Statics and Dynamics Quiz
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A propped cantilever beam (fixed at A, roller at B) of length 4 m4\text{ m} is statically indeterminate. Using the compatibility method, the roller reaction is determined to be RB=3wL8=6 kNR_B = \tfrac{3wL}{8} = 6\text{ kN} (upward) for a uniform downward load w=4 kN/mw = 4\text{ kN/m} over the full span. The fixed-end reactions are then: RA=wL−RB=10 kNR_A = wL - R_B = 10\text{ kN} upward and MA=8 kN⋅mM_A = 8\text{ kN}\cdot\text{m} clockwise (i.e., the wall applies a clockwise moment on the beam at A).
Using a section cut at x=3 mx = 3\text{ m} from the fixed support A and the left free-body diagram, what is the internal bending moment MM at the cut? (Positive moment = sagging.)
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