Question

1. (8 points) A beam is applied 4kip force and 20kip*ft moment. The allowable normal stress is 24 ksi and the allowable shear stress is 14.5 ksi. Select the lightest W6 I-Beam (wide flange beam) size for this structure. 4Kip 1 2 2o kip.ft kift* aft

Answer 1

A kip 20 ip-ft - RA RB 0 3 (ft) Let the left support have a vertical reaction RA and the right support have a vertical reaction Rg. Sum of forces along the y-axis is equal to zero for static equilibrium: ++ SF,=0 RA+RB - 4= 0 RA+RB-4=0 RA+RB = +4kip ---(1) Sum of moments about the left support is equal to zero for static equilibrium: +OSM=0 RB (3-0) + (-4) (1) - 20 = 0 RB (3-0)+(-4) (+1) - 20 =0 RB = +8kip -(2) Substitute (2) into (1): RA + RB = +4 RA+8=14 RA=–4kip

Moment for 0 SX51 M2) 4 kip V 3 (ft) T Take a cut for 0 <<1: +0 SM = 0 +(-4) (2-0) - M (2) = 0 M(2) = -4.0 MO) = -4.5 for 0<x<1

Moment for 1 5x53 #kip M2) + 4 kip V 0 3 I (ft) 1 Take a cut for 1 <153: +02M, = 0 +(-4) (2-0)+(-4) (2-1) - M (2)=0 M22) = +4 - 80 ..M22) = +4-82 for 1<3 <3

Bending (kip-ft) Moment 0 -4 -20 1

AS we know ,

$\small M=20 \ kip-ft=240000 \ lb-in$

$\small \\\\\sigma_b=24 \ ksi=24000 \ psi$

$\small \\\\\sigma_b=\frac{M}{z} \\\\z=\frac{M}{\sigma} \\\\z=\frac{240000}{24000} \\\\z=10 \ in^3$

As per w6 beam table

The beam W6x16 has z value of 10.2 in³

So the lightest W6 I-Beam is

W6x16

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