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

✖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.ⓘ Bending Moment in Column [M_b]			+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%
✖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.ⓘ Bending Stress in Column [σ_b]			+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%

✖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 Bending Stress for Strut with Axial and Transverse Point Load [k]

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

STEP 0: Pre-Calculation Summary

Formula Used

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))
k = sqrt((M_b*c)/(σ_b*A_sectional))
This formula uses 1 Functions, 5 Variables

Functions Used

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.
Bending Moment in Column - (Measured in Newton Meter) - 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.
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.
Bending Stress in Column - (Measured in Pascal) - 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.
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.

STEP 1: Convert Input(s) to Base Unit

Bending Moment in Column: 48 Newton Meter --> 48 Newton Meter No Conversion Required
Distance from Neutral Axis to Extreme Point: 10 Millimeter --> 0.01 Meter (Check conversion here)
Bending Stress in Column: 0.04 Megapascal --> 40000 Pascal (Check conversion here)
Column Cross Sectional Area: 1.4 Square Meter --> 1.4 Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

k = sqrt((M_b*c)/(σ_b*A_sectional)) --> sqrt((48*0.01)/(40000*1.4))

Evaluating ... ...

k = 0.0029277002188456

STEP 3: Convert Result to Output's Unit

0.0029277002188456 Meter -->2.9277002188456 Millimeter (Check conversion here)

FINAL ANSWER

2.9277002188456 ≈ 2.9277 Millimeter <-- Least Radius of Gyration of Column

(Calculation completed in 00.012 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 Bending Stress for Strut with Axial and Transverse Point Load

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National Institute Of Technology (NIT), Hamirpur

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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 Bending Stress for Strut with Axial and Transverse 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.

How to Calculate 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 calculator 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 calculate 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 calculate Radius of Gyration given Bending Stress for Strut with Axial and Transverse Point Load using this online calculator? To use this online calculator 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. Here is how the Radius of Gyration given Bending Stress for Strut with Axial and Transverse Point Load calculation can be explained with given input values -> 2927.7 = sqrt((48*0.01)/(40000*1.4)).

FAQ

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

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 and is represented as k = sqrt((M_b*c)/(σ_b*A_sectional)) or 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)). 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, Distance from Neutral Axis to Extreme Point is the distance between the neutral axis and the extreme point, 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 & 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.

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

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 is calculated using 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 calculate Radius of Gyration given Bending Stress for Strut with Axial and Transverse Point Load, you need 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). With our tool, you need to enter the respective value for Bending Moment in Column, Distance from Neutral Axis to Extreme Point, Bending Stress in Column & Column Cross Sectional Area 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 Bending Moment in Column, Distance from Neutral Axis to Extreme Point, Bending Stress in Column & Column Cross Sectional Area. We can use 2 other way(s) to calculate the same, which is/are as follows -

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))))))

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