Steel Column Capacity Calculator

Purpose and model boundary

This model estimates nominal, LRFD factored, and ASD allowable axial compressive strength for a prismatic steel column using the AISC 360 Chapter E flexural-buckling relationship. It supports a first-pass comparison of a concentric axial load with selected or user-entered section properties. It is not a complete structural design, code compliance determination, or sealed calculation.

The spreadsheet remains the calculation authority. The page sends the named inputs to the workbook and presents the returned values, capacity curve, and status without recreating the equations in browser code.

Inputs and units

For a stored section, the workbook looks up gross area and radius of gyration. For custom mode, it uses the two entered properties directly.

Governing relationships

With E = 29,000 ksi, the column slenderness and Euler stress are:

λ = KL / r

F_e = π²E / λ²

The AISC transition slenderness is:

λ_c = 4.71 × sqrt(E / F_y)

The workbook selects the critical compressive stress branch:

• when λ ≤ λ_c: F_cr = 0.658^(F_y / F_e) × F_y;
• when λ > λ_c: F_cr = 0.877 × F_e.

It then calculates:

• nominal capacity: P_n = F_cr × A_g;
• LRFD factored capacity: φP_n = 0.90 × P_n;
• ASD allowable capacity: P_n / 1.67;
• factored utilization: P_u / (φP_n);
• allowable utilization: P_u / (P_n / 1.67);
• Euler load: F_e × A_g;
• yield capacity: F_y × A_g.

Calculation sequence

1. Section selection determines whether stored or custom area and radius are used.
2. The grade selection looks up yield strength and is checked against the section/grade applicability map.
3. K, length, and radius produce slenderness; slenderness produces Euler stress and selects the inelastic or elastic branch.
4. Critical stress is multiplied by gross area to obtain nominal, factored, and allowable capacities.
5. Applied load is divided by factored and allowable capacity for the two utilization measures.
6. The published chart repeats the factored-capacity calculation over the workbook's unbraced-length series and compares it with the applied-load reference.
7. The workbook evaluates Model_Status in the precedence shown below.

Outputs and interpretation

Allowable_Axial_Capacity is the primary ASD result; Factored_Axial_Capacity is the corresponding LRFD resistance. They are alternative design formats and should not be mixed with the wrong load combination. Buckling_Mode states which AISC branch governs. Slenderness_Ratio, Elastic_Buckling_Stress, Critical_Buckling_Stress, and the two utilization values expose the capacity calculation. The plotted length curve is a sensitivity view for the same section, grade, and K.

Validation and status logic

The workbook evaluates status in this order:

Because status tests slenderness before utilization, a column that triggers both conditions reports the slenderness message.

Assumptions and limitations

• The member is straight, prismatic, concentrically loaded, and represented by the gross area and governing radius supplied by the workbook or user.
• The calculation implements the AISC flexural-buckling stress relationship for a nonslender compression member. It does not check local slenderness reductions, torsional or flexural-torsional buckling, built-up-member provisions, or single-angle provisions.
• End restraint is reduced to the user-supplied K; the workbook does not derive effective length from a frame stability analysis.
• Eccentricity, connection effects, residual stress beyond the adopted column curve, second-order frame effects, imperfections, fire, fatigue, and seismic detailing are not separately modeled.
• Stored properties are a small reference subset, not the complete AISC shapes database. Custom properties are not independently verified.
• Applied load is not generated from load combinations and the model does not select LRFD versus ASD for the user.

Restrictions and non-computing states

This calculator restricts section and grade to declared choices, uses formula-backed visibility for custom properties, and requires nonnegative numeric inputs. The workbook additionally requires positive K, length, area, and radius and rejects incompatible stored section/grade pairs. A zero applied load is permitted and produces zero utilization. Protected formulas can display zeros during an invalid state; those values are not capacities to use.

Errors and warnings

A rejected entry means the submitted value did not satisfy the published input rules and no workbook capacity decision was made. A workbook NOT VALID status identifies an incompatible material selection or a non-computing geometry. CHECK means the capacity is calculated but slenderness or factored utilization requires engineering review. A connection or calculation-service failure is an availability problem, not a structural conclusion.

The workbook follows AISC 360 Chapter E flexural buckling, as documented in the delivered audit using AISC 360-16 Specification and Commentary. Section-property context comes from the AISC 16th Edition Basic Design Value Cards, with grade applicability context from the AISC material specification FAQ. The adopted local code and a qualified structural engineer govern actual design.