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Unformatted text preview: Beam: Shear and Moment Diagrams A beam is supported as shown in the figure; it is intended to resist concentrated vertical load F 1 , located L 1 from the left end, and distributed vertical load F d2 , which acts over a length L 2 from the right end of the beam. The beam is sectioned into units with endpoints A, B, C, and D. The assignment in this problem is to draw the Shear and Moment diagrams for this beam. The X direction is along the beam. F 1 F d2 L L 1 L 2 A B C D The first step is to draw a freebody diagram (FBD) of the overall beam to calculate the reaction forces at A and D . To determine the reaction forces, the distributed vertical load may be replaced with a concentrated vertical load F 2 , which acts at a length L 2 /2 from the right end of the beam. F 1 F 2 L L 1 L /2 2 A x A y D y We write three equations of static equilibrium: 2 / 2 2 1 1 2 1 L L F L F L D M F F D A F A F y Az y y y x x The reaction force solutions are: y y x y D F F A A L L L F L F D 2 1 2 2 1 1 2 / To determine the shear forces in each subsection of the beam, freebody diagrams of each subsection are drawn, representing the forces on the left and right sides. For this problem, the shear forces are: x F F A x v F A x v A x v d y CD y BC y AB 2 1 1 The shear forces in the first two subsections AB and BC are constant. The shear forces in the first two subsections AB and BC are constant....
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 Spring '10
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