# COMBINED AXIAL AND BENDING LOADS CLASS NOTES

**COMBINED AXIAL AND**

** BENDING LOADS CLASS NOTES**

## It is applicable for a beam column.

## A beam carries transverse loads

## (bending loads) and a column

## carries an axial compressive load.

## Examples of such beams are

## chimneys, dams, retaining wall,

## trees, poles and building

## structures. Axial compressive

## load is due to the self weight

## and the bending is due to the

## wind affect. There are two combinations.

## (i) Axial tensile load with bending

## (ii) Axial compressive load with bending

## The second gives second order effects.

## The bending transverse load causes

## deflection in the member. Adding

## axial compressive force to the

## deflected member creates additional

## bending moment. This in turn creates

## more moment, which creates more

## deflection. This continues till member

## becomes unstable.

**Fig. A beam under combined Axial and bending loading**

**STRESSES IN A BEAM COLUMN**

#### (i) Axial stresses are compressive stresses of CONSTANT value, σ_{A} =W/A

#### (ii) Bending stresses are both simultaneously tensile and compressive stresses and are of VARYING values

#### σ_{b} = (M/I) y

#### (iii) Maximum compressive stress σ_{max} = σ_{A} + σ_{b}

#### (iv)Maximum tensile stress σ_{max} = σ_{b} – σ_{A} i.e. tensile stress is there only if σ_{b} > σ_{A}.

**There are three possible cases**

**Fig. Three possible Cases of Axial & bending Combined**

### Case 1 Bending stress is greater the axial stress

### σ_{b} > σ_{A}

#### First σ_{max} = σ_{A} + σ_{b Compressive}

#### Second σ_{max} = σ_{b} – σ_{A Tensile}

**Neutral axis will not coincide with the centroid axis. Neutral axis is towards compressive fibers.**

**Case 2 Bending stress is equal to the axial stress**

** σ**_{b} = σ_{A}

_{b}= σ

_{A}

#### First σ_{max} = σ_{A} + σ_{b Compressive}

#### Second σ_{max} = σ_{b} – σ_{A = 0 }

_{Neutral axis will coincide with the centroid axis. }

**Case 3 Bending stress is lesser than the axial stress**

**σ**_{b} < σ_{A}

_{b}< σ

_{A}

#### First σ_{max} = σ_{A} + σ_{b Compressive}

#### Second σ_{max} = σ_{b} – σ_{A Compressive}

**Neutral axis will not coincide with the centroid axis. Neutral axis will be towards tensile fibers.**

#### In each case, for safe design

#### First Maximum compressive stress ≤ Allowable compressive stress

#### Second Maximum tensile stress ≤ Allowable tensile stress

# Eccentric Loading

**Fig. Eccentric loading equals combined axial & bending loadings**

`It is applicable for cases where self weight is not negligible as compared to the external load. The example of such cases is a beam column. A beam carries transverse loads (bending loads) and a column carries an axial compressive load. Examples of beam column are chimneys, dams, retaining wall, trees, poles, buildings and structures. Axial compressive load is due to the self weight and the bending is due to the wind effect or water pressure.`

Eccentric loading=Axil load +Moment = Axial and bending combined

https://www.mesubjects.net/wp-admin/post.php?post=3454&action=edit Bending stresses