The reinforced concrete girder shown in Figure P7.44a is prestressed by a steel cable that...

The reinforced concrete girder shown in Figure P7.44a is prestressed by a steel cable that induces a compression force of 450 kips with an eccentricity of 7 in. The external effect of the prestressing is to apply an axial force of 450 kips and equal end moment M_P = 262.5 kip · ft at the ends of the girder (Figure P7.44b). The axial force causes the beam to shorten but produces no bending deflections. The end moments M_P bend the beam upward (Figure P7.44c) so that the entire weight of the beam is supported at the ends, and the member acts as a simply supported beam. As the beam bends upward, the weight of the beam acts as a uniform load to produce downward deflection. Determine the initial camber of the beam at midspan immediately after the cable is tensioned. Note: Over time the initial deflection will increase due to creep by a factor of approximately 100 to 200 percent. The deflection at midspan due to the two end moments equals ML²/(8EI). Given: I = 46,656 in.⁴, A = 432 in.², beam weight w_G = 0.45 kip/ft, and E = 5000 kips/in.².

Figure P7.44: