ENGINEERING – TRUCTURAL ENGINEERING — CONCRETE CALCULATOR
Column Interaction Diagram
A precise tool.
What is the Column Interaction Diagram & How does it work?
The axial‑load‑bending‑moment interaction diagram represents the combined capacity of a reinforced‑concrete column. It is plotted in the P‑M space, where P is the axial load and M is the bending moment. The curve is derived from the strain‑compatibility and equilibrium equations for concrete and steel. For a rectangular column, the nominal axial capacity is obtained from The interaction ratio (rho = frac{P}{P_n} + frac{M}{M_n}) is compared with unity. If (rho le 1) the column is considered safe under the specified load combination; otherwise a redesign or strengthening is required.
P_n = 0.85 f’_c (A_g – A_s) + f_y A_s
P_n = nominal axial load capacity (kN)
f’_c = concrete compressive strength (MPa)
A_g = gross cross‑sectional area (mm²)
A_s = steel reinforcement area (mm²)
f_y = steel yield strength (MPa)
f’_c = concrete compressive strength (MPa)
A_g = gross cross‑sectional area (mm²)
A_s = steel reinforcement area (mm²)
f_y = steel yield strength (MPa)
Parameters
Result
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Frequently Asked Questions
What is an axial-load-bending-moment interaction diagram?
It's a plot in P-M space showing the combined capacity of a reinforced-concrete column under axial load and bending moment.
How do you calculate the nominal axial load capacity for a rectangular column?
Use the formula P_n = 0.85 f'_c (A_g - A_s) + f_y A_s, where f'_c is concrete compressive strength, A_g is gross area, and A_s is steel area.
What does the P-M space represent in this diagram?
P-M space represents the axial load (P) versus bending moment (M) capacity of a reinforced-concrete column.
Why are strain compatibility and equilibrium equations used in this calculation?
These equations ensure that the stresses and strains in both concrete and steel are compatible and balanced under combined loads.
What is the significance of the 0.85 factor in the formula for P_n?
The 0.85 factor accounts for safety and the reduction in compressive strength due to cracking in concrete.
Results are for informational purposes only and do not constitute professional advice.