## What is a compression member?

Compression members are structural elements that carry compressive axial force. They are the vertical members of a building that support beams and their design, which is governed by buckling and strength. Columns are known as struct or compression members, which are subjected to compressive forces. These members provide stiffness to the building and avoid any imperfection regarding the transfer of axial load. For instance, webs in a truss, braces in a framed structure, tiers, and so on.

## Buckling of the column

### Column buckling

It is the bending of a long slender column subjected to axial compressive load. The load (P_{cr}) at which column start to buckle or bend is known as the critical buckling load. The column becomes unserviceable if the axial compressive load exceeds the critical buckling load.

The critical axial load of buckling is given by the Euler equation, which is expressed as,

${P}_{cr}=\frac{{\mathrm{\pi}}^{2}{\mathrm{EI}}_{Min}}{{L}_{e}^{2}}$

Where the effective length ${L}_{e}$ can be expressed as ${L}_{e}=\frac{L}{H}$

Here, $E$ = Modulus of rigidity of the column

${I}_{Min}$ = Moment of inertia of the cross-section of the column. ${I}_{Min}=Min\left[{I}_{XX}or{I}_{yy}\right]$

${L}_{e}andL$= Effective length and total length of the column respectively.

### Different end conditions

Column with effective length l and length L when subjected to different end conditions such as both the ends fixed, one end fixed and the other free, both the ends are pin jointed and one end pinned jointed and the other free, undergoes different nature of buckling. Depending upon the nature of the column, the value of the end effective length must be chosen.

For each condition, the value of critical axial load given by the Euler formula changes, and it defines the strength of the column. The strength of the column depends upon the slenderness ratio and the cross-sectional area of the column. It is often defined as the safe load-carrying capacity.

In tension members, when an axial load is applied, the member tends to lengthen and not buckle due to tension members because the tensile axial load is responsible for the straightness of a member. However, in the compression members, a change in material properties is done by applying load that tends to magnify the bending.

### Local buckling

It occurs when the compression member does not hold enough strength to maintain the width and thickness ratio. It also depends on the yield stress. This occurs before any kind of buckling.

### Torsional buckling

The twisting of the entire cross-section of the compression member with its shear center is known as torsional buckling. It occurs in a rolled wide-flange section. This buckling occurs when torque increases the limited value of a torsion.

## Compression member failures

### Pure compression failures

Columns are the compression members that carry an axial load and transfer them to foundations. If the axial stress in the column is greater than the load-bearing capacity of a column then the column can fail and this type of failure is known as the pure compression failure. Reinforcement of the column is done to avoid sudden failures.

### Bending and stress failure

This is a combined failure that occurs in a column. In this failure, an eccentric moment is developed in the column causing bend moments, and if the axial stress is increased then the compression failure can occur too. Eccentricity plays an important role in this failure.

### Shear failure

Shear stress in a building is carried out by shear walls and columns. However, if shear walls are not present then the shear load is aced by the column. Shear loads are the lateral loads acting on a column due to wind, earthquake, and others. To avoid the shear failure, links are provided by the structural designer. It can also be avoided by increasing the cross-sectional area of the axial compression member.

## Member subjected to bending

Those members in which load is applied perpendicularly on their longitudinal axis is known as bending member. For instance, beam, purlin, and so on.

Beams are the horizontal structural element of the building resting on columns. Beams tend to transfer their loads to the column after receiving them from the slabs. When a load is applied to the beam, it experiences a bending moment, which tends to develop internal stresses in the beam. This action results in the deformation of the beam by bending laterally and forming a curve, in which the inside of the curve faces an axial compression and the outwards portion faces the tension. The beam is an elastic material and tensile with compressive strains, which result in compressive and tensile stress due to the stress-strain curve (Hook’s law). By increasing load, stress also increases, and this increased load is then calculated.

Bending stress in a member is calculated by,

${\sigma}_{b}=\frac{My}{{I}_{NA}}$

Where ${\sigma}_{b}$ = Bending stress in the member

$M$ = Bending moment associated with the member

$y$ = Distance of fiber from the neutral axis

${I}_{NA}$ = Moment of inertia about the neutral axis

## Failure in the members subjected to bending

Failure in beams is referred to as deflection. It is of two types:

- Flexural failure
- Shear failure

### Flexural failure

Flexural or bending failure occurs when the applied load exceeds the load-bearing or flexural capacity of the beam. It is calculated by the maximum yield stress encountered by the material of the beam when a load is applied. It is termed as the flexural failure or modulus of rupture and also the strength of the beam. Its unit is MPa.

This failure is further classified as a brittle and ductile failure. In brittle failure, no warning is given and the beam ruptures without showing any sign of deflection, whereas in ductile failure, failure depends on the elasticity of the member. This failure results in the maximum deflection of the beam.

### Shear failure

This failure occurs when the maximum permissible shear stress of a member gets extended after applying shear stress and the strength corresponding to this stress, which is known as shear strength. Failure cracks appear at the end of the beam where it is connected to the other member at 45 degrees. A diagonal crack is formed at the cross-section of the beam. Shear failure is checked by the maximum deflection in the beam and stirrups are provided to avoid shear failures.

## Context and Application

Members subjected to axial compression such as columns are widely used and are failed by buckling but beams fail by flexural or bending. Material properties are also the cause of failure in beams and columns.

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## Practice Problems

1. Which of the following is a compression member?

- Slab
- Strut
- Beam
- Ties

Correct option- b

Explanation: The strut is a compression member.

2. What is the SI unit of bending stress?

- Kg
- KN
- MPa
- N

Correct option- c

Explanation: The SI unit of bending stress is MPa.

3. How flange of a compression steel member is attached to another member?

- Stirrups
- Stiffeners
- Gusset plate
- Ties

Correct option- c

Explanation: Gusset plate is used to attach one steel member to another or flange with other flanges of the steel member.

4. What is the effective length of the column of one side hinge and the other side fixed?

- 0.5
- 0.2
- 1
- 0.9

Correct option- c

Explanation: Effective length of a column, hinge at one end, and fixed at another is 1.

5. What deformation takes place when the compression member is axially loaded?

- Collapse
- Breaking into two parts
- Buckling
- Crushed

Correct option- c

Explanation: When a compression member is axially loaded it causes the member to buckle.

## Related Concepts

- Column
- Beam
- Strut
- Buckling

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