Solution 5.6-17Ratio of weights of three beamsSECTION 5.6Design of Beams315Beam 1: Rectangle (h52b)Beam 2: Square (a5side dimension)Beam 3: Circle (d5diameter)L, g, Mmax, and smaxare the same in all three beams.S5section modulusSince Mand sare the same, the section moduli mustbe the same.(1) RECTANGLE:A152b252¢3S2≤2/352.6207S2/3S5bh2652b33Êb5¢3S2≤1/3S5Ms(2) SQUARE:A25a25(6S)2/353.3019S(3) CIRCLE:Weights are proportional to the cross-sectional areas(since Land gare the same in all 3 cases).W1 : W2 : W35A1 : A2 : A3A1 : A2 : A352.6207 : 3.3019 : 3.6905W1 : W2 : W351 : 1.260 : 1.408A35pd245p4¢32Sp≤2/353.6905S2/3S5pd332Êd5¢32Sp≤1/3S5a36Êa5(6S)1/3Problem 5.6-18A horizontal shelf ADof length L5 900 mm, width b5 300 mm, and thickness t 5 20 mm is supported by brackets at Band C[see part (a) of the figure]. The brackets are adjustable and may be placedin any desired positions between the ends of the shelf. A uniform load ofintensity 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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