Compression Members
Columns don't crush — they buckle. Slenderness is everything.
A column rarely fails by crushing — it fails by buckling, bowing sideways long before the steel reaches its yield stress. So the whole of compression design turns on one idea: slenderness. Fix the effective length from the end conditions, find the slenderness ratio about the weak axis, read the design stress off a buckling curve, and the capacity follows.
Learning objectives
By the end of this lesson, you will be able to — mapped to the course outcomes for Design of Structures I:
Distinguish short and slender columns and the way each fails.
Find the effective length from the end conditions (K) and the slenderness ratio λ = KL/r about the weak axis.
Compute the design compressive stress fcd from the buckling curve and the capacity Pd = Ae·fcd.
Describe single, laced and battened built-up columns and their slenderness penalties.
Short, slender, and the effective length
Short columns crush; slender ones buckle. The effective length KL = K·L, where K depends on the end restraints (0.65 fixed–fixed to 2.0 for a cantilever), and the slenderness λ = KL/r uses the minimum radius of gyration — buckling picks the weak axis.[1]
The buckling curve and the capacity
The design compressive stress fcd is read from one of four buckling curves (classes a–d), falling steeply as slenderness rises and never exceeding fy/γm0. The capacity is Pd = Ae·fcd.[1]
fcd from the column curve
The design compressive stress fcd is not a single number — it is read from one of four buckling curves (classes a/b/c/d) by the section's shape and axis (Table 10). Class a is the strongest (least imperfection), class d the weakest. fcd ≤ fy/γm0 always.[1]
Column capacity calculator
Enter the area, radius of gyration, length, end condition and buckling class; the tool computes the slenderness, the design stress and the axial capacity, and plots fcd against slenderness. An ISHB 250 over 3.5 m carries about 1114 kN.[1]
Compression member · axial capacity (IS 800 cl. 7)
λ = KL/r; fcd from the buckling curve; Pd = A·fcd. Fe410, E = 200 GPa.
0.0 kN
Axial capacity Pd
0.0
Slenderness λ = KL/r
0.0 MPa
Design stress fcd
fcd falls as slenderness rises — buckling class c.
At a glance
| Aspect | One | The other |
|---|---|---|
| Failure mode | Short column: crushing / yielding (~fy/γm0) | Slender column: buckling (fcd ≪ fy) |
| End conditions | Both fixed: K = 0.65 (shorter KL, stronger) | Cantilever (fixed–free): K = 2.0 (longest, weakest) |
| Which radius | Use r_min (weak axis) | Never r_max — buckling picks the weak axis |
| Single vs built-up | Single rolled: simple, limited r | Built-up laced/battened: larger r, longer reach |
| Lacing vs battens | Lacing: stiffer in shear | Battens: simpler, +10% slenderness penalty |
Key terms
KL/r — the key measure of buckling-proneness; higher means weaker.
√(I/A); design uses r_min, the value about the weak axis.
K·L — equivalent pinned-pinned length; K from end conditions (Table 11).
Table 10 category fixing the column curve and imperfection factor α.
0.21 / 0.34 / 0.49 / 0.76 for classes a/b/c/d — models residual stress and crookedness.
Reduced stress from the buckling curve; fcd ≤ fy/γm0.
π²E/λ² — the elastic critical stress of an ideal slender column.
Short crushes near fy; slender buckles at fcd well below fy.
Worked example
An ISHB 250 column (A = 6971 mm², r = 53.6 mm), pinned–pinned, 3.5 m, Fe410, buckling class c. λ = 3500/53.6 = 65.3; fcc = π²·E/λ² = 462.9 MPa; λ̄ = √(250/462.9) = 0.735; with α = 0.49, φ = 0.901, so fcd = 159.8 MPa and Pd = 6971×159.8 ≈ 1114 kN. Fix the ends (K = 0.65) in the calculator and watch the capacity climb.
Self-assessment
1. The imperfection factor α for buckling class c is —
2. For a column fixed at one end and free at the other (a cantilever/flagpole), the effective length factor K is —
3. In computing slenderness, the radius of gyration to use is —
Recap
References & further reading
- [1]IS 800:2007 — General Construction in Steel, Code of Practice (Section 7: compression members; cl. 7.1; Tables 3, 7, 9, 10, 11). Bureau of Indian Standards.
- [2]SP 6 (Part 1) — ISI Handbook for Structural Engineers: Structural Steel Sections. Bureau of Indian Standards.
- [3]N. Subramanian, Design of Steel Structures (2nd ed.). Oxford University Press, 2016.
- [4]S.K. Duggal, Limit State Design of Steel Structures (2nd ed.). McGraw-Hill Education, 2014.
Further reading
- N. Subramanian, Design of Steel Structures — compression-member chapters.
- S.K. Duggal, Limit State Design of Steel Structures.
- S.S. Bhavikatti, Design of Steel Structures by Limit State Method as per IS 800-2007.
Sources gathered and fact-checked June 2026. Published values vary by source, sample and method — treat as indicative and confirm against the cited standard before structural use.