Modulus of Rigidity given Angle of Twist of Hollow Shaft on basis of Torsional Rigidity Calculator

✖Torsional Moment in Hollow Shaft is the reaction induced in a structural shaft hollow element when an external force or moment is applied to the element, causing the element to twist.ⓘ Torsional Moment in Hollow Shaft [Mt_hollowshaft]			+10% -10%
✖Length of Hollow Shaft is the distance between two ends of a hollow shaft.ⓘ Length of Hollow Shaft [L_h]			+10% -10%
✖Angle of Twist of Hollow Shaft is the angle through which the fixed end of a hollow shaft rotates with respect to the free end.ⓘ Angle of Twist of Hollow Shaft [θ_hollow]			+10% -10%
✖Outer Diameter of Hollow Shaft is defined as the length of the longest chord of the surface of the hollow circular shaft.ⓘ Outer Diameter of Hollow Shaft [d_o]			+10% -10%
✖The Ratio of Inner to Outer Diameter of Hollow Shaft is defined as the inner diameter of the shaft divided by the outer diameter.ⓘ Ratio of Inner to Outer Diameter of Hollow Shaft [C]			+10% -10%

✖Modulus of Rigidity of Hollow Shaft is the elastic coefficient when a shear force is applied resulting in lateral deformation. It gives us a measure of how rigid a body is.ⓘ Modulus of Rigidity given Angle of Twist of Hollow Shaft on basis of Torsional Rigidity [G_h]

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Modulus of Rigidity given Angle of Twist of Hollow Shaft on basis of Torsional Rigidity Solution

STEP 0: Pre-Calculation Summary

Formula Used

Modulus of Rigidity of Hollow Shaft = 584*Torsional Moment in Hollow Shaft*Length of Hollow Shaft/(Angle of Twist of Hollow Shaft*Outer Diameter of Hollow Shaft^4*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4))
G_h = 584*Mt_hollowshaft*L_h/(θ_hollow*d_o^4*(1-C^4))
This formula uses 6 Variables

Variables Used

Modulus of Rigidity of Hollow Shaft - (Measured in Pascal) - Modulus of Rigidity of Hollow Shaft is the elastic coefficient when a shear force is applied resulting in lateral deformation. It gives us a measure of how rigid a body is.
Torsional Moment in Hollow Shaft - (Measured in Newton Meter) - Torsional Moment in Hollow Shaft is the reaction induced in a structural shaft hollow element when an external force or moment is applied to the element, causing the element to twist.
Length of Hollow Shaft - (Measured in Meter) - Length of Hollow Shaft is the distance between two ends of a hollow shaft.
Angle of Twist of Hollow Shaft - (Measured in Radian) - Angle of Twist of Hollow Shaft is the angle through which the fixed end of a hollow shaft rotates with respect to the free end.
Outer Diameter of Hollow Shaft - (Measured in Meter) - Outer Diameter of Hollow Shaft is defined as the length of the longest chord of the surface of the hollow circular shaft.
Ratio of Inner to Outer Diameter of Hollow Shaft - The Ratio of Inner to Outer Diameter of Hollow Shaft is defined as the inner diameter of the shaft divided by the outer diameter.

STEP 1: Convert Input(s) to Base Unit

Torsional Moment in Hollow Shaft: 320000 Newton Millimeter --> 320 Newton Meter (Check conversion here)
Length of Hollow Shaft: 330 Millimeter --> 0.33 Meter (Check conversion here)
Angle of Twist of Hollow Shaft: 23.58 Degree --> 0.411548637620186 Radian (Check conversion here)
Outer Diameter of Hollow Shaft: 46 Millimeter --> 0.046 Meter (Check conversion here)
Ratio of Inner to Outer Diameter of Hollow Shaft: 0.85 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

G_h = 584*Mt_hollowshaft*L_h/(θ_hollow*d_o^4*(1-C^4)) --> 584*320*0.33/(0.411548637620186*0.046^4*(1-0.85^4))

Evaluating ... ...

G_h = 70016766790.6141

STEP 3: Convert Result to Output's Unit

70016766790.6141 Pascal -->70016.7667906141 Newton per Square Millimeter (Check conversion here)

FINAL ANSWER

70016.7667906141 ≈ 70016.77 Newton per Square Millimeter <-- Modulus of Rigidity of Hollow Shaft

(Calculation completed in 00.007 seconds)

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Osmania University (OU), Hyderabad

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< Design of Hollow Shaft Calculators

Tensile Stress in Hollow Shaft when Subjected to Axial Force

LaTeX Go Tensile Stress in Hollow Shaft = Axial Force on Hollow Shaft/(pi/4*(Outer Diameter of Hollow Shaft^2-Inner Diameter of Hollow Shaft^2))

Inner Diameter of Hollow Shaft given Ratio of Diameters

LaTeX Go Inner Diameter of Hollow Shaft = Ratio of Inner to Outer Diameter of Hollow Shaft*Outer Diameter of Hollow Shaft

Ratio of Inner Diameter to Outer Diameter

LaTeX Go Ratio of Inner to Outer Diameter of Hollow Shaft = Inner Diameter of Hollow Shaft/Outer Diameter of Hollow Shaft

Outer Diameter given Ratio of Diameters

LaTeX Go Outer Diameter of Hollow Shaft = Inner Diameter of Hollow Shaft/Ratio of Inner to Outer Diameter of Hollow Shaft

Modulus of Rigidity given Angle of Twist of Hollow Shaft on basis of Torsional Rigidity Formula

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Define Modulus of Rigidity

Shear modulus also known as Modulus of rigidity is 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. 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 of Hollow Shaft on basis of Torsional Rigidity?

Modulus of Rigidity given Angle of Twist of Hollow Shaft on basis of Torsional Rigidity calculator uses Modulus of Rigidity of Hollow Shaft = 584*Torsional Moment in Hollow Shaft*Length of Hollow Shaft/(Angle of Twist of Hollow Shaft*Outer Diameter of Hollow Shaft^4*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)) to calculate the Modulus of Rigidity of Hollow Shaft, Modulus of Rigidity given Angle of Twist of Hollow Shaft on basis of Torsional Rigidity formula is defined as the measure of the shaft's stiffness in torsion, which is essential in designing hollow shafts to withstand twisting forces and resist deformation. Modulus of Rigidity of Hollow Shaft is denoted by G_h symbol.

How to calculate Modulus of Rigidity given Angle of Twist of Hollow Shaft on basis of Torsional Rigidity using this online calculator? To use this online calculator for Modulus of Rigidity given Angle of Twist of Hollow Shaft on basis of Torsional Rigidity, enter Torsional Moment in Hollow Shaft (Mt_hollowshaft), Length of Hollow Shaft (L_h), Angle of Twist of Hollow Shaft (θ_hollow), Outer Diameter of Hollow Shaft (d_o) & Ratio of Inner to Outer Diameter of Hollow Shaft (C) and hit the calculate button. Here is how the Modulus of Rigidity given Angle of Twist of Hollow Shaft on basis of Torsional Rigidity calculation can be explained with given input values -> 0.070017 = 584*320*0.33/(0.411548637620186*0.046^4*(1-0.85^4)).

FAQ

What is Modulus of Rigidity given Angle of Twist of Hollow Shaft on basis of Torsional Rigidity?

Modulus of Rigidity given Angle of Twist of Hollow Shaft on basis of Torsional Rigidity formula is defined as the measure of the shaft's stiffness in torsion, which is essential in designing hollow shafts to withstand twisting forces and resist deformation and is represented as G_h = 584*Mt_hollowshaft*L_h/(θ_hollow*d_o^4*(1-C^4)) or Modulus of Rigidity of Hollow Shaft = 584*Torsional Moment in Hollow Shaft*Length of Hollow Shaft/(Angle of Twist of Hollow Shaft*Outer Diameter of Hollow Shaft^4*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)). Torsional Moment in Hollow Shaft is the reaction induced in a structural shaft hollow element when an external force or moment is applied to the element, causing the element to twist, Length of Hollow Shaft is the distance between two ends of a hollow shaft, Angle of Twist of Hollow Shaft is the angle through which the fixed end of a hollow shaft rotates with respect to the free end, Outer Diameter of Hollow Shaft is defined as the length of the longest chord of the surface of the hollow circular shaft & The Ratio of Inner to Outer Diameter of Hollow Shaft is defined as the inner diameter of the shaft divided by the outer diameter.

How to calculate Modulus of Rigidity given Angle of Twist of Hollow Shaft on basis of Torsional Rigidity?

Modulus of Rigidity given Angle of Twist of Hollow Shaft on basis of Torsional Rigidity formula is defined as the measure of the shaft's stiffness in torsion, which is essential in designing hollow shafts to withstand twisting forces and resist deformation is calculated using Modulus of Rigidity of Hollow Shaft = 584*Torsional Moment in Hollow Shaft*Length of Hollow Shaft/(Angle of Twist of Hollow Shaft*Outer Diameter of Hollow Shaft^4*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)). To calculate Modulus of Rigidity given Angle of Twist of Hollow Shaft on basis of Torsional Rigidity, you need Torsional Moment in Hollow Shaft (Mt_hollowshaft), Length of Hollow Shaft (L_h), Angle of Twist of Hollow Shaft (θ_hollow), Outer Diameter of Hollow Shaft (d_o) & Ratio of Inner to Outer Diameter of Hollow Shaft (C). With our tool, you need to enter the respective value for Torsional Moment in Hollow Shaft, Length of Hollow Shaft, Angle of Twist of Hollow Shaft, Outer Diameter of Hollow Shaft & Ratio of Inner to Outer Diameter of Hollow Shaft 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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