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Maximum Shear Stress in Shaft Bending and Torsion Formula

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Maximum Shear Stress in Shaft is the highest stress that a shaft can withstand without failing, critical in shaft design to ensure strength and durability. Check FAQs

τ smax = \sqrt{{(\frac{σ x}{2})}^{2} + 𝜏^{2}}

τ_smax - Maximum Shear Stress in Shaft?σ_x - Normal Stress in Shaft?𝜏 - Torsional Shear Stress in Shaft?

Maximum Shear Stress in Shaft Bending and Torsion Example

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Here is how the Maximum Shear Stress in Shaft Bending and Torsion equation looks like with Values.

Here is how the Maximum Shear Stress in Shaft Bending and Torsion equation looks like with Units.

Here is how the Maximum Shear Stress in Shaft Bending and Torsion equation looks like.

126.3545 = \sqrt{{(\frac{250.6}{2})}^{2} + {16.29}^{2}}

126.3545N/mm² = \sqrt{{(\frac{250.6N/mm²}{2})}^{2} + {16.29N/mm²}^{2}}

126.3545 = \sqrt{{(\frac{250.6}{2})}^{2} + {16.29}^{2}}

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Maximum Shear Stress in Shaft Bending and Torsion Solution

Follow our step by step solution on how to calculate Maximum Shear Stress in Shaft Bending and Torsion?

FIRST Step Consider the formula

τ smax = \sqrt{{(\frac{σ x}{2})}^{2} + 𝜏^{2}}

Next Step Substitute values of Variables

∴

τ smax = \sqrt{{(\frac{250.6N/mm²}{2})}^{2} + {16.29N/mm²}^{2}}

Next Step Convert Units

∴

τ smax = \sqrt{{(\frac{2.5E+8Pa}{2})}^{2} + {1.6E+7Pa}^{2}}

Next Step Prepare to Evaluate

∴

τ smax = \sqrt{{(\frac{2.5E+8}{2})}^{2} + {1.6E+7}^{2}}

Next Step Evaluate

∴

τ smax = 126354477.957847Pa

Next Step Convert to Output's Unit

∴

τ smax = 126.354477957847N/mm²

LAST Step Rounding Answer

∴

τ smax = 126.3545N/mm²

Maximum Shear Stress in Shaft Bending and Torsion Formula Elements

Variables

Functions

Maximum Shear Stress in Shaft

Maximum Shear Stress in Shaft is the highest stress that a shaft can withstand without failing, critical in shaft design to ensure strength and durability.

Symbol: τ_smax

Measurement: StressUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Maximum Shear Stress in Shaft

Normal Stress in Shaft

Normal Stress in Shaft is the force per unit area that a shaft can withstand without undergoing deformation or failure during its operation.

Symbol: σ_x

Measurement: StressUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Normal Stress in Shaft

Torsional Shear Stress in Shaft

Torsional Shear Stress in Shaft is the stress developed in a shaft due to twisting or rotational force, affecting its strength and structural integrity.

Symbol: 𝜏

Measurement: StressUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Torsional Shear Stress in Shaft

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 Shaft Design on Strength Basis category

Go Tensile Stress in Shaft when it is Subjected to Axial Tensile Force

σ t = 4 \cdot \frac{P ax}{π \cdot d^{2}}

Go Diameter of Shaft given Tensile Stress in Shaft

d = \sqrt{4 \cdot \frac{P ax}{π \cdot σ t}}

Go Axial Force given Tensile Stress in Shaft

P ax = σ t \cdot π \cdot \frac{d^{2}}{4}

Go Bending Stress in Shaft Pure Bending Moment

σ b = \frac{32 \cdot M b}{π \cdot d^{3}}

How to Evaluate Maximum Shear Stress in Shaft Bending and Torsion?

Maximum Shear Stress in Shaft Bending and Torsion evaluator uses Maximum Shear Stress in Shaft = sqrt((Normal Stress in Shaft/2)^2+Torsional Shear Stress in Shaft^2) to evaluate the Maximum Shear Stress in Shaft, Maximum Shear Stress in Shaft Bending and Torsion formula is defined as a measure of the maximum shear stress that occurs in a shaft when it is subjected to both bending and torsional loads, providing a critical value for shaft design and analysis in mechanical engineering applications. Maximum Shear Stress in Shaft is denoted by τ_smax symbol.

How to evaluate Maximum Shear Stress in Shaft Bending and Torsion using this online evaluator? To use this online evaluator for Maximum Shear Stress in Shaft Bending and Torsion, enter Normal Stress in Shaft (σ_x) & Torsional Shear Stress in Shaft (𝜏) and hit the calculate button.

FAQs on Maximum Shear Stress in Shaft Bending and Torsion

What is the formula to find Maximum Shear Stress in Shaft Bending and Torsion?

The formula of Maximum Shear Stress in Shaft Bending and Torsion is expressed as Maximum Shear Stress in Shaft = sqrt((Normal Stress in Shaft/2)^2+Torsional Shear Stress in Shaft^2). Here is an example- 0.000126 = sqrt((250600000/2)^2+16290000^2).

How to calculate Maximum Shear Stress in Shaft Bending and Torsion?

With Normal Stress in Shaft (σ_x) & Torsional Shear Stress in Shaft (𝜏) we can find Maximum Shear Stress in Shaft Bending and Torsion using the formula - Maximum Shear Stress in Shaft = sqrt((Normal Stress in Shaft/2)^2+Torsional Shear Stress in Shaft^2). This formula also uses Square Root (sqrt) function(s).

Can the Maximum Shear Stress in Shaft Bending and Torsion be negative?

No, the Maximum Shear Stress in Shaft Bending and Torsion, measured in Stress cannot be negative.

Which unit is used to measure Maximum Shear Stress in Shaft Bending and Torsion?

Maximum Shear Stress in Shaft Bending and Torsion 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 Maximum Shear Stress in Shaft Bending and Torsion can be measured.

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Maximum Shear Stress in Shaft Bending and Torsion Formula

Maximum Shear Stress in Shaft Bending and Torsion Example

Maximum Shear Stress in Shaft Bending and Torsion Solution

Maximum Shear Stress in Shaft Bending and Torsion Formula Elements

Other formulas in Shaft Design on Strength Basis category

How to Evaluate Maximum Shear Stress in Shaft Bending and Torsion?

FAQs on Maximum Shear Stress in Shaft Bending and Torsion

Variable Name