For posttensioned beams, the reduction multiplier 10 is

0.75 + 0.06vfc where f0 and the reinforcement stress are in ksi.

8.8.6 ACI Expression for Cracking Mitigation

The ACI expression used for crack control in reinforced concrete structural elements through bar spacing is extended to prestressed concrete bonded beams, on the assumption of the desirability of a "seamless transition'' between serviceability requirements for nonprestressed members and fully prestressed members. However, the mechanism of crack generation differs in the prestressed beam from that in reinforced concrete due to initially imposed precompression. Also, effects of environmental conditions are considerably more serious in the case of prestressed concrete elements due to the corrosion risks to the tendons. These provisions stipulate that the spacing of the bonded tendons should not exceed | of the maximum spacing permitted for nonprestressed reinforcement. The ACI expression for prestressed members becomes

but not to exceed 8(36/Af;0). In SI units, the expression becomes

but not to exceed 200(252/Afs, where Afs is in MPa and cs is in mm)

Afs = difference between the stress computed in the prestressing tendon at service load based on cracked section analysis, and the decompression stress fdc in the prestressing tendon. The code permits using the effective prestress fpe in lieu of fdc, ksi. A limit Afs = 36 ksi, and no check needed if Afs is less than 20 ksi. cc = clear cover from the nearest surface in tension to the flexural tension reinforcement, in.

While the code follows the author's definition of Afs given in Section 8.8.5, Equations 8.105 and 8.106 still lack the practicability of use as a crack control measure and the | factor used in the expressions is arbitrary and not substantiated by test results. It should be emphasized that beams have finite web widths. Such spacing provisions as presented in the Code are essentially unworkable, since actual spacing of the tendons in almost all practical cases is 1ess than the code equation limits, hence almost all beams satisfy the code, though cracking levels may be detrimental in bridge decks, liquid containment vessels, and other prestressed concrete structures in severe environment or subject to overload. They require additional mild steel reinforcement to control the crack width. Therefore, the expressions presented in Section 8.8.5 in conjunction with Table 8.14 from the ACI 224 Report [14] should be used for safe mitigation of cracking in prestressed concrete members.

TABLE 8.14 Maximum Tolerable Flexural Crack Widths

Crack width

TABLE 8.14 Maximum Tolerable Flexural Crack Widths

Crack width

Exposure condition



Dry air or protective membrane

0 0

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