804_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

804_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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798 CHAPTER 10 Statically Indeterminate Beams R EACTIONS ( EQS . 1 AND 2) M A ± R B L ± 3 EI d B L 2 ; R A ± R B ± 3 EI d B L 3 D EFLECTION ( FROM EQ . 7): S LOPE ( FROM EQ . 6): ² ¿ ±³ 3 d B x 2 L 3 (2 L ³ x ) ²± ³ d B x 2 2 L 3 (3 L ³ x ) ; Problem 10.3-4 A cantilever beam of length L and loaded by uniform load of intensity q has a fixed support at A and spring support at B with rotational stiffness k R . A rotation at B , , results in a reaction moment M B = k R . Find rotation and displacement at end B . Use the second-order differential equation of the deflection curve to solve for displacements at end B . d B u B * u B u B y x AL B k R q M A R A M B Solution 10.3-4 q = intensity of uniform load E QUILIBRIUM (1) (2) (3) B ENDING MOMENT D IFFERENTIAL EQUATION EIv ¿ ± R A x 2 2 ³ M A x ³ qx 3 6 + C 1 EIv ± M ± R A x ³ M A
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