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 horizontally 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.
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Basic Equation
The shear resistance of precast concrete components must meet the following requirement (22.5):
...
where:
Vc = nominal shear strength provided by concrete
Vs = 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 Vc 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.
For composite members, the shear area (and the depth thereof), is dependent on whether the composite topping is to be considered a part of the shear resisting section. The final strength of the precast section at all times to calculate the shear resistance, even when the user selects the use of the composite section. 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 members (both prestressed and non-prestressed), the minimum shear strength is based on plain concrete shear strength, which is 4/3 * √(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 Vc. Some sections (typically the sections which consist of webs and top/bottom flanges), only the polygon which encompasses the web is used (and extending this polygon into the top and bottom flanges, if present). This polygon is extended into the topping if the composite shear resistance section option is selected by the user.
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 Vc).
The option exists to limit d to the same minimum as prestressed, 0.8h. Although this does not exist in the code, this can give users closer to expected results for layers with compression reinforcement. Often beams with compression reinforcement do not develop a compression block deep enough to put them in compression, for these cases the d from flexure is often very low.
Prestressed Members
For prestressed members, the analysis uses the traditional Vci/Vcw equations to determine the shear capacity of the concrete (22.5.8.3). The approximate method, Table 22.5.8.2, is also available for calculating the concrete shear strength.. The nominal concrete shear strength determined using this approach includes the upper and lower limits as noted in ACI 318.
Minimum Shear Strength
The concrete shear strength is also assumed to have a minimum strength equal to the plain concrete shear strength as defined in Table 14.5.5.1.