Punching shear checks to ACI 318
Aspects of Tekla Structural Designer's punching shear design that are specific to ACI 318.
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
 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
 One way action  beam action in long or narrow slabs or between closeby 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 nonuniform reinforcement arrangements (i.e. orthogonal).

Length of loaded and critical perimeters
Columns
The length of the loaded perimeter, u_{0} at the column face and critical perimeter, b_{0} 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, u_{0} = 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, b_{0} = 2 x (D_{Bound} + B_{Bound} + 2 x d)
Note d = d_{drop} if a drop is present
Circular columns
Loaded perimeter, u_{0} = π x D
Equivalent rectangle properties:
D_{Equiv} = u_{0} /4
B_{Equiv} = u_{0} /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
Loaded perimeter, u_{0} = 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, u_{0} = 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, b_{0} = 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, b_{0} = 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, b_{0} = 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 u_{0} / u_{0Bound}

B_{Equiv} = B_{Bound} x u_{0} / u_{0Bound}
The equivalent perimeter is used in three situations

adjustment of the loaded perimeter length/shape u_{0} 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

Properties are obtained for the principal axis system
 Peripheral section properties determined using line approach (start and end coordinates)  ACI 421.1R08 guidance
Modification of control perimeters to take account of slab openings
If NOT working to ACI 31819
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 31808 Figure R11.11.6 ; ACI 31811 Figure R11.11.6 ; ACI 31814 Figure R22.6.4.3
If working to ACI 31819
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 31819 Section 22.6.4.3, Figure R22.6.4.3
User Modification of control perimeters
 b_{o}  user reduction
When applied, the length of the perimeter is reduced by the specified amount.
Pad base punching shear checks
 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 shear force at a perimeter uses the value from the column reduced by pile loads within the perimeter
 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