731_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

731_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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SECTION 9.4 Deflections by Integration of the Shear Force and Load Equations 725 Solution 9.4-5 Cantilever beam (cosine load) L OAD EQUATION (E Q . 9-12c) B . C .1 EI n ±±± ² VE I n ±±± ( L ) ² 0 B . C .2 EI n ±± ² ME I n ±± ( L ) ² 0 EI ³ ¿ ² q 0 a 2 L p b 3 sin p x 2 L + q 0 Lx 2 p ´ 2 q 0 L 2 x p + C 3 C 2 ²´ 2 q 0 L 2 p EI ³ ² q 0 a 2 L p b 2 cos p x 2 L + 2 q 0 Lx p + C 2 C 1 ² 2 q 0 L p EI ³ –¿ q 0 a 2 L p b sin p x 2 L + C 1 EI ³ –– q q 0 cos p x 2 L B . C .3 n ± (0) ² 0 ± C 3 ² 0 B . C .4 n (0) ² 0 (These results agree with Case 10, Table G-1.) d B ²´³ ( L ) ² 2 q 0 L 4 3 p 4 EI ( p 3 ´ 24) ; a 48 L 3 cos p x 2 L ´ 48 L 3 + 3 p 3 Lx 2 ´ p 3 x 3 b ; ³²´ q 0 L 3 p 4 EI C 4 ² 16 q 0 L 4 p 4 EI q 0 a 2 L p b 4 cos p x 2 L + q 0 Lx 3 3 p ´ q 0 L 2 x 2 p + C 4 Problem 9.4-6 A cantilever beam AB is subjected to a parabolically varying load of intensity q ² q 0 ( L 2 ´ x 2 )/ L 2 , where q 0 is the maximum intensity of the load (see figure). Derive the equation of the deflection curve, and then determine the deflection d B and angle of rotation u B at the free end. Use the fourth-order differential equation of the deflection curve (the load equation). A y x L 2 ´ x 2 L 2 B q = q 0 q 0 L Solution 9.4-6
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