# COLUMNS & STRUTS

**COLUMNS & STRUTS**

## Column is a vertical member under axial compressive load. Type of column is decided by a slenderness ratio defined later. For various types of columns, value of slenderness ratio differ with different materials of the column.

## For example, Values of slenderness ratio

## Type of column |
## STEEL |
## WOOD |
## RCC |

## Short |
## ≤30 |
## ≤ 10 |
## ≤ 30 |

## Medium |
## ≥ 30 & ≤ 120 |
## ≥ 10 & ≤ 30 |
## ≥ 30 & ≤ 50 |

## Long |
## ≥ 120 |
## ≥ 30 |
## ≥ 50 |

## Firstly short column

## Secondly Medium column

## Thirdly long column

**SHORT COLUMN**

#### Fail by contraction in case of ductile column. These fail by crushing in case of brittle materials.

#### Formula used is P = σ_{yp} A ductile materials

#### P = σ_{ ultimate} A brittle materials

#### Short column have the maximum load carrying capacity.

**LONG COLUMNS**

#### These columns fail by lateral displacement at a much lower stress than the yield stress. This failure due to lateral displacement is called buckling. Buckling is also referred as instability. Long columns have the least load carrying capacity. If possible, long column may be avoided. Euler equation governs long columns.

**EULER’S FORMULA FOR LONG COLUMNS**

#### P_{EULER}=P _{critical}=P _{crippling}=P _{buckling}= π^{2}EA/(L_{e}/k _{min})^{2}

#### P_{EULER}=P _{cr }= P _{crippling}=P _{buckling} , N (NEWTONS)

#### E = Young’s modulus, N/mm^{2}

#### Take E _{steel}= 200 x 1000 N/mm^{2}

#### A Area of cross section in mm^{2}

#### Le is effective length. It is the length in which BOW is completed as shown.