Columns, Slenderness And Buckling

A short, stocky column fails by crushing. A long, slim one fails by bending sideways while the material is nowhere near its limit.

That second mode is buckling, and it decides the size of most columns in a real building. Which means a column cannot be designed on strength alone.

What slenderness actually measures

The ratio of the column's effective length to the dimension of its cross section, expressed through the radius of gyration.

Two columns of the same material and the same area can behave completely differently depending on how that area is distributed. A hollow section with the material pushed out to the perimeter is far stiffer against buckling than a solid bar of the same area, which is why structural steel columns are hollow sections or I-sections rather than solid.

Which gives the first design lever: move the material away from the centre.

Effective length, which is the part people get wrong

Buckling capacity depends on the effective length, not the physical length.

The effective length is the physical length multiplied by a factor that depends on how the ends are restrained. A column pinned at both ends buckles over its full length. A column fixed at both ends buckles over about half of it, which roughly quadruples its capacity, because capacity varies with the square of the effective length.

That quadrupling is why end restraint is worth more than material.

The common errors sit here.

Assuming fixity that does not exist. A base plate bolted to a footing is often assumed fixed and behaves closer to pinned, because the bolts and the grout allow rotation. A small rotation at the base is a large change in effective length.

Ignoring a sway condition. A frame free to move sideways has a much longer effective length than the same frame braced against sway, and the difference is not small. This is where [shear walls and lateral stability](/blog/shear-walls-and-lateral-stability-in-apartments) feeds straight into column design.

Forgetting the weak axis. A column restrained about one axis and not the other buckles about the unrestrained one. An I-section braced in the plane of the frame and unbraced perpendicular to it will fail the direction nobody checked.

Restraint is cheap and it has to be real

A single brace at mid-height halves the effective length and quadruples the capacity. Nothing else in column design offers that return.

Which makes the restraint a structural element in its own right. A brace has to carry a force, be connected to carry it, and connect to something that can take it. A member that touches the column and goes nowhere restrains nothing.

In practice the restraint comes from the floors, which is why a column's design depends on the floors actually acting as a diaphragm, covered in [diaphragm action and how floors brace a building](/blog/diaphragm-action-and-how-floors-brace-a-building).

Load applied off centre

A column loaded precisely down its axis is a theoretical object. Real columns carry load with some eccentricity, from a beam connecting to one side, from a construction tolerance, or from the column not being perfectly straight.

Eccentric load produces a moment, the moment produces deflection, the deflection increases the eccentricity, and the moment grows. That amplification is a second-order effect, and on a slender column it is the governing condition rather than a correction.

Which means out-of-straightness and out-of-plumb are design inputs, not just quality items, and the tolerances in [tolerances in concrete construction](/blog/tolerances-in-concrete-construction) and [steel fabrication tolerances](/blog/steel-fabrication-tolerances-and-site-fit) have a direct capacity consequence.

Concrete columns behave differently

Three differences that matter.

Creep reduces stiffness over time, so a concrete column under sustained load is more slender in effect than it was on day one. The mechanism is in [shrinkage and creep](/blog/shrinkage-and-creep-in-concrete-structures).

Confinement adds capacity. Closely spaced ligatures restrain the concrete laterally and raise both its strength and its ductility. Which is why ligature spacing in a column is a capacity item and not a detailing convenience, and why it ends up in the congestion discussed in [reinforcement detailing](/blog/reinforcement-detailing-and-congestion).

Cracking reduces the effective section, so the stiffness used in the buckling check is lower than the uncracked value.

Where it bites in an existing building

A column that was adequate becomes inadequate when its restraint is removed.

Which happens more often than people expect: a floor removed to create a void, a wall taken out that was bracing a column, a mezzanine added that changes where the restraint sits, or a slab penetration that interrupts the diaphragm. Each of those lengthens an effective length somewhere.

That is why removing a wall or opening a floor is a whole-building question rather than a local one, and it is the same assessment as [removing a load bearing wall](/blog/removing-a-load-bearing-wall-what-it-takes) and [mezzanine floors in existing warehouses](/blog/mezzanine-floors-in-existing-warehouses).

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