05-05 Chap Gere

# 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 3 25 mm flange plates and a 600 mm 3 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 5 65 lb/in. 5 170.57 in. 4 Q 5 Q flange 5 A f d f 5 (5)(0.75)(4.375) 5 16.406 in. 3 V max 5 f allow I Q 5 (65 lb / in.)(170.57 in. 4 ) 16.406 in. 3 5 676 lb I 5 bh 3 12 2 ( b 2 t ) h 1 3 12 5 1 12 (5)(9.5) 3 2 1 12 (4.375)(8) 3 f 5 VQ I Ê V max 5 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 5 2(900) 5 1800 kN/m 5 1638 3 10 6 mm 4 Q 5 Q flange 5 A F d F 5 (280)(25)(312.5) 5 2.1875 3 10 6 mm 3 5 1.35 MN V max 5 f allow I Q 5 (1800 kN / m)(1638 3 10 6 mm 4 ) 2.1875 3 10 6 mm 3 I 5 bh 3 12 2 ( b 2 t ) h 1 3 12 5 1 12 (280)(650) 3 2 1 12 (265)(600) 3 f 5 VQ I Ê V max 5 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. 3 1 in. flange plates and a 64 in. 3 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 5 300 k F 5 force per inch of length of one weld f 5 shear flow 5 46,220 in. 4 Q 5 Q flange 5 A F D F 5 (18)(1.0)(32.5) 5 585 in. 3 F 5 VQ 2 I 5 (300 k)(585 in. 3 ) 2(46,220 in. 4 ) 5 1900 lb / in. I 5 bh 3 12 2 ( b 2 t ) h 1 3 12 5 1 12 (18)(66) 3 2 1 12 (17.625)(64) 3 F 5 VQ 2 I f 5 2 F 5 VQ I
Problem 5.11-4 A box beam of wood is constructed of two 260 mm 3 50 mm boards and two 260 mm 3 25 mm boards (see figure). The boards are nailed at a longitudinal spacing s 5 100 mm. If each nail has an allowable shear force F 5 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 5 260 b 1 5 260 2 2(50) 5 160 h 5 310 h 1 5 260 s 5 nail spacing 5 100 mm F 5 allowable shear force for one nail 5 1200 N f 5 shear flow between one flange and both webs Q 5 Q flange 5 A F d F 5 (260)(25)(142.5) 5 926.25 3 10 3 mm 3 5 10.7 kN V max 5 f allow I Q 5 (24 kN / m)(411.125 3 10 6 mm 4 ) 926.25 3 10 3 mm 3 I 5 1 12 ( bh 3 2 b 1 h 3 1 ) 5 411.125 3 10 6 mm 4

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## This note was uploaded on 03/19/2008 for the course E M 316 taught by Professor Korkolis during the Spring '08 term at University of Texas at Austin.

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

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