Unformatted text preview: 09Ch09.qxd 9/27/08 1:30 PM Page 709 SECTION 9.2 Differential Equations of the Deflection Curve 709 Solution 9.2-3 Cantilever beam
120LEI 10L2x + 5Lx2 x3) Take four consecutive derivatives and obtain:
LEI –– x) From Eq. (9-12c):
q q0 a 1 EI –– x
L ; The load is a downward triangular load of maximum
intensity q0. Problem 9.2-4 The deflection curve for a cantilever beam AB (see figure) is given by the following equation:
360L2EI (45L4 40L3x + 15L2x2 x4) (a) Describe the load acting on the beam.
(b) Determine the reactions RA and MA at the support. Solution 9.2-4 Cantilever beam
40L3x + 15L2x2
20L3x2 + 10L2x2
8 L3x + 6 L2x2
( 2 L3 + 3L2x
L2EI – – –¿ –– (a) LOAD (EQ. 9-12c)
q EI –– q0 a 1 (b) REACTIONS RA AND MA (EQ. 9-12b AND EQ. 9-12a)
M 2 x L2 b EI –¿
EI – q0
q0 12L2 ; The load is a downward parabolic load of maximum
; At x 0: M ( MA 2L3 + 3L2x
4 x3) ;
8L3x + 6L2x2 x4) ; NOTE: Reaction RA is positive upward.
Reaction MA is positive clockwise (minus means MA is
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This note was uploaded on 12/22/2011 for the course MEEG 310 taught by Professor Staff during the Fall '11 term at University of Delaware.
- Fall '11