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Total Angle of Twist Formula

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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. Check FAQs

𝜽 = \frac{T shaft \cdot L shaft}{G pa \cdot J}

𝜽 - Total Angle of Twist?T_shaft - Torque?L_shaft - Shaft Length?G_pa - Shear Modulus?J - Polar Moment of Inertia?

Total Angle of Twist Example

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Here is how the Total Angle of Twist equation looks like with Values.

Here is how the Total Angle of Twist equation looks like with Units.

Here is how the Total Angle of Twist equation looks like.

2.1199 = \frac{0.625 \cdot 0.42}{34.85 \cdot 0.2036}

2.1199° = \frac{0.625N*m \cdot 0.42m}{34.85Pa \cdot 0.2036m⁴}

2.1199 = \frac{0.625 \cdot 0.42}{34.85 \cdot 0.2036}

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Total Angle of Twist Solution

Follow our step by step solution on how to calculate Total Angle of Twist?

FIRST Step Consider the formula

𝜽 = \frac{T shaft \cdot L shaft}{G pa \cdot J}

Next Step Substitute values of Variables

∴

𝜽 = \frac{0.625N*m \cdot 0.42m}{34.85Pa \cdot 0.2036m⁴}

Next Step Prepare to Evaluate

∴

𝜽 = \frac{0.625 \cdot 0.42}{34.85 \cdot 0.2036}

Next Step Evaluate

∴

𝜽 = 0.0370000304809775rad

Next Step Convert to Output's Unit

∴

𝜽 = 2.11994558841581°

LAST Step Rounding Answer

∴

𝜽 = 2.1199°

Total Angle of Twist Formula Elements

Variables

Total Angle of Twist

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.

Symbol: 𝜽

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Total Angle of Twist

Torque

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.

Symbol: T_shaft

Measurement: TorqueUnit: N*m

Note: Value should be greater than 0.

Formulas to find Torque

Shaft Length

Shaft Length is the distance between two ends of shaft.

Symbol: L_shaft

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Shaft Length

Shear Modulus

Shear Modulus is the slope of the linear elastic region of the shear stress-strain curve.

Symbol: G_pa

Measurement: StressUnit: Pa

Note: Value should be greater than 0.

Formulas to find Shear Modulus

Polar Moment of Inertia

The Polar moment of Inertia is a shaft or beam's resistance to being distorted by torsion, as a function of its shape.

Symbol: J

Measurement: Second Moment of AreaUnit: m⁴

Note: Value can be positive or negative.

Formulas to find Polar Moment of Inertia

Other formulas in Stress and Strain category

Go Elongation Circular Tapered Bar

Δ c = \frac{4 \cdot W load \cdot L bar}{π \cdot D 1 \cdot D 2 \cdot e}

Go Moment of Inertia for Hollow Circular Shaft

J h = \frac{π}{32} \cdot ({d ho}^{4} - {d hi}^{4})

Go Moment of Inertia about Polar Axis

J = \frac{π \cdot {d s}^{4}}{32}

Go Elongation of Prismatic Bar due to its Own Weight

Δ p = \frac{W load \cdot L bar}{2 \cdot A \cdot e}

How to Evaluate Total Angle of Twist?

Total Angle of Twist evaluator uses Total Angle of Twist = (Torque*Shaft Length)/(Shear Modulus*Polar Moment of Inertia) to evaluate 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 evaluate Total Angle of Twist using this online evaluator? To use this online evaluator 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.

FAQs on Total Angle of Twist

What is the formula to find Total Angle of Twist?

The formula of Total Angle of Twist is expressed as Total Angle of Twist = (Torque*Shaft Length)/(Shear Modulus*Polar Moment of Inertia). Here is an example- 121.4639 = (0.625*0.42)/(34.85*0.203575).

How to calculate Total Angle of Twist?

With Torque (T_shaft), Shaft Length (L_shaft), Shear Modulus (G_pa) & Polar Moment of Inertia (J) we can find Total Angle of Twist using the formula - Total Angle of Twist = (Torque*Shaft Length)/(Shear Modulus*Polar Moment of Inertia).

Can the Total Angle of Twist be negative?

No, the Total Angle of Twist, measured in Angle cannot be negative.

Which unit is used to measure Total Angle of Twist?

Total Angle of Twist is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which Total Angle of Twist can be measured.

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Total Angle of Twist Formula

Total Angle of Twist Example

Total Angle of Twist Solution

Total Angle of Twist Formula Elements

Other formulas in Stress and Strain category

How to Evaluate Total Angle of Twist?

FAQs on Total Angle of Twist

Variable Name