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)))))
rleast = (0.20*((EAR/((Fyw/(fs*Fa))-1))*(sqrt(fs*Pcompressive/(4*εcolumn)))))
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
rleast = (0.20*((EAR/((Fyw/(fs*Fa))-1))*(sqrt(fs*Pcompressive/(4*εcolumn))))) --> (0.20*((6/((2700000/(2.8*10000000))-1))*(sqrt(2.8*400/(4*10560000)))))
Evaluating ... ...
rleast = -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 00.004 seconds)

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10+ Formula By I.S. Code For Mild Steel Calculators

Value Obtained from Secant Formula given Allowable Axial Compression Stress
Go Value obtained from Secant Formula = (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))))))
Least Radius of Gyration given Allowable Axial Compression Stress
Go 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)))))
Effective Column Length given Allowable Axial Compression Stress
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
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
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
Slenderness Ratio given Allowable Axial Compression Stress
Go Slenderness Ratio = ((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)))))
Value Obtained from Secant given Axial Compression Stress Slenderness Ratio Greater than 160
Go Value obtained from Secant Formula = Allowable compression stress/(1.2-(Effective Column Length/(800*Least Radius of Gyration Column)))
Least Radius of Gyration given Allowable Axial Compression Stress Slenderness Ratio More 160
Go Least Radius of Gyration Column = Effective Column Length/(800*(1.2-(Allowable compression stress/Value obtained from Secant Formula)))
Allowable Axial Compression Stress for Slenderness Ratio greater than 160
Go Allowable compression stress = Value obtained from Secant Formula*(1.2-(Effective Column Length/(800*Least Radius of Gyration Column)))
Effective Column Length given Allowable Axial Compression Stress, SL Ratio Greater than 160
Go Effective Column Length = 1.2-(Allowable compression stress/Value obtained from Secant Formula)*(800*Least Radius of Gyration Column)

Least Radius of Gyration given Allowable Axial Compression Stress Formula

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)))))
rleast = (0.20*((EAR/((Fyw/(fs*Fa))-1))*(sqrt(fs*Pcompressive/(4*εcolumn)))))

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, The Least radius of gyration given allowable axial compression stress formula is defined as the radial distance to a point which 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 rleast 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 (Fyw), Factor of Safety (fs), Allowable compression stress (Fa), Column Compressive load (Pcompressive) & Modulus of Elasticity Column 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 -> -7028.595045 = (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?
The Least radius of gyration given allowable axial compression stress formula is defined as the radial distance to a point which 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 rleast = (0.20*((EAR/((Fyw/(fs*Fa))-1))*(sqrt(fs*Pcompressive/(4*εcolumn))))) 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?
The Least radius of gyration given allowable axial compression stress formula is defined as the radial distance to a point which 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 = (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 (Fyw), Factor of Safety (fs), Allowable compression stress (Fa), Column Compressive load (Pcompressive) & Modulus of Elasticity Column 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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