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435_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 435_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 05Ch05.qxd 9/24/08 4:59 AM Page 429 429 SECTION 5.6 Design of Beams Solution 5.6-22 Beam of square cross section with corners removed RATIO OF SECTION MODULI S S0 b )2 (1 + 3 b )(1 Eq. (1) GRAPH OF EQ. (1) a length of each side b a amount removed Beam is bent about the z axis. a 12 ENTIRE CROSS SECTION (AREA 0) I0 a4 12 c0 S0 I0 c0 a3 12 12 (a) VALUE OF b dS ab d b S0 SQUARE mnpq (AREA 1) I1 b )4a4 12 (1 S/S0 0 Take the derivative and solve this equation for b . b PARALLELOGRAM mm, n, n (AREA 2) 1 I2 (base)(height)3 3 I2 FOR A MAXIMUM VALUE OF (1 b )a 3 1 ( b a 12) c d 3 12 b a4 (1 6 1 9 ; (b) MAXIMUM VALUE OF S/S0 Substitute b 1/9 into Eq. (1). (S/S0)max 1.0535 The section modulus is increased by 5.35% when ; the triangular areas are removed. 3 b) REDUCED CROSS SECTION (AREA qmm, n, p, pq) a4 I I1 + 2I2 (1 + 3 b )(1 b )3 12 c (1 12 b) a S I c 12 a3 (1 + 3 b )(1 12 b )2 b — 9 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? d h b (a) h d b — 9 (b) ...
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