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Mcr = Sb(0. 5lVfffi + fce - fd) Vcw = 0 . 3 (l-p7 + 0 . 3fc) bw d + Vp

where Mcr for shear analysis is equal to the moment causing flexural cracking at section due to externally applied load

fc bw d

Avfy d Ayfy d

Min. Av: the smaller of

80 f. dp V b where bw, s, and d are in millimeters and fy is in MPa.

8.7.4 Design of Prestressed Concrete Beams Subjected to Combined

Torsion, Shear, and Bending in Accordance with the ACI 318-02 Code

8.7.4.1 Compatibility Torsion

In statically indeterminate systems, stiffness assumptions, compatibility of strains at the joints, and redistribution of stresses may affect the stress resultants, leading to a reduction of the resulting torsional shearing stresses. A reduction is permitted in the value of the factored moment used in the design of the member if part of this moment can be redistributed to the intersecting members. The ACI Code permits a maximum factored torsional moment at the critical section h/2 from the face of the supports for prestressed concrete members as follows:

Acp = area enclosed by outside perimeter of concrete cross-section = xoyo pcp = outside perimeter of concrete cross-section Acp, in. = 2(x0 + y0)

where /c is the average compressive stress in the concrete at the centroidal axis due to effective prestress only after allowing for all losses.

Neglect of the full effect of the total value of external torsional moment in this case does not, in effect, lead to failure of the structure but may result in excessive cracking if f 4yf (A2p/ppc) is considerably smaller in value than the actual factored torque.

If the actual factored torque is less than that given in Equation 8.68, the beam has to be designed for the lesser torsional value. Torsional moments are neglected however if for prestressed concrete

8.7.4.2 Torsional Moment Strength

The size of the cross-section is chosen on the basis of reducing unsightly cracking and preventing the crushing of the surface concrete caused by the inclined compressive stresses due to shear and torsion defined by the left-hand side of the expressions in Equation 8.70. The geometrical dimensions for torsional moment strength in both reinforced and prestressed members are limited by the following expressions:

1. Solid sections

2. Hollow sections

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