Bending Stress Formula and Bending Stress Calculator

Bending Stress Formula and Bending Stress Calculator

The effect of the uniform load is considered because the bending moment effect it. To calculate the bending stress, you need to know the total bending moment acting on the point of interest. So here, you will learn the bending stress formula with the calculator.

Here, we explain the calculation of normal stresses that occurred at the cross-sections of structures because of the bending moment effect. You can use the calculations prepared for you to calculate your calculations easily and fastly. 

Normal Stresses Due To Bending Moment Calculator

How to Use Bending Stress Calculator of Bending Stress Formula?

The use of the bending stress calculator above is very simple. Firstly, you just need to enter the required values;

  • Bending moment value on the point where the calculations are done.
  • The moment of inertia of the cross-section(you can use this calculator to calculate the moment of inertia for your certain cross-section) of the structural member where calculations are done.
  • The distance of the point of the cross-section where calculation will be made, from the neutral axis of the cross-section. 

And then, click on the ‘Calculate’ button to see the normal stress value on that point. If you want to make additional calculations, click on the ‘Reset’ button to make a new calculation. 

What is the Bending Stress Formula?

Bending stress formula.

So, it is very basic. You just need to specify the parameters correctly. 

Firstly, you need to calculate the bending stress formula. Bending moments can occur due to the different loading conditions such as uniform loads, singular loads, multiple loads. You need to obtain the bending moment diagram to see the total bending moment at the point of calculation. 

Cross-section of the structural member that you are making your bending stress calculations must be constant. Otherwise, calculations will be very different complex. Calculate the area moment of inertia of the cross-section around the neutral axis. 

Furthermore, in this cross-section, you may need a bending stress value on a point that has a distance from the neutral axis. Specify this distance which appear as ‘y’ in the bending stress formula. 

If you make the calculation, you will have the total bending moment stress on that point. 

Strength of Materials (Dover Books on Physics)

Also, if you are interested, you can take a look at this Strength of Materials outline book from Amazon! You can find all the summaries of the strength of materials topics from it at a lower price!

Bending Stress Test on Engineering Materials

We expressed the tensile stress and compression stress tests of engineering materials in Mechanicalland. In these kinds of standardized tests, we obtain the whole characteristics of materials to use in engineering calculations. Also, there is another material strength test we call as Bending(Flexure).

Bending stress test.
Application of bending test on a specimen.

As you know in the manufacturing industry, we use bending stress operations frequently such as forming metal plates and sheets, etc. The information that originated from these kinds of material testings can be used in the design of these manufacturing processes.

We call the strength value ‘transverse rupture strength’ is obtained from bending(flexure) tests of materials. The formula of this ‘transverse rupture strength’ value is as below;

F = Applied force on the specimen(N)(lb),

L = Length of the specimen between supports(mm)(in),

b and t: Dimensions of the specimen(mm)(in).

They calculate the TRS as MPa(lb/in^2) if you use the above units.

Effect of Bending Stress Formula

If we take a look at the application of the bending stress formula test, there is a rectangular standardized material specimen that we support by two basic supports. And there is a force that we apply from the middle section of this specimen. The contraption of the bending(flexure) test is very basic like that. We call this kind of test as ‘three-point bending stress test’.

Furthermore, the deformation mechanics of the test specimen includes; compressive stress and strain in the concave region of the deformed specimen and tensile stress and strain in the convex region. The specimen will be deformed with these kinds of stress and strain values. 

Failure of the specimens that undergo bending(flexure) stress formula testing occurs at the convex side because the tensile stress at the convex side exceeds the ultimate tensile stress value of the specimen.

This is the very basic information about the bending(flexure) stress test of material specimens in materials science.

Take Care About Your Units!

While you are making your calculations, you need to use proper sets of units both for forces, moments, and lengths. All the units must be consistent in your parameters. You can use this calculator with your unit set both in SI and imperial.


So, this is the general importance of the bending stress formula and bending stress calculator.

Mechanicalland does not accept any responsibility for calculations made by users in calculators. A good engineer must check calculations again and again.

Also, you can find out much more calculators like this in Mechanicalland! Take a look at the other engineering calculators available in Mechanicalland!

Finally, do not forget to leave your comments and questions below about the bending stress calculator of bending moments. 

Your precious feedbacks are very important for us.

FAQs About Bending Stress Formula and Calculator

What is the formula for bending stress?

In this formula, you need to divide the bending moment with the moment of inertia of the cross-section. And you need to multiply this value by the distance from the neutral axis of bending stress. So, it is very simple to calculate it.

What is bending stress?

Bending stress is the total stress that takes place because of the application of bending moments to structural members. So, we can calculate the bending stresses by using its formula.

How do you calculate bending?

We can calculate the bending by using the bending stress formula above. So, it is very simple to calculate the bending stresses due to the bending moments on structural members.

How do you calculate the bending stress of a shaft?

Bending stresses are not important for shafts, because shafts are circular members that carry twisting moment and rotational power. But if you want to calculate it, you need to define the bending moment application on the shaft. And you need to put this value inside the formula. And then, you need to calculate the area moment of inertia of the cross-section. You need to put them in the formula above to see the result.

What causes the bending stress?

There are different causes of bending stresses on structural members. But the most important one is the bending moment. Also, the cause of the bending moment is the bending force acting perpendicularly to the structural member.

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