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Radius of Circular Section given Maximum Shear Stress Formula

GoRadius of Circular Section given Width of Beam at Considered Level Formula

GoRadius of Circular Section given Average Shear Stress Formula

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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. Check FAQs

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

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

Radius of Circular Section given Maximum Shear Stress Example

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

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

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

13.6088 = \sqrt{\frac{4}{3} \cdot \frac{4.8}{3.1416 \cdot 11}}

13.6088mm = \sqrt{\frac{4}{3} \cdot \frac{4.8kN}{3.1416 \cdot 11MPa}}

13.6088 = \sqrt{\frac{4}{3} \cdot \frac{4.8}{3.1416 \cdot 11}}

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Radius of Circular Section given Maximum Shear Stress Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

r = \sqrt{\frac{4}{3} \cdot \frac{4.8kN}{π \cdot 11MPa}}

Next Step Substitute values of Constants

∴

r = \sqrt{\frac{4}{3} \cdot \frac{4.8kN}{3.1416 \cdot 11MPa}}

Next Step Convert Units

∴

r = \sqrt{\frac{4}{3} \cdot \frac{4800N}{3.1416 \cdot 1.1E+7Pa}}

Next Step Prepare to Evaluate

∴

r = \sqrt{\frac{4}{3} \cdot \frac{4800}{3.1416 \cdot 1.1E+7}}

Next Step Evaluate

∴

r = 0.0136087647945802m

Next Step Convert to Output's Unit

∴

r = 13.6087647945802mm

LAST Step Rounding Answer

∴

r = 13.6088mm

Radius of Circular Section given Maximum Shear Stress Formula Elements

Variables

Constants

Functions

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

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

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

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 to find Radius of Circular Section

Go Radius of Circular Section given Width of Beam at Considered Level

r = \sqrt{{(\frac{B}{2})}^{2} + y^{2}}

Go Radius of Circular Section given Average Shear Stress

r = \sqrt{\frac{F s}{π \cdot 𝜏 avg}}

Other formulas in Radius of Circular Section category

Go Width of Beam at Considered Level given Radius of Circular Section

B = 2 \cdot \sqrt{r^{2} - y^{2}}

Go Width of Beam at Considered Level given Shear Stress for Circular Section

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

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

Radius of Circular Section given Maximum Shear Stress evaluator uses Radius of Circular Section = sqrt(4/3*Shear Force on Beam/(pi*Maximum Shear Stress on Beam)) to evaluate the Radius of Circular Section, The Radius of Circular Section given Maximum Shear Stress formula is defined as a measure of the radius of a circular section that can withstand a maximum shear stress, providing a critical value for structural integrity in engineering design and analysis. Radius of Circular Section is denoted by r symbol.

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

FAQs on Radius of Circular Section given Maximum Shear Stress

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

The formula of Radius of Circular Section given Maximum Shear Stress is expressed as Radius of Circular Section = sqrt(4/3*Shear Force on Beam/(pi*Maximum Shear Stress on Beam)). Here is an example- 13608.76 = sqrt(4/3*4800/(pi*11000000)).

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

With Shear Force on Beam (F_s) & Maximum Shear Stress on Beam (𝜏_max) we can find Radius of Circular Section given Maximum Shear Stress using the formula - Radius of Circular Section = sqrt(4/3*Shear Force on Beam/(pi*Maximum Shear Stress on Beam)). This formula also uses Archimedes' constant and Square Root (sqrt) function(s).

What are the other ways to Calculate Radius of Circular Section?

Here are the different ways to Calculate Radius of Circular Section-

Radius of Circular Section=sqrt((Width of Beam Section/2)^2+Distance from Neutral Axis^2)
Radius of Circular Section=sqrt(Shear Force on Beam/(pi*Average Shear Stress on Beam))

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

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

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

Radius of Circular Section given Maximum Shear Stress is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Radius of Circular Section given Maximum Shear Stress can be measured.

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