Question

# A rectangular simply supported prestressed concrete beam of span L is subjected to a prestressing force of P acting centrally at and sections and the prestress tendons are parabolically draped with maximum eccentricity of emax at the mid span section. The uniformly distributed upward load(w) on the beam due to prestressing will be:

A
16Pemax/L2
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B
4Pemax/L2
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C
12Pemax/L2
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D
8Pemax/L2
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Solution

## The correct option is D 8Pemax/L2 The parabolic cable profile actually acts like a cable in the suspension bridge. The cable has the property that at every point of it the BM is zero. Rv=wl2 BM at C = 0 Rv×l2=RH×emax+w(l2)22 wl2×l2=RH×emax+wl28 RH=wl28emax Pcosθ=wl28emax w=8Pemaxcosθl2 For small value of θ cos θ∼––1 Hence, w=8PemaxL2

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