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Unformatted text preview: 09Ch09.qxd 9/27/08 1:33 PM Page 749 749 SECTION 9.6 Moment-Area Method Problem 9.6-6 A cantilever beam ACB supports two concentrated loads P1 and P2 P1 as shown in the figure.
Calculate the deflections dB and dC at points B and C, respectively. Assume
P1 10 kN, P2 5 kN, L 2.6 m, E 200 GPa, and I 20.1 106 mm4. C A P2
2 Solution 9.6-6 Cantilever beam (forces P1 and P2)
EI dB DIAGRAMS 1 P1L L L
ba ba + b + a
b (L) a b
3EI ; (downward) DEFLECTION dC
dC tC/A QC first moment of areas to the left
of point C with respect to point C
dc P2 L L L
1 P1L L L
ba ba b + a
ba ba b
E 10 kN P2 200 GPa I 5 kN L 20.1 6 Use absolute values of areas. tB/A QB ; (downward) SUBSTITUTE NUMERICAL VALUES: first moment of areas with respect dB 4.554 mm + 7.287 mm 11.84 mm dC DEFLECTION dB
48EI 2.6 m 10 mm4 1 P2L L L
ba ba b
3 1.822 mm + 2.277 mm 4.10 mm ;
; (deflections are downward) to point B Problem 9.6-7 Obtain formulas for the angle of rotation uA at support A and the
deflection dmax at the midpoint for a simple beam AB with a uniform load of
intensity q (see figure). q
A B 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