05-01ChapGere.0013 - A-PDF Split DEMO : Purchase from...

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Unformatted text preview: A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark SECTION 5.5 Normal Stresses in Beams Solution 5.5-14 Circular core From Appendix D, Cases 9 and 15: y C y 297 Iy r d 2 r4 4 r4 2 ab r2 b d 2 a 2ab3 r4 MAXIMUM BENDING STRESS smax smax For smax Mc Iy 3 c r sin b d sin b 2 64M sin b d (4b sin 4b) 60 /3 rad: 3 radians Iy d 64 4 d4 64 d4 64 d4 64 d 32 2 4 radians b b b b r sin sin b cos b d4 32 2 d4 32 2 (sin b cos b)(1 2 sin b cos3 b 2 cos2b) b r cos 576M (8 3 9)d 10.96 M d3 d4 32 2 d4 (4b 128 sin 4b) 1 sin 4b 4 1 sin 2b ( cos 2b) 2 Problem 5.5-15 A simple beam AB of span length L 24 ft is subjected to two wheel loads acting at distance d 5 ft apart (see figure). Each wheel transmits a load P 3.0 k, and the carriage may occupy any position on the beam. Determine the maximum bending stress max due to the wheel loads if the beam is an I-beam having section modulus S 16.2 in.3 P d P C A B L Solution 5.5-15 P x A d Wheel loads on a beam P Substitute x into the equation for M: L d P S 24 ft 288 in. 5 ft 60 in. 3k 16.2 in.3 Mmax P L 2L d 2 2 B MAXIMUM BENDING STRESS smax Mmax S P L 2LS RA L MAXIMUM BENDING MOMENT RA M dM dx P (L L RAx x) P (L L dx 4x) x d) P (2L L d 2x) Substitute numerical values: smax d 2 2 30 in.) 2 3k (288 in. 2(288 in.)(16.2 in.3 ) 21.4 ksi P (2Lx L d 2x2 ) 0 x L 2 d 4 P (2L L ...
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This note was uploaded on 09/20/2009 for the course COE 3001 taught by Professor Armanios during the Spring '08 term at Georgia Tech.

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