Twisting a shaft causes shear stress τ=Tr/J and angle θ=TL/GJ.
A circular shaft under torque T has shear stress τ=Tr/J (J=πd⁴/32) and twist angle θ=TL/(GJ). Stress is zero at the axis and highest at the surface. Hollow shafts are efficient.
A 40 mm shaft carrying 500 N·m has τ≈40 MPa.
Torsion sizes shafts and tubes that transmit power, and the twist angle matters for accuracy in drive trains and machine tools.
Twisting a shaft causes shear stress τ=Tr/J and angle θ=TL/GJ.
Torsion sizes shafts and tubes that transmit power, and the twist angle matters for accuracy in drive trains and machine tools.
Shear stress is highest at the outer surface, so material near the centre carries little load, and removing it saves weight with little loss of strength.
Angle of twist must stay within the limit of the machine, such as gear alignment or positional accuracy.
Typical applications include calculating the shear stress in a drive shaft carrying a given torque, checking the angle of twist in a long transmission shaft and designing a hollow tube that is lighter than a solid bar for the same torque.
Study "Factor of safety" first (topic 51 of 106 in Engineering Mechanics). It covers the groundwork this topic builds on.
G is shear modulus. Non-circular sections need special formulas. Thin-walled tubes use shear flow.
A 40 mm shaft carrying 500 N·m has τ≈40 MPa.
The next topic is "Power transmission shafts", which builds directly on this one.
It is classed as Intermediate in Engineering Mechanics (topic 52 of 106). It is an intermediate topic. Work through the beginner topics in Engineering Mechanics first.
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