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Radius of Gyration given Bending Stress for Strut with Axial and Transverse Point Load Formula

GoRadius of Gyration if Maximum Bending Moment is given for Strut with Axial and Point Load Formula

GoRadius of Gyration given Maximum Stress induced for Strut with Axial and Point Load Formula

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Least Radius of Gyration of Column is a measure of the distribution of its cross-sectional area around its centroidal axis. Check FAQs

k = \sqrt{\frac{M b \cdot c}{σ b \cdot A sectional}}

k - Least Radius of Gyration of Column?M_b - Bending Moment in Column?c - Distance from Neutral Axis to Extreme Point?σ_b - Bending Stress in Column?A_sectional - Column Cross Sectional Area?

Radius of Gyration given Bending Stress for Strut with Axial and Transverse Point Load Example

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Here is how the Radius of Gyration given Bending Stress for Strut with Axial and Transverse Point Load equation looks like with Values.

Here is how the Radius of Gyration given Bending Stress for Strut with Axial and Transverse Point Load equation looks like with Units.

Here is how the Radius of Gyration given Bending Stress for Strut with Axial and Transverse Point Load equation looks like.

2.9277 = \sqrt{\frac{48 \cdot 10}{0.04 \cdot 1.4}}

2.9277mm = \sqrt{\frac{48N*m \cdot 10mm}{0.04MPa \cdot 1.4m²}}

2.9277 = \sqrt{\frac{48 \cdot 10}{0.04 \cdot 1.4}}

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Strength of Materials » fx Radius of Gyration given Bending Stress for Strut with Axial and Transverse Point Load

Radius of Gyration given Bending Stress for Strut with Axial and Transverse Point Load Solution

Follow our step by step solution on how to calculate Radius of Gyration given Bending Stress for Strut with Axial and Transverse Point Load?

FIRST Step Consider the formula

k = \sqrt{\frac{M b \cdot c}{σ b \cdot A sectional}}

Next Step Substitute values of Variables

∴

k = \sqrt{\frac{48N*m \cdot 10mm}{0.04MPa \cdot 1.4m²}}

Next Step Convert Units

∴

k = \sqrt{\frac{48N*m \cdot 0.01m}{40000Pa \cdot 1.4m²}}

Next Step Prepare to Evaluate

∴

k = \sqrt{\frac{48 \cdot 0.01}{40000 \cdot 1.4}}

Next Step Evaluate

∴

k = 0.0029277002188456m

Next Step Convert to Output's Unit

∴

k = 2.9277002188456mm

LAST Step Rounding Answer

∴

k = 2.9277mm

Radius of Gyration given Bending Stress for Strut with Axial and Transverse Point Load Formula Elements

Variables

Functions

Least Radius of Gyration of Column

Least Radius of Gyration of Column is a measure of the distribution of its cross-sectional area around its centroidal axis.

Symbol: k

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Least Radius of Gyration of Column

Bending Moment in Column

Bending Moment in Column is the reaction induced in a column when an external force or moment is applied to the element, causing the element to bend.

Symbol: M_b

Measurement: Moment of ForceUnit: N*m

Note: Value should be greater than 0.

Formulas to find Bending Moment in Column

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

Bending Stress in Column

Bending Stress in Column is the normal stress that is induced at a point in a column subjected to loads that cause it to bend.

Symbol: σ_b

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Bending Stress in Column

Column Cross Sectional Area

Column Cross Sectional Area is the area of a column that is obtained when a column is sliced perpendicular to some specified axis at a point.

Symbol: A_sectional

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Column Cross Sectional Area

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 to find Least Radius of Gyration of Column

Go Radius of Gyration if Maximum Bending Moment is given for Strut with Axial and Point Load

k = \sqrt{\frac{M max \cdot c}{A sectional \cdot σb max}}

Go Radius of Gyration given Maximum Stress induced for Strut with Axial and Point Load

k = \sqrt{((W p \cdot ((\frac{\sqrt{I \cdot \frac{ε column}{P compressive}}}{2 \cdot P compressive}) \cdot \tan ((\frac{l column}{2}) \cdot (\sqrt{\frac{P compressive}{I \cdot \frac{ε column}{P compressive}}})))) \cdot \frac{c}{A sectional \cdot ((σb max - (\frac{P compressive}{A sectional})))})}

Other formulas in Strut Subjected to Compressive Axial Thrust and a Transverse Point Load at the Centre category

Go Bending Moment at Section for Strut with Axial and Transverse Point Load at Center

M b = - (P compressive \cdot δ) - (W p \cdot \frac{x}{2})

Go Compressive Axial Load for Strut with Axial and Transverse Point Load at Center

P compressive = - \frac{M b + (W p \cdot \frac{x}{2})}{δ}

Go Deflection at Section for Strut with Axial and Transverse Point Load at Center

δ = P compressive - \frac{M b + (W p \cdot \frac{x}{2})}{P compressive}

Go Transverse Point Load for Strut with Axial and Transverse Point Load at Center

W p = (- M b - (P compressive \cdot δ)) \cdot \frac{2}{x}

How to Evaluate Radius of Gyration given Bending Stress for Strut with Axial and Transverse Point Load?

Radius of Gyration given Bending Stress for Strut with Axial and Transverse Point Load evaluator uses Least Radius of Gyration of Column = sqrt((Bending Moment in Column*Distance from Neutral Axis to Extreme Point)/(Bending Stress in Column*Column Cross Sectional Area)) to evaluate the Least Radius of Gyration of Column, The Radius of Gyration given Bending Stress for Strut with Axial and Transverse Point Load formula is defined as a measure of the distance from the axis of rotation to a point where the whole area of the cross-section can be assumed to be concentrated, providing a way to calculate the bending stress of a strut under axial and transverse point load. Least Radius of Gyration of Column is denoted by k symbol.

How to evaluate Radius of Gyration given Bending Stress for Strut with Axial and Transverse Point Load using this online evaluator? To use this online evaluator for Radius of Gyration given Bending Stress for Strut with Axial and Transverse Point Load, enter Bending Moment in Column (M_b), Distance from Neutral Axis to Extreme Point (c), Bending Stress in Column (σ_b) & Column Cross Sectional Area (A_sectional) and hit the calculate button.

FAQs on Radius of Gyration given Bending Stress for Strut with Axial and Transverse Point Load

What is the formula to find Radius of Gyration given Bending Stress for Strut with Axial and Transverse Point Load?

The formula of Radius of Gyration given Bending Stress for Strut with Axial and Transverse Point Load is expressed as Least Radius of Gyration of Column = sqrt((Bending Moment in Column*Distance from Neutral Axis to Extreme Point)/(Bending Stress in Column*Column Cross Sectional Area)). Here is an example- 2927.7 = sqrt((48*0.01)/(40000*1.4)).

How to calculate Radius of Gyration given Bending Stress for Strut with Axial and Transverse Point Load?

With Bending Moment in Column (M_b), Distance from Neutral Axis to Extreme Point (c), Bending Stress in Column (σ_b) & Column Cross Sectional Area (A_sectional) we can find Radius of Gyration given Bending Stress for Strut with Axial and Transverse Point Load using the formula - Least Radius of Gyration of Column = sqrt((Bending Moment in Column*Distance from Neutral Axis to Extreme Point)/(Bending Stress in Column*Column Cross Sectional Area)). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Least Radius of Gyration of Column?

Here are the different ways to Calculate Least Radius of Gyration of Column-

Least Radius of Gyration of Column=sqrt((Maximum Bending Moment In Column*Distance from Neutral Axis to Extreme Point)/(Column Cross Sectional Area*Maximum Bending Stress))
Least Radius of Gyration of Column=sqrt(((Greatest Safe Load*(((sqrt(Moment of Inertia in Column*Modulus of Elasticity/Column Compressive Load))/(2*Column Compressive Load))*tan((Column Length/2)*(sqrt(Column Compressive Load/(Moment of Inertia in Column*Modulus of Elasticity/Column Compressive Load))))))*(Distance from Neutral Axis to Extreme Point)/(Column Cross Sectional Area*((Maximum Bending Stress-(Column Compressive Load/Column Cross Sectional Area))))))

Can the Radius of Gyration given Bending Stress for Strut with Axial and Transverse Point Load be negative?

No, the Radius of Gyration given Bending Stress for Strut with Axial and Transverse Point Load, measured in Length cannot be negative.

Which unit is used to measure Radius of Gyration given Bending Stress for Strut with Axial and Transverse Point Load?

Radius of Gyration given Bending Stress for Strut with Axial and Transverse Point Load 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 Bending Stress for Strut with Axial and Transverse Point Load can be measured.

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Radius of Gyration given Bending Stress for Strut with Axial and Transverse Point Load Formula

​GoRadius of Gyration if Maximum Bending Moment is given for Strut with Axial and Point Load Formula

​GoRadius of Gyration given Maximum Stress induced for Strut with Axial and Point Load Formula

Radius of Gyration given Bending Stress for Strut with Axial and Transverse Point Load Example

Radius of Gyration given Bending Stress for Strut with Axial and Transverse Point Load Solution

Radius of Gyration given Bending Stress for Strut with Axial and Transverse Point Load Formula Elements

Other Formulas to find Least Radius of Gyration of Column

Other formulas in Strut Subjected to Compressive Axial Thrust and a Transverse Point Load at the Centre category

How to Evaluate Radius of Gyration given Bending Stress for Strut with Axial and Transverse Point Load?

FAQs on Radius of Gyration given Bending Stress for Strut with Axial and Transverse Point Load

Variable Name

GoRadius of Gyration if Maximum Bending Moment is given for Strut with Axial and Point Load Formula

GoRadius of Gyration given Maximum Stress induced for Strut with Axial and Point Load Formula