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Total Angle of Twist Calculator

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Stress and Strain Strain Stress

✖Torque 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 [T_shaft]			+10% -10%
✖Shaft Length is the distance between two ends of shaft.ⓘ Shaft Length [L_shaft]			+10% -10%
✖Shear Modulus 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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Total Angle of Twist Solution

STEP 0: Pre-Calculation Summary

Formula Used

Total Angle of Twist = (Torque*Shaft Length)/(Shear Modulus*Polar Moment of Inertia)
𝜽 = (T_shaft*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 - (Measured in Newton Meter) - Torque 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 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: 0.625 Newton Meter --> 0.625 Newton Meter No Conversion Required
Shaft Length: 0.42 Meter --> 0.42 Meter No Conversion Required
Shear Modulus: 34.85 Pascal --> 34.85 Pascal No Conversion Required
Polar Moment of Inertia: 0.203575 Meter⁴ --> 0.203575 Meter⁴ No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

𝜽 = (T_shaft*L_shaft)/(G_pa*J) --> (0.625*0.42)/(34.85*0.203575)

Evaluating ... ...

𝜽 = 0.0370000304809775

STEP 3: Convert Result to Output's Unit

0.0370000304809775 Radian -->2.11994558841581 Degree (Check conversion here)

FINAL ANSWER

2.11994558841581 ≈ 2.119946 Degree <-- Total Angle of Twist

(Calculation completed in 00.004 seconds)

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< Stress and Strain Calculators

Elongation Circular Tapered Bar

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

Moment of Inertia for Hollow Circular Shaft

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

Elongation of Prismatic Bar due to its Own Weight

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

Moment of Inertia about Polar Axis

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

Total Angle of Twist Formula

Total Angle of Twist = (Torque*Shaft Length)/(Shear Modulus*Polar Moment of Inertia)
𝜽 = (T_shaft*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*Shaft Length)/(Shear Modulus*Polar Moment of Inertia) to calculate the Total Angle of Twist, The Total Angle of Twist formula is defined as the measure of the twisting deformation of a shaft under torque, which is a critical parameter in the design and analysis of mechanical systems, particularly in the context of stress and strain. 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 (T_shaft), 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 -> 121.4639 = (0.625*0.42)/(34.85*0.203575).

FAQ

What is Total Angle of Twist?

The Total Angle of Twist formula is defined as the measure of the twisting deformation of a shaft under torque, which is a critical parameter in the design and analysis of mechanical systems, particularly in the context of stress and strain and is represented as 𝜽 = (T_shaft*L_shaft)/(G_pa*J) or Total Angle of Twist = (Torque*Shaft Length)/(Shear Modulus*Polar Moment of Inertia). Torque 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 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 formula is defined as the measure of the twisting deformation of a shaft under torque, which is a critical parameter in the design and analysis of mechanical systems, particularly in the context of stress and strain is calculated using Total Angle of Twist = (Torque*Shaft Length)/(Shear Modulus*Polar Moment of Inertia). To calculate Total Angle of Twist, you need Torque (T_shaft), 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, 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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