## Shear-Strength Design of Prestressed Concrete

The ACI 318 Building Code requires that prestressed concrete beams be designed to resist diagonal tension by strength theory. There are two types of diagonal-tension cracks that can occur in prestressed-concrete flexural members: flexural-shear cracks initiated by flexural-tension cracks, and web-shear cracks caused by principal tensile stresses that exceed the tensile strength of the concrete.

The factored shear force Vu computed from Eq. (9.38) can be used to calculate the diagonal-tension stress. The distance d from the extreme compression surface to the centroid of the tension reinforcement should not be taken less than 0.80 the overall depth h of the beam.

When the beam reaction in the direction of the applied shear introduces compression into the end region of the member, the shear does not need to be checked within a distance h/2 from the face of the support.

Minimum Shear Reinforcement. The ACI 318 Building Code requires that a minimum area of shear reinforcement be provided in prestressed-concrete members, except where the factored shear force Vu is less than 0.5Vc, where Vc is the assumed shear that can be carried by the concrete; or where the depth h of the member is less than 10 in, 2.5 times the thickness of the compression flange, or one-half the thickness of the web; or where tests show that the required nominal (ultimate) flexural and shear capacity can be developed without shear reinforcement.

When shear reinforcement is required, the amount provided perpendicular to the beam axis within a distance s should be not less than Av given by Eq. (9.81). If, however, the effective prestress force is equal to or greater than 40% of the tensile strength of the flexural reinforcement, a minimum area Av computed from Eq. (9.130) may be used.

The ACI 318 Building Code does not permit the yield strength ƒy of shear reinforcement to be assumed greater than 60,000 psi except the design yield strength of deformed welded wire fabric should not exceed 80,000 psi. The Code also requires that stirrups be placed perpendicular to the beam axis and spaced not farther apart than 24 in or 0.75h, where h is the overall depth of the member.

The area of shear reinforcement required to carry the shear in excess of the shear that can be carried by the concrete can be determined from Eq. (9.40a).

Maximum Shear. For prestressed concrete members subjected to an effective prestress force equal to at least 40% of the tensile strength of the flexural reinforcement, the shear strength provided by the concrete is limited to that which would cause significant inclined cracking and, unless Eqs. (9.132) and (9.133) are used, can be taken as equal to the larger of

In a pretensioned beam in which the section h/2 from the face of the support is closer to the end of the beam than the transfer length of the tendon, the reduced prestress in the concrete at sections falling within the transfer length should be considered when calculating Vcw. The prestress may be assumed to vary linearly along the centroidal axis from zero at the beam end to the end of the transfer length. This distance can be assumed to be 50 diameters for strand and 100 diameters for single wire.

(‘‘PCI Design Handbook,’’ Precast / Prestressed Concrete Institute.)