Beam ABCD has a simple support at A, an internal hinge at B, and simple supports at C and D. AB = BC = 4 m and CD = 10 m. For a moving concentrated load of 50 kN, find the magnitude of the maximum bending moment at C in kN m.
A load moving on AB gives a downward transfer to the right-hand beam at hinge B of $R_B=50x/4$, where $x$ is measured from A. The resulting hogging moment at C is $-R_B(4)$, reaching −200 kN m when the load reaches B. A load on overhang BC gives moment at C equal to minus load times its distance from C, also bounded by 200 kN m. Loads on CD produce no moment at C through the unloaded free-ended overhang. Thus the maximum magnitude is 200 kN m.
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