrinëjamas alternatyvas daþnai reikia ver-

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tinti ne tik ekonominiu, bet taip pat ir kokybiniu, techniniu, teisiniu, socialiniu ir kitokiu atþvilgiu. Remiantis informaciniø, ekspertiniø, sprendimø paramos ir elektroninës prekybos sistemø analize, buvo sukurta daugiakriterinë nekilnojamojo turto elektroninës prekybos (NTEP) sistema. Ði sistema sudaryta ið duomenø bazës bei duomenø bazës valdymo sistemos, modeliø bazës bei modeliø bazës valdymo sistemos ir vartotojo interfeiso. Duomenø bazëje nekilnojamàjá turtà apraðant kiekybine ir koncepcine formomis, pateikiama ávairius jo aspektus (ekonominius, kokybinius, techninius, teisinius, socialinius, ekologinius ir kt.) apibûdinanti informacija. Remdamasi ðia informacija NTEP sistema gali ávertinti nekilnojamàjá turtà ávairiais aspektais (t. y. rinkos vertës, mokestinës, investicinës vertës, esamo naudojimo rinkos vertës ir kt. verèiø nustatymas); ji gali ávertinti kriterijus, turinèius átakos vertei (pavyzdþiui, nekilnojamojo turto vietos, nusidëvëjimo, pasiûlos, paklausos ir kt. ávertinimas), nustatyti maksimalaus ir geriausio panaudojimo variantà (pavyzdþiui, pirkëjas bûstà renkasi maksimaliai tenkindamas gyvenimo bûtinumo, komfortiðkumo bei asmeninius poreikius). Taikant sukurtà PEB sistemà, nustatyta poilsio sodybos, esanèios Anomislio kaime, Toliejø seniûnijoje, Molëtø rajone, rinkos vertë (42 000 Lt) ir kompleksiðkai ávertintos vertinamojo ir lyginamøjø objektø teigiamos ir neigiamos savybës.

Harpin, S. The definitive European Internet start-up guide, Macmillan press ltd, New York, 2000. 383 p.

2.

Eager, B.; McCall, C. Online marketing. A division of Macmillan, Indianapolis, 2000. 297 p.

3.

Patel, B. Trading online. Pearson education limited. London, 1999. 362 p.

Janal, D. S. Marketing on the Internet. John Wiley & Sons inc, 2000. 392 p.

5.

Chen, H.; Chung, Y. M.; Ramsey, M. Intelligent spider for Internet searching. In: Proceedings of the 30th Hawaii International Conference on Systems Science. IEEE Press, Los Alamitos, CA, 1997, p. 178–188.

6.

Dekleva, S.; Zupancic, J. Key issues in information systems management: a Delphi study in Slovenia. Information and Management, 1996, p. 1–11.

7.

Goul, M.; Philippakis, A.; Kiang, M. Y.; Fernandes, D.; Otondo, R. Requirements for the design of a protocol suite to automate DSS deployment on the World Wide Web: a client/server approach. Decision Support Systems, 1997, p. 151–170.

8.

Zavadskas, E. K.; Kaklauskas, A.; Raslanas, S.; Krutinis, M.; Malienë, V. Property e-business system. Joint meeting of CIB W55/W65 and TG23/TG31/TG35 working commissions. Department of construction management & engineering, University of Reading, UK, 2000, p. 56–58.

9.

Zavadskas, E. K.; Kaklauskas, A.; Raslanas, S.; Krutinis, M. A multiple criteria property e-business system. In: Meeting of the European working group “Multicriteria AIDS for decisions”. Vilnius, 2000, p. 21–24.

10. Kaklauskas, A.; Zavadskas, E. K. Web based decision support (Internetinë sprendimø parama). Vilnius: Technika, 2002. 291 p. (in Lithuanian). 11. Zavadskas, E. K.; Kaklauskas, A.; Raslanas, S. Analysis of general state, simulation and forecast of real estate development in Lithuania, real estate, economics, management (Àíàëèç îáùåãî ñîñòîÿíèÿ, ìîäåëèðîâàíèå è ïðîãíîç ðàçâèòèÿ ñåêòîðà íåäâèæèìîñòè â Ëèòâå, íåäâèæèìîñòü, ýêîíîìèêà, óïðàâëåíèå). ACB, 3–4/ 2002, p. 76–80 (in Russian).

Literatûra 1.

4.

12. Zavadskas, E. K.; Kaklauskas, A.; Raslanas, S.; Malienë, V. The application of multi-criteria methods for valuation recreation property. Civil Engineering (Statyba), Vol 7, No 4. Vilnius: Technika, 2001, p. 327–333 (in German).

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PROF. HABIL. DR. RIMGAUDO ABRAIÈIO MONOGRAFIJOS „TECHNINËS KERAMIKOS TECHNOLOGIJA IR SAVYBËS“ II DALIES RECENZIJA Atsirandant vis daugiau techninës keramikos panaudojimo galimybiø, pasigendama knygø valstybine kalba apie mokslinius darbus ir technologijø ðioje srityje spartø tobulëjimà. Profesoriaus habilituoto daktaro Rimgaudo Abraièio 1999 m. iðleista knyga „Techninës keramikos technologijos“ jau tapo retenybe. Todël jo sumanymas iðleisti naujà knygà yra sveikintinas, tuo labiau, kad tai pirmoji Lietuvoje didelë monografija techninës keramikos klausimais. Rengiant monografijà atliktas kruopðtus ir sudëtingas darbas. Joje iðanalizuoti naujausi techninës keramikos technologijos laimëjimai. Kadangi buvo parengta didelës apimties monografija, knygos recenzentas prof. S. Boèkus pasiûlë jà iðspausdinti dviem knygomis. Pirmoji knygos dalis, iðleista 2002 m., buvo gerai ávertinta prof. A. Laukaièio recenzijoje, iðspausdintoje Lietuvos mokslø akademijos þurnale „Energetika“ (2003, Nr. 1). Antroji knygos dalis, iðvydusi ðviesà 2003 m., dar laukia platesnio ávertinimo. Monografijos antroji dalis pradedama oksidiniø medþiagø, jø savybiø ir panaudojimo pristatymu. Apraðoma korundinës keramikos jos gamybos technologija, cheminis atsparumas. Pristatoma bioinertinë ir bioaktyvi keramika. Sunkiai besilydanèiø medþiagø pluoðtinës formos gaminiai – tai efektyvi keraminiø medþiagø klasë. Pirmajame skyriuje aptariami monokristalai, kompozitai ir padengimai. Antrasis knygos skyrius skirtas urano junginiams ir jø panaudojimo problemoms. Uranas su deguonimi sudaro ávairaus oksidacijos laipsnio oksidus, todël jie apraðomi plaèiau. Nagrinëjamos jø bûvio diagramos bei terminis atsparumas. Apraðomas uranilo ryðys – pagrindinë aukðèiausio valentinio bûvio urano egzistavimo forma. Plaèiai apraðoma ir urano-plutonio-deguonies sistema. Urano junginiø gaminiai ir jø panaudojimas nagrinëjamas pradedant nuo jø radioaktyvumo, branduoliø skilimo, baigiant reaktoriø tipais ir konkreèiai Ignalinos AE branduoliniu reaktoriumi RBMK-1500. Pateikiami reaktoriaus saugos principai ir skilimo produktø barjerai. Supaþindinama su ðilumos iðsiskyrimo procesu reaktoriaus medþiagose. Iðnagrinëtos maþai apraðytos branduolinio kuro gamybos technologijos ir charakteristikos. Pabrëþiami kuro tableèiø gamybos ypatumai. Nagrinëjamas urano oksido milteliø sukepimo proceso sàryðys su produkcijos kokybe bei struktûriniø kuro tableèiø charakteristikø tobulinimas, siekiant geresnio jø panaudojimo. Apraðomi árenginiai ir mechaniniø medþiagø bandymø branduoliniuose reaktoriuose metodikos.

Magnio oksido ir cirkonio dioksido keramikos analizuojamos treèiajame ir ketvirtajame skyriuose. Tai aukðtatemperatûriai oksidai, plaèiai taikomi technikoje. Senëjant magnio oksido keramikai keièiasi jo struktûra, o cirkonio dioksido stabilizavimo procesas vyksta labai patikimai. Tai ir leidþia iðsaugoti keramikos struktûrà. Pateikta iðsami proceso analizë. Elektrokeraminës medþiagos – tai titano oksido arba ðarminiø þemës metalø titanatai. Be to, tai junginiai, kuriø didelë dielektrinë skvarba. Apraðoma kondensatorinë keramika ið titano oksido medþiagos, gamybos technologijoje kartais pasitaikantys ávairûs poliarizacijos mechanizmai, krûvio ir srovës susidarymas dielektrikuose. Plaèiai apraðomos elektrotechninës porceliano medþiagos. Visa tai pateikta penktajame skyriuje. Techninës keramikos magnetinës savybës sukuriamos ir valdomos gamybos metu, todël ypaè svarbu iðmanyti ðià technologijà. Ðeðtajame skyriuje analizuojamos pagrindinës polikristaliniø feroelektrikø ir pjezoelektrikø savybës, bario titanato keramika ir pjezokeramikos sintezë. Kermetø gamyboje taikoma daugybë technologijø. Septintajame skyriuje aptariamos technikoje plaèiausiai taikomos technologijos. Tam taikomos termitinës reakcijos. Ypaè svarbios yra þinios apie milteliø uþsiliepsnojimo ir sprogimo savybes. Anksèiau ðios savybës bûdavo aptariamos tik specialiuosiuose þinynuose. Ðioje monografijoje autorius atkreipia á tai dëmesá, stengdamasis apsaugoti technologus nuo galimø pavojø. Pateikiamas ir keraminiø milteliø toksiðkumo ávertinimas bei jø poveikis gyvajam organizmui. Plaèiai paplitusi silikatø ir aliumosilikatø keramika sudaro didelæ medþiagø grupæ. Ðios medþiagos turi dominuojanèià fazæ ir dvigubas bei trigubas kristalines sudëtis. Gamybai naudojamos pigios ir plaèiai þinomos þaliavos – molis ir talkas. Sukepimo temperatûroje susidaro kristalinës ir skystosios faziø pusiausvyra. Aðtuntajame skyriuje nagrinëjami ir tirpikliai. Tai tokios medþiagos, kurios iðdegant gaminius sàveikauja su ákrovos þaliavomis, sudarydamos lengvai besilydanèius junginius. Apþvelgiamos steatitinës, mulitinës, mulitinës-korundinës, divininës, kordieritinës, celzianinës, lièio, cirkonio, ðpineliø keramikos gamybos technologijos. Bedeguoniø junginiø keramikai skirtas devintasis skyrius. Tai karbidai, nitridai, boridai, silicidai. Ðie junginiai turi kovalentiná cheminio ryðio tipà, kartais su daline jonine dedamàja. Tai rodo mechaniniø savybiø stabilumà plaèiu temperatûrø intervalu, didelá ðilumos laidumà. Ðioms medþiagoms taikoma trapiøjø medþiagø

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privalumai ir trûkumai. Iðnagrinëti ir oksidiniai kuro elementai, jø veikimo schemos, praktinis pritaikymas. Techninës keramikos technologijos visà laikà tobulëja – nuolat taikant naujus tyrimø metodus gaunami atsakymai ir á svarbius gamybos vystymo klausimus. Knygoje yra neþymiø trûkumø. Pavyzdþiui, technologijos naujoves galbût reikëtø apraðyti kiek plaèiau. Kai kur neiðvengta ir korektûros klaidø. Apskritai prof. R. Abraièio monografijos „Techninës keramikos technologija ir savybës“ antroji dalis yra informatyvi, lengvai skaitoma, joje apþvelgiama daug ðios srities naujoviø. Todël galime teigti, jog sulaukëme brandaus ilgameèio darbo rezultatø techninës keramikos savybiø ir technologijø tema. Ði knyga bus naudinga mokslininkams – medþiagotyros, ið dalies ir statybos inþinerijos specialistams, ji pravers ir studentams, studijuojantiems techninæ keramikà.

konstrukcinio stiprumo skaièiavimo metodika, kuria ávertinamas átempimø intensyvumo koeficientas. Unikaliø savybiø techninës keramikos gamyba remiasi naujausia teorija, technologijomis, kryptingai sintetinant medþiagà, numatant bûsimà jos struktûrà. Tokios struktûros dirbiniø paslaptys atskleistos deðimtajame skyriuje. Jame raðoma apie veiksnius, turinèius átakos medþiagø savybëms, etapø tarpusavio ryðiams, agregacijos átakai, reguliavimui modifikuojanèiais priedais, jø parinkimui, rekristalizacijos procesams ir greièiams bei gavimo technologiniams metodams. Taip sukuriama ypaè stipri cirkonio dioksido keramika. Ji plaèiai naudojama elektronikoje, maðinø gamyboje, aviacijos technikoje, raketø gamyboje. Kaip kompleksiðkai panaudoti techninæ keramikà, apraðyta vienuoliktame knygos skyriuje. Nagrinëjami keraminiai kuro elementai ir juose vykstantys procesai, kuriuose reakcijos cheminë energija paverèiama elektros energija. Pristatytos tipiniø kuro elementø schemos, jø

Prof. habil. dr. Romualdas Maèiulaitis

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SANTRAUKOS P. Aliavdin, V. Simbirkin, V. Toropov. Mûriniø sienø plokðtumø atsparumas ðlyèiai ir gniuþdymui // Journal of Civil Engineering and Management. Vilnius: Technika, 2004, Vol X, Suppl 1, p. 3–9. Pateikti mûriniø bandiniø – sienuèiø tyrimø rezultatai. Bandiniams naudotos efektyvios plytos, apkrauta sienuèiø plokðtuma: • horizontaliàja (ðonine) koncentruota apkrova, esant skirtingam vertikalios priekrovos lygiui; • sukoncentruota gniuþdymo jëga, pridëta ávairiais atstumais nuo sienos kraðto. Iðvestos sienuèiø ðlyties stiprumo ir deformavimo priklausomybës nuo gniuþdymo átempiø, veikianèiø statmenai kirpimo plokðtumai. Be to, ávertintas mûro glemþimo stipris priklausomai nuo koncentruotos apkrovos pridëjimo vietos sienutës kraðto atþvilgiu. Atlikta tyrimø rezultatø analizë, o gauti rezultatai palyginti su rezultatais, gautais, taikant ávairiø projektavimo normø metodikas. Atliktas eksperimentiniø bandiniø skaitinis modeliavimas taikant baigtiniø elementø metodà. Raktaþodþiai: mûrinës konstrukcijos, natûralaus dydþio bandiniai, ðlytis, gniuþdymas, stipris, poslinkiai.

D. Baèinskas, G. Kaklauskas, E. Geda. Baigtiniø elementø programos ATENA pritaikymas aukðta temperatûra paveiktø gelþbetoniniø sijø netiesinei analizei // Journal of Civil Engineering and Management. Vilnius: Technika, 2004, Vol X, Suppl 1, p. 11–18. Gaisro paveiktø gelþbetoniniø elementø átempiø ir deformacijø bûvis yra sudëtingas. Pateikiama gelþbetoniniø konstrukcijø, paveiktø aukðta temperatûra ir apkrautø iðorine apkrova, skaitinio modeliavimo strategija. Literatûroje apraðytø eksperimentiniø sijø apkrovos ir álinkiø diagramos nustatytos, taikant baigtiniø elementø programà ATENA. Skaitiniam modeliavimui naudoti Eurocode 2 fiziniai betono ir armatûros modeliai. Lyginami skaitinës analizës ir eksperimentiniai tyrimø rezultatai. Raktaþodþiai: gelþbetoniniø konstrukcijø projektavimas gaisro atveju, baigtiniø elementø netiesinë analizë, gaisro bandymai, atsparumas gaisrui, betono ir armatûros medþiagø modeliai.

Z. Bednarek, R. Kamoèka. Statybiniø plienø temperatûriniø deformacijø analizë, veikiant kintamiems temperatûriniams laukams // Journal of Civil Engineering and Management. Vilnius: Technika, 2004, Vol X, Suppl 1, p. 19–22. Pateikta temperatûriniu lauku paveikto plieno deformacijø, sparèiai kylant temperatûrai, analizë. AIII klasës, 34GS markës statybiniam plienui pateikti temperatûrinio plëtimosi sukeltø temperatûriniø deformacijø bei tiesinio temperatûrinio plëtimosi koeficiento eksperimentiniø tyrimø rezultatai. Bandymai atlikti esant tiesiniam temperatûros kitimui bei skirtingiems kaitinimo greièiams. Atlikta kaitinimo greièio átakos temperatûrinëms deformacijoms ir temperatûrinio plëtimosi koeficientui analizë. Raktaþodþiai: temperatûrinis plëtimasis, temperatûrinës deformacijos, tiesinio temperatûrinio plëtimosi koeficientas, statybinis plienas.

R. Èechavièius. Spragotiniø ilginiø dantytøjø „Bulldog“ tipo sprausteliø metalo-medþio jungèiø slinktis // Journal of Civil Engineering and Management. Vilnius: Technika, 2004, Vol X, Suppl 1, p. 23–29. Kompozitiniai metalo-medþio spragotiniai ilginiai, sukurti AB „MacMillan“ (Kanada), pasiþymi daugeliu technologiniø ir konstrukciniø privalumø. Tokiø ilginiø medinës juostos su metaliniais trikampio tinklelio elementais yra jungiamos vienpusiais dantytaisiais „Bulldog“ tipo sprausteliais. Apraðyti keturiø tokiø natûralaus dydþio spragotiniø ilginiø (tarpatramis – 3,0 m) bandymai. Bandymais nustatyta, kad metalo-medþio jungèiø su „Bulldog“ tipo sprausteliais atsparumas, slinkties modulis bei statinës slinkties dydis priklauso nuo kampo tarp jëgos ir medienos pluoðtø krypties, slinkties modulio ir statinës slinkties skaitinës reikðmës yra gerokai didesnës nei pateiktos eksperimentinëse Europos normose (Eurocode 5). Bandymais nustatyta, kad áràþos tarp santvaros tinklelio elementø persiskirsto tuomet, kai metalo-medþio jungèiø su „Bulldog“ tipo sprausteliais slinkties deformacijos tampa artimos ribiniam (2 mm) dydþiui. Raktaþodþiai: kompozitinë konstrukcija, metalo-medþio jungtis, „Bulldog“ tipo spraustelis, slinktis, atsparumas, bandymas.

W. Lu, P. Makelainen, J. Kesti, J. Lindborg. Ðaltai formuotø plieno lakðtø optimalus projektavimas taikant genetinius algoritmus // Journal of Civil Engineering and Management. Vilnius: Technika, 2004, Vol X, Suppl 1, p. 31–37. Profiliuoti ðaltai formuoti plieno lakðtai daþnai naudojami stogo, grindø sistemø bei sienø apdarui. Dël didelës rinkoje esanèiø profiliø ávairovës naudinga nustatyti optimalià lakðto formà. Ðaltai formuotø profiliuotø plieno lakðtø matmenims optimizuoti naudoti genetiniai algoritmai. Optimizavimo tikslas – nustatyti profiliuotø lakðtø optimalius matmenis, kai lakðto svoris yra minimalus esant nustatytai atrëmimo schemai. Lakðtai projektuojami remiantis Eurocode 3 1.3 dalies nurodymais. Gautos nesudëtingos lakðtø formos gali bûti pateiktos plieniniø konstrukcijø projektuotojams bei plieno gamintojams. Raktiniai þodþiai: ðaltai formuotas plienas, profiliuoti lakðtai, optimizavimas, genetinis algoritmas.

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A. Naujokaitis. Relations between the characteristics of components of decorative compact silicate concrete mix // Journal of Civil Engineering and Management. Vilnius: Technika, 2004, Vol X, Suppl 1, p. 39–43. The article investigates the influence of components of decorative compact silicate concrete mix and the dependence of its characteristics. The work reveals the characteristics of components influencing the properties of silicate decorative concretes with precise dimensions. The greatest influence is produced by the granulometric composition of a mix. It has an effect on the homogeneity of mix compaction, the precision of dimensions of formed product and on the product compaction. The analysis was performed by means of computer-registered data of a new press. For the investigation under production conditions the quartz sands from Giraitë deposit, medium fine to fine ones and practically free of any impurities, were used. A new technique for selecting the mix compositions with colouring pigments is offered. It takes into account the characteristics of binders with a pigment. The research results can be used in the production of decorative products with precise dimensions. Keywords: components, silicate concrete, concrete composition, sand, grain composition, pigments, sand fineness, products with precise-dimensions, compaction rate.

M. J. Sulewska. Pylimø tankinimo kontrolë ðiuolaikiniu metodu // Journal of Civil Engineering and Management. Vilnius: Technika, 2004, Vol X, Suppl 1, p. 45–50. Lengvasis dinaminis zondas – prietaisas lauko bandymams. Jis taikomas ávairiø tipø grunto pylimø laikomosios galios ir sutankinimo kokybës greitai kontrolei. Tai ðiuolaikinis átaisas, kuris daþnai taikomas Vokietijoje, o ðiuo metu ir Lenkijoje. Straipsnyje pateikti lengvojo dinaminio zondo kalibravimo laboratorijoje ir statybos aikðtelëje pavyzdys bei ðio átaisø pritaikymas realaus pylimo tyrimui. Raktiniai þodþiai: pylimai, sutankinimo kontrolë, lengvas dinaminis zondas, grunto dinaminis deformacijø modulis.

R. Ðukys. Perspectives and problems of health and safety in construction // Journal of Civil Engineering and Management. Vilnius: Technika, 2004, Vol X, Suppl 1, p. 51–55. Now, when Lithuania became a part of the EU, it is important to estimate results of integration effects in social, economic and other areas. One of underlying areas is workers’ health and safety. Building is one of the most dangerous work areas (work nature and place often changes, a lot of work is done under dangerous conditions and in bad weather). The purpose of research is to estimate qualitative and quantitative effects, which Lithuania’s building companies experience while implementing EU Councils Directive 92/57EEC “About minimal health and safety requirements on temporal and movable building sites”. Statistical analytical, poll, analysis, analogical, financial reports summation and other methods were used in this research. Financial costs, costs at the government level, positive consequences are determined and recommendations are elaborated. Keywords: integration, health and safety, EU Councils Directive 92/57EEC, financial costs, contracts.

S. Vakrinienë, P. Èyras, R. Ðukys. Traumata prevention resources optimization in construction // Journal of Civil Engineering and Management. Vilnius: Technika, 2004, Vol X, Suppl 1, p. 57–63. Analysis of data on accidents in construction companies shows that their main reasons are non-compliance of standard acts, wrongly organised work, the absence of security measures, wrongly organised work place, insufficient training of workers. Employers must know how to optimally distribute resources for accident prevention. That would help (on the average or with a particular probability) to reduce number of accidents and reduce social insurance costs. In this article the task of stochastic programming is analysed which models the resources reserved for preventing an accidents in construction. To get resources for accidents prevention at work, optimal distribution strategy, with desirable precision, we need to solve task of separable programming, whose zone of allowable plan is not prominent. In the article Lagrange multiplier’s essence for the studied problem and global extremums abstraction rule are estimated. When solving problems, pretty precise and reliable function dependencies between tasks parameters and solution are achieved. They allow to optimize the use of resources reserved for accidents at work in construction and shows expected numbers of avoided injuries dependence on confidence level and on variation of resources reserved for accidents at works in construction. Keywords: Accidents, prevention, optimal distribution of resources, stochastic programming, Lagrange function, KuhnTucker conditions, confidence level, resources variation.

V. Volkova. Dinamiðkai netiesiniø sistemø poliharmoniniø svyravimø identifikacija // Journal of Civil Engineering and Management. Vilnius: Technika, 2004, Vol X, Suppl 1, p. 65–70. Atliekant svyravimø analitiná tyrimà, bûtina turëti matematinius modelius. Tam naudojami techniniø brëþiniø ir apraðymø duomenys bei kita dokumentacija, susijusi su atskirø parametrø reikðmëmis. Kai kuriais atvejais ðios informacijos nepakanka. Pastaruoju atveju efektyviausi yra identifikacijos metodai. Juose matematiniai modeliai sudaromi pagal eksperimentiniø tyrimø duomenis. Raktaþodþiai: identifikacija, fazinës trajektorijos, poliharmoniniai svyravimai, dinamiðkai netiesinës sistemos.

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E. K. Zavadskas, A. Kaklauskas, S. Raslanas, M. Krutinis. Pecularities of multi-criteria e-trade system application in real estate sector // Journal of Civil Engineering and Management. Vilnius: Technika, 2004, Vol X, Suppl 1, p. 71–78. One of the major problems in Internet based information systems is to find what you want. Thousands of alternative products and services may be found on the Internet. How can customers find the rational products and services there? Once product or service information is found, the customer usually wants to compare alternatives. There are five types of aids to comparison shopping: search on hypertext files by agents, search alternatives on databases, alternative search and tabular comparison, comparison of alternative products and services from multiple malls, search and multiple criteria decision-making. Therefore, the efficiency of Internet based information systems may be increased by applying multiple criteria decision support systems developed by the authors. The authors have developed Internet Based DSS for Real Estate. Proposed Internet Based DSS for Real Estate can create value in the following ways: help customers assess their needs, identify suitable real estate to fulfil needs, compare and evaluate real estate, help customers evaluate the usefulness of the real estate in the after-purchase evaluation stage, etc. Keywords: Internet based information systems, DSS, multi-criteria analysis.

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ÐÅÔÅÐÀÒÛ Ï. Àëÿâäèí, Â. Ñèìáèðêèí, Â. Òîðîïîâ. Ñîïðîòèâëåíèå êèðïè÷íûõ ñòåí ñäâèãó è ñæàòèþ â èõ ïëîñêîñòè // Journal of Civil Engineering and Management. Âèëüíþñ: Òåõíèêà, 2004, X ò., Ïðèë. 1. C. 3–9. Ïðåäñòàâëåíû ðåçóëüòàòû èñïûòàíèé êèðïè÷íûõ îáðàçöîâ–ñòåíîê, âûïîëíåííûõ èç ýôôåêòèâíîãî êèðïè÷à, ïðè íàãðóæåíèè èõ â ñâîåé ïëîñêîñòè: • ãîðèçîíòàëüíîé (áîêîâîé) ñîñðåäîòî÷åííîé íàãðóçêîé ïðè ðàçëè÷íîì óðîâíå âåðòèêàëüíîãî ïðèãðóçà; • ñîñðåäîòî÷åííîé ñæèìàþùåé ñèëîé, ïðèëîæåííîé íà ðàçëè÷íîì ðàññòîÿíèè îò êðàÿ ñòåíêè. Âûÿâëåíû çàâèñèìîñòè ïðî÷íîñòè è äåôîðìàòèâíîñòè ñòåíîê ïðè ñäâèãå îò óðîâíÿ ñæèìàþùèõ íàïðÿæåíèé, äåéñòâóþùèõ ïåðïåíäèêóëÿðíî ïëîñêîñòè ñðåçà. Äàíà îöåíêà ïðî÷íîñòè êëàäêè íà ñìÿòèå â çàâèñèìîñòè îò ìåñòà ïðèëîæåíèÿ ñîñðåäîòî÷åííîé íàãðóçêè îòíîñèòåëüíî êðàÿ ñòåíêè. Âûïîëíåí àíàëèç ðåçóëüòàòîâ èñïûòàíèé è ñîïîñòàâëåíèå ðàñ÷åòíûõ ìåòîäèê, ïðèíÿòûõ â ðàçëè÷íûõ íîðìàõ ïðîåêòèðîâàíèÿ, à òàêæå ïðîâåäåíî ÷èñëåííîå ìîäåëèðîâàíèå ðàáîòû îïûòíûõ îáðàçöîâ íà îñíîâå ìåòîäà êîíå÷íûõ ýëåìåíòîâ. Êëþ÷åâûå ñëîâà: êàìåííûå êîíñòðóêöèè, êðóïíîìàñøòàáíûå èñïûòàíèÿ, ñäâèã, ñæàòèå, ïðî÷íîñòü, ïåðåìåùåíèÿ.

Ä. Áà÷èíñêàñ, Ã. Êàêëàóñêàñ, Å. Ãåäà. Ïðèìåíåíèå ïðîãðàììû ATENA â íåëèíåéíîì àíàëèçå æåëåçîáåòîííûõ áàëîê ïîäâåðæåííûõ âîçäåéñòâèþ âûñîêèõ òåìïåðàòóð // Journal of Civil Engineering and Management. Âèëüíþñ: Òåõíèêà, 2004, X ò., Ïðèë. 1. C. 11–18. Ñëîæíûì ÿâëÿåòñÿ íàïðÿæåííî-äåôîðìèðîâàííîå ñîñòîÿíèå æåëåçîáåòîííûõ ýëåìåíòîâ, ïîäâåðæåííûõ âîçäåéñòâèþ ïîæàðà. Ïðåäñòàâëåíà ñòðàòåãèÿ ÷èñëåííîãî ìîäåëèðîâàíèÿ íàãðóæåííûõ æåëåçîáåòîííûõ êîíñòðóêöèé, ïîäâåðæåííûõ âîçäåéñòâèþ âûñîêèõ òåìïåðàòóð. Äëÿ áàëîê äèàãðàììû íàãðóçêà-ïðîãèá áûëè ïîëó÷åíû ïðè ïîìîùè ïðîãðàììû ÀÒÅNÀ, èñïîëüçóþùåé â ðàñ÷¸òàõ ìåòîä êîíå÷íûõ ýëåìåíòîâ. Ïðè ÷èñëåííîì ìîäåëèðîâàíèè ïðèìåíÿëèñü ôèçè÷åñêèå ìîäåëè Eurocode 2 äëÿ áåòîíà è àðìàòóðû. Ïðåäñòàâëåí ñðàâíèòåëüíûé àíàëèç ðåçóëüòàòîâ ÷èñëåííîãî ìîäåëèðîâàíèÿ è ýêñïåðèìåíòàëüíûõ äàííûõ, ïîëó÷åííûõ èç ëèòåðàòóðíûõ èñòî÷íèêîâ. Êëþ÷åâûå ñëîâà: ïðîåêòèðîâàíèå æåëåçîáåòîííûõ êîíñòðóêöèé, ïîäâåðæåííûõ âîçäåéñòâèþ ïîæàðà, íåëèíåéíûé àíàëèç ñ èñïîëüçîâàíèåì ìåòîäà êîíå÷íûõ ýëåìåíòîâ, èñïûòàíèÿ ïðè ïîæàðå, îãíåñòîéêîñòü, ìîäåëè ìàòåðèàëîâ áåòîíà è àðìàòóðû.

Ç. Áåíäàðåê, Ð. Êàìî÷êà. Àíàëèç òåìïåðàòóðíûõ äåôîðìàöèé ñòðîèòåëüíûõ ñòàëåé ïîä âîçäåéñòâèåì ïåðåìåííûõ òåìïåðàòóðíûõ ïîëåé // Journal of Civil Engineering and Management. Âèëüíþñ: Òåõíèêà, 2004, X ò., Ïðèë. 1. C. 19–22. Ïðåäñòàâëåí àíàëèç äåôîðìàöèé ñòàëüíûõ ýëåìåíòîâ ïðè áûñòðîì ðîñòå òåìïåðàòóðû, âûçâàííûõ âîçäåéñòâèåì òåìïåðàòóðíûõ ïîëåé. Ïðåäñòàâëåíû ðåçóëüòàòû ýêñïåðèìåíòàëüíûõ èññëåäîâàíèé êîýôôèöèåíòà ëèíåéíîãî òåìïåðàòóðíîãî ðàñøèðåíèÿ è òåìïåðàòóðíûõ äåôîðìàöèé ñòðîèòåëüíîé ñòàëè êëàññà ÀIII, ìàðêè 34ÃÑ. Èñïûòàíèÿ ïðîâîäèëèñü ïðè ëèíåéíîì èçìåíåíèè òåìïåðàòóðû ñ ðàçëè÷íîé ñêîðîñòüþ å¸ ðîñòà. Ïðåäñòàâëåí àíàëèç âîçäåéñòâèÿ ñêîðîñòè ðîñòà òåìïåðàòóðû íà âåëè÷èíó òåìïåðàòóðíûõ äåôîðìàöèé è çíà÷åíèå êîýôôèöèåíòà òåìïåðàòóðíîãî ðàñøèðåíèÿ. Êëþ÷åâûå ñëîâà: òåìïåðàòóðíîå ðàñøèðåíèå, òåìïåðàòóðíûå äåôîðìàöèè, êîýôôèöèåíò ëèíåéíîãî òåìïåðàòóðíîãî ðàñøèðåíèÿ, ñòðîèòåëüíàÿ ñòàëü..

Ð. ×åõàâè÷þñ. Ïîäàòëèâîñòü çóá÷àòûõ øïîíîê òèïà "Áóëüäîã" â ìåòàëëî-äåðåâÿííûõ ñîåäèíåíèÿõ ñêâîçíûõ ïðîãîíîâ // Journal of Civil Engineering and Management. Âèëüíþñ: Òåõíèêà, 2004, X ò., Ïðèë. 1. C. 23–29. Êîìïîçèòíûå ìåòàëëî-äåðåâÿííûå ñêâîçíûå ïðîãîíû, ñîçäàííûå â ÀÎ "ÌàêÌèëëàí" (Êàíàäà), îáëàäàþò ðÿäîì òåõíîëîãè÷åñêèõ è êîíñòðóêòèâíûõ ïðåèìóùåñòâ. Äåðåâÿííûå ïîÿñà òàêèõ ïðîãîíîâ ñ ìåòàëëè÷åñêèìè ýëåìåíòàìè òðåóãîëüíîé ðåøåòêè ñîåäèíÿþòñÿ ïðè ïîìîùè îäíîñòîðîííèõ çóá÷àòûõ øïîíîê òèïà "Áóëüäîã".  ñòàòüå îïèñàíû èñïûòàíèÿ ÷åòûðåõ òàêèõ ïðîãîíîâ â íàòóðàëüíóþ âåëè÷èíó (ïðîëåò – 3 ì). Èñïûòàíèÿìè óñòàíîâëåíî, ÷òî íåñóùàÿ ñïîñîáíîñòü, ìîäóëü ïîäàòëèâîñòè è âåëè÷èíà ñòàòè÷åñêîé ïîäàòëèâîñòè çóá÷àòûõ øïîíîê òèïà Áóëüäîã" â ìåòàëëîäåðåâÿííûõ ñîåäèíåíèÿõ çàâèñÿò îò óãëà ìåæäó óñèëèåì è ñëîÿìè äðåâåñèíû. Óñòàíîâëåíî, ÷òî âåëè÷èíû ìîäóëÿ ïîäàòëèâîñòè è ñòàòè÷åñêîé ïîäàòëèâîñòè îêàçàëèñü çíà÷èòåëüíî áîëüøèìè, ÷åì âåëè÷èíû, ïðåäñòàâëåííûå â ýêñïåðèìåíòàëüíûõ íîðìàõ Åâðîïû (Eurocode 5). Èñïûòàíèÿìè òàêæå óñòàíîâëåíî, ÷òî ïåðåðàñïðåäåëåíèå óñèëèé ìåæäó ñòàëüíûìè ýëåìåíòàìè ðåøåòêè íà÷èíàåòñÿ ïðè ïðèáëèæåíèè ïîäàòëèâîñòè çóá÷àòûõ øïîíîê òèïà "Áóëüäîã" ê ïðåäåëüíîé âåëè÷èíå (2 ìì). Êëþ÷åâûå ñëîâà: êîìïîçèòíàÿ êîíñòðóêöèÿ, ìåòàëëî-äåðåâÿííîå ñîåäèíåíèå, øïîíêà òèïà "Áóëüäîã", ïîäàòëèâîñòü, íåñóùàÿ ñïîñîáíîñòü, èñïûòàíèå..

ÐÅÔÅÐÀÒÛ ....................................................................................................................................................................... IIb Â. Ëó, Ï. Ìàêåëàéíåí, È. Êåñòè, Þ. Ëèíäáîðã. Îïòèìàëüíîå ïðîåêòèðîâàíèå õîëîäíî ôîðìîâàííûõ ñòàëüíûõ ëèñòîâ ñ èñïîëüçîâàíèåì ãåíåòè÷åñêèõ àëãîðèòìîâ // Journal of Civil Engineering and Management. Âèëüíþñ: Òåõíèêà, 2004, X ò., Ïðèë. 1. C. 31–37. Ïðîôèëèðîâàííûå õîëîäíî ôîðìîâàííûå ñòàëüíûå ëèñòû ÷àñòî èñïîëüçóþòñÿ äëÿ ïîêðûòèÿ êðûø, íàñòèëà ïîëîâ è îòäåëêè ñòåí. Èç-çà îáèëèÿ âèäîâ ðàçëè÷íûõ ïðîôèëåé íà ðûíêå âûãîäíî îáëàäàòü ïðîôèëåì îïòèìàëüíîé ôîðìû.  ñòàòüå îïèñàí ïîäáîð îïòèìàëüíûõ ðàçìåðîâ ëèñòà äëÿ õîëîäíî ôîðìîâàííîãî ïðîôèëÿ ñ èñïîëüçîâàíèåì ãåíåòè÷åñêèõ àëãîðèòìîâ. Öåëüþ îïòèìèçàöèè áûëî ïðè èçâåñòíîé îïîðíîé ñõåìå ïîäîáðàòü îïòèìàëüíûå ðàçìåðû ïðîôèëèðîâàííîãî ëèñòà ñ öåëüþ ìèíèìèçèðîâàòü åãî âåñ. Ëèñòû ïðîåêòèðóþòñÿ ñîãëàñíî ðåêîìåíäàöèÿì ÷àñòè 3.1 Eurocode 3. Ïðîôèëèðîâàííûå ëèñòû íåñëîæíîé ôîðìû, ïîëó÷åííîé ñ èñïîëüçîâàíèåì îïèñàííîé ïðîöåäóðû, ìîãóò áûòü ïðåäñòàâëåíû ïðîèçâîäèòåëÿì è ïðîåêòèðîâùèêàì. Êëþ÷åâûå ñëîâà: õîëîäíî ôîðìîâàííàÿ ñòàëü, ïðîôèëèðîâàííûå ëèñòû, îïòèìèçàöèÿ, ãåíåòè÷åñêèé àëãîðèòì.

À. Íàóéîêàéòèñ. Âëèÿíèå ñâîéñòâ ñìåñè äåêîðàòèâíîãî ïëîòíîãî ñèëèêàòíîãî áåòîíà íà êà÷åñòâî èçäåëèé // Journal of Civil Engineering and Management. Âèëüíþñ: Òåõíèêà, 2004, X ò., Ïðèë. 1. C. 39–43. Èññëåäîâàíà çàâèñèìîñòü òåõíîëîãè÷åñêèõ ôàêòîðîâ îò ñâîéñòâ ñìåñè äåêîðàòèâíîãî ïëîòíîãî ñèëèêàòíîãî áåòîíà. Öåëüþ èññëåäîâàíèÿ áûëî îïðåäåëèòü, êàêèå òåõíîëîãè÷åñêèå ôàêòîðû ñèëèêàòíûõ ñìåñåé âëèÿþò íà ìèíèìàëüíûå îòêëîíåíèÿ îò ñòàíäàðòíûõ ðàçìåðîâ èçäåëèé äåêîðàòèâíîãî ñèëèêàòíîãî áåòîíà. Âûÿâëåíî, ÷òî íàèáîëüøåå çíà÷åíèå èìååò ãðàíóëîìåòðè÷åñêèé ñîñòàâ ñìåñè, âëèÿþùèé íà îäíîðîäíîñòü óïëîòíåíèé, ðàçìåðû è ïëîòíîñòü èçäåëèé. Èññëåäîâàíèå ïðîâîäèëîñü íà íîâîì ïðåññå, ðåãèñòðèðîâàâøåì äàííûå èññëåäîâàíèé â êîìïüþòåðå. Äëÿ èññëåäîâàíèé â ïðîèçâîäñòâåííûõ óñëîâèÿõ ïðèìåíÿëñÿ ïåñîê èç ìåñòîðîæäåíèÿ «Ãèðàéòå», ïðàêòè÷åñêè ìàëî çàãðÿçí¸ííûé ïðèìåñÿìè, ñðåäíåé òîíêîñòè è ìåëêèé. Ïðè èññëåäîâàíèè îïðåäåë¸í íîâûé ìåòîä ïîäáîðà ñîñòàâà äåêîðàòèâíîãî ñèëèêàòíîãî áåòîíà ñ êðàñÿùèìè ïèãìåíòàìè è îöåíêè ñâîéñòâ âÿæóùåãî ïèãìåíòà. Äàííûå èññëåäîâàíèé ïðèìåíÿþòñÿ äëÿ èçãîòîâëåíèÿ äåêîðàòèâíûõ ñèëèêàòîáåòîííûõ èçäåëèé â ïðîèçâîäñòâåííûõ óñëîâèÿõ. Êëþ÷åâûå ñëîâà: êîìïîíåíòû, ñèëèêàòíûé áåòîí, ñîñòàâ áåòîíà, ïåñîê, ãðàíóëîìåòðè÷åñêèé ñîñòàâ, äèñïåðñíîñòü ïåñêà, èçäåëèå òî÷íûõ ðàçìåðîâ, êîýôôèöèåíò óïëîòíåíèÿ.

Ì. È. Ñóëåâñêà. Êîíòðîëü óïëîòíåíèÿ íàñûïåé ñ èñïîëüçîâàíèåì ñîâðåìåííûõ ìåòîäîâ // Journal of Civil Engineering and Management. Âèëüíþñ: Òåõíèêà, 2004, X ò., Ïðèë. 1. C. 45–50. Ëåãêèé äèíàìè÷åñêèé çîíä – ýòî ïðèñïîñîáëåíèå äëÿ ïîëåâûõ èñïûòàíèé. Îí èñïîëüçóåòñÿ äëÿ áûñòðîãî êîíòðîëÿ íåñóùåé ñïîñîáíîñòè è êà÷åñòâà óïëîòíåíèÿ ãðóíòîâûõ íàñûïåé ðàçëè÷íîãî òèïà. Ýòîò ñîâðåìåííûé ìåòîä øèðîêî ïðèìåíÿåòñÿ â Ãåðìàíèè, à òåïåðü è â Ïîëüøå. Ïðåäñòàâëåíû ïðèìåðû êàëèáðîâêè ýòîãî ïðèñïîñîáëåíèÿ â ëàáîðàòîðíûõ óñëîâèÿõ è íà ñòðîèòåëüíîé ïëîùàäêå, à òàêæå ïðèìåíåíèå ë¸ãêîãî äèíàìè÷åñêîãî çîíäà äëÿ èññëåäîâàíèÿ ðåàëüíîé íàñûïè. Êëþ÷åâûå ñëîâà: íàñûïü, êîíòðîëü óïëîòíåíèÿ, ë¸ãêèé äèíàìè÷åñêèé çîíä, ìîäóëü äèíàìè÷åñêîé äåôîðìàöèè ãðóíòà.

Ð. Øóêèñ. Ïðîáëåìû è ïåðñïåêòèâû áåçîïàñíîñòè òðóäà è çäîðîâüÿ ðàáîòíèêîâ â ñòðîèòåëüñòâå // Journal of Civil Engineering and Management. Âèëüíþñ: Òåõíèêà, 2004, X ò., Ïðèë. 1. C. 51–55.  Ïîñëå âñòóïëåíèÿ Ëèòâû â Åâðîïåéñêèé Ñîþç åé âàæíî îïðåäåëèòü ïîñëåäñòâèÿ èíòåãðàöèè â ñîöèàëüíîé, ýêîíîìè÷åñêîé, õîçÿéñòâåííîé è äðóãèõ îáëàñòÿõ. Îäíîé èç íàèáîëåå ïðèîðèòåòíûõ îáëàñòåé ÿâëÿåòñÿ áåçîïàñíîñòü è çäîðîâüå òðóäÿùèõñÿ. Ñòðîèòåëüñòâî èç-çà ñïåöèôèêè ðàáîò (÷àñòîé ñìåíû âèäà è ìåñòà ðàáîòû, ðàáîò ñ ïîâûøåííûì ðèñêîì è â ðàçëè÷íûõ êëèìàòè÷åñêèõ óñëîâèÿõ) ÿâëÿåòñÿ îäíîé èç îïàñíåéøèõ ñôåð â õîçÿéñòâåííîé îáëàñòè. Öåëüþ èññëåäîâàíèé áûëî êàê ìîæíî òî÷íåå îïðåäåëèòü êîëè÷åñòâåííûå è êà÷åñòâåííûå âîçäåéñòâèÿ, èñïûòûâàåìûå ñòðîèòåëüíûìè îðãàíèçàöèÿìè Ëèòâû ïðè âíåäðåíèè äåðåêòèâû Åâðîïåéñêîãî Ñîþçà 92/52/ÅÅÑ COUNCIL DIRECTIVE 92/57/EEC of 24 June 1992 on the implementation of minimum safety and health requirements at temporary or mobile constructions sites (eighth individual Directive within the meaning of Article 16 (1) of Directive 89/ 391/EEC). Èññëåäîâàíèÿ ïðîâîäèëèñü ñ èñïîëüçîâàíèåì ñòàòèñòèêî-àíàëèòè÷åñêèõ ìåòîäîâ íàó÷íîãî èññëåäîâàíèÿ, îïðîñà, àíàëèçà, àíàëîãèé, îáîáùåíèÿ ôèíàíñîâûõ îò÷åòîâ è äð. Âî âðåìÿ èññëåäîâàíèÿ áûëè îïðåäåëåíû ôèíàíñîâûå ðàñõîäû îðãàíèçàöèé, ðàñõîäû íà ãîñóäàðñòâåííîì óðîâíå, ïîëîæèòåëüíîå âîçäåéñòâèå äèðåêòèâû, ïîäãîòîâëåíû ðåêîìåíäàöèè ïî ïðèìåíåíèþ ðóêîâîäÿùèõ ïðèíöèïîâ äèðåêòèâû.  Êëþ÷åâûå ñëîâà: èíòåãðàöèÿ, áåçîïàñíîñòü è çäîðîâüå òðóäÿùèõñÿ, äèðåêòèâà Åâðîïåéñêîãî ñîþçà 92/52/ÅÅÑ, ôèíàíñîâûå ðàñõîäû, ñòðîèòåëüñòâî.

Ñ. Âàêðèíåíå, Ï. ×èðàñ, Ð. Øóêèñ. Îïòèìèçàöèÿ ñðåäñòâ äëÿ ïðåâåíöèè òðàâì â ñòðîèòåëüñòâå // Journal of Civil Engineering and Management. Âèëüíþñ: Òåõíèêà, 2004, X ò., Ïðèë. 1. C. 57–63. Àíàëèç ñòàòèñòè÷åñêèõ äàííûõ î íåñ÷àñòíûõ ñëó÷àÿõ â ñòðîèòåëüñòâå ïîêàçûâàåò, ÷òî îñíîâíûìè ïðè÷èíàìè íåñ÷àñòíûõ ñëó÷àåâ ÿâëÿþòñÿ íåñîáëþäåíèå òðåáîâàíèé íîðìàòèâíûõ äîêóìåíòîâ, íåóäîâëåòâîðèòåëüíàÿ îðãàíèçàöèÿ ðàáîò, íåèñïîëüçîâàíèå ñðåäñòâ çàùèòû, ïëîõàÿ îðãàíèçàöèÿ ðàáî÷åãî ìåñòà è íåäîñòàòî÷íîå îáó÷åíèå

IIc

..................................................................................................................................................................................... ÐÅÔÅÐÀÒÛ ðàáî÷èõ. Ðàáîòîäàòåëþ âàæíî çíàòü, êàê îïòèìàëüíî ðàñïðåäåëèòü ñðåäñòâà äëÿ ïðåäîòâðàùåíèÿ íåñ÷àñòíûõ ñëó÷àåâ. Ýòî ïîçâîëèëî áû â ñðåäíåì èëè ñ îïðåäåëåííîé ñòåïåíüþ âåðîÿòíîñòè óìåíüøèòü ÷èñëî íåñ÷àñòíûõ ñëó÷àåâ è òåì ñàìûì ñíèçèòü âûïëàòû ñîöèàëüíîãî ñòðàõîâàíèÿ.  ñòàòüå ðåøàåòñÿ çàäà÷à ñòîõàñòè÷åñêîãî ïðîãðàììèðîâàíèÿ, êîòîðàÿ ìîäåëèðóåò ïðîáëåìó îïòèìàëüíîãî ðàñïðåäåëåíèÿ ñðåäñòâ äëÿ ïðåâåíöèè íåñ÷àñòíûõ ñëó÷àåâ â ñòðîèòåëüñòâå. ×òîáû ñ äîñòàòî÷íîé íàä¸æíîñòüþ ïîëó÷èòü îïòèìàëüíóþ ñòðàòåãèþ ðàñïðåäåëåíèÿ ñðåäñòâ äëÿ ïðåâåíöèè íåñ÷àñòíûõ ñëó÷àåâ â ñòðîèòåëüñòâå, íåîáõîäèìî ðåøèòü çàäà÷ó ñåïàðàáåëüíîãî ïðîãðàììèðîâàíèÿ. Îïðåäåëåíî çíà÷åíèå ìíîæèòåëÿ Ëàãðàíæà è ïðàâèëà âûäåëåíèÿ ãëîáàëüíîãî ýêñòðåìóìà äëÿ ýòîé çàäà÷è è èññëåäóåìîé ïðîáëåìû. Ðåøåíèåì ïðèìåðîâ ïîëó÷åíû òî÷íûå è íàä¸æíûå ôóíêöèîíàëüíûå çàâèñèìîñòè ìåæäó ðåøåíèåì çàäà÷è è åãî ïàðàìåòðàìè. Ýòî ïîçâîëÿåò îïòèìèçèðîâàòü ñðåäñòâà, âûäåëÿåìûå äëÿ ïðåäîòâðàùåíèÿ íåñ÷àñòíûõ ñëó÷àåâ â ñòðîèòåëüñòâå, è ïîêàçûâàåò çàâèñèìîñòü âîçìîæíîãî ïðåäîòâðàùåíèÿ ÷èñëà òðàâì îò óðîâíÿ äîñòîâåðíîñòè è âàðèàöèè ñðåäñòâ, âûäåëÿåìûõ äëÿ ýòèõ öåëåé â ñòðîèòåëüñòâå. Êëþ÷åâûå ñëîâà: íåñ÷àñòíûå ñëó÷àè, ïðåâåíöèÿ, îïòèìàëüíîå ðàñïðåäåëåíèå ñðåäñòâ, ñòîõàñòè÷åñêîå ïðîãðàììèðîâàíèå, ôóíêöèÿ Ëàãðàíæà, óñëîâèÿ Êóíî-Òàêåðà, óðîâåíü äîñòîâåðíîñòè, âàðèàöèÿ ñðåäñòâ..

Â. Âîëêîâà. Èäåíòèôèêàöèÿ ïîëèãàðìîíè÷åñêèõ êîëåáàíèé íåëèíåéíûõ äèíàìè÷åñêèõ ñèñòåì // Journal of Civil Engineering and Management. Âèëüíþñ: Òåõíèêà, 2004, X ò., Ïðèë. 1. C. 65–70. Ïðè àíàëèòè÷åñêîì èññëåäîâàíèè êîëåáàíèé âîçíèêàåò íåîáõîäèìîñòü ïîñòðîåíèÿ ìàòåìàòè÷åñêîé ìîäåëè. Ñ ýòîé öåëüþ èñïîëüçóþò äàííûå òåõíè÷åñêèõ ÷åðòåæåé, îïèñàíèé è äðóãóþ äîêóìåíòàöèþ î ñòðóêòóðå è çíà÷åíèÿõ îòäåëüíûõ ïàðàìåòðîâ.  íåêîòîðûõ ñëó÷àÿõ ýòà èíôîðìàöèÿ íåäîñòàòî÷íà, òîãäà íàèáîëåå ýôôåêòèâíûì ñòàíîâèòñÿ ïðèìåíåíèå ìåòîäîâ èäåíòèôèêàöèè. Îíè çàêëþ÷àþòñÿ â ïîñòðîåíèè ìàòåìàòè÷åñêîé ìîäåëè îáúåêòà ïî ýêñïåðèìåíòàëüíûì çàïèñÿì. Êëþ÷åâûå ñëîâà: èäåíòèôèêàöèÿ, ôàçîâûå òðàåêòîðèè, ïîëèãàðìîíè÷åñêèå êîëåáàíèÿ, íåëèíåéíûå äèíàìè÷åñêèå ñèñòåìû.

Ý.-Ê. Çàâàäñêàñ, À. Êàêëàóñêàñ, Ñ. Ðàñëàíàñ, Ì. Êðóòèíèñ. Îñîáåííîñòè ïðèìåíåíèÿ ìíîãîêðèòåðèàëüíîé ñèñòåìû ýëåêòðîííîé òîðãîâëè íåäâèæèìûì èìóùåñòâîì // Journal of Civil Engineering and Management. Âèëüíþñ: Òåõíèêà, 2004, X ò., Ïðèë. 1. C. 71–78. Îäíîé èç îñíîâíûõ ïðîáëåì, êàñàþùèõñÿ èíòåðíåòíûõ èíôîðìàöèîííûõ ñèñòåì, ÿâëÿåòñÿ òî, ÷òî â íèõ òðóäíî íàéòè íóæíîå èçäåëèå èëè óñëóãó.  èíòåðíåòå ïðåäëàãàþòñÿ òûñÿ÷è âèäîâ îäíîãî è òîãî æå èçäåëèÿ èëè óñëóãè. Êàê ïîòðåáèòåëÿì íàéòè íóæíûå èì èçäåëèÿ è óñëóãè? Íàéäÿ èçäåëèå èëè óñëóãó, ïîòðåáèòåëü îáû÷íî õî÷åò ñðàâíèòü èõ ñ àëüòåðíàòèâíûìè ïðåäëîæåíèÿìè. Ñóùåñòâóåò íåñêîëüêî òèïîâ èíñòðóìåíòîâ, ïîçâîëÿþùèõ ñðàâíèòü àíàëîãè÷íûå ïðåäëîæåíèÿ: ïîèñê â ãèïåðòåêñòîâûõ äîêóìåíòàõ ñ èñïîëüçîâàíèåì ïîñðåäíèêîâ, ïîèñê àëüòåðíàòèâíûõ èçäåëèé â áàçàõ äàííûõ, ïîèñê è ñðàâíåíèå àëüòåðíàòèâíûõ èçäåëèé â òàáëèöàõ, ïîèñê àëüòåðíàòèâíûõ èçäåëèé è óñëóã â ýëåêòðîííûõ òîðãîâûõ ñàéòàõ, ïîèñê è ïðèíÿòèå ìíîãîêðèòåðèàëüíûõ ðåøåíèé. Àâòîðû ñîçäàëè èíòåðíåòíóþ ýëåêòðîííóþ ñèñòåìó òîðãîâëè íåäâèæèìûì èìóùåñòâîì (ÝÒÍÈ). Ïðåäëàãàåìàÿ ñèñòåìà ÝÒÍÈ ìîæåò ïîâûñèòü ñòîèìîñòü íåäâèæèìîãî èìóùåñòâà ñëåäóþùèì îáðàçîì: ñ åå ïîìîùüþ ïîòðåáèòåëè ìîãóò ëåã÷å îïðåäåëèòü ñâîè ïîòðåáíîñòè, íåäâèæèìîå èìóùåñòâî, ñîîòâåòñòâóþùåå ýòèì ïîòðåáíîñòÿì, ñðàâíèòü è îöåíèòü ðàçíûå ïðåäëàãàåìûå âàðèàíòû íåäâèæèìîãî èìóùåñòâà, îöåíèòü ïîëåçíîñòü íåäâèæèìîãî èìóùåñòâà ïîñëå åãî ïðèîáðåòåíèÿ è ò. ä. Êëþ÷åâûå ñëîâà: èíòåðíåòíûå èíôîðìàöèîííûå ñèñòåìû, ÝÒÍÈ, ìíîãîêðèòåðèàëüíûé àíàëèç.

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