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

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

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

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