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%
✖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 [A_cs]			+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 in Eccentric Loading [k_G]

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Radius of Gyration in Eccentric Loading Solution

STEP 0: Pre-Calculation Summary

Formula Used

Radius of Gyration = sqrt(Moment of Inertia/Cross-Sectional Area)
k_G = sqrt(I/A_cs)
This formula uses 1 Functions, 3 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

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.
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.
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

Moment of Inertia: 1.125 Kilogram Square Meter --> 1.125 Kilogram Square Meter No Conversion Required
Cross-Sectional Area: 13 Square Meter --> 13 Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

k_G = sqrt(I/A_cs) --> sqrt(1.125/13)

Evaluating ... ...

k_G = 0.294174202707276

STEP 3: Convert Result to Output's Unit

0.000294174202707276 Meter -->0.294174202707276 Millimeter (Check conversion here)

FINAL ANSWER

0.294174202707276 ≈ 0.294174 Millimeter <-- Radius of Gyration

(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)

Radius of Gyration in Eccentric Loading Formula

LaTeX Go

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

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 that 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 Radius of Gyration in Eccentric Loading?

Radius of Gyration in Eccentric Loading calculator uses Radius of Gyration = sqrt(Moment of Inertia/Cross-Sectional Area) to calculate the Radius of Gyration, The Radius of Gyration in Eccentric Loading formula 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 is denoted by k_G symbol.

How to calculate Radius of Gyration in Eccentric Loading using this online calculator? To use this online calculator for Radius of Gyration in Eccentric Loading, enter Moment of Inertia (I) & Cross-Sectional Area (A_cs) and hit the calculate button. Here is how the Radius of Gyration in Eccentric Loading calculation can be explained with given input values -> 294.1742 = sqrt(1.125/13).

FAQ

What is Radius of Gyration in Eccentric Loading?

The Radius of Gyration in Eccentric Loading formula 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 and is represented as k_G = sqrt(I/A_cs) or Radius of Gyration = sqrt(Moment of Inertia/Cross-Sectional Area). Moment of Inertia is the measure of the resistance of a body to angular acceleration about a given axis & 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 Radius of Gyration in Eccentric Loading?

The Radius of Gyration in Eccentric Loading formula 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 is calculated using Radius of Gyration = sqrt(Moment of Inertia/Cross-Sectional Area). To calculate Radius of Gyration in Eccentric Loading, you need Moment of Inertia (I) & Cross-Sectional Area (A_cs). With our tool, you need to enter the respective value for Moment of Inertia & 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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