05-02ChapGere.0007

05-02ChapGere.0007 - crane in a testing laboratory moves...

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Solution 5.6-10 Trapeze bar (regular octagon) 310 CHAPTER 5 Stresses in Beams (Basic Topics) P 5 1.2 kN L 5 2.1 m s allow 5 200 MPa Determine minimum height h . M AXIMUM BENDING MOMENT P ROPERTIES OF THE CROSS SECTION Use Appendix D, Case 25, with n 5 8 b 5 length of one side (from triangle) For b 5 45º: M OMENT OF INERTIA I C 5 8 b 4 192 (2.41421)[3(2.41421) 2 1 1] 5 1.85948 b 4 I C 5 nb 4 192 ¢ cot b 2 ¢ 3 cot 2 b 2 1 1 h b 5 cot 45 8 2 5 2.41421 b h 5 tan 45 8 2 5 0.41421 cot b 2 5 h b tan b 2 5 b h b 5 360 8 n 5 360 8 8 5 45 8 M max 5 PL 4 5 (1.2 kN)(2.1 m) 4 5 630 N ? m b 5 0.41421 h [ I C 5 1.85948(0.41421 h ) 4 5 0.054738 h 4 S ECTION MODULUS M INIMUM HEIGHT h h 3 5 28.7735 3 10 2 6 m 3 h 5 0.030643 m [ h min 5 30.6 mm A LTERNATIVE SOLUTION ( n 5 8) Substitute numerical values: h 3 5 28.7735 3 10 2 6 m 3 h min 5 30.643 mm S 5 ¢ 4 Ï 2 2 5 6 h 3 Ê h 3 5 3 PL 2(4 Ï 2 2 5) s allow I C 5 ¢ 11 1 8 Ï 2 12 b 4 5 ¢ 4 Ï 2 2 5 12 h 4 b 5 ( Ï 2 2 1) h Ê h 5 ( Ï 2 1 1) b M 5 PL 4 Ê b 5 45 8 Ê tan b 2 5 Ï 2 2 1 Ê cot b 2 5 Ï 2 1 1 0.109476 h 3 5 630N ? m 200 MPa 5 3.15 3 10 2 6 m 3 s 5 M S Ê S 5 M s S 5 I C h / 2 5 0.054738 h 4 h / 2 5 0.109476 h 3 h C L L 2 b P C C h 2 b b b 2 h 2 b 2 Problem 5.6-11 A two-axle carriage that is part of an overhead traveling
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Unformatted text preview: crane in a testing laboratory moves slowly across a simple beam AB (see figure). The load transmitted to the beam from the front axle is 2000 lb and from the rear axle is 4000 lb. The weight of the beam itself may be disregarded. (a) Determine the minimum required section modulus S for the beam if the allowable bending stress is 15.0 ksi, the length of the beam is 16 ft, and the wheelbase of the carriage is 5 ft. (b) Select a suitable I-beam ( S shape) from Table E-2, Appendix E. 5 ft 16 ft 4000 lb 2000 lb A 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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