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05-05 Chap Gere - 350 CHAPTER 5 Stresses in Beams Built-Up...

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Built-Up Beams Problem 5.11-1 A prefabricated wood I-beam serving as a floor joist has the cross section shown in the figure. The allowable load in shear for the glued joints between the web and the flanges is 65 lb/in. in the longitudinal direction. Determine the maximum allowable shear force V max for the beam. Solution 5.11-1 Wood I-beam 350 CHAPTER 5 Stresses in Beams 0.75 in. 0.75 in. 0.625 in. z y O 8 in. 5 in. 0.75 in. 0.75 in. t = 0.625 in. z y O h 1 = 8 b = 5 h = 9.5 Problem 5.11-2 A welded steel girder having the cross section shown in the figure is fabricated of two 280 mm 25 mm flange plates and a 600 mm 15 mm web plate. The plates are joined by four fillet welds that run continuously for the length of the girder. Each weld has an allowable load in shear of 900 kN/m. Calculate the maximum allowable shear force V max for the girder. z y O 280 mm 15 mm 25 mm 25 mm 600 mm All dimensions in inches. Find V max based upon shear in the glued joints. Allowable load in shear for the glued joints is 65 lb/in. f allow 65 lb/in. 170.57 in. 4 Q Q flange A f d f (5)(0.75)(4.375) 16.406 in. 3 V max f allow I Q (65 lb in.)(170.57 in. 4 ) 16.406 in. 3 676 lb I bh 3 12 ( b t ) h 1 3 12 1 12 (5)(9.5) 3 1 12 (4.375)(8) 3 f VQ I V max f allow I Q
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Solution 5.11-2 Welded steel girder SECTION 5.11 Built-Up Beams 351 All dimensions in millimeters. Allowable load in shear for one weld is 900 kN/m. f allow 2(900) 1800 kN/m 1638 10 6 mm 4 Q Q flange A F d F (280)(25)(312.5) 2.1875 10 6 mm 3 1.35 MN V max f allow I Q (1800 kN m)(1638 10 6 mm 4 ) 2.1875 10 6 mm 3 I bh 3 12 ( b t ) h 1 3 12 1 12 (280)(650) 3 1 12 (265)(600) 3 f VQ I V max f allow I Q z y O b = 280 t = 15 25 25 h 1 = 600 weld h = 650 Problem 5.11-3 A welded steel girder having the cross section shown in the figure is fabricated of two 18 in. 1 in. flange plates and a 64 in. 3/8 in. web plate. The plates are joined by four longitudinal fillet welds that run continuously throughout the length of the girder. If the girder is subjected to a shear force of 300 kips, what force F (per inch of length of weld) must be resisted by each weld? Solution 5.11-3 Welded steel girder z y O 18 in. in. 1 in. 1 in. 64 in. 3 8 z y O b = 18 t = 0.375 1.0 1.0 h 1 = 64 weld h = 66 All dimensions in inches. V 300 k F force per inch of length of one weld f shear flow 46,220 in. 4 Q Q flange A F D F (18)(1.0)(32.5) 585 in. 3 F VQ 2 I (300 k)(585 in. 3 ) 2(46,220 in. 4 ) 1900 lb in. I bh 3 12 ( b t ) h 1 3 12 1 12 (18)(66) 3 1 12 (17.625)(64) 3 F VQ 2 I f 2 F VQ I
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Problem 5.11-4 A box beam of wood is constructed of two 260 mm 50 mm boards and two 260 mm 25 mm boards (see figure). The boards are nailed at a longitudinal spacing s 100 mm. If each nail has an allowable shear force F 1200 N, what is the maximum allowable shear force V max ? Solution 5.11-4 Wood box beam 352 CHAPTER 5 Stresses in Beams z y O 50 mm 25 mm 25 mm 50 mm 260 mm 260 mm All dimensions in millimeters. b 260 b 1 260 2(50) 160 h 310 h 1 260 s nail spacing 100 mm F allowable shear force for one nail 1200 N f shear flow between one flange and both webs Q Q flange A F d F (260)(25)(142.5) 926.25 10 3 mm 3 10.7 kN V max f allow I Q (24 kN m)(411.125 10 6 mm 4 ) 926.25 10 3 mm 3 I 1 12 ( bh 3 b 1 h 3 1 ) 411.125 10 6 mm 4 f VQ I V max f allow I Q f allow 2 F s 2(1200 N) 100 mm 24 kN m Problem 5.11-5 A box beam constructed of four wood boards of size 6 in. 1 in. (actual dimensions) is shown in the figure. The boards are
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