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

GoRadius of Gyration given Bending Stress for Strut with Axial and Transverse 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 max \cdot c}{A sectional \cdot σb max}}

k - Least Radius of Gyration of Column?M_max - Maximum Bending Moment In Column?c - Distance from Neutral Axis to Extreme Point?A_sectional - Column Cross Sectional Area?σb^max - Maximum Bending Stress?

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

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

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

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

0.239 = \sqrt{\frac{16 \cdot 10}{1.4 \cdot 2}}

0.239mm = \sqrt{\frac{16N*m \cdot 10mm}{1.4m² \cdot 2MPa}}

0.239 = \sqrt{\frac{16 \cdot 10}{1.4 \cdot 2}}

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Strength of Materials » fx Radius of Gyration if Maximum Bending Moment is given for Strut with Axial and Point Load

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

Follow our step by step solution on how to calculate Radius of Gyration if Maximum Bending Moment is given for Strut with Axial and Point Load?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

k = \sqrt{\frac{16N*m \cdot 10mm}{1.4m² \cdot 2MPa}}

Next Step Convert Units

∴

k = \sqrt{\frac{16N*m \cdot 0.01m}{1.4m² \cdot 2E+6Pa}}

Next Step Prepare to Evaluate

∴

k = \sqrt{\frac{16 \cdot 0.01}{1.4 \cdot 2E+6}}

Next Step Evaluate

∴

k = 0.000239045721866879m

Next Step Convert to Output's Unit

∴

k = 0.239045721866879mm

LAST Step Rounding Answer

∴

k = 0.239mm

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

Maximum Bending Moment In Column

Maximum Bending Moment In Column is the highest moment of force that causes the column to bend or deform under applied loads.

Symbol: M_max

Measurement: Moment of ForceUnit: N*m

Note: Value should be greater than 0.

Formulas to find Maximum 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

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

Maximum Bending Stress

Maximum Bending Stress is the highest stress experienced by a material when subjected to bending forces. It occurs at the point on a beam or structural element where the bending moment is greatest.

Symbol: σb^max

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Maximum Bending Stress

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 given Bending Stress for Strut with Axial and Transverse Point Load

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

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 if Maximum Bending Moment is given for Strut with Axial and Point Load?

Radius of Gyration if Maximum Bending Moment is given for Strut with Axial and Point Load evaluator uses 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)) to evaluate the Least Radius of Gyration of Column, The Radius of Gyration if Maximum Bending Moment is given for Strut with Axial and Point Load formula is defined as a measure of the distribution of the area of a strut's cross-section around its axis, which is crucial in determining the strut's resistance to bending and buckling under compressive axial thrust and transverse point load. Least Radius of Gyration of Column is denoted by k symbol.

How to evaluate Radius of Gyration if Maximum Bending Moment is given for Strut with Axial and Point Load using this online evaluator? To use this online evaluator for Radius of Gyration if Maximum Bending Moment is given for Strut with Axial and Point Load, enter Maximum Bending Moment In Column (M_max), Distance from Neutral Axis to Extreme Point (c), Column Cross Sectional Area (A_sectional) & Maximum Bending Stress (σb^max) and hit the calculate button.

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

What is the formula to find Radius of Gyration if Maximum Bending Moment is given for Strut with Axial and Point Load?

The formula of Radius of Gyration if Maximum Bending Moment is given for Strut with Axial and Point Load is expressed as 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)). Here is an example- 239.0457 = sqrt((16*0.01)/(1.4*2000000)).

How to calculate Radius of Gyration if Maximum Bending Moment is given for Strut with Axial and Point Load?

With Maximum Bending Moment In Column (M_max), Distance from Neutral Axis to Extreme Point (c), Column Cross Sectional Area (A_sectional) & Maximum Bending Stress (σb^max) we can find Radius of Gyration if Maximum Bending Moment is given for Strut with Axial and Point Load using the formula - 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)). 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((Bending Moment in Column*Distance from Neutral Axis to Extreme Point)/(Bending Stress in Column*Column Cross Sectional Area))
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 if Maximum Bending Moment is given for Strut with Axial and Point Load be negative?

No, the Radius of Gyration if Maximum Bending Moment is given for Strut with Axial and Point Load, measured in Length cannot be negative.

Which unit is used to measure Radius of Gyration if Maximum Bending Moment is given for Strut with Axial and Point Load?

Radius of Gyration if Maximum Bending Moment is given for Strut with Axial and 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 if Maximum Bending Moment is given for Strut with Axial and Point Load can be measured.

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

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

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

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

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

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

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

Variable Name

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

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