Least Radius of Gyration given Allowable Axial Compression Stress Slenderness Ratio More 160 Calculator

✖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%
✖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%
✖Value obtained from secant formula is the stress value on the column of mild steel.ⓘ Value obtained from Secant Formula [σ_c']			+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 Slenderness Ratio More 160 [r_least]

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Least Radius of Gyration given Allowable Axial Compression Stress Slenderness Ratio More 160

Formula

`"r"_{"least"} = "L"_{"eff"}/(800*(1.2-("F"_{"a"}/"σ"_{"c'"})))`

Example

`"3.191447mm"="3000mm"/(800*(1.2-("10MPa"/"400.25MPa")))`

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Least Radius of Gyration given Allowable Axial Compression Stress Slenderness Ratio More 160 Solution

STEP 0: Pre-Calculation Summary

Formula Used

Least Radius of Gyration Column = Effective Column Length/(800*(1.2-(Allowable compression stress/Value obtained from Secant Formula)))
r_least = L_eff/(800*(1.2-(F_a/σ_c')))
This formula uses 4 Variables

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 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.
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.
Value obtained from Secant Formula - (Measured in Pascal) - Value obtained from secant formula is the stress value on the column of mild steel.

STEP 1: Convert Input(s) to Base Unit

Effective Column Length: 3000 Millimeter --> 3 Meter (Check conversion here)
Allowable compression stress: 10 Megapascal --> 10000000 Pascal (Check conversion here)
Value obtained from Secant Formula: 400.25 Megapascal --> 400250000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_least = L_eff/(800*(1.2-(F_a/σ_c'))) --> 3/(800*(1.2-(10000000/400250000)))

Evaluating ... ...

r_least = 0.00319144694875611

STEP 3: Convert Result to Output's Unit

0.00319144694875611 Meter -->3.19144694875611 Millimeter (Check conversion here)

FINAL ANSWER

3.19144694875611 ≈ 3.191447 Millimeter <-- Least Radius of Gyration Column

(Calculation completed in 00.004 seconds)

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Home » Physics » Strength of Materials » Column And Struts » Formula By I.S. Code For Mild Steel » Least Radius of Gyration given Allowable Axial Compression Stress Slenderness Ratio More 160

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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 Slenderness Ratio More 160 Formula

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

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 has been shown to help reduce the risk of hamstring strains.

How to Calculate Least Radius of Gyration given Allowable Axial Compression Stress Slenderness Ratio More 160?

Least Radius of Gyration given Allowable Axial Compression Stress Slenderness Ratio More 160 calculator uses Least Radius of Gyration Column = Effective Column Length/(800*(1.2-(Allowable compression stress/Value obtained from Secant Formula))) to calculate the Least Radius of Gyration Column, Least radius of gyration given allowable axial compression stress slenderness ratio more 160 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 Allowable Axial Compression Stress Slenderness Ratio More 160 using this online calculator? To use this online calculator for Least Radius of Gyration given Allowable Axial Compression Stress Slenderness Ratio More 160, enter Effective Column Length (L_eff), Allowable compression stress (F_a) & Value obtained from Secant Formula (σ_c') and hit the calculate button. Here is how the Least Radius of Gyration given Allowable Axial Compression Stress Slenderness Ratio More 160 calculation can be explained with given input values -> 3191.447 = 3/(800*(1.2-(10000000/400250000))).

FAQ

What is Least Radius of Gyration given Allowable Axial Compression Stress Slenderness Ratio More 160?

Least radius of gyration given allowable axial compression stress slenderness ratio more 160 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 = L_eff/(800*(1.2-(F_a/σ_c'))) or Least Radius of Gyration Column = Effective Column Length/(800*(1.2-(Allowable compression stress/Value obtained from Secant 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, Allowable compression stress is the maximum stress (tensile, compressive or bending) that is allowed to be applied on a structural material & Value obtained from secant formula is the stress value on the column of mild steel.

How to calculate Least Radius of Gyration given Allowable Axial Compression Stress Slenderness Ratio More 160?

Least radius of gyration given allowable axial compression stress slenderness ratio more 160 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 = Effective Column Length/(800*(1.2-(Allowable compression stress/Value obtained from Secant Formula))). To calculate Least Radius of Gyration given Allowable Axial Compression Stress Slenderness Ratio More 160, you need Effective Column Length (L_eff), Allowable compression stress (F_a) & Value obtained from Secant Formula (σ_c'). With our tool, you need to enter the respective value for Effective Column Length, Allowable compression stress & Value obtained from Secant Formula 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 Column Length, Allowable compression stress & Value obtained from Secant Formula. We can use 1 other way(s) to calculate the same, which is/are as follows -

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)))))

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