806_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

806_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 10Ch10.qxd 9/27/08 800 7:29 AM Page 800 CHAPTER 10 Statically Indeterminate Beams Problem 10.3-6 A propped cantilever beam of length L is loaded by a parabolically distributed load with maximum intensity q0 at B. x2 q0 — L2 () y (a) Use the fourth-order differential equation of the deflection curve to solve for reactions at A and B and also the equation of the deflection curve. (b) Repeat (a) if the parabolic load is replaced by q0 sin (px/2L). A MA q0 x B L RA RB SOLUTION 10.3-6 q (a) Parabolic load q0 REACTIONS x2 L2 RA 7 qL 60 0 V(0) DIFFERENTIAL EQUATION EI –– q EI –¿ q0 EI – q0 2 (1) + C1 (2) 3L2 EI x q0 q0 L MA x4 q0 EI ¿ 12L2 5 + C1 60L x6 x + C2x + C3 2 360L (4) 0 ‹ C1L + C2 B.C. 2 ¿ (0) 0 ‹ C3 B.C. 3 (0) 0 ‹ C4 B.C. 4 (L) 0 ‹ C1L + 3C2 C2 SHEAR FORCE (EQ. 2) x + 7 qL 60 0 ; x6 360L2 q0 L2 12 360L2EI 1 x 6 + 7L3x 3 (6) q0 sin a (b) Loading q q0 L2 60 (7) or q0 0 6q0 L4x 22 ; px b 2L DIFFERENTIAL EQUATION EI –– 1 q L2 30 0 7 x3 q0 L 60 6 + x2 1 q0 L2 30 2 0 Solve Eqs. (6) and (7): 3L2 q0 (5) 1 – (L) q0 EI x3 x2 + C2 6 2 B.C. V ; DEFLECTION CURVE (EQ. 5) + C1 2 3 1 q L2 30 0 2 2 7 qL 60 0 13 qL 60 0 V(L) (3) + C1x + C2 + C3x + C4 C1 RB FROM EQUILIBRIUM x3 M x2 ; q0 sin a px b 2L (1) 2L px cos a b + C1 p 2L (2) q EI –¿ q0 EI – M q0 a 2L 2 px b sin a b + C1 x + C2 p 2L (3) ...
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