Moment of Inertia of Circular Section given Shear Stress Calculator

✖Shear Force on Beam is the force which causes shear deformation to occur in the shear plane.ⓘ Shear Force on Beam [F_s]			+10% -10%
✖The Radius of Circular Section is the distance from center of circle to the the circle.ⓘ Radius of Circular Section [R]			+10% -10%
✖Distance from Neutral Axis is the distance of the considered layer from the neutral layer.ⓘ Distance from Neutral Axis [y]			+10% -10%
✖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.ⓘ Shear Stress in Beam [𝜏_beam]			+10% -10%
✖Width of Beam Section is the width of the rectangular cross-section of the beam parallel to the axis in consideration.ⓘ Width of Beam Section [B]			+10% -10%

✖Moment of Inertia of Area of Section is the second moment of the area of the section about the neutral axis.ⓘ Moment of Inertia of Circular Section given Shear Stress [I]

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Formula

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Moment of Inertia of Circular Section given Shear Stress

Formula

`"I" = ("F"_{"s"}*2/3*("R"^2-"y"^2)^(3/2))/("𝜏"_{"beam"}*"B")`

Example

`"0.009216m⁴"=("4.8kN"*2/3*(("1200mm")^2-("5mm")^2)^(3/2))/("6MPa"*"100mm")`

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Moment of Inertia of Circular Section given Shear Stress Solution

STEP 0: Pre-Calculation Summary

Formula Used

Moment of Inertia of Area of Section = (Shear Force on Beam*2/3*(Radius of Circular Section^2-Distance from Neutral Axis^2)^(3/2))/(Shear Stress in Beam*Width of Beam Section)
I = (F_s*2/3*(R^2-y^2)^(3/2))/(𝜏_beam*B)
This formula uses 6 Variables

Variables Used

Moment of Inertia of Area of Section - (Measured in Meter⁴) - Moment of Inertia of Area of Section is the second moment of the area of the section about the neutral axis.
Shear Force on Beam - (Measured in Newton) - Shear Force on Beam is the force which causes shear deformation to occur in the shear plane.
Radius of Circular Section - (Measured in Meter) - The Radius of Circular Section is the distance from center of circle to the the circle.
Distance from Neutral Axis - (Measured in Meter) - Distance from Neutral Axis is the distance of the considered layer from the neutral layer.
Shear Stress in Beam - (Measured in Pascal) - 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.
Width of Beam Section - (Measured in Meter) - Width of Beam Section is the width of the rectangular cross-section of the beam parallel to the axis in consideration.

STEP 1: Convert Input(s) to Base Unit

Shear Force on Beam: 4.8 Kilonewton --> 4800 Newton (Check conversion here)
Radius of Circular Section: 1200 Millimeter --> 1.2 Meter (Check conversion here)
Distance from Neutral Axis: 5 Millimeter --> 0.005 Meter (Check conversion here)
Shear Stress in Beam: 6 Megapascal --> 6000000 Pascal (Check conversion here)
Width of Beam Section: 100 Millimeter --> 0.1 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

I = (F_s*2/3*(R^2-y^2)^(3/2))/(𝜏_beam*B) --> (4800*2/3*(1.2^2-0.005^2)^(3/2))/(6000000*0.1)

Evaluating ... ...

I = 0.00921576000104167

STEP 3: Convert Result to Output's Unit

0.00921576000104167 Meter⁴ --> No Conversion Required

FINAL ANSWER

0.00921576000104167 ≈ 0.009216 Meter⁴ <-- Moment of Inertia of Area of Section

(Calculation completed in 00.020 seconds)

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< 4 Moment of Inertia Calculators

Moment of Inertia of Circular Section given Shear Stress

Go Moment of Inertia of Area of Section = (Shear Force on Beam*2/3*(Radius of Circular Section^2-Distance from Neutral Axis^2)^(3/2))/(Shear Stress in Beam*Width of Beam Section)

Moment of Inertia of Circular Section given Maximum Shear Stress

Go Moment of Inertia of Area of Section = Shear Force on Beam/(3*Maximum Shear Stress on Beam)*Radius of Circular Section^2

Area Moment of Considered Area about Neutral Axis

Go First Moment of Area = 2/3*(Radius of Circular Section^2-Distance from Neutral Axis^2)^(3/2)

Moment of Inertia of Circular Section

Go Moment of Inertia of Area of Section = pi/4*Radius of Circular Section^4

Moment of Inertia of Circular Section given Shear Stress Formula

What is shear stress and strain?

When a force acts parallel to the surface of an object, it exerts a shear stress. Let's consider a rod under uniaxial tension. The rod elongates under this tension to a new length, and the normal strain is a ratio of this small deformation to the rod's original length.

How to Calculate Moment of Inertia of Circular Section given Shear Stress?

Moment of Inertia of Circular Section given Shear Stress calculator uses Moment of Inertia of Area of Section = (Shear Force on Beam*2/3*(Radius of Circular Section^2-Distance from Neutral Axis^2)^(3/2))/(Shear Stress in Beam*Width of Beam Section) to calculate the Moment of Inertia of Area of Section, Moment of Inertia of Circular Section given Shear Stress is a geometrical property of an area that reflects how its points are distributed with regard to an arbitrary axis. Moment of Inertia of Area of Section is denoted by I symbol.

How to calculate Moment of Inertia of Circular Section given Shear Stress using this online calculator? To use this online calculator for Moment of Inertia of Circular Section given Shear Stress, enter Shear Force on Beam (F_s), Radius of Circular Section (R), Distance from Neutral Axis (y), Shear Stress in Beam (𝜏_beam) & Width of Beam Section (B) and hit the calculate button. Here is how the Moment of Inertia of Circular Section given Shear Stress calculation can be explained with given input values -> 0.009216 = (4800*2/3*(1.2^2-0.005^2)^(3/2))/(6000000*0.1).

FAQ

What is Moment of Inertia of Circular Section given Shear Stress?

Moment of Inertia of Circular Section given Shear Stress is a geometrical property of an area that reflects how its points are distributed with regard to an arbitrary axis and is represented as I = (F_s*2/3*(R^2-y^2)^(3/2))/(𝜏_beam*B) or Moment of Inertia of Area of Section = (Shear Force on Beam*2/3*(Radius of Circular Section^2-Distance from Neutral Axis^2)^(3/2))/(Shear Stress in Beam*Width of Beam Section). Shear Force on Beam is the force which causes shear deformation to occur in the shear plane, The Radius of Circular Section is the distance from center of circle to the the circle, Distance from Neutral Axis is the distance of the considered layer from the neutral layer, 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 & Width of Beam Section is the width of the rectangular cross-section of the beam parallel to the axis in consideration.

How to calculate Moment of Inertia of Circular Section given Shear Stress?

Moment of Inertia of Circular Section given Shear Stress is a geometrical property of an area that reflects how its points are distributed with regard to an arbitrary axis is calculated using Moment of Inertia of Area of Section = (Shear Force on Beam*2/3*(Radius of Circular Section^2-Distance from Neutral Axis^2)^(3/2))/(Shear Stress in Beam*Width of Beam Section). To calculate Moment of Inertia of Circular Section given Shear Stress, you need Shear Force on Beam (F_s), Radius of Circular Section (R), Distance from Neutral Axis (y), Shear Stress in Beam (𝜏_beam) & Width of Beam Section (B). With our tool, you need to enter the respective value for Shear Force on Beam, Radius of Circular Section, Distance from Neutral Axis, Shear Stress in Beam & Width of Beam Section and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Moment of Inertia of Area of Section?

In this formula, Moment of Inertia of Area of Section uses Shear Force on Beam, Radius of Circular Section, Distance from Neutral Axis, Shear Stress in Beam & Width of Beam Section. We can use 2 other way(s) to calculate the same, which is/are as follows -

Moment of Inertia of Area of Section = Shear Force on Beam/(3*Maximum Shear Stress on Beam)*Radius of Circular Section^2
Moment of Inertia of Area of Section = pi/4*Radius of Circular Section^4

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