Modulus of Rigidity given Angle of Twist Solution

STEP 0: Pre-Calculation Summary
Formula Used
Modulus of Rigidity of Shaft = 584*Torsional Moment in Shaft*Length of Shaft from Torsional Rigidity/(Angle of Twist in Shaft*Diameter of Shaft from Torsional Rigidity^4)
G = 584*Mtshaft*L/(θ*dtorl^4)
This formula uses 5 Variables
Variables Used
Modulus of Rigidity of Shaft - (Measured in Pascal) - Modulus of Rigidity of Shaft is the elastic coefficient when a shear force is applied resulting in lateral deformation. It gives us a measure of how rigid is s shaft.
Torsional Moment in Shaft - (Measured in Newton Meter) - Torsional Moment in Shaft is the reaction induced in a structural shaft element when an external force or moment is applied to the element, causing the element to twist.
Length of Shaft from Torsional Rigidity - (Measured in Meter) - Length of Shaft from Torsional Rigidity is the length of the shaft calculated on the basis of torsional rigidity.
Angle of Twist in Shaft - (Measured in Radian) - Angle of Twist in Shaft is the angle through which the fixed end of a shaft rotates with respect to the free end.
Diameter of Shaft from Torsional Rigidity - (Measured in Meter) - Diameter of Shaft from Torsional Rigidity is the diameter of the external surface of a shaft calculated on the basis of torsional rigidity.
STEP 1: Convert Input(s) to Base Unit
Torsional Moment in Shaft: 330000 Newton Millimeter --> 330 Newton Meter (Check conversion here)
Length of Shaft from Torsional Rigidity: 450 Millimeter --> 0.45 Meter (Check conversion here)
Angle of Twist in Shaft: 15.42 Degree --> 0.269129770657475 Radian (Check conversion here)
Diameter of Shaft from Torsional Rigidity: 43.5 Millimeter --> 0.0435 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
G = 584*Mtshaft*L/(θ*dtorl^4) --> 584*330*0.45/(0.269129770657475*0.0435^4)
Evaluating ... ...
G = 89995445597.7508
STEP 3: Convert Result to Output's Unit
89995445597.7508 Pascal -->89995.4455977508 Newton per Square Millimeter (Check conversion here)
FINAL ANSWER
89995.4455977508 89995.45 Newton per Square Millimeter <-- Modulus of Rigidity of Shaft
(Calculation completed in 00.004 seconds)

Credits

Created by Kethavath Srinath
Osmania University (OU), Hyderabad
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5 Torsional Rigidity Calculators

Shaft Diameter given Angle of Twist in Shaft
Go Diameter of Shaft from Torsional Rigidity = (584*Torsional Moment in Shaft*Length of Shaft from Torsional Rigidity/(Modulus of Rigidity of Shaft*Angle of Twist in Shaft))^(1/4)
Length of Shaft Subjected to Torsional Moment given Angle of Twist
Go Length of Shaft from Torsional Rigidity = Angle of Twist in Shaft*(Modulus of Rigidity of Shaft*Diameter of Shaft from Torsional Rigidity^4)/(584*Torsional Moment in Shaft)
Torsional Moment given Angle of Twist in Shaft
Go Torsional Moment in Shaft = Angle of Twist in Shaft*(Modulus of Rigidity of Shaft*Diameter of Shaft from Torsional Rigidity^4)/(Length of Shaft from Torsional Rigidity*584)
Modulus of Rigidity given Angle of Twist
Go Modulus of Rigidity of Shaft = 584*Torsional Moment in Shaft*Length of Shaft from Torsional Rigidity/(Angle of Twist in Shaft*Diameter of Shaft from Torsional Rigidity^4)
Angle of Twist of Shaft
Go Angle of Twist in Shaft = 584*Torsional Moment in Shaft*Length of Shaft from Torsional Rigidity/(Modulus of Rigidity of Shaft*Diameter of Shaft from Torsional Rigidity^4)

Modulus of Rigidity given Angle of Twist Formula

Modulus of Rigidity of Shaft = 584*Torsional Moment in Shaft*Length of Shaft from Torsional Rigidity/(Angle of Twist in Shaft*Diameter of Shaft from Torsional Rigidity^4)
G = 584*Mtshaft*L/(θ*dtorl^4)

Define Modulus of Rigidity?

Shear Modulus of elasticity is one of the measures of mechanical properties of solids. Other elastic moduli are Young’s modulus and bulk modulus. The shear modulus of material gives us the ratio of shear stress to shear strain in a body.

How to Calculate Modulus of Rigidity given Angle of Twist?

Modulus of Rigidity given Angle of Twist calculator uses Modulus of Rigidity of Shaft = 584*Torsional Moment in Shaft*Length of Shaft from Torsional Rigidity/(Angle of Twist in Shaft*Diameter of Shaft from Torsional Rigidity^4) to calculate the Modulus of Rigidity of Shaft, The Modulus of Rigidity given Angle of Twist formula is defined as the measure of the rigidity of the body, given by the ratio of shear stress to shear strain. Often denoted by G sometimes by S or μ. Modulus of Rigidity of Shaft is denoted by G symbol.

How to calculate Modulus of Rigidity given Angle of Twist using this online calculator? To use this online calculator for Modulus of Rigidity given Angle of Twist, enter Torsional Moment in Shaft (Mtshaft), Length of Shaft from Torsional Rigidity (L), Angle of Twist in Shaft (θ) & Diameter of Shaft from Torsional Rigidity (dtorl) and hit the calculate button. Here is how the Modulus of Rigidity given Angle of Twist calculation can be explained with given input values -> 0.089995 = 584*330*0.45/(0.269129770657475*0.0435^4).

FAQ

What is Modulus of Rigidity given Angle of Twist?
The Modulus of Rigidity given Angle of Twist formula is defined as the measure of the rigidity of the body, given by the ratio of shear stress to shear strain. Often denoted by G sometimes by S or μ and is represented as G = 584*Mtshaft*L/(θ*dtorl^4) or Modulus of Rigidity of Shaft = 584*Torsional Moment in Shaft*Length of Shaft from Torsional Rigidity/(Angle of Twist in Shaft*Diameter of Shaft from Torsional Rigidity^4). Torsional Moment in Shaft is the reaction induced in a structural shaft element when an external force or moment is applied to the element, causing the element to twist, Length of Shaft from Torsional Rigidity is the length of the shaft calculated on the basis of torsional rigidity, Angle of Twist in Shaft is the angle through which the fixed end of a shaft rotates with respect to the free end & Diameter of Shaft from Torsional Rigidity is the diameter of the external surface of a shaft calculated on the basis of torsional rigidity.
How to calculate Modulus of Rigidity given Angle of Twist?
The Modulus of Rigidity given Angle of Twist formula is defined as the measure of the rigidity of the body, given by the ratio of shear stress to shear strain. Often denoted by G sometimes by S or μ is calculated using Modulus of Rigidity of Shaft = 584*Torsional Moment in Shaft*Length of Shaft from Torsional Rigidity/(Angle of Twist in Shaft*Diameter of Shaft from Torsional Rigidity^4). To calculate Modulus of Rigidity given Angle of Twist, you need Torsional Moment in Shaft (Mtshaft), Length of Shaft from Torsional Rigidity (L), Angle of Twist in Shaft (θ) & Diameter of Shaft from Torsional Rigidity (dtorl). With our tool, you need to enter the respective value for Torsional Moment in Shaft, Length of Shaft from Torsional Rigidity, Angle of Twist in Shaft & Diameter of Shaft from Torsional Rigidity 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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