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 MP = 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 MP 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 .

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450 kips Mp=262.5 kip. ft 450 kips prestressed tendon Moment diagram Forces applied to concrete by prestress (b) 60 Beam dimensions (a) 450 kips Mp=262.5 kip. ft -262.5 kip. ft LA 450 kips 12" 36" section A-A initial camber WG Deflected shape; prestress and weight of beam act (c)