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Unformatted text preview: 10Ch10.qxd 9/27/08 7:36 AM Page 821 821 SECTION 10.4 Method of Superposition Problem 10.4-12 The figure shows a nonprismatic, propped cantilever
beam AB with flexural rigidity 2EI from A to C and EI from C to B.
Determine all reactions of the beam due to the uniform load
of intensity q. (Hint: Use the results of Problems 9.7-1 and 9.7-2.) q MA
RA B EI C 2EI A L
2 RB Solution 10.4-12 Nonprismatic beam
Select RB as the redundant. FORCE-DISPLACEMENT RELATIONS RELEASED STRUCTURE From Prob. 9.7-2: dB
I1 : I I2 : 2I qL4
‹ (dB)1 I1
256EI From Prob. 9.7-1:
(dB)1 downward deflection of end B due to load q PL3
I2 ‹ (dB) 2 3RBL3
dB (dB)1 (dB) 2 0 or
(dB) 2 upward deflection due to reaction RB 17qL4
16EI RB 0 17qL
48 ; EQUILIBRIUM
RA qL MA qL2
48 RB Problem 10.4-13 A beam ABC is fixed at end A and supported by beam
DE at point B (see figure). Both beams have the same cross section and
are made of the same material.
(a) Determine all reactions due to the load P.
(b) What is the numerically largest bending moment in either beam? ; P
A B C
E D MA
4 RE L
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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