Moment of Inertia given Radius of Gyration in Eccentric Loading Solution

STEP 0: Pre-Calculation Summary
Formula Used
Moment of Inertia = (Radius of Gyration^2)*Cross-Sectional Area
I = (kG^2)*Acs
This formula uses 3 Variables
Variables Used
Moment of Inertia - (Measured in Kilogram Square Meter) - Moment of Inertia is the measure of the resistance of a body to angular acceleration about a given axis.
Radius of Gyration - (Measured in Millimeter) - The radius of gyration or gyradius is defined as the radial distance to a point that would have a moment of inertia the same as the body's actual distribution of mass.
Cross-Sectional Area - (Measured in Square Meter) - Cross-Sectional Area is the area of a two-dimensional shape that is obtained when a three-dimensional shape is sliced perpendicular to some specified axis at a point.
STEP 1: Convert Input(s) to Base Unit
Radius of Gyration: 0.29 Millimeter --> 0.29 Millimeter No Conversion Required
Cross-Sectional Area: 13 Square Meter --> 13 Square Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
I = (kG^2)*Acs --> (0.29^2)*13
Evaluating ... ...
I = 1.0933
STEP 3: Convert Result to Output's Unit
1.0933 Kilogram Square Meter --> No Conversion Required
FINAL ANSWER
1.0933 Kilogram Square Meter <-- Moment of Inertia
(Calculation completed in 00.004 seconds)

Credits

Created by Kethavath Srinath
Osmania University (OU), Hyderabad
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Cummins College of Engineering for Women (CCEW), Pune
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18 Eccentric Loading Calculators

Cross-Sectional Area given Total Stress is where Load doesn't lie on Plane
Go Cross-Sectional Area = Axial Load/(Total Stress-(((Eccentricity with respect to Principal Axis YY*Axial Load*Distance from YY to Outermost Fiber)/(Moment of Inertia about Y-Axis))+((Eccentricity with respect to Principal Axis XX*Axial Load*Distance from XX to Outermost Fiber)/(Moment of Inertia about X-Axis))))
Distance from YY to outermost fiber given Total Stress where Load doesn't lie on Plane
Go Distance from YY to Outermost Fiber = (Total Stress-((Axial Load/Cross-Sectional Area)+((Eccentricity with respect to Principal Axis XX*Axial Load*Distance from XX to Outermost Fiber)/(Moment of Inertia about X-Axis))))*Moment of Inertia about Y-Axis/(Eccentricity with respect to Principal Axis YY*Axial Load)
Distance from XX to outermost fiber given Total Stress where Load doesn't lie on Plane
Go Distance from XX to Outermost Fiber = ((Total Stress-(Axial Load/Cross-Sectional Area)-((Eccentricity with respect to Principal Axis YY*Axial Load*Distance from YY to Outermost Fiber)/(Moment of Inertia about Y-Axis)))*Moment of Inertia about X-Axis)/(Axial Load*Eccentricity with respect to Principal Axis XX)
Eccentricity w.r.t axis XX given Total Stress where Load doesn't lie on Plane
Go Eccentricity with respect to Principal Axis XX = ((Total Stress-(Axial Load/Cross-Sectional Area)-((Eccentricity with respect to Principal Axis YY*Axial Load*Distance from YY to Outermost Fiber)/(Moment of Inertia about Y-Axis)))*Moment of Inertia about X-Axis)/(Axial Load*Distance from XX to Outermost Fiber)
Total Stress in Eccentric Loading when Load doesn't lie on Plane
Go Total Stress = (Axial Load/Cross-Sectional Area)+((Eccentricity with respect to Principal Axis YY*Axial Load*Distance from YY to Outermost Fiber)/(Moment of Inertia about Y-Axis))+((Eccentricity with respect to Principal Axis XX*Axial Load*Distance from XX to Outermost Fiber)/(Moment of Inertia about X-Axis))
Moment of Inertia about XX given Total Stress where Load doesn't lie on Plane
Go Moment of Inertia about X-Axis = (Eccentricity with respect to Principal Axis XX*Axial Load*Distance from XX to Outermost Fiber)/(Total Stress-((Axial Load/Cross-Sectional Area)+((Eccentricity with respect to Principal Axis YY*Axial Load*Distance from YY to Outermost Fiber)/Moment of Inertia about Y-Axis)))
Moment of Inertia about YY given Total Stress where Load doesn't lie on Plane
Go Moment of Inertia about Y-Axis = (Eccentricity with respect to Principal Axis YY*Axial Load*Distance from YY to Outermost Fiber)/(Total Stress-((Axial Load/Cross-Sectional Area)+((Eccentricity with respect to Principal Axis XX*Axial Load*Distance from XX to Outermost Fiber)/Moment of Inertia about X-Axis)))
Eccentricity wrt axis YY given Total Stress where Load doesn't lie on Plane
Go Eccentricity with respect to Principal Axis YY = ((Total Stress-(Axial Load/Cross-Sectional Area)-(Eccentricity with respect to Principal Axis XX*Axial Load*Distance from XX to Outermost Fiber)/(Moment of Inertia about X-Axis))*Moment of Inertia about Y-Axis)/(Axial Load*Distance from YY to Outermost Fiber)
Moment of Inertia of Cross-Section given Total Unit Stress in Eccentric Loading
Go Moment of Inertia about Neutral Axis = (Axial Load*Outermost Fiber Distance*Distance from Load applied)/(Total Unit Stress-(Axial Load/Cross-Sectional Area))
Cross-Sectional Area given Total Unit Stress in Eccentric Loading
Go Cross-Sectional Area = Axial Load/(Total Unit Stress-((Axial Load*Outermost Fiber Distance*Distance from Load applied/Moment of Inertia about Neutral Axis)))
Total Unit Stress in Eccentric Loading
Go Total Unit Stress = (Axial Load/Cross-Sectional Area)+(Axial Load*Outermost Fiber Distance*Distance from Load applied/Moment of Inertia about Neutral Axis)
Critical Buckling Load given Deflection in Eccentric Loading
Go Critical Buckling Load = (Axial Load*(4*Eccentricity of Load+pi*Deflection in Eccentric Loading))/(Deflection in Eccentric Loading*pi)
Eccentricity given Deflection in Eccentric Loading
Go Eccentricity of Load = (pi*(1-Axial Load/Critical Buckling Load))*Deflection in Eccentric Loading/(4*Axial Load/Critical Buckling Load)
Deflection in Eccentric Loading
Go Deflection in Eccentric Loading = (4*Eccentricity of Load*Axial Load/Critical Buckling Load)/(pi*(1-Axial Load/Critical Buckling Load))
Load for Deflection in Eccentric Loading
Go Axial Load = (Critical Buckling Load*Deflection in Eccentric Loading*pi)/(4*Eccentricity of Load+pi*Deflection in Eccentric Loading)
Radius of Gyration in Eccentric Loading
Go Radius of Gyration = sqrt(Moment of Inertia/Cross-Sectional Area)
Cross-Sectional Area given Radius of Gyration in Eccentric Loading
Go Cross-Sectional Area = Moment of Inertia/(Radius of Gyration^2)
Moment of Inertia given Radius of Gyration in Eccentric Loading
Go Moment of Inertia = (Radius of Gyration^2)*Cross-Sectional Area

Moment of Inertia given Radius of Gyration in Eccentric Loading Formula

Moment of Inertia = (Radius of Gyration^2)*Cross-Sectional Area
I = (kG^2)*Acs

Define Moment of Inertia

The moment of inertia, otherwise known as the mass moment of inertia, angular mass, or rotational inertia, of a rigid body, is a quantity that determines the torque needed for a desired angular acceleration about a rotational axis; similar to how mass determines the force needed for the desired acceleration. It depends on the body's mass distribution and the axis chosen, with larger moments requiring more torque to change the body's rate of rotation.

How to Calculate Moment of Inertia given Radius of Gyration in Eccentric Loading?

Moment of Inertia given Radius of Gyration in Eccentric Loading calculator uses Moment of Inertia = (Radius of Gyration^2)*Cross-Sectional Area to calculate the Moment of Inertia, Moment of Inertia given Radius of Gyration in Eccentric Loading formula is a quantity expressing a body's tendency to resist angular acceleration. Moment of Inertia is denoted by I symbol.

How to calculate Moment of Inertia given Radius of Gyration in Eccentric Loading using this online calculator? To use this online calculator for Moment of Inertia given Radius of Gyration in Eccentric Loading, enter Radius of Gyration (kG) & Cross-Sectional Area (Acs) and hit the calculate button. Here is how the Moment of Inertia given Radius of Gyration in Eccentric Loading calculation can be explained with given input values -> 117 = (0.00029^2)*13.

FAQ

What is Moment of Inertia given Radius of Gyration in Eccentric Loading?
Moment of Inertia given Radius of Gyration in Eccentric Loading formula is a quantity expressing a body's tendency to resist angular acceleration and is represented as I = (kG^2)*Acs or Moment of Inertia = (Radius of Gyration^2)*Cross-Sectional Area. The radius of gyration or gyradius is defined as the radial distance to a point that would have a moment of inertia the same as the body's actual distribution of mass & Cross-Sectional Area is the area of a two-dimensional shape that is obtained when a three-dimensional shape is sliced perpendicular to some specified axis at a point.
How to calculate Moment of Inertia given Radius of Gyration in Eccentric Loading?
Moment of Inertia given Radius of Gyration in Eccentric Loading formula is a quantity expressing a body's tendency to resist angular acceleration is calculated using Moment of Inertia = (Radius of Gyration^2)*Cross-Sectional Area. To calculate Moment of Inertia given Radius of Gyration in Eccentric Loading, you need Radius of Gyration (kG) & Cross-Sectional Area (Acs). With our tool, you need to enter the respective value for Radius of Gyration & Cross-Sectional Area 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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