766_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

766_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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760 CHAPTER 9 Deflections of Beams I NTEGRATE EQS . (7) AND (8) (9) (10) B . C . 3 Deflection at support A n (0) ± 0 From Eq. (9): C 3 ± 0 D EFECTION AT POINT B ( FROM THE LEFT ) Substitute (11) B . C . 4 Continuity of deflections at point B ( n B ) Right ± ( n B ) Left From Eqs. (10) and (11): C 4 ±² 13 qL 4 12,288 qL 24 a L 4 b 3 ² q 48 a L 4 b 4 ² qL 3 48 a L 4 b + C 4 ±² 35 qL 4 6144 EI ³ B ±² 35 qL 4 6144 x ± L 4 into Eq. (9) with C 3 ± 0 EI ³± qL x 3 24 ² qx 4 48 ² qL 3 x 48 + C 4 a L 4 x L 2 b EI ³± qL x 3 12 ² qx 4 24 ² 7 qL 3 x 256 + C 3 a 0 x L 4 b D EFECTION OF THE BEAM ( FROM E QS . 9 AND 10) M AXIMUM DEFLECTION ( AT THE MIDPOINT E) (From the preceding equation for v .) d max ±² v a L 2 b ± 31 qL 4 4096 EI (positive downward) ; a L 4 x L 2 b ; ³± ² q 12,288 EI (13 L 4 + 256 L 3 x ²
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Unformatted text preview: 512 Lx 3 + 256 x 4 ) a x L 4 b ; qx 768 EI 1 21 L 3 64 Lx 2 + 32 x 3 2 Problem 9.7-5 A beam ABC has a rigid segment from A to B and a flexible segment with moment of inertia I from B to C (see figure). A concentrated load P acts at point B . Determine the angle of rotation u A of the rigid segment, the deflection d B at point B , and the maximum deflection d max . A I C B P Rigid L 3 2 L 3 09Ch09.qxd 9/27/08 1:35 PM Page 760...
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