Principle Stress Maximum Principle Stress Theory Calculator

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Design of Hollow Shaft

ASME Code for Shaft Desgin

Maximum Shear Stress and Principal Stress Theory

Shaft Design on Strength Basis

Torsional Rigidity

✖Bending Moment in Hollow Shaft is the reaction induced in a structural shaft hollow element when an external force or moment is applied to the element, causing the element to bend.ⓘ Bending Moment in Hollow Shaft [M_{b h}]			+10% -10%
✖Torsional Moment in Hollow Shaft is the reaction induced in a structural shaft hollow element when an external force or moment is applied to the element, causing the element to twist.ⓘ Torsional Moment in Hollow Shaft [Mt_hollowshaft]			+10% -10%
✖Outer Diameter of Hollow Shaft is defined as the length of the longest chord of the surface of the hollow circular shaft.ⓘ Outer Diameter of Hollow Shaft [d_o]			+10% -10%
✖The Ratio of Inner to Outer Diameter of Hollow Shaft is defined as the inner diameter of the shaft divided by the outer diameter.ⓘ Ratio of Inner to Outer Diameter of Hollow Shaft [C]			+10% -10%

✖Maximum Principle Stress in Hollow Shaft is defined as the normal stress calculated at an angle when shear stress is considered zero.ⓘ Principle Stress Maximum Principle Stress Theory [τ]

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Formula

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Principle Stress Maximum Principle Stress Theory

Formula

`"τ" = 16*("M"_{"b h"}+sqrt("M"_{"b h"}^2+"Mt"_{"hollowshaft"}^2))/(pi*"d"_{"o"}^3*(1-"C"^4))`

Example

`"129.86N/mm²"=16*("5.5E5N*mm"+sqrt(("5.5E5N*mm")^2+("3.2E5N*mm")^2))/(pi*("46mm")^3*(1-("0.85")^4))`

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Principle Stress Maximum Principle Stress Theory Solution

STEP 0: Pre-Calculation Summary

Formula Used

Maximum Principle Stress in Hollow Shaft = 16*(Bending Moment in Hollow Shaft+sqrt(Bending Moment in Hollow Shaft^2+Torsional Moment in Hollow Shaft^2))/(pi*Outer Diameter of Hollow Shaft^3*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4))
τ = 16*(M_{b h}+sqrt(M_{b h}^2+Mt_hollowshaft^2))/(pi*d_o^3*(1-C^4))
This formula uses 1 Constants, 1 Functions, 5 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

Maximum Principle Stress in Hollow Shaft - (Measured in Pascal) - Maximum Principle Stress in Hollow Shaft is defined as the normal stress calculated at an angle when shear stress is considered zero.
Bending Moment in Hollow Shaft - (Measured in Newton Meter) - Bending Moment in Hollow Shaft is the reaction induced in a structural shaft hollow element when an external force or moment is applied to the element, causing the element to bend.
Torsional Moment in Hollow Shaft - (Measured in Newton Meter) - Torsional Moment in Hollow Shaft is the reaction induced in a structural shaft hollow element when an external force or moment is applied to the element, causing the element to twist.
Outer Diameter of Hollow Shaft - (Measured in Meter) - Outer Diameter of Hollow Shaft is defined as the length of the longest chord of the surface of the hollow circular shaft.
Ratio of Inner to Outer Diameter of Hollow Shaft - The Ratio of Inner to Outer Diameter of Hollow Shaft is defined as the inner diameter of the shaft divided by the outer diameter.

STEP 1: Convert Input(s) to Base Unit

Bending Moment in Hollow Shaft: 550000 Newton Millimeter --> 550 Newton Meter (Check conversion here)
Torsional Moment in Hollow Shaft: 320000 Newton Millimeter --> 320 Newton Meter (Check conversion here)
Outer Diameter of Hollow Shaft: 46 Millimeter --> 0.046 Meter (Check conversion here)
Ratio of Inner to Outer Diameter of Hollow Shaft: 0.85 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

τ = 16*(M_{b h}+sqrt(M_{b h}^2+Mt_hollowshaft^2))/(pi*d_o^3*(1-C^4)) --> 16*(550+sqrt(550^2+320^2))/(pi*0.046^3*(1-0.85^4))

Evaluating ... ...

τ = 129859984.024973

STEP 3: Convert Result to Output's Unit

129859984.024973 Pascal -->129.859984024973 Newton per Square Millimeter (Check conversion here)

FINAL ANSWER

129.859984024973 ≈ 129.86 Newton per Square Millimeter <-- Maximum Principle Stress in Hollow Shaft

(Calculation completed in 00.004 seconds)

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Created by Kethavath Srinath

Osmania University (OU), Hyderabad

Kethavath Srinath has created this Calculator and 1000+ more calculators!

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Vishwakarma Government Engineering College (VGEC), Ahmedabad

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< 23 Design of Hollow Shaft Calculators

Outer Diameter of Hollow Shaft given Principle Stress

Go Outer Diameter of Hollow Shaft = (16*(Bending Moment in Hollow Shaft+sqrt(Bending Moment in Hollow Shaft^2+Torsional Moment in Hollow Shaft^2))/(pi*Maximum Principle Stress in Hollow Shaft*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)))^(1/3)

Ratio of Diameters given Principle Stress

Go Ratio of Inner to Outer Diameter of Hollow Shaft = (1-16*(Bending Moment in Hollow Shaft+sqrt(Bending Moment in Hollow Shaft^2+Torsional Moment in Hollow Shaft^2))/(pi*Outer Diameter of Hollow Shaft^3*Maximum Principle Stress in Hollow Shaft))^(1/4)

Principle Stress Maximum Principle Stress Theory

Go Maximum Principle Stress in Hollow Shaft = 16*(Bending Moment in Hollow Shaft+sqrt(Bending Moment in Hollow Shaft^2+Torsional Moment in Hollow Shaft^2))/(pi*Outer Diameter of Hollow Shaft^3*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4))

Outer Diameter of Hollow Shaft given Angle of Twist Torsional Rigidity

Go Outer Diameter of Hollow Shaft = (584*Torsional Moment in Hollow Shaft*Length of Hollow Shaft/(Modulus of Rigidity of Hollow Shaft*Angle of Twist of Hollow Shaft*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)))^(1/4)

Ratio of Diameters given Angle of Twist of Hollow Shaft and Torsional Rigidity

Go Ratio of Inner to Outer Diameter of Hollow Shaft = (1-584*Torsional Moment in Hollow Shaft*Length of Hollow Shaft/(Modulus of Rigidity of Hollow Shaft*Outer Diameter of Hollow Shaft^4*Angle of Twist of Hollow Shaft))^(1/4)

Length of Shaft given Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity

Go Length of Hollow Shaft = Angle of Twist of Hollow Shaft*(Modulus of Rigidity of Hollow Shaft*Outer Diameter of Hollow Shaft^4*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4))/(584*Torsional Moment in Hollow Shaft)

Torsional Moment given Angle of Twist on Basis of Torsional Rigidity

Go Torsional Moment in Hollow Shaft = Angle of Twist of Hollow Shaft*(Modulus of Rigidity of Hollow Shaft*Outer Diameter of Hollow Shaft^4*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4))/(584*Length of Hollow Shaft)

Modulus of Rigidity given Angle of Twist of Hollow Shaft on basis of Torsional Rigidity

Go Modulus of Rigidity of Hollow Shaft = 584*Torsional Moment in Hollow Shaft*Length of Hollow Shaft/(Angle of Twist of Hollow Shaft*Outer Diameter of Hollow Shaft^4*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4))

Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity

Go Angle of Twist of Hollow Shaft = 584*Torsional Moment in Hollow Shaft*Length of Hollow Shaft/(Modulus of Rigidity of Hollow Shaft*Outer Diameter of Hollow Shaft^4*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4))

Ratio of Diameters given Tensile Stress in Hollow Shaft

Go Ratio of Inner to Outer Diameter of Hollow Shaft = sqrt(1-(Axial Force on Hollow Shaft/(pi/4*Tensile Stress in Hollow Shaft*Outer Diameter of Hollow Shaft^2)))

Outer Diameter of Shaft given Torsional Shear Stress

Go Outer Diameter of Hollow Shaft = (16*Torsional Moment in Hollow Shaft/(pi*Torsional Shear Stress in Hollow Shaft*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)))^(1/3)

Ratio of Diameter given Torsional Shear Stress in Hollow Shaft

Go Ratio of Inner to Outer Diameter of Hollow Shaft = (1-16*Torsional Moment in Hollow Shaft/(pi*Outer Diameter of Hollow Shaft^3*Torsional Shear Stress in Hollow Shaft))^(1/4)

Torsional Shear Stress when Shaft is Subjected to Pure Torsional Moment

Go Torsional Shear Stress in Hollow Shaft = 16*Torsional Moment in Hollow Shaft/(pi*Outer Diameter of Hollow Shaft^3*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4))

Torsional Moment given Torsional Shear Stress in Hollow Shaft

Go Torsional Moment in Hollow Shaft = Torsional Shear Stress in Hollow Shaft*(pi*Outer Diameter of Hollow Shaft^3*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4))/16

Outer Diameter of Hollow Shaft given Bending Stress of Hollow Shaft

Go Outer Diameter of Hollow Shaft = (32*Bending Moment in Hollow Shaft/(pi*Bending Stress in Hollow Shaft*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)))^(1/3)

Ratio of Diameters given Bending Stress of Hollow Shaft

Go Ratio of Inner to Outer Diameter of Hollow Shaft = (1-32*Bending Moment in Hollow Shaft/(pi*Outer Diameter of Hollow Shaft^3*Bending Stress in Hollow Shaft))^(1/4)

Bending Moment given Bending Stress in Hollow Shaft

Go Bending Moment in Hollow Shaft = Bending Stress in Hollow Shaft*(pi*Outer Diameter of Hollow Shaft^3*(1-(Ratio of Inner to Outer Diameter of Hollow Shaft^4)))/32

Bending Stress in Hollow Shaft

Go Bending Stress in Hollow Shaft = 32*Bending Moment in Hollow Shaft/(pi*Outer Diameter of Hollow Shaft^3*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4))

Tensile Stress in Hollow Shaft when Subjected to Axial Force

Go Tensile Stress in Hollow Shaft = Axial Force on Hollow Shaft/(pi/4*(Outer Diameter of Hollow Shaft^2-Inner Diameter of Hollow Shaft^2))

Axial Tensile Force given Tensile Stress in Hollow Shaft

Go Axial Force on Hollow Shaft = Tensile Stress in Hollow Shaft*pi/4*(Outer Diameter of Hollow Shaft^2-Inner Diameter of Hollow Shaft^2)

Inner Diameter of Hollow Shaft given Ratio of Diameters

Go Inner Diameter of Hollow Shaft = Ratio of Inner to Outer Diameter of Hollow Shaft*Outer Diameter of Hollow Shaft

Ratio of Inner Diameter to Outer Diameter

Go Ratio of Inner to Outer Diameter of Hollow Shaft = Inner Diameter of Hollow Shaft/Outer Diameter of Hollow Shaft

Outer Diameter given Ratio of Diameters

Go Outer Diameter of Hollow Shaft = Inner Diameter of Hollow Shaft/Ratio of Inner to Outer Diameter of Hollow Shaft

Principle Stress Maximum Principle Stress Theory Formula

Define Maximum Principle Stress Theory

Rankin stated max principal stress theory as follows- a material fails by fracturing when the largest. principal stress exceeds the ultimate strength σu in a simple tension test.

How to Calculate Principle Stress Maximum Principle Stress Theory?

Principle Stress Maximum Principle Stress Theory calculator uses Maximum Principle Stress in Hollow Shaft = 16*(Bending Moment in Hollow Shaft+sqrt(Bending Moment in Hollow Shaft^2+Torsional Moment in Hollow Shaft^2))/(pi*Outer Diameter of Hollow Shaft^3*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)) to calculate the Maximum Principle Stress in Hollow Shaft, The Principle Stress Maximum Principle Stress Theory 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 Principle Stress in Hollow Shaft is denoted by τ symbol.

How to calculate Principle Stress Maximum Principle Stress Theory using this online calculator? To use this online calculator for Principle Stress Maximum Principle Stress Theory, enter Bending Moment in Hollow Shaft (M_{b h}), Torsional Moment in Hollow Shaft (Mt_hollowshaft), Outer Diameter of Hollow Shaft (d_o) & Ratio of Inner to Outer Diameter of Hollow Shaft (C) and hit the calculate button. Here is how the Principle Stress Maximum Principle Stress Theory calculation can be explained with given input values -> 0.00013 = 16*(550+sqrt(550^2+320^2))/(pi*0.046^3*(1-0.85^4)).

FAQ

What is Principle Stress Maximum Principle Stress Theory?

The Principle Stress Maximum Principle Stress Theory 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 τ = 16*(M_{b h}+sqrt(M_{b h}^2+Mt_hollowshaft^2))/(pi*d_o^3*(1-C^4)) or Maximum Principle Stress in Hollow Shaft = 16*(Bending Moment in Hollow Shaft+sqrt(Bending Moment in Hollow Shaft^2+Torsional Moment in Hollow Shaft^2))/(pi*Outer Diameter of Hollow Shaft^3*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)). Bending Moment in Hollow Shaft is the reaction induced in a structural shaft hollow element when an external force or moment is applied to the element, causing the element to bend, Torsional Moment in Hollow Shaft is the reaction induced in a structural shaft hollow element when an external force or moment is applied to the element, causing the element to twist, Outer Diameter of Hollow Shaft is defined as the length of the longest chord of the surface of the hollow circular shaft & The Ratio of Inner to Outer Diameter of Hollow Shaft is defined as the inner diameter of the shaft divided by the outer diameter.

How to calculate Principle Stress Maximum Principle Stress Theory?

The Principle Stress Maximum Principle Stress Theory 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 Principle Stress in Hollow Shaft = 16*(Bending Moment in Hollow Shaft+sqrt(Bending Moment in Hollow Shaft^2+Torsional Moment in Hollow Shaft^2))/(pi*Outer Diameter of Hollow Shaft^3*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)). To calculate Principle Stress Maximum Principle Stress Theory, you need Bending Moment in Hollow Shaft (M_{b h}), Torsional Moment in Hollow Shaft (Mt_hollowshaft), Outer Diameter of Hollow Shaft (d_o) & Ratio of Inner to Outer Diameter of Hollow Shaft (C). With our tool, you need to enter the respective value for Bending Moment in Hollow Shaft, Torsional Moment in Hollow Shaft, Outer Diameter of Hollow Shaft & Ratio of Inner to Outer Diameter of Hollow 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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