Allowable Compressive Stress when Slenderness Ratio is Greater than Cc 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%
✖Effective Length Factor is the factor used for the members in the frame. It depends on the ratio of compression member stiffness to the end restraint stiffness.ⓘ Effective Length Factor [k]			+10% -10%
✖Effective Column Length of a column is the length of an equivalent pin-ended column that has the same load-carrying capacity and buckling behaviour as the actual column with different end conditions.ⓘ Effective Column Length [l]			+10% -10%
✖Radius of Gyration is the distance from the axis of rotation to a point where the total mass of any body is supposed to be concentrated.ⓘ Radius of Gyration [r]			+10% -10%

✖Allowable Compression Stress is the maximum stress (tensile, compressive or bending) that is allowed to be applied on a structural material.ⓘ Allowable Compressive Stress when Slenderness Ratio is Greater than Cc [F_a]

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Allowable Compressive Stress when Slenderness Ratio is Greater than Cc

Formula

`"F"_{"a"} = (12*pi^2*"E"_{"s"})/(23*(("k"*"l")/"r")^2)`

Example

`"1539.773MPa"=(12*pi^2*"200000MPa")/(23*(("0.75"*"3000mm")/"87mm")^2)`

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Allowable Compressive Stress when Slenderness Ratio is Greater than Cc Solution

STEP 0: Pre-Calculation Summary

Formula Used

Allowable Compression Stress = (12*pi^2*Modulus of Elasticity of Steel)/(23*((Effective Length Factor*Effective Column Length)/Radius of Gyration)^2)
F_a = (12*pi^2*E_s)/(23*((k*l)/r)^2)
This formula uses 1 Constants, 5 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

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.
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.
Effective Length Factor - Effective Length Factor is the factor used for the members in the frame. It depends on the ratio of compression member stiffness to the end restraint stiffness.
Effective Column Length - (Measured in Meter) - Effective Column Length of a column is the length of an equivalent pin-ended column that has the same load-carrying capacity and buckling behaviour as the actual column with different end conditions.
Radius of Gyration - (Measured in Meter) - Radius of Gyration is the distance from the axis of rotation to a point where the total mass of any body is supposed to be concentrated.

STEP 1: Convert Input(s) to Base Unit

Modulus of Elasticity of Steel: 200000 Megapascal --> 200000000000 Pascal (Check conversion here)
Effective Length Factor: 0.75 --> No Conversion Required
Effective Column Length: 3000 Millimeter --> 3 Meter (Check conversion here)
Radius of Gyration: 87 Millimeter --> 0.087 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

F_a = (12*pi^2*E_s)/(23*((k*l)/r)^2) --> (12*pi^2*200000000000)/(23*((0.75*3)/0.087)^2)

Evaluating ... ...

F_a = 1539772716.76589

STEP 3: Convert Result to Output's Unit

1539772716.76589 Pascal -->1539.77271676589 Megapascal (Check conversion here)

FINAL ANSWER

1539.77271676589 ≈ 1539.773 Megapascal <-- Allowable Compression Stress

(Calculation completed in 00.021 seconds)

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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

Allowable Compressive Stress when Slenderness Ratio is Greater than Cc Formula

Allowable Compression Stress = (12*pi^2*Modulus of Elasticity of Steel)/(23*((Effective Length Factor*Effective Column Length)/Radius of Gyration)^2)
F_a = (12*pi^2*E_s)/(23*((k*l)/r)^2)

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 Allowable Compressive Stress when Slenderness Ratio is Greater than Cc?

Allowable Compressive Stress when Slenderness Ratio is Greater than Cc calculator uses Allowable Compression Stress = (12*pi^2*Modulus of Elasticity of Steel)/(23*((Effective Length Factor*Effective Column Length)/Radius of Gyration)^2) to calculate the Allowable Compression Stress, The Allowable Compressive Stress when Slenderness Ratio is Greater than Cc formula is defined as the maximum limit of compressive stress that can be taken by the section when the condition specified is satisfied when the unbraced segment factor is greater than the slenderness ratio. Allowable Compression Stress is denoted by F_a symbol.

How to calculate Allowable Compressive Stress when Slenderness Ratio is Greater than Cc using this online calculator? To use this online calculator for Allowable Compressive Stress when Slenderness Ratio is Greater than Cc, enter Modulus of Elasticity of Steel (E_s), Effective Length Factor (k), Effective Column Length (l) & Radius of Gyration (r) and hit the calculate button. Here is how the Allowable Compressive Stress when Slenderness Ratio is Greater than Cc calculation can be explained with given input values -> 0.00154 = (12*pi^2*200000000000)/(23*((0.75*3)/0.087)^2).

FAQ

What is Allowable Compressive Stress when Slenderness Ratio is Greater than Cc?

The Allowable Compressive Stress when Slenderness Ratio is Greater than Cc formula is defined as the maximum limit of compressive stress that can be taken by the section when the condition specified is satisfied when the unbraced segment factor is greater than the slenderness ratio and is represented as F_a = (12*pi^2*E_s)/(23*((k*l)/r)^2) or Allowable Compression Stress = (12*pi^2*Modulus of Elasticity of Steel)/(23*((Effective Length Factor*Effective Column Length)/Radius of Gyration)^2). 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, Effective Length Factor is the factor used for the members in the frame. It depends on the ratio of compression member stiffness to the end restraint stiffness, Effective Column Length of a column is the length of an equivalent pin-ended column that has the same load-carrying capacity and buckling behaviour as the actual column with different end conditions & Radius of Gyration is the distance from the axis of rotation to a point where the total mass of any body is supposed to be concentrated.

How to calculate Allowable Compressive Stress when Slenderness Ratio is Greater than Cc?

The Allowable Compressive Stress when Slenderness Ratio is Greater than Cc formula is defined as the maximum limit of compressive stress that can be taken by the section when the condition specified is satisfied when the unbraced segment factor is greater than the slenderness ratio is calculated using Allowable Compression Stress = (12*pi^2*Modulus of Elasticity of Steel)/(23*((Effective Length Factor*Effective Column Length)/Radius of Gyration)^2). To calculate Allowable Compressive Stress when Slenderness Ratio is Greater than Cc, you need Modulus of Elasticity of Steel (E_s), Effective Length Factor (k), Effective Column Length (l) & Radius of Gyration (r). With our tool, you need to enter the respective value for Modulus of Elasticity of Steel, Effective Length Factor, Effective Column Length & Radius of Gyration 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 Allowable Compression Stress?

In this formula, Allowable Compression Stress uses Modulus of Elasticity of Steel, Effective Length Factor, Effective Column Length & Radius of Gyration. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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