Steel Column Sizing Calculator (Buckling Check)
Find the smallest steel section satisfying Euler buckling and yield checks for a column under axial load with given end conditions and grade.
How this works
For an axially-loaded column we apply two checks and pick the smaller of the two as the governing capacity, then divide by a factor of safety:
P_y = σ_y × A (yield)
P_e = π² × E × I / (kL)² (Euler buckling)
P_perm = min(P_y, P_e) / 1.67 (working-stress allowable)
k = effective-length factor:
fixed-fixed = 0.65
fixed-pinned = 0.80
pinned-pinned = 1.00
fixed-free = 2.00We iterate ISMB I-beams, SHS hollow sections, and IS 1161 medium-class round pipes, in ascending size, and return the first section whose P_perm covers the applied axial load. Slenderness λ = kL / r_min is also reported — IS 800 caps it at 180 for primary compression members.
Worked example
A 3.5 m tall pinned-pinned column carrying 200 kN of axial load, grade Fe415:
- k = 1.00, kL = 3500 mm
- Iterate sections — typical recommended section: SHS 100×100×4 or SHS 100×100×6.
Switch the end condition to fixed-fixed (k = 0.65) and the same column easily passes with a lighter section because the buckling capacity jumps by roughly 1/(0.65)² ≈ 2.4×.
Sources
- IS 800 — General Construction in Steel (Code of Practice)
- IS 808 / IS 1161 / IS 4923 — Section property tables
- Euler critical buckling load — classical column theory
FAQ
What checks does this calculator perform?
Two service-load checks for an axially-loaded column: yield capacity P_y = σ_y × A, and Euler buckling capacity P_e = π² × E × I / (kL)². The permissible load is the smaller of the two divided by a factor of safety of 1.67 (IS 800 working-stress style). The first catalog section whose permissible load equals or exceeds the applied axial load is returned. ISMB I-beams, SHS hollow sections, and round pipes (IS 1161 medium class) are all considered.
How does the end condition change the answer?
The effective-length factor k captures how the column ends are restrained: 0.65 for fixed-fixed, 0.80 for fixed-pinned, 1.00 for pinned-pinned, and 2.00 for fixed-free (cantilever). Buckling capacity scales with 1/(kL)², so a fixed-fixed column carries roughly 9.5 times the load of an otherwise-identical fixed-free cantilever of the same length. Modelling the actual end fixity correctly is the most important judgement call in column design.
Why are channels and angles excluded?
Channels (ISMC) and angles (ISA) are common in light truss members and bracing but their cross-sections are highly asymmetric, so a simple Euler / yield iteration is not appropriate — they need an additional torsional-flexural buckling check that this calculator does not implement. ISMB I-beams, SHS, and round pipes have section properties that are well-behaved enough for the simplified iteration to give a useful preliminary size.
What does "slenderness" mean and what is acceptable?
Slenderness λ = kL / r_min is the ratio of effective length to the section's minimum radius of gyration. IS 800 caps λ at 180 for compression members carrying loads other than wind / seismic, and at 250 for members carrying only wind / seismic. Very high slenderness (above 180) means buckling dominates and the column needs to be larger or shorter, even if the Euler check passes numerically.
Why do ISMB sections sometimes look very large for small loads?
ISMB sections have asymmetric I_x and I_y. We use I_x in the Euler check, which is non-conservative for an unbraced column that can buckle about the weak axis. For unbraced columns, prefer the SHS or PIPE family — they are doubly-symmetric so I_x = I_y and the answer is correct without any further analysis. ISMB makes sense only when the column is laterally braced about the weak axis (e.g. by adjacent walls or beams).
What does "No standard section satisfies these constraints" mean?
The combination of axial load, height, end condition, and grade is too demanding for any single ISMB / SHS / PIPE in the catalog. Options: pick a heavier hot-rolled section family (heavy ISWB / ISHB), specify a built-up section, reduce the unbraced length by adding mid-height bracing, or stiffen the end conditions (e.g. pin-pin to fixed-pin) by detailing a moment connection. This message is a flag to involve a structural engineer.
Is this a substitute for a structural engineer?
No. It is a preliminary sizing aid for typical residential and small commercial columns under pure axial load. It does not consider combined axial-and-bending interaction, lateral loads (wind, seismic), connection design, fire rating, secondary moments from imperfections, or composite action. For any habitable structure the final column size must be set by a licensed structural engineer.