Slab Punching Manual Eng.docx

Punching in the Slab Design Module

1. Problem analysis: The process of design due to punching consists of the following stages: 1.1. CALCULATION OF CRITICAL AREA AND CRITICAL PERIMETER – For every code calculations consist in determining the area subjected to action of a punching force. In calculation of this zone edges of a slab and of openings are considered. Calculations of the extent and shape of the zone and that whether slab edges and openings are considered depend on the code. 1.2. CALCULATION OF LIMIT PUCHING FORCES OR LIMIT STRESSES - This stage of calculations includes determining maximal, allowed by the code, values of punching force or maximal stresses that can be carried by a concrete section. The limit (maximal) force is a product of the critical area and stresses allowed by the code. 1.3. CALCULATION OF PUNCHING FORCES OR STRESSES RESULTING FROM EXTERNAL IMPACT – Each of the codes determines the manner how a force or stress caused by the external impact should be received on the punching area. In the simplest case, calculations involve multiplication of a punching force by an appropriate factor, whereas in the most complicated cases, calculations of stresses with consideration of acting moments are required. 1.4. CHECK OF THE LOAD CAPACITY CONDITION– consists in comparing stresses or forces caused by the external impact with the limit values. There are three states possible:  If calculated stresses are lesser than admissible ones for a concrete section, reinforcement is not required.  If stresses are greater than admissible stresses for a concrete section and simultaneously lesser than admissible ones (there is a need for better distinction from allowable stresses for concrete), reinforcement is required.  If stresses are greater than admissible stresses, it means that slab section is too small. In case when reinforcement is not required or when slab section is too small, results are presented in a form of the maximal punching force (for calculations based on stresses, the force is calculated from stresses multiplied by the punching area) and the ratio of admissible force to equivalent acting force. If reinforcement is required, then calculations of the reinforcement needed are carried out by the program. 1.5. CALCULATION OF NECESSARY REINFORCEMENT – if stresses are greater than admissible stresses for a concrete section and simultaneously lesser than admissible ones, then calculation of punching reinforcement is necessary. Calculations are carried out according to the code guidelines concerning bar reinforcement. The following items are presented in the program: required reinforcement area and range of a zone within which reinforcement is required. These values are shown in the table on the Punching tab; apart from that, the program presents value of a punching force (for calculations based on stresses, the force is calculated from stresses multiplied by the punching area) and ratio of the load capacity with reinforcement considered to the equivalent acting force. The range of reinforcement zone is presented additionally in drawings. 2. Calculation parameters and result presentation: 2.1. Geometrical and additional parameters Geometrical parameters used in design due to punching have been grouped on the second tab (Punching) of the ”Results” dialog box on the ”Slab – provided reinforcement” layout. Options included in this dialog box enable analysis of punching in slabs induced by the loading with concentrated forces and reaction forces of slab supports.

The option set allows the user to:  view and define the punching verification points  group the verification points (unify the geometry)  assign geometrical properties of the head to supports (columns) If in a structure supports at points are defined, they are automatically entered on the point list and denoted by the letter S with successive numbers. For each support type the following items can be read:  coordinates in the Position field  number of the node to which a support is assigned (in the Node number field)  maximum reaction value of a support in the Maximum punching force field  support geometry if that has been defined while defining the support in the Advanced dialog box. This data is accessible after selecting each of the points provided on the point list. Independently from supports, there may be user-defined verification points. To define a new verification point, the user should press the New button in the Verification points field. Each time when this operation is completed, the verification point denoted by letter P and successive number is added to the point list. Once a verification point is chosen, the fields allowing definition of the point position, load geometry and values of punching force become active. These values are being saved (no additional operation to confirm them is needed). To delete the added verification point, the user should select it and press the Delete button. The points, which are the supports defined in structure geometry (denoted by the letter S) cannot be deleted.

The program allows defining heads over the supports (columns) that are taken into consideration in the punching calculations. To do it, the user should switch on the Head option (the fields with the dimensions become available) and define the head dimensions. For the head on rectangular support these are the lengths of the head sides on the level where head meets the slab (denoted by the letters a and b) and the head height denoted by the letter h. For the heads over the circular supports these are: d head diameter and h head height (for a circular head) or the lengths of the head sides (denoted by the letters a and b) - for a rectangular head. When a support belongs to a group, the head is applied to all elements of this group. Both, the additional verification points and supports can be grouped to make the geometry modification easier. The points may be grouped manually by selecting from the name list and pressing the > button; there is also a possibility to group all the supports automatically: the >> button should be pressed. Additional verification points can be grouped if they have the same geometry type. For supports, compatibility of the support dimensions is also necessary. If the condition of the compatibility of support dimensions is not satisfied, the verification points or supports not compatible with the first item on the list are deleted at the moment when the group is being confirmed. When grouping points with different dimensions, the dimension values are assumed on the basis of the first point defined in the group. When a new point is added to the group, its dimensions are automatically changed to the ones compatible with the group dimensions. Grouping of the supports with different head dimensions is done by analogy. Once a group is defined, any change of any group component refers to the entire group and is modified. This dialog box may include additional options - depending on the selected code of RC structure design. For the ACI 318-99 code, the above dialog box also contains the Type option which determines position for each support: within slab, on slab edge or in slab corner. The support type is used in calculation of the admissible punching force [ACI 318-99 11.12.2.2]. For EC2 (Belgium NAD) code, the  coefficient is available in the above dialog box. The parameter determines position of each support: within slab, on slab edge or in slab corner. This parameter value is used in calculation of the punching force [ENV 1992-1-1 EC2 4.3.4.3]. 2.2. Reinforcement parameters Parameters concerning reinforcement due to punching are determined on the Reinforcement for punching tab in the Calculation Options dialog box:

This tab enables defining parameters of steel used for reinforcement due to punching - steel grade and strength. Here on this tab bar diameters are also determined – for ACI 318-99 code - bar numbers are compatible with ASTM.

The Bar type field is used for defining a type of reinforcement applied. Since other codes besides ACI 318-99 (ACI 318-99 metric) do not distinguish between inclined bar reinforcement and bent bar reinforcement on the calculation level, the ”bent bars” option is inaccessible for them. For inclined and bent bars it is necessary to define the angle at which they are inclined to the slab plane. 2.3. Results Results of punching calculations are presented in a table in the bottom part of the second tab (Punching) of the ”Results” dialog box on the ”Slab – provided reinforcement” layout. To obtain results, generation of zones of longitudinal reinforcement due to bending is required. If the zones are not generated, the user should choose the Analysis / Calculations option from the menu and afterwards – in the Calculation Option Set dialog box – run calculations after switching on the option ensuring that once calculations are performed the result layout opens (or the current layout if calculations are run from that layout). Once calculations of longitudinal reinforcement are completed, modifications of options made on the ”Punching” tab or in the Calculation Options / Reinf. for punching dialog box are being updated and result in automatic recalculation of punching conditions. It is not required to run again longitudinal reinforcement calculations. In the table presenting the results of punching analysis for each verification point the following values are presented:  admissible punching force calculated by the program according to the appropriate code requirements  generalized design force defined in the ”Maximum punching force” field for the additional verification points or read from FEM calculation results for supports  critical perimeter calculated on the basis of code requirements  reinforcement, which includes: - reinforcement range from the member center in both perpendicular directions L1 and L2 - perimeter of reinforcement zone (if required) - total area of reinforcement - number and diameter of bars calculated on the basis of the total area and settings of the options for punching  safety factor being the ratio of the maximum punching force to the admissible punching force. Punching analysis results for individual points are presented in the color corresponding to the calculation result:  in blue – for points that fulfill the punching conditions and do not require reinforcement  in green - for points that fulfill the punching conditions and require reinforcement  in red - for points that do not fulfill the punching conditions despite applying reinforcement

The critical perimeter is presented graphically on the ”Slab – reinforcement” layout as a green line around columns. The range of punching reinforcement is shown graphically in a final drawing of a slab (formwork).

3.

Detailed description of code calculations: 3.1. ACI 318-99 3.1.1. Calculations according to chapter [11] 3.1.2. Critical perimeter is positioned in the distance of 0.5d from the column edge (surface where a force is applied), slab edge or from the point where its thickness changes [based on 11.12.1.2] 3.1.3. In calculation of a critical perimeter the neighboring openings are taken into account.

For reinforcement due to punching, the effect of openings is reduced by half according to [11.12.5.2].

3.1.4. Calculations are based on the admissible stresses on the punching surface. ACI code provides the following formulas for calculation of the maximal punching force:

 4  Vc( a )   2    f c '  b0  d (11-35) c     d  Vc(b )   S  2   f c '  b0  d (11-36)  b0  Vc( c )  4 

f c '  b0  d (11-37)

Vc( a )  Vc  min Vc( b ) [based on 11.12.2.1] V ( c )  c where: fc’ b0 d c S

– concrete compressive resistance – critical perimeter – section height without a cover – ratio of the longer column side (surface where a force is applied) to the shorter one – factor that equals, correspondingly, 40 for interior columns, 30 for edge columns, 20 for corner columns, The program converts these values to admissible stresses by division through punching area b 0 d to make the calculations uniform with those performed for structures composed of columns and plates.

  vn 

Vc (11-42) b0  d

3.1.5. Check of the punching capacity condition of a concrete section:   Vn  Vu (11-1) where:  – factor =0.85 On the basis of [11.12.6.2], this relationship may be transformed to the following form:

  v n  vu

where: vn vn

– admissible stress – stress resulting from the external impact

Stress resulting from the external impact is calculated taking force eccentricities into account (structures composed of columns and plates):

vu 

Vu  v  M ux  c x  v  M uy  c y [based on R 11.12.6.2]   Ac J cx J cy

3.1.6. If the condition discussed in 3.1.5 is not satisfied, calculations of reinforcement due to punching are carried out. Applying the formula determined in the code: Vn  Vc  Vs ( 11-2) where: Vc – concrete load capacity Vs – steel load capacity assuming that

Vc  2 

f c '  b0  d [11.12.3.1]

after converting it to stresses analogously as in point 3.1.5, the user obtains the following:

vn 

  Vc  Vs  bo  d

(11-43)

calculation of the demanded amount of reinforcing steel for punching reinforcement: for reinforcement with: perpendicular bars

Vs 

Av  f y  d s

(11-15)

bent bars

Vs 

Av  f y  (sin(  )  cos( ))  d s

(11-16)

inclined bars

Vs  Av  f y  sin(  )  3  where: Av

– bar area

f c '  b0  d (11-17)

fy – steel strength  – angle of bar inclination d – section height without a cover s – bar spacing 3.1.7. Calculation of the reinforcement range results from the shape of a punching zone b 0

a

b0  2  a  2  b 4 2

3.1.8. Check of the capacity condition of a section reinforced due to punching:

Vn  6 

f c '  b0  d [11.12.3.2]

3.1.9. Since the bar spacing s is not presented in results, the program provides the total reinforcement area which satisfies the code conditions and is calculated from the following formula:

As 

Av  d s

3.1.10. NOTE: Numbering of the code points –square parentheses designation and formula numbers are compatible with ACI 318-99 3.2. BAEL 91 3.2.1. Calculations according to point: [A.5.2] 3.2.2. Critical perimeter is positioned in the distance of 0.5d from the column edge (surface where a force is applied), slab edge or from the point where its thickness changes 3.2.3. In calculation of the critical perimeter, neighboring openings are taken into account 3.2.4. Calculations are based on the admissible punching force. The design condition is represented by the formula below:

Qc  0,045 

f cj

 uc  h

b ULS   p  1.5

ALS   p  1.15 where: Qc fcj

– maximal punching force – non-factored concrete resistance

uc – critical perimeter 3.2.5. If the condition discussed in 3.2.4. is not satisfied, reinforcement due to punching is calculated. 3.2.6. The critical perimeter uc is being extended until the following condition is satisfied:

Qc  0,045 

f cj

b

 uc  h

3.2.7. Between the column face and thus-determined perimeter the reinforcement should be distributed. It is calculated from the formula:

At   s 

 u  0.3  f tj  k s  0.9  f e  cos( )  sin(  )  t

0.6  0.06  f c 28 [A.2.1,12] f tj  min  3.3[ MPa] where: s k s t u

– factor equal to 1.15 – factor equal to 1.0 – bar spacing – slab thickness – stress on the critical perimeter:

u 

Qu uc  d

The reinforcement calculated has to fulfill the following condition:

At  f e  0.4[ MPa] u c  st 3.2.8. Since the bar spacing s is not presented in results, the program provides the total reinforcement area which satisfies the code conditions and is calculated from the following formula:

As 

At  d s

3.3. BS 8118 Part 1 3.3.1. Calculation according to point: [3.7] 3.3.2. The basis for calculations are admissible stresses on punching surfaces. 3.3.3. The distance between the critical perimeter and the column face equals 1.5d [3.7.7.6] 3.3.4. In calculations of critical perimeter the neighboring openings are taken into account in compliance with [3.7.7.7] and slab edges in compliance with [3.7.7.8]

3.3.5. The calculations are based on the admissible shear stresses present on the critical perimeter.

vlim

0.8 fcu   min  N [based on 3.7.7.2] 5 [  mm 2 ]

3.3.6. In design the effective forces are used, which consider the effect of bending moments calculated as follows: for interior columns:

 M  Veff  Vt  1  1.5  t  (25) Vt  x   where: x – length of this side of critical perimeter which is parallel to the bending axis M t for edge columns:

 Mt   (26) Veff  Vt  1.25  1.5  V  x t   for corner columns:

Veff  1.25  Vt Stresses occurring on the critical area are calculated from the following formula:

Veff

v max 

uo  d

[3.7.7.2]

where: u0 – critical perimeter d – section height without a cover 3.3.7. Check of the punching capacity condition: 1

 A 3 100  S  bv  d  vc  0.79  

1

 400  4    d 

m

[based on table 3.9]

AS  3 [ based on table 3.9] bv  d

100 

400  1 [ based on table 3.9] d where: m – correction factor equal to 1.25 bv – d – As – average area of longitudinal reinforcement for directions x and y NOTE: if fcu > 25 N/mm2 , fcu not greater than 40 N/mm2 is assumed in calculations, however, the final vc is multiplied by the coefficient equal to: 1

 f cu  3   [ based on table 3.9]  25  Load capacity condition: vmax  vc [based on 3.7.7.4] 3.3.8. If the condition discussed in 3.3.7. is not fulfilled, calculations of reinforcement due to punching are performed. The formula provided in the code is applied:

A

sv

 sin(  ) 

v  vc   u  d 0.87 f yv

(29)

where:  – angle of reinforcement inclination fyv – non-factored shear resistance of reinforcing steel Asv – area of shear reinforcement NOTE: the value (v - vc) introduced in the formula is not lesser than 0.4 N/mm2 [3.7.7.5] 3.3.9. Additional conditions concerning reinforcement due to punching: It is required that the thickness of the plate reinforced due to punching be greater than 200mm [3.7.7.5] 3.3.10. The rule of design:

If punching reinforcement is required, then after completing the analysis of the critical perimeter described in point 3.3.3, the next perimeter is being analyzed – the perimeter 0.75d distant from the previous one. The capacity condition discussed in point 3.3.7. is checked again for it. If it is not satisfied, then successive reinforcement is calculated. The procedure lasts until the perimeter which fulfills the capacity condition of point 3.3.7, is found.

3.3.11. The rule of reinforcement distribution In case when there are several punching zones that require reinforcement, only these bars are distributed within successive zones that have not been considered in the previous zone. It results from overlapping of zones by the width 0.75d. 3.3.12. NOTE: Numbering of the code points – square parentheses designation and formula numbers are compatible with BS 8110:Part 1:1985. 3.4. EC2 – Norme Belge NBN B 15-002 (Eurocode 2) 3.4.1. Calculations according to point: [4.3.4] 3.4.2. It is required that the longitudinal reinforcement ratio of an element verified due to punching equal not less than 0.5% in both directions [4.3.4.1] (full compatibility with Eurocode 2); if this condition is not met, section reinforcement is increased to reach the appropriate value. 3.4.3. Calculations of the perimeter are performed in compliance with [4.3.4.2] (full compatibility with Eurocode 2)

3.4.4. In calculations of the critical perimeter, neighboring openings are considered in compliance with the following

as well as slab edges according to [4.3.4.2.2] (full compatibility with Eurocode 2). 3.4.5. The basis for calculations are admissible shear stresses occurring on the critical perimeter. Calculation of stresses are carried out as follows:

Sd 

VSd   u

(4.50) (full compatibility with Eurocode 2)

where: VSd – maximal punching force  – factor considering effects of the force acting on eccentricity u – critical perimeter The  factor is defined by the user in the Results/ Punching dialog box separately for each of the columns. The default value of the factor equals 1.15 – as for interior columns. For corner columns the value 1.5 is required, whereas for edge columns 1.4. 3.4.6. Maximal values of stresses due to punching are calculated from the formulas:

1   v Rd1  0.1  k  (100   l  f ck ) 3  0.15   cp   d (4.56 B)  

where

k  1

200 d

d

– slab thickness [mm]

 l  (  lx   ly )  0.015 lx ly

 cp 

– horizontal reinforcement ratio in the direction x – horizontal reinforcement ratio in the direction y

N pd

- refers to prestressed structures and is not considered in punching analysis.

Ac

The maximal admissible stress for sections reinforced due to punching equals: v Rd 2  1.6  v Rd1 (4.57) (full compatibility with Eurocode 2) 3.4.7. Check of the punching capacity condition: Capacity condition: vsd  vrd1 [based on 3.7.7.4] (full compatibility with Eurocode 2). 3.4.8. If the condition discussed in 3.4.6. is not satisfied, calculations of reinforcement due to punching are performed. The formula determined in the code is applied here:

v Rd 3  v Rd1 

A

sw

 f yd  sin(  ) u

(4.58) (full compatibility with Eurocode 2).

3.4.9. Additional conditions concerned with punching reinforcement: It is required that the thickness of a plate reinforced due to punching be not lesser than 200mm [5.4.3.3(1)]( full compatibility with Eurocode 2). The ratio of punching reinforcement has to be greater than: Concrete classes Steel grades BE220 (S220) BE220 (S220) BE220 (S220) C12/15 to C20/25 0,096 0,054 0,042 C25/30 to C35/40 0,144 0,078 0,066 C40/50 to C50/60 0,18 0,096 0,078 [5.4.3.3(2)] (full compatibility with Eurocode 2). The ratio of reinforcement due to punching has to be greater than:

w  where: Acrit Aload

A

sw

 sin(  )

Acirt  Aload

[4.3.4.5.2 (4)] (full compatibility with Eurocode 2).

– area contained within critical perimeter – area to which load is applied

3.4.10. A safety coefficient is expressed by the formula:

v Rd 3 v Sd

3.4.11. NOTE: Numbering of the code points – square parentheses designation and formula numbers are compliant with EC2 – Norme Belge NBN B 15-002 1e éd. décembre 1995. If a given point of Belgian NAD is identical as in Eurocode 2, such a point has been given explanatory notes (full compatibility with Eurocode 2). 3.5. PN-B-03264 3.5.1. Calculations are performed according to point [5.6] 3.5.2. It is required that the longitudinal reinforcement ratio of an element verified due to punching be not lesser than 0.5% in both directions [5.6.1] 3.5.3. Angle of stress propagation (the pyramid of critical surface) equals 45 o [5.6.2]

3.5.4. The basis for calculations is the admissible punching force. It is calculated as follows: N Rd  f ctd  u p  d (based on 64) where: NRd fctd up

– design (factored) section capacity – design (factored) tensile resistance of concrete – critical perimeter (arithmetic average of the perimeters of the surface acted upon by a force and the surface generated on the reinforcement level assuming that lateral planes of the pyramid are inclined at 45o angle) d – section height without a cover 3.5.5. Check of the punching capacity condition of a concrete section: N Sd  N Rd (based on 64) where: NSd – design punching force A load applied within the punching zone is not considered by the program!!! It implies a more severe capacity condition than the one imposed by the code: N Sd  ( g  q)  A  N Rd (based on 64) where: g – slab unit weight (slab dead load) q – load evenly distributed on the plate surface A – area cut off by sections on the (medium) level of bending reinforcement area 3.5.6. If the condition discussed in 4.5.5. is not satisfied, calculations of punching reinforcement are performed. The following formula specified in the code is applied:

N Rd   Asw1  f ywd   Asw2  f ywd  sin(  ) ( based on 68)

the program distinguishes two cases:

N Rd   Asw1  f ywd for perpendicular bars

N Rd   Asw2  f ywd  sin(  ) for inclined bars

On the basis of the above formulas calculation of the required reinforcement area A sw1 or Asw2 is performed. 3.5.7. Check of the capacity condition of a section reinforced due to punching: N Sd  N Rd (based on 68)

N Sd  N Rd  1.4  f ctd  u p  d (67) where designations – as in points 3.5.3 and 3.5.4 3.5.8. Structural conditions of inclination of punching reinforcement 30 o <<60 o 3.5.9. The reinforcement range equals [9.1.1.4]:  min. 1.2d from column face for perpendicular reinforcement



min. 1.5d from column face for inclined reinforcement