Contents

- What is Effective length of column?
- Effective length of column definition
- Effective length of column formula
- Effective length of column for different end conditions
- How to find effective length of column
- What are the equivalent and effective length of columns?
- Difference between unsupported length and effective length of column.
- Frequently Asked Questions

**What is Effective length of column?**

The column is the vertical compression member of the structure. The column is used to transfer the load of the superstructure to the substructure or foundation safely.

The column is mainly subjected to the axial load which exceeds 3 times its lateral dimensions. The length of the column is 3 times more than the lateral dimensions.

The longitudinal distance between two stories or tie levels can be characterized as the length of a column section. The length of a column, from a structural standpoint, is the distance between two places where a column receives its fixidity of support, limiting its movement in all directions.

The height between the buckling column’s points of contra-flexure, i.e. between two floors, is the structurally effective length of the column.

The bending stiffness that the beam carries meets the column, including the sway or non-sway properties of the frames, determines the effective length of the column. If the beam is stiff, it will not bend considerably under load and will offer column fixity; if the beam is flexible, it will bend readily and will not provide lateral constraints.

The greater the load-bearing capacity and the lower the risk of lateral buckling, the shorter the effective length of a column. It is necessary to keep in mind that column ends are not entirely fixed and not perfectly hinged in practice.

The short column is defined as the ratio of effective length to least lateral dimension (slenderness ratio) is less than 12 and the short column is generally failed by the compressive strength or crushing due to its short length.

Short columns have a ratio of effective length to the least lateral dimension of less than 12, and thus are more likely to break due to compressive stress or crushing. Because their height is lower, their weight-bearing ability is higher.

A long column is defined as a long column with a ratio of effective length to a least lateral dimension greater than 12. Long columns are prone to beam buckling owing to compressive load. And their load-carrying capacity in a short column is more important than their height.

OR

The column whose slenderness ratio is more than 12 is known as the long column. The long column is subjected to buckling due to its length.

**Effective length of column definition**

The length of an appropriate pin-ended column with about the same load-carrying capability as the component under study is the effective column length. The higher the load-bearing capacity and that the lower the risk of lateral buckling, the shorter the effective length of a column.

It is important to note that in actuality, column ends are neither fully fixed nor perfectly hinged. To get a reasonable approximation to actual constraint circumstances, the designer may have to interpolate between the theoretical values provided.

In other words, According to the structure point of view, the effective length of column is defined as the vertical distance between the two points of contra flexure of the buckled column that is between two floors.

Also Read: A Complete Guide on Stub Column

**Effective length of column formula**

The Effective length of column (Le) = K x L

Whereas

K is the effective length factor that depends on the degree of fixity at the ends of the column

L is the unsupported length of the column.

**Effective length of column for different end conditions**

The column end conditions significantly influence the amount of load that a column can sustain. Any column having fixed end conditions on either endpoint is better than the column of the identical size, length, as well as composition except with loose ends. Both columns’ load-carrying capacity will be different.

After understanding the column end criteria, the effective length of a column is determined. The effective length changes as the column end conditions differ. The column end criteria are shown below.

- Both Ends Hinged
- Both Ends Fixed
- One End Fixed and Other Hinged
- One End Fixed and Other Free

**Effective length of column fixed at both ends**

This is one of the utmost column end condition. The maximum load is carried by both ends of a fixed column, and the effective length under this situation is half of the entire column length. As the column equivalent length reduces, so does its load bearing capability increases.

The two fixed ends of this design of column are securely attached to the beam construction and do not rotate. Whenever an axial force is added to a laterally fixed point on a long column, compressive stress is created, and the column buckles in the middle of its short length.

The effective length will be 50% of the column length since the effective length factor is 0.5.

**Effective length of column hinged at both ends**

The column hinged at both ends is one of the column end conditions. Throughout this case, the effective length is equivalent to the column length. This criterion can be used to determine the effective duration of other end conditions. Either end of the column would be pinned, rounded, and pivoted in this case of the column.

The long column is fixed at both ends and is allowed to move as well as rotate from around hinged support, however, all transitional movement is restricted. Whenever an axial force is applied at the vertical hinge point of a long column, compressive tension is created, and the column buckles along its whole length.

In this situation, the amount of the effective length factor K is 1.

therefore, the effective length equals the length of the column.

**Effective length of cantilever column**

This end condition causes the column to bear the least load of any of the others. In such a state, the column is extremely weak.

In this sort of column, one end is fixed and technically attached to the support, while the other end is free and subject to rotation, resulting in a significant moment.

When an axial force is applied to a vertically fixed point on a long column, compressive stress is created, and the column buckles in half its length. Since the effective length factor is 2, the effective length is two times the column’s length.

**How to find effective length of column**

The effective length of the column may be calculated using the formula K x L, which involves multiplying the effective length factor by the column length.

The column end criteria are as follows:

Use effective length factor K of 1 for both ends hinged, i.e. effective length = L.

Use K as 0.5 for Both Ends Fixed, which equals effective length = 0.5L.

Use K as 0.7, one end fixed and the other end hinged that equals effective length = 0.7L,

Use K as 2, which equals effective length = 2L, with one end fixed and the other free.

## What are the equivalent and effective length of columns?

The equivalent length of a column is given in terms of the actual length and depends upon the end conditions of the column.

S.no |
End Condition |
Relationship between the equivalent length and the actual length |

1 | Both Ends Hinged | Le=L |

2 | One end fixed, other free | Le=2L |

3 | Both Ends Fixed | Le=l/2 |

4 | One End fixed, other hinged | Le = L/√2 |

**Difference between unsupported length and effective length of column.**

**Unsupported length **

The undisturbed space between the floor as well as the lower beam is the unsupported length of a column. Calculate the effective length factor and multiply it by the unsupported length of the column to have the effective length of the column.

The clear space between the bottom of the beam, slab, or column capital above and the top of the beam or slab below is the unsupported length of a column.

A column’s unsupported length can vary in two orthogonal directions, depending on the supporting components in those directions.

**Effective length of column**

The distance between the hinges’ axes is the effective length of a part hinged at both ends. The effective length of a general end restraint is the length of an end-hinged member with the same load-bearing resistance as the member in consideration.

Also Read: Plinth Beam: Its Purpose, Importance & Protection in Building

## Frequently Asked Questions

### Types of Column End Conditions

• Both Ends Hinged

• Both Ends Fixed

• One End Fixed and Other Hinged

• One End Fixed and Other Free

### What is column End Condition?

The compressive strength of the column depends on the column end Condition. The column whose both ends are fixed is strong enough to bear the load of the superstructure and it will be stronger than the same column the ends are free. And the ability to carry the load will be different for columns with their different end condition. The effective length of the column depends on the end condition of the column.

### The effective length of the column depends on its support reaction or end restrained

1. If the end of the column is effectively held in a position restrained against rotation at both ends = 0.5 L.

2. If the end of the column is effectively held in position at both ends and restrained against rotation at one end =0.7 L.

3. If the end of the column is effectively held in position at both ends but not restrained against rotation= 1.0L

4. Effectively held in position and restrained against rotation at one end, and at other end restrained against rotation but not held in position=2.0L

### What is the Both end Hinged Column?

The column whose both ends are hinged or pinned and in this type of end condition the effective length of the column is equal to the actual length of the column.

This is the standard end condition l_{e} = L

Where:

le = Equivalent length

L = Actual Length

### When both end of column are fixed?

The column whose both ends are fixed. This is the strongest end condition because both the ends are fixed which does rotate around the end and the effective length of the column is half of the actual length of the column.

le = L/2

### One end fixed and the other hinged column?

The column whose one end is fixed and other hinged and in this condition the one end is strong which is fixed and other is fixed because of the hinged end.

The effective length of the column = le = L/√2

### One End fixed and other free column means?

The column whose one end is fixed and other end is free and this end conditioned column is very weak.

The effective length of column = le= 2L.

Also Read : A Complete Guide on Different Types of Beam and its Classification

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