The length of a column (L) is the distance between two points where a column obtains its fixity of support. The height between the buckled column’s points of contraflexure is defined as the Â effective length (Lc) of the column. Effective length of steel column is expressed as K times the length (L) of column. K is called as effective length factor.

Lc = K x L

## What factors affect the effecting length?

Primarily two factors affect the selection of the effective length of the column.

- Whether the frame is sway or no-sway,
- bending stiffnesses of the beams that meet at the column. If the beam is particularly stiff, it will not bend much under load and will offer column fixity, however if the beam is flexible, it will bend readily and will not provide lateral constraints.

## How to chose the effective length of steel column?

There are two main approaches available in **American national standardÂ ANSI/AISC 360-16 Specification for Structural Steel Buildings**:

- Table C.A.7.1
- Fig C.A.7.2 Alignment Charts

### Table C.A.7.1 for effective length

This table give the theoretical and design values of K. Theoretical values of K are based on the ideal behavior of column end joints. i.e. A pin is a perfect pin with no rotational stiffness and a fixed support is an ideal fixed support with infinite rotational stiffness. In practical case, this ideal behavior is almost impossible to achieve. Therefore design values K are recommended to be used.

### Fig C.A.7.1 and C.A.7.2 Alignment Charts

The most frequent approach for finding K is to utilize the alignment charts. Alignment charts are shown in Figure C-A-7.1 for frames with inhibited sidesway (Non sway frames) and Figure C-A-7.2 for frames with uninhibited sidesway (Sway frames).

Read more: What is difference between sway and non sway frame?

- The subscripts A and B correspond to the joints at the ends of the column under consideration.
- Ecol is the column’s elastic modulus
- Icol is its moment of inertia
- Lcol is its unsupported length.
- The elastic modulus of the girder is Eg
- The moment of inertia of the girder is Ig
- The unsupported length of the girder or other restraining element is Lg.
- Icol and Lg are measured along axes perpendicular to the plane of buckling under consideration.

It is vital to remember that the alignment charts are based on idealized settings. As a result, modifications are frequently necessary.

#### K value adjustments for girders with different end conditions

Correction factor of K for beam stiffness for the case when beam end conditions are different than those assumed for development of alignment charts.

The original assumptions of alignment charts for end conditions are as follows

- Rotations at opposite ends of the restraining beams are equal in magnitude and opposite in direction for columns in frames with sidesway inhibition, resulting in single curvature bending.
- Rotations at opposite ends of the restraining beams are equivalent in magnitude and direction for columns in frames with unrestricted sidesway, resulting in reverse curvature bending.

#### K values adjustment of inelastic behavior

The original assumptions of alignment charts is also that columns behave in elastic manner. However, to account for the inelastic response of column, effective length factors of steel columns can be modified by factor Â b, which can be calculated using the following formulations given in American national standardÂ ANSI/AISC 360-16 Specification for Structural Steel Buildings:

b can alternatively calculated from Table 4-21 of the

## How to chose the effective length of steel column? Flow Chart

This flow chart guides you to pick the right value of effective length in design. It follows the guidelines of **Â ANSI/AISC 360-16 Specification for Structural Steel Buildings**: