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751_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 751_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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SECTION 9.6 Moment-Area Method 745 Moment-Area Method The problems for Section 9.6 are to be solved by the moment-area method. All beams have constant flexural rigidity EI . Problem 9.6-1 A cantilever beam AB is subjected to a uniform load of intensity q acting throughout its length (see figure). Determine the angle of rotation u B and the deflection d B at the free end. If P 2 ACTS ALONE (to the left) (upward) D EFLECTIONS DUE TO THE LOAD P (to the right) (upward) d v P 1 L 3 2 EI 4 P 2 L 3 3 EI L 3 6 EI ( 3 P 1 + 8 P 2 ) d H P 1 L 3 3 EI P 2 L 3 2 EI L 3 6 EI (2 P 1 3 P 2 ) d ¿¿ v P 2 L 3 3 EI u B L P 2 L 3 3 EI a P 2 L 2 EI b L 4 P 2 L 3 3 EI d ¿¿ H P 2 L 3 2 EI P RINCIPAL DIRECTIONS The deflection of point C is in the same direction as the load P . Rearrange and simplity: tan 2 a 2 tan a 1 0 (quadratic equation) Solving, a 22.5 ° , 112.5 ° , 67.5 ° , 157.5 ° ; tan a 1 ; 1 2 tan a P 2 P

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751_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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