The concrete I-beam of figure below is pre-stressed with four stranded cables having total area Ap=0.575 sq. in. Eccentricity of the steel varies para-bolically from 0 at the supports to 7.58 in at the center of the 30-ft span. The effective stress in the steel after losses is 132000psi.
(a) What uniformly distributed superimposed load will produce cracking of the beam, given that the modulus of rupture fr=475 psi?
(b) What superimposed load will produce a balanced condition of external and equivalent pre-stress load, such that uniform axial compression will be obtained in the concrete?
(c) For the balanced load just computed, would the midspan deflection be downward, upward, or zero? Explain.

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10"–>| 4" 3"- 17.58" 20" 4" Ap = 0.575 in.2 10"- (a) 10"–>| 4" 3"- 17.58" 20" 4" Ap = 0.575 in.2 10"- (a)