Problem #4-Steel Flexural Members (25 points) A W21x48 beam (ASTM A992, Fy = 50

Question

Problem #4-Steel Flexural Members (25 points) A W21x48 beam (ASTM A992, Fy = 50 ksi) spans a distance, L, of 21 feet between simple supports, and carries a design (factored) load, wu, of 7 k/ft, as shown in the figure below. The beam is braced at 1/3 points along the span (braced locations are indicated with an "X" in the figure). Determine whether the beam is capable of safely supporting the design load in flexure according to LRFD criteria. You may use any tabulated information in the FE Reference Handbook, if a citation is also provided for where the information may be found to justify your response. Your answer must include a quantitative evaluation (not visual only. Wu

Explanation / Answer

Given beam span = 21 ft

Beam is braced at one-third points

unbraced length =L= 21/3=7 ft

Maximum design moment in beam = Mu=7*212/8=385.875 kip-ft

Given beam section is w21x48

Lp = 5.86kip-ft

Lr = 16.5 kip-ft

Mp = 398 kip-ft

Mr = 244 kip-ft

Lp<L<Lr

Moment capapcity of beam = 398-[(398-244)/(16.5-5.86)]*(7-5.86) = 381.5 kip-ft

Cb between the third points per Table 3-1,AISC 360-10 = 1.01

Moment capapcity = 1.01*381.5 = 385.315 kip-ft

The moment capapcity of beam is just less than the demand. beam is not adequate since its capapcity is marginally lower than the demand moment per LRFD

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