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Using the method of consistent deformations, determine the magnitude of the reaction at A. Let w = 18 kN/m and L = 9 m.

We can use Castigliano’s Second Theorem to calculate the deflections of trusses, beams, and frames.

Draw the influence line for the shear at B. What is the line’s maximum value? Let L1 = 3 m and L2 = 7 m.

Determine the beam deflection at point B. Assume E = 186 GPa and I = 232 × 106 mm4 are constant.

The truss is pin supported at A and rocker supported at E. Assume all members are pin connected. Determine the magnitude of the force in member AI. Let F1 = 650 lb, F2 = 600 lb, and L = 5 ft.

The roof truss is pin supported at A and roller supported at E. Determine the magnitude of the force in member CD. Let F1 = 10 kN and F2 = 6 kN.

A truck exerts wheel reactions P1 = 9 kips and P2 = 3 kips on the deck of a bridge. Determine the maximum positive moment at C. Assume the truck only travels in the direction shown. The influence lines for VC and MC are shown, along with the peak values of the influence lines.

Draw the influence line for the vertical reaction at A. What is the line’s minimum value? Let L1 = 6 m and L2 = 3 m.

The truss is pin supported at A and rocker supported at E. Assume all members are pin connected. Determine the magnitude of the force in member EF. Let F1 = 150 lb, F2 = 800 lb, and L = 5 ft.

The beam supports a uniform live load of 523 lb/ft. Determine the maximum positive shear that can be developed at point B. Assume the support at A is a pin and C is a roller. The influence lines for VB and MB are shown, along with the peak values of the influence lines.