A simply-supported W21x111 interior beam made of A992 steel supports a single fl

Question

A simply-supported W21x111 interior beam made of A992 steel supports a single floor level with a span length of 50 ft and a tributary width of 25 ft. The compression flange of the beam is braced at each end and at midspan. The beam will be subjected to a uniform dead load (excluding self-weight) of 75 psf and a nominal (unreduced) live load of 50 psf. Serviceability requirements are set at a maximum deflection of L/240 for the combination of dead load and live load, and L/360 under the live load alone.

a). The beam's factored moment capacity

b). The beam's factored shear force capacity

c). The beam's allowable deflections for dead & live load and live load by itself

d). The ultimate moment demand

e). The ultimate shear force demand

f). The maximum deflections for dead & live load and live load by itself.

g). Considering results from parts a).-f). is the W21x111 sufficient to resist this loading?

Explanation / Answer

a) Unbraced length of beam=50/2=25 ft

Per Table 3-2 of AISC, moment capacity of beam for Unbraced length of 25 ft=1050- (1050-654)/(31.2-10.2)*(25-10.2)=771 kip-ft

b)beam's shear force capacity per Table 3-2 =355 kips

c)total allowable deflection=L/240=50*12/240=2.5 inches

Live load deflection limit=L/360=50*12/360=1.67 inches

d)Dead load on beam=75*25=1875 plf

Self weight of beam=111 plf

Total dead load=1875+111=1986 plf=1.986 kip/ft

Total live load=50*25=1250 plf=1.25 kip/ft

Total factored load=(1.2*1.986)+(1.6*1.25)=4.3832kip/ft

Ultimate moment in beam=4.3833*50²/8=1369.75 kip-ft

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