The structure shown in Fig. P3.146(a) consists of a steel I beam AB and a steel cable AC...

The structure shown in Fig. P3.146(a) consists of a steel I beam AB and a steel cable AC, and load P is horizontal. For the geometry and loading shown, the cable will likely be considerably more flexible than the I beam, and the structure shown in Fig. P3.146(b) is an appropriate model where the I beam is rigid and the cable is a spring with stiffness k = 2000 lb/in.

(a) Let P = 5000 lb, and assume the displacement of the structure is small. Thus, using the geometry shown in Fig. P3.146(b) where the I beam is vertical and the cable has 45° orientation, determine the forces supported by the I beam and cable. Using these forces, determine the horizontal displacement d of point A, assuming the spring is unstretched when the I beam is vertical.

(b) Let d = in., for this case the I beam is no longer vertical and the cable’s orientation is no longer 45°. Determine the force P needed to produce this value of d, assuming the spring is unstretched when the I beam is vertical.

(c) Comparing the analyses in Parts (a) and (b), which of these provides the more accurate results (explain)?