2 An A992 W12x58 is used as a 14 ft column in a braced frame

2. An A992 W12x58 is used as a 14 ft column in a braced frame to carry a compressive dead load of 60 kips and live load of 120 kips. Will this column be adequate to carry a dead load moment of 30 ft-kips and live load moment of 60 ft-kips at each end, bending the column in single curvature about the strong axis? The analysis results are from a first-order analysis. Determine by (a) LRFD and (b) ASD

Solution

a)dead load axial load=60 kips

Live load axial load=120 kips

Dead load moment=30 kip-ft

Live load moment=60 kip-ft

Factored axial load=1.2*60 +1.6*120 =264 kips

Factored moment =1.2*30 + 1.6*60 =132 kip-ft

Axial load capacity of w12x58 for effective length of 14ft =551 kips per table 4-1 of AISC 360

Moment capacity of w12x58 for Unbraced length of 14 ft=324-((324-205)/(29.8-8.87))*(14-8.87)=294.8 kip ft

Interaction check:

(264/551)+(8/9)(132/294.8) =0.8771

Section is adequate per LRFD

b) ASD calcs

Total axial load in column=60+120=180 kips

Total moment in column=30+60=90 kip-ft

Axial load capacity of column=367 kips

Moment capacity of section=216-((216-136)/(29.8-8.87)*(14-8.87)=196.4 kip-ft

Interaction check

180/367 +(8/9)(90/196.4) = 0.8981

Section is adequate in ASD