09-01ChapGere.0010

09-01ChapGere.0010 - 556 A-PDF Deflections of Beams CHAPTER...

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Unformatted text preview: 556 A-PDF Deflections of Beams CHAPTER 9 Split DEMO : Purchase from www.A-PDF.com to remove the watermark Solution 9.3-12 Beam with a guided support REACTIONS AND DEFLECTION CURVE y q qL2 MB = 2 x BENDING-MOMENT EQUATION (EQ. 9-12a) EIv EIv B.C. M qLx2 2 v(L) qLx3 6 v(0) qLx qx3 6 0 qx2 2 C1 qL3 3 C2 A B L RA = qL C1 qx4 24 qL3x 3 EIv y A B x B B.C. v 0 C2 0 qx (8L3 4Lx2 24 EI 5 qL4 24 EI x3 ) B v(L) Problem 9.3-13 Derive the equations of the deflection curve for a simple beam AB loaded by a couple M0 acting at distance a from the left-hand support (see figure). Also, determine the deflection 0 at the point where the load is applied. (Note: Use the second-order differential equation of the deflection curve.) y M0 A B x a L b Solution 9.3-13 Simple beam (couple M0) B.C. B.C. BENDING-MOMENT EQUATION (EQ. 9-12a) EIv EIv EIv EIv B.C. 3 v(L) 4 (v)Left 0 C4 (v)Right 2 M M0 x L C1 (0 (0 x x x) a) a) (a x (a a x L) at x M0 x2 2L M C4 C1 v M0 a 2 M0 L a a L 3 C1L 1 (v )Left (v )Right at x C2 C1 M0a M0 x3 6L C1x C3 (0 0 C1x x M0 Lx L M0 (L L x2 2 C2 L) v M0 (2L2 6L M0 x (6aL 6 LEI M0 (3a2L 6 LEI v(a) 6aL 3a2 3a2 ) 2L2 x2 ) (0 x a) 3a2x 2L2x 3Lx2 (a L) x3 ) x L) EIv B.C. a) 0 2 v(0) 0 C3 2 M0 x3 M0 x EIv 2 6L M0 ax (a x C4 L) a)(2a 3 LEI M0 ab(2a L) 3LEI M0 a(L NOTE: 0 is positive downward. The pending results agree with Case 9, Table G-2. ...
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