Total Angle of Twist 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%
✖Shaft Length is the distance between two ends of shaft.ⓘ Shaft Length [L_shaft]			+10% -10%
✖Shear Modulus in Pa is the slope of the linear elastic region of the shear stress-strain curve.ⓘ Shear Modulus [G_pa]			+10% -10%
✖The Polar moment of Inertia is a shaft or beam's resistance to being distorted by torsion, as a function of its shape.ⓘ Polar Moment of Inertia [J]			+10% -10%

✖The Total Angle of Twist is the angle through which a radial section of a body (as a wire or a shaft) deflects from its normal position when the body is subjected to torque.ⓘ Total Angle of Twist [𝜽]

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Formula

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Total Angle of Twist

Formula

`"𝜽" = ("τ"*"L"_{"shaft"})/("G"_{"pa"}*"J")`

Example

`"2.219914°"=("50N*m"*"0.42m")/("10.00015Pa"*"54.2m⁴")`

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Total Angle of Twist Solution

STEP 0: Pre-Calculation Summary

Formula Used

Total Angle of Twist = (Torque Exerted on Wheel*Shaft Length)/(Shear Modulus*Polar Moment of Inertia)
𝜽 = (τ*L_shaft)/(G_pa*J)
This formula uses 5 Variables

Variables Used

Total Angle of Twist - (Measured in Radian) - The Total Angle of Twist is the angle through which a radial section of a body (as a wire or a shaft) deflects from its normal position when the body is subjected to torque.
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.
Shaft Length - (Measured in Meter) - Shaft Length is the distance between two ends of shaft.
Shear Modulus - (Measured in Pascal) - Shear Modulus in Pa is the slope of the linear elastic region of the shear stress-strain curve.
Polar Moment of Inertia - (Measured in Meter⁴) - The Polar moment of Inertia is a shaft or beam's resistance to being distorted by torsion, as a function of its shape.

STEP 1: Convert Input(s) to Base Unit

Torque Exerted on Wheel: 50 Newton Meter --> 50 Newton Meter No Conversion Required
Shaft Length: 0.42 Meter --> 0.42 Meter No Conversion Required
Shear Modulus: 10.00015 Pascal --> 10.00015 Pascal No Conversion Required
Polar Moment of Inertia: 54.2 Meter⁴ --> 54.2 Meter⁴ No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

𝜽 = (τ*L_shaft)/(G_pa*J) --> (50*0.42)/(10.00015*54.2)

Evaluating ... ...

𝜽 = 0.0387448062817803

STEP 3: Convert Result to Output's Unit

0.0387448062817803 Radian -->2.21991387799839 Degree (Check conversion here)

FINAL ANSWER

2.21991387799839 ≈ 2.219914 Degree <-- Total Angle of Twist

(Calculation completed in 00.004 seconds)

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Created by Pragati Jaju

College Of Engineering (COEP), Pune

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National Institute Of Technology (NIT), Hamirpur

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< 18 Stress and Strain Calculators

Elongation Circular Tapered Bar

Go Elongation = (4*Load*Length of Bar)/(pi*Diameter of Bigger End*Diameter of Smaller End*Elastic Modulus)

Total Angle of Twist

Go Total Angle of Twist = (Torque Exerted on Wheel*Shaft Length)/(Shear Modulus*Polar Moment of Inertia)

Moment of Inertia for Hollow Circular Shaft

Go Polar Moment of Inertia = pi/32*(Outer Diameter of Hollow Circular Section^(4)-Inner Diameter of Hollow Circular Section^(4))

Equivalent Bending Moment

Go Equivalent Bending Moment = Bending Moment+sqrt(Bending Moment^(2)+Torque Exerted on Wheel^(2))

Deflection of Fixed Beam with Uniformly Distributed Load

Go Deflection of Beam = (Width of Beam*Beam Length^4)/(384*Elastic Modulus*Moment of Inertia)

Deflection of Fixed Beam with Load at Center

Go Deflection of Beam = (Width of Beam*Beam Length^3)/(192*Elastic Modulus*Moment of Inertia)

Elongation of Prismatic Bar due to its Own Weight

Go Elongation = (2*Load*Length of Bar)/(Area of Prismatic Bar*Elastic Modulus)

Axial Elongation of Prismatic Bar due to External Load

Go Elongation = (Load*Length of Bar)/(Area of Prismatic Bar*Elastic Modulus)

Hooke's Law

Go Young's Modulus = (Load*Elongation)/(Area of Base*Initial Length)

Equivalent Torsional Moment

Go Equivalent Torsion Moment = sqrt(Bending Moment^(2)+Torque Exerted on Wheel^(2))

Rankine's Formula for Columns

Go Rankine’s Critical Load = 1/(1/Euler’s Buckling Load+1/Ultimate Crushing Load for Columns)

Slenderness Ratio

Go Slenderness Ratio = Effective Length/Least Radius of Gyration

Moment of Inertia about Polar Axis

Go Polar Moment of Inertia = (pi*Diameter of Shaft^(4))/32

Bulk Modulus given Volume Stress and Strain

Go Bulk Modulus = Volume Stress/Volumetric Strain

Shear Modulus

Go Shear Modulus = Shear Stress/Shear Strain

Bulk Modulus given Bulk Stress and Strain

Go Bulk Modulus = Bulk Stress/Bulk Strain

Young's Modulus

Go Young's Modulus = Stress/Strain

Elastic Modulus

Go Young's Modulus = Stress/Strain

Total Angle of Twist Formula

Total Angle of Twist = (Torque Exerted on Wheel*Shaft Length)/(Shear Modulus*Polar Moment of Inertia)
𝜽 = (τ*L_shaft)/(G_pa*J)

What is angle of twist?

For a shaft under torsional loading, the angle through which fixed end of a shaft rotates with respect to the free end is called the angle of twist.The angle of twist on a line shaft involves its geometry, and the torque applied to it. Engineers use this calculation to determine the rotational displacement of a shaft given a certain load.

How to Calculate Total Angle of Twist?

Total Angle of Twist calculator uses Total Angle of Twist = (Torque Exerted on Wheel*Shaft Length)/(Shear Modulus*Polar Moment of Inertia) to calculate the Total Angle of Twist, The Total Angle of Twist is defined as the angle through which a radial section of a body (as a wire or a shaft) deflects from its normal position when the body is subjected to torque. Total Angle of Twist is denoted by 𝜽 symbol.

How to calculate Total Angle of Twist using this online calculator? To use this online calculator for Total Angle of Twist, enter Torque Exerted on Wheel (τ), Shaft Length (L_shaft), Shear Modulus (G_pa) & Polar Moment of Inertia (J) and hit the calculate button. Here is how the Total Angle of Twist calculation can be explained with given input values -> 127.1917 = (50*0.42)/(10.00015*54.2).

FAQ

What is Total Angle of Twist?

The Total Angle of Twist is defined as the angle through which a radial section of a body (as a wire or a shaft) deflects from its normal position when the body is subjected to torque and is represented as 𝜽 = (τ*L_shaft)/(G_pa*J) or Total Angle of Twist = (Torque Exerted on Wheel*Shaft Length)/(Shear Modulus*Polar Moment of Inertia). 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, Shaft Length is the distance between two ends of shaft, Shear Modulus in Pa is the slope of the linear elastic region of the shear stress-strain curve & The Polar moment of Inertia is a shaft or beam's resistance to being distorted by torsion, as a function of its shape.

How to calculate Total Angle of Twist?

The Total Angle of Twist is defined as the angle through which a radial section of a body (as a wire or a shaft) deflects from its normal position when the body is subjected to torque is calculated using Total Angle of Twist = (Torque Exerted on Wheel*Shaft Length)/(Shear Modulus*Polar Moment of Inertia). To calculate Total Angle of Twist, you need Torque Exerted on Wheel (τ), Shaft Length (L_shaft), Shear Modulus (G_pa) & Polar Moment of Inertia (J). With our tool, you need to enter the respective value for Torque Exerted on Wheel, Shaft Length, Shear Modulus & Polar Moment of Inertia 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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