LECTURE 36 COE-3001-A

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Unformatted text preview: . Mello/Georgia Tech Aerospace qa3 ( ✓B ) 1 = 6EI 20 Appendix G- 1: case 4 ☞ “Point load (P) contribu=on to deflec=on P L3 P L2 ( B )2 = ( ✓B ) 2 = and angle of rota=on at end B” 3EI 2EI ☞ Combine individual solu=ons B = ( B ) 1 + ( B )2 AND (✓B ) = (✓B )1 + (✓B )2 qa3 P L3 qa3 P L2 (4L a) + ( ✓B ) = + B= 24EI 3EI 6EI 2EI 4/9/13 M. Mello/Georgia Tech Aerospace 21 EXAMPLE 8- 7 Problem: Can=lever beam supports a uniform load intensity q ac=ng over the right- hand half of the beam. The beam has length L and constant flexural rigidity EI. Determine: 1.  Deflec=on δB at the free end of the beam 2.  angle of rota=on ΘB at the free end of the beam SOLUTION: Take alterna=ve approach this =me and demonstrate the method of integra=ng a concentrated load solu=on across the distance over which the load intensity q is applied (x=- L/2 to x=L) ☞ consult consult Appendix G- 1 case 5 point load (P) contribu=on at the free end. 4/9/13 M. Mello/Georgia Tech Aerospace 22 EXAMPLE 8- 7: Appendix G- 1: case 4 ☞ replace P by qdx AND replace a with x d B (qdx)(x2 ) = (3L 6EI (qdx)(x2 ) d✓B = 2EI 4/9/13 x) resul=ng differen=al deflec=on at the free end due to qdx at x resul=ng differen=al angle of rota=on at the free end due to qdx at x M. Mello/Georgia Tech Aerospace 23 EXAMPLE 8- 7 (finish) ☞ Now integrate each differen=al expression from (x=- L/2 to x=L) in order to capture the cumula=ve effect of the load intensity distribu=on (q) on the deflec=on and angle of rota=on at the free end of the beam (qdx)(x2 ) (qdx)(x2 ) dB= (3L x) d✓B = 6EI 2EI ZL ZL q q ✓B = x2 (3L x)dx x2 dx B= 6EI L/2 2EI L/2 L 7qL3 q x4 3 ✓B = xL B= 48EI 6EI 4 L/2 41qL4 B= 384EI ☞ We could have easily used case 3 of Appendix G- 1 and obtained the same answer without this integra=on procedure. ☞ Integra=on procedure is useful when we don’t have the tabulated solu=on for a distribu=on q(x). This example demonstrates and validates an alterna=ve approach. 4/9/13 M. Mello/Georgia Tech Aerospace 24 EXAMPLE 8- 8 Problem: Compound beam has a roller support at A, an internal hinge at B, and a fixed support at C. Segment AB has length (a) and segment BC has length (b). A Concentrated load (P) acts...
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This note was uploaded on 09/19/2013 for the course CEE 3001 taught by Professor Zhu during the Spring '09 term at Georgia Institute of Technology.

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