# Combined Loading Effects On Circular Shafts

In engineering design, engineers are generally dealing with the combined effects of loading on different mechanical parts or structures. Because of these different loading conditions, there can be different kinds of stresses that can occur on a design point. In this case, an engineer must understand the loading conditions and must apply design parameters to reach a safe design.

One can understand the combined loading effects on mechanical elements if one takes a look at this circular shaft example. You can use these formulations in different engineering problems.

Think about a solid shaft that undergoes different loading conditions such as twisting moment and bending force. A singular force at the end of the shaft may produce these two effects on the shaft. Because of these forces, shear force, twisting moment, and bending moment occur on the shaft cross-section.

According to your design or structure, you need to define the most critical point that failure would occur because of the different loading conditions. And you need to make your safe design according to this point. If the combined stresses do not exceed the safety margin, your structure will be safe. Combined effects of cross-section (Image Source:D. K. Singh – Strength of Materials-Springer, 2020, pg.627).

But first of all, you can calculate the different loading conditions one by one on that point to find the total stress because of these singular loads.

## Calculation Of Twisting Moment

If we take a look at the effect of the twisting moment which can be produced with the action of loads, torsional shear stress will occur on the cross-section of the shaft. Maximum torsional stresses will occur on the surface.

If we apply the torsion formula;

T is the twisting moment that is applied on the shaft. ‘d’ is the diameter of the shaft. Hence, the calculation of the torsional stress effect on the shaft is very simple as that. You can use the calculator below to calculate it easily.

## Torsional Stress Calculator

The use of the calculator above is very simple. You just need to enter the required values stated above. Then click on the ‘Calculate!’ button to see the result. If you want to make another calculation, click on the ‘Reset’ button.

## Calculation Of The Bending Moment

Because of the bending moment acting on the shaft, there will be tensile stress would occur. If we take a look at the calculation of this tensile stress;

In this formula, ‘M’ is the value of the bending moment, and ‘d’ is the diameter of the shaft. You can also use the calculator below.

## Calculation Of Bending Force

Again, the bending force on the shaft produces a shear force which must be included in the calculations. At the outermost surface, the effect of the shear force is maximum. Let’s take a look at the calculation of the shear force effect on a shaft;

Again here, ‘V’ is the vertical bending force and the ‘d’ is the diameter of the shaft. You can use the calculator below to calculate it.

## Calculation Of The Principal Stresses

To make the safety calculations, you need to calculate the principal stresses because of these combined stress effects. You can use this link to calculate the principal stresses for your system. After the calculation of your principal stresses, you can use different stress theories to calculate the safety of your system.

## Conclusion

Strength of Materials (Dover Books on Physics)

If you are interested in the ‘Strength Of Materials’ subject, check the recommended outline book by Mechanicalland by clicking on the link or the ‘Shop Now’ button from Amazon! There are lots of other books are available and you can reach them through these links to Amazon!

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