Explanation Given information: Apply the sign conventions for calculating reactions 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 positive and the counter clockwise moment as negative. Consider the flexural rigidity EI of the beam is constant. Sketch the Free Body Diagram of the beam as shown in Figure 1. Refer to Figure 1. Use equilibrium equations: Summation of moments about A is equal to 0. ∑ M A = 0 − R E × 16 − 10 × 12 + 80 + 10 × 4 = 0 R E = 0 Summation of forces along y -direction is equal to 0. + ↑ ∑ F y = 0 R A + 10 − 10 = 0 R A = 0 Calculate the bending moment at each point as shown below. M A = 0 M B = 0 M C Left = − 10 × 4 = − 40 kN ⋅ m M D Right = − 10 × 4 + 80 = 40 kN ⋅ m Sketch the M E I diagram for the beam as shown in Figure 2. Sketch the elastic curve of the beam as shown in Figure 3

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ISBN: 9781260083330

Author: Leet, Kenneth

Publisher: MCGRAW-HILL HIGHER EDUCATION

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The trusses and frames are the two most important structural members of civil engineering. Trusses are the interconnection of links and other structural members. The interconnection with other members makes the system behave as a single member that suppo…

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Chapter 7, Problem 9P

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Calculate the slope at A and C and the deflection at B using moment-area method.

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Fundamentals Of Structural Analysis:

Ch. 7 - Prob. 1P Ch. 7 - Prob. 2P Ch. 7 - Prob. 3P Ch. 7 - Prob. 4P Ch. 7 - Prob. 5P Ch. 7 - Prob. 6P Ch. 7 - Prob. 7P Ch. 7 - Prob. 8P Ch. 7 - Prob. 9P Ch. 7 - Prob. 10P

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