05-02ChapGere.0016

05-02ChapGere.0016 - max 5 1.0535 Problem 5.6-23 The cross...

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Solution 5.6-22 Beam of square cross section with corners removed SECTION 5.6 Design of Beams 319 a 5 length of each side b a 5 amount removed Beam is bent about the z axis. E NTIRE CROSS SECTION (A REA 0) S QUARE mnpq (A REA 1) P ARALLELOGRAM mm,n,n (A REA 2) (base)(height) 3 R EDUCED CROSS SECTION (A REA qmm,n,p,pq ) c 5 (1 2 b ) a 1 2 Ê S 5 I c 5 1 2 a 3 12 (1 1 3 b )(1 2 b ) 2 I 5 I 1 1 2 I 2 5 a 4 12 (1 1 3 b )(1 2 b ) 3 I 2 5 1 3 ( b a 1 2 ) B (1 2 b ) a 1 2 R 3 5 b a 4 6 (1 2 b ) 3 I 2 5 1 3 I 1 5 (1 2 b ) 4 a 4 12 I 0 5 a 4 12 Ê c 0 5 a 1 2 Ê S 0 5 I 0 c 0 5 a 3 1 2 12 R ATIO OF SECTION MODULI Eq. (1) G RAPH OF E Q . (1) (a) V ALUE OF b FOR A MAXIMUM VALUE OF S/S 0 Take the derivative and solve this equation for b . (b) M AXIMUM VALUE OF S/S 0 Substitute b 5 1/9 into Eq. (1). ( S / S 0 ) max 5 1.0535 The section modulus is increased by 5.35% when the triangular areas are removed. b 5 1 9 d d b ¢ S S 0 5 0 S S 0 5 (1 1 3 b )(1 2 b ) 2 a a C z y b a q b a p p 1 m 1 m (1 ] b ) a n n 1 b 5 1 9 b 1.10 1.00 .90 0 0.1 0.2 0.3 Eq. (1) ( S S 0 )
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Unformatted text preview: max 5 1.0535 Problem 5.6-23 The cross section of a rectangular beam having width b and height h is shown in part (a) of the figure. For reasons unknown to the beam designer, it is planned to add structural projections of width b /9 and height d to the top and bottom of the beam [see part (b) of the figure]. For what values of d is the bending-moment capacity of the beam increased? For what values is it decreased? h b — 9 b — 9 d d h (a) (b) b A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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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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