COMBINED AXIAL AND BENDING

 

 

https://www.mesubjects.net/wp-admin/post.php?post=3503&action=edit              Q. ANs on bending

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

 

COMBINED AXIAL AND

BENDING

It is applicable for 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

and building structures. Axial compressive

load is due to the self weight and the

bending is due to the wind affect.

STRESSES IN A BEAM COLUMN

(i) Axial stresses are compressive stresses of CONSTANT value, σA =W/A

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

σb = (M/I) y

(iii) Maximum compressive stress      σmax =  σA + σb

(iv)Maximum tensile stress σmax =  σb – σA i.e. tensile stress is there only if σb > σA.

There are three possible cases

Case 1   Bending stress is greater the axial stress

σb > σA

First          σmax =  σA + σb  Compressive

Second     σmax =  σb – σA   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

   σb = σA

First        σmax =  σA + σb  Compressive

Second    σmax =  σb – σA = 0 

Neutral axis will coincide with the centroid axis. 

Case 3   Bending stress is lesser than the axial stress

σb < σA

First           σmax =  σA + σb  Compressive

Second       σmax =  σb – σA  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

 

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