Radius of gyration given maximum stress induced for strut with axial and point load Calculator

✖Greatest Safe Load is the maximum safe point load allowable at the center of the beam.ⓘ Greatest Safe Load [Wp]			+10% -10%
✖Moment of Inertia Column is the measure of the resistance of a body to angular acceleration about a given axis.ⓘ Moment of Inertia Column [I]			+10% -10%
✖Modulus of Elasticity Column is a quantity that measures an object or substance's resistance to being deformed elastically when stress is applied to it.ⓘ Modulus of Elasticity Column [ε_column]			+10% -10%
✖Column Compressive load is the load applied to a column that is compressive in nature.ⓘ Column Compressive load [P_compressive]			+10% -10%
✖Column Length is the distance between two points where a column gets its fixity of support so its movement is restrained in all directions.ⓘ Column Length [l_column]			+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%
✖Column Cross Sectional Area is the area of a two-dimensional shape that is obtained when a three dimensional shape is sliced perpendicular to some specified axis at a point.ⓘ Column Cross Sectional Area [A_sectional]			+10% -10%
✖Maximum bending stress is the normal stress that is induced at a point in a body subjected to loads that cause it to bend.ⓘ Maximum bending stress [σb^max]			+10% -10%

✖Least Radius of Gyration Column is the smallest value of the radius of gyration is used for structural calculations.ⓘ Radius of gyration given maximum stress induced for strut with axial and point load [r_least]

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Radius of gyration given maximum stress induced for strut with axial and point load

Formula

`"r"_{"least"} = sqrt((("Wp"*(((sqrt("I"*"ε"_{"column"}/"P"_{"compressive"}))/(2*"P"_{"compressive"}))*tan(("l"_{"column"}/2)*(sqrt("P"_{"compressive"}/("I"*"ε"_{"column"}/"P"_{"compressive"}))))))*("c")/("A"_{"sectional"}*(("σb"^{"max"}-("P"_{"compressive"}/"A"_{"sectional"}))))))`

Example

`"0.012524mm"=sqrt((("0.1kN"*(((sqrt("5600cm⁴"*"10.56MPa"/"0.4kN"))/(2*"0.4kN"))*tan(("5000mm"/2)*(sqrt("0.4kN"/("5600cm⁴"*"10.56MPa"/"0.4kN"))))))*("10mm")/("1.4m²"*(("2MPa"-("0.4kN"/"1.4m²"))))))`

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Radius of gyration given maximum stress induced for strut with axial and point load Solution

STEP 0: Pre-Calculation Summary

Formula Used

Least Radius of Gyration Column = sqrt(((Greatest Safe Load*(((sqrt(Moment of Inertia Column*Modulus of Elasticity Column/Column Compressive load))/(2*Column Compressive load))*tan((Column Length/2)*(sqrt(Column Compressive load/(Moment of Inertia Column*Modulus of Elasticity Column/Column Compressive load))))))*(Distance from Neutral Axis to Extreme Point)/(Column Cross Sectional Area*((Maximum bending stress-(Column Compressive load/Column Cross Sectional Area))))))
r_least = sqrt(((Wp*(((sqrt(I*ε_column/P_compressive))/(2*P_compressive))*tan((l_column/2)*(sqrt(P_compressive/(I*ε_column/P_compressive))))))*(c)/(A_sectional*((σb^max-(P_compressive/A_sectional))))))
This formula uses 2 Functions, 9 Variables

Functions Used

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., 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., sqrt(Number)

Variables Used

Least Radius of Gyration Column - (Measured in Meter) - Least Radius of Gyration Column is the smallest value of the radius of gyration is used for structural calculations.
Greatest Safe Load - (Measured in Newton) - Greatest Safe Load is the maximum safe point load allowable at the center of the beam.
Moment of Inertia Column - (Measured in Meter⁴) - Moment of Inertia Column is the measure of the resistance of a body to angular acceleration about a given axis.
Modulus of Elasticity Column - (Measured in Pascal) - Modulus of Elasticity Column is a quantity that measures an object or substance's resistance to being deformed elastically when stress is applied to it.
Column Compressive load - (Measured in Newton) - Column Compressive load is the load applied to a column that is compressive in nature.
Column Length - (Measured in Meter) - Column Length is the distance between two points where a column gets its fixity of support so its movement is restrained in all directions.
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.
Column Cross Sectional Area - (Measured in Square Meter) - Column Cross Sectional Area is the area of a two-dimensional shape that is obtained when a three dimensional shape is sliced perpendicular to some specified axis at a point.
Maximum bending stress - (Measured in Pascal) - Maximum bending stress is the normal stress that is induced at a point in a body subjected to loads that cause it to bend.

STEP 1: Convert Input(s) to Base Unit

Greatest Safe Load: 0.1 Kilonewton --> 100 Newton (Check conversion here)
Moment of Inertia Column: 5600 Centimeter⁴ --> 5.6E-05 Meter⁴ (Check conversion here)
Modulus of Elasticity Column: 10.56 Megapascal --> 10560000 Pascal (Check conversion here)
Column Compressive load: 0.4 Kilonewton --> 400 Newton (Check conversion here)
Column Length: 5000 Millimeter --> 5 Meter (Check conversion here)
Distance from Neutral Axis to Extreme Point: 10 Millimeter --> 0.01 Meter (Check conversion here)
Column Cross Sectional Area: 1.4 Square Meter --> 1.4 Square Meter No Conversion Required
Maximum bending stress: 2 Megapascal --> 2000000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_least = sqrt(((Wp*(((sqrt(I*ε_column/P_compressive))/(2*P_compressive))*tan((l_column/2)*(sqrt(P_compressive/(I*ε_column/P_compressive))))))*(c)/(A_sectional*((σb^max-(P_compressive/A_sectional)))))) --> 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))))))

Evaluating ... ...

r_least = 1.25243860328387E-05

STEP 3: Convert Result to Output's Unit

1.25243860328387E-05 Meter -->0.0125243860328387 Millimeter (Check conversion here)

FINAL ANSWER

0.0125243860328387 ≈ 0.012524 Millimeter <-- Least Radius of Gyration Column

(Calculation completed in 00.004 seconds)

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Home » Physics » Strength of Materials » Column And Struts » Strut With lateral load » Strut Subjected To Compressive Axial Thrust And A Transverse Point Load At The Centre » Radius of gyration given maximum stress induced for strut with axial and point load

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< 23 Strut Subjected To Compressive Axial Thrust And A Transverse Point Load At The Centre Calculators

Radius of gyration given maximum stress induced for strut with axial and point load

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

Distance of extreme layer from neutral axis given maximum stress induced for strut

Go Distance from Neutral Axis to Extreme Point = (Maximum bending stress-(Column Compressive load/Column Cross Sectional Area))*(Column Cross Sectional Area*(Least Radius of Gyration Column^2))/((Greatest Safe Load*(((sqrt(Moment of Inertia Column*Modulus of Elasticity Column/Column Compressive load))/(2*Column Compressive load))*tan((Column Length/2)*(sqrt(Column Compressive load/(Moment of Inertia Column*Modulus of Elasticity Column/Column Compressive load)))))))

Maximum stress induced for strut with axial and transverse point load at center

Go Maximum bending stress = (Column Compressive load/Column Cross Sectional Area)+((Greatest Safe Load*(((sqrt(Moment of Inertia Column*Modulus of Elasticity Column/Column Compressive load))/(2*Column Compressive load))*tan((Column Length/2)*(sqrt(Column Compressive load/(Moment of Inertia Column*Modulus of Elasticity Column/Column Compressive load))))))*(Distance from Neutral Axis to Extreme Point)/(Column Cross Sectional Area*(Least Radius of Gyration Column^2)))

Cross-sectional area given maximum stress induced for strut with axial and point load

Go Column Cross Sectional Area = (Column Compressive load/Maximum bending stress)+((Greatest Safe Load*(((sqrt(Moment of Inertia Column*Modulus of Elasticity Column/Column Compressive load))/(2*Column Compressive load))*tan((Column Length/2)*(sqrt(Column Compressive load/(Moment of Inertia Column*Modulus of Elasticity Column/Column Compressive load))))))*(Distance from Neutral Axis to Extreme Point)/(Maximum bending stress*(Least Radius of Gyration Column^2)))

Maximum deflection for strut with axial and transverse point load at center

Go Deflection at Section = Greatest Safe Load*((((sqrt(Moment of Inertia Column*Modulus of Elasticity Column/Column Compressive load))/(2*Column Compressive load))*tan((Column Length/2)*(sqrt(Column Compressive load/(Moment of Inertia Column*Modulus of Elasticity Column/Column Compressive load)))))-(Column Length/(4*Column Compressive load)))

Transverse point load given maximum deflection for strut

Go Greatest Safe Load = Deflection at Section/((((sqrt(Moment of Inertia Column*Modulus of Elasticity Column/Column Compressive load))/(2*Column Compressive load))*tan((Column Length/2)*(sqrt(Column Compressive load/(Moment of Inertia Column*Modulus of Elasticity Column/Column Compressive load)))))-(Column Length/(4*Column Compressive load)))

Maximum bending moment for strut with axial and transverse point load at center

Go Maximum Bending Moment In Column = Greatest Safe Load*(((sqrt(Moment of Inertia Column*Modulus of Elasticity Column/Column Compressive load))/(2*Column Compressive load))*tan((Column Length/2)*(sqrt(Column Compressive load/(Moment of Inertia Column*Modulus of Elasticity Column/Column Compressive load)))))

Transverse point load given maximum bending moment for strut

Go Greatest Safe Load = Maximum Bending Moment In Column/(((sqrt(Moment of Inertia Column*Modulus of Elasticity Column/Column Compressive load))/(2*Column Compressive load))*tan((Column Length/2)*(sqrt(Column Compressive load/(Moment of Inertia Column*Modulus of Elasticity Column/Column Compressive load)))))

Radius of gyration if maximum bending moment is given for strut with axial and point load

Go Least Radius of Gyration Column = sqrt((Maximum Bending Moment In Column*Distance from Neutral Axis to Extreme Point)/(Column Cross Sectional Area*Maximum bending stress))

Radius of gyration given bending stress for strut with axial and transverse point load

Go Least Radius of Gyration Column = sqrt((Bending Moment in Column*Distance from Neutral Axis to Extreme Point)/(Bending Stress in Column*Column Cross Sectional Area))

Deflection at section for strut with axial and transverse point load at center

Go Deflection at Section = Column Compressive load-(Bending Moment in Column+(Greatest Safe Load*Distance of deflection from end A/2))/(Column Compressive load)

Distance of extreme layer from neutral axis if max bending moment is given for strut with point load

Go Distance from Neutral Axis to Extreme Point = Maximum bending stress*(Column Cross Sectional Area*(Least Radius of Gyration Column^2))/(Maximum Bending Moment In Column)

Maximum bending stress if maximum bending moment is given for strut with axial and point load

Go Maximum bending stress = (Maximum Bending Moment In Column*Distance from Neutral Axis to Extreme Point)/(Column Cross Sectional Area*(Least Radius of Gyration Column^2))

Maximum bending moment if maximum bending stress is given for strut with axial and point load

Go Maximum Bending Moment In Column = Maximum bending stress*(Column Cross Sectional Area*(Least Radius of Gyration Column^2))/(Distance from Neutral Axis to Extreme Point)

Cross sectional area if maximum bending moment is given for strut with axial and point load

Go Column Cross Sectional Area = (Maximum Bending Moment In Column*Distance from Neutral Axis to Extreme Point)/((Least Radius of Gyration Column^2)*Maximum bending stress)

Bending moment given bending stress for strut with axial and transverse point load at center

Go Bending Moment in Column = Bending Stress in Column*(Column Cross Sectional Area*(Least Radius of Gyration Column^2))/(Distance from Neutral Axis to Extreme Point)

Cross-sectional area given bending stress for strut with axial and transverse point load

Go Column Cross Sectional Area = (Bending Moment in Column*Distance from Neutral Axis to Extreme Point)/(Bending Stress in Column*(Least Radius of Gyration Column^2))

Distance of extreme layer from neutral axis given bending stress for strut

Go Distance from Neutral Axis to Extreme Point = Bending Stress in Column*(Column Cross Sectional Area*(Least Radius of Gyration Column^2))/(Bending Moment in Column)

Bending stress for strut with axial and transverse point load at center

Go Bending Stress in Column = (Bending Moment in Column*Distance from Neutral Axis to Extreme Point)/(Column Cross Sectional Area*(Least Radius of Gyration Column^2))

Distance of deflection from end A for strut with axial and transverse point load at center

Go Distance of deflection from end A = (-Bending Moment in Column-(Column Compressive load*Deflection at Section))*2/(Greatest Safe Load)

Compressive axial load for strut with axial and transverse point load at center

Go Column Compressive load = -(Bending Moment in Column+(Greatest Safe Load*Distance of deflection from end A/2))/(Deflection at Section)

Transverse point load for strut with axial and transverse point load at center

Go Greatest Safe Load = (-Bending Moment in Column-(Column Compressive load*Deflection at Section))*2/(Distance of deflection from end A)

Bending moment at section for strut with axial and transverse point load at center

Go Bending Moment in Column = -(Column Compressive load*Deflection at Section)-(Greatest Safe Load*Distance of deflection from end A/2)

Radius of gyration given maximum stress induced for strut with axial and point load Formula

What is transverse point loading?

Transverse loading is a load applied vertically to the plane of the longitudinal axis of a configuration, such as a wind load. It causes the material to bend and rebound from its original position, with inner tensile and compressive straining associated with the change in curvature of the material.

How to Calculate 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 calculator uses Least Radius of Gyration Column = sqrt(((Greatest Safe Load*(((sqrt(Moment of Inertia Column*Modulus of Elasticity Column/Column Compressive load))/(2*Column Compressive load))*tan((Column Length/2)*(sqrt(Column Compressive load/(Moment of Inertia Column*Modulus of Elasticity Column/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 calculate the Least Radius of Gyration Column, The Radius of gyration given maximum stress induced for strut with axial and point load formula is defined as the radial distance to a point which would have a moment of inertia the same as the body's actual distribution of mass if the total mass of the body were concentrated there. Least Radius of Gyration Column is denoted by r_least symbol.

How to calculate Radius of gyration given maximum stress induced for strut with axial and point load using this online calculator? To use this online calculator for Radius of gyration given maximum stress induced for strut with axial and point load, enter Greatest Safe Load (Wp), Moment of Inertia Column (I), Modulus of Elasticity Column (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. Here is how the Radius of gyration given maximum stress induced for strut with axial and point load calculation can be explained with given input values -> 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)))))).

FAQ

What is Radius of gyration given maximum stress induced for strut with axial and point load?

The Radius of gyration given maximum stress induced for strut with axial and point load formula is defined as the radial distance to a point which would have a moment of inertia the same as the body's actual distribution of mass if the total mass of the body were concentrated there and is represented as r_least = sqrt(((Wp*(((sqrt(I*ε_column/P_compressive))/(2*P_compressive))*tan((l_column/2)*(sqrt(P_compressive/(I*ε_column/P_compressive))))))*(c)/(A_sectional*((σb^max-(P_compressive/A_sectional)))))) or Least Radius of Gyration Column = sqrt(((Greatest Safe Load*(((sqrt(Moment of Inertia Column*Modulus of Elasticity Column/Column Compressive load))/(2*Column Compressive load))*tan((Column Length/2)*(sqrt(Column Compressive load/(Moment of Inertia Column*Modulus of Elasticity Column/Column Compressive load))))))*(Distance from Neutral Axis to Extreme Point)/(Column Cross Sectional Area*((Maximum bending stress-(Column Compressive load/Column Cross Sectional Area)))))). Greatest Safe Load is the maximum safe point load allowable at the center of the beam, Moment of Inertia Column is the measure of the resistance of a body to angular acceleration about a given axis, Modulus of Elasticity Column is a quantity that measures an object or substance's resistance to being deformed elastically when stress is applied to it, Column Compressive load is the load applied to a column that is compressive in nature, Column Length is the distance between two points where a column gets its fixity of support so its movement is restrained in all directions, Distance from Neutral Axis to Extreme Point is the distance between the neutral axis and the extreme point, Column Cross Sectional Area is the area of a two-dimensional shape that is obtained when a three dimensional shape is sliced perpendicular to some specified axis at a point & Maximum bending stress is the normal stress that is induced at a point in a body subjected to loads that cause it to bend.

How to calculate Radius of gyration given maximum stress induced for strut with axial and point load?

The Radius of gyration given maximum stress induced for strut with axial and point load formula is defined as the radial distance to a point which would have a moment of inertia the same as the body's actual distribution of mass if the total mass of the body were concentrated there is calculated using Least Radius of Gyration Column = sqrt(((Greatest Safe Load*(((sqrt(Moment of Inertia Column*Modulus of Elasticity Column/Column Compressive load))/(2*Column Compressive load))*tan((Column Length/2)*(sqrt(Column Compressive load/(Moment of Inertia Column*Modulus of Elasticity Column/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 calculate Radius of gyration given maximum stress induced for strut with axial and point load, you need Greatest Safe Load (Wp), Moment of Inertia Column (I), Modulus of Elasticity Column (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). With our tool, you need to enter the respective value for Greatest Safe Load, Moment of Inertia Column, Modulus of Elasticity Column, Column Compressive load, Column Length, Distance from Neutral Axis to Extreme Point, Column Cross Sectional Area & Maximum bending stress and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Least Radius of Gyration Column?

In this formula, Least Radius of Gyration Column uses Greatest Safe Load, Moment of Inertia Column, Modulus of Elasticity Column, Column Compressive load, Column Length, Distance from Neutral Axis to Extreme Point, Column Cross Sectional Area & Maximum bending stress. We can use 2 other way(s) to calculate the same, which is/are as follows -

Least Radius of Gyration 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 Column = sqrt((Maximum Bending Moment In Column*Distance from Neutral Axis to Extreme Point)/(Column Cross Sectional Area*Maximum bending stress))

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