2002 Shrinkage And Creep Effects On Pre Stressed Concrete St

4e Conférence spécialisée en génie des structures de la Société canadienne de génie civil 4th Structural Specialty Conference of the Canadian Society for Civil Engineering Montréal, Québec, Canada 5-8 juin 2002 / June 5-8, 2002

Shrinkage and Creep Effects on Prestressed Concrete Structures Denis Lefebvre, Eng., M.A.Sc., CivilDesign Inc. Engineering Software, Longueuil, Canada SUMMARY: Shrinkage and creep effects are influenced by characteristics of concrete, exposure conditions air and construction stages, which are sequential for prestressed concrete structures. In turn, shrinkage and creep effects induce additional internal forces and defections to the structure. The purpose of this paper is to bring out the influence of different parameters on prestressed concrete structures behaviour. In this paper, the author compares three mathematical models, each one of these models defining shrinkage and creep behaviour. The studied models are those of Canadian standard S6-00 (CEB-FIP 1978), Eurocode AFNOR-1999 (CEB-FIP 1990) and American standard ACI-209 1992. Finally, the author presents two examples in which he varied the delay between the casting of the section and the slab, and exposure conditions. These analyses will allow the author to compare these effects on prestressed concrete structures according to Canadian standard S6-00 and American standard ACI 203.

1. Comparison Between Models 1.1 The Shrinkage Model (εsh) Shrinkage of concrete is essentially due to water evaporating from concrete and hydration of its components with time. During the last past years, European and American engineers looked into two phenomena causing total shrinkage of concrete: endogenous shrinkage and shrinkage due to drying. From experimental measurements, they elaborated models (using extrapolation) to calculate concrete shrinkage effect in time. With the most interesting models, the author compares different shrinkage εsh results using identical parameters and conditions. The compared models are taken from the following standards: •= •= •=

CEB-FIP 1978, also used in Canadian CSA/CAN S6-00 standard; CEB-FIP 1990 or Eurocode AFNOR 1999; American model of ACI 203, 1992;

1

Conditions and characteristics of concrete are as follows: •= •= •= •= •= •=

Relative Humidity RH = 70%; Normal Density; Normal slump test; Cement with normal setting; 7 days of humid cure; Ratio volume/surface V/S or rv varying from 50 to 250 mm;

Mathematical models are available in each standard except for the Canadian standard S6-00 where graphs are presented. Readers can refer to Mrs Michaud master's thesis [4], which dealt with these different mathematical models. 1.1.1 Comparison of Limit Values As we can see on Graph 1, shrinkage values obtained from the three models vary a lot. CEB-FIP 1978 model gives smaller values then those obtained from the American model for smaller values of V/S, whereas results and tendencies are inverted when V/S values are bigger. Limit values lead towards different shrinkage values for different rv ratios according to CEB-FIP 1978 and ACI-203 models. AFNOR-1999 model always tends towards the same shrinkage values no matter the rv ratio. Shrinkage values of AFNOR-1999 new model are a little more important than those of the old standard CEB-FIP 1978 with a behaviour that has radically changed where all values tend towards the same shrinkage value at infinite. Please note that an experimental study from New Zealand [1] has shown that for small rv values, CEB-FIP 1978 model gave results two times smaller in opposition to the American model, which gave good results. Model CEB-1978 AFNOR-1999 ACI-203

Maximum Value (rv=50 mm) Minimum Value (rv=250 mm) -6 -6 (x10 ) (x10 ) 273 231 366 366 517 201 Table 1. Shrinkage Limit Values according to Standard.

2

Comparison of Shrinkage Effects 50MPa Normal Concrete at 7 Days of Humid Cure (rv = V/S) CEB-1978 rv = 50mm CEB-1978 rv = 100mm

600

CEB-1978 rv = 150mm CEB-1978 rv = 200mm

ACI 203 rv = 50mm

CEB-1978 rv = 250 CEB-1999 rv = 50mm CEB-1999 rv =100mm

500

CEB-1999 rv = 150mm CEB-1999 rv = 200mm CEB-1999 rv = 250mm

Epsilon_sh (shrinkage) /1,000,000

ACI-92 rv = 50mm ACI-92 rv = 100mm

400

ACI-92 rv = 150mm

AFNOR-1999 rv = 50mm

ACI-92 rv = 200mm ACI-92 rv = 250mm

300

200

S6-00

100 CEB-FIP 1978 rv = 50mm

0 1

10

100

1000 Number of Days Graph 1

3

10000

100000

1.2 The Creep Model (εc) Deflection due to creep causes an additional deflection with time in opposition to an instantaneous elastic deflection. This deflection occurs when concrete is subjected to a stress that is more or less maintained in time. Causes are explained in Mrs Michaud master's thesis [4]. As for shrinkage effects, we are going to compare values of creep factor φ (t-to) obtained from quoted standards models. We remind you that the creep factor represents the factor that multiplies elastic deflection, which gives us the deflection due to creep. This value can vary from 0 to 3. Exposure conditions and concrete characteristics are the same as they were for the study of shrinkage models. Mathematical models for creep are also available for quoted standards, except for Canadian standard S600, as it was for shrinkage. 1.2.1 Comparison of Limit Values As for shrinkage, we obtained important differences between models. Results of CEB-FIP 1978 model are two times smaller than those obtained from American model. European AFNOR-1999 new model gives results in between those obtained from American model and old European CEB-FIP 1978 model. We can imagine that during the twelve years separating the old model from the new one, European have polished their models as much for shrinkage than for creep. In other respects, the New Zealand [1] study concluded that CEB-FIP 1978 model was closer to experimental values than was the American one, which gave values almost twice bigger. We hope that modifications done on AFNOR-1999 creep model did not distort the very good correlations that existed between values obtained from model and experimental values. Graph 2 shows these differences. According to established conditions, limit values tend towards different creep factors for all models according to ratio rv. Limit values are indicated in Table 2. Model CEB-1978 AFNOR-1999 ACI-203

Maximum Value (rv=50 mm) Minimum Value (rv=250 mm) 2.29 2.06 1.91 1.59 1.46 1.05 Table 2. Limit Values of Creep Factor according to Standards.

4

Comparison of Creep Effects 50MPa Normal Concrete at 7 Days of Humid Cure (rv = V/S) CEB-1978 rv = 50mm

2.50

CEB-1978 rv = 100mm CEB-FIP 1978 rv = 50mm

CEB-1978 rv = 150mm CEB-1978 rv = 200mm CEB-1978 rv = 250mm AFNOR-1999 rv = 50mm

S6-00

AFNOR-1999 rv = 100mm

2.00

AFNOR-1999 rv = 150mm AFNOR-1999 rv = 200mm AFNOR-1999 rv = 250mm

Phi(t,to) = Epsilon_c / Epsilon_e

ACI-203 rv = 50mm ACI-203 rv = 100mm ACI-203 rv = 150mm

1.50

ACI-203 rv = 200mm ACI-203 rv = 250mm ACI 203 rv = 50mm

AFNOR-1999 rv = 50mm

1.00

ACI 203 rv = 250mm

0.50

0.00 1

10

100

1000

Duration of Load Application (t-to) days Graph 2

5

10000

100000

2. Consequences on Bridge Spans When designing bridges with prestressed concrete beams, shrinkage and creep effects must be taken into consideration in the calculation of deflection, stresses, and internal forces (bending moments and shear forces). The purpose of next examples is to heighten engineers' awareness of shrinkage and creep effects on bridge behaviour. 2.1 First Case: Single Span Characteristics: AASHTO V Beam, 38m long Concrete f’c=50MPa, f’ci (18 hours)=40MPa Vapour cure for section and humid cure for slab. 16 strands 0.5in, G270 steel, oblique and 48 strands 0.5in, G270 steel, straight. Slab effective width: 1750mm

Figure 1. Position of Prestressing Cables. Generally, for this type of structure, prestress is applied after 18 hours of vapour cure. Then, about 30 days later, the slab is cast over the beam. In the case of a single beam that is free to move and not yet composite, shrinkage and creep effects will not caused any force in this element. However, the beam will deform due to prestress and then, secondary deformation will occur because of shrinkage and creep of beam. This is the behaviour that we are going to study using standard S6-00 (CEB-FIP 1978) model and ACI 203 model (in parenthesis). In this example, which is quite simple, there is a variation of stresses in the section that is due to prestress loss, which in turn, are caused by relaxation, shrinkage and creep. The calculation of beam deflection and other effects such as shrinkage and creep is carried on by superposition and subdividing time intervals according to a logarithmic diagram in order to reduce numerical integration steps. CEB-FIP 1978 Model (ACI 203 Model) Deflection at Centre (rv=50 mm) Shrinkage Construction Stage (mm) (mm) Transfer of prestress 71.4 (71.4) 0.0 At 30 days 146.2 (108.5) 6.6 (7.5) At 60 days 157.1 (117.1) 8.0 (10.5) At 100 days 166.4 (123.3) 9.3 (12.6) At 365 days 192.2 (136.8) 13.9 (16.6) At 10,000 days 228.5 (152.3) 21.6 (19.6) Table 3. Deflection of Section with Variation of Delay between Casting of Section and Slab.

6

After 30 days, the beam upwards curvature has doubled. At this construction stage, if the slab dead load causes a downward deflection of less than 75 mm, total upwards deflection will be bigger after addition of the slab following initial prestressing. We noticed that initial curvature grows bigger as the delay increases between the casting of the section and the slab. Deflection at centre is smaller according to ACI 203 standard and is equal to 67% of the deflection calculated with CEB-FIP 1978 model. At the casting of the slab, differential shrinkage is induced between the slab and AASHTO section when the cure is completed. Actually, the slab will begin to shrink with a speed and amplitude that are different from the section's, which has partly shrunk. Differential shrinkage doesn't cause any forces (bending moment and shear force) in the composite section but rather auto-equilibrated stresses creating a new composite beam deflection. Deflection at centre Construction Stage (mm) 3- At Transfer of Prestress 71.4 At 30 days 146.2 5- After addition of slab (+0 day) 106.2 6- At end of cure (+7 days) 91.5 8- After addition of extra dead loads (+0 days) 83.7 9- Long term (10,000 days) 121.6 (83.0) Table 4. Deflection for a delay of 30 days (Section-Slab). Deflection at centre Construction Stage (mm) 3- At Transfer of Prestress 71.4 At 60 days 157.1 5- After addition of slab (+0 day) 117.2 6- At end of cure (+7 days) 104.1 8- After addition of extra dead loads (+0 days) 96.4 9- Long term (10,000 days) 124.4 (78.9) Table 5. Deflection for a delay of 60 days (Section-Slab).

Deflection at centre Construction Stage (mm) 3- At Transfer of Prestress 71.4 At 100 days 166.4 5- After addition of slab (+0 day) 126.5 6- At end of cure (+7 days) 114.5 8- After addition of extra dead loads (+0 days) 106.7 9- Long term (10,000 days) 126.7 (75.7) Table 6. Deflection for a delay of 100 days (Section-Slab). For a long-term period, the increase in the deflection is not as fast as for a single beam that is not composite. For a single beam, the calculated deflection was equal to 228.5 mm (Table 3). However, its long-term deflection is equal to 126.7mm (Table 6). The difference comes partly from the new stress distribution in the section and slab and also from differential shrinkage between the two components, which leads to a downward deflection. The same applies for standard ACI 203 model but deflection is equal to 76 mm instead of 127 mm (Table 6).

7

Figure 2. Creep and Differential Shrinkage Effects on Section It is interesting to notice that the delay between the casting of section and slab has almost no effects on final deflection. The increasing in the deflection, which is caused by creep after the casting of section, has decreased due to a bigger differential shrinkage between slab and section. Differences between calculated stresses for the three delays (30, 60 and 100 days) gave a maximum variation of 1 MPa, for this example. 2.2 Second Example: Semi Continuous System with Three Spans Characteristics: Spans: 27320 mm, 32200 mm and 27320mm. Beams: AASHTO VI Concrete f’c=50MPa, f’ci (18 hours) =40MPa for section and standard 50MPa for slab. Vapour cure for sections and humid cure for slab. 14-26 strands 0.5in, G270 steel for exterior spans, 22-42 strands 0.5in, G270 steel for intermediate span. Slab effective width: 3600mm 800mm c/c between intermediate supports (semi continuous)

Figure 3. Position of Prestressing Cables. For this semi continuous system, we are going to study the beam behaviour by looking at bending moments due to shrinkage and creep instead of looking at deflections. Delays and exposure conditions will vary and bending diagrams will be compared.

Delay Days 30 60 100 365

Shrinkage/Creep Shrinkage only Not much exposed Much exposed Not much exposed Much exposed kN.m kN.m kN.m kN.m 1876 (1878) 2270 (1833) 115 -203 1648 (1415) 2040 (1387) -8 -327 1442 (1046) 1831 (1031) -146 -465 802 (182) 1176 (188) -687 -1009 Table 7. Bending Moments due to Shrinkage and Creep.

8

"Not much exposed" refers to an exposure condition for which only surfaces underneath the slab, between AASHTO beams, are exposed. "Much exposed" refers to the latter plus exposure of the top surface of the slab (Figure 4).

Figure 4. Exposure Conditions The delay corresponds to the number of days between casting of section and slab. Note that negative moments located at supports, which are caused by moving loads, vary from – 2450 kN.m to +460 kN.m. Consequently, bending moments caused by shrinkage and creep effects are very important for the design of semi continuous joints.

Figure 5. Superposition of Shrinkage and Creep Effects. CEB-FIP 1978 Shrinkage and Creep Models: Table 7 shows that as the exposure surface and delay increase, differential shrinkage effects increase also. However, as surface of exposure increases, so do final moments due to shrinkage and creep. Shrinkage effects increase stresses in concrete partly in the same way as prestressing does, so creep effects are increased. As delay increases, we notice a reduction of final shrinkage/creep bending moments. ACI 203 Shrinkage and Creep Models: Shrinkage and creep bending moment's behaviour is quite different from CEB-FIP 1978 models. The explanation is that the significance of creep model relatively to shrinkage model is different in each standard. There is more creep effect than shrinkage effect in CEB-FIP 1978 models, in opposition to ACI 203 models.

9

We want to remind that the New Zealand study [1] concluded that ACI 203 shrinkage model was more appropriate and so was the CEB-FIP 1978 model for creep.

3. Conclusion The dissimilarity of results between shrinkage and creep models is a bit disappointing. It is certain that research groups have worked professionally and according to the rules. But obviously, there are particularities in each model so that they cannot be compared. However, in spite of these differences, the engineer must understand that the final result will depend on a mix of differential shrinkage, prestress loss, secondary moments due to prestress and the state of stresses in the section and slab. These phenomena are influencing each other. Furthermore, if we consider that mathematical models behave differently, we get a multitude of responses. So, it is mostly important that engineers be acquainted with materials that they will be using because they influence f’ci (t) modulus, Young modulus, and shrinkage/creep parameters. Exposure conditions must be defined and be close to reality, as much as possible. We recommend that engineers whom are not sure about delays or exposure conditions, carried on some analyses with different parameters. MC

All analyses have been executed with VisualDesign

Analysis Software.

References [1] Bryant A.H., Wood, J.A. and Fenwick R.C. (1984) Creep and Shrinkage in Concrete Bridges, Road Research Unit, National Roads Board, Wellington, New Zealand. [2] Code Canadien sur le calcul des ponts routiers, CAN/CSA-S6-00, chapitre 8. [3] EUROCODES AFNOR-1999, Annexe 1 Dispositions complémentaires relatives à la détermination des effets des déformations différés du béton. Page A.3. [4] Michaud Marie-Claude (2000), Master's thesis Déformations différées des ponts fait de poutres préfabriquées en béton précontraint avec dalle coulée en place, chapitre 2 Comportement différé du béton, École Polytechnique, Montréal, Canada.

10