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Shear Stress Distribution for Circular Section 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 \cdot \frac{2}{3} \cdot {(r^{2} - y^{2})}^{\frac{3}{2}}}{I \cdot B}

𝜏_max - Maximum Shear Stress on Beam?F_s - Shear Force on Beam?r - Radius of Circular Section?y - Distance from Neutral Axis?I - Moment of Inertia of Area of Section?B - Width of Beam Section?

Shear Stress Distribution for Circular Section Example

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

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

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

32.9134 = \frac{4.8 \cdot \frac{2}{3} \cdot {(1200^{2} - 5^{2})}^{\frac{3}{2}}}{0.0017 \cdot 100}

32.9134MPa = \frac{4.8kN \cdot \frac{2}{3} \cdot {({1200mm}^{2} - {5mm}^{2})}^{\frac{3}{2}}}{0.0017m⁴ \cdot 100mm}

32.9134 = \frac{4.8 \cdot \frac{2}{3} \cdot {(1200^{2} - 5^{2})}^{\frac{3}{2}}}{0.0017 \cdot 100}

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Shear Stress Distribution for Circular Section Solution

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

FIRST Step Consider the formula

𝜏 max = \frac{F s \cdot \frac{2}{3} \cdot {(r^{2} - y^{2})}^{\frac{3}{2}}}{I \cdot B}

Next Step Substitute values of Variables

∴

𝜏 max = \frac{4.8kN \cdot \frac{2}{3} \cdot {({1200mm}^{2} - {5mm}^{2})}^{\frac{3}{2}}}{0.0017m⁴ \cdot 100mm}

Next Step Convert Units

∴

𝜏 max = \frac{4800N \cdot \frac{2}{3} \cdot {({1.2m}^{2} - {0.005m}^{2})}^{\frac{3}{2}}}{0.0017m⁴ \cdot 0.1m}

Next Step Prepare to Evaluate

∴

𝜏 max = \frac{4800 \cdot \frac{2}{3} \cdot {({1.2}^{2} - {0.005}^{2})}^{\frac{3}{2}}}{0.0017 \cdot 0.1}

Next Step Evaluate

∴

𝜏 max = 32913428.5751488Pa

Next Step Convert to Output's Unit

∴

𝜏 max = 32.9134285751488MPa

LAST Step Rounding Answer

∴

𝜏 max = 32.9134MPa

Shear Stress Distribution 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

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

Distance from Neutral Axis

Distance from Neutral Axis is the perpendicular distance from a point in an element to the neutral axis, it is the line where element experiences no stress when the beam is subjected to bending.

Symbol: y

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Distance from Neutral Axis

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

Width of Beam Section

Width of Beam Section is the width of the rectangular cross-section of the beam parallel to the axis in consideration.

Symbol: B

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Width of Beam Section

Other formulas in Average Shear Stress category

Go Average Shear Stress for Circular Section given Maximum Shear Stress

𝜏 avg = \frac{3}{4} \cdot 𝜏 max

Go Average Shear Stress for Circular Section

𝜏 avg = \frac{F s}{π \cdot r^{2}}

Go Average Shear Force for Circular Section

F s = π \cdot r^{2} \cdot 𝜏 avg

Go Shear Force using Maximum Shear Stress

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

How to Evaluate Shear Stress Distribution for Circular Section?

Shear Stress Distribution for Circular Section evaluator uses Maximum Shear Stress on Beam = (Shear Force on Beam*2/3*(Radius of Circular Section^2-Distance from Neutral Axis^2)^(3/2))/(Moment of Inertia of Area of Section*Width of Beam Section) to evaluate the Maximum Shear Stress on Beam, The Shear Stress Distribution for Circular Section formula is defined as a measure of the maximum shear stress occurring at a given point in a circular section, typically in a beam or shaft, which is essential in mechanical engineering to determine the structural integrity and potential failure points of a circular cross-section under various loads. Maximum Shear Stress on Beam is denoted by 𝜏_max symbol.

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

FAQs on Shear Stress Distribution for Circular Section

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

The formula of Shear Stress Distribution for Circular Section is expressed as Maximum Shear Stress on Beam = (Shear Force on Beam*2/3*(Radius of Circular Section^2-Distance from Neutral Axis^2)^(3/2))/(Moment of Inertia of Area of Section*Width of Beam Section). Here is an example- 3.3E-5 = (4800*2/3*(1.2^2-0.005^2)^(3/2))/(0.00168*0.1).

How to calculate Shear Stress Distribution for Circular Section?

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

Can the Shear Stress Distribution for Circular Section be negative?

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

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

Shear Stress Distribution 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 Shear Stress Distribution for Circular Section can be measured.

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Shear Stress Distribution for Circular Section Formula

Shear Stress Distribution for Circular Section Example

Shear Stress Distribution for Circular Section Solution

Shear Stress Distribution for Circular Section Formula Elements

Other formulas in Average Shear Stress category

How to Evaluate Shear Stress Distribution for Circular Section?

FAQs on Shear Stress Distribution for Circular Section

Variable Name