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

✖Maximum Bending Moment In Column is the highest moment of force that causes the column to bend or deform under applied loads.ⓘ Maximum Bending Moment In Column [M_max]			+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 if Maximum Bending Moment is given for Strut with Axial and Point Load [k]

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

STEP 0: Pre-Calculation Summary

Formula Used

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))
k = sqrt((M_max*c)/(A_sectional*σb^max))
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.
Maximum Bending Moment In Column - (Measured in Newton Meter) - Maximum Bending Moment In Column is the highest moment of force that causes the column to bend or deform under applied loads.
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

Maximum Bending Moment In Column: 16 Newton Meter --> 16 Newton Meter No Conversion Required
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((M_max*c)/(A_sectional*σb^max)) --> sqrt((16*0.01)/(1.4*2000000))

Evaluating ... ...

k = 0.000239045721866879

STEP 3: Convert Result to Output's Unit

0.000239045721866879 Meter -->0.239045721866879 Millimeter (Check conversion here)

FINAL ANSWER

0.239045721866879 ≈ 0.239046 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 if Maximum Bending Moment is given for Strut with Axial and Point Load

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Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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Birsa Institute of Technology (BIT), Sindri

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

LaTeX Go

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 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 calculator 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 calculate 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 calculate Radius of Gyration if Maximum Bending Moment is given for Strut with Axial and Point Load using this online calculator? To use this online calculator 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. Here is how the Radius of Gyration if Maximum Bending Moment is given for Strut with Axial and Point Load calculation can be explained with given input values -> 239.0457 = sqrt((16*0.01)/(1.4*2000000)).

FAQ

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

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 and is represented as k = sqrt((M_max*c)/(A_sectional*σb^max)) or 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)). Maximum Bending Moment In Column is the highest moment of force that causes the column to bend or deform under applied loads, 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 if Maximum Bending Moment is given for Strut with Axial and Point Load?

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 is calculated using 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 calculate Radius of Gyration if Maximum Bending Moment is given for Strut with Axial and Point Load, you need 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). With our tool, you need to enter the respective value for Maximum Bending Moment In Column, 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 Maximum Bending Moment In Column, 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(((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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