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Principle Shear Stress(maximum shear stress theory of failure) Solution

STEP 0: Pre-Calculation Summary
Formula Used
maximum_shear_stress = (16/pi*Diameter of shaft^3)*sqrt((Torsional Moment*Combined Shock and Fatigue Factor to torsion)^2+(Combined Shock and Fatigue Factor to Bending*Bending moment)^2)
t)max = (16/pi*d^3)*sqrt(((M t ) t*kt)^2+(kb*M)^2)
This formula uses 1 Constants, 1 Functions, 5 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Functions Used
sqrt - Squre root function, sqrt(Number)
Variables Used
Diameter of shaft - The Diameter of shaft is defined as the diameter of the hole in the iron laminations that contains the shaft. (Measured in Centimeter)
Torsional Moment - Torsional Moment is the torque applied to generate a torsion (twist) within the object. (Measured in Newton Meter)
Combined Shock and Fatigue Factor to torsion- Combined Shock and Fatigue Factor to torsion is a commonly used figure of merit for estimating the amount of shock experienced by a naval target from an underwater explosion.
Combined Shock and Fatigue Factor to Bending- Combined Shock and Fatigue Factor to Bending is a commonly used figure of merit for estimating the amount of shock experienced by a naval target from an underwater explosion.
Bending moment - The Bending moment is the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend. (Measured in Newton Meter)
STEP 1: Convert Input(s) to Base Unit
Diameter of shaft: 10 Centimeter --> 0.1 Meter (Check conversion here)
Torsional Moment: 100 Newton Meter --> 100 Newton Meter No Conversion Required
Combined Shock and Fatigue Factor to torsion: 2 --> No Conversion Required
Combined Shock and Fatigue Factor to Bending: 2 --> No Conversion Required
Bending moment: 50 Newton Meter --> 50 Newton Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
t)max = (16/pi*d^3)*sqrt(((M t ) t*kt)^2+(kb*M)^2) --> (16/pi*0.1^3)*sqrt((100*2)^2+(2*50)^2)
Evaluating ... ...
t)max = 1.13882006946748
STEP 3: Convert Result to Output's Unit
1.13882006946748 Pascal --> No Conversion Required
FINAL ANSWER
1.13882006946748 Pascal <-- Maximum shear stress
(Calculation completed in 00.016 seconds)

4 ASME Code for Shaft Desgin Calculators

Equivalent Bending Moment When Shaft is Subjected to Fluctuating Loads
equivalent_bending_moment = Combined Shock and Fatigue Factor to Bending*Bending moment+sqrt((Torsional Moment*Combined Shock and Fatigue Factor to torsion)^2+(Combined Shock and Fatigue Factor to Bending*Bending moment)^2) Go
Diameter of the Shaft When Principle Shear Stress is Given
diameter_of_shaft = ((16/pi*Maximum shear stress)*sqrt((Torsional Moment*Combined Shock and Fatigue Factor to torsion)^2+(Combined Shock and Fatigue Factor to Bending*Bending moment)^2))^(1/3) Go
Principle Shear Stress(maximum shear stress theory of failure)
maximum_shear_stress = (16/pi*Diameter of shaft^3)*sqrt((Torsional Moment*Combined Shock and Fatigue Factor to torsion)^2+(Combined Shock and Fatigue Factor to Bending*Bending moment)^2) Go
Equivalent Torsional Moment When Shaft is Subjected to Fluctuating Loads
equivalent_torsion_moment = sqrt((Torsional Moment*Combined Shock and Fatigue Factor to torsion)^2+(Combined Shock and Fatigue Factor to Bending*Bending moment)^2) Go

Principle Shear Stress(maximum shear stress theory of failure) Formula

maximum_shear_stress = (16/pi*Diameter of shaft^3)*sqrt((Torsional Moment*Combined Shock and Fatigue Factor to torsion)^2+(Combined Shock and Fatigue Factor to Bending*Bending moment)^2)
t)max = (16/pi*d^3)*sqrt(((M t ) t*kt)^2+(kb*M)^2)

Define Maximum Shear Stress Theory of Failure?

The Maximum Shear Stress theory states that failure occurs when the maximum shear stress from a combination of principal stresses equals or exceeds the value obtained for the shear stress at yielding in the uniaxial tensile test.

How to Calculate Principle Shear Stress(maximum shear stress theory of failure)?

Principle Shear Stress(maximum shear stress theory of failure) calculator uses maximum_shear_stress = (16/pi*Diameter of shaft^3)*sqrt((Torsional Moment*Combined Shock and Fatigue Factor to torsion)^2+(Combined Shock and Fatigue Factor to Bending*Bending moment)^2) to calculate the Maximum shear stress, The Principle Shear Stress(maximum shear stress theory of failure) formula 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. Maximum shear stress and is denoted by t)max symbol.

How to calculate Principle Shear Stress(maximum shear stress theory of failure) using this online calculator? To use this online calculator for Principle Shear Stress(maximum shear stress theory of failure), enter Diameter of shaft (d), Torsional Moment ((M t ) t), Combined Shock and Fatigue Factor to torsion (kt), Combined Shock and Fatigue Factor to Bending (kb) and Bending moment (M) and hit the calculate button. Here is how the Principle Shear Stress(maximum shear stress theory of failure) calculation can be explained with given input values -> 1.13882 = (16/pi*0.1^3)*sqrt((100*2)^2+(2*50)^2).

FAQ

What is Principle Shear Stress(maximum shear stress theory of failure)?
The Principle Shear Stress(maximum shear stress theory of failure) formula 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 and is represented as t)max = (16/pi*d^3)*sqrt(((M t ) t*kt)^2+(kb*M)^2) or maximum_shear_stress = (16/pi*Diameter of shaft^3)*sqrt((Torsional Moment*Combined Shock and Fatigue Factor to torsion)^2+(Combined Shock and Fatigue Factor to Bending*Bending moment)^2). The Diameter of shaft is defined as the diameter of the hole in the iron laminations that contains the shaft, Torsional Moment is the torque applied to generate a torsion (twist) within the object, Combined Shock and Fatigue Factor to torsion is a commonly used figure of merit for estimating the amount of shock experienced by a naval target from an underwater explosion, Combined Shock and Fatigue Factor to Bending is a commonly used figure of merit for estimating the amount of shock experienced by a naval target from an underwater explosion and The Bending moment is the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend.
How to calculate Principle Shear Stress(maximum shear stress theory of failure)?
The Principle Shear Stress(maximum shear stress theory of failure) formula 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 is calculated using maximum_shear_stress = (16/pi*Diameter of shaft^3)*sqrt((Torsional Moment*Combined Shock and Fatigue Factor to torsion)^2+(Combined Shock and Fatigue Factor to Bending*Bending moment)^2). To calculate Principle Shear Stress(maximum shear stress theory of failure), you need Diameter of shaft (d), Torsional Moment ((M t ) t), Combined Shock and Fatigue Factor to torsion (kt), Combined Shock and Fatigue Factor to Bending (kb) and Bending moment (M). With our tool, you need to enter the respective value for Diameter of shaft, Torsional Moment, Combined Shock and Fatigue Factor to torsion, Combined Shock and Fatigue Factor to Bending and Bending moment 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 Diameter of shaft, Torsional Moment, Combined Shock and Fatigue Factor to torsion, Combined Shock and Fatigue Factor to Bending and Bending moment. We can use 4 other way(s) to calculate the same, which is/are as follows -
  • maximum_shear_stress = (16/pi*Diameter of shaft^3)*sqrt((Torsional Moment*Combined Shock and Fatigue Factor to torsion)^2+(Combined Shock and Fatigue Factor to Bending*Bending moment)^2)
  • diameter_of_shaft = ((16/pi*Maximum shear stress)*sqrt((Torsional Moment*Combined Shock and Fatigue Factor to torsion)^2+(Combined Shock and Fatigue Factor to Bending*Bending moment)^2))^(1/3)
  • equivalent_torsion_moment = sqrt((Torsional Moment*Combined Shock and Fatigue Factor to torsion)^2+(Combined Shock and Fatigue Factor to Bending*Bending moment)^2)
  • equivalent_bending_moment = Combined Shock and Fatigue Factor to Bending*Bending moment+sqrt((Torsional Moment*Combined Shock and Fatigue Factor to torsion)^2+(Combined Shock and Fatigue Factor to Bending*Bending moment)^2)
Where is the Principle Shear Stress(maximum shear stress theory of failure) calculator used?
Among many, Principle Shear Stress(maximum shear stress theory of failure) calculator is widely used in real life applications like {FormulaUses}. Here are few more real life examples -
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