Concrete Column P-M Interaction Check
Evaluate a rectangular reinforced concrete column under combined axial compression and uniaxial bending. Generates key points on the P-M interaction diagram — maximum axial capacity (φPn,max), balanced point, pure bending capacity — and checks whether the applied load combination (Pu, Mu) falls inside the interaction envelope. Applies variable φ-factors for compression-controlled vs. tension-controlled behavior.
What this calculates
Maximum factored axial capacity φPn,max = 0.80·φ·[0.85·f'c·(Ag − Ast) + fy·Ast] per Section 22.4.2, balanced neutral axis depth (cb), moment at balanced condition (φMn,bal), pure bending capacity (φMn,0), and whether the (Pu, Mu) point is inside the interaction envelope.
Inputs
Factored axial compression demand
Factored bending moment demand
Column width (perpendicular to bending)
Column depth (in the direction of bending)
Specified compressive strength
Reinforcement yield strength (Grade 60 typical)
Total area of longitudinal reinforcement
Clear concrete cover to the outside of the ties
Outputs
Maximum factored axial capacity (0.80·φPo)
Moment at the balanced condition
Moment capacity at zero axial load
Pass/fail: is (Pu, Mu) inside the interaction diagram
Methodology
Uses strain compatibility per ACI 318-19 Section 22.2. Assumes εcu = 0.003 at the extreme compression fiber, and varies the neutral axis depth c from full section (pure compression) to zero (pure tension). At each c, the Whitney stress block depth a = β1·c defines the concrete compression resultant, and steel strains are determined from similar triangles. The φ-factor varies from 0.65 (compression-controlled, εt ≤ 0.002) to 0.90 (tension-controlled, εt ≥ 0.005) with linear interpolation between. The maximum axial load is capped at 0.80·φPo for tied columns per Section 22.4.2.1.
Code References
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