Civil's Guide

Column Design

Column Design

Columns that are subjected to axial loads are only considered columns if \(h\leq4b\), otherwise, they are considered as walls. During the design process, it is important to identify whether the columns structure is a braced frame (shear walls and cores) or unbraced, as these are factors when calculating the effective length of columns. In a braced frame, lateral loads are not resisted by the columns and in unbraced frames, they are resisted by columns. Also, columns can be identified as either slender or stocky columns.

Types of RC columns

  • Rectangular
  • Cicular
  • Encased Steel section
  • Concrete filled steel tube

Columns mainly act in compression, but bending moments always exist (construction tolerance, imperfections…)

Short columns – concrete crushes in compression

Slender columns – buckling may happen

The effective length of a column is determined by the following: 

\(\lambda=\frac{l_0}{i}=\frac{l_0}{\sqrt(I/A)}\)

L depends on the end condition of the column (i.e, is the column fixed at the bottom and top or pinned?) The table below shows the effective length factors for arious conditions.

Slenderness Ratio

The slenderness ratio is a non-dimensional value that can be calculated below:

\(\lambda=\frac{l_0}{i}=\frac{l_0}{\sqrt(I/A)}\)

  • Where
  • \(l_0\) = effective height
  • i = radius of gyration
  • I = second moment of area
  • A = cross-sectional area

Limiting slenderness ratio – short or slender?

When \(\lambda\leq\lambda_{lim}\) The column is short and \(2^{nd}\) order moments can be ignored.

When \(\lambda\geq\lambda_{lim}\) The column is slender and \(2^{nd}\) must be considered.

  • \(\lambda=20\times A\times B\times C/ \sqrt(n)\) (Eq. 5.13N)
  • A = 0.7
  • B = 1.1
  • C = 1.7 – \(r_m\), where \(r_m = M_{01}/M_{02}\) (moment ratio bewteen the moment at the top and bottom of the column)
  • In the following cases, \(r_m\) should be taken as 1.0 (i.e. C = 0.7)
  • For braced members in which the first order moments arise only from or predominantly due to imperfections or transverse loading
  • For unbraced members in general

Failure modes of columns

The possible failure mechanism are either crushing or buckling

The crushing load is \(N_{ud}=0.567f_{ck}A_c+0.87f_{yk}A_s\)

Critical buckling load of pin-ended column: \(N_{crit}=\frac{\pi^2 EI}{l^2}\)

  • For typical columns:
  • For \(l/i<50\), \(N_{crit}>>N_{ud},\), short column, concrete crushing
  • For \(l/i>110\), \(N_{crit}>>N_{ud},\), slender column, buckling
  • For \(l/i\) between 50 and 110, intermediate column, crushing with possible buckling

Column Design - Reinforcement Detailing

  • At least 4 bars for rectangular section and 6 for circular section. Bar diameter \(\phi \geq 12mm\)
  • Links to form steel cage and confine concrete
  • Minimum size =1/4 x size of compression bar & \(\geq 6mm\)
  • Maximum spacing =min (20x size of the smallest compression bar, the least lateral dimension, 400mm)
  • Every longitudinal bar placed in a corner should be held transver reinforcement
  • No compression bar should be further than 150 mm from a restrained bar.