Rectangular Concrete Column

How it calculates

The Rectangular Concrete Column (ACI 318-19) calculator builds uniaxial P-M interaction from the rectangular stress block, checks biaxial bending by the Bresler method, and magnifies moments for slender columns in non-sway frames. Compared with the ACI 318-14 version, the tension-controlled strain limit for φ changes from 0.005 to εty + 0.003.

Interaction diagram

The P-M interaction uses εcu = 0.003 and the stress block factor β1, which varies with f'c:

• f'c ≤ 4000 psi: β1 = 0.85
• 4000 psi < f'c < 8000 psi: β1 = 0.85 - 0.05 × (f'c - 4000) / 1000
• f'c ≥ 8000 psi: β1 = 0.65

φ = 0.65 when εt ≤ εty and 0.90 when εt ≥ εty + 0.003, with linear transition between. εty is taken as 0.002 for fy = 60 ksi and fy/Es otherwise. Failure mode and the governing φ are reported for each axis. Pure axial capacity is φPn = 0.65 × 0.80Po.

Slenderness (non-sway frame)

A column is slender about an axis when kL/r exceeds 34 + 12(M1/M2) or 40. With no applied moment, the limit is 22. M1/M2 is negative for single curvature.

For slender columns, moments are magnified:

Mc = δ × Mu where δ = Cm / (1 - Pu / 0.75Pc), not less than 1.0

with Cm = 0.6 - 0.4 × (M1/M2). Pc = π²(EI)eff / (kL)², with (EI)eff reduced for sustained load. The calculator flags δ above 1.4 and Pu above Pc.

Biaxial bending (Bresler method)

The Bresler reciprocal load method gives the biaxial capacity:

1/φPn = 1/φPnx + 1/φPny - 1/φPo

Pu / φPn ≤ 1.0 must be satisfied. If either moment is below its minimum eccentricity moment, the uniaxial capacity about the other axis is used. When Pu < 0.1Po, a linear moment check Mux/φMnx + Muy/φMny ≤ 1.0 is also applied.

The calculator conservatively uses the maximum axial load and maximum moments from all strength combinations in the interaction check.

Detailing checks

Reinforcement ratio is checked between 1% and 8%. Cover to ties must be at least 1.5 in, and clear bar spacing at least the larger of 1.5 in and 1.5 bar diameters. Load combinations that produce net uplift are flagged as not supported.