Outer Diameter of Hollow Shaft given Principle Stress Calculator

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

✖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 given Principle Stress [d_o]

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Outer Diameter of Hollow Shaft given Principle Stress Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
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.
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.
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)
Maximum Principle Stress in Hollow Shaft: 129.8 Newton per Square Millimeter --> 129800000 Pascal (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

d_o = (16*(M_{b h}+sqrt(M_{b h}^2+Mt_hollowshaft^2))/(pi*τ*(1-C^4)))^(1/3) --> (16*(550+sqrt(550^2+320^2))/(pi*129800000*(1-0.85^4)))^(1/3)

Evaluating ... ...

d_o = 0.046007084849036

STEP 3: Convert Result to Output's Unit

0.046007084849036 Meter -->46.007084849036 Millimeter (Check conversion here)

FINAL ANSWER

46.007084849036 ≈ 46.00708 Millimeter <-- Outer Diameter of Hollow Shaft

(Calculation completed in 00.007 seconds)

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Home » Physics » Design of Automobile Elements » Design of Shafts » Mechanical » Design of Hollow Shaft » Outer Diameter of Hollow Shaft given Principle Stress

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Created by Kethavath Srinath

Osmania University (OU), Hyderabad

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< Design of Hollow Shaft Calculators

Tensile Stress in Hollow Shaft when Subjected to Axial Force

LaTeX 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))

Inner Diameter of Hollow Shaft given Ratio of Diameters

LaTeX 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

LaTeX 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

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

Outer Diameter of Hollow Shaft given Principle Stress Formula

LaTeX Go

Define Principle 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 Outer Diameter of Hollow Shaft given Principle Stress?

Outer Diameter of Hollow Shaft given Principle Stress calculator uses 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) to calculate the Outer Diameter of Hollow Shaft, Outer Diameter of Hollow Shaft given Principle Stress formula is defined as a measure of the outer diameter of a hollow shaft, which is a critical parameter in the design of hollow shafts, taking into account the principle stress, bending moment, and torque, to ensure the shaft's structural integrity and performance. Outer Diameter of Hollow Shaft is denoted by d_o symbol.

How to calculate Outer Diameter of Hollow Shaft given Principle Stress using this online calculator? To use this online calculator for Outer Diameter of Hollow Shaft given Principle Stress, enter Bending Moment in Hollow Shaft (M_{b h}), Torsional Moment in Hollow Shaft (Mt_hollowshaft), Maximum Principle Stress in Hollow Shaft (τ) & Ratio of Inner to Outer Diameter of Hollow Shaft (C) and hit the calculate button. Here is how the Outer Diameter of Hollow Shaft given Principle Stress calculation can be explained with given input values -> 46007.08 = (16*(550+sqrt(550^2+320^2))/(pi*129800000*(1-0.85^4)))^(1/3).

FAQ

What is Outer Diameter of Hollow Shaft given Principle Stress?

Outer Diameter of Hollow Shaft given Principle Stress formula is defined as a measure of the outer diameter of a hollow shaft, which is a critical parameter in the design of hollow shafts, taking into account the principle stress, bending moment, and torque, to ensure the shaft's structural integrity and performance and is represented as d_o = (16*(M_{b h}+sqrt(M_{b h}^2+Mt_hollowshaft^2))/(pi*τ*(1-C^4)))^(1/3) or 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). 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, Maximum Principle Stress in Hollow Shaft is defined as the normal stress calculated at an angle when shear stress is considered zero & 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 Outer Diameter of Hollow Shaft given Principle Stress?

Outer Diameter of Hollow Shaft given Principle Stress formula is defined as a measure of the outer diameter of a hollow shaft, which is a critical parameter in the design of hollow shafts, taking into account the principle stress, bending moment, and torque, to ensure the shaft's structural integrity and performance is calculated using 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). To calculate Outer Diameter of Hollow Shaft given Principle Stress, you need Bending Moment in Hollow Shaft (M_{b h}), Torsional Moment in Hollow Shaft (Mt_hollowshaft), Maximum Principle Stress in Hollow Shaft (τ) & 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, Maximum Principle Stress in 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.

How many ways are there to calculate Outer Diameter of Hollow Shaft?

In this formula, Outer Diameter of Hollow Shaft uses Bending Moment in Hollow Shaft, Torsional Moment in Hollow Shaft, Maximum Principle Stress in Hollow Shaft & Ratio of Inner to Outer Diameter of Hollow Shaft. We can use 3 other way(s) to calculate the same, which is/are as follows -

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

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