Course · lesson 2 of 7

Compression members and columns

Columns and struts are pushed, and pushed members can buckle. This lesson explains why, how effective length and slenderness set the strength, and how to find the compressive resistance C_r to SANS 10162-1, by hand and in the STATIX steel member calculator.

1. Learning outcomes

After this lesson you can:

explain the difference between squashing and buckling, and why real columns fail below the Euler load;
choose the effective length KL for each axis from the end conditions and the bracing;
work out KL/r and the slenderness λ, and check the section class for compression;
find C_r from the SANS 10162-1 column curve about both axes;
check a column in the STATIX steel member calculator.

2. Before you start

Lesson 1 (tension members) and the free STATIX steel member calculator.
Your own copy of SANS 10162-1 is useful; this lesson gives clause numbers only.
A pocket calculator with a power key (x^y) and about 50 minutes.

3. What a strut does

What a strut does. A short, stocky member pushed at its ends fails when the whole section yields. A long, slender one bends sideways and fails at a much lower load. Most real columns sit in between, and the design rule covers the whole range.

Where the load comes from. Each floor beam passes its end reaction to the column; the column adds them up storey by storey, so the lowest storey carries the most. In a braced building, bracing or cores take the sideways loads and the columns are mainly axially loaded.

4. Euler and real columns

Euler's load, π²EI/(KL)², is for a perfectly straight, stress-free strut; it shoots up for short members. Real columns are capped by the squash load and fall below both curves in the middle range, because they are never perfectly straight and carry residual stresses from rolling.

Why real columns fail below Euler. Every member has a small initial bow, so the load acts at a lever arm from the start. And rolled sections cool unevenly, which leaves parts of them already stressed in compression; those parts yield early. The column curve and its n are calibrated on these effects.

5. Effective length

Effective length KL: the length of the buckled shape between its points of no bending. The theory values assume perfect fixity; real “fixed” ends rotate a little, so designers use the larger design values. The STATIX K list offers both (0.65 fixed-fixed, 0.80 fixed-pinned, 1.0, 1.2 sway, 2.1 cantilever).

STATIX takes the effective lengths per axis in this order: typed KL_x and KL_y win; otherwise K_x and K_y times the system length; otherwise the one KL you typed for both axes.

6. Slenderness

Radius of gyration and slenderness. Each axis has its own r. An H-section is much stiffer about its strong axis x than about its weak axis y, so for the same length it buckles about y, with the flanges swinging sideways. λ puts KL/r on a scale that works for any steel grade.

The slenderness limit. SANS 10162-1 limits KL/r of compression members to 200. STATIX shows it as a separate check; the utilisation of the member comes from the resistance C_r.

7. The column curve (SANS 10162-1, 13.3.1)

The SANS 10162-1 column curve (13.3.1): C_r = φ A F_y (1 + λ²ⁿ)^−1/n, φ = 0.9. The exponent n sets the shape: 1.34 for hot-rolled H and I sections and most members; 2.24 for hot-finished or stress-relieved tubes, which have smaller residual stresses. The STATIX steel member calculator uses n = 1.34 for every section, which is on the safe side for hot-finished tubes.

F_e = π² E / (KL/r)² E = 200 000 MPa λ = √(F_y / F_e) C_r = φ A F_y (1 + λ²ⁿ)^−1/n, φ = 0.9 work out C_r about each axis; the smaller governs

For I-sections the code also has a torsional buckling check (13.3.2). For rolled UC and UB columns of normal length it rarely governs, so this lesson leaves it out.

8. Two axes and bracing

Two axes, two lengths. A brace (a side rail, a floor beam, a wall) that stops the column moving sideways about its weak axis halves the weak-axis buckling length. The strong axis is not braced, so its length stays the same. Check both axes: the one with the larger KL/r governs.

9. Local buckling and the class

Local buckling and the section class for compression (SANS 10162-1, clause 11, Table 3). Thin flanges and webs can ripple before the column as a whole buckles. If each plate is stocky enough the full area counts; if not, the section is class 4 and only an effective area works (13.3.3). Most rolled H-sections in S355 pass.

10. In STATIX

The compression route in the STATIX steel member calculator: pick the section and grade, enter N as a positive number, give the effective length (one KL, or K values, or KL_x and KL_y under More inputs, which win), and read C_r and the utilisation.