# 3 Bending Stress Examples: Detailed Facts

This article discusses about bending stress example. When an object curves as a result of stress applied on it, then the corresponding stress is called as bending stress.

The radius of curvature is visual proof that the object is under the state of bending. Bending can lead to mechanical failure for mechanical tools. The tools may break due to excessive bending and hence it is very important to know the amount of bending stress being applied.

## What do you mean by bending?

As discussed in above section, when an object curves due to the stress applied on it then it is said that the object is bending.

Amount of bending taking place depends on the rigidity of the material and the stress applied on the material. If the material is less rigid and more stress is applied then it will undergo more bending and has a greater chances of breaking.

## Bending stress formula

Stress can be defined as the force applied on a unit surface area of work piece. Bending stress is the stress acting per unit area that is responsible for curving or bending of the work piece.

Bending stress depends on bending moment, moment of inertia and the distance from the neutral axis where the load is applied. The formula for bending stress can be given as follows-

σ = MY/I

Where,

sigma is bending stress

M is bending moment

I is moment of inertia

Y is distance from neutral axis

## What is bending moment?

Bending moment is the reaction induced in the work piece when an external force is applied to it. The bending moment at a section of the beam can be defined as the sum of all bending moments acting along that point.

Positive bending moment causes sagging and negative bending moment causes hogging. The point where the bending moment changes from negative to positive or vice versa is called as point of contraflexure.

## Bending stress example in daily life

Dealing with bending stress in mechanical industry is everyday job. Lets see examples of bending stress that we see in everyday life.

• Bending of hanger due to weight of clothes.
• Bending of fan propeller at its end due to self weight.
• Bending of curtain rod due to weight of curtain.
• Hair acts as cantilever, when we comb our hair we apply bending stress on hair.
• Folding of paper in origami.
• Breaking of biscuit in two halves is a result of excessive bending stress.

## Maximum bending stress example

Let us assume the data given below-

Bending moment, M= 50,000Nm

Distance from neutral axis, y= 0.2169m

Moment of inertia, I=4.74 x 10^-4 m^4

Now let us calculate bending stress from the data given above.

Formula for finding bending stress is-

σ = MY/I

Substituting the values in the formula, we get

Bending stress= 22.815 MPa

## What is a cantilever beam?

A cantilever beam is a type of structural element which is firmly supported at one end and free at other end. The support may be a flat wall or firmly pinned joint.

A cantilever beam will have a moment and two reaction forces at the fixed end, the free end will have no reaction force acting on it. While solving the problems related to cantilever beams, we apply equilibrium conditions to find the reaction forces and moment.

## Examples of cantilever beam

Cantilever beam is nothing but a beam extending from a fixed support to a free end. The examples of cantilever beam are as follows-

• Bridge under construction.
• Balconies protruding out of rooms.
• Building is an example of cantilever with fixed end at ground and free end is the top floor.
• Wings of an aeroplane.

## Cantilever beam bending stress example

Let us assume the following given data for a cantilever beam-

Bending moment, M= 1962 N-mm

Section Modulus, Z= 12mm^3

The bending stress can be given by the formula-

σ = M/Z

Substituting all the values in above formula we get,

Bending stress= 163.5 MPa

## Combined axial and bending stress

When both axial stress and bending stress are applied, the system experiences deformation in longitudinal as well as plane normal to the longitudinal plane.

To calculate the combined stress acting on the work piece, following formula is used-

For compressive axial force and bending-

For tensile axial force and bending-

First part of the formula represents axial stress and latter represents bending stress.

## Combined axial and bending stress example

Let us assume the following data for a work piece experiencing both axial and bending stress-

Cross section area, A=8000mm^2

Bending moment, M= 12800kN-mm

Section modulus, Z= 266666.67 mm^3

We calculate the bending stress from the formula given above

Substituting the values we get,

Bending stress= 80 Mpa

## What is a simply supported beam?

A simply supported beam is a structural element which is fixed at one and supported at other end by a roller. A roller permits movement in one direction only and restricts movement in another.

Unlike cantilever beams, the simply supported beam has a reaction force acting at the end opposite to fixed end. The examples of simply supported beams include truss structure, bridges etc.

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