Length of Shaft given Total Angle of Twist for Shaft Calculator

✖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 [G]			+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%
✖Diameter of shaft at left end is the shorter side diameter of tapering shaft.ⓘ Diameter of shaft at left end [D₁]			+10% -10%
✖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 given Total Angle of Twist for Shaft [L]

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Length of Shaft given Total Angle of Twist for Shaft Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))
L = (θ*pi*G*(D₂-D₁))/(32*τ*(1/(D₁^3)-1/(D₂^3)))
This formula uses 1 Constants, 6 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Length of Shaft - (Measured in Meter) - The Length of Shaft is the distance between two ends of 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.
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.
Diameter of shaft at right end - (Measured in Meter) - Diameter of shaft at right end is the longer side diameter of tapering shaft.
Diameter of shaft at left end - (Measured in Meter) - Diameter of shaft at left end is the shorter side diameter of tapering shaft.
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.

STEP 1: Convert Input(s) to Base Unit

Angle of twist: 30 --> No Conversion Required
Modulus of rigidity of Shaft: 4E-05 Megapascal --> 40 Pascal (Check conversion here)
Diameter of shaft at right end: 5000 Millimeter --> 5 Meter (Check conversion here)
Diameter of shaft at left end: 3000 Millimeter --> 3 Meter (Check conversion here)
Torque Exerted on Wheel: 50 Newton Meter --> 50 Newton Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

L = (θ*pi*G*(D₂-D₁))/(32*τ*(1/(D₁^3)-1/(D₂^3))) --> (30*pi*40*(5-3))/(32*50*(1/(3^3)-1/(5^3)))

Evaluating ... ...

L = 162.288906212228

STEP 3: Convert Result to Output's Unit

162.288906212228 Meter -->162288.906212228 Millimeter (Check conversion here)

FINAL ANSWER

162288.906212228 ≈ 162288.9 Millimeter <-- Length of Shaft

(Calculation completed in 00.004 seconds)

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National Institute Of Technology (NIT), Hamirpur

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< Torsion of Tapering Shafts Calculators

Total Angle of Twist for Shaft

LaTeX 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

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

Diameter of Shaft at Left End

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

Torque on Tapering Shaft

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

Length of Shaft given Total Angle of Twist for Shaft Formula

LaTeX Go

What is angle of twist and angle of shear?

The angle of shear is given by the 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 Length of Shaft given Total Angle of Twist for Shaft?

Length of Shaft given Total Angle of Twist for Shaft calculator uses 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))) to calculate the Length of Shaft, Length of shaft given total angle of twist for shaft is defined as the measurement or extent of something from end to end. Length of Shaft is denoted by L symbol.

How to calculate Length of Shaft given Total Angle of Twist for Shaft using this online calculator? To use this online calculator for Length of Shaft given Total Angle of Twist for Shaft, enter Angle of twist (θ), Modulus of rigidity of Shaft (G), Diameter of shaft at right end (D₂), Diameter of shaft at left end (D₁) & Torque Exerted on Wheel (τ) and hit the calculate button. Here is how the Length of Shaft given Total Angle of Twist for Shaft calculation can be explained with given input values -> 1.6E+8 = (30*pi*40*(5-3))/(32*50*(1/(3^3)-1/(5^3))).

FAQ

What is Length of Shaft given Total Angle of Twist for Shaft?

Length of shaft given total angle of twist for shaft is defined as the measurement or extent of something from end to end and is represented as L = (θ*pi*G*(D₂-D₁))/(32*τ*(1/(D₁^3)-1/(D₂^3))) or 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))). Angle of twist is the angle through which the fixed end of a shaft rotates with respect to the free end, 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, Diameter of shaft at right end is the longer side diameter of tapering shaft, Diameter of shaft at left end is the shorter side diameter of tapering shaft & 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.

How to calculate Length of Shaft given Total Angle of Twist for Shaft?

Length of shaft given total angle of twist for shaft is defined as the measurement or extent of something from end to end is calculated using 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))). To calculate Length of Shaft given Total Angle of Twist for Shaft, you need Angle of twist (θ), Modulus of rigidity of Shaft (G), Diameter of shaft at right end (D₂), Diameter of shaft at left end (D₁) & Torque Exerted on Wheel (τ). With our tool, you need to enter the respective value for Angle of twist, Modulus of rigidity of Shaft, Diameter of shaft at right end, Diameter of shaft at left end & Torque Exerted on Wheel 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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