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Radius of Gyration given Maximum Stress induced 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 if Maximum Bending Moment is given 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{((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})))})}

k - Least Radius of Gyration of Column?W_p - Greatest Safe Load?I - Moment of Inertia in Column?ε_column - Modulus of Elasticity?P_compressive - Column Compressive Load?l_column - Column Length?c - Distance from Neutral Axis to Extreme Point?A_sectional - Column Cross Sectional Area?σb^max - Maximum Bending Stress?

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

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

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

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

0.0125 = \sqrt{((0.1 \cdot ((\frac{\sqrt{5600 \cdot \frac{10.56}{0.4}}}{2 \cdot 0.4}) \cdot \tan ((\frac{5000}{2}) \cdot (\sqrt{\frac{0.4}{5600 \cdot \frac{10.56}{0.4}}})))) \cdot \frac{10}{1.4 \cdot ((2 - (\frac{0.4}{1.4})))})}

0.0125mm = \sqrt{((0.1kN \cdot ((\frac{\sqrt{5600cm⁴ \cdot \frac{10.56MPa}{0.4kN}}}{2 \cdot 0.4kN}) \cdot \tan ((\frac{5000mm}{2}) \cdot (\sqrt{\frac{0.4kN}{5600cm⁴ \cdot \frac{10.56MPa}{0.4kN}}})))) \cdot \frac{10mm}{1.4m² \cdot ((2MPa - (\frac{0.4kN}{1.4m²})))})}

0.0125 = \sqrt{((0.1 \cdot ((\frac{\sqrt{5600 \cdot \frac{10.56}{0.4}}}{2 \cdot 0.4}) \cdot \tan ((\frac{5000}{2}) \cdot (\sqrt{\frac{0.4}{5600 \cdot \frac{10.56}{0.4}}})))) \cdot \frac{10}{1.4 \cdot ((2 - (\frac{0.4}{1.4})))})}

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

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

FIRST Step Consider the formula

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})))})}

Next Step Substitute values of Variables

∴

k = \sqrt{((0.1kN \cdot ((\frac{\sqrt{5600cm⁴ \cdot \frac{10.56MPa}{0.4kN}}}{2 \cdot 0.4kN}) \cdot \tan ((\frac{5000mm}{2}) \cdot (\sqrt{\frac{0.4kN}{5600cm⁴ \cdot \frac{10.56MPa}{0.4kN}}})))) \cdot \frac{10mm}{1.4m² \cdot ((2MPa - (\frac{0.4kN}{1.4m²})))})}

Next Step Convert Units

∴

k = \sqrt{((100N \cdot ((\frac{\sqrt{5.6E-5m⁴ \cdot \frac{1.1E+7Pa}{400N}}}{2 \cdot 400N}) \cdot \tan ((\frac{5m}{2}) \cdot (\sqrt{\frac{400N}{5.6E-5m⁴ \cdot \frac{1.1E+7Pa}{400N}}})))) \cdot \frac{0.01m}{1.4m² \cdot ((2E+6Pa - (\frac{400N}{1.4m²})))})}

Next Step Prepare to Evaluate

∴

k = \sqrt{((100 \cdot ((\frac{\sqrt{5.6E-5 \cdot \frac{1.1E+7}{400}}}{2 \cdot 400}) \cdot \tan ((\frac{5}{2}) \cdot (\sqrt{\frac{400}{5.6E-5 \cdot \frac{1.1E+7}{400}}})))) \cdot \frac{0.01}{1.4 \cdot ((2E+6 - (\frac{400}{1.4})))})}

Next Step Evaluate

∴

k = 1.25243860328387E-05m

Next Step Convert to Output's Unit

∴

k = 0.0125243860328387mm

LAST Step Rounding Answer

∴

k = 0.0125mm

Radius of Gyration given Maximum Stress induced 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

Greatest Safe Load

Greatest Safe Load is the maximum safe point load allowable at the center of the beam.

Symbol: W_p

Measurement: ForceUnit: kN

Note: Value should be greater than 0.

Formulas to find Greatest Safe Load

Moment of Inertia in Column

Moment of Inertia in Column is the measure of the resistance of a column to angular acceleration about a given axis.

Symbol: I

Measurement: Second Moment of AreaUnit: cm⁴

Note: Value should be greater than 0.

Formulas to find Moment of Inertia in Column

Modulus of Elasticity

Modulus of Elasticity is a quantity that measures an object or substance's resistance to being deformed elastically when stress is applied to it.

Symbol: ε_column

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Modulus of Elasticity

Column Compressive Load

Column Compressive Load is the load applied to a column that is compressive in nature.

Symbol: P_compressive

Measurement: ForceUnit: kN

Note: Value should be greater than 0.

Formulas to find Column Compressive Load

Column Length

Column Length is the distance between two points where a column gets its fixity of support so its movement is restrained in all directions.

Symbol: l_column

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Column Length

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

tan

The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle.

Syntax: tan(Angle)

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 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}}

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}

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

Radius of Gyration given Maximum Stress induced for Strut with Axial and Point Load evaluator uses 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)))))) to evaluate the Least Radius of Gyration of Column, The Radius of Gyration given Maximum Stress induced for Strut with Axial and Point Load formula is defined as a measure of the distance from the axis of rotation to a point where the entire strut's mass can be considered to be concentrated, which is critical in determining the strut's stability 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 given Maximum Stress induced for Strut with Axial and Point Load using this online evaluator? To use this online evaluator for Radius of Gyration given Maximum Stress induced for Strut with Axial and Point Load, enter Greatest Safe Load (W_p), Moment of Inertia in Column (I), Modulus of Elasticity (ε_column), Column Compressive Load (P_compressive), Column Length (l_column), 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 given Maximum Stress induced for Strut with Axial and Point Load

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

The formula of Radius of Gyration given Maximum Stress induced for Strut with Axial and Point Load is expressed as 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)))))). Here is an example- 12.52439 = sqrt(((100*(((sqrt(5.6E-05*10560000/400))/(2*400))*tan((5/2)*(sqrt(400/(5.6E-05*10560000/400))))))*(0.01)/(1.4*((2000000-(400/1.4)))))).

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

With Greatest Safe Load (W_p), Moment of Inertia in Column (I), Modulus of Elasticity (ε_column), Column Compressive Load (P_compressive), Column Length (l_column), 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 given Maximum Stress induced for Strut with Axial and Point Load using the formula - 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)))))). This formula also uses Tangent (tan), 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((Maximum Bending Moment In Column*Distance from Neutral Axis to Extreme Point)/(Column Cross Sectional Area*Maximum Bending Stress))

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

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

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

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

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

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

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

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

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