Figure 8 shows a simply-supported beam of length L subjected to a distributed lo

Question

Figure 8 shows a simply-supported beam of length L subjected to a distributed load that varies linearly from zero at A to omega0 per unit length at B. Sketch the shear force diagram for the beam and hence determine possible locations for the maximum bending moment Mmax. Describe clearly a procedure from which we could determine the optimal choice for the distances a, b defining the location of the supports, in order to minimize Mmax. You might like to try to determine the corresponding values of a/L and b/L for extra credit, but be warned that this is challenging. You may need to use Maple to solve it. Figure 8

Explanation / Answer

taking moment about left support=0 wL^2/2 * (L-a) + Rb (L-b-a)=0 than find Ry by sum Fy=0

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