Diameter of Shaft given Principle Shear Stress Calculator

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Design of Shafts

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ASME Code for Shaft Desgin

Design of Hollow Shaft

Maximum Shear Stress and Principal Stress Theory

Shaft Design on Strength Basis

Torsional Rigidity

✖Maximum shear stress in shaft from ASME is the maximum amount of shear stress arising due to shear forces and is calculated using ASME code for shaft design.ⓘ Maximum Shear Stress in Shaft from ASME [𝜏_{max ASME}]			+10% -10%
✖Torsional Moment in Shaft is the reaction induced in a structural shaft element when an external force or moment is applied to the element, causing the element to twist.ⓘ Torsional Moment in Shaft [Mt_shaft]			+10% -10%
✖Combined Shock Fatigue Factor of Torsion Moment is a factor accounting for the combined shock and fatigue load applied with torsion moment.ⓘ Combined Shock Fatigue Factor of Torsion Moment [k_t]			+10% -10%
✖Combined Shock Fatigue Factor of Bending Moment is a factor accounting for the combined shock and fatigue load applied with bending moment.ⓘ Combined Shock Fatigue Factor of Bending Moment [k_b]			+10% -10%
✖Bending Moment in Shaft is the reaction induced in a structural shaft element when an external force or moment is applied to the element, causing the element to bend.ⓘ Bending Moment in Shaft [M_b]			+10% -10%

✖Diameter of Shaft from ASME is the required diameter of the shaft according to the American Society of Mechanical Engineers Code for shaft design.ⓘ Diameter of Shaft given Principle Shear Stress [d_ASME]

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Formula

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Diameter of Shaft given Principle Shear Stress

Formula

`"d"_{"ASME"} = (16/(pi*"𝜏"_{"max ASME"})*sqrt(("Mt"_{"shaft"}*"k"_{"t"})^2+("k"_{"b"}*"M"_{"b"})^2))^(1/3)`

Example

`"59.75829mm"=(16/(pi*"78N/mm²")*sqrt(("3.3E5N*mm"*"1.3")^2+("1.8"*"1.8E6N*mm")^2))^(1/3)`

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Download Design of Automobile Elements Formula PDF

Diameter of Shaft given Principle Shear Stress Solution

STEP 0: Pre-Calculation Summary

Formula Used

Diameter of Shaft from ASME = (16/(pi*Maximum Shear Stress in Shaft from ASME)*sqrt((Torsional Moment in Shaft*Combined Shock Fatigue Factor of Torsion Moment)^2+(Combined Shock Fatigue Factor of Bending Moment*Bending Moment in Shaft)^2))^(1/3)
d_ASME = (16/(pi*𝜏_{max ASME})*sqrt((Mt_shaft*k_t)^2+(k_b*M_b)^2))^(1/3)
This formula uses 1 Constants, 1 Functions, 6 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

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

Diameter of Shaft from ASME - (Measured in Meter) - Diameter of Shaft from ASME is the required diameter of the shaft according to the American Society of Mechanical Engineers Code for shaft design.
Maximum Shear Stress in Shaft from ASME - (Measured in Pascal) - Maximum shear stress in shaft from ASME is the maximum amount of shear stress arising due to shear forces and is calculated using ASME code for shaft design.
Torsional Moment in Shaft - (Measured in Newton Meter) - Torsional Moment in Shaft is the reaction induced in a structural shaft element when an external force or moment is applied to the element, causing the element to twist.
Combined Shock Fatigue Factor of Torsion Moment - Combined Shock Fatigue Factor of Torsion Moment is a factor accounting for the combined shock and fatigue load applied with torsion moment.
Combined Shock Fatigue Factor of Bending Moment - Combined Shock Fatigue Factor of Bending Moment is a factor accounting for the combined shock and fatigue load applied with bending moment.
Bending Moment in Shaft - (Measured in Newton Meter) - Bending Moment in Shaft is the reaction induced in a structural shaft element when an external force or moment is applied to the element, causing the element to bend.

STEP 1: Convert Input(s) to Base Unit

Maximum Shear Stress in Shaft from ASME: 78 Newton per Square Millimeter --> 78000000 Pascal (Check conversion here)
Torsional Moment in Shaft: 330000 Newton Millimeter --> 330 Newton Meter (Check conversion here)
Combined Shock Fatigue Factor of Torsion Moment: 1.3 --> No Conversion Required
Combined Shock Fatigue Factor of Bending Moment: 1.8 --> No Conversion Required
Bending Moment in Shaft: 1800000 Newton Millimeter --> 1800 Newton Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d_ASME = (16/(pi*𝜏_{max ASME})*sqrt((Mt_shaft*k_t)^2+(k_b*M_b)^2))^(1/3) --> (16/(pi*78000000)*sqrt((330*1.3)^2+(1.8*1800)^2))^(1/3)

Evaluating ... ...

d_ASME = 0.0597582905278687

STEP 3: Convert Result to Output's Unit

0.0597582905278687 Meter -->59.7582905278687 Millimeter (Check conversion here)

FINAL ANSWER

59.7582905278687 ≈ 59.75829 Millimeter <-- Diameter of Shaft from ASME

(Calculation completed in 00.020 seconds)

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Home » Physics » Design of Automobile Elements » Design of Shafts » ASME Code for Shaft Desgin » Diameter of Shaft given Principle Shear Stress

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< 5 ASME Code for Shaft Desgin Calculators

Equivalent Bending Moment when Shaft is Subjected to Fluctuating Loads

Go Equivalent Bending Moment for Fluctuating Load = Combined Shock Fatigue Factor of Bending Moment*Bending Moment in Shaft+sqrt((Torsional Moment in Shaft*Combined Shock Fatigue Factor of Torsion Moment)^2+(Combined Shock Fatigue Factor of Bending Moment*Bending Moment in Shaft)^2)

Diameter of Shaft given Principle Shear Stress

Go Diameter of Shaft from ASME = (16/(pi*Maximum Shear Stress in Shaft from ASME)*sqrt((Torsional Moment in Shaft*Combined Shock Fatigue Factor of Torsion Moment)^2+(Combined Shock Fatigue Factor of Bending Moment*Bending Moment in Shaft)^2))^(1/3)

Principle Shear Stress Maximum Shear Stress Theory of Failure

Go Maximum Shear Stress in Shaft from ASME = 16/(pi*Diameter of Shaft from ASME^3)*sqrt((Torsional Moment in Shaft*Combined Shock Fatigue Factor of Torsion Moment)^2+(Combined Shock Fatigue Factor of Bending Moment*Bending Moment in Shaft)^2)

Design of Shaft using ASME Code

Go Maximum Shearing Stress = (16*sqrt((Combined Shock and Fatigue Factor to Bending*Bending Moment)^2+(Combined Shock and Fatigue Factor to Torsion*Torsional Moment)^2))/(pi*Diameter of Shaft^3)

Equivalent Torsional Moment when Shaft is Subjected to Fluctuating Loads

Go Equivalent Torsion Moment for Fluctuating Load = sqrt((Torsional Moment in Shaft*Combined Shock Fatigue Factor of Torsion Moment)^2+(Combined Shock Fatigue Factor of Bending Moment*Bending Moment in Shaft)^2)

Diameter of Shaft given Principle Shear Stress Formula

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 Shaft given Principle Shear Stress?

Diameter of Shaft given Principle Shear Stress calculator uses Diameter of Shaft from ASME = (16/(pi*Maximum Shear Stress in Shaft from ASME)*sqrt((Torsional Moment in Shaft*Combined Shock Fatigue Factor of Torsion Moment)^2+(Combined Shock Fatigue Factor of Bending Moment*Bending Moment in Shaft)^2))^(1/3) to calculate the Diameter of Shaft from ASME, The Diameter of Shaft given Principle Shear Stress formula is defined as the diameter of the shaft on which we are applying the bending and torsional moments. Diameter of Shaft from ASME is denoted by d_ASME symbol.

How to calculate Diameter of Shaft given Principle Shear Stress using this online calculator? To use this online calculator for Diameter of Shaft given Principle Shear Stress, enter Maximum Shear Stress in Shaft from ASME (𝜏_{max ASME}), Torsional Moment in Shaft (Mt_shaft), Combined Shock Fatigue Factor of Torsion Moment (k_t), Combined Shock Fatigue Factor of Bending Moment (k_b) & Bending Moment in Shaft (M_b) and hit the calculate button. Here is how the Diameter of Shaft given Principle Shear Stress calculation can be explained with given input values -> 59758.29 = (16/(pi*78000000)*sqrt((330*1.3)^2+(1.8*1800)^2))^(1/3).

FAQ

What is Diameter of Shaft given Principle Shear Stress?

The Diameter of Shaft given Principle Shear Stress formula is defined as the diameter of the shaft on which we are applying the bending and torsional moments and is represented as d_ASME = (16/(pi*𝜏_{max ASME})*sqrt((Mt_shaft*k_t)^2+(k_b*M_b)^2))^(1/3) or Diameter of Shaft from ASME = (16/(pi*Maximum Shear Stress in Shaft from ASME)*sqrt((Torsional Moment in Shaft*Combined Shock Fatigue Factor of Torsion Moment)^2+(Combined Shock Fatigue Factor of Bending Moment*Bending Moment in Shaft)^2))^(1/3). Maximum shear stress in shaft from ASME is the maximum amount of shear stress arising due to shear forces and is calculated using ASME code for shaft design, Torsional Moment in Shaft is the reaction induced in a structural shaft element when an external force or moment is applied to the element, causing the element to twist, Combined Shock Fatigue Factor of Torsion Moment is a factor accounting for the combined shock and fatigue load applied with torsion moment, Combined Shock Fatigue Factor of Bending Moment is a factor accounting for the combined shock and fatigue load applied with bending moment & Bending Moment in Shaft is the reaction induced in a structural shaft element when an external force or moment is applied to the element, causing the element to bend.

How to calculate Diameter of Shaft given Principle Shear Stress?

The Diameter of Shaft given Principle Shear Stress 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 from ASME = (16/(pi*Maximum Shear Stress in Shaft from ASME)*sqrt((Torsional Moment in Shaft*Combined Shock Fatigue Factor of Torsion Moment)^2+(Combined Shock Fatigue Factor of Bending Moment*Bending Moment in Shaft)^2))^(1/3). To calculate Diameter of Shaft given Principle Shear Stress, you need Maximum Shear Stress in Shaft from ASME (𝜏_{max ASME}), Torsional Moment in Shaft (Mt_shaft), Combined Shock Fatigue Factor of Torsion Moment (k_t), Combined Shock Fatigue Factor of Bending Moment (k_b) & Bending Moment in Shaft (M_b). With our tool, you need to enter the respective value for Maximum Shear Stress in Shaft from ASME, Torsional Moment in Shaft, Combined Shock Fatigue Factor of Torsion Moment, Combined Shock Fatigue Factor of Bending Moment & Bending Moment 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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