Modulus of Rigidity of Shaft given Total Angle of Twist for Shaft Calculator

✖Torque Exerted on Wheel is described as the turning effect of force on the axis of rotation. In brief, it is a moment of force. It is characterized by τ.ⓘ Torque Exerted on Wheel [τ]			+10% -10%
✖The Length of Shaft is the distance between two ends of shaft.ⓘ Length of Shaft [L]			+10% -10%
✖Diameter of shaft at left end is the shorter side diameter of tapering shaft.ⓘ Diameter of shaft at left end [D₁]			+10% -10%
✖Diameter of shaft at right end is the longer side diameter of tapering shaft.ⓘ Diameter of shaft at right end [D₂]			+10% -10%
✖Angle of twist is the angle through which the fixed end of a shaft rotates with respect to the free end.ⓘ Angle of twist [θ]			+10% -10%

✖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 a body is.ⓘ Modulus of Rigidity of Shaft given Total Angle of Twist for Shaft [G]

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Formula

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Modulus of Rigidity of Shaft given Total Angle of Twist for Shaft

Formula

`"G" = (32*"τ"*"L"*(1/("D"_{"1"}^3)-1/("D"_{"2"}^3)))/(pi*"θ"*("D"_{"2"}-"D"_{"1"}))`

Example

`"1.7E^-6MPa"=(32*"50N*m"*"7000mm"*(1/(("3000mm")^3)-1/(("5000mm")^3)))/(pi*"30"*("5000mm"-"3000mm"))`

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Modulus of Rigidity of Shaft given Total Angle of Twist for Shaft Solution

STEP 0: Pre-Calculation Summary

Formula Used

Modulus of rigidity of Shaft = (32*Torque Exerted on Wheel*Length of Shaft*(1/(Diameter of shaft at left end^3)-1/(Diameter of shaft at right end^3)))/(pi*Angle of twist*(Diameter of shaft at right end-Diameter of shaft at left end))
G = (32*τ*L*(1/(D₁^3)-1/(D₂^3)))/(pi*θ*(D₂-D₁))
This formula uses 1 Constants, 6 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

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 a body is.
Torque Exerted on Wheel - (Measured in Newton Meter) - Torque Exerted on Wheel is described as the turning effect of force on the axis of rotation. In brief, it is a moment of force. It is characterized by τ.
Length of Shaft - (Measured in Meter) - The Length of Shaft is the distance between two ends of shaft.
Diameter of shaft at left end - (Measured in Meter) - Diameter of shaft at left end is the shorter side diameter of tapering shaft.
Diameter of shaft at right end - (Measured in Meter) - Diameter of shaft at right end is the longer side diameter of tapering shaft.
Angle of twist - Angle of twist is the angle through which the fixed end of a shaft rotates with respect to the free end.

STEP 1: Convert Input(s) to Base Unit

Torque Exerted on Wheel: 50 Newton Meter --> 50 Newton Meter No Conversion Required
Length of Shaft: 7000 Millimeter --> 7 Meter (Check conversion here)
Diameter of shaft at left end: 3000 Millimeter --> 3 Meter (Check conversion here)
Diameter of shaft at right end: 5000 Millimeter --> 5 Meter (Check conversion here)
Angle of twist: 30 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

G = (32*τ*L*(1/(D₁^3)-1/(D₂^3)))/(pi*θ*(D₂-D₁)) --> (32*50*7*(1/(3^3)-1/(5^3)))/(pi*30*(5-3))

Evaluating ... ...

G = 1.72531817814977

STEP 3: Convert Result to Output's Unit

1.72531817814977 Pascal -->1.72531817814977E-06 Megapascal (Check conversion here)

FINAL ANSWER

1.72531817814977E-06 ≈ 1.7E-6 Megapascal <-- Modulus of rigidity of Shaft

(Calculation completed in 00.020 seconds)

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< 7 Torsion of Tapering Shafts Calculators

Modulus of Rigidity of Shaft given Total Angle of Twist for Shaft

Go Modulus of rigidity of Shaft = (32*Torque Exerted on Wheel*Length of Shaft*(1/(Diameter of shaft at left end^3)-1/(Diameter of shaft at right end^3)))/(pi*Angle of twist*(Diameter of shaft at right end-Diameter of shaft at left end))

Torque on Shaft given Total Angle of Twist for Shaft

Go Torque Exerted on Wheel = (Angle of twist*pi*Modulus of rigidity of Shaft*(Diameter of shaft at right end-Diameter of shaft at left end))/(32*Length of Shaft*(1/(Diameter of shaft at left end^3)-1/(Diameter of shaft at right end^3)))

Length of Shaft given Total Angle of Twist for Shaft

Go Length of Shaft = (Angle of twist*pi*Modulus of rigidity of Shaft*(Diameter of shaft at right end-Diameter of shaft at left end))/(32*Torque Exerted on Wheel*(1/(Diameter of shaft at left end^3)-1/(Diameter of shaft at right end^3)))

Total Angle of Twist for Shaft

Go Angle of twist = (32*Torque Exerted on Wheel*Length of Shaft*(1/(Diameter of shaft at left end^3)-1/(Diameter of shaft at right end^3)))/(pi*Modulus of rigidity of Shaft*(Diameter of shaft at right end-Diameter of shaft at left end))

Shear Stress on Left Surface of Shaft

Go Shear stress on surface of shaft = (16*Torque Exerted on Wheel)/(pi*Diameter of Shaft)

Diameter of Shaft at Left End

Go Diameter of Shaft = (16*Torque Exerted on Wheel)/(Shear stress on surface of shaft*pi)

Torque on Tapering Shaft

Go Torque Exerted on Wheel = (Shear stress on surface of shaft*pi*Diameter of Shaft)/16

Modulus of Rigidity of Shaft given Total Angle of Twist for Shaft Formula

What is angle of twist and angle of shear?

The angle of shear is given by angle of the deformation that comes up on the sides when deformation force or shearing stress is exerted on an object. The angle of twist is given as the angle along with which an element of a rotating machine rotates or twists w.r.t its free end.

How to Calculate Modulus of Rigidity of Shaft given Total Angle of Twist for Shaft?

Modulus of Rigidity of Shaft given Total Angle of Twist for Shaft calculator uses Modulus of rigidity of Shaft = (32*Torque Exerted on Wheel*Length of Shaft*(1/(Diameter of shaft at left end^3)-1/(Diameter of shaft at right end^3)))/(pi*Angle of twist*(Diameter of shaft at right end-Diameter of shaft at left end)) to calculate the Modulus of rigidity of Shaft, Modulus of rigidity of shaft given total angle of twist for shaft 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 of Shaft given Total Angle of Twist for Shaft using this online calculator? To use this online calculator for Modulus of Rigidity of Shaft given Total Angle of Twist for Shaft, enter Torque Exerted on Wheel (τ), Length of Shaft (L), Diameter of shaft at left end (D₁), Diameter of shaft at right end (D₂) & Angle of twist (θ) and hit the calculate button. Here is how the Modulus of Rigidity of Shaft given Total Angle of Twist for Shaft calculation can be explained with given input values -> 1.7E-12 = (32*50*7*(1/(3^3)-1/(5^3)))/(pi*30*(5-3)).

FAQ

What is Modulus of Rigidity of Shaft given Total Angle of Twist for Shaft?

Modulus of rigidity of shaft given total angle of twist for shaft 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 = (32*τ*L*(1/(D₁^3)-1/(D₂^3)))/(pi*θ*(D₂-D₁)) or Modulus of rigidity of Shaft = (32*Torque Exerted on Wheel*Length of Shaft*(1/(Diameter of shaft at left end^3)-1/(Diameter of shaft at right end^3)))/(pi*Angle of twist*(Diameter of shaft at right end-Diameter of shaft at left end)). Torque Exerted on Wheel is described as the turning effect of force on the axis of rotation. In brief, it is a moment of force. It is characterized by τ, The Length of Shaft is the distance between two ends of shaft, Diameter of shaft at left end is the shorter side diameter of tapering shaft, Diameter of shaft at right end is the longer side diameter of tapering shaft & Angle of twist is the angle through which the fixed end of a shaft rotates with respect to the free end.

How to calculate Modulus of Rigidity of Shaft given Total Angle of Twist for Shaft?

Modulus of rigidity of shaft given total angle of twist for shaft 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 = (32*Torque Exerted on Wheel*Length of Shaft*(1/(Diameter of shaft at left end^3)-1/(Diameter of shaft at right end^3)))/(pi*Angle of twist*(Diameter of shaft at right end-Diameter of shaft at left end)). To calculate Modulus of Rigidity of Shaft given Total Angle of Twist for Shaft, you need Torque Exerted on Wheel (τ), Length of Shaft (L), Diameter of shaft at left end (D₁), Diameter of shaft at right end (D₂) & Angle of twist (θ). With our tool, you need to enter the respective value for Torque Exerted on Wheel, Length of Shaft, Diameter of shaft at left end, Diameter of shaft at right end & Angle of twist 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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