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Shear Stress Calculation On Different Cross Sections

Shear stresses are a very important parameter in mechanical design and an engineer must understand the phenomena of shear stress. Maximum shear stress must be calculated for a cross-section to see whether the design is safe or not. 

Here, we will show you how to find shear stress on a certain point of a cross-section. You can understand it very easily. 

How To Calculate Shear Stresses On Different Cross Sections?

Shear stresses are the result of the vertical bending forces, acting from the perpendicular direction of the part axis. And we want to calculate the shear stress on a cross-section that shear force acting upon it. Actually, it has a very basic principle. 

First of all, you need to understand the neutral plane on this cross-section. In certain cross-sections, the neutral axis or neutral plane passes through the center of gravity of the cross-sectional area. And, you want to calculate the shear stress that occurs on a certain point on this cross-section, because of the shear force acting on this cross-section. 

Cross-section example to understand shear stress calculation for cross-sections(Image Source:D. K. Singh – Strength of Materials-Springer, 2020, pg.228).

Take a look at the cross-section example above. There is a shear force acting upon this cross-section say it is ‘F’. 

CD line is the line that contains our point that we want to calculate the shear stress. Also, you can see that the neutral axis is very straightforward above. 

And the center of gravity of the area above the CD line is shown with ‘G’. The distance between this ‘G’ and the neutral axis is denoted as ‘y(prime)’. 

The distance between the CD line and neutral axis is denoted as ‘y’. 

Calculate The Moment Of Inertia

First of all, you need to calculate the moment of inertia of the whole cross-section concerning the neutral axis. You will use this moment of inertia value in shear stress calculations. 

Calculate The Area

Then you need to calculate the area above the line which contains the point that you want to calculate shear stress(which is CD in the example above). 

Calculate The Moment Area

Then you need to multiply this area with the distance(y(prime)) of the center of gravity(which is G in the example above) of this area to the neutral axis. This will give you the first moment of the area.

Put The Values Into The Equation To Find Shear Stress

If you put the values that you find, you will find the shear stress on that line. In here, ‘b’ is the thickness of the part or cross-section which is perpendicular to shear force.

You must take care of units and you need to use the same unit sets to find correct results. You can use the MB-Unit Converter tool to obtain the same sets of units.

Conclusion

You can apply this principle to each type of cross-section. 

Do not forget to leave your comments and questions below about the shear stress calculations in cross-sections in mechanics. 

Your precious feedbacks are very important for us. 

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