Maximum permissible shear stress Solution

STEP 0: Pre-Calculation Summary
Formula Used
Maximum Shear Stress = Torque*Radius of Shaft/Polar Moment of Inertia
τmax = T*R/J
This formula uses 4 Variables
Variables Used
Maximum Shear Stress - (Measured in Pascal) - Maximum Shear Stress is the greatest extent a shear force can be concentrated in a small area.
Torque - (Measured in Newton Meter) - Torque is a measure of the force that can cause an object to rotate about an axis.
Radius of Shaft - (Measured in Millimeter) - The Radius of Shaft is the line segment extending from the center of a circle or sphere to the circumference or bounding surface.
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.
STEP 1: Convert Input(s) to Base Unit
Torque: 28 Kilonewton Meter --> 28000 Newton Meter (Check conversion here)
Radius of Shaft: 110 Millimeter --> 110 Millimeter No Conversion Required
Polar Moment of Inertia: 0.0041 Meter⁴ --> 0.0041 Meter⁴ No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
τmax = T*R/J --> 28000*110/0.0041
Evaluating ... ...
τmax = 751219512.195122
STEP 3: Convert Result to Output's Unit
751219512.195122 Pascal -->751.219512195122 Megapascal (Check conversion here)
FINAL ANSWER
751.219512195122 751.2195 Megapascal <-- Maximum Shear Stress
(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

Maximum permissible shear stress Formula

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

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 meter, or in pounds per square inch while torque is expressed in newton meters or foot-pound force.

How to Calculate Maximum permissible shear stress?

Maximum permissible shear stress calculator uses Maximum Shear Stress = Torque*Radius of Shaft/Polar Moment of Inertia to calculate the Maximum Shear Stress, The Maximum permissible shear stress is defined as the limit up-to which the material can withstand shear. Maximum Shear Stress is denoted by τmax symbol.

How to calculate Maximum permissible shear stress using this online calculator? To use this online calculator for Maximum permissible shear stress, enter Torque (T), Radius of Shaft (R) & Polar Moment of Inertia (J) and hit the calculate button. Here is how the Maximum permissible shear stress calculation can be explained with given input values -> 7.5E-7 = 28000*0.11/0.0041.

FAQ

What is Maximum permissible shear stress?
The Maximum permissible shear stress is defined as the limit up-to which the material can withstand shear and is represented as τmax = T*R/J or Maximum Shear Stress = Torque*Radius of Shaft/Polar Moment of Inertia. Torque is a measure of the force that can cause an object to rotate about an axis, The Radius of Shaft is the line segment extending from the center of a circle or sphere to the circumference or bounding surface & 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.
How to calculate Maximum permissible shear stress?
The Maximum permissible shear stress is defined as the limit up-to which the material can withstand shear is calculated using Maximum Shear Stress = Torque*Radius of Shaft/Polar Moment of Inertia. To calculate Maximum permissible shear stress, you need Torque (T), Radius of Shaft (R) & Polar Moment of Inertia (J). With our tool, you need to enter the respective value for Torque, Radius of Shaft & 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.
How many ways are there to calculate Maximum Shear Stress?
In this formula, Maximum Shear Stress uses Torque, Radius of Shaft & Polar Moment of Inertia. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Maximum Shear Stress = (Modulus of Rigidity*(Angle of Twist)*Radius of Shaft)/Length of Shaft
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