05-03ChapGere.0011

05-03ChapGere.0011 - L , the shear stress governs the...

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Problem 5.8-6 A beam of rectangular cross section (width b and height h ) supports a uniformly distributed load along its entire length L . The allowable stresses in bending and shear are s allow and t allow , respectively. (a) If the beam is simply supported, what is the span length L 0 below which the shear stress governs the allowable load and above which the bending stress governs? (b) If the beam is supported as a cantilever, what is the length L 0 below which the shear stress governs the allowable load and above which the bending stress governs? Solution 5.8-6 Beam of rectangular cross section SECTION 5.8 Shear Stresses in Rectangular Beams 331 b 5 width h 5 height L 5 length U NIFORM LOAD q 5 intensity of load A LLOWABLE STRESSES s allow and t allow (a) S IMPLE BEAM B ENDING (1) S HEAR (2) Equate (1) and (2) and solve for L 0 : L 0 5 h ¢ s allow t allow q allow 5 4 t allow bh 3 L t max 5 3 V 2 A 5 3 qL 4 bh V max 5 qL 2 Ê A 5 bh q allow 5 4 s allow bh 2 3 L 2 s max 5 M max S 5 3 qL 2 4 bh 2 M max 5 qL 2 8 Ê S 5 bh 2 6 (b) C ANTILEVER BEAM B ENDING (3) S HEAR (4) Equate (3) and (4) and solve for L 0 : N OTE : If the actual length is less than
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Unformatted text preview: L , the shear stress governs the design. If the length is greater than L , the bending stress governs. L 5 h 2 s allow t allow q allow 5 2 t allow bh 3 L t max 5 3 V 2 A 5 3 qL 2 bh V max 5 qL A 5 bh s max 5 M max S 5 3 qL 2 bh 2 q allow 5 s allow bh 2 3 L 2 M max 5 qL 2 2 S 5 bh 2 6 Problem 5.8-7 A laminated wood beam on simple supports is built up by gluing together three 2 in. 3 4 in. boards (actual dimensions) to form a solid beam 4 in. 3 6 in. in cross section, as shown in the figure. The allowable shear stress in the glued joints is 65 psi and the allowable bending stress in the wood is 1800 psi. If the beam is 6 ft long, what is the allowable load P acting at the midpoint of the beam? (Disregard the weight of the beam.) 2 in . 2 in . 2 in . 4 in . P 3 ft L 5 6 ft A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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