Punching shear calculations are provided for columns/pedestals that land on concrete slabs. Here is some information on those calculations.

Punching shear is a phenomenon where a concentrated force on a slab causes a shear failure cone that "punches" through.

Punching shear calculations require a demand value and a capacity value. Many hand calculations will consider a punching shear force against a punching shear capacity force. This works if only shear force is present, but is insufficient if a moment is occurring on the column/pedestal. Thus, a stress demand/stress approach is taken. The applied shears and moments, along with the shape of the punching shear failure cone are used to calculate a maximum punching shear stress.

The effective depth of the slab is used to define the punching shear perimeter at a distance of d/2 beyond the edge of the column/pedestal.

The effective depth is based on the smallest depth to centroid of reinforcing for the Design Strips that encompass the pedestal. In cases where no design strips are defined at the pedestal location, the program will assume the bar size and cover specified in the first rule defined in the Design Rules spreadsheet.

Length of the critical section along the local axes. This value is used to define the punching shear perimeter as well as to define how much of the moment is transferred by eccentricity of shear (as opposed to the portion transferred by flexure).

Note:

- For further discussion refer to ACI section 11.12.1.2 and 13.5.3

This is a property (Jc) of the critical section which is analogous to polar moment of inertia about the local

Note:

- This calculation is very different depending on interior, edge or corner punching shear cases.
- For further discussion and equations refer ACI 318-14 Section 48.4.4.2.3 (ACI 318-11 Section R11.11.7.2) and Chapter 13-8 of the
__Reinforced Concrete Mechanics and Design__textbook by MacGregor & Wight.

These give the distance from the shear perimeter edge to the centroid of the shear perimeter. For an interior punching shear perimeter this will always be L1/2 or L2/2. For edge and corner cases this value is calculated as the moment of area of the shear perimeter/area of the sides.

Note:

- For further discussion and equations refer to Chapter 13-8 of the
__Reinforced Concrete Mechanics and Design__textbook by MacGregor & Wight.

This is calculated from the dimensions of the assumed punching shear perimeter. It represents the fraction of the unbalanced moment for each axis that is transferred by eccentricity of shear.

Note:

- For further discussion refer to ACI 318-14 Sections 8.4.4.2.2 and 8.4.2.3 (ACI 318-11 sections 11.11.7.1 and 13.5.3).

The Total Stress is the direct shear stress plus the shear stress due to moment. This calculation uses the geometry of the punching shear failure cone along with the induced shear and moment forces to come up with a maximum stress. This will always occur at one of the failure cone corner locations. For an example calculation see the ACI 318-14 Section R8.4.4.2.3 (ACI 318-11 Section R11.11.7.2).

Note:

- See the Punching Shear Loading section for more information.

This represents the shear **stress** capacity of the slab calculated based on the three ACI equations for two way or punching shear capacity of the slab. Refer to ACI 318-14 Section 22.6 (ACI 318-11 Section 11.11.7.2) for more information. When ACI 318-19 is selected, the shear strength of concrete (Vc) uses equations in Table 22.6.5.2. Note that an additional size effect factor λs is added in the equation, λs is a function of effective depth of the slab d, and is calculated per Equation (22.5.5.1.3).

Note:

- This value does NOT include any additional capacity due to shear reinforcing in the slab.

Minimum Slab Reinforcement at Punching Shear Critical Section

ACI 318-19 requires a minimum slab reinforcement at punching shear critical section if vuv>φ2λφ√f’c per Section 8.6.1.2. The As,min is calculated and presented in the punching shear result of columns under this condition. Please note that the reinforcement design in elevated slabs does NOT consider this requirement, users need to consider separately the required additional slab reinforcement at punching shear critical section to account for this code requirement. RISA provides the calculations of As,min per Equation (8.6.1.2) in the Detail Report. Please refer to Elevated Slabs - Punching Shear Results for additional information.

Punching shear loading includes a direct shear component, as well as biaxial moments. It is these combined forces that are used to determine the punching shear stress and code check.

The direct punching shear demand is not exactly just the axial force in the Pedestal/Post. The area within the punching shear perimeter loading is assumed to pass directly into the support, so that force must be discounted.

This includes

For the image above the Vu demand equals P_{pedestal} - P_{direct}

The moments used are also not necessarily just the moments directly from the Pedestal/Post. If the centroid of punching shear area is not the same as the centerline of the Pedestal/Post, then there will be an eccentricity that also adds/subtracts moment.

Take the edge punching shear situation shown below:

The punching shear perimeter is to the right of the center of Pedestal/Post location. This causes a moment in the punching shear calculation even if a moment is not explicitly applied on the Pedestal/Post. This eccentricity is automatically accounted for in the punching shear stress calculation.

This same inherent eccentricity occurs in corner punching shear conditions. In this case, however, you get an induced moment in both local axes directions because of the centroid of shear perimeter location. This, similar to the edge condition, is automatically considered in the calculation of the maximum shear stress.

Note:

- The moments due to eccentricity are not accounted for in the detail report moment output. The moments shown there are taken directly from the Pedestal/Post.

The program considers as many as nine different punching shear perimeters for each column in the model. different scenarios. We look at the interior, four edges, and four corner cases and determine which configuration produces the largest code check and present that in the results.

For example, let's consider a Pedestal/Post that has an interior punching shear perimeter close to a corner.

Here the program will also check out any EDGE punching shear perimeter considerations. The two below would be the most likely ones for this given geometry.

However, these other two edge conditions will also be checked:

In most cases these odd situations will not govern. However, large moments in a given direction can cause punching shear perimeters with larger areas to govern in specific cases.

The program will also check out any CORNER punching shear considerations. The one below would be the most likely for this given geometry.

However, these other three corner conditions will also be checked:

In most cases these odd situations will not govern. However, large moments in a given direction can cause punching shear perimeters with larger areas to govern in specific cases.

Whichever configuration produces a maximum code check will be reported in the punching shear results.

Note:

- The punching shear perimeter lengths shown pictorially above will be shown as the L1 and L2 value for punching shear calculations.
- To limit the total punching shear checks for a given column we have added two caveats to the above behavior. For any of the four Edge or four Corner cases, the program will NOT perform a punching shear check if:
- The punching shear perimeter of any punching shear case is more than 50% larger than the minimum Edge/Corner punching shear perimeter.
- The punching shear perimeter of a punching shear case encompasses a column within it.

When the program tests all different cases to determine whether a corner or edge situation governs, it bases the controlling case on the maximum code check produced. There are cases where an edge case is governing that by inspection you might think it would be a corner case. See the images below:

Corner Case | Edge Case 1 | Edge Case 2 |

In these two punching shear scenarios shown above, by inspection you would likely expect the corner condition to control over the edge ones. Punching shear capacity is based on a minimum of three equations in the ACI code. One of these equations has an alpha term in it, where alpha is smallest for a corner condition. If this equation governs, this would guarantee the corner condition would have the smallest capacity. However, if this equation does not govern then these capacities may not be as different as you might expect.

Also, the demand portion of the equation will be different based on the geometry of the shear perimeter. It is possible that the edge cases produce a larger maximum stress than the corner cases.

In summary, our testing has shown that these non-intuitive scenarios where an edge controls over a corner have occurred in some instances.

It is possible to have different slab thicknesses within a single column/pedestal's punching shear perimeter. If there is a different thickness at any point along the punching shear perimeter, the program will use the thinnest thickness for the entire calculation. When there is a different thickness, there will be a warning message in the Detail Report. The L1 and L2 values, for use in calculating the b_{o}, will use the depth at the location of the pedestal/column.

It may be possible for multiple, closely spaced Pedestal/Post to create a punching shear perimeter around the GROUP of piers at a lower force level than would be observed by investigating any one of the individual Pedestal/Post. This is NOT currently considered in the punching shear code checks.

Individual Punching Shear Perimeter | Group Punching Shear Perimeter |

When a beam or wall panel is co-linear with the Pedestal/Post joint, the program will not provide a punching shear check on the Pedestal/Post. In these cases a code check of NC or "no calc" will be listed.

Wall Co-Linear with a Column | Beam Co-Linear with a Column |

Note:

- This would also refer to situations where a column from a floor above lands on either a beam or a wall. In that case punching shear checks would be omitted as well.

When a beam or column isn't co-linear with the column but is located within the punching shear perimeter then punching shear checks will still be performed. However, the calculations will not be influenced by the presence of that column or beam.

The punching shear perimeters are always investigated with respect to the Pedestal/Post local axes. As shown below, there may be cases where these local axes do not correspond to the slab edge or corner geometry adjacent to that Pedestal/Post. In cases like these it is possible for this to result in an artificially large assumed punching shear perimeter.

If either the slab edge is sloping or a column local axis is rotated it is possible to get edge shear perimeters as shown below:

The program calculates this perimeter by drawing a line along the local axis direction along the centerline of the Pedestal/Post as shown below:

From here the program offsets this line on either side of the Pedestal/Post at a distance d/2 from the face. This produces a shear perimeter that looks like this:

Though this shear perimeter is not technically correct it typically produces a nearly identical shear perimeter to the actual shear perimeter shown above.

If either the slab edge is sloping or a column local axis is rotated it is possible to get a corner shear perimeter. The program will start by trying to draw the full shear perimeter. When this happens in this case we find that the shear perimeter has two parts of it that run into a slab edge. When this occurs the program considers this a corner. In this case

In reality the punching shear is likely somewhere between these two extremes. What the program does here is similar to what is done for the edge case, now just done for both axes on one side only. Lines are drawn along the local axes of the Pedestal/Post until they reach the edge:

From here the program offsets this line on the side away from the edge at a distance d/2 from the face. This produces a shear perimeter that looks like this:

The red line represents the L1 and L2 values the program uses to calculate punching shear perimeter. This perimeter doesn't actually hit the edge of the slab in our calculation, but this puts us in a situation where we are between the two extremes shown above and is a conservative approximation.

Note:

- Pedestal/Posts are defined as a single node in the model. If this node lands inside of the slab then a punching shear check will be performed. If the single node does NOT land on the slab then the Pedestal/Post will not be considered attached to the slab and no punching shear check will be done.

When calculating the punching shear perimeter for a round Pedestal/Post, the program always converts the dimension into an equivalent square of equal perimeter. This greatly simplifies the calculation of punching perimeters when close to an edge or corner.

For an example of this let's use a 12" diameter. The perimeter = Pi*Diameter = 37.7 in.

An equivalent square would have a side dimension = 37.7 in/4 = 9.424"

Thus, a 12" diameter round Pedestal/Post would be considered a 9.424" x 9.424" square for use in punching shear checks.

The program currently does not allow for shear reinforcement. The only capacity considered for punching shear is the concrete itself. ACI 318-14 sections 22.6.6 (shear reinforcement), 22.6.9 (shearheads) and 22.6.8 (headed shear stud reinforcement) are not supported. ACI 318-11 sections 11.11.3 (shear reinforcement), 11.11.4 (shearheads) and 11.11.5 (headed shear stud reinforcement) are not supported.

It is possible that punching shear failures can occur around walls (especially walls with a short length). It is also possible that punching shear failures can occur around point loads or non-concrete columns bearing on the slab. RISAFloor ES does not currently check for punching shear for these situations.