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Interpolating Column Interaction Diagram

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A column design interaction diagram, already on a design-strength basis, has a straight segment between (φPn, φMn) = (2,000 kN, 150 kN·m) and (3,000 kN, 90 kN·m). Using linear interpolation along this segment, what design moment resistance is available at Pu = 2,500 kN?
  1. A78 kN·m
  2. B100 kN·m
  3. C120 kN·m
  4. D150 kN·m
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Answer: C. 120 kN·m

Equation: linear interpolation, φMn = M₁ + r(M₂ − M₁), r = (Pu − P₁)/(P₂ − P₁). Substitution: r = (2,500 − 2,000)/1,000 = 0.50; φMn = 150 + 0.50(90 − 150) = 120 kN·m. Wrong: 78 kN·m applies φ = 0.65 again to a value that is already a design strength; 100 kN·m uses r = 2,500/3,000 instead of measuring from the first point; 150 kN·m is the upper endpoint, ignoring that the axial load lies halfway.
kN·m
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