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Unformatted text preview: 09Ch09.qxd 9/27/08 708 1:30 PM Page 708 CHAPTER 9 Deflections of Beams Problem 9.2-2 The deflection curve for a simple beam AB (see figure) is given by the following equation:
4 p EI sin px
L (a) Describe the load acting on the beam.
(b) Determine the reactions RA and RB at the supports.
(c) Determine the maximum bending moment Mmax. Solution 9.2-2 Simple beam 4 q0 L
4 p EI
¿ 3 p EI sin (b) REACTIONS (EQ. 9-12b) px
L cos V px
L EI –¿ At x 0: V At x q0 L
L L: V q0 L
p RA q0 L2 – px
p EI –¿ –– q0
L q0 L
p RB q0 L
L RB ; q0 L
p ; (c) MAXIMUM BENDING MOMENT (EQ. 9-12a)
M (a) LOAD (EQ. 9-12c)
EI –– q0 sin
The load has the shape of a sine curve, acts downward,
and has maximum intensity q0. 10L2x + 5Lx2 q0 L2
2 p sin px
L For maximum moment, x Problem 9.2-3 The deflection curve for a cantilever beam AB (see figure) is
given by the following equation:
120LEI EI – x3) Mmax L
p2 ; y A B
x Describe the load acting on the beam. Probs. 9.2-3 and 9.2.-4 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