Steel columns & bases

Compression members in steel

Columns in buildings and industrial sheds, struts and top chords of trusses, and bracing members carry axial compression. Unlike tension members, their strength is governed mainly by buckling, so the slenderness and the shape of the section matter as much as the area.

Common sections: rolled I and H sections (ISHB, ISWB), circular and rectangular hollow sections (most efficient), single and double angles (truss members), channels back-to-back, and built-up sections of channels or angles connected by lacing or battens.

Effective length and slenderness

$KL$ = effective length (depends on end restraint); $r$ = radius of gyration about the relevant axis. Buckling happens about the axis with the larger $KL/r$.

Slenderness limit for members carrying dead and imposed compression: 180 (250 for wind/earthquake-only compression). Truss members: effective length of discontinuous angle struts is taken as 0.7–1.0 of the centre-to-centre length depending on end connections (two or more bolts / welded vs single bolt).

Why real columns fall below Euler's load

Euler's elastic critical stress is $f_{cc}=\frac{{\pi }^{2}E}{(KL/r{)}^2}$. Real columns carry less because of initial crookedness, eccentricity of load, residual stresses from rolling and welding, and yielding before elastic buckling for stocky members. IS 800:2007 adopts the Perry–Robertson approach with imperfection factors.

IS 800 design compressive strength

For $\lambda \le 0.2$, buckling does not reduce strength: $f_{cd}=f_y/{\gamma }_{m0}$. IS 800 also tabulates $f_{cd}$ against $KL/r$ for each class, so hand design usually reads values from tables.

Purpose

A steel column carries a large load on a small area; the concrete foundation or pedestal below cannot take such a high stress. The column base spreads the load over enough concrete area so the bearing stress stays within the permissible value, and anchors the column against uplift, shear and moment.

Bearing strength of concrete

Required base plate area: $A=\frac{P_u}{0.6f_{ck}}$.

Slab base

The base plate projects beyond the column; each projection bends as a cantilever under the uniform upward bearing pressure $w$.

Details:

• Column end machined (milled) for full bearing on the base plate, with welds or cleats sized for erection and for the load not transmitted by bearing; otherwise welds must carry the full load.
• Base plate levelled on grout (non-shrink cement grout, about 25–50 mm).
• Anchor bolts (holding-down bolts) — at least 2 (usually 4) — hold the column in position during erection and resist uplift and shear.

Gusseted base

For heavy columns, a thick slab base becomes uneconomical. Gusset plates on the flanges and cleat angles transfer part of the load from the column to the base plate over a larger area, reducing the cantilever projection and the plate thickness. The base plate is designed for bending between gussets; gussets and connecting welds/bolts are designed for the portion of the load they carry. In gusseted bases the column end, gussets and angles are usually machined so that load is shared by bearing and fasteners.

Bases with moment

With axial load $P$ and moment $M$, the eccentricity $e=M/P$:

• If $e\le L/6$ ($L$ = plate length), the whole plate is in compression: $\sigma =\frac{P}{BL}\left(1\pm \frac{6e}{L}\right)$.
• If $e>L/6$, part of the plate lifts; anchor bolts on the tension side resist uplift. Equilibrium of the bolt tension and the triangular (or rectangular block) concrete pressure gives the bolt force and the bearing length.