Angle of twist of solid cylindrical rod in degrees Solution

STEP 0: Pre-Calculation Summary
Formula Used
Angle of twist of shaft in degree = (584*Torsional moment on shaft*Length of Shaft/(Modulus of Rigidity*(Diameter of circular section of shaft^4)))*(pi/180)
𝜽d = (584*τ*l/(C*(dc^4)))*(pi/180)
This formula uses 1 Constants, 5 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Variables Used
Angle of twist of shaft in degree - (Measured in Radian) - Angle of twist of shaft in degree is the angle through which the fixed end of a shaft rotates with respect to the free end.
Torsional moment on shaft - (Measured in Newton Meter) - Torsional moment on shaft is described as the turning effect of force on the axis of rotation. In brief, it is a moment of force.
Length of Shaft - (Measured in Meter) - Length of shaft is defined as the distance between the two opposite ends of a shaft.
Modulus of Rigidity - (Measured in Pascal) - Modulus of Rigidity 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 circular section of shaft - (Measured in Meter) - Diameter of circular section of shaft is the diameter of the circular cross-section of the specimen.
STEP 1: Convert Input(s) to Base Unit
Torsional moment on shaft: 51000 Newton Millimeter --> 51 Newton Meter (Check conversion here)
Length of Shaft: 1100 Millimeter --> 1.1 Meter (Check conversion here)
Modulus of Rigidity: 84000 Newton per Square Millimeter --> 84000000000 Pascal (Check conversion here)
Diameter of circular section of shaft: 34 Millimeter --> 0.034 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
𝜽d = (584*τ*l/(C*(dc^4)))*(pi/180) --> (584*51*1.1/(84000000000*(0.034^4)))*(pi/180)
Evaluating ... ...
𝜽d = 0.00509399039483966
STEP 3: Convert Result to Output's Unit
0.00509399039483966 Radian -->0.291864150504547 Degree (Check conversion here)
FINAL ANSWER
0.291864150504547 0.291864 Degree <-- Angle of twist of shaft in degree
(Calculation completed in 00.004 seconds)

Credits

Created by Vaibhav Malani
National Institute of Technology (NIT), Tiruchirapalli
Vaibhav Malani has created this Calculator and 600+ more calculators!
Verified by Anshika Arya
National Institute Of Technology (NIT), Hamirpur
Anshika Arya has verified this Calculator and 2500+ more calculators!

9 Design of Shaft for Torsional Moment Calculators

Angle of twist of hollow cylindrical rod in degrees
Go Angle of twist of shaft in degree = (584*Torsional moment on shaft*Length of Shaft/(Modulus of Rigidity*((Outer Diameter of Hollow Circular Section^4)-(Inner Diameter of Hollow Circular Section^4))))*(pi/180)
Angle of twist of solid cylindrical rod in degrees
Go Angle of twist of shaft in degree = (584*Torsional moment on shaft*Length of Shaft/(Modulus of Rigidity*(Diameter of circular section of shaft^4)))*(pi/180)
Angle of twist of shaft in radians given torque, length of shaft, polar moment of inertia
Go Angle of twist of shaft = (Torsional moment on shaft*Length of Shaft)/(Polar moment of inertia for circular section*Modulus of Rigidity)
Polar moment of inertia of shaft given shear stress and torsional moment
Go Polar moment of inertia for circular section = Torsional moment on shaft*Radial Distance from Axis of Rotation/Torsional shear stress in twisted shaft
Torsional shear stress in shaft due to torsional moment
Go Torsional shear stress in twisted shaft = Torsional moment on shaft*Radial Distance from Axis of Rotation/Polar moment of inertia for circular section
Torsional moment on shaft given shear stress
Go Torsional moment on shaft = Torsional shear stress in twisted shaft*Polar moment of inertia for circular section/Radial Distance from Axis of Rotation
Polar moment of inertia of hollow circular cross-section
Go Polar moment of inertia for circular section = pi*((Outer Diameter of Hollow Circular Section^4)-(Inner Diameter of Hollow Circular Section^4))/32
Power transmitted by shaft given speed of shaft and torque
Go Power = 2*pi*Speed of Shaft in RPM*Torsional moment on shaft/(60)
Polar moment of inertia of circular cross section
Go Polar moment of inertia for circular section = pi*(Diameter of circular section of shaft^4)/32

Angle of twist of solid cylindrical rod in degrees Formula

Angle of twist of shaft in degree = (584*Torsional moment on shaft*Length of Shaft/(Modulus of Rigidity*(Diameter of circular section of shaft^4)))*(pi/180)
𝜽d = (584*τ*l/(C*(dc^4)))*(pi/180)

What is angle of twist?

For a shaft under torsional loading, the angle through which the fixed end of a shaft rotates with respect to the free end is called the angle of twist.

How to Calculate Angle of twist of solid cylindrical rod in degrees?

Angle of twist of solid cylindrical rod in degrees calculator uses Angle of twist of shaft in degree = (584*Torsional moment on shaft*Length of Shaft/(Modulus of Rigidity*(Diameter of circular section of shaft^4)))*(pi/180) to calculate the Angle of twist of shaft in degree, The angle of twist of solid cylindrical rod in degrees formula is defined as the angle through which the solid cylindrical rod is twisted about its central axis when torque is applied onto it or torsion is acting onto the rod. Angle of twist of shaft in degree is denoted by 𝜽d symbol.

How to calculate Angle of twist of solid cylindrical rod in degrees using this online calculator? To use this online calculator for Angle of twist of solid cylindrical rod in degrees, enter Torsional moment on shaft (τ), Length of Shaft (l), Modulus of Rigidity (C) & Diameter of circular section of shaft (dc) and hit the calculate button. Here is how the Angle of twist of solid cylindrical rod in degrees calculation can be explained with given input values -> 16.72258 = (584*51*1.1/(84000000000*(0.034^4)))*(pi/180).

FAQ

What is Angle of twist of solid cylindrical rod in degrees?
The angle of twist of solid cylindrical rod in degrees formula is defined as the angle through which the solid cylindrical rod is twisted about its central axis when torque is applied onto it or torsion is acting onto the rod and is represented as 𝜽d = (584*τ*l/(C*(dc^4)))*(pi/180) or Angle of twist of shaft in degree = (584*Torsional moment on shaft*Length of Shaft/(Modulus of Rigidity*(Diameter of circular section of shaft^4)))*(pi/180). Torsional moment on shaft is described as the turning effect of force on the axis of rotation. In brief, it is a moment of force, Length of shaft is defined as the distance between the two opposite ends of a shaft, Modulus of Rigidity 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 circular section of shaft is the diameter of the circular cross-section of the specimen.
How to calculate Angle of twist of solid cylindrical rod in degrees?
The angle of twist of solid cylindrical rod in degrees formula is defined as the angle through which the solid cylindrical rod is twisted about its central axis when torque is applied onto it or torsion is acting onto the rod is calculated using Angle of twist of shaft in degree = (584*Torsional moment on shaft*Length of Shaft/(Modulus of Rigidity*(Diameter of circular section of shaft^4)))*(pi/180). To calculate Angle of twist of solid cylindrical rod in degrees, you need Torsional moment on shaft (τ), Length of Shaft (l), Modulus of Rigidity (C) & Diameter of circular section of shaft (dc). With our tool, you need to enter the respective value for Torsional moment on shaft, Length of Shaft, Modulus of Rigidity & Diameter of circular section of shaft and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Angle of twist of shaft in degree?
In this formula, Angle of twist of shaft in degree uses Torsional moment on shaft, Length of Shaft, Modulus of Rigidity & Diameter of circular section of shaft. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Angle of twist of shaft in degree = (584*Torsional moment on shaft*Length of Shaft/(Modulus of Rigidity*((Outer Diameter of Hollow Circular Section^4)-(Inner Diameter of Hollow Circular Section^4))))*(pi/180)
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!