Least Radius of Gyration given Allowable Axial Compression Stress Calculator

✖The effective interest rate is the true rate of interest earned.ⓘ Effective Interest Rate [EAR]			+10% -10%
✖Specified minimum yield stress for column represents the minimum tensile stress or yield stress required by the flexural member, say, web.ⓘ Specified minimum yield stress for column [F_yw]			+10% -10%
✖Factor of Safety expresses how much stronger a system is than it needs to be for an intended load.ⓘ Factor of Safety [f_s]			+10% -10%
✖Allowable compression stress is the maximum stress (tensile, compressive or bending) that is allowed to be applied on a structural material.ⓘ Allowable compression stress [F_a]			+10% -10%
✖Column Compressive load is the load applied to a column that is compressive in nature.ⓘ Column Compressive load [P_compressive]			+10% -10%
✖Modulus of Elasticity Column is a quantity that measures an object or substance's resistance to being deformed elastically when stress is applied to it.ⓘ Modulus of Elasticity Column [ε_column]			+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 Allowable Axial Compression Stress [r_least]

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Least Radius of Gyration given Allowable Axial Compression Stress Solution

STEP 0: Pre-Calculation Summary

Formula Used

Least Radius of Gyration Column = (0.20*((Effective Interest Rate/((Specified minimum yield stress for column/(Factor of Safety*Allowable compression stress))-1))*(sqrt(Factor of Safety*Column Compressive load/(4*Modulus of Elasticity Column)))))
r_least = (0.20*((EAR/((F_yw/(f_s*F_a))-1))*(sqrt(f_s*P_compressive/(4*ε_column)))))
This formula uses 1 Functions, 7 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.
Effective Interest Rate - The effective interest rate is the true rate of interest earned.
Specified minimum yield stress for column - (Measured in Pascal) - Specified minimum yield stress for column represents the minimum tensile stress or yield stress required by the flexural member, say, web.
Factor of Safety - Factor of Safety expresses how much stronger a system is than it needs to be for an intended load.
Allowable compression stress - (Measured in Pascal) - Allowable compression stress is the maximum stress (tensile, compressive or bending) that is allowed to be applied on a structural material.
Column Compressive load - (Measured in Newton) - Column Compressive load is the load applied to a column that is compressive in nature.
Modulus of Elasticity Column - (Measured in Pascal) - Modulus of Elasticity Column is a quantity that measures an object or substance's resistance to being deformed elastically when stress is applied to it.

STEP 1: Convert Input(s) to Base Unit

Effective Interest Rate: 6 --> No Conversion Required
Specified minimum yield stress for column: 2.7 Megapascal --> 2700000 Pascal (Check conversion here)
Factor of Safety: 2.8 --> No Conversion Required
Allowable compression stress: 10 Megapascal --> 10000000 Pascal (Check conversion here)
Column Compressive load: 0.4 Kilonewton --> 400 Newton (Check conversion here)
Modulus of Elasticity Column: 10.56 Megapascal --> 10560000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_least = (0.20*((EAR/((F_yw/(f_s*F_a))-1))*(sqrt(f_s*P_compressive/(4*ε_column))))) --> (0.20*((6/((2700000/(2.8*10000000))-1))*(sqrt(2.8*400/(4*10560000)))))

Evaluating ... ...

r_least = -0.00683857812580755

STEP 3: Convert Result to Output's Unit

-0.00683857812580755 Meter -->-6.83857812580755 Millimeter (Check conversion here)

FINAL ANSWER

-6.83857812580755 ≈ -6.838578 Millimeter <-- Least Radius of Gyration Column

(Calculation completed in 00.008 seconds)

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Home » Physics » Strength of Materials » Column And Struts » Mechanical » Formula By I.S. Code For Mild Steel » Least Radius of Gyration given Allowable Axial Compression Stress

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< Formula By I.S. Code For Mild Steel Calculators

Effective Column Length given Allowable Axial Compression Stress

LaTeX Go Effective Column Length = (((Specified minimum yield stress for column/(Factor of Safety*Allowable compression stress))-1)/(0.20*((sqrt(Factor of Safety*Column Compressive load/(4*Modulus of Elasticity Column))))))*Least Radius of Gyration Column

Allowable Axial Compression Stress for Slenderness Ratio 0 to 160

LaTeX Go Allowable compression stress = (Specified minimum yield stress for column/Factor of Safety)/(1+(0.20*((Effective Interest Rate/Least Radius of Gyration Column)*(sqrt(Factor of Safety*Column Compressive load/(4*Modulus of Elasticity Column))))))

Minimum Yield Stress for Allowable Axial Compression Stress for Slenderness Ratio between 0 to 160

LaTeX Go Specified minimum yield stress for column = Allowable compression stress*(1+(0.20*((Effective Interest Rate/Least Radius of Gyration Column)*(sqrt(Factor of Safety*Column Compressive load/(4*Modulus of Elasticity Column))))))*Factor of Safety

Allowable Axial Compression Stress for Slenderness Ratio greater than 160

LaTeX Go Allowable compression stress = Value obtained from Secant Formula*(1.2-(Effective Column Length/(800*Least Radius of Gyration Column)))

Least Radius of Gyration given Allowable Axial Compression Stress Formula

LaTeX Go

Which is example of eccentric loading?

Examples of eccentric loading activities include performing a calf raise off the ledge of a stair, an exercise that has been shown to decrease the risk of Achilles tendon injuries. Another example is the nordic curl exercise, which have been shown to help reduce the risk of hamstring strains.

How to Calculate Least Radius of Gyration given Allowable Axial Compression Stress?

Least Radius of Gyration given Allowable Axial Compression Stress calculator uses Least Radius of Gyration Column = (0.20*((Effective Interest Rate/((Specified minimum yield stress for column/(Factor of Safety*Allowable compression stress))-1))*(sqrt(Factor of Safety*Column Compressive load/(4*Modulus of Elasticity Column))))) to calculate the Least Radius of Gyration Column, Least Radius of Gyration given Allowable Axial Compression Stress formula is defined as a measure of the minimum radius of gyration of a column, which is a critical parameter in determining the stability of a structural member under axial compressive loads, ensuring the safety and integrity of the structure. Least Radius of Gyration Column is denoted by r_least symbol.

How to calculate Least Radius of Gyration given Allowable Axial Compression Stress using this online calculator? To use this online calculator for Least Radius of Gyration given Allowable Axial Compression Stress, enter Effective Interest Rate (EAR), Specified minimum yield stress for column (F_yw), Factor of Safety (f_s), Allowable compression stress (F_a), Column Compressive load (P_compressive) & Modulus of Elasticity Column (ε_column) and hit the calculate button. Here is how the Least Radius of Gyration given Allowable Axial Compression Stress calculation can be explained with given input values -> -6838.578126 = (0.20*((6/((2700000/(2.8*10000000))-1))*(sqrt(2.8*400/(4*10560000))))).

FAQ

What is Least Radius of Gyration given Allowable Axial Compression Stress?

Least Radius of Gyration given Allowable Axial Compression Stress formula is defined as a measure of the minimum radius of gyration of a column, which is a critical parameter in determining the stability of a structural member under axial compressive loads, ensuring the safety and integrity of the structure and is represented as r_least = (0.20*((EAR/((F_yw/(f_s*F_a))-1))*(sqrt(f_s*P_compressive/(4*ε_column))))) or Least Radius of Gyration Column = (0.20*((Effective Interest Rate/((Specified minimum yield stress for column/(Factor of Safety*Allowable compression stress))-1))*(sqrt(Factor of Safety*Column Compressive load/(4*Modulus of Elasticity Column))))). The effective interest rate is the true rate of interest earned, Specified minimum yield stress for column represents the minimum tensile stress or yield stress required by the flexural member, say, web, Factor of Safety expresses how much stronger a system is than it needs to be for an intended load, Allowable compression stress is the maximum stress (tensile, compressive or bending) that is allowed to be applied on a structural material, Column Compressive load is the load applied to a column that is compressive in nature & Modulus of Elasticity Column is a quantity that measures an object or substance's resistance to being deformed elastically when stress is applied to it.

How to calculate Least Radius of Gyration given Allowable Axial Compression Stress?

Least Radius of Gyration given Allowable Axial Compression Stress formula is defined as a measure of the minimum radius of gyration of a column, which is a critical parameter in determining the stability of a structural member under axial compressive loads, ensuring the safety and integrity of the structure is calculated using Least Radius of Gyration Column = (0.20*((Effective Interest Rate/((Specified minimum yield stress for column/(Factor of Safety*Allowable compression stress))-1))*(sqrt(Factor of Safety*Column Compressive load/(4*Modulus of Elasticity Column))))). To calculate Least Radius of Gyration given Allowable Axial Compression Stress, you need Effective Interest Rate (EAR), Specified minimum yield stress for column (F_yw), Factor of Safety (f_s), Allowable compression stress (F_a), Column Compressive load (P_compressive) & Modulus of Elasticity Column (ε_column). With our tool, you need to enter the respective value for Effective Interest Rate, Specified minimum yield stress for column, Factor of Safety, Allowable compression stress, Column Compressive load & Modulus of Elasticity Column 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 Column?

In this formula, Least Radius of Gyration Column uses Effective Interest Rate, Specified minimum yield stress for column, Factor of Safety, Allowable compression stress, Column Compressive load & Modulus of Elasticity Column. We can use 1 other way(s) to calculate the same, which is/are as follows -

Least Radius of Gyration Column = Effective Column Length/(800*(1.2-(Allowable compression stress/Value obtained from Secant Formula)))

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