05-01ChapGere.0015

05-01ChapGere.0015 - 2.81 in. 4 M max 5 (200 lb)(5.0 ft) 1...

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Solution 5.5-17 Cantilever beam (channel section) SECTION 5.5 Normal Stresses in Beams 299 Problem 5.5-18 A cantilever beam AB of triangular cross section has length L 5 0.8 m, width b 5 80 mm, and height h 5 120 mm (see figure). The beam is made of brass weighing 85 kN/m 3 . (a) Determine the maximum tensile stress s t and maximum compressive stress s c due to the beam’s own weight. (b) If the width b is doubled, what happens to the stresses? (c) If the height h is doubled, what happens to the stresses? Solution 5.5-18 Triangular beam I 5 2.81 in. 4 c 1 5 0.606 in. c 2 5 2.133 in. 5 1000 lb-ft 1 640 lb-ft 5 1640 lb-ft 5 19,680 lb-in. M AXIMUM TENSILE STRESS 5 4,240 psi M AXIMUM COMPRESSIVE STRESS 5 14,940 psi s c 5 Mc 2 I 5 (19,680 lb-in.)(2.133 in.) 2.81 in. 4 s t 5 Mc 1 I 5 (19,680 lb-in.)(0.606 in.)
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Unformatted text preview: 2.81 in. 4 M max 5 (200 lb)(5.0 ft) 1 (20 lb / ft)(8.0 ft) 8.0 ft 2 A B 5.0 ft 8.0 ft 3.0 ft 20 lb/ft z y C 0.606 in. 200 lb 2.133 in. h A B b L L q h b z C y h/3 2h 3 L 5 0.8 m b 5 80 mm h 5 120 mm 5 85 kN/m 3 (a) M AXIMUM STRESSES Tensile stress: s t 5 Mc 1 I z 5 3 g L 2 h I z 5 I C 5 bh 3 36 c 1 5 h 3 c 2 5 2 h 3 q 5 g A 5 g bh 2 M max 5 qL 2 2 5 g bhL 2 4 Compressive stress: s c 5 2 s t Substitute numerical values: s t 5 1.36 MPa s c 5 2.72 MPa (b) W IDTH b IS DOUBLED No change in stresses. (c) H EIGHT h IS DOUBLED Stresses are reduced by half. A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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