Limitations and assumptions

Applicability of wall punching checks

Punching checks of walls on slabs are made but should be viewed with particular caution.

In particular there is some debate regarding the applicability of a punching check from a long wall - the check doesn’t consider the potential for stress concentrations at the ends of the wall.

Columns and walls not perpendicular to slabs

The program treats all columns and walls that are not perpendicular to slabs as if they are for the punching areas developed. The relevant load is resolved to act perpendicular to the slab for punching checks.

This is conservative as the punching area/perimeter will be smaller than that for the angled column or wall.

Overlapping control perimeters

The calculations are beyond scope in the following situations:

If two control areas touch then both areas are set to Beyond Scope.
If an edge or corner area contains another column or wall then both areas are set to Beyond Scope.

The exception to this is the pile pair check in the design of pile caps.

Slab shear strength

ACI318 refers to two forms of slab shear strength

One way action - beam action in long or narrow slabs or between close-by points of application of load/reaction.
Two way action - punching along a truncated cone around a concentrated load or reaction area.

Tekla Structural Designer only considers punching shear (two way action) and not beam action in slab design.

Definitions

The following definitions are applied

Loaded perimeter – the perimeter of the loaded area e.g. face of column or wall or drop panel
Critical Perimeter – the first punching shear perimeter – at d/2 from the loaded perimeter in ACI
Trial perimeter – is the check punching shear perimeter of smallest length, depending on the reinforcement arrangement, at n x d/2 from the loaded perimeter.
n^th Trial Perimeter – the n^th punching shear perimeter – at n x d/2 from the loaded perimeter with n = [1, 2, …]
Outer perimeter – the shear perimeter at which the punching shear check passes with no reinforcement requirement
b_o is the length of the 1st critical perimeter
b_on is the length of the n^th critical perimeter
Tension reinforcement - slab longitudinal reinforcement at the punching check slab surface. When aligned patch reinforcement shall be combined with panel reinforcement in all cases with the exception of wall punching checks. Reinforcement is only valid for punching shear checks if provided in both orthogonal directions.
Average effective depth d to the tension reinforcement d = (d_y + d_z) / 2
where d_y and d_z are the effective depths in the two orthogonal directions. There is a value of d for top steel and a different value for bottom steel.
If a slab around the check position changes depth, the thinnest slab and its d values are used.
Note this definition changes in the presence of a drop panel.
Drop or Drop panel – a thickening of the slab (either up or down or both) local to a column in a slab

Loaded, critical and outer perimeters

Loaded perimeter
- Minimum length perimeter enclosing the loaded area, which for a regular column will be the column section perimeter.
- In some cases of irregular column shapes, such as the L, T, and elbow shapes below, it will be different (shorter) than the actual column section perimeter.
- In the case of columns with drops there are two loaded perimeters - one for the column and one at the edge of the drop, (uses each effective depth).
- The loaded perimeter is not used directly in ACI detailed calculations.

Critical Perimeter
- Reinforcement requirement is checked at this perimeter
- It is of rectangular shape and located at a distance of half the effective depth from the perimeter equivalent rectangle section for all section shapes
- There are two critical perimeters in the case of columns with drops - one for the column and one for the drop (uses each effective depth)
- More than one consecutive critical perimeter can exist if reinforcement is required at punching check positions where the arrangement can not be designed

Outer Perimeter
- Not visible in the drawings.
- Is the punching shear perimeter with enough length to allow for concrete to resist shear stress on it’s own.
- Reinforcement is no longer required at this perimeter.
- No other perimeters are required to be checked beyond the outer perimeter.
- The distance from bounding rectangle section to the outer perimeter is used to calculate the required length of reinforcement.
- Its shape follows the control/critical perimeter shapes but changes with the use of non-uniform reinforcement arrangements (i.e. orthogonal).

Length of loaded and critical perimeters

Columns

The length of the loaded perimeter, u₀ at the column face and critical perimeter, b₀ is calculated as determined below.

Each possible column shape also has a bounding rectangle or circle calculated to aid in the design calculations.

Rectangular columns

Loaded perimeter, u₀ = 2 x (D + B)

Bounding rectangle properties:

D_Bound = D

B_Bound = B

Bounding Perimeter, u_0Bound = 2 x (D_Bound + B_Bound)

a_n = max(D,B)

b_n = min(D,B)

β = a_n / b_n

Critical perimeter, b₀ = 2 x (D_Bound + B_Bound + 2 x d)

Note d = d_drop if a drop is present

Circular columns

Loaded perimeter, u₀ = π x D

Equivalent rectangle properties:

D_Equiv = u₀ /4

B_Equiv = u₀ /4

Bounding rectangle properties:

D_Bound = D

B_Bound = D

Bounding Perimeter, u_0Bound = 2 x (D_Bound + B_Bound)

β = 1.0

Critical perimeter, b_o = 2 x (D_Equiv + B_Equiv + 2d)

Note d = d_drop if a drop is present

Columns which have a re-entrant corner, i.e. where an internal angle is greater than 180 degrees, the length of a side and the slab/column interface is adjusted as indicated in the sketches below with the perimeter taken as the shortest distance around the column.

Loaded perimeter, u₀ = shortest distance around the column, as shown above.

Bounding rectangle properties:

D_Bound = D

B_Bound = B

Bounding Perimeter, u_0Bound = 2 x (D_Bound + B_Bound)

Walls

The length of the loaded perimeter at the wall face is calculated as determined below.

Loaded perimeter, u₀ = 2 x (D + B)

Bounding rectangle properties:

D_Bound = D_load

B_Bound = B_load

Bounding Perimeter, u_0Bound = 2 x (D_Bound + B_Bound)

a_n = max(D,B)

b_n = min(D,B)

β = a_n / b_n

Critical perimeter, b₀ = 2 x (D_Bound + B_Bound + 2 x d)

Note d is for the slab

Point loads

The length of the loaded perimeter at the point load may be calculated as determined below.

Loaded perimeter = 2 x (D_load + B_load)

Bounding rectangle properties:

D_Bound = D_load

B_Bound = B_load

Bounding Perimeter, u_0Bound = 2 x (D_Bound + B_Bound)

a_n = max(D,B)

b_n = min(D,B)

β = a_n / b_n

Critical perimeter, b₀ = 2 x (D_Bound + B_Bound + 2 x d)

Note d is for the slab

Additional loaded perimeter drops

The additional loaded perimeter for a column/wall with a drop is defined by the perimeter of the rectangular drop

u_0drop = 2 x B_drop x D_drop

a_n = max(D_drop,B_drop)

b_n = min(D_drop,B_drop)

β = a_n / b_n

Critical perimeter, b₀ = 2 x (D_drop + B_drop + 2 x d)

Note d is for the slab around the drop

The equivalent perimeter

For any column and wall shape, the equivalent perimeter -

For “rectangular” shapes of column (all except circle and polygon of n sides) and walls, the equivalent loaded perimeter -

D_Equiv = D_Bound x u₀ / u_0Bound
B_Equiv = B_Bound x u₀ / u_0Bound

The equivalent perimeter is used in three situations

adjustment of the loaded perimeter length/shape u₀ for edge and corner columns/walls
for the rectangle from which the critical and subsequent trial perimeters are determined
Reduction in V_Ed (the area is the area inside the equivalent rectangle).

Peripheral section properties

When using an orthogonal reinforcement arrangement:

Properties are obtained for the principal axis system
Peripheral section properties determined using line approach (start and end coordinates) - ACI 421.1R-08 guidance

Modification of control perimeters to take account of slab openings

If NOT working to ACI 318-19

If any openings are present in the slab and if the nearest opening edge is not greater than 10 x h (h = slab thickness) from the face of the column then the length of the loaded perimeter at the column face, b_o and out from there to b_on are reduced to take account of the presence of the opening(s) as indicated in ACI 318-08 Figure R11.11.6 ; ACI 318-11 Figure R11.11.6 ; ACI 318-14 Figure R22.6.4.3

Note: When a perimeter length has been reduced to cater for openings - as the exact position of the opening in relation to the reinforcement strips is not known, the calculations conservatively ignore any patch reinforcement in the punching checks - only the slab reinforcement is used.

If working to ACI 318-19

If any openings are present in the slab and if the nearest opening edge is not greater than 4 x h (h = slab thickness) from the face of the column then the length of the critical perimeter at the column face, b_o and out from there to b_on are reduced to take account of the presence of the opening(s) as indicated in ACI 318-19 Section 22.6.4.3, Figure R22.6.4.3

User Modification of control perimeters

If you want to consider the effect of openings, but do not want to place them in the slab, this can be done by defining the following property:

b_o - user reduction

When applied, the length of the perimeter is reduced by the specified amount.

Pad base punching shear checks

When working to ACI 318, the punching shear checks for pad bases follow the same basic principle as used for mats, the main differences being:

Column local axes are always parallel with the pad base edges in the pad base punching checks.
Loads from the column are always above the pad base (one direction).
No openings can be placed in pad bases.
No shear reinforcement is used in pad bases.

Pile cap punching shear checks

When working to ACI 318, punching shear checks are performed for the column and the individual and paired piles.

The punching shear check for the column is similar to that for pad bases, but with the following difference:

the shear force at a perimeter uses the value from the column reduced by pile loads within the perimeter

The punching shear check for the pile is similar to that for pad bases, but with the following differences:

variable d is replaced with d_red where d_red =min (h – “pile penetration depth”, average reinforcement effective depth)
no moments act on top of the pile, only axial load considered

Punching shear checks to ACI 318

Punching shear checks to ACI 318

Limitations and assumptions

Applicability of wall punching checks

Columns and walls not perpendicular to slabs

Overlapping control perimeters

Slab shear strength

Definitions

Loaded, critical and outer perimeters

Length of loaded and critical perimeters

Columns

Walls

Point loads

Additional loaded perimeter drops

The equivalent perimeter

Peripheral section properties

Modification of control perimeters to take account of slab openings

User Modification of control perimeters

Pad base punching shear checks

Pile cap punching shear checks