How do you calculate torsional stress in a shaft?

Torsional stress is the internal force that resists the twisting of a shaft or a rod when it is subjected to a torque. It is an important factor to consider in the design and analysis of mechanical components that transmit power or motion. In this article, you will learn how to calculate torsional stress in a shaft using some basic formulas and examples.

1 What is torsion?

Torsion is the action of applying a torque to a shaft or a rod, which causes it to twist along its axis. Torque is the product of the force and the perpendicular distance from the axis of rotation. For example, when you turn a wrench to tighten a bolt, you are applying a torque to the bolt, which creates torsion in the bolt. Torsion can also be caused by external loads, such as wind or gravity, that act on a shaft or a rod.

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Matthias Niessner

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Wichtig wäre noch der Hinweis, dass das Drehen mit einer Kraft (wie beim Schraubenschlüssel) nicht nur eine Momentenwirkung hat, sondern zu einer Moment- UND einer Kraftwirkung führt. An der Schraube wird gedreht und quer gezogen. Ein reines Moment würde man mit einem Kräftepaar erhalten (Beispiel Radkreuz mit 2 Armen und 2 Kräften zum Drehen der Schraube).

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2 How does torsion affect a shaft?

Torsion affects a shaft by creating shear stress and shear strain along its cross-section. Shear stress is the force per unit area that acts parallel to the cross-section of the shaft. Shear strain is the angular deformation of the cross-section due to torsion. The shear stress and shear strain vary along the radius of the shaft, with the maximum values occurring at the outer surface and the minimum values occurring at the center. The relationship between shear stress and shear strain is given by the shear modulus of elasticity, which is a property of the material of the shaft.

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3 What is the formula for torsional stress?

The formula for torsional stress in a circular shaft is given by: τ = T*r/J where τ is the torsional stress, T is the torque, r is the radius of the shaft, and J is the polar moment of inertia of the cross-section. The polar moment of inertia is a measure of the resistance of the cross-section to torsion. It depends on the shape and size of the cross-section. For a circular shaft, J is given by: J = π*r^4/2 where r is the radius of the shaft. For other shapes, such as hollow or rectangular shafts, J can be calculated using different formulas or tables.

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Matthias Niessner

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Bitte bei der Gleichung π*r^4/2 eine Klammer spendieren. Einige Studenten haben tatsächlich π*r^2 gerechnet wegen 4/2=2... Der Ausdruck (π*r^4)/2 wäre eindeutiger, auch wenn Potenzen immer Vorrang vor Punktrechnung haben. Noch eine Verbesserung: τ = T*r/J ist nicht der Torsionsspannungsverlauf, sondern der Wert am Rand, wenn r der Radius oder halbe Durchmesser der Welle ist. Schöner wäre es, die Funktion τ=τ(r)= T*r/J mit r als Abstand zur Achse zu schreiben und J = (π*R^4)/2 mit R als Radius bzw. halber Durchmesser der Welle.

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4 How do you calculate torsional stress in a shaft?

To calculate torsional stress in a shaft, you need to know the torque, the radius, and the polar moment of inertia of the cross-section. You can use the formula for torsional stress to find the shear stress at any point along the radius of the shaft. For example, if you have a solid circular shaft with a radius of 10 mm and a torque of 100 Nm, you can find the torsional stress at the outer surface by plugging in the values into the formula: τ = T*r/J τ = 100*0.01/(π*0.01^4/2) τ = 63.66 MPa This means that the shaft experiences a shear stress of 63.66 MPa at the outer surface due to torsion. You can also find the torsional stress at the center of the shaft by setting r to zero, which gives: τ = T*0/J τ = 0 MPa This means that the shaft experiences no shear stress at the center due to torsion.

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5 What are some applications of torsional stress?

Torsional stress is relevant for many applications in engineering and mechanics, such as shafts, rods, gears, springs, propellers, and turbines. These components are often exposed to torque and torsion, which affect their performance and durability. By calculating torsional stress, you can design and analyze these components to ensure that they can withstand the required load and avoid failure due to excessive shear stress or strain. You can also use torsional stress to determine other parameters, such as the angle of twist, the power transmitted, and the stiffness of the shaft.

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6 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?

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How do you calculate torsional stress in a shaft?

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1 What is torsion?

2 How does torsion affect a shaft?

3 What is the formula for torsional stress?

4 How do you calculate torsional stress in a shaft?

5 What are some applications of torsional stress?

6 Here’s what else to consider

Mechanics

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How do you calculate torsional stress in a shaft?

1

2

3

4

5

6

1 What is torsion?

2 How does torsion affect a shaft?

3 What is the formula for torsional stress?

4 How do you calculate torsional stress in a shaft?

5 What are some applications of torsional stress?

6 Here’s what else to consider

Mechanics

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