4 A simply supported beam spans 60 ft must carry three colum

4. A simply supported beam spans 60 ft must carry three column factored load s othe el if the kips each (see figure). Select the most economical W-section assuming A992 ste nominal depth is limited to 30 inches if (a) full lateral support for the compression (b) lateral support for the compression flange is provided at the beam end supports flange and and the concentrated forces. 120 k 120 k 120 k 15 ft 15 ft 15 ft 15 ft

Solution

a) The maximum moment in the beam will be at midspan

Reaction at left support=reaction at right support=3*120/2=180 kips

moment in beam at midspan = 180*30 - 120*15=3600 kip-ft

This is the required design moment

since the beam compression flange is fully braced, the lightest 30 in deep having plastic moment capapcity greater than 3600 kip ft = W27x307 (which has nominal depth of 29.6 in and has plastic moment capacity of 3860 kip-ft)

b) in this case the unbraced length of beam =15 ft

therefore, the lightest 30 in deep beam having moment capacity greater than 3600 kip-ft for unbraced length of 15 ft = W27x307 (which has a nominal depth of 29.6 in and moment capapcity of 3746 kip-ft for unbraced length of 15 ft)