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

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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. Check FAQs

k G = \sqrt{\frac{C \cdot c}{1 - (\frac{σ}{σ E})} \cdot ((\frac{σ max}{σ}) - 1)}

k_G - Radius of Gyration?C - Maximum Initial Deflection?c - Distance from Neutral Axis to Extreme Point?σ - Direct Stress?σ_E - Euler Stress?σ_max - Maximum Stress at Crack Tip?

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

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Here is how the Radius of Gyration given Maximum Stress for Columns with Initial Curvature equation looks like with Values.

Here is how the Radius of Gyration given Maximum Stress for Columns with Initial Curvature equation looks like with Units.

Here is how the Radius of Gyration given Maximum Stress for Columns with Initial Curvature equation looks like.

312 = \sqrt{\frac{300 \cdot 49.9187}{1 - (\frac{8E-6}{0.3})} \cdot ((\frac{6E-5}{8E-6}) - 1)}

312mm = \sqrt{\frac{300mm \cdot 49.9187mm}{1 - (\frac{8E-6MPa}{0.3MPa})} \cdot ((\frac{6E-5MPa}{8E-6MPa}) - 1)}

312 = \sqrt{\frac{300 \cdot 49.9187}{1 - (\frac{8E-6}{0.3})} \cdot ((\frac{6E-5}{8E-6}) - 1)}

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

Follow our step by step solution on how to calculate Radius of Gyration given Maximum Stress for Columns with Initial Curvature?

FIRST Step Consider the formula

k G = \sqrt{\frac{C \cdot c}{1 - (\frac{σ}{σ E})} \cdot ((\frac{σ max}{σ}) - 1)}

Next Step Substitute values of Variables

∴

k G = \sqrt{\frac{300mm \cdot 49.9187mm}{1 - (\frac{8E-6MPa}{0.3MPa})} \cdot ((\frac{6E-5MPa}{8E-6MPa}) - 1)}

Next Step Convert Units

∴

k G = \sqrt{\frac{0.3m \cdot 0.0499m}{1 - (\frac{8Pa}{300000Pa})} \cdot ((\frac{60Pa}{8Pa}) - 1)}

Next Step Prepare to Evaluate

∴

k G = \sqrt{\frac{0.3 \cdot 0.0499}{1 - (\frac{8}{300000})} \cdot ((\frac{60}{8}) - 1)}

Next Step Evaluate

∴

k G = 0.3120000037501m

Next Step Convert to Output's Unit

∴

k G = 312.0000037501mm

LAST Step Rounding Answer

∴

k G = 312mm

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

Variables

Functions

Radius of Gyration

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.

Symbol: k_G

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Radius of Gyration

Maximum Initial Deflection

Maximum Initial Deflection is the degree to which a structural element is displaced under a load.

Symbol: C

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Maximum Initial Deflection

Distance from Neutral Axis to Extreme Point

Distance from Neutral Axis to Extreme Point is the distance between the neutral axis and the extreme point.

Symbol: c

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Distance from Neutral Axis to Extreme Point

Direct Stress

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.

Symbol: σ

Measurement: PressureUnit: MPa

Note: Value can be positive or negative.

Formulas to find Direct Stress

Euler Stress

Euler stress is the stress in column with curvature due to Euler load.

Symbol: σ_E

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Euler Stress

Maximum Stress at Crack Tip

Maximum Stress at Crack Tip is the highest stress concentration that occurs at the tip of a crack in a material under load.

Symbol: σ_max

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Maximum Stress at Crack Tip

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.

Syntax: sqrt(Number)

Other formulas in Columns With Initial Curvature category

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

x = (a \sin (\frac{y'}{C})) \cdot \frac{l}{π}

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

l = \frac{π \cdot x}{a \sin (\frac{y'}{C})}

Go Euler Load

P E = \frac{(π^{2}) \cdot ε column \cdot I}{l^{2}}

Go Modulus of Elasticity given Euler Load

ε column = \frac{P E \cdot (l^{2})}{π^{2} \cdot I}

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

Radius of Gyration given Maximum Stress for Columns with Initial Curvature evaluator 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 evaluate 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 evaluate Radius of Gyration given Maximum Stress for Columns with Initial Curvature using this online evaluator? To use this online evaluator 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.

FAQs on Radius of Gyration given Maximum Stress for Columns with Initial Curvature

What is the formula to find Radius of Gyration given Maximum Stress for Columns with Initial Curvature?

The formula of Radius of Gyration given Maximum Stress for Columns with Initial Curvature is expressed as 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)). Here is an example- 312000 = sqrt((0.3*0.04991867)/(1-(8/300000))*((60/8)-1)).

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

With 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) we can find Radius of Gyration given Maximum Stress for Columns with Initial Curvature using the formula - 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)). This formula also uses Square Root (sqrt) function(s).

Can the Radius of Gyration given Maximum Stress for Columns with Initial Curvature be negative?

No, the Radius of Gyration given Maximum Stress for Columns with Initial Curvature, measured in Length cannot be negative.

Which unit is used to measure Radius of Gyration given Maximum Stress for Columns with Initial Curvature?

Radius of Gyration given Maximum Stress for Columns with Initial Curvature is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Radius of Gyration given Maximum Stress for Columns with Initial Curvature can be measured.

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

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

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

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

Other formulas in Columns With Initial Curvature category

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

FAQs on Radius of Gyration given Maximum Stress for Columns with Initial Curvature

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