What is a P-M interaction diagram for concrete columns?

A P-M interaction diagram plots all combinations of axial load P and moment M that a column section can resist at its nominal capacity. Points inside the curve are safe; points outside indicate failure.

What is the minimum longitudinal reinforcement in a concrete column per ACI 318-19?

Per ACI 318-19 Section 10.6.1.1, the minimum steel ratio ρg = 0.01 (1%) and maximum is 0.08 (8%) of the gross cross-sectional area.

What is the balanced failure point on an interaction diagram?

The balanced point occurs when concrete reaches its maximum strain (εcu = 0.003) simultaneously with steel yielding (εs = fy/Es). It defines the boundary between compression- and tension-controlled failure.

What reduction factor φ applies to tied concrete columns?

For compression-controlled tied columns, φ = 0.65 per ACI 318-19 Table 21.2.1. φ increases linearly to 0.90 as the section transitions to tension-controlled.

How is biaxial bending handled in column design?

Biaxial bending is checked using the reciprocal load equation (Bresler method): 1/Pni = 1/Pnx + 1/Pny − 1/P0, or by constructing a 3D interaction volume and checking that the (Pu, Mux, Muy) point falls within it.

Concrete Design

Column Design

ACI 318-19

Knowledge Projects

Dark ColorDark MonoLight ColorLight Mono

RC Column Design

ACI 318-19 §22.4 — Axial + uniaxial bending

Loads

P_u?

M_u?

Eccentricityauto?

Load combinations (Pu, Mu)

Store additional Pu/Mu pairs to see multiple demand points on the P-M diagram.

Geometry

Section shape

Confinement

Width (b)

Depth (h)

Cover

Height (L)

Material

f'c

Reinforcement

Bar Size (mm)

Layout

No. Bars

Astauto?

ρgauto?

âœ“ 1-8% OK

Confinement

Tie bar (mm)

Spacing s

Ash,req = 771; Ash,min = 411; Ash,prov = 157 ✗

Layout:

Elevation

Cross Section

3D View

P-M Diagram

Step	Formula	Substitution	Result
Ag	b×h	400×400	160000 mm²
Ast	n×π/4·db²	8×π/4×25²	3927 mm²
ρg	Ast/Ag	3927/160000	0.0245	✓

Step	Formula	Substitution	Result
φPn(max)	φ·0.80[0.85f'c(Ag-Ast)+fy·Ast]	0.65×0.80×[0.85×30×(160000-3927) + 420×3927]	2927.2 kN

Step	Formula	Substitution	Result
e	Mu/Pu	65/950	68 mm
φPn	φPn(e)	from interaction diagram	2552.1 kN	✓
φMn	φMn(e)	from interaction diagram	174.6 kN·m	✓

Step	Formula	Substitution	Result
DCR(axial)	Pu/φPn	950/2552.1	0.37	✓
DCR(moment)	Mu/φMn	65/174.6	0.37	✓

Results

Column DCR

0.37 · PASS

Axial37%

Moment37%

φPn2552.1 kN

Pu950 kN

φMn174.6 kN·m

Mu65 kN·m

φPn(max)2927.2 kN

φPnB1186.6 kN

φMnB284.4 kN·m

φMn0 (P=0)231.5 kN·m

Ag160,000 mm²

Ast3,927 mm²

ρg2.45%

e68 mm

This calculation is for preliminary design verification only. All results must be independently verified by a licensed professional engineer before use in construction documents.

Loading tool...

Concrete Design

Column Design

ACI 318-19

Knowledge Projects

Dark ColorDark MonoLight ColorLight Mono

RC Column Design

ACI 318-19 §22.4 — Axial + uniaxial bending

Loads

P_u?

M_u?

Eccentricityauto?

Load combinations (Pu, Mu)

Store additional Pu/Mu pairs to see multiple demand points on the P-M diagram.

Geometry

Section shape

Confinement

Width (b)

Depth (h)

Cover

Height (L)

Material

f'c

Reinforcement

Bar Size (mm)

Layout

No. Bars

Astauto?

ρgauto?

âœ“ 1-8% OK

Confinement

Tie bar (mm)

Spacing s

Ash,req = 771; Ash,min = 411; Ash,prov = 157 ✗

Layout:

Elevation

Cross Section

3D View

P-M Diagram

Step	Formula	Substitution	Result
Ag	b×h	400×400	160000 mm²
Ast	n×π/4·db²	8×π/4×25²	3927 mm²
ρg	Ast/Ag	3927/160000	0.0245	✓

Step	Formula	Substitution	Result
φPn(max)	φ·0.80[0.85f'c(Ag-Ast)+fy·Ast]	0.65×0.80×[0.85×30×(160000-3927) + 420×3927]	2927.2 kN

Step	Formula	Substitution	Result
e	Mu/Pu	65/950	68 mm
φPn	φPn(e)	from interaction diagram	2552.1 kN	✓
φMn	φMn(e)	from interaction diagram	174.6 kN·m	✓

Step	Formula	Substitution	Result
DCR(axial)	Pu/φPn	950/2552.1	0.37	✓
DCR(moment)	Mu/φMn	65/174.6	0.37	✓

Results

Column DCR

0.37 · PASS

Axial37%

Moment37%

φPn2552.1 kN

Pu950 kN

φMn174.6 kN·m

Mu65 kN·m

φPn(max)2927.2 kN

φPnB1186.6 kN

φMnB284.4 kN·m

φMn0 (P=0)231.5 kN·m

Ag160,000 mm²

Ast3,927 mm²

ρg2.45%

e68 mm

This calculation is for preliminary design verification only. All results must be independently verified by a licensed professional engineer before use in construction documents.

Column Design

RC Column Design

Loads

Geometry

Material

Reinforcement

Confinement

RC Column Design

Given:

Material Properties:

Section Properties

Max Axial Capacity

Capacity at Load

DCR Check

Column Design

RC Column Design

Loads

Geometry

Material

Reinforcement

Confinement

RC Column Design

Given:

Material Properties:

Section Properties

Max Axial Capacity

Capacity at Load

DCR Check