Moment of Inertia of Hollow Rectangle about Centroidal Axis x-x Parallel to Breadth Calculator

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✖Breadth of Rectangular Section is the shortest length.ⓘ Breadth of Rectangular Section [B]			+10% -10%
✖Length of Rectangular Section is the total distance from one end to other end, length is the longest side of rectangle.ⓘ Length of Rectangular Section [L_rect]			+10% -10%
✖Inner Breadth of Hollow Rectangular Section is the shorter breadth of the rectangle.ⓘ Inner Breadth of Hollow Rectangular Section [B_inner]			+10% -10%
✖Inner Length of Hollow Rectangle is the shorter length of the rectangle.ⓘ Inner Length of Hollow Rectangle [L_inner]			+10% -10%

✖Moment of Inertia about x-x axis is defined as the quantity expressed by the body resisting angular acceleration.ⓘ Moment of Inertia of Hollow Rectangle about Centroidal Axis x-x Parallel to Breadth [J_xx]

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Moment of Inertia of Hollow Rectangle about Centroidal Axis x-x Parallel to Breadth

Formula

`"J"_{"xx"} = (("B"*"L"_{"rect"}^3)-("B"_{"inner"}*"L"_{"inner"}^3))/12`

Example

`"1.224596m⁴"=(("1.99m"*("2.01m")^3)-("0.75m"*("1.25m")^3))/12`

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Moment of Inertia of Hollow Rectangle about Centroidal Axis x-x Parallel to Breadth Solution

STEP 0: Pre-Calculation Summary

Formula Used

Moment of Inertia about x-x axis = ((Breadth of Rectangular Section*Length of Rectangular Section^3)-(Inner Breadth of Hollow Rectangular Section*Inner Length of Hollow Rectangle^3))/12
J_xx = ((B*L_rect^3)-(B_inner*L_inner^3))/12
This formula uses 5 Variables

Variables Used

Moment of Inertia about x-x axis - (Measured in Meter⁴) - Moment of Inertia about x-x axis is defined as the quantity expressed by the body resisting angular acceleration.
Breadth of Rectangular Section - (Measured in Meter) - Breadth of Rectangular Section is the shortest length.
Length of Rectangular Section - (Measured in Meter) - Length of Rectangular Section is the total distance from one end to other end, length is the longest side of rectangle.
Inner Breadth of Hollow Rectangular Section - (Measured in Meter) - Inner Breadth of Hollow Rectangular Section is the shorter breadth of the rectangle.
Inner Length of Hollow Rectangle - (Measured in Meter) - Inner Length of Hollow Rectangle is the shorter length of the rectangle.

STEP 1: Convert Input(s) to Base Unit

Breadth of Rectangular Section: 1.99 Meter --> 1.99 Meter No Conversion Required
Length of Rectangular Section: 2.01 Meter --> 2.01 Meter No Conversion Required
Inner Breadth of Hollow Rectangular Section: 0.75 Meter --> 0.75 Meter No Conversion Required
Inner Length of Hollow Rectangle: 1.25 Meter --> 1.25 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

J_xx = ((B*L_rect^3)-(B_inner*L_inner^3))/12 --> ((1.99*2.01^3)-(0.75*1.25^3))/12

Evaluating ... ...

J_xx = 1.22459602

STEP 3: Convert Result to Output's Unit

1.22459602 Meter⁴ --> No Conversion Required

FINAL ANSWER

1.22459602 ≈ 1.224596 Meter⁴ <-- Moment of Inertia about x-x axis

(Calculation completed in 00.020 seconds)

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Institute of Aeronautical Engineering (IARE), Hyderabad

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< 7 Moment of Inertia in Solids Calculators

Moment of Inertia of Hollow Rectangle about Centroidal Axis x-x Parallel to Breadth

Go Moment of Inertia about x-x axis = ((Breadth of Rectangular Section*Length of Rectangular Section^3)-(Inner Breadth of Hollow Rectangular Section*Inner Length of Hollow Rectangle^3))/12

Moment of inertia of hollow circle about diametrical axis

Go Moment of Inertia for Solids = (pi/64)*(Outer Diameter of Hollow Circular Section^4-Inner Diameter of Hollow Circular Section^4)

Moment of inertia of rectangle about centroidal axis along x-x parallel to breadth

Go Moment of Inertia about x-x axis = Breadth of Rectangular Section*(Length of Rectangular Section^3/12)

Moment of inertia of rectangle about centroidal axis along y-y parallel to length

Go Moment of Inertia about y-y axis = Length of Rectangular Section*(Breadth of Rectangular Section^3)/12

Moment of inertia of triangle about centroidal axis x-x parallel to base

Go Moment of Inertia about x-x axis = (Base of Triangle*Height of Triangle^3)/36

Moment of inertia of semicircular section about its base

Go Moment of Inertia for Solids = 0.393*Radius of semi circle^4

Moment of inertia of semicircular section through center of gravity, parallel to base

Go Moment of Inertia for Solids = 0.11*Radius of semi circle^4

Moment of Inertia of Hollow Rectangle about Centroidal Axis x-x Parallel to Breadth Formula

What is moment of inertia?

Moment of inertia is defined as the quantity expressed by the body resisting angular acceleration which is the sum of the product of the mass of every particle with its square of a distance from the axis of rotation.

How to Calculate Moment of Inertia of Hollow Rectangle about Centroidal Axis x-x Parallel to Breadth?

Moment of Inertia of Hollow Rectangle about Centroidal Axis x-x Parallel to Breadth calculator uses Moment of Inertia about x-x axis = ((Breadth of Rectangular Section*Length of Rectangular Section^3)-(Inner Breadth of Hollow Rectangular Section*Inner Length of Hollow Rectangle^3))/12 to calculate the Moment of Inertia about x-x axis, Moment of Inertia of Hollow Rectangle about Centroidal Axis x-x Parallel to Breadth formula is defined as the 1/12 times of difference in product of breadth, cube of length and product of inner breadth, cube of inner length. Moment of Inertia about x-x axis is denoted by J_xx symbol.

How to calculate Moment of Inertia of Hollow Rectangle about Centroidal Axis x-x Parallel to Breadth using this online calculator? To use this online calculator for Moment of Inertia of Hollow Rectangle about Centroidal Axis x-x Parallel to Breadth, enter Breadth of Rectangular Section (B), Length of Rectangular Section (L_rect), Inner Breadth of Hollow Rectangular Section (B_inner) & Inner Length of Hollow Rectangle (L_inner) and hit the calculate button. Here is how the Moment of Inertia of Hollow Rectangle about Centroidal Axis x-x Parallel to Breadth calculation can be explained with given input values -> 1.224596 = ((1.99*2.01^3)-(0.75*1.25^3))/12.

FAQ

What is Moment of Inertia of Hollow Rectangle about Centroidal Axis x-x Parallel to Breadth?

Moment of Inertia of Hollow Rectangle about Centroidal Axis x-x Parallel to Breadth formula is defined as the 1/12 times of difference in product of breadth, cube of length and product of inner breadth, cube of inner length and is represented as J_xx = ((B*L_rect^3)-(B_inner*L_inner^3))/12 or Moment of Inertia about x-x axis = ((Breadth of Rectangular Section*Length of Rectangular Section^3)-(Inner Breadth of Hollow Rectangular Section*Inner Length of Hollow Rectangle^3))/12. Breadth of Rectangular Section is the shortest length, Length of Rectangular Section is the total distance from one end to other end, length is the longest side of rectangle, Inner Breadth of Hollow Rectangular Section is the shorter breadth of the rectangle & Inner Length of Hollow Rectangle is the shorter length of the rectangle.

How to calculate Moment of Inertia of Hollow Rectangle about Centroidal Axis x-x Parallel to Breadth?

Moment of Inertia of Hollow Rectangle about Centroidal Axis x-x Parallel to Breadth formula is defined as the 1/12 times of difference in product of breadth, cube of length and product of inner breadth, cube of inner length is calculated using Moment of Inertia about x-x axis = ((Breadth of Rectangular Section*Length of Rectangular Section^3)-(Inner Breadth of Hollow Rectangular Section*Inner Length of Hollow Rectangle^3))/12. To calculate Moment of Inertia of Hollow Rectangle about Centroidal Axis x-x Parallel to Breadth, you need Breadth of Rectangular Section (B), Length of Rectangular Section (L_rect), Inner Breadth of Hollow Rectangular Section (B_inner) & Inner Length of Hollow Rectangle (L_inner). With our tool, you need to enter the respective value for Breadth of Rectangular Section, Length of Rectangular Section, Inner Breadth of Hollow Rectangular Section & Inner Length of Hollow Rectangle 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 about x-x axis?

In this formula, Moment of Inertia about x-x axis uses Breadth of Rectangular Section, Length of Rectangular Section, Inner Breadth of Hollow Rectangular Section & Inner Length of Hollow Rectangle. We can use 2 other way(s) to calculate the same, which is/are as follows -

Moment of Inertia about x-x axis = Breadth of Rectangular Section*(Length of Rectangular Section^3/12)
Moment of Inertia about x-x axis = (Base of Triangle*Height of Triangle^3)/36

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