Least Radius of Gyration given Crippling Load and Rankine's Constant Calculator

✖Rankine's Constant is the constant of Rankine's empirical formula.ⓘ Rankine's Constant [α]			+10% -10%
✖Effective Column Length can be defined as the length of an equivalent pin-ended column having the same load-carrying capacity as the member under consideration.ⓘ Effective Column Length [L_eff]			+10% -10%
✖Column Crushing stress is a special type of localized compressive stress which occurs at the surface of contact of two members that are relatively at rest.ⓘ Column Crushing Stress [σ_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]			+10% -10%
✖Crippling Load is the load over which a column prefers to deform laterally rather than compressing itself.ⓘ Crippling Load [P]			+10% -10%

✖Least Radius of Gyration Column is the smallest value of the radius of gyration is used for structural calculations.ⓘ Least Radius of Gyration given Crippling Load and Rankine's Constant [r_least]

⎘ Copy

👎

Formula

✖

Least Radius of Gyration given Crippling Load and Rankine's Constant

Formula

`"r"_{"least"} = sqrt(("α"*"L"_{"eff"}^2)/("σ"_{"c"}*"A"/"P"-1))`

Example

`"47.02mm"=sqrt(("0.00038"*("3000mm")^2)/("750MPa"*"2000mm²"/"588.9524kN"-1))`

Calculator

LaTeX

Reset

👍

Download Euler and Rankine's Theory Formulas PDF

Least Radius of Gyration given Crippling Load and Rankine's Constant Solution

STEP 0: Pre-Calculation Summary

Formula Used

Least Radius of Gyration Column = sqrt((Rankine's Constant*Effective Column Length^2)/(Column Crushing Stress*Column Cross Sectional Area/Crippling Load-1))
r_least = sqrt((α*L_eff^2)/(σ_c*A/P-1))
This formula uses 1 Functions, 6 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 Column - (Measured in Meter) - Least Radius of Gyration Column is the smallest value of the radius of gyration is used for structural calculations.
Rankine's Constant - Rankine's Constant is the constant of Rankine's empirical formula.
Effective Column Length - (Measured in Meter) - Effective Column Length can be defined as the length of an equivalent pin-ended column having the same load-carrying capacity as the member under consideration.
Column Crushing Stress - (Measured in Pascal) - Column Crushing stress is a special type of localized compressive stress which occurs at the surface of contact of two members that are relatively at rest.
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.
Crippling Load - (Measured in Newton) - Crippling Load is the load over which a column prefers to deform laterally rather than compressing itself.

STEP 1: Convert Input(s) to Base Unit

Rankine's Constant: 0.00038 --> No Conversion Required
Effective Column Length: 3000 Millimeter --> 3 Meter (Check conversion here)
Column Crushing Stress: 750 Megapascal --> 750000000 Pascal (Check conversion here)
Column Cross Sectional Area: 2000 Square Millimeter --> 0.002 Square Meter (Check conversion here)
Crippling Load: 588.9524 Kilonewton --> 588952.4 Newton (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_least = sqrt((α*L_eff^2)/(σ_c*A/P-1)) --> sqrt((0.00038*3^2)/(750000000*0.002/588952.4-1))

Evaluating ... ...

r_least = 0.0470199991326862

STEP 3: Convert Result to Output's Unit

0.0470199991326862 Meter -->47.0199991326862 Millimeter (Check conversion here)

FINAL ANSWER

47.0199991326862 ≈ 47.02 Millimeter <-- Least Radius of Gyration Column

(Calculation completed in 00.004 seconds)

You are here -

Home » Physics » Strength of Materials » Column And Struts » Euler and Rankine's Theory » Least Radius of Gyration given Crippling Load and Rankine's Constant

Credits

Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

Anshika Arya has created this Calculator and 2000+ more calculators!

Verified by Payal Priya

Birsa Institute of Technology (BIT), Sindri

Payal Priya has verified this Calculator and 1900+ more calculators!

< 19 Euler and Rankine's Theory Calculators

Effective Length of Column given Crippling Load and Rankine's Constant

Go Effective Column Length = sqrt((Column Crushing Stress*Column Cross Sectional Area/Crippling Load-1)*(Least Radius of Gyration Column^2)/Rankine's Constant)

Least Radius of Gyration given Crippling Load and Rankine's Constant

Go Least Radius of Gyration Column = sqrt((Rankine's Constant*Effective Column Length^2)/(Column Crushing Stress*Column Cross Sectional Area/Crippling Load-1))

Rankine's Constant given Crippling Load

Go Rankine's Constant = ((Column Crushing Stress*Column Cross Sectional Area)/Crippling Load-1)*((Least Radius of Gyration Column)/Effective Column Length)^2

Cross-Sectional Area of Column given Crippling Load and Rankine's Constant

Go Column Cross Sectional Area = (Crippling Load*(1+Rankine's Constant*(Effective Column Length/Least Radius of Gyration Column)^2))/Column Crushing Stress

Ultimate Crushing Stress given Crippling Load and Rankine's Constant

Go Column Crushing Stress = (Crippling Load*(1+Rankine's Constant*(Effective Column Length/Least Radius of Gyration Column)^2))/Column Cross Sectional Area

Crippling Load given Rankine's Constant

Go Crippling Load = (Column Crushing Stress*Column Cross Sectional Area)/(1+Rankine's Constant*(Effective Column Length/Least Radius of Gyration Column)^2)

Effective Length of Column given Crippling Load by Euler's Formula

Go Effective Column Length = sqrt((pi^2*Modulus of Elasticity Column*Moment of Inertia Column)/(Euler’s Buckling Load))

Crushing Load by Rankine's Formula

Go Crushing Load = (Rankine’s Critical Load*Euler’s Buckling Load)/(Euler’s Buckling Load-Rankine’s Critical Load)

Crippling Load by Euler's Formula given Crippling Load by Rankine's Formula

Go Euler’s Buckling Load = (Crushing Load*Rankine’s Critical Load)/(Crushing Load-Rankine’s Critical Load)

Crippling Load by Rankine's Formula

Go Rankine’s Critical Load = (Crushing Load*Euler’s Buckling Load)/(Crushing Load+Euler’s Buckling Load)

Modulus of Elasticity given Crippling Load by Euler's Formula

Go Modulus of Elasticity Column = (Euler’s Buckling Load*Effective Column Length^2)/(pi^2*Moment of Inertia Column)

Moment of Inertia given Crippling Load by Euler's Formula

Go Moment of Inertia Column = (Euler’s Buckling Load*Effective Column Length^2)/(pi^2*Modulus of Elasticity Column)

Crippling Load by Euler's Formula

Go Euler’s Buckling Load = (pi^2*Modulus of Elasticity Column*Moment of Inertia Column)/(Effective Column Length^2)

Modulus of Elasticity given Rankine's Constant

Go Modulus of Elasticity Column = Column Crushing Stress/(pi^2*Rankine's Constant)

Rankine's Constant

Go Rankine's Constant = Column Crushing Stress/(pi^2*Modulus of Elasticity Column)

Ultimate Crushing Stress given Rankine's Constant

Go Column Crushing Stress = Rankine's Constant*pi^2*Modulus of Elasticity Column

Cross-Sectional Area of Column given Crushing Load

Go Column Cross Sectional Area = Crushing Load/Column Crushing Stress

Crushing Load given Ultimate Crushing Stress

Go Crushing Load = Column Crushing Stress*Column Cross Sectional Area

Ultimate Crushing Stress given Crushing Load

Go Column Crushing Stress = Crushing Load/Column Cross Sectional Area

< 14 Rankine's Formula Calculators

Effective Length of Column given Crippling Load and Rankine's Constant

Go Effective Column Length = sqrt((Column Crushing Stress*Column Cross Sectional Area/Crippling Load-1)*(Least Radius of Gyration Column^2)/Rankine's Constant)

Least Radius of Gyration given Crippling Load and Rankine's Constant

Go Least Radius of Gyration Column = sqrt((Rankine's Constant*Effective Column Length^2)/(Column Crushing Stress*Column Cross Sectional Area/Crippling Load-1))

Rankine's Constant given Crippling Load

Go Rankine's Constant = ((Column Crushing Stress*Column Cross Sectional Area)/Crippling Load-1)*((Least Radius of Gyration Column)/Effective Column Length)^2

Cross-Sectional Area of Column given Crippling Load and Rankine's Constant

Go Column Cross Sectional Area = (Crippling Load*(1+Rankine's Constant*(Effective Column Length/Least Radius of Gyration Column)^2))/Column Crushing Stress

Ultimate Crushing Stress given Crippling Load and Rankine's Constant

Go Column Crushing Stress = (Crippling Load*(1+Rankine's Constant*(Effective Column Length/Least Radius of Gyration Column)^2))/Column Cross Sectional Area

Crippling Load given Rankine's Constant

Go Crippling Load = (Column Crushing Stress*Column Cross Sectional Area)/(1+Rankine's Constant*(Effective Column Length/Least Radius of Gyration Column)^2)

Crushing Load by Rankine's Formula

Go Crushing Load = (Rankine’s Critical Load*Euler’s Buckling Load)/(Euler’s Buckling Load-Rankine’s Critical Load)

Crippling Load by Rankine's Formula

Go Rankine’s Critical Load = (Crushing Load*Euler’s Buckling Load)/(Crushing Load+Euler’s Buckling Load)

Modulus of Elasticity given Rankine's Constant

Go Modulus of Elasticity Column = Column Crushing Stress/(pi^2*Rankine's Constant)

Rankine's Constant

Go Rankine's Constant = Column Crushing Stress/(pi^2*Modulus of Elasticity Column)

Ultimate Crushing Stress given Rankine's Constant

Go Column Crushing Stress = Rankine's Constant*pi^2*Modulus of Elasticity Column

Cross-Sectional Area of Column given Crushing Load

Go Column Cross Sectional Area = Crushing Load/Column Crushing Stress

Crushing Load given Ultimate Crushing Stress

Go Crushing Load = Column Crushing Stress*Column Cross Sectional Area

Ultimate Crushing Stress given Crushing Load

Go Column Crushing Stress = Crushing Load/Column Cross Sectional Area

Least Radius of Gyration given Crippling Load and Rankine's Constant Formula

Least Radius of Gyration Column = sqrt((Rankine's Constant*Effective Column Length^2)/(Column Crushing Stress*Column Cross Sectional Area/Crippling Load-1))
r_least = sqrt((α*L_eff^2)/(σ_c*A/P-1))

What is Ultimate Compressive Strength?

Ultimate Compressive Strength is defined as the force at which a specimen with a certain cross-section, and consisting of a particular fracturing material, fails when it is subjected to compression. The ultimate compressive strength is normally measured in N/mm2 (force per area) and is thus stress.

How to Calculate Least Radius of Gyration given Crippling Load and Rankine's Constant?

Least Radius of Gyration given Crippling Load and Rankine's Constant calculator uses Least Radius of Gyration Column = sqrt((Rankine's Constant*Effective Column Length^2)/(Column Crushing Stress*Column Cross Sectional Area/Crippling Load-1)) to calculate the Least Radius of Gyration Column, The Least Radius of Gyration given Crippling Load and Rankine's Constant formula is defined as the radial distance to a point that 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 Least Radius of Gyration given Crippling Load and Rankine's Constant using this online calculator? To use this online calculator for Least Radius of Gyration given Crippling Load and Rankine's Constant, enter Rankine's Constant (α), Effective Column Length (L_eff), Column Crushing Stress (σ_c), Column Cross Sectional Area (A) & Crippling Load (P) and hit the calculate button. Here is how the Least Radius of Gyration given Crippling Load and Rankine's Constant calculation can be explained with given input values -> 47020 = sqrt((0.00038*3^2)/(750000000*0.002/588952.4-1)).

FAQ

What is Least Radius of Gyration given Crippling Load and Rankine's Constant?

The Least Radius of Gyration given Crippling Load and Rankine's Constant formula is defined as the radial distance to a point that 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((α*L_eff^2)/(σ_c*A/P-1)) or Least Radius of Gyration Column = sqrt((Rankine's Constant*Effective Column Length^2)/(Column Crushing Stress*Column Cross Sectional Area/Crippling Load-1)). Rankine's Constant is the constant of Rankine's empirical formula, Effective Column Length can be defined as the length of an equivalent pin-ended column having the same load-carrying capacity as the member under consideration, Column Crushing stress is a special type of localized compressive stress which occurs at the surface of contact of two members that are relatively at rest, 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 & Crippling Load is the load over which a column prefers to deform laterally rather than compressing itself.

How to calculate Least Radius of Gyration given Crippling Load and Rankine's Constant?

The Least Radius of Gyration given Crippling Load and Rankine's Constant formula is defined as the radial distance to a point that 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((Rankine's Constant*Effective Column Length^2)/(Column Crushing Stress*Column Cross Sectional Area/Crippling Load-1)). To calculate Least Radius of Gyration given Crippling Load and Rankine's Constant, you need Rankine's Constant (α), Effective Column Length (L_eff), Column Crushing Stress (σ_c), Column Cross Sectional Area (A) & Crippling Load (P). With our tool, you need to enter the respective value for Rankine's Constant, Effective Column Length, Column Crushing Stress, Column Cross Sectional Area & Crippling Load and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

Home

FREE PDFs

🔍 Search