Moment of Inertia of Rectangular Section about Neutral Axis 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%
✖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%
✖Depth of Rectangular Section is the distance from the top or surface to the bottom of the section.ⓘ Depth of Rectangular Section [d_rec]			+10% -10%
✖Distance from Neutral Axis is the distance of the considered layer from the neutral layer.ⓘ Distance from Neutral Axis [y]			+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 Rectangular Section about Neutral Axis [I]

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Formula

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Moment of Inertia of Rectangular Section about Neutral Axis

Formula

`"I" = "F"_{"s"}/(2*"𝜏"_{"beam"})*("d"_{"rec"}^2/4-"y"^2)`

Example

`"8.1E^-6m⁴"="4.8kN"/(2*"6MPa")*(("285mm")^2/4-("5mm")^2)`

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Moment of Inertia of Rectangular Section about Neutral Axis Solution

STEP 0: Pre-Calculation Summary

Formula Used

Moment of Inertia of Area of Section = Shear Force on Beam/(2*Shear Stress in Beam)*(Depth of Rectangular Section^2/4-Distance from Neutral Axis^2)
I = F_s/(2*𝜏_beam)*(d_rec^2/4-y^2)
This formula uses 5 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.
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.
Depth of Rectangular Section - (Measured in Meter) - Depth of Rectangular Section is the distance from the top or surface to the bottom of the section.
Distance from Neutral Axis - (Measured in Meter) - Distance from Neutral Axis is the distance of the considered layer from the neutral layer.

STEP 1: Convert Input(s) to Base Unit

Shear Force on Beam: 4.8 Kilonewton --> 4800 Newton (Check conversion here)
Shear Stress in Beam: 6 Megapascal --> 6000000 Pascal (Check conversion here)
Depth of Rectangular Section: 285 Millimeter --> 0.285 Meter (Check conversion here)
Distance from Neutral Axis: 5 Millimeter --> 0.005 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

I = F_s/(2*𝜏_beam)*(d_rec^2/4-y^2) --> 4800/(2*6000000)*(0.285^2/4-0.005^2)

Evaluating ... ...

I = 8.1125E-06

STEP 3: Convert Result to Output's Unit

8.1125E-06 Meter⁴ --> No Conversion Required

FINAL ANSWER

8.1125E-06 ≈ 8.1E-6 Meter⁴ <-- Moment of Inertia of Area of Section

(Calculation completed in 00.004 seconds)

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< 10+ Shear Stress in Rectangular Section Calculators

Moment of Inertia of Rectangular Section about Neutral Axis

Go Moment of Inertia of Area of Section = Shear Force on Beam/(2*Shear Stress in Beam)*(Depth of Rectangular Section^2/4-Distance from Neutral Axis^2)

Shear Stress for Rectangular Section

Go Shear Stress in Beam = Shear Force on Beam/(2*Moment of Inertia of Area of Section)*(Depth of Rectangular Section^2/4-Distance from Neutral Axis^2)

Shear Force for Rectangular Section

Go Shear Force on Beam = (2*Moment of Inertia of Area of Section*Shear Stress in Beam)/(Depth of Rectangular Section^2/4-Distance from Neutral Axis^2)

Average Shear Stress for Rectangular Section

Go Average Shear Stress on Beam = Shear Force on Beam/(Beam Width at Considered Level*Depth of Rectangular Section)

Shear Stress Variation across Neutral Axis for Rectangular Section

Go Shear Stress in Beam = 3/2*Shear Force on Beam/(Beam Width at Considered Level*Depth of Rectangular Section)

Shear Force Variation across Neutral Axis for Rectangular Section

Go Shear Force on Beam = 2/3*Shear Stress in Beam*Beam Width at Considered Level*Depth of Rectangular Section

Distance of C.G of Area (above Considered Level) from Neutral Axis for Rectangular Section

Go Distance of CG of Area from NA = 1/2*(Distance from Neutral Axis+Depth of Rectangular Section/2)

Distance of Considered Level from Neutral Axis for Rectangular Section

Go Distance from Neutral Axis = 2*(Distance of CG of Area from NA-Depth of Rectangular Section/4)

Average Shear Stress given Maximum Shear Stress for Rectangular Section

Go Average Shear Stress on Beam = 2/3*Maximum Shear Stress on Beam

Maximum Shear Stress for Rectangular Section

Go Maximum Shear Stress on Beam = 3/2*Average Shear Stress on Beam

Moment of Inertia of Rectangular Section about Neutral Axis Formula

Moment of Inertia of Area of Section = Shear Force on Beam/(2*Shear Stress in Beam)*(Depth of Rectangular Section^2/4-Distance from Neutral Axis^2)
I = F_s/(2*𝜏_beam)*(d_rec^2/4-y^2)

In which section maximum shear stress position is not at the neutral axis of section?

Nevertheless, the maximum shear stress does not always occur at the neutral axis. For instance, in the case of a cross section having nonparallel sides, such as a triangular section, the maximum value of Q/b (and thus τxy) occurs at mid height, h/2, while the neutral axis is located at a distance h/3 from the base.

How to Calculate Moment of Inertia of Rectangular Section about Neutral Axis?

Moment of Inertia of Rectangular Section about Neutral Axis calculator uses Moment of Inertia of Area of Section = Shear Force on Beam/(2*Shear Stress in Beam)*(Depth of Rectangular Section^2/4-Distance from Neutral Axis^2) to calculate the Moment of Inertia of Area of Section, The Moment of inertia of rectangular section about neutral axis formula is defined as the quantity expressed by the body resisting angular acceleration. Moment of Inertia of Area of Section is denoted by I symbol.

How to calculate Moment of Inertia of Rectangular Section about Neutral Axis using this online calculator? To use this online calculator for Moment of Inertia of Rectangular Section about Neutral Axis, enter Shear Force on Beam (F_s), Shear Stress in Beam (𝜏_beam), Depth of Rectangular Section (d_rec) & Distance from Neutral Axis (y) and hit the calculate button. Here is how the Moment of Inertia of Rectangular Section about Neutral Axis calculation can be explained with given input values -> 8.1E-6 = 4800/(2*6000000)*(0.285^2/4-0.005^2).

FAQ

What is Moment of Inertia of Rectangular Section about Neutral Axis?

The Moment of inertia of rectangular section about neutral axis formula is defined as the quantity expressed by the body resisting angular acceleration and is represented as I = F_s/(2*𝜏_beam)*(d_rec^2/4-y^2) or Moment of Inertia of Area of Section = Shear Force on Beam/(2*Shear Stress in Beam)*(Depth of Rectangular Section^2/4-Distance from Neutral Axis^2). Shear Force on Beam is the force which causes shear deformation to occur in the shear plane, 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, Depth of Rectangular Section is the distance from the top or surface to the bottom of the section & Distance from Neutral Axis is the distance of the considered layer from the neutral layer.

How to calculate Moment of Inertia of Rectangular Section about Neutral Axis?

The Moment of inertia of rectangular section about neutral axis formula is defined as the quantity expressed by the body resisting angular acceleration is calculated using Moment of Inertia of Area of Section = Shear Force on Beam/(2*Shear Stress in Beam)*(Depth of Rectangular Section^2/4-Distance from Neutral Axis^2). To calculate Moment of Inertia of Rectangular Section about Neutral Axis, you need Shear Force on Beam (F_s), Shear Stress in Beam (𝜏_beam), Depth of Rectangular Section (d_rec) & Distance from Neutral Axis (y). With our tool, you need to enter the respective value for Shear Force on Beam, Shear Stress in Beam, Depth of Rectangular Section & Distance from Neutral Axis and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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