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Principle Stress Maximum Principle Stress Theory Formula

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Maximum Principle Stress in Hollow Shaft is defined as the normal stress calculated at an angle when shear stress is considered zero. Check FAQs

τ = 16 \cdot \frac{M b h + \sqrt{{M b h}^{2} + {Mt hollowshaft}^{2}}}{π \cdot {d o}^{3} \cdot (1 - C^{4})}

τ - Maximum Principle Stress in Hollow Shaft?M_{b h} - Bending Moment in Hollow Shaft?Mt_hollowshaft - Torsional Moment in Hollow Shaft?d_o - Outer Diameter of Hollow Shaft?C - Ratio of Inner to Outer Diameter of Hollow Shaft?π - Archimedes' constant?

Principle Stress Maximum Principle Stress Theory Example

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Here is how the Principle Stress Maximum Principle Stress Theory equation looks like with Values.

Here is how the Principle Stress Maximum Principle Stress Theory equation looks like with Units.

Here is how the Principle Stress Maximum Principle Stress Theory equation looks like.

129.86 = 16 \cdot \frac{550000 + \sqrt{550000^{2} + 320000^{2}}}{3.1416 \cdot 46^{3} \cdot (1 - {0.85}^{4})}

129.86N/mm² = 16 \cdot \frac{550000N*mm + \sqrt{{550000N*mm}^{2} + {320000N*mm}^{2}}}{3.1416 \cdot {46mm}^{3} \cdot (1 - {0.85}^{4})}

129.86 = 16 \cdot \frac{550000 + \sqrt{550000^{2} + 320000^{2}}}{3.1416 \cdot 46^{3} \cdot (1 - {0.85}^{4})}

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Principle Stress Maximum Principle Stress Theory Solution

Follow our step by step solution on how to calculate Principle Stress Maximum Principle Stress Theory?

FIRST Step Consider the formula

τ = 16 \cdot \frac{M b h + \sqrt{{M b h}^{2} + {Mt hollowshaft}^{2}}}{π \cdot {d o}^{3} \cdot (1 - C^{4})}

Next Step Substitute values of Variables

∴

τ = 16 \cdot \frac{550000N*mm + \sqrt{{550000N*mm}^{2} + {320000N*mm}^{2}}}{π \cdot {46mm}^{3} \cdot (1 - {0.85}^{4})}

Next Step Substitute values of Constants

∴

τ = 16 \cdot \frac{550000N*mm + \sqrt{{550000N*mm}^{2} + {320000N*mm}^{2}}}{3.1416 \cdot {46mm}^{3} \cdot (1 - {0.85}^{4})}

Next Step Convert Units

∴

τ = 16 \cdot \frac{550N*m + \sqrt{{550N*m}^{2} + {320N*m}^{2}}}{3.1416 \cdot {0.046m}^{3} \cdot (1 - {0.85}^{4})}

Next Step Prepare to Evaluate

∴

τ = 16 \cdot \frac{550 + \sqrt{550^{2} + 320^{2}}}{3.1416 \cdot {0.046}^{3} \cdot (1 - {0.85}^{4})}

Next Step Evaluate

∴

τ = 129859984.024973Pa

Next Step Convert to Output's Unit

∴

τ = 129.859984024973N/mm²

LAST Step Rounding Answer

∴

τ = 129.86N/mm²

Principle Stress Maximum Principle Stress Theory Formula Elements

Variables

Constants

Functions

Maximum Principle Stress in Hollow Shaft

Maximum Principle Stress in Hollow Shaft is defined as the normal stress calculated at an angle when shear stress is considered zero.

Symbol: τ

Measurement: StressUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Maximum Principle Stress in Hollow Shaft

Bending Moment in Hollow Shaft

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.

Symbol: M_{b h}

Measurement: TorqueUnit: N*mm

Note: Value should be greater than 0.

Formulas to find Bending Moment in Hollow Shaft

Torsional Moment in Hollow Shaft

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.

Symbol: Mt_hollowshaft

Measurement: TorqueUnit: N*mm

Note: Value should be greater than 0.

Formulas to find Torsional Moment in Hollow Shaft

Outer Diameter of Hollow Shaft

Outer Diameter of Hollow Shaft is defined as the length of the longest chord of the surface of the hollow circular shaft.

Symbol: d_o

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Outer Diameter of Hollow 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.

Symbol: C

Measurement: NAUnit: Unitless

Note: Value should be less than 1.

Formulas to find Ratio of Inner to Outer Diameter of Hollow Shaft

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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.

Syntax: sqrt(Number)

Other formulas in Design of Hollow Shaft category

Go Ratio of Inner Diameter to Outer Diameter

C = \frac{d i}{d o}

Go Inner Diameter of Hollow Shaft given Ratio of Diameters

d i = C \cdot d o

Go Outer Diameter given Ratio of Diameters

d o = \frac{d i}{C}

Go Tensile Stress in Hollow Shaft when Subjected to Axial Force

σ tp = \frac{P ax hollow}{\frac{π}{4} \cdot ({d o}^{2} - {d i}^{2})}

How to Evaluate Principle Stress Maximum Principle Stress Theory?

Principle Stress Maximum Principle Stress Theory evaluator 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 evaluate the Maximum Principle Stress in Hollow Shaft, Principle Stress Maximum Principle Stress Theory formula is defined as the maximum stress a hollow shaft can withstand, considering the bending moment and torque, to ensure the shaft's structural integrity and safety in mechanical design applications. Maximum Principle Stress in Hollow Shaft is denoted by τ symbol.

How to evaluate Principle Stress Maximum Principle Stress Theory using this online evaluator? To use this online evaluator 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.

FAQs on Principle Stress Maximum Principle Stress Theory

What is the formula to find Principle Stress Maximum Principle Stress Theory?

The formula of Principle Stress Maximum Principle Stress Theory is expressed as 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)). Here is an example- 0.00013 = 16*(550+sqrt(550^2+320^2))/(pi*0.046^3*(1-0.85^4)).

How to calculate Principle Stress Maximum Principle Stress Theory?

With 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) we can find Principle Stress Maximum Principle Stress Theory using the formula - 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)). This formula also uses Archimedes' constant and Square Root (sqrt) function(s).

Can the Principle Stress Maximum Principle Stress Theory be negative?

No, the Principle Stress Maximum Principle Stress Theory, measured in Stress cannot be negative.

Which unit is used to measure Principle Stress Maximum Principle Stress Theory?

Principle Stress Maximum Principle Stress Theory is usually measured using the Newton per Square Millimeter[N/mm²] for Stress. Pascal[N/mm²], Newton per Square Meter[N/mm²], Kilonewton per Square Meter[N/mm²] are the few other units in which Principle Stress Maximum Principle Stress Theory can be measured.

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Principle Stress Maximum Principle Stress Theory Formula

Principle Stress Maximum Principle Stress Theory Example

Principle Stress Maximum Principle Stress Theory Solution

Principle Stress Maximum Principle Stress Theory Formula Elements

Other formulas in Design of Hollow Shaft category

How to Evaluate Principle Stress Maximum Principle Stress Theory?

FAQs on Principle Stress Maximum Principle Stress Theory

Variable Name