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

✖Moment of Inertia is the measure of the resistance of a body to angular acceleration about a given axis.ⓘ Moment of Inertia [I]			+10% -10%
✖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.ⓘ Radius of Gyration [k_G]			+10% -10%

✖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.ⓘ Cross-Sectional Area given Radius of Gyration in Eccentric Loading [A_cs]

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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)
A_cs = I/(k_G^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

A_cs = I/(k_G^2) --> 1.125/(0.29^2)

Evaluating ... ...

A_cs = 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)

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Osmania University (OU), Hyderabad

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< Eccentric Loading Calculators

Moment of Inertia of Cross-Section given Total Unit Stress in Eccentric Loading

LaTeX 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

LaTeX 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

LaTeX Go Total Unit Stress = (Axial Load/Cross-Sectional Area)+(Axial Load*Outermost Fiber Distance*Distance from Load applied/Moment of Inertia about Neutral Axis)

Radius of Gyration in Eccentric Loading

LaTeX Go Radius of Gyration = sqrt(Moment of Inertia/Cross-Sectional Area)

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

LaTeX Go

Cross-Sectional Area = Moment of Inertia/(Radius of Gyration^2)
A_cs = I/(k_G^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 A_cs 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 (k_G) 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 A_cs = I/(k_G^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 (k_G). 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))))

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