Question

The 24 ft beam shown is laterally braced at the ends and at the centerline of the beam span. The beam supports two concentrated live loads of 15 kips at the / and points. Assume 50 ksi steel and use a calculated value of Cb. You may neglect the beam self-weight. Select the lightest W-shape. As part of your answer indicate the following: Problem 3 (20 points) Member selected W X Cb Mu DMa PL PL 12 ft 6 ft 6 ft

Answer 1

Given beam is braced at ends and midpoint

Live load=15 kips

For the given loading, the bemding moment diagram will be such that it varies linerly fron 0 to (15*6)=90 kip-ft between the left support and the concentrated load, then is constant between the concentrated loads with value of 90 kip-ft and then refuced linearly from 90 to 0 beyong the second load all the way to second support

Per AISC

Cb=12.5Mmax/(2.5Mmax+3Ma+4Mb+3Mc) per AISC nomenclature

Mmax=90 kip-ft

Ma=15*3=45 kip-ft

Mb=90 kip-ft

Mc=90 kio-ft

Cb=(12.5*90)/(2.5*90 + 3*45+ 4*90+ 3*90)=1.136

Factored load=1.6*15=24 kips

Favtored momemt in beam=24*6=144 ft

Unbraced length=12 ft

Moment calacity requured requured without Cb=144/1.136=126.8 kip-ft

Lightest beam that has moment capacity greater than 126.8 for unbraces lemgth of 12 ft is w14x34 per Table 3-2 of AISC 360

Moment capacity without Cb=161.4 kip-ft

Momemt capacity with Cb=161.4*1.136=183.4 kip-ft