AHSANULLAH UNIVERSITY OF

SCIENCE AND TECHNOLOGY

Name: Farjana Akter ID:10.01.03.140

Prestressed Concrete Lab

4TH YEAR AND 2ND SEMESTER SECTION C

BENDING MOMENT STRESS (UNIAXIAL & BIAXIAL )

WELCOME TO PRESENTATION ON

Defines bending moment

A bending moment is a measure of the bending effect due to forces acting on a beam, which is applied to an element so that the element bends.

Sign Convention:Positive: if the external load tends to make the beam sagNegative: if the external load tends to make the beam hog (bend upwards)

Stress: is the internal resisting force per unit area. σ =F/A

Bending moment stresses are internal stresses caused by bending moments acting at a given distance from the neutral axis. It is also known as flexural stress.

Defines Bending Moment stress

Their magnitude is given by the formula:Bending Moment stress

Beams are almost always designed on the basis of bending stress. Distribution of Bending stress through a beam is shown in figure:Bending stresses are tensile or compressive stresses in the Beam. A simply-supported beam always has tensile stresses at the bottom of the beam and compressive stresses at the top of the beam.

Depending on the orientation of the beam with respect to the direction of the forces applied

Bending Moment Stress are of two types:

1. Uni-axial Bending Stress 2. Bi-axial Bending Stress

If loads are applied in one direction only which produce stress system is an uni-axial bending stress.

For example: Columns are usually subjected to two bending moments about two perpendicular axes (X and Y) as well as an axial force in the vertical Z direction due to loading.

Uni-axial Bending Stress:

With the shown sign convention, bending about X-axis causes compression in the top part and tension in the bottom region, whereas bending about Y-axis causes compression in the left hand part and tension in the right part. For symmetric sections subjected to uni-axial bending, the neutral axis is parallel to the moment axis.

Uni-axial Bending Stress:

If loads are applied in both x and y-directions, the plate willhave a bi-directional stress distribution. It is also known as unsymmetrical (skew) bending.

Bi-axial Bending Stress: 

In biaxial bending (d), the top-left part is subjected to double compression and the bottom right part is subjected to double tension. The remaining parts are subjected to combined compression and tension. This means that the two moments are not independent but coupled. The resulting neutral axis is inclined with an angle depending on the moment values as well as the section properties.

Bi-axial Bending Stress:

According to biaxial bending stress :

for Beam , σx = -(Mz y/Iz ) +

(Myz/Iy)

1. Load contour method

2. Reciprocal load method

• There are two method in which biaxial bending stress are represented by an equivalent uni-axial bending moment stress:

The analysis of bi-axial bending stress (manual calculation )for column is quite impractical. A number of computer programs for biaxial bending are available in commercially such as PCACOLUMN &HBCOLUMN

Don’t over stress

OR else Failure

THANKS EVERYONE