Maximum Shear Stress in Shaft Bending and Torsion Solution

STEP 0: Pre-Calculation Summary
Formula Used
Maximum Shear Stress in Shaft = sqrt((Normal Stress in Shaft/2)^2+Torsional Shear Stress in Shaft^2)
τsmax = sqrt((σx/2)^2+𝜏^2)
This formula uses 1 Functions, 3 Variables
Functions Used
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)
Variables Used
Maximum Shear Stress in Shaft - (Measured in Pascal) - Maximum Shear Stress in Shaft refers to the concentrated amount of force a shaft receives in a small area while in shear.
Normal Stress in Shaft - (Measured in Pascal) - Normal Stress in Shaft is the stress that occurs when a shaft is loaded by an axial force.
Torsional Shear Stress in Shaft - (Measured in Pascal) - Torsional Shear Stress in Shaft is the shear stress produced in the shaft due to the twisting.
STEP 1: Convert Input(s) to Base Unit
Normal Stress in Shaft: 250.6 Newton per Square Millimeter --> 250600000 Pascal (Check conversion here)
Torsional Shear Stress in Shaft: 16.29 Newton per Square Millimeter --> 16290000 Pascal (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
τsmax = sqrt((σx/2)^2+𝜏^2) --> sqrt((250600000/2)^2+16290000^2)
Evaluating ... ...
τsmax = 126354477.957847
STEP 3: Convert Result to Output's Unit
126354477.957847 Pascal -->126.354477957847 Newton per Square Millimeter (Check conversion here)
FINAL ANSWER
126.354477957847 126.3545 Newton per Square Millimeter <-- Maximum Shear Stress in Shaft
(Calculation completed in 00.004 seconds)

Credits

Created by Kethavath Srinath
Osmania University (OU), Hyderabad
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Indian Institute of Information Technology, Design and Manufacturing (IIITDM), Jabalpur
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16 Shaft Design on Strength Basis Calculators

Diameter of Shaft given Tensile Stress in Shaft
Go Diameter of Shaft on Strength Basis = sqrt(4*Axial Force on Shaft/(pi*Tensile Stress in Shaft))
Diameter of Shaft given Torsional Shear Stress in Shaft Pure Torsion
Go Diameter of Shaft on Strength Basis = (16*Torsional Moment in Shaft/(pi*Torsional Shear Stress in Shaft))^(1/3)
Torsional Moment given Torsional Shear Stress in Shaft Pure Torsion
Go Torsional Moment in Shaft = Torsional Shear Stress in Shaft*pi*(Diameter of Shaft on Strength Basis^3)/16
Torsional Shear Stress in Shaft Pure Torsion
Go Torsional Shear Stress in Shaft = 16*Torsional Moment in Shaft/(pi*Diameter of Shaft on Strength Basis^3)
Diameter of Shaft given Bending Stress Pure Bending
Go Diameter of Shaft on Strength Basis = ((32*Bending Moment in Shaft)/(pi*Bending Stress in Shaft))^(1/3)
Torsional Shear Stress given Principal Shear Stress in Shaft
Go Torsional Shear Stress in Shaft = sqrt(Principal Shear Stress in Shaft^2-(Normal Stress in Shaft/2)^2)
Normal Stress given Principal Shear Stress in Shaft Bending and Torsion
Go Normal Stress in Shaft = 2*sqrt(Principal Shear Stress in Shaft^2-Torsional Shear Stress in Shaft^2)
Maximum Shear Stress in Shaft Bending and Torsion
Go Maximum Shear Stress in Shaft = sqrt((Normal Stress in Shaft/2)^2+Torsional Shear Stress in Shaft^2)
Bending Stress in Shaft Pure Bending Moment
Go Bending Stress in Shaft = (32*Bending Moment in Shaft)/(pi*Diameter of Shaft on Strength Basis^3)
Bending Moment given Bending Stress Pure Bending
Go Bending Moment in Shaft = (Bending Stress in Shaft*pi*Diameter of Shaft on Strength Basis^3)/32
Tensile Stress in Shaft when it is Subjected to Axial Tensile Force
Go Tensile Stress in Shaft = 4*Axial Force on Shaft/(pi*Diameter of Shaft on Strength Basis^2)
Axial Force given Tensile Stress in Shaft
Go Axial Force on Shaft = Tensile Stress in Shaft*pi*(Diameter of Shaft on Strength Basis^2)/4
Power transmitted by Shaft
Go Power Transmitted by Shaft = 2*pi*Speed of Shaft*Torque transmitted by Shaft
Normal Stress given Both Bending and Torsional act on Shaft
Go Normal Stress in Shaft = Bending Stress in Shaft+Tensile Stress in Shaft
Tensile Stress given Normal Stress
Go Tensile Stress in Shaft = Normal Stress in Shaft-Bending Stress in Shaft
Bending Stress given Normal Stress
Go Bending Stress in Shaft = Normal Stress in Shaft-Tensile Stress in Shaft

Maximum Shear Stress in Shaft Bending and Torsion Formula

Maximum Shear Stress in Shaft = sqrt((Normal Stress in Shaft/2)^2+Torsional Shear Stress in Shaft^2)
τsmax = sqrt((σx/2)^2+𝜏^2)

Define Principal Shear Stress

It is defined as the normal stress calculated at an angle when shear stress is considered as zero. The normal stress can be obtained for maximum and minimum values.

How to Calculate Maximum Shear Stress in Shaft Bending and Torsion?

Maximum Shear Stress in Shaft Bending and Torsion calculator uses Maximum Shear Stress in Shaft = sqrt((Normal Stress in Shaft/2)^2+Torsional Shear Stress in Shaft^2) to calculate the Maximum Shear Stress in Shaft, The Maximum Shear Stress in Shaft Bending and Torsion formula is defined as the normal stress calculated at an angle when shear stress is considered zero. The normal stress can be obtained for maximum and minimum values. Maximum Shear Stress in Shaft is denoted by τsmax symbol.

How to calculate Maximum Shear Stress in Shaft Bending and Torsion using this online calculator? To use this online calculator for Maximum Shear Stress in Shaft Bending and Torsion, enter Normal Stress in Shaft x) & Torsional Shear Stress in Shaft (𝜏) and hit the calculate button. Here is how the Maximum Shear Stress in Shaft Bending and Torsion calculation can be explained with given input values -> 0.000126 = sqrt((250600000/2)^2+16290000^2).

FAQ

What is Maximum Shear Stress in Shaft Bending and Torsion?
The Maximum Shear Stress in Shaft Bending and Torsion formula is defined as the normal stress calculated at an angle when shear stress is considered zero. The normal stress can be obtained for maximum and minimum values and is represented as τsmax = sqrt((σx/2)^2+𝜏^2) or Maximum Shear Stress in Shaft = sqrt((Normal Stress in Shaft/2)^2+Torsional Shear Stress in Shaft^2). Normal Stress in Shaft is the stress that occurs when a shaft is loaded by an axial force & Torsional Shear Stress in Shaft is the shear stress produced in the shaft due to the twisting.
How to calculate Maximum Shear Stress in Shaft Bending and Torsion?
The Maximum Shear Stress in Shaft Bending and Torsion formula is defined as the normal stress calculated at an angle when shear stress is considered zero. The normal stress can be obtained for maximum and minimum values is calculated using Maximum Shear Stress in Shaft = sqrt((Normal Stress in Shaft/2)^2+Torsional Shear Stress in Shaft^2). To calculate Maximum Shear Stress in Shaft Bending and Torsion, you need Normal Stress in Shaft x) & Torsional Shear Stress in Shaft (𝜏). With our tool, you need to enter the respective value for Normal Stress in Shaft & Torsional Shear Stress in Shaft 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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