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: 8220100257063

Author: BEER

Publisher: YUZU

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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

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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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