Combined Axial & Bending Check
The tool evaluates the linear interaction (unity) equation used to screen beam-columns — members that carry axial force and bending at the same time.
Enter Values
Before you rely on this: First-pass guide only. Verify safety-critical or regulated work against the relevant standards, your project requirements and a qualified professional.
How to use this calculator
- Enter the axial demand P and the member's axial capacity P_allow (both in kN), using the same code basis (both factored, or both allowable).
- Enter the bending demand M and the bending capacity M_allow (both in kN·m), again on a consistent basis.
- Read the utilisation ratio: ≤ 1.0 passes, > 1.0 fails. The spare-capacity figure tells you how far you are from the unity limit.
How it works
The tool evaluates the linear interaction (unity) equation used to screen beam-columns — members that carry axial force and bending at the same time. It sums the two demand-to-capacity ratios: utilisation = P / P_allow + M / M_allow (equivalently fa/Fa + fb/Fb in stress terms). If the sum is ≤ 1.0 the combination of loads sits inside the member's capacity envelope and the check passes; if it exceeds 1.0 the member is overstressed for that load combination.
The demand and capacity for each action must be expressed on the same basis: either both limit-state (factored) values or both allowable (working-stress) values, and both about the same bending axis. Real design standards replace this straight-line rule with axis-specific interaction curves that also include a moment-amplification factor for P-Δ and P-δ (second-order) effects, a buckling term, and separate checks for biaxial bending and section vs member capacity. This calculator is a fast conservative screen, not the full code check.
Worked example
Column carrying axial load plus a moment. A member has an axial demand P = 200 kN against an axial capacity P_allow = 500 kN, and a bending demand M = 30 kN·m against a bending capacity M_allow = 60 kN·m. Axial term = 200 / 500 = 0.4. Bending term = 30 / 60 = 0.5. Utilisation = 0.4 + 0.5 = 0.9, which is ≤ 1.0, so the member PASSES with 10.0 % spare capacity to the unity limit. Because the ratio is close to 1.0, check that moment amplification (P-Δ effects) has been accounted for in M before relying on this pass.
Common mistakes
- Mixing bases — comparing a factored (ultimate) demand against an allowable (service) capacity, or vice versa. Keep both P values and both M values on the same code basis.
- Forgetting moment amplification: for slender members the real design moment M is larger than the first-order moment because of P-Δ / P-δ effects. A pass here on the un-amplified moment can still fail the full standard check.
- Using a bending capacity about the wrong axis, or ignoring biaxial bending. This linear check handles a single bending axis — add the second axis term (My/My_allow) yourself if the member bends both ways.
Frequently asked questions
What does the utilisation (unity) ratio mean?
It is the sum of the axial and bending demand-to-capacity ratios, P/P_allow + M/M_allow. A value of 1.0 means the member is exactly at its combined capacity for that load case. Below 1.0 there is spare capacity; above 1.0 the member is overstressed.
Can I use factored loads or working (allowable) loads?
Either — as long as you are consistent. Enter both demands and both capacities on the same basis: either all limit-state/factored values (AS 4100, Eurocode) or all allowable-stress values (ASD). Never mix a factored demand with an allowable capacity.
Is a pass here enough to accept the member?
No. This is a simplified linear screen. It does not include moment amplification for second-order (P-Δ / P-δ) effects, member buckling interaction, biaxial bending, or the section-vs-member capacity split that real standards require. Use it to size and sanity-check, then confirm with the full code check (AS 4100 / Eurocode 3 / AISC 360) and a competent engineer.
How do I handle bending about two axes?
Add the second bending term. The extended check is P/P_allow + Mx/Mx_allow + My/My_allow ≤ 1.0. This tool covers one bending axis; compute the second term separately and add it before comparing to 1.0.
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