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Maximum Shear Stress for Circular Section Formula

GoMaximum Shear Stress for Circular Section given Average Shear Stress Formula

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Maximum Shear Stress on Beam is the highest value of shear stress that occurs at any point within the beam when subjected to external loading, such as transverse forces. Check FAQs

𝜏 max = \frac{F s}{3 \cdot I} \cdot r^{2}

𝜏_max - Maximum Shear Stress on Beam?F_s - Shear Force on Beam?I - Moment of Inertia of Area of Section?r - Radius of Circular Section?

Maximum Shear Stress for Circular Section Example

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Here is how the Maximum Shear Stress for Circular Section equation looks like with Values.

Here is how the Maximum Shear Stress for Circular Section equation looks like with Units.

Here is how the Maximum Shear Stress for Circular Section equation looks like.

1.3714 = \frac{4.8}{3 \cdot 0.0017} \cdot 1200^{2}

1.3714MPa = \frac{4.8kN}{3 \cdot 0.0017m⁴} \cdot {1200mm}^{2}

1.3714 = \frac{4.8}{3 \cdot 0.0017} \cdot 1200^{2}

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Maximum Shear Stress for Circular Section Solution

Follow our step by step solution on how to calculate Maximum Shear Stress for Circular Section?

FIRST Step Consider the formula

𝜏 max = \frac{F s}{3 \cdot I} \cdot r^{2}

Next Step Substitute values of Variables

∴

𝜏 max = \frac{4.8kN}{3 \cdot 0.0017m⁴} \cdot {1200mm}^{2}

Next Step Convert Units

∴

𝜏 max = \frac{4800N}{3 \cdot 0.0017m⁴} \cdot {1.2m}^{2}

Next Step Prepare to Evaluate

∴

𝜏 max = \frac{4800}{3 \cdot 0.0017} \cdot {1.2}^{2}

Next Step Evaluate

∴

𝜏 max = 1371428.57142857Pa

Next Step Convert to Output's Unit

∴

𝜏 max = 1.37142857142857MPa

LAST Step Rounding Answer

∴

𝜏 max = 1.3714MPa

Maximum Shear Stress for Circular Section Formula Elements

Variables

Maximum Shear Stress on Beam

Maximum Shear Stress on Beam is the highest value of shear stress that occurs at any point within the beam when subjected to external loading, such as transverse forces.

Symbol: 𝜏_max

Measurement: PressureUnit: MPa

Note: Value can be positive or negative.

Formulas to find Maximum Shear Stress on Beam

Shear Force on Beam

Shear Force on Beam is the force which causes shear deformation to occur in the shear plane.

Symbol: F_s

Measurement: ForceUnit: kN

Note: Value can be positive or negative.

Formulas to find Shear Force on Beam

Moment of Inertia of Area of Section

Moment of Inertia of Area of Section is a geometric property that quantifies how a cross-sectional area is distributed relative to an axis.

Symbol: I

Measurement: Second Moment of AreaUnit: m⁴

Note: Value should be greater than 0.

Formulas to find Moment of Inertia of Area of Section

Radius of Circular Section

Radius of Circular Section is the distance from the center of a circle to any point on its boundary, it represent the characteristic size of a circular cross-section in various applications.

Symbol: r

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Radius of Circular Section

Other Formulas to find Maximum Shear Stress on Beam

Go Maximum Shear Stress for Circular Section given Average Shear Stress

𝜏 max = \frac{4}{3} \cdot 𝜏 avg

Other formulas in Maximum Shear Stress category

Go Maximum Shear Force given Radius of Circular Section

F s = 𝜏 max \cdot \frac{3}{4} \cdot π \cdot r^{2}

Go Maximum Shear Stress given Radius of Circular Section

𝜏 beam = \frac{4}{3} \cdot \frac{F s}{π \cdot r^{2}}

How to Evaluate Maximum Shear Stress for Circular Section?

Maximum Shear Stress for Circular Section evaluator uses Maximum Shear Stress on Beam = Shear Force on Beam/(3*Moment of Inertia of Area of Section)*Radius of Circular Section^2 to evaluate the Maximum Shear Stress on Beam, The Maximum Shear Stress for Circular Section formula is defined as a measure of the maximum shear stress that occurs in a circular section, which is a critical parameter in mechanical engineering to determine the structural integrity of circular components under various loads. Maximum Shear Stress on Beam is denoted by 𝜏_max symbol.

How to evaluate Maximum Shear Stress for Circular Section using this online evaluator? To use this online evaluator for Maximum Shear Stress for Circular Section, enter Shear Force on Beam (F_s), Moment of Inertia of Area of Section (I) & Radius of Circular Section (r) and hit the calculate button.

FAQs on Maximum Shear Stress for Circular Section

What is the formula to find Maximum Shear Stress for Circular Section?

The formula of Maximum Shear Stress for Circular Section is expressed as Maximum Shear Stress on Beam = Shear Force on Beam/(3*Moment of Inertia of Area of Section)*Radius of Circular Section^2. Here is an example- 1.4E-6 = 4800/(3*0.00168)*1.2^2.

How to calculate Maximum Shear Stress for Circular Section?

With Shear Force on Beam (F_s), Moment of Inertia of Area of Section (I) & Radius of Circular Section (r) we can find Maximum Shear Stress for Circular Section using the formula - Maximum Shear Stress on Beam = Shear Force on Beam/(3*Moment of Inertia of Area of Section)*Radius of Circular Section^2.

What are the other ways to Calculate Maximum Shear Stress on Beam?

Here are the different ways to Calculate Maximum Shear Stress on Beam-

Maximum Shear Stress on Beam=4/3*Average Shear Stress on Beam

Can the Maximum Shear Stress for Circular Section be negative?

Yes, the Maximum Shear Stress for Circular Section, measured in Pressure can be negative.

Which unit is used to measure Maximum Shear Stress for Circular Section?

Maximum Shear Stress for Circular Section is usually measured using the Megapascal[MPa] for Pressure. Pascal[MPa], Kilopascal[MPa], Bar[MPa] are the few other units in which Maximum Shear Stress for Circular Section can be measured.

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