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758_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

758_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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D EFLECTION d AT THE MIDPOINT C 1 2 a M 0 2 EI b a L 2 b a L 6 b M 0 L 2 48 EI with respect to C t C 2 / A C 2 C 1 first moment of area between A and C Distance CC 1 1 2 ( BB 1 ) M 0 L 2 12 EI (These results agree with Case 7 of Table G-2.) M 0 L 2 16 EI (Downward) ; d CC 1 C 2 C 1 M 0 L 2 12 EI M 0 L 2 48 EI Problem 9.6-10 The simple beam AB shown in the figure supports two equal concentrated loads P , one acting downward and the other upward. Determine the angle of rotation u A at the left-hand end, the deflection d 1 under the downward load, and the deflection d 2 at the midpoint of the beam. Solution 9.6-10 Simple beam with two loads Because the beam is symmetric and the load is antisymmetric, the deflection at the midpoint is zero. d 2 0 ; A NGLE OF ROTATION u A AT END A D EFLECTION d 1 UNDER THE DOWNWARD LOAD Pa 2 ( L 2 a ) 2 6 LEI
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