Cross-Sectional Area given Radius of Gyration in Eccentric Loading Solution

STEP 0: Pre-Calculation Summary
Formula Used
Cross-Sectional Area = Moment of Inertia/(Radius of Gyration^2)
Acs = I/(kG^2)
This formula uses 3 Variables
Variables Used
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.
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.
STEP 1: Convert Input(s) to Base Unit
Moment of Inertia: 1.125 Kilogram Square Meter --> 1.125 Kilogram Square Meter No Conversion Required
Radius of Gyration: 0.29 Millimeter --> 0.29 Millimeter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Acs = I/(kG^2) --> 1.125/(0.29^2)
Evaluating ... ...
Acs = 13.3769322235434
STEP 3: Convert Result to Output's Unit
13.3769322235434 Square Meter --> No Conversion Required
FINAL ANSWER
13.3769322235434 13.37693 Square Meter <-- Cross-Sectional Area
(Calculation completed in 00.004 seconds)

Credits

Created by Kethavath Srinath
Osmania University (OU), Hyderabad
Kethavath Srinath has created this Calculator and 1000+ more calculators!
Verified by Rudrani Tidke
Cummins College of Engineering for Women (CCEW), Pune
Rudrani Tidke has verified this Calculator and 50+ more calculators!

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

Cross-Sectional Area given Radius of Gyration in Eccentric Loading Formula

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

Define Radius of Gyration

The radius of gyration or gyradius of a body about an axis of rotation is defined as the radial distance to a point which would have a moment of inertia the same as the body's actual distribution of mass if the total mass of the body were concentrated there.

How to Calculate Cross-Sectional Area given Radius of Gyration in Eccentric Loading?

Cross-Sectional Area given Radius of Gyration in Eccentric Loading calculator uses Cross-Sectional Area = Moment of Inertia/(Radius of Gyration^2) to calculate the Cross-Sectional Area, The Cross-Sectional Area given Radius of Gyration in Eccentric Loading formula is the area of a two-dimensional shape that is obtained when a three-dimensional object is sliced perpendicular to some specified axis at a point. Cross-Sectional Area is denoted by Acs symbol.

How to calculate Cross-Sectional Area given Radius of Gyration in Eccentric Loading using this online calculator? To use this online calculator for Cross-Sectional Area given Radius of Gyration in Eccentric Loading, enter Moment of Inertia (I) & Radius of Gyration (kG) and hit the calculate button. Here is how the Cross-Sectional Area given Radius of Gyration in Eccentric Loading calculation can be explained with given input values -> 0.125 = 1.125/(0.00029^2).

FAQ

What is Cross-Sectional Area given Radius of Gyration in Eccentric Loading?
The Cross-Sectional Area given Radius of Gyration in Eccentric Loading formula is the area of a two-dimensional shape that is obtained when a three-dimensional object is sliced perpendicular to some specified axis at a point and is represented as Acs = I/(kG^2) or Cross-Sectional Area = Moment of Inertia/(Radius of Gyration^2). Moment of Inertia is the measure of the resistance of a body to angular acceleration about a given axis & 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.
How to calculate Cross-Sectional Area given Radius of Gyration in Eccentric Loading?
The Cross-Sectional Area given Radius of Gyration in Eccentric Loading formula is the area of a two-dimensional shape that is obtained when a three-dimensional object is sliced perpendicular to some specified axis at a point is calculated using Cross-Sectional Area = Moment of Inertia/(Radius of Gyration^2). To calculate Cross-Sectional Area given Radius of Gyration in Eccentric Loading, you need Moment of Inertia (I) & Radius of Gyration (kG). With our tool, you need to enter the respective value for Moment of Inertia & Radius of Gyration 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 Cross-Sectional Area?
In this formula, Cross-Sectional Area uses Moment of Inertia & Radius of Gyration. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Cross-Sectional Area = Axial Load/(Total Unit Stress-((Axial Load*Outermost Fiber Distance*Distance from Load applied/Moment of Inertia about Neutral Axis)))
  • 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))))
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!