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02-04ChapGere.0006

# 02-04ChapGere.0006 - 90 8 5 120 8 s u 5 s x cos 2 u 5 2...

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SECTION 2.6 Stresses on Inclined Sections 127 Problem 2.6-9 A compression member in a bridge truss is fabri- cated from a wide-flange steel section (see figure). The cross-sectional area A 5 7.5 in. 2 and the axial load P 5 90 k. Determine the normal and shear stresses acting on all faces of stress elements located in the web of the beam and oriented at (a) an angle u 5 0°, (b) an angle u 5 30°, and (c) an angle u 5 45°. In each case, show the stresses on a sketch of a properly oriented element. Solution 2.6-9 Truss member in compression P P u P 5 90 k A 5 7.5 in. 2 (a) u5 0 8 (b) u5 30 8 Use Eqs. (2-29a) and (2-29b): s u 5 s x cos 2 u 5 ( 2 12.0 ksi)(cos 30 8 ) 2 52 9.0 ksi t u 52 s x sin u cos u 52 ( 2 12.0 ksi)(sin 30 8 )(cos 30 8 ) 5 5.2 ksi u 5 30 81
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Unformatted text preview: 90 8 5 120 8 s u 5 s x cos 2 u 5 ( 2 12.0 ksi)(cos 120 8 ) 2 5 2 3.0 ksi 5 2 12.0 ksi (Compression) s x 5 2 P A 5 2 90 k 7.5 in. 2 t u 5 2 s x sin u cos u 5 2 ( 2 12.0 ksi)(sin 120 8 ) (cos 120 8 ) 5 2 5.2 ksi N OTE : All stresses have units of ksi. (c) u 5 45 8 s u 5 s x cos 2 u 5 ( 2 12.0 ksi)(cos 45 8 ) 2 5 2 6.0 ksi t u 5 2 s x sin u cos u 5 2 ( 2 12.0 ksi)(sin 45 8 ) (cos 45 8 ) 5 6.0 ksi N OTE : All stresses have units of ksi. P P u y x 12.0 ksi 12.0 ksi y x 9.0 3.0 3.0 5.2 9.0 5.2 u = 30 ° y x 6.0 6.0 6.0 6.0 6.0 6.0 u = 45 ° A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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