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Unformatted text preview: 10Ch10.qxd 9/27/08 796 7:29 AM Page 796 CHAPTER 10 Statically Indeterminate Beams SHEAR FORCE (FROM EQUILIBRIUM)
V 3M 0
2L RA SHEAR-FORCE AND BENDING-MOMENT DIAGRAMS ; BENDING MOMENT (FROM EQ. 3)
2L ; L) SLOPE (FROM EQ. 4)
¿ M0 x
4LEI ; 3x) DEFLECTION (FROM EQ. 5)
M0 x 2
4LEI ; x) Problem 10.3-2 A fixed-end beam AB of length L supports a y uniform load of intensity q (see figure).
Beginning with the second-order differential equation of the
deflection curve (the bending-moment equation), obtain the reactions,
shear forces, bending moments, slopes, and deflections of the beam.
Construct the shear-force and bending-moment diagrams, labeling all
critical ordinates. q A MA x B
L RA RB Solution 10.3-2 Fixed-end beam (uniform load)
Select MA as the redundant reaction. B.C. REACTIONS (FROM SYMMETRY AND EQUILIBRIUM) EI RA RB qL
2 MB RAx qx 2
2 MA EI ¿ M MA +
M Ax + q
2 q Lx 2
22 ‹ C1 MA + q
2 x 2) (1) x4
b + C2
12 2 (0) 0 ‹ C2 3 (L) 0 ‹ MA x3
b + C1
12 RB qL
2 MA qL2
12 MB SHEAR FORCE (FROM EQUILIBRIUM)
(2) (3) REACTIONS
RA x 2) 0 q Lx 3
M Ax 2
26 B.C. DIFFERENTIAL EQUATIONS
EI – 0 B.C. MA BENDING MOMENT (FROM EQUILIBRIUM)
M 1 ¿ (0) V RA qx q
2 2x) ; ; ...
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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