05-02ChapGere.0012

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Solution 5.6-17 Ratio of weights of three beams SECTION 5.6 Design of Beams 315 Beam 1: Rectangle ( h 5 2 b ) Beam 2: Square ( a 5 side dimension) Beam 3: Circle ( d 5 diameter) L , g , M max , and s max are the same in all three beams. S 5 section modulus Since M and s are the same, the section moduli must be the same. (1) R ECTANGLE : A 1 5 2 b 2 5 2 ¢ 3 S 2 2 / 3 5 2.6207 S 2 / 3 S 5 bh 2 6 5 2 b 3 3 Ê b 5 ¢ 3 S 2 1 / 3 S 5 M s (2) S QUARE : A 2 5 a 2 5 (6 S ) 2/3 5 3.3019 S (3) C IRCLE : Weights are proportional to the cross-sectional areas (since L and g are the same in all 3 cases). W 1 : W 2 : W 3 5 A 1 : A 2 : A 3 A 1 : A 2 : A 3 5 2.6207 : 3.3019 : 3.6905 W 1 : W 2 : W 3 5 1 : 1.260 : 1.408 A 3 5 p d 2 4 5 p 4 ¢ 32 S p 2 / 3 5 3.6905 S 2 / 3 S 5 p d 3 32 Ê d 5 ¢ 32 S p 1 / 3 S 5 a 3 6 Ê a 5 (6 S ) 1 / 3 Problem 5.6-18 A horizontal shelf AD of length L 5 900 mm, width b 5 300 mm, and thickness t 5 20 mm is supported by brackets at B and C [see part (a) of the figure]. The brackets are adjustable and may be placed in any desired positions between the ends of the shelf. A uniform load of intensity q , which includes the weight of the shelf itself, acts on the shelf [see part (b) of the figure]. Determine the maximum permissible value of the load
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