Table of Contents

## Column

Column is the vertical structural member which is subjected to compressive forces with or without bending moment. The inclined compression member is called strut. The vertical compressive member whose effective length is not more than three times their lateral dimension are called pedestals.

## Types of columns:

**On the basis of slenderness ratio:**

They are of two types on the basis of slenderness ratio. Slenderness ratio is defined as the ratio of effective length (l_{e}) to the least dimension (b or D).

**Short column:**

When the column with slenderness ratio l_{ex}/d and l_{ey}/b both is less than 12 then that is known as short column.

**Long column:**

When the column with slenderness ratio l_{ex}/d and l_{ey}/b either one or both is more than 12 then that is known as long or slender column.

2. **On the basis of resistance to lateral loads:**

**Braced columns:**

Braced columns are that types of column which do not have to resist any lateral loads like wind or earthquake loads. The shear wall are provided to resist the lateral load in tall buildings.

**Unbraced Columns:**

Unbraced columns are that types of column which have to resist lateral load in addition to vertical loads. Bracing can be done in one or more directions, depending upon the likely hood of the occurrence of the horizontal loads.

3. **On the basis of loading:**

**Axially loaded:**

The columns which are carrying purely axial loads are called axially loaded column. Practically, this types of columns hardly exist.

**Uni-axially loaded:**

The columns which are subjected to moment in only one direction either about x-axis or y-axis are known as uni-axially loaded.

**Bi-axially loaded:**

The columns which are subjected to moment in both direction are known as bi-axially loaded.

*Normally the column presence in the corner of building are bi-axial whereas the column of other edges are uniaxial. All columns shall be designed for minimum eccentricity, equal to unsupported length / 500 plus lateral dimension / 30, subject to a minimum of 20mm. Where bi-axially bending is considered, it is sufficient to ensure the eccentricity exceeds the minimum about one axis at a time.*

**Calculation of effective length of column:**

The clear height of column is generally taken as the unsupported length or height. The effective length is defined as the length between the points of contra flexure of a buckled column. In simple words, it is the length which corresponding to the length of pin-joined column that carries the same axial load as the given column. The effective length of columns depend on the end conditions.

The effective column height is less than the clear height in case of braced columns whereas equal or more that clear height in case of unbraced or partially braced columns.

From the table 28 of IS 456:2000, the effective length of column for different end conditions can be calculated.

End Condition | Theoretical value | Recommended value |

Both end fixed | 0.5 l | 0.65 l |

One fixed one hinged | 0.7 l | 0.80 l |

Both hinged | 1.0 l | 1.00 l |

One free one fixed | 2.0 l | 2.00 l |

Where, l is unsupported length of compression member

**Modes of failure:**

**Pure compression failure**

Steel and concrete reach the yield stress value at failure and column fails under axial load without undergoing any lateral deformation. It occurs for short column having slenderness ratio less than 12.

2. **Combined compression and bending failure**

When slender columns are even loaded axially undergo deflection along their length and the deflection produces the additional moment. And the failure occurs due to combined action of these direct loads and bending moment. It occurs for slender column having slenderness ratio between 12 and 30.

3. **Elastic instability failure**

The very slender columns become unstable under small loads even before the material reaches yield stresses due to occurrence of elastic buckling. It is highly recommended to avoid the use of column having slenderness ratio more than 30 in which this unacceptable failure occurs.

**Methods of design of compression member:**

**Use****of Equilibrium Equations:**

The three equation of equilibrium are used in this methods. These equation are i. sum of horizontal forces, ii. Sum of vertical forces, and iii. Sum of moment equal to zero. The use of equilibrium equation is complex and tedious due to the need of many trials to solve the equilibrium equations.

2. **Use of Interaction diagram:**

Infinite safe combination of axial load and bending can act safely on the column for every axial load. And these combination can be found easily by using interaction diagram. It is very simple and are preferred in the analysis and design of column subjected to compressive force and bending moment.

Interaction diagrams are those which gives the safe combination of axial load and bending moment for the particular value of p/f_{ck} in the design of column. These diagram are drawn in terms of P_{u}/ f_{ck}bD and M_{u}/ f_{ck}bD^{2}.

Where,

P_{u }and M_{u }= design actual compressive force and bending moment

b, D = smaller and larger lateral dimension

p = percentage of longitudinal reinforcement

**Basic assumption in design of compression member:**

- Maximum compression strain in concrete is subjected to axial compressive forces is taken equal to 0.002
- Maximum compression strain in concrete is subjected to axial compressive force and bending moment is taken equal to 0.0035.
- The plane section normal to the axis remain plane after bending.
- The tensile strength of the concrete is ignored.

**Point to be known before column design:**

- The minimum dimension shall not be less than 300 mm or 20d where d is diameter of largest reinforcement bar.
- The cross-sectional aspect ratio (smaller to larger dimension) shall not be less than 0.45
- The lapping shall be provided at central half of the clear span length and not more than 50% shall be lapped.
- The percentage of steel reinforcement should not be greater than 6% in lapping zone and 4% in normal.
- The minimum steel reinforcement should be provided is 0.8%.

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