# Combined Torsion And Axial Loads On Mechanical Elements(With Calculators)

In mechanical engineering and mechanical design, people are dealing with various kinds of problems such as combined load effects. In static systems which are exposed to different loads, all the effects of these loads must be determined in the most critical section of that mechanical element.

Strength of Materials, Third Edition

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According to these most critical loading conditions, a safety calculation must be accomplished to see whether the system can withstand these loads or not. If it is not, the general design of a system must be reconsidered.

In this article, we will take a look at the combined torsion and axial loads on mechanical elements and what kinds of stresses that they cause.

## Combined Torsion And Axial Loads On Circular Shafts Representation of a circular shaft(Image Source: D. K. Singh – Strength of Materials-Springer, 2020, pg.638).

A circular shaft will be the best representative of mechanical elements to show the combined loading effects on it. You can apply to your systems the general principles that are applied here on the circular shaft.

Think about a circular shaft undergoing the effects of torsion and axial loads. There is a twisting moment(T) and axial load(P).

Shear stress(τ) is induced on the shaft because of the twisting moment and normal stress(σ) is induced because of the axial load. Let’s take a look at these stresses.

## Shear Stress Calculation Due To Twisting Moment

If a twisting moment is applied to a circular shaft, there will be shear stress-induced on this shaft. And the biggest shear stress occurs on the surface of the shaft. Shear stress can be calculated via this formula;

In this formula, ‘D’ is the diameter that the shear stress occurs. If you want to see the maximum shear stress, you need to use this formulation for circular shafts. The 0.098 comes from the polar moment of inertia of the circular cross-section. You need to use the polar moment of inertia formulations for different cross-sections.

You can use the calculator below to calculate the shear stress due to the twisting moment on a structural element. The use of this calculator is very simple. You just need to enter the required values inside the brackets, then click on the ‘Calculate!’ button. If you want to make another calculation, just click on the ‘Reset’ button then enter the new values.

## Normal Stress Calculation Due To The Axial Load

As we stated above, axial load causes normal stress perpendicular to the cross-section of the shaft. There is no maximum or minimum point of this normal stress. Normal stress is the same for all sides of the cross-section. The normal stress can be calculated via this formula;

In this formula, ‘F’ is the normal force acting axially to the shaft and the ‘D’ is the diameter of the shaft.

You can use the calculator below to calculate normal stress due to the normal force acting along the axis of the structural elements.

In this formula, ‘F’ is the normal force acting axially to the shaft and the ‘D’ is the diameter of the shaft.

You can use the calculator below to calculate normal stress due to the normal force acting along the axis of the structural elements.

## Calculation Of Combined Effects

The combined effects must be obtained from these two types of stresses. The acting directions of these stresses must be well defined by you to obtain a safe design. You need to show the stresses on stress elements and find out the principal stresses via formulations or Mohr’s circle method.

Once you find the maximum principal stresses on a critical point, you need to compare this stress result to the safety stress that material remains durable. This generally yield the strength of the material of the part which is divided by the safety factor.

## Conclusion

Calculations of the combined effects of multiple loads on mechanical elements have very simple principles like this. You need to have an engineering capability to apply these principles to other types of engineering problems that include combined stresses.

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

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