Explanation The flexural rigidity of the beam is EI . Show the free-body diagram of the superimposed beam as in Figure 1. Loading I: The downward uniformly distributed load ( udl ) is spread throughout the portion AB . Refer to case 2 in Appendix D “Beam Deflections and Slopes” in the textbook. Write the equation for slope and deflection for udl spread throughout the cantilever beam as follows; y = − w L 4 8 E I θ = − w L 3 6 E I Find the deflection at point B due to udl as follows; ( y B ) w = − w L 4 8 E I Find the slope at point B due to udl as follows; ( θ B ) w = − w L 3 6 E I Loading II: The upward reaction B y is acting at point B . Refer to case 1 in Appendix D “Beam Deflections and Slopes” in the textbook. Write the equation for slope and deflection for point load acting in a cantilever beam as follows; y = P L 3 3 E I θ = P L 2 2 E I Find the deflection at point B due to vertical reaction as follows; ( y B ) P = B y L 3 3 E I Find the slope at point B due to vertical reaction as follows; ( θ B ) P = B y L 2 2 E I Loading III: The clockwise moment is acting at point B . Refer to case 3 in Appendix D “Beam Deflections and Slopes” in the textbook. Write the equation for slope and deflection for moment acting in a cantilever beam as follows; y = − M L 2 2 E I θ = − M L E I Find the deflection at point B due to moment as follows; ( y B ) M = − M B L 2 2 E I Find the slope at point B due to moment as follows; ( θ B ) M = − M B L E I Find the resultant deflection at point B as follows; y B = ( y B ) w + ( y B ) P + ( y B ) M = 0 Substitute − w L 4 8 E I for ( y B ) w , B y L 3 3 E I for ( y B ) P , and − M B L 2 2 E I for ( y B ) M

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ISBN: 9780100257061

Author: BEER

Publisher: YUZU

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Any functioning component, such as machine parts, structural members, pressure vessels, and so on, are all under the influence of more than one force. When anybody is under the influence of more than one force such as shear forces, bending moments, axial…

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Chapter 9.4, Problem 84P

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Find the reaction at point B of the beam using superposition method.

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Chapter 9.4, Problem 83P

Chapter 9.4, Problem 85P

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EBK MECHANICS OF MATERIALS

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Find the reaction at point B of the beam using superposition method.

Solution Summary: The author shows the free-body diagram of the superimposed beam as in Figure 1.

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Find the reaction at point B of the beam using superposition method.

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