Torsional moment on shaft given shear stress Solution

STEP 0: Pre-Calculation Summary
Formula Used
Torsional moment on shaft = Torsional shear stress in twisted shaft*Polar moment of inertia for circular section/Radial Distance from Axis of Rotation
τ = 𝜏*J/r
This formula uses 4 Variables
Variables Used
Torsional moment on shaft - (Measured in Newton Meter) - Torsional moment on shaft is described as the turning effect of force on the axis of rotation. In brief, it is a moment of force.
Torsional shear stress in twisted shaft - (Measured in Pascal) - Torsional shear stress in twisted shaft or Torsional stress is the shear stress produced in the shaft due to the twisting.
Polar moment of inertia for circular section - (Measured in Meter⁴) - Polar moment of inertia for circular section is the measure of the specimen's resistance to torsion.
Radial Distance from Axis of Rotation - (Measured in Meter) - Radial Distance from Axis of Rotation is taken as the distance between the projections onto the two planes.
STEP 1: Convert Input(s) to Base Unit
Torsional shear stress in twisted shaft: 35 Newton per Square Millimeter --> 35000000 Pascal (Check conversion ​here)
Polar moment of inertia for circular section: 38000 Millimeter⁴ --> 3.8E-08 Meter⁴ (Check conversion ​here)
Radial Distance from Axis of Rotation: 25 Millimeter --> 0.025 Meter (Check conversion ​here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
τ = 𝜏*J/r --> 35000000*3.8E-08/0.025
Evaluating ... ...
τ = 53.2
STEP 3: Convert Result to Output's Unit
53.2 Newton Meter -->53200 Newton Millimeter (Check conversion ​here)
FINAL ANSWER
53200 Newton Millimeter <-- Torsional moment on shaft
(Calculation completed in 00.020 seconds)

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National Institute of Technology (NIT), Tiruchirapalli
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Design of Shaft for Torsional Moment Calculators

Angle of twist of shaft in radians given torque, length of shaft, polar moment of inertia
​ LaTeX ​ Go Angle of twist of shaft = (Torsional moment on shaft*Length of Shaft)/(Polar moment of inertia for circular section*Modulus of Rigidity)
Torsional shear stress in shaft due to torsional moment
​ LaTeX ​ Go Torsional shear stress in twisted shaft = Torsional moment on shaft*Radial Distance from Axis of Rotation/Polar moment of inertia for circular section
Polar moment of inertia of hollow circular cross-section
​ LaTeX ​ Go Polar moment of inertia for circular section = pi*((Outer Diameter of Hollow Circular Section^4)-(Inner Diameter of Hollow Circular Section^4))/32
Polar moment of inertia of circular cross section
​ LaTeX ​ Go Polar moment of inertia for circular section = pi*(Diameter of circular section of shaft^4)/32

Torsional moment on shaft given shear stress Formula

​LaTeX ​Go
Torsional moment on shaft = Torsional shear stress in twisted shaft*Polar moment of inertia for circular section/Radial Distance from Axis of Rotation
τ = 𝜏*J/r

What is torsional moment?

In the field of solid mechanics, torsion is the twisting of an object due to an applied torque. Torsion is expressed in either the Pascal (Pa), an SI unit for newtons per square metre, or in pounds per square inch (psi) while torque is expressed in newton metres (N·m) or foot-pound force (ft·lbf).

How to Calculate Torsional moment on shaft given shear stress?

Torsional moment on shaft given shear stress calculator uses Torsional moment on shaft = Torsional shear stress in twisted shaft*Polar moment of inertia for circular section/Radial Distance from Axis of Rotation to calculate the Torsional moment on shaft, Torsional moment on shaft given shear stress formula is defined as a moment that twists a structure. Unlike axial loads that produce a uniform, or average, stress over the object's cross section, a torque creates a distribution of stress over the cross-section. Torsional moment on shaft is denoted by τ symbol.

How to calculate Torsional moment on shaft given shear stress using this online calculator? To use this online calculator for Torsional moment on shaft given shear stress, enter Torsional shear stress in twisted shaft (𝜏), Polar moment of inertia for circular section (J) & Radial Distance from Axis of Rotation (r) and hit the calculate button. Here is how the Torsional moment on shaft given shear stress calculation can be explained with given input values -> 5.3E+7 = 35000000*3.8E-08/0.025.

FAQ

What is Torsional moment on shaft given shear stress?
Torsional moment on shaft given shear stress formula is defined as a moment that twists a structure. Unlike axial loads that produce a uniform, or average, stress over the object's cross section, a torque creates a distribution of stress over the cross-section and is represented as τ = 𝜏*J/r or Torsional moment on shaft = Torsional shear stress in twisted shaft*Polar moment of inertia for circular section/Radial Distance from Axis of Rotation. Torsional shear stress in twisted shaft or Torsional stress is the shear stress produced in the shaft due to the twisting, Polar moment of inertia for circular section is the measure of the specimen's resistance to torsion & Radial Distance from Axis of Rotation is taken as the distance between the projections onto the two planes.
How to calculate Torsional moment on shaft given shear stress?
Torsional moment on shaft given shear stress formula is defined as a moment that twists a structure. Unlike axial loads that produce a uniform, or average, stress over the object's cross section, a torque creates a distribution of stress over the cross-section is calculated using Torsional moment on shaft = Torsional shear stress in twisted shaft*Polar moment of inertia for circular section/Radial Distance from Axis of Rotation. To calculate Torsional moment on shaft given shear stress, you need Torsional shear stress in twisted shaft (𝜏), Polar moment of inertia for circular section (J) & Radial Distance from Axis of Rotation (r). With our tool, you need to enter the respective value for Torsional shear stress in twisted shaft, Polar moment of inertia for circular section & Radial Distance from Axis of Rotation and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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