Explanation Calculation: Sketch the Free Body diagram as shown in Figure 1. Refer to Figure 1. Apply the Equations of Equilibrium as shown below. Take moment about the point D is Equal to zero. ∑ M D = 0 R B × L + P a = 0 R B = − P a L Consider a section at a distance x from A over the portion AD . Sketch the Free Body Diagram of the section from A as shown in Figure 2. Refer to Figure 2. Apply the Equations of Equilibrium as shown below. Take moment about the section is Equal to zero. ∑ M = 0 M + P x = 0 M = − P x Calculate the strain energy ( U A D ) over portion AD as shown below. U A D = ∫ a b M 2 2 E I d x Substitute − P x for M and apply the limits. U A D = ∫ 0 a ( − P x ) 2 2 E I d x = 1 2 E I ∫ 0 a P 2 x 2 d v = P 2 2 E I ( x 3 3 ) 0 a = P 2 a 3 6 E I Consider a section at a distance v from B over the portion DB . Sketch the Free Body Diagram of the section from B as shown in Figure 3. Refer to Figure 3. Apply the Equations of Equilibrium as shown below. Take moment about the section is Equal to zero. ∑ M = 0 M + a P L v = 0 M = − a P L v Calculate the strain energy ( U D B ) over portion DB as shown below. U D B = ∫ a b M 2 2 E I d v Substitute − a P L v for M and apply the limits

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Author: Ferdinand P. Beer, E. Russell Johnston Jr., John T. DeWolf, David F. Mazurek

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Chapter 11.3, Problem 25P

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Find the strain energy for the prismatic beam AB.

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Chapter 11 Solutions

Mechanics of Materials, 7th Edition

Ch. 11.3 - Determine the modulus of resilience for each of...Ch. 11.3 - Determine the modulus of resilience for each of...Ch. 11.3 - Determine the modulus of resilience for each of...Ch. 11.3 - Determine the modulus of resilience for each of...Ch. 11.3 - The stress-strain diagram shown has been drawn...Ch. 11.3 - The stress-strain diagram shown has been drawn...Ch. 11.3 - Prob. 7P Ch. 11.3 - Prob. 8P Ch. 11.3 - Using E = 29 106 psi, determine (a) the strain...Ch. 11.3 - Using E = 200 GPa, determine (a) the strain energy...

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Find the strain energy for the prismatic beam AB .

Solution Summary: The author calculates the strain energy for the prismatic beam AB by drawing the Free Body diagram as shown in Figure 1.

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Find the strain energy for the prismatic beam AB.

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