Diameter of Circular Shaft for Equivalent Torque and Maximum Shear Stress Calculator

✖Equivalent Torque is the torque which will produce the same maximum shear stress as produced by the bending moment and torque acting separately.ⓘ Equivalent Torque [T_e]			+10% -10%
✖Maximum Shear Stress is the greatest extent a shear force can be concentrated in a small area.ⓘ Maximum Shear Stress [τ_max]			+10% -10%

✖Diameter of circular shaft is denoted by d.ⓘ Diameter of Circular Shaft for Equivalent Torque and Maximum Shear Stress [Φ]

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Formula

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Diameter of Circular Shaft for Equivalent Torque and Maximum Shear Stress

Formula

`"Φ" = ((16*"T"_{"e"})/(pi*("τ"_{"max"})))^(1/3)`

Example

`"157.1413mm"=((16*"32kN*m")/(pi*("42MPa")))^(1/3)`

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Diameter of Circular Shaft for Equivalent Torque and Maximum Shear Stress Solution

STEP 0: Pre-Calculation Summary

Formula Used

Diameter of Circular Shaft = ((16*Equivalent Torque)/(pi*(Maximum Shear Stress)))^(1/3)
Φ = ((16*T_e)/(pi*(τ_max)))^(1/3)
This formula uses 1 Constants, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Diameter of Circular Shaft - (Measured in Meter) - Diameter of circular shaft is denoted by d.
Equivalent Torque - (Measured in Newton Meter) - Equivalent Torque is the torque which will produce the same maximum shear stress as produced by the bending moment and torque acting separately.
Maximum Shear Stress - (Measured in Pascal) - Maximum Shear Stress is the greatest extent a shear force can be concentrated in a small area.

STEP 1: Convert Input(s) to Base Unit

Equivalent Torque: 32 Kilonewton Meter --> 32000 Newton Meter (Check conversion here)
Maximum Shear Stress: 42 Megapascal --> 42000000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Φ = ((16*T_e)/(pi*(τ_max)))^(1/3) --> ((16*32000)/(pi*(42000000)))^(1/3)

Evaluating ... ...

Φ = 0.157141272610147

STEP 3: Convert Result to Output's Unit

0.157141272610147 Meter -->157.141272610147 Millimeter (Check conversion here)

FINAL ANSWER

157.141272610147 ≈ 157.1413 Millimeter <-- Diameter of Circular Shaft

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Strength of Materials » Principal Stress » Equivalent Bending Moment & Torque » Diameter of Circular Shaft for Equivalent Torque and Maximum Shear Stress

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Created by Rithik Agrawal

National Institute of Technology Karnataka (NITK), Surathkal

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< 7 Equivalent Bending Moment & Torque Calculators

Location of Principal Planes

Go Theta = (((1/2)*atan((2*Shear Stress xy)/(Stress along y Direction-Stress along x Direction))))

Diameter of Circular Shaft given Equivalent Bending Stress

Go Diameter of Circular Shaft = ((32*Equivalent Bending Moment)/(pi*(Bending Stress)))^(1/3)

Diameter of Circular Shaft for Equivalent Torque and Maximum Shear Stress

Go Diameter of Circular Shaft = ((16*Equivalent Torque)/(pi*(Maximum Shear Stress)))^(1/3)

Bending Stress of Circular Shaft given Equivalent Bending Moment

Go Bending Stress = (32*Equivalent Bending Moment)/(pi*(Diameter of Circular Shaft^3))

Equivalent Bending Moment of Circular Shaft

Go Equivalent Bending Moment = Bending Stress/(32/(pi*(Diameter of Circular Shaft^3)))

Maximum Shear Stress due to Equivalent Torque

Go Maximum Shear Stress = (16*Equivalent Torque)/(pi*(Diameter of Circular Shaft^3))

Equivalent Torque given Maximum Shear Stress

Go Equivalent Torque = Maximum Shear Stress/(16/(pi*(Diameter of Circular Shaft^3)))

Diameter of Circular Shaft for Equivalent Torque and Maximum Shear Stress Formula

Diameter of Circular Shaft = ((16*Equivalent Torque)/(pi*(Maximum Shear Stress)))^(1/3)
Φ = ((16*T_e)/(pi*(τ_max)))^(1/3)

What is Combined Bending and Torsion?

Combined bending , direct and torsional stresses in shafts are arised when such as in propeller shafts of ships where a shaft is subjected to direct thrust in addition to bending moment and torsion. In such cases the direct stresses due to bending moment and the axial thrust have to be combined into a single resultant.

How to Calculate Diameter of Circular Shaft for Equivalent Torque and Maximum Shear Stress?

Diameter of Circular Shaft for Equivalent Torque and Maximum Shear Stress calculator uses Diameter of Circular Shaft = ((16*Equivalent Torque)/(pi*(Maximum Shear Stress)))^(1/3) to calculate the Diameter of Circular Shaft, The Diameter of Circular Shaft for Equivalent Torque and Maximum Shear Stress formula is defined as diameter of the shaft of the member attached to the system. Diameter of Circular Shaft is denoted by Φ symbol.

How to calculate Diameter of Circular Shaft for Equivalent Torque and Maximum Shear Stress using this online calculator? To use this online calculator for Diameter of Circular Shaft for Equivalent Torque and Maximum Shear Stress, enter Equivalent Torque (T_e) & Maximum Shear Stress (τ_max) and hit the calculate button. Here is how the Diameter of Circular Shaft for Equivalent Torque and Maximum Shear Stress calculation can be explained with given input values -> 0.157141 = ((16*32000)/(pi*(42000000)))^(1/3).

FAQ

What is Diameter of Circular Shaft for Equivalent Torque and Maximum Shear Stress?

The Diameter of Circular Shaft for Equivalent Torque and Maximum Shear Stress formula is defined as diameter of the shaft of the member attached to the system and is represented as Φ = ((16*T_e)/(pi*(τ_max)))^(1/3) or Diameter of Circular Shaft = ((16*Equivalent Torque)/(pi*(Maximum Shear Stress)))^(1/3). Equivalent Torque is the torque which will produce the same maximum shear stress as produced by the bending moment and torque acting separately & Maximum Shear Stress is the greatest extent a shear force can be concentrated in a small area.

How to calculate Diameter of Circular Shaft for Equivalent Torque and Maximum Shear Stress?

The Diameter of Circular Shaft for Equivalent Torque and Maximum Shear Stress formula is defined as diameter of the shaft of the member attached to the system is calculated using Diameter of Circular Shaft = ((16*Equivalent Torque)/(pi*(Maximum Shear Stress)))^(1/3). To calculate Diameter of Circular Shaft for Equivalent Torque and Maximum Shear Stress, you need Equivalent Torque (T_e) & Maximum Shear Stress (τ_max). With our tool, you need to enter the respective value for Equivalent Torque & Maximum Shear Stress and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Diameter of Circular Shaft?

In this formula, Diameter of Circular Shaft uses Equivalent Torque & Maximum Shear Stress. We can use 1 other way(s) to calculate the same, which is/are as follows -

Diameter of Circular Shaft = ((32*Equivalent Bending Moment)/(pi*(Bending Stress)))^(1/3)

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