Statics and Dynamics Quiz
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A beam of length LL is pinned at the left end and roller-supported at the right end. A linearly varying distributed load acts on the beam: the intensity is w1w_1 at the left support and w2w_2 at the right support, with w1≠w2w_1 \neq w_2. The standard centroid formula for a trapezoidal load places the equivalent resultant at xˉ=L3⋅w1+2w2w1+w2\bar{x} = \frac{L}{3}\cdot\frac{w_1 + 2w_2}{w_1 + w_2} from the left end.
A student uses this formula with w1=0w_1 = 0 (triangular load, zero at left, peak w2=w0w_2 = w_0 at right) and obtains xˉ=2L3\bar{x} = \frac{2L}{3}. A second student uses the formula for the same load but measures xx from the right support, obtaining xˉ′=L3\bar{x}' = \frac{L}{3} from the right, i.e., xˉ=2L3\bar{x} = \frac{2L}{3} from the left. The students compare their results. Which statement is correct?
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