Slenderness Ratio Used for Separation Calculator

✖The Modulus of Elasticity of Steel or elastic modulus is the resistance of the structure or object from being deformed elastically when a stress is applied.ⓘ Modulus of Elasticity of Steel [E_s]			+10% -10%
✖Yield Stress of Steel is the stress at which the material begins to deform plastically, meaning it will not return to its original shape when the applied force is removed.ⓘ Yield Stress of Steel [F_y]			+10% -10%

✖Factor for Allowable Stress Design is the usual term used to demarcate between inelastic and elastic member buckling.ⓘ Slenderness Ratio Used for Separation [C_c]

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Formula

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Slenderness Ratio Used for Separation

Formula

`"C"_{"c"} = sqrt((2*(pi^2)*"E"_{"s"})/"F"_{"y"})`

Example

`"125.6637"=sqrt((2*(pi^2)*"200000MPa")/"250MPa")`

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Slenderness Ratio Used for Separation Solution

STEP 0: Pre-Calculation Summary

Formula Used

Factor for Allowable Stress Design = sqrt((2*(pi^2)*Modulus of Elasticity of Steel)/Yield Stress of Steel)
C_c = sqrt((2*(pi^2)*E_s)/F_y)
This formula uses 1 Constants, 1 Functions, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

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

Factor for Allowable Stress Design - Factor for Allowable Stress Design is the usual term used to demarcate between inelastic and elastic member buckling.
Modulus of Elasticity of Steel - (Measured in Pascal) - The Modulus of Elasticity of Steel or elastic modulus is the resistance of the structure or object from being deformed elastically when a stress is applied.
Yield Stress of Steel - (Measured in Pascal) - Yield Stress of Steel is the stress at which the material begins to deform plastically, meaning it will not return to its original shape when the applied force is removed.

STEP 1: Convert Input(s) to Base Unit

Modulus of Elasticity of Steel: 200000 Megapascal --> 200000000000 Pascal (Check conversion here)
Yield Stress of Steel: 250 Megapascal --> 250000000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

C_c = sqrt((2*(pi^2)*E_s)/F_y) --> sqrt((2*(pi^2)*200000000000)/250000000)

Evaluating ... ...

C_c = 125.663706143592

STEP 3: Convert Result to Output's Unit

125.663706143592 --> No Conversion Required

FINAL ANSWER

125.663706143592 ≈ 125.6637 <-- Factor for Allowable Stress Design

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Design of Steel Structures » Allowable-Stress Design » Allowable-Stress Design for Building Columns » Slenderness Ratio Used for Separation

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Created by Chandana P Dev

NSS College of Engineering (NSSCE), Palakkad

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Meerut Institute of Engineering and Technology (MIET), Meerut

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< 6 Allowable-Stress Design for Building Columns Calculators

Safety Factor for Allowable Compressive Stress

Go Safety Factor = 5/3+((3*((Effective Length Factor*Effective Column Length)/Radius of Gyration))/(8*Factor for Allowable Stress Design))-((((Effective Length Factor*Effective Column Length)/Radius of Gyration)^3)/(8*Factor for Allowable Stress Design^3))

Allowable Compressive Stress when Slenderness Ratio is Less than Cc

Go Allowable Compression Stress = ((1-((((Effective Length Factor*Effective Column Length)/Radius of Gyration)^2)/(2*Factor for Allowable Stress Design^2)))*Yield Stress of Steel)/Safety Factor

Allowable Compressive Stress when Slenderness Ratio is Greater than Cc

Go Allowable Compression Stress = (12*pi^2*Modulus of Elasticity of Steel)/(23*((Effective Length Factor*Effective Column Length)/Radius of Gyration)^2)

Slenderness Ratio Used for Separation

Go Factor for Allowable Stress Design = sqrt((2*(pi^2)*Modulus of Elasticity of Steel)/Yield Stress of Steel)

Factor for Unbraced Segment of any Cross-Section

Go Factor for Allowable Stress Design = 1986.66/sqrt(Yield Stress of Steel)

Effective Length Factor

Go Effective Length Factor = Effective Column Length/Actual Unbraced Length

Slenderness Ratio Used for Separation Formula

Factor for Allowable Stress Design = sqrt((2*(pi^2)*Modulus of Elasticity of Steel)/Yield Stress of Steel)
C_c = sqrt((2*(pi^2)*E_s)/F_y)

What is Allowable Stress Design or ASD?

In the Allowable Stress (or working stress) Design, member stresses computed under the action of service (or working) loads are compared to some predesignated stresses called allowable stresses. The allowable stresses are usually expressed as a function of the yield stress or tensile stress of the material.

Define Radius of Gyration & Slenderness Ratio.

The radius of gyration is defined as the imaginary distance from the centroid at which the area of the cross-section is imagined to be focused on a point to obtain the same moment of inertia. It is the perpendicular distance from point mass to the axis of rotation.
The slenderness ratio can also be defined as the ratio of the effective length of the column to the minimum radius of gyration1. It serves as a measure of the column’s ability to withstand buckling pressure. In structural engineering, slenderness is a measure of the propensity of a column to buckle.

How to Calculate Slenderness Ratio Used for Separation?

Slenderness Ratio Used for Separation calculator uses Factor for Allowable Stress Design = sqrt((2*(pi^2)*Modulus of Elasticity of Steel)/Yield Stress of Steel) to calculate the Factor for Allowable Stress Design, The Slenderness Ratio Used for Separation formula is defined as the demarcating between the elastic member buckling from inelastic member buckling. Factor for Allowable Stress Design is denoted by C_c symbol.

How to calculate Slenderness Ratio Used for Separation using this online calculator? To use this online calculator for Slenderness Ratio Used for Separation, enter Modulus of Elasticity of Steel (E_s) & Yield Stress of Steel (F_y) and hit the calculate button. Here is how the Slenderness Ratio Used for Separation calculation can be explained with given input values -> 125.6637 = sqrt((2*(pi^2)*200000000000)/250000000).

FAQ

What is Slenderness Ratio Used for Separation?

The Slenderness Ratio Used for Separation formula is defined as the demarcating between the elastic member buckling from inelastic member buckling and is represented as C_c = sqrt((2*(pi^2)*E_s)/F_y) or Factor for Allowable Stress Design = sqrt((2*(pi^2)*Modulus of Elasticity of Steel)/Yield Stress of Steel). The Modulus of Elasticity of Steel or elastic modulus is the resistance of the structure or object from being deformed elastically when a stress is applied & Yield Stress of Steel is the stress at which the material begins to deform plastically, meaning it will not return to its original shape when the applied force is removed.

How to calculate Slenderness Ratio Used for Separation?

The Slenderness Ratio Used for Separation formula is defined as the demarcating between the elastic member buckling from inelastic member buckling is calculated using Factor for Allowable Stress Design = sqrt((2*(pi^2)*Modulus of Elasticity of Steel)/Yield Stress of Steel). To calculate Slenderness Ratio Used for Separation, you need Modulus of Elasticity of Steel (E_s) & Yield Stress of Steel (F_y). With our tool, you need to enter the respective value for Modulus of Elasticity of Steel & Yield Stress of Steel 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 Factor for Allowable Stress Design?

In this formula, Factor for Allowable Stress Design uses Modulus of Elasticity of Steel & Yield Stress of Steel. We can use 1 other way(s) to calculate the same, which is/are as follows -

Factor for Allowable Stress Design = 1986.66/sqrt(Yield Stress of Steel)

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