A 40-ft simply supported prestressed concrete beam has a parabolic tendon with eccentricity 8 in at midspan and zero at ends. The effective prestress force is 450 kips. What is the midspan camber due to prestress alone, assuming E = 4.5 x 10^6 psi and I = 12,500 in^4?

Why is this the answer?

For a parabolic tendon with eccentricity e at midspan and zero at ends, the upward deflection is delta = (5/48) * (P * e * L^2) / (E * I). Converting units: L = 480 in, P = 450,000 lb, e = 8 in, E = 4.5e6 psi, I = 12,500 in^4. Delta = (5/48) * (450,000 * 8 * 480^2) / (4.5e6 * 12,500) = 0.384 in. Re-evaluating the formula for a constant moment equivalent: M = P*e. Deflection = (M*L^2)/(8*E*I) = (450*8 * 480^2) / (8 * 4500 * 12500) = 0.3686 in. The provided formula in the original explanation is dimensionally incorrect.

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