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ARC322 Homework 21 SOLUTION

# ARC322 Homework 21 SOLUTION - ARC322 points NO POINTS 2008...

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ARC322 Homework 21 25 points … NO POINTS 2008 KEY 1. Design a wood beam that simply spans 14ft. The beams are on 6ft centers. The beam carries a DL of 35lb/ft 2 and a LL of 40lb/ft 2 . The beam sits atop a 2x4 wall. Use DFLSS. Member Selection: M = w L 2 /8 = (75 lb/ft 2 x 6 ft)(14 ft) 2 /8 = 11,025 ft-lb S = M/ f = (11,025 ft-lb x 12 in/ft)/1500 lb/in 2 = 88.2 in 3 Select 3x16 S = 96.90 in 3 > 88.2 in 3 … OK 2 points Horizontal Shear: V = (75 lb/ft 2 x 6 ft) x 14 ft / 2 = 3150 lb v = 1.5V/A = 1.5 x 3150 lb / 38.13 in 2 = 123.91 lb/in 2 123.91 lb/in 2 > 85 lb/in 2 … NOT OK Try 4x14 v = 1.5V/A = 1.5 x 3150 lb / 46.38 in 2 = 101.88 lb/in 2 101.88 lb/in 2 > 85 lb/in 2 … NOT OK Note … they were not required to show failed trials … if they did, 2 points Extra Credit Try 4x16 v = 1.5V/A = 1.5 x 3150 lb / 53.38 in 2 = 88.52 lb/in 2 88.52 lb/in 2 > 85 lb/in 2 … NOT OK Try 6x12 v = 1.5V/A = 1.5 x 3150 lb / 63.25 in 2 = 74.70 lb/in 2 2 points 74.70 lb/in 2 < 85 lb/in 2 … OK 1 point Deflection: D = 5WL 3 /384EI = (5 x 6300 lb x (14 ft x 12 in/ft) 3 )/384 x 1,600,000 lb/in 2 x 697.1 in 4 D = 0.349 in 2 Points L/240 = (14 ft x 12 in/ft)/240 = 0.7 in > 0.349 in ... OK 1 Point Compession Perpendicular to Grain: Contact area = 3.5 in x 5.5 in = 19.25 in 2 Compression Stress = P/A = 3150 lb / 19.25 in

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ARC322 Homework 21 SOLUTION - ARC322 points NO POINTS 2008...

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