Problem 1.  A simply supported beam of length L = 20 ft is constructed of the given prestressed box beam cross section. The tendons are harped at midspan with an eccentricity of 9 in. The end eccentricities are zero. Given the following:

wo = 0.283 k/ft

wd = 2.72 k/ft

wl = 3.2 k/ft

Pi = 210 k

Pe = 168 k

1. Verify that the moment of inertia of the box beam is 16,444 in2

2. Determine the extreme fiber stresses at transfer at the critical section

3. Determine the extreme fiber stresses at service loads at the critical section.

FOR EXTRA CREDIT:  If the beam were to be extended by a 10 ft overhang (total length of beam = 30 ft) and the eccentricity at the support where the overhang is supported is –9 in (the end is still at e = 0.0) compare your results for question 2 above.  Also, what are the extreme fiber stresses at service loads at the critical section for positive moment as well as negative moment?  Hint:  DRAW SHEAR AND MOMENT DIAGRAMS FOR A SIMPLE BEAM WITH AN OVERHANG!