Problem 2.  Using a pretensioned, straight tendon profile in the given simply supported inverted T-beam, verify that S1 = 3754 in3 and S2 = 5292 in3.  Determine the largest acceptable eccentricity e and smallest P possible at midspan and support so that the given allowable stresses are not violated.  Determine the cracking moment for the beam.  Determine the nominal capacity of the beam by strain compatibility and by the simplified ACI equation method.

Given:  f’ci = 4 ksi  f’c = 6 ksi

wd = 1 k/ft  wl = 2 k/ft 

fpu = 270 ksi  fpy = 230 ksi

R = 0.85

1/2'” diameter stress relieved strand

fti = 0.190 ksi, fti = 0.380 ksi at support

fci = -1.8 ksi

fts = 0.581 ksi

fcs = -2.4 ksi

Span length = 40 ft