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Maximum Shear Stress given Radius of Circular Section Formula

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Shear Stress in Beam is force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress. Check FAQs

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

𝜏_beam - Shear Stress in Beam?F_s - Shear Force on Beam?r - Radius of Circular Section?π - Archimedes' constant?

Maximum Shear Stress given Radius of Circular Section Example

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Here is how the Maximum Shear Stress given Radius of Circular Section equation looks like with Values.

Here is how the Maximum Shear Stress given Radius of Circular Section equation looks like with Units.

Here is how the Maximum Shear Stress given Radius of Circular Section equation looks like.

0.0014 = \frac{4}{3} \cdot \frac{4.8}{3.1416 \cdot 1200^{2}}

0.0014MPa = \frac{4}{3} \cdot \frac{4.8kN}{3.1416 \cdot {1200mm}^{2}}

0.0014 = \frac{4}{3} \cdot \frac{4.8}{3.1416 \cdot 1200^{2}}

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Home » Physics » Mechanical » Strength of Materials » Maximum Shear Stress given Radius of Circular Section

Maximum Shear Stress given Radius of Circular Section Solution

Follow our step by step solution on how to calculate Maximum Shear Stress given Radius of Circular Section?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

𝜏 beam = \frac{4}{3} \cdot \frac{4.8kN}{π \cdot {1200mm}^{2}}

Next Step Substitute values of Constants

∴

𝜏 beam = \frac{4}{3} \cdot \frac{4.8kN}{3.1416 \cdot {1200mm}^{2}}

Next Step Convert Units

∴

𝜏 beam = \frac{4}{3} \cdot \frac{4800N}{3.1416 \cdot {1.2m}^{2}}

Next Step Prepare to Evaluate

∴

𝜏 beam = \frac{4}{3} \cdot \frac{4800}{3.1416 \cdot {1.2}^{2}}

Next Step Evaluate

∴

𝜏 beam = 1414.71060526129Pa

Next Step Convert to Output's Unit

∴

𝜏 beam = 0.00141471060526129MPa

LAST Step Rounding Answer

∴

𝜏 beam = 0.0014MPa

Maximum Shear Stress given Radius of Circular Section Formula Elements

Variables

Constants

Shear Stress in Beam

Shear Stress in Beam is force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.

Symbol: 𝜏_beam

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

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.

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.

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

Credits

Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

Anshika Arya has created this Formula and 2000+ more formulas!

Verified by Dipto Mandal

Indian Institute of Information Technology (IIIT), Guwahati

Dipto Mandal has verified this Formula and 400+ more formulas!

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 for Circular Section

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

Go Maximum Shear Stress for Circular Section given Average Shear Stress

𝜏 max = \frac{4}{3} \cdot 𝜏 avg

How to Evaluate Maximum Shear Stress given Radius of Circular Section?

Maximum Shear Stress given Radius of Circular Section evaluator uses Shear Stress in Beam = 4/3*Shear Force on Beam/(pi*Radius of Circular Section^2) to evaluate the Shear Stress in Beam, The Maximum Shear Stress given Radius of Circular Section formula is defined as a measure of the maximum shear stress that occurs in a circular section of a beam, which is a critical parameter in the design of beams and shafts to resist failure due to shear forces. Shear Stress in Beam is denoted by 𝜏_beam symbol.

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

FAQs on Maximum Shear Stress given Radius of Circular Section

What is the formula to find Maximum Shear Stress given Radius of Circular Section?

The formula of Maximum Shear Stress given Radius of Circular Section is expressed as Shear Stress in Beam = 4/3*Shear Force on Beam/(pi*Radius of Circular Section^2). Here is an example- 1.4E-9 = 4/3*4800/(pi*1.2^2).

How to calculate Maximum Shear Stress given Radius of Circular Section?

With Shear Force on Beam (F_s) & Radius of Circular Section (r) we can find Maximum Shear Stress given Radius of Circular Section using the formula - Shear Stress in Beam = 4/3*Shear Force on Beam/(pi*Radius of Circular Section^2). This formula also uses Archimedes' constant .

Can the Maximum Shear Stress given Radius of Circular Section be negative?

No, the Maximum Shear Stress given Radius of Circular Section, measured in Pressure cannot be negative.

Which unit is used to measure Maximum Shear Stress given Radius of Circular Section?

Maximum Shear Stress given Radius of 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 given Radius of Circular Section can be measured.

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