Explanation Given information: The structure is given in the Figure. Apply the sign conventions for calculating reaction forces and moments using the three equations of equilibrium as shown below. For summation of forces along x -direction is equal to zero ( ∑ F x = 0 ) , consider the forces acting towards right side as positive ( → + ) and the forces acting towards left side as negative ( ← − ) . For summation of forces along y -direction is equal to zero ( ∑ F y = 0 ) , consider the upward force as positive ( ↑ + ) and the downward force as negative ( ↓ − ) . For summation of moment about a point is equal to zero ( ∑ M at a point = 0 ) , consider the clockwise moment as negative and the counter clockwise moment as positive. Calculation: Let A x and A y be the horizontal and vertical reactions at the hinged support A . Let B x and B y be the horizontal and vertical reactions at the hinged support B . Sketch the free body diagram of the given structure as shown in Figure 1. Use equilibrium equations: For the member AC , the summation of moments about C is equal to 0. ∑ M C A C = 0 A x ( 20 ) + 1 2 ( 3 ) ( 20 ) ( 2 3 × 20 ) = 0 20 A x = − 400 A x = 20 k ← Therefore, the horizontal reaction at A is A x = 20 k ← _ . Summation of moments about B is equal to 0. ∑ M B = 0 − A y ( 20 ) − A x ( 4 ) + 1 2 ( 3 ) ( 20 ) ( 20 3 − 4 ) + 1 2 ( 3 ) ( 20 ) ( 40 3 ) = 0 Substitute 20 k for A x

Calculate the support reactions for the given structures.

Structural Analysis, Si Edition

5th Edition

ISBN: 9781285051505

Author: Aslam Kassimali

Publisher: Cengage Learning

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