1.A rectangular beam of 12 in. width and 18 in. depth is pre-stressed by a force of 20 kip applied through a tendon of wires of 2 in. diameter located 3 in. from the bottom. The beam carries a load of 2 k/ft over a span of 20 ft. The pre-stress losses are 25%. Compute the stresses in concrete at the (1) transfer stage, and (2) service load stage. The density of concrete is 145 lbs/ft3. 2. The compressive strength of concrete is 5000 psi. Accordingly, the allowable stresses are the following: ftt = the allowable tensile stress in concrete at initial transfer of pre-stress = -190 psi fct = the allowable compression stress in concrete at initial transfer of pre-stress = 2400 psi fcs = the allowable compression stress in concrete under service loads = 30,000 psi fts = the allowable tensile stress in concrete under service loads = -424 psi Check whether the beam of Problem 18.15 is adequate. 3. Design a rectangular pre-stressed beam section (on allowable stress basis) that supports a live load of 2.5 k/ft on a span of 30 ft. Pre-stress losses = 22%. fc 6000 psi, ftt = -208 psi, fct = 2880 psi, fcs = 3600 psi, fts = -465 psi.