Aerospace 9 example 8 3 cont

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Unformatted text preview: ☞ condi=on 1: deflec=on at x=0 is zero P bx3 EIv = + C1 x + C3 (0 x a) 6L P b(0)3 EIv = + C1 (0) + C3 6L C3 = 0 ) C4 = 0 since C3 = C4 ☞ condi=on 2: deflec=on at x=L is zero P bx3 P ( x a) 3 EIv = + C2 x + C4 ( a < x < L ) 6L 6 P b( L ) 3 P ( L a) 3 0= + C2 ( L) + 0 6L 6 P b( L 2 b 2 ) P bL2 P b3 C2 = C1 = 0= + C2 L 6L 6 6 4/9/13 M. Mello/Georgia Tech Aerospace 11 EXAMPLE 8- 3 (cont.) •  DETERMINE EQUATIONS OF THE DEFLECTION CURVE ☞ RESTATE DEFLECTION EQUATIONS WITH UNKNOWN CONSTANTS P bx3 EIv = + C1 x + C3 (0 x a) 6L P bx3 P ( x a) 3 EIv = + C2 x + C4 ( a x L) 6L 6 ☞ RECALL AND SUBSTITUTE CONSTANTS OF INTEGRATION (FROM PREVIOUS PAGE) P b( L 2 b 2 ) C = C2 = AND, C3 = C4 = 0 1 6L v= P bx ( L2 6LEI b2 x2 ) v= P bx ( L2 6LEI 2 2 4/9/13 b x) (0 x a) P ( x a) 3 6EI ( a x L) M. Mello/Georgia Tech Aerospace 12 EXAMPLE 8- 3 (cont.) •  DETERMINE EQUATIONS OF THE BEAM SLOPE ☞ RESTATE BEAM SLOPE EQUATIONS WITH UNKNOWN CONSTANTS P bx2 EIv = + C1 2L 0 P bx2 EIv = 2L 0 (0 x a) a)2 P (x 2 ( a x L) + C2 ☞ RECALL AND SUBSTITUTE CONSTANTS OF INTEGRATION (FROM PREVIOUS PAGE) P b( L 2 b 2 ) C = C2 = AND, 1 6L C3 = C4 = 0 ☞ OR… TAKE DERIVATIVES OF THE DEFLECTION EQUATIONS WE JUST OBTAINED! 0 v= 0 v= 4/9/13 Pb ( L2 6LEI b2 Pb ( L2 6LEI 2 b 3x 2 ) 2 3x ) (0 x a) P ( x a) 2 2EI ( a x L) M. Mello/Georgia Tech Aerospace 13 Compete these remaining por=ons of this problem as part of next assignment 4/9/13 M. Mello/Georgia Tech Aerospace 14 EXAMPLE 8- 3 (finish for homework) •  DETERMINE angle of rotaBon ΘA and ΘB at the supports ☞ Apply slope formulas at x=0 and x=L 0 Pb = v (L2 b2 3x2 ) (0 x a) 6LEI 0 Pb P ( x a) 2 2 2 2 v b 3x ) ( a x L) = 6LEI (L 2EI •  DETERMINE maximum deflecBon δmax of the beam ☞ Set slope formula to zero and solve for x1 Pb 0 v= (L2 b2 3x2 ) (0 x a) 6LEI •  DETERMINE maximum deflecBon δmax ☞ Subs=tute x1 into defec=on formula 0 v= 4/9/13 Pb ( L2 6LEI b2 3x 2 ) (0 x a) M. Mello/Georgia Tech Aerospace 15 EXAMPLE 8- 3 (finish for homework) •  DETERMINE maximum deflecBon δmax ☞ Subs=tute x1 into defec=on formula 0 v= Pb ( L2 6LEI b2 Pb ( L2 6LEI b2 3x 2 ) (0 x a) •  DETERMINE deflecBon δC at the midpoint C of the beam ☞ Subs=tute x=L/2 into deflec=on formula 0 v= 4/9/13 3x 2 ) (0 x a) M. Mello/Georgia Tech Aerospace 16 QuesBons for Assignment #9 (will be posted as well) •  Locate the two ad...
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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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