ACI 318 Equations for Calculation of Allowable Shear Stress on the Unreinforced Section

The allowable shear stress is calculated by selecting the appropriate equation from ACI 318-14: 22.6.5.2 or 22.6.5.5.

Equation 22.6.5.2(a) controls in non-prestressed concrete zones with large column aspect ratios. As the aspect ratio of the column gets larger, the allowable punching shear stress approaches the allowable one-way shear stress.

Equation 22.6.5.2(b) is intended to correlate the allowable shear stress in non-prestressed zones with the ratio b_o/d. This equation generally controls in thinner slabs with large columns or at critical sections outside column caps.

Equation 22.6.5.2(c) is the upper bound of allowable shear stress for non-prestressed zones, $4\sqrt{{f^{\prime }}_c}$.

Equation 22.6.5.5 is for application to prestressed punching zones. In order to qualify as prestressed, a zone must meet the following criterion:

1. The effective prestress, f_pc at the column shall not be less than 125 psi. The effective prestress is calculated by averaging the precompression in all the elements within the punching check radius. This could result in non-prestressed equations being used in drop caps of prestressed slabs where the precompression drops below 125 psi in the cap. Additionally, if large restraining elements are used (i.e., shear walls) that divert the prestressing force in a region, the non-prestressed equations would correctly be used where the average precompression is below 125 psi.
2. f’_c shall not be taken greater than 5000 psi. If a concrete strength is input greater than 5000 psi, a maximum f’_c of 5,000 psi will be used in prestressed punching zones, but the allowable shear stress will still be calculated using equations 22.6.5.5.
3. The column must not be closer to a discontinuous edge than four times the slab thickness. In this check the slab thickness is taken as the average slab thickness over the critical section. A discontinuous edge is defined as an edge that extends beyond the perimeter of the defined punching check. An opening that is contained completely within the punching check is not considered a discontinuous edge, regardless of its size.

If any of the above conditions are not met, equations 22.6.5.2 are applied.

For the ACI 318-08, ACI 318-11, and ACI 318-14 standards, lightweight concrete is considered.

ACI 318 Maximum Reinforced Section Stress

The reinforced shear stresses v_u on the column sections are limited to a maximum of ϕv_n, where $v_n=6\sqrt{{f^{\prime }}_c}$ per ACI 318-05 11.12.3.2. This limit can be raised to $v_n=8\sqrt{{f^{\prime }}_c}$ (This was originally suggested in ACI 421.1R-99). The higher limit is also applied to all sections in previous ACI standards . Sections with unreinforced stresses larger than these values cannot be successfully reinforced with SSR.

per

22.6.6.2

ACI 318 Calculation of Punching Resistance with SSR

Where SSR is used the punching resistance is calculated as follows:

v_n = v_c + v_s

ACI 318 Miscellaneous Provisions

The spacing to the first stud is calculated as 0.4 d in accordance with ACI 421.1R-99 equation 3.12. This spacing is rounded down to the nearest 1/8 in. for US units or 5 mm for metric units.

The maximum typical stud spacing for ACI 318-99, ACI 318-02, and ACI 318-05 is 0.5d, but can be increased to 0.75 d when v_u/ϕ is less than or equal to $6\sqrt{{f^{\prime }}_c}$ by using the suggestion in ACI 421.1R-99 for a higher limit for spacing. The maximum typical stud spacing for ACI 318-08, ACI 318-11, and ACI 318-14 is 0.75 d when v_u/ϕ is less than or for prestressed slabs conforming to 22.6.5.4 and 0.5d otherwise (8.7.7.1.2).

The maximum tangential spacing of rails at the face of the column is limited to 2d in accordance with ACI 421.1R-99 appendix A.2 and ACI 318-14 8.7.7.1. Tangential spacing requirements are not checked at locations other than the face of the column/support.