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 [W_p]			+10% -10%
✖Moment of Inertia in Column is the measure of the resistance of a column to angular acceleration about a given axis.ⓘ Moment of Inertia in Column [I]			+10% -10%
✖Modulus of Elasticity is a quantity that measures an object or substance's resistance to being deformed elastically when stress is applied to it.ⓘ Modulus of Elasticity [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 column that is obtained when a column is sliced perpendicular to some specified axis at a point.ⓘ Column Cross Sectional Area [A_sectional]			+10% -10%
✖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.ⓘ Maximum Bending Stress [σb^max]			+10% -10%

✖Least Radius of Gyration of Column is a measure of the distribution of its cross-sectional area around its centroidal axis.ⓘ Radius of Gyration given Maximum Stress induced for Strut with Axial and Point Load [k]

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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 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))))))
k = sqrt(((W_p*(((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 of Column - (Measured in Meter) - Least Radius of Gyration of Column is a measure of the distribution of its cross-sectional area around its centroidal axis.
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 in Column - (Measured in Meter⁴) - Moment of Inertia in Column is the measure of the resistance of a column to angular acceleration about a given axis.
Modulus of Elasticity - (Measured in Pascal) - Modulus of Elasticity 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 column that is obtained when a column is sliced perpendicular to some specified axis at a point.
Maximum Bending Stress - (Measured in Pascal) - 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.

STEP 1: Convert Input(s) to Base Unit

Greatest Safe Load: 0.1 Kilonewton --> 100 Newton (Check conversion here)
Moment of Inertia in Column: 5600 Centimeter⁴ --> 5.6E-05 Meter⁴ (Check conversion here)
Modulus of Elasticity: 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

k = sqrt(((W_p*(((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 ... ...

k = 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 of Column

(Calculation completed in 00.004 seconds)

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Home » Physics » Strength of Materials » Column And Struts » Strut With Lateral Load » Mechanical » 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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< Strut Subjected to Compressive Axial Thrust and a Transverse Point Load at the Centre Calculators

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

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

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

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

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

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

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

LaTeX Go Bending Moment in Column = -(Column Compressive Load*Deflection at Column 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

LaTeX Go

What is Radius of Gyration?

The Radius of Gyration is a geometric property that describes the distribution of an object's cross-sectional area around an axis. It is used primarily in structural engineering to assess how a structural member resists buckling and helps determine its stiffness. The radius of gyration gives insight into how the material is spread out from the centroid of the cross-section and plays an important role in stability analysis of columns and beams.

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 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 calculate 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 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 (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. 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 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 and is represented as k = sqrt(((W_p*(((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 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)))))). Greatest Safe Load is the maximum safe point load allowable at the center of the beam, Moment of Inertia in Column is the measure of the resistance of a column to angular acceleration about a given axis, Modulus of Elasticity 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 column that is obtained when a column is sliced perpendicular to some specified axis at a point & 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.

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 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 is calculated using 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 calculate Radius of Gyration given Maximum Stress induced for Strut with Axial and Point Load, you need 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). With our tool, you need to enter the respective value for Greatest Safe Load, Moment of Inertia in Column, Modulus of Elasticity, 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 of Column?

In this formula, Least Radius of Gyration of Column uses Greatest Safe Load, Moment of Inertia in Column, Modulus of Elasticity, 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 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))

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