To determine To draw: The shear and moment diagrams for the beam. Explanation Method adopted: Graphical method Given information: The beam is bolted or pinned at A and rests on a bearing pad at B that exerts a uniform distributed loading on the beam over its 2-ft length. The uniform loading of 2 kip/ft is acting on the beam. Assumption: Consider that the right side force as positive and left side as negative in horizontal components of forces. Consider that the upward force as positive and downward as negative in vertical components of forces. Consider that the clockwise moment as negative and anticlockwise moment as positive. Apply the Equation of equilibrium wherever applicable. Determine the reactions: Entire beam: Show the free-body diagram of the entire beam as in Figure 1. Moment about point A : Determine the vertical reaction at point B by taking moment about point A . ∑ M A = 0 B y ( 10 ) − 2 × 8 × ( 1 + 8 2 ) = 0 10 B y = 80 B y = 8 kip The vertical reaction a point B will be spread as uniformly distributed load of 4 kip/ft Along the vertical direction: Determine the vertical reaction at point A by resolving the vertical component of forces. ∑ F y = 0 A y − ( 2 × 8 ) + B y = 0 (1) Substitute 8 kip for B y in Equation (1). A y − 16 + 8 = 0 A y = 8 kip Along the horizontal direction: Determine the horizontal direction at point A by resolving the horizontal component of forces. ∑ F x = 0 A x = 0 Determine the shear force: The substitution of reaction values is included in the calculation. Consider x from left end. Show the calculation of shear force values as follows: Shear force: Shear force at x = 0 : V | x = 0 ( Just left ) = 0 V | x = 0 ( Just left ) = A y = 8 kip Shear force at x = 1 ft : V | x = 1 ft = 8 kip Shear force at x = 5 ft : V | x = 5 ft = A y − 2 × 4 = 8 − 8 = 0 Shear force at x = 9 ft : V | x = 9 ft = A y − 2 × 8 = 8 − 16 = − 8 kip Shear force at x = 11 ft : V | x = 11 ft = A y − 2 × 8 + 4 × 2 = 8 − 16 + 8 = 0 Show the calculated shear force values as in Table 1

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ISBN: 9789810694364

Author: Russell C Hibbeler

Publisher: Pearson Education

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Chapter 6.2, Problem 6.30P

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To draw: The shear and moment diagrams for the beam.

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