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]

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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 00.020 seconds)

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< Euler and Rankine's Theory Calculators

Crushing Load by Rankine's Formula

LaTeX 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

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

Crippling Load by Rankine's

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

Crushing Load given Ultimate Crushing Stress

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

< Rankine's Formula Calculators

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

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

Crippling Load given Rankine's Constant

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

Crippling Load by Rankine's

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

Cross-Sectional Area of Column given Crushing Load

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

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

LaTeX Go

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 a measure that determines the minimum radius of gyration of a column under a crippling load, considering the effective length, cross-sectional area, and crippling stress, which is essential in Euler and Rankine's theory of column design. 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 a measure that determines the minimum radius of gyration of a column under a crippling load, considering the effective length, cross-sectional area, and crippling stress, which is essential in Euler and Rankine's theory of column design 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 a measure that determines the minimum radius of gyration of a column under a crippling load, considering the effective length, cross-sectional area, and crippling stress, which is essential in Euler and Rankine's theory of column design 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.

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