Shear Strength

Code References

ACI 318-14

Definition

For the purposes of this discussion, one-way (or vertical) shear is defined as the shear force perpendicular to the axis or span of the member. Also, the discussion in this section is limited to precast concrete members that span vertically and are governed by the ACI 318 Specification. Note, one-way shear is how it is defined in the ACI 318 code, it is also known as beam action shear.

Basic Equation

The shear resistance of precast concrete components must meet the following requirement (22.5):

where:

V_c = nominal shear strength provided by concrete

V_s = nominal shear strength provided by shear reinforcement

φ = reduction factor as defined in the governing specification

Calculation of Vc

All values of f^’_c used in determining V_c are reduced by the appropriate factor if using lightweight concrete. Note that the analysis uses the base area of prestressing strand, ignoring development length, to determine if a member is prestressed or non-prestressed. The full depth is also used in the calculation of d (with a lower limit of 0.8*H), except where d is used in the term V*d/M, then the actual d is used with the limit of 0.8*H.

For all beams (both prestressed and non-prestressed), the minimum shear strength is 2 * √(F’c).

Shear Area

The shear area is calculated based on the polygons which make up the cross section, which are used in place of the bd term in the equations for V_c. The shear area is computed by going down d and computing the area of the polygon above that location.

Mild Reinforced (non-prestressed) Members

For non-prestressed members, the analysis uses the appropriate equation based on the sign of the of the axial load (compression – 22.5.6, tension – 22.5.7, or none – 22.5.5). Note that both the ‘tension’ and the ‘compression’ equations become the ‘no axial load’ equation when the axial load is equal to zero. For both no axial force and axial compression, both the detailed and the simplified methods are used, and the program selects the greater of the two values (the axial tension section does not include a detailed method for the calculation of V_c).

Prestressed Members

For horizontal prestressed members, the analysis uses the traditional V_ci/V_cw equations to determine the shear capacity of the concrete (22.5.8.3). The approximate method for calculating V_c as shown in the equations tabulated in the ACI 318 code (Table 22.5.8.2) is typically reserved for members that span vertically. The nominal concrete shear strength determined using this approach includes the upper and lower limits as noted in ACI 318.

Calculation of Vs

When no transverse reinforcement has been defined, the amount of shear required to be resisted by shear reinforcement, V_s, is calculated by:

The strength of the provided transverse reinforcement, when applicable, is computed by summing all of the zones the location overlaps with. Eriksson Columncomputes the total transverse provided based on the transverse inputs and used in Eq. 22.5.10.5.3.

Required Shear Reinforcement

For most columns, minimum shear reinforcement is required where V_u > 0.5φV_c. Minimum transverse reinforcement is computed following section 10.6.2.2. Av minimum will always be displayed in the output whether it is required or not, however when it is not required it will not be included in the Av Required total in the output. An checkbox, under shear options, may be used to zero out minimum transverse when it is not required.

Note that there are two V_s terms used in the program, one is V_s,reqd, based on V_u-V_c, and the second is V_s,prov, based on the area of shear steel input by the user.

The program also calculates a maximum value of φV_n (22.5.1.2), which is essentially an upper limit on V_s.

One way shear capacity is calculated at every analysis point in the member. At each point Eriksson Column computes either the required area of steel, or checks the provided area of steel against the calculated amount. Maximum spacing is also computed at every point along the member. For this equation fpe is assumed to be equal to the average prestress on the member (P/A).

Cross Section Limits

The cross section limits are checking against ACI 318-14 22.5.1.2. If the limits fail an error will be displayed in the analysis report.

References

ACI Committee 318, Building Code Requirements for Structural Concrete (ACI 318-14), American Concrete Institute, Detroit, 2014.

Aswad, Burnley, Cleland, Orndorff, and Wynings, “Load Testing of Prestressed Concrete Double Tees Without Web Reinforcement,” PCI Journal, V. 49, No. 2, March-April 2004, pp. 66-77.

PCI Industry Handbook Committee, PCI Design Handbook, 8^th Ed., PCI, Chicago, 2017.