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Diameter of the Shaft When Principle Shear Stress is Given Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)
d = ((16/pi*t)max)*sqrt(((M t ) t*kt)^2+(kb*M)^2))^(1/3)
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
Maximum shear stress - Maximum shear stress that acts coplanar with cross section of material, arises due to shear forces. (Measured in Pascal)
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
Maximum shear stress: 12 Pascal --> 12 Pascal No Conversion Required
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
d = ((16/pi*t)max)*sqrt(((M t ) t*kt)^2+(kb*M)^2))^(1/3) --> ((16/pi*12)*sqrt((100*2)^2+(2*50)^2))^(1/3)
Evaluating ... ...
d = 23.9081214170664
STEP 3: Convert Result to Output's Unit
23.9081214170664 Meter -->2390.81214170664 Centimeter (Check conversion here)
FINAL ANSWER
2390.81214170664 Centimeter <-- Diameter of shaft
(Calculation completed in 00.020 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

Diameter of the Shaft When Principle Shear Stress is Given Formula

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)
d = ((16/pi*t)max)*sqrt(((M t ) t*kt)^2+(kb*M)^2))^(1/3)

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 Diameter of the Shaft When Principle Shear Stress is Given?

Diameter of the Shaft When Principle Shear Stress is Given calculator uses 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) to calculate the Diameter of shaft, The Diameter of the Shaft When Principle Shear Stress is Given formula is defined as the diameter of the shaft on which we are applying the bending and torsional moments. Diameter of shaft and is denoted by d symbol.

How to calculate Diameter of the Shaft When Principle Shear Stress is Given using this online calculator? To use this online calculator for Diameter of the Shaft When Principle Shear Stress is Given, enter Maximum shear stress ((σt)max), 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 Diameter of the Shaft When Principle Shear Stress is Given calculation can be explained with given input values -> 2390.812 = ((16/pi*12)*sqrt((100*2)^2+(2*50)^2))^(1/3).

FAQ

What is Diameter of the Shaft When Principle Shear Stress is Given?
The Diameter of the Shaft When Principle Shear Stress is Given formula is defined as the diameter of the shaft on which we are applying the bending and torsional moments and is represented as d = ((16/pi*t)max)*sqrt(((M t ) t*kt)^2+(kb*M)^2))^(1/3) or 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). Maximum shear stress that acts coplanar with cross section of material, arises due to shear forces, 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 Diameter of the Shaft When Principle Shear Stress is Given?
The Diameter of the Shaft When Principle Shear Stress is Given formula is defined as the diameter of the shaft on which we are applying the bending and torsional moments is calculated using 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). To calculate Diameter of the Shaft When Principle Shear Stress is Given, you need Maximum shear stress ((σt)max), 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 Maximum shear stress, 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 Diameter of shaft?
In this formula, Diameter of shaft uses Maximum shear stress, 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 Diameter of the Shaft When Principle Shear Stress is Given calculator used?
Among many, Diameter of the Shaft When Principle Shear Stress is Given calculator is widely used in real life applications like {FormulaUses}. Here are few more real life examples -
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