Concentric Capacity of a Short Column
Mediumcolumnaxial-strengthnominal
A short reinforced-concrete column has gross area Ag = 160,000 mm², total longitudinal steel Ast = 3,200 mm², f′c = 28 MPa, and fy = 420 MPa. Use P₀ = 0.85f′c(Ag − Ast) + fyAst for concentric load. Find the nominal strength P₀ before any φ or axial-load cap.
- A5,152 kN
- B5,076 kN
- C3,299 kN
- D4,061 kN
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Answer: B. 5,076 kN
Equation: P₀ = 0.85f′c(Ag − Ast) + fyAst. Inputs: Ag − Ast = 156,800 mm². Substitution: 0.85(28)(156,800) = 3,731,840 N; fyAst = 420(3,200) = 1,344,000 N; P₀ = 5,075,840 N = 5,076 kN. Wrong: 5,152 kN uses the full Ag in the concrete term (counts the steel area twice); 3,299 kN applies φ = 0.65 to a nominal result; 4,061 kN applies the 0.80 axial cap, also not requested.
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