Radius of Gyration given Maximum Stress for Columns with Initial Curvature Calculator

✖Maximum Initial Deflection is the degree to which a structural element is displaced under a load.ⓘ Maximum Initial Deflection [C]			+10% -10%
✖Distance from Neutral Axis to Extreme Point is the distance between the neutral axis and the extreme point.ⓘ Distance from Neutral Axis to Extreme Point [c]			+10% -10%
✖Direct Stress refers to the internal resistance offered by a material to an external force or load, acting perpendicularly to the cross-sectional area of the material.ⓘ Direct Stress [σ]			+10% -10%
✖Euler stress is the stress in column with curvature due to Euler load.ⓘ Euler Stress [σ_E]			+10% -10%
✖Maximum Stress at Crack Tip is the highest stress concentration that occurs at the tip of a crack in a material under load.ⓘ Maximum Stress at Crack Tip [σ_max]			+10% -10%

✖Radius of Gyration is the radial distance from the axis of rotation at which the entire area or mass can be assumed to be concentrated to produce the same moment of inertia.ⓘ Radius of Gyration given Maximum Stress for Columns with Initial Curvature [k_G]

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Radius of Gyration given Maximum Stress for Columns with Initial Curvature Solution

STEP 0: Pre-Calculation Summary

Formula Used

Radius of Gyration = sqrt((Maximum Initial Deflection*Distance from Neutral Axis to Extreme Point)/(1-(Direct Stress/Euler Stress))*((Maximum Stress at Crack Tip/Direct Stress)-1))
k_G = sqrt((C*c)/(1-(σ/σ_E))*((σ_max/σ)-1))
This formula uses 1 Functions, 6 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 Meter) - Radius of Gyration is the radial distance from the axis of rotation at which the entire area or mass can be assumed to be concentrated to produce the same moment of inertia.
Maximum Initial Deflection - (Measured in Meter) - Maximum Initial Deflection is the degree to which a structural element is displaced under a load.
Distance from Neutral Axis to Extreme Point - (Measured in Meter) - Distance from Neutral Axis to Extreme Point is the distance between the neutral axis and the extreme point.
Direct Stress - (Measured in Pascal) - Direct Stress refers to the internal resistance offered by a material to an external force or load, acting perpendicularly to the cross-sectional area of the material.
Euler Stress - (Measured in Pascal) - Euler stress is the stress in column with curvature due to Euler load.
Maximum Stress at Crack Tip - (Measured in Pascal) - Maximum Stress at Crack Tip is the highest stress concentration that occurs at the tip of a crack in a material under load.

STEP 1: Convert Input(s) to Base Unit

Maximum Initial Deflection: 300 Millimeter --> 0.3 Meter (Check conversion here)
Distance from Neutral Axis to Extreme Point: 49.91867 Millimeter --> 0.04991867 Meter (Check conversion here)
Direct Stress: 8E-06 Megapascal --> 8 Pascal (Check conversion here)
Euler Stress: 0.3 Megapascal --> 300000 Pascal (Check conversion here)
Maximum Stress at Crack Tip: 6E-05 Megapascal --> 60 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

k_G = sqrt((C*c)/(1-(σ/σ_E))*((σ_max/σ)-1)) --> sqrt((0.3*0.04991867)/(1-(8/300000))*((60/8)-1))

Evaluating ... ...

k_G = 0.3120000037501

STEP 3: Convert Result to Output's Unit

0.3120000037501 Meter -->312.0000037501 Millimeter (Check conversion here)

FINAL ANSWER

312.0000037501 ≈ 312 Millimeter <-- Radius of Gyration

(Calculation completed in 00.004 seconds)

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< Columns With Initial Curvature Calculators

Length of Column given Initial Deflection at Distance X from end A

LaTeX Go Length of Column = (pi*Distance of Deflection from end A)/(asin(Initial Deflection/Maximum Initial Deflection))

Value of Distance 'X' given Initial Deflection at Distance X from end A

LaTeX Go Distance of Deflection from end A = (asin(Initial Deflection/Maximum Initial Deflection))*Length of Column/pi

Modulus of Elasticity given Euler Load

LaTeX Go Modulus of Elasticity of Column = (Euler Load*(Length of Column^2))/(pi^2*Moment of Inertia)

Euler Load

LaTeX Go Euler Load = ((pi^2)*Modulus of Elasticity of Column*Moment of Inertia)/(Length of Column^2)

Radius of Gyration given Maximum Stress for Columns with Initial Curvature Formula

LaTeX Go

What is Buckling or Crippling Load?

Buckling Load is the highest load at which the column will buckle. Crippling load is the max load beyond that load, it cant use further it becomes disable to use.

How to Calculate Radius of Gyration given Maximum Stress for Columns with Initial Curvature?

Radius of Gyration given Maximum Stress for Columns with Initial Curvature calculator uses Radius of Gyration = sqrt((Maximum Initial Deflection*Distance from Neutral Axis to Extreme Point)/(1-(Direct Stress/Euler Stress))*((Maximum Stress at Crack Tip/Direct Stress)-1)) to calculate the Radius of Gyration, The Radius of Gyration given Maximum Stress for Columns with Initial Curvature formula is defined as a measure of the distribution of the material around the axis of the column, which is essential in determining the stability of the column under various loads, considering the initial curvature of the column. Radius of Gyration is denoted by k_G symbol.

How to calculate Radius of Gyration given Maximum Stress for Columns with Initial Curvature using this online calculator? To use this online calculator for Radius of Gyration given Maximum Stress for Columns with Initial Curvature, enter Maximum Initial Deflection (C), Distance from Neutral Axis to Extreme Point (c), Direct Stress (σ), Euler Stress (σ_E) & Maximum Stress at Crack Tip (σ_max) and hit the calculate button. Here is how the Radius of Gyration given Maximum Stress for Columns with Initial Curvature calculation can be explained with given input values -> 312000 = sqrt((0.3*0.04991867)/(1-(8/300000))*((60/8)-1)).

FAQ

What is Radius of Gyration given Maximum Stress for Columns with Initial Curvature?

The Radius of Gyration given Maximum Stress for Columns with Initial Curvature formula is defined as a measure of the distribution of the material around the axis of the column, which is essential in determining the stability of the column under various loads, considering the initial curvature of the column and is represented as k_G = sqrt((C*c)/(1-(σ/σ_E))*((σ_max/σ)-1)) or Radius of Gyration = sqrt((Maximum Initial Deflection*Distance from Neutral Axis to Extreme Point)/(1-(Direct Stress/Euler Stress))*((Maximum Stress at Crack Tip/Direct Stress)-1)). Maximum Initial Deflection is the degree to which a structural element is displaced under a load, Distance from Neutral Axis to Extreme Point is the distance between the neutral axis and the extreme point, Direct Stress refers to the internal resistance offered by a material to an external force or load, acting perpendicularly to the cross-sectional area of the material, Euler stress is the stress in column with curvature due to Euler load & Maximum Stress at Crack Tip is the highest stress concentration that occurs at the tip of a crack in a material under load.

How to calculate Radius of Gyration given Maximum Stress for Columns with Initial Curvature?

The Radius of Gyration given Maximum Stress for Columns with Initial Curvature formula is defined as a measure of the distribution of the material around the axis of the column, which is essential in determining the stability of the column under various loads, considering the initial curvature of the column is calculated using Radius of Gyration = sqrt((Maximum Initial Deflection*Distance from Neutral Axis to Extreme Point)/(1-(Direct Stress/Euler Stress))*((Maximum Stress at Crack Tip/Direct Stress)-1)). To calculate Radius of Gyration given Maximum Stress for Columns with Initial Curvature, you need Maximum Initial Deflection (C), Distance from Neutral Axis to Extreme Point (c), Direct Stress (σ), Euler Stress (σ_E) & Maximum Stress at Crack Tip (σ_max). With our tool, you need to enter the respective value for Maximum Initial Deflection, Distance from Neutral Axis to Extreme Point, Direct Stress, Euler Stress & Maximum Stress at Crack Tip 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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