What Is Column End Conditions | What Are Effective Lengths of Columns | Equivalent Lengths of Columns for Various End Conditions.

What Is Column?

A compression member, i.e., column, is an important element of every reinforced concrete structure. These are used to transfer a load of superstructure to the foundation safely. Mainly columns, struts, and pedestals are used as compression members in buildings, bridges, supporting systems of tanks, factories, and many more such structures.

A column is defined as a vertical compression member who is mainly subjected to the effective length and axial loads of which exceeds three times its least lateral dimension. The compression member whose effective length is less than three times its least lateral dimension is called Pedestal

The compression member who is inclined or horizontal and is subjected to axial loads is called Strut. Struts are used in trusses. The function of columns is to transfer the load of the structure vertically downwards to transfer it to a foundation. Apart from the wall performs the following functions also:

(a) It encloses building areas into different compartments and provides privacy.

(b) It provides safety from burglary and insects.

(c) It keeps the building warm in cools in summer and winter.

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What Is Column End Conditions?

How much load a column can bear also depends on column end conditions. The column with fixed end conditions at both ends will be stronger, then the second column of the same size, length, and material but having both ends free.

The ability to carry a load will be different for both columns. The effective length of a column is calculated after knowing the column end conditions. Effective length changes with the change in column end conditions. The following are the column end conditions.

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Type of Column End Conditions

• Both Ends Hinged.
• Both Ends Fixed.
• One End Fixed and Other Hinged.
• One End Fixed and Other Free.

#1. Both Ends Hinged-

The effective length of other end conditions can be found with reference to this condition. This is the standard column end condition. Effective length in this condition is equal to the length of the column.

In this condition, both ends of the column are either pinned, pivoted, or rounded. As shown in the figure below.

l_e  =  L

Where,

l_e  =  Equivalent  length

L = Actual Length

 

Both Ends Hinged

#2. Both Ends Fixed-

Column load-bearing capacity increases with the decrease in column equivalent length. This is the strongest column end condition. Both ends fixed column carries the maximum load, and effective length for this condition is considered as half of the total column length. As shown in the figure below.

l_e =  L/2

Where,

l_e =  Equivalent  length

L = Actual Length

Both Ends Fixed

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#3. One End Fixed and Other Hinged-

In this condition, one end of a column is stronger, while the other end is very weak. The equivalent length for this end is as follows.

l_e = L/√2

Where,

l_e =  Equivalent  length

L = Actual Length

#4. One End Fixed and Other Free-

This end condition makes columns to bear the smallest load than all other end conditions. The column in such a condition is very weak. Equivalent length for one end fixed and other free is as follows.

l_e= 2L

Where,

l_e =  Equivalent  length

L = Actual Length

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What Are Effective Lengths of Columns?

The equivalent or effective length is defined as the distance between two adjacent points of contra flexure on the column. The point of contra flexure is defined as the point on the column where there is a change in the direction of the axis of the column.

The critical loads for columns with various support conditions can be related to the critical load of a pained-end column through the concept of an effective length. To demonstrate this idea, consider the deflected shape of a column fixed at the base and free at the top as below fig.

 

This column buckles in a curve that is one-quarter of a complete sine wave. If we extend the deflection curve as below figure, It becomes one-half of a complete sine wave, which is the deflection curve for the pinned-end column.

The effective length L_e for any column is the length of the equipment pinned-end column. That is, it is the length of a pinned-end column having a deflection curve that exactly matches all or part of the deflection curve of the original column.

Another way of expressing this idea is to say that the effective length of a column in the distance between points of inflection (that is, points of zero moments) in its deflection curve, assuming that the curve is extended (if necessary) until points of inflection are reached.

Thus, for a fixed-free column, the effective length is L_e = 2L.

Because the effective length is the length of an equivalent pinned-end column, we can write a general formula for critical loads as follows:

P_cr = π²EI  / L_e²

If we know the effective length of a column (no matter how complex the end conditions may be), we can substitute into the preceding equation and determine the critical load.

For instance, in the case of a fixed-free column, we can substitute L_e = 2L and obtain.

The effective length is often expressed in terms of an effective-length factor K: L_e = KL

Where L is the actual length of the column. Thus, the critical load is

P_cr = π²EI  / KL²

The factor K equals 2 for a column fixed at the base and free at the top and equals 1 for a pinned-end column.

The effective- length factor is often included in design formulas for columns.

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Various k Factors and Column Effective Length

Sr.No.	Shape of Column	Column Postion	Effective Length Factor	Effective Length
1.		Both End Fixed.	k = 0.5	Le = 0.5 l a
2.		One End Pinned Joint and One End Fixed Joint.	k = 0.7	Le = 0.7 l a
3.		Both End Pinned Joint.	k = 1.0	Le = 1.0 l a
4.		One end Fixed Joint and One End Free.	k = 2.0	Le = 2.0 l a

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Equivalent Lengths of Columns for Various End Conditions.

Sr.No.	Shape of Column	Detail of Column	Recommended design valuek	Theoretical k Value
1.		Effectively held in position and restrained in direction at one end but not held in position or restrained in direction at the other end.	k = 2.00L	k = 2.00L
2.		Effectively held in position and restrained in direction at one end and at the other end partially restrained in direction but not held in position.	k = 2.10L	k = 2.00L
3.		Effectively held in position and restrained in direction at one end and at the other end effectively restrained in direction but not held in position	k = 1.00L	k = 1.00L
4.		Effectively held in position at both ends but not restrained in direction	k = 1.20L	k = 1.00L
5.		Effectively held in position at both ends and restrained in direction at one end.	k = 0.80L	k = 0.70L
6.		Effectively held in position and restrained in direction at both ends.	k = 0.65L	k = 0.50L

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