05-04ChapGere.0008

# 05-04ChapGere.0008 - section modulus of the beam from Table...

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Problem 5.10-6 Dimensions of cross section: b 5 120 mm, t 5 7 mm, h 5 350 mm, h 1 5 330 mm, and V 5 60 kN. Solution 5.10-6 Wide-flange beam SECTION 5.10 Shear Stresses in the Webs of Beams with Flanges 345 b 5 120 mm t 5 7 mm h 5 350 mm h 1 5 330 mm V 5 60 kN M OMENT OF INERTIA (Eq. 5-47) (a) M AXIMUM SHEAR STRESS IN THE WEB (Eq. 5-48a) t max 5 V 8 It ( bh 2 2 bh 1 2 1 th 1 2 ) 5 28.40 MPa I 5 1 12 ( bh 3 2 bh 1 3 1 th 1 3 ) 5 90.34 3 10 6 mm 4 (b) M INIMUM SHEAR STRESS IN THE WEB (Eq. 5-48b) (c) A VERAGE SHEAR STRESS IN THE WEB (Eq. 5-50) (d) S HEAR FORCE IN THE WEB (Eq. 5-49) V web V 5 0.977 V web 5 th 1 3 (2 t max 1 t min ) 5 58.63 kN t max t aver 5 1.093 t aver 5 V th 1 5 25.97 MPa t min 5 Vb 8 It ( h 2 2 h 1 2 ) 5 19.35 MPa t h 1 b h Problem 5.10-7 A cantilever beam AB of length L 5 6.5 ft supports a uniform load of intensity q that includes the weight of the beam (see figure). The beam is a steel W 10 3 12 wide-flange shape (see Table E-1, Appendix E). Calculate the maximum permissible load q based upon (a) an allowable bending stress s allow 5 16 ksi, and (b) an allowable shear stress t allow 5 8.5 ksi. ( Note: Obtain the moment of inertia and
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Unformatted text preview: section modulus of the beam from Table E-1.) Solution 5.10-7 Cantilever beam W 10 3 12 A B q L = 6.5 ft W 10 3 12 From Table E-1: b 5 3.960 in. t 5 0.190 in. h 5 9.87 in. h 1 5 9.87 in. 2 2(0.210 in.) 5 9.45 in. I 5 53.8 in. 4 S 5 10.9 in. 3 L 5 6.5 ft 5 78 in. s allow 5 16,000 psi t allow 5 8,500 psi (a) M AXIMUM LOAD BASED UPON BENDING STRESS M max 5 qL 2 2 Ê s 5 M max S Ê q 5 2 S s L 2 5 57.33 lb/in. 5 688 lb/ft (b) M AXIMUM LOAD BASED UPON SHEAR STRESS (Eq. 5-48a) Substitute numerical values: q max 5 181.49 lb/in. 5 2180 lb/ft N OTE : Bending stress governs. q allow 5 688 lb/ft q max 5 V max L 5 8 It ( t allow ) L ( bh 2 2 bh 2 1 1 th 1 2 ) V max 5 qL Ê t max 5 V max 8 It ( bh 2 2 bh 1 2 1 th 1 2 ) q max 5 2 S s allow L 2 5 2(10.9 in. 3 )(16,000 psi) (78 in.) 2 t h 1 b h A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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