A beam with an overhang is subjected to a varying load, as shown in Figure . Determine the reactions at supports A and B.
Fig. Beam with an overhang.
Solution
Free-body diagram. The free-body diagram of the entire beam is shown in Figure.
Computation of reactions. Observe that the distributed loading in the beam is triangular. The distributed load is first replaced with a single resultant force, as shown in Figure The magnitude of the single resultant force is equal to the area under the triangular loading. Thus, P = ()(6 m)(10 kN/m), and its centroid is at the center of the loading (6m). Applying the equations of equilibrium provides the following:
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