Radius with known Maximum permissible shear stress Solution

STEP 0: Pre-Calculation Summary
Formula Used
Radius of Shaft = Maximum Shear Stress*Polar Moment of Inertia/Torque
R = τmax*J/T
This formula uses 4 Variables
Variables Used
Radius of Shaft - (Measured in Meter) - The Radius of Shaft is the line segment extending from the center of a circle or sphere to the circumference or bounding surface.
Maximum Shear Stress - (Measured in Pascal) - Maximum Shear Stress is the greatest extent a shear force can be concentrated in a small area.
Polar Moment of Inertia - (Measured in Meter⁴) - Polar Moment of Inertia is the moment of inertia of a cross-section with respect to its polar axis, which is an axis at right angles to the plane of the cross-section.
Torque - (Measured in Newton Meter) - Torque is a measure of the force that can cause an object to rotate about an axis.
STEP 1: Convert Input(s) to Base Unit
Maximum Shear Stress: 42 Megapascal --> 42000000 Pascal (Check conversion here)
Polar Moment of Inertia: 0.0041 Meter⁴ --> 0.0041 Meter⁴ No Conversion Required
Torque: 28 Kilonewton Meter --> 28000 Newton Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
R = τmax*J/T --> 42000000*0.0041/28000
Evaluating ... ...
R = 6.15
STEP 3: Convert Result to Output's Unit
6.15 Meter -->6150 Millimeter (Check conversion here)
FINAL ANSWER
6150 Millimeter <-- Radius of Shaft
(Calculation completed in 00.004 seconds)

Credits

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National Institute of Technology Karnataka (NITK), Surathkal
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18 Torsion Calculators

Shaft length for given maximum permissible shear stress and modulus of rigidity
Go Length of Shaft = (Modulus of Rigidity*(Angle of Twist)*Radius of Shaft)/Maximum Shear Stress
Maximum permissible shear stress for given Radius and modulus of rigidity
Go Maximum Shear Stress = (Modulus of Rigidity*(Angle of Twist)*Radius of Shaft)/Length of Shaft
Modulus of rigidity given maximum permissible shear stress
Go Modulus of Rigidity = (Maximum Shear Stress*Length of Shaft)/(Angle of Twist*Radius of Shaft)
Twist angle given maximum permissible shear stress
Go Angle of Twist = (Maximum Shear Stress*Length of Shaft)/(Radius of Shaft*Modulus of Rigidity)
Shaft length for given Polar MOI, Twisting Moment, Modulus of rigidity, and Twist angle
Go Length of Shaft = (Modulus of Rigidity*(Angle of Twist)*Polar Moment of Inertia)/Torque
Twist angle given Shaft length and modulus of rigidity
Go Angle of Twist = (Torque*Length of Shaft)/(Polar Moment of Inertia*Modulus of Rigidity)
Polar moment of inertia
Go Polar Moment of Inertia = (Torque*Length of Shaft)/(Angle of Twist*Modulus of Rigidity)
Modulus of rigidity
Go Modulus of Rigidity = (Torque*Length of Shaft)/(Angle of Twist*Polar Moment of Inertia)
Twisting Moment given Polar MOI and Twist Angle
Go Torque = (Modulus of Rigidity*Angle of Twist*Polar Moment of Inertia)/Length of Shaft
Polar Moment of Inertia of Hollow Shaft
Go Polar Moment of Inertia = pi/32*(Outer Diameter of Shaft^4-Inner Dia of Shaft^4)
Twisting Moment given Maximum Permissible Shear Stress
Go Torque = (Polar Moment of Inertia*Maximum Shear Stress)/Radius of Shaft
Polar Moment of Inertia given twisting moment along with maximum permissible shear stress
Go Polar Moment of Inertia = Torque*Radius of Shaft/Maximum Shear Stress
Radius given Twisting moment and Polar Moment of Inertia of shaft
Go Radius of Shaft = Maximum Shear Stress*Polar Moment of Inertia/Torque
Radius with known Maximum permissible shear stress
Go Radius of Shaft = Maximum Shear Stress*Polar Moment of Inertia/Torque
Maximum permissible shear stress
Go Maximum Shear Stress = Torque*Radius of Shaft/Polar Moment of Inertia
Radius given Torsional Section Modulus
Go Radius of Shaft = Polar Moment of Inertia/Polar Modulus
Radius of Shaft using Polar Modulus
Go Radius of Shaft = Polar Moment of Inertia/Polar Modulus
Torsional Section Modulus
Go Polar Modulus = Polar Moment of Inertia/Radius of Shaft

Radius with known Maximum permissible shear stress Formula

Radius of Shaft = Maximum Shear Stress*Polar Moment of Inertia/Torque
R = τmax*J/T

What is Torsion?

n the field of solid mechanics, torsion is the twisting of an object due to an applied torque. Torsion is expressed in either the Pascal, an SI unit for newtons per square metre, or in pounds per square inch while torque is expressed in newton metres or foot-pound force.

How to Calculate Radius with known Maximum permissible shear stress?

Radius with known Maximum permissible shear stress calculator uses Radius of Shaft = Maximum Shear Stress*Polar Moment of Inertia/Torque to calculate the Radius of Shaft, The Radius with known Maximum permissible shear stress is defined as the radius of the shaft cross-section. Radius of Shaft is denoted by R symbol.

How to calculate Radius with known Maximum permissible shear stress using this online calculator? To use this online calculator for Radius with known Maximum permissible shear stress, enter Maximum Shear Stress max), Polar Moment of Inertia (J) & Torque (T) and hit the calculate button. Here is how the Radius with known Maximum permissible shear stress calculation can be explained with given input values -> 6.15 = 42000000*0.0041/28000.

FAQ

What is Radius with known Maximum permissible shear stress?
The Radius with known Maximum permissible shear stress is defined as the radius of the shaft cross-section and is represented as R = τmax*J/T or Radius of Shaft = Maximum Shear Stress*Polar Moment of Inertia/Torque. Maximum Shear Stress is the greatest extent a shear force can be concentrated in a small area, Polar Moment of Inertia is the moment of inertia of a cross-section with respect to its polar axis, which is an axis at right angles to the plane of the cross-section & Torque is a measure of the force that can cause an object to rotate about an axis.
How to calculate Radius with known Maximum permissible shear stress?
The Radius with known Maximum permissible shear stress is defined as the radius of the shaft cross-section is calculated using Radius of Shaft = Maximum Shear Stress*Polar Moment of Inertia/Torque. To calculate Radius with known Maximum permissible shear stress, you need Maximum Shear Stress max), Polar Moment of Inertia (J) & Torque (T). With our tool, you need to enter the respective value for Maximum Shear Stress, Polar Moment of Inertia & Torque 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 Radius of Shaft?
In this formula, Radius of Shaft uses Maximum Shear Stress, Polar Moment of Inertia & Torque. We can use 3 other way(s) to calculate the same, which is/are as follows -
  • Radius of Shaft = Polar Moment of Inertia/Polar Modulus
  • Radius of Shaft = Maximum Shear Stress*Polar Moment of Inertia/Torque
  • Radius of Shaft = Polar Moment of Inertia/Polar Modulus
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