A column in the upper story of a building is subjected to a compressive load fro

Question

A column in the upper story of a building is subjected to a compressive load from the following sources: dead load = 30.8 kips, occupancy live load = 1.7 kips, roof live load = 18.7 kips, and snow load = 19.7 kips. a. If load and resistance factor design is used, determine the factored load (required strength) to be used in the design of the column. Which AISC load combination controls? b. What is the required design strength of the column? c. What is the required nominal strength of the column for a resistance factor phi of 0.90? d. If allowable strength design is used, determine the required load capacity (required strength) to be used in the design of the column. Which AISC load combination controls? e. What is the required nominal strength of the column for a safety factor Ohm of 1.67?

Explanation / Answer

a) Dead load (D) = 26 kips Occupancy load (L) = 15 kips Roof live load (Lr) = 5 kips Snow load (S) = 8 kips Rain Load (r ) = 5 kips Wind load (W) = 8 kips Load combination 1 1.4 D 36.4 kips Load combination 2 1.2 D + 1.6L +0.5*max(Lr,S, R) 67.2 kips Maximum Load Load combination 3 1.2 D + 1.6*max(Lr,S, R) +max(1*L,0.5*W) 64.0 kips Load combination 4 1.2 D + 1*W +1*L +0.5*max(Lr,S, R) 63.2 kips Load combination 5 1.2 D + 1*L +0.5*S 55.2 kips Load combination 6 0.9*D -1*W 15.4 kips Minimum Load Maximum factored load in compression is 67.2 kips governed by load combination 2 b) Required design strength of Column is the maximum factored load in compression Pu = 67.2 kips c) If resistance factor is 0.9, then the nominal strength = Pu/0.9 Pnom = 74.7 kips d) Load combination 1 D 26 kips Load combination 2 D + max(Lr, S , R) 34 kips Load combination 3 D + 0.75*L + 0.75*max(Lr, Sr, R) 43.3 kips Load combination 4 D + 0.6*W 30.8 kips Load combination 5 D + 0.75*L + 0.75*max(Lr, Sr, R) + 0.75*(0.6W) 46.9 kips Maximum Load Load combination 6 0.6*D + 0.6*W 10.8 kips Minimum Load Maximum factored load in compression is 46.9 kips governed by load combination5 So required load capacity need to be used is 46.9 kips e) factor to be applied on required load capacity is 1.67. So nominal strength = 46.9*1.67 Pnom. = 78 kips

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