Elastic Local Buckling Stress Solution

STEP 0: Pre-Calculation Summary
Formula Used
Elastic Local Buckling Stress = (Local Buckling Coefficient*pi^2*Modulus of Elasticity for Steel Elements)/(12*Flat Width Ratio^2*(1-Poission Ratio for Plates^2))
fcr = (k*pi^2*Es)/(12*wt^2*(1-μ^2))
This formula uses 1 Constants, 5 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Variables Used
Elastic Local Buckling Stress - (Measured in Pascal) - Elastic Local Buckling Stress of structural profiles is typically considered by individually examining the stability of the isolated plates that make up the cross-section.
Local Buckling Coefficient - Local Buckling Coefficient is the factor when thin cold form structures are subjected to local buckling.
Modulus of Elasticity for Steel Elements - (Measured in Pascal) - The Modulus of Elasticity for Steel Elements is the measure of the stress–strain relationship on the object.
Flat Width Ratio - Flat Width Ratio is the ratio of width w of a single flat element to the thickness t of the element.
Poission Ratio for Plates - The Poission Ratio for Plates is defined as the ratio of lateral strain to longitudinal strain.
STEP 1: Convert Input(s) to Base Unit
Local Buckling Coefficient: 2 --> No Conversion Required
Modulus of Elasticity for Steel Elements: 200000 Megapascal --> 200000000000 Pascal (Check conversion here)
Flat Width Ratio: 13 --> No Conversion Required
Poission Ratio for Plates: 0.3 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
fcr = (k*pi^2*Es)/(12*wt^2*(1-μ^2)) --> (2*pi^2*200000000000)/(12*13^2*(1-0.3^2))
Evaluating ... ...
fcr = 2139195093.11168
STEP 3: Convert Result to Output's Unit
2139195093.11168 Pascal -->2139.19509311168 Megapascal (Check conversion here)
FINAL ANSWER
2139.19509311168 2139.195 Megapascal <-- Elastic Local Buckling Stress
(Calculation completed in 00.004 seconds)

Credits

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NSS College of Engineering (NSSCE), Palakkad
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15 Cold Formed or Light Weighted Steel Structures Calculators

Plate Slenderness Factor
Go Plate Slenderness Factor = (1.052/sqrt(Local Buckling Coefficient))*Flat Width Ratio*sqrt(Maximum Compressive Edge Stress/Modulus of Elasticity for Steel Elements)
Flat Width Ratio of Stiffened Element using Elastic Local Buckling Stress
Go Flat Width Ratio = sqrt((Local Buckling Coefficient*pi^2*Modulus of Elasticity for Steel Elements)/(12*Elastic Local Buckling Stress*(1-Poission Ratio for Plates^2)))
Flat Width Ratio given Plate Slenderness Factor
Go Flat Width Ratio = Plate Slenderness Factor*sqrt((Local Buckling Coefficient*Modulus of Elasticity for Steel Elements)/Maximum Compressive Edge Stress)*(1/1.052)
Elastic Local Buckling Stress
Go Elastic Local Buckling Stress = (Local Buckling Coefficient*pi^2*Modulus of Elasticity for Steel Elements)/(12*Flat Width Ratio^2*(1-Poission Ratio for Plates^2))
Compressive Stress when Flat Width Ratio is between 10 and 25
Go Maximum Compressive Stress of Concrete = ((5*Design Stress)/3)-8640-((1/15)*(Design Stress-12950)*Flat Width Ratio)
Flat Width Ratio of Stiffened Element using Moment of Inertia
Go Flat Width Ratio = sqrt((Minimum Area Moment of Inertia/(1.83*Thickness of Steel Compression Element^4))^2+144)
Minimum Allowable Moment of Inertia
Go Minimum Area Moment of Inertia = 1.83*(Thickness of Steel Compression Element^4)*sqrt((Flat Width Ratio^2)-144)
Flat Width Ratio given Depth of Stiffener Lip
Go Flat Width Ratio = sqrt((Depth of Stiffener Lip/(2.8*Thickness of Steel Compression Element))^6+144)
Depth of Stiffener Lip
Go Depth of Stiffener Lip = 2.8*Thickness of Steel Compression Element*((Flat Width Ratio)^2-144)^(1/6)
Reduction Factor for Cold Form Strength Determination
Go Reduction Factor = (1-(0.22/Plate Slenderness Factor))/Plate Slenderness Factor
Nominal Strength using Allowable Design Strength
Go Nominal Strength = Safety Factor for Design Strength*Allowable Design Strength
Allowable Design Strength
Go Allowable Design Strength = Nominal Strength/Safety Factor for Design Strength
Flat Width Ratio for Deflection Determination
Go Flat Width Ratio = 5160/sqrt(Computed Unit Stress of Cold formed Element)
Flat Width Ratio for Safe Load Determination
Go Flat Width Ratio = 4020/sqrt(Computed Unit Stress of Cold formed Element)
Compressive Stress when Basic Design Stress restricted to 20000 psi
Go Maximum Compressive Stress of Concrete = 24700-470*Flat Width Ratio

Elastic Local Buckling Stress Formula

Elastic Local Buckling Stress = (Local Buckling Coefficient*pi^2*Modulus of Elasticity for Steel Elements)/(12*Flat Width Ratio^2*(1-Poission Ratio for Plates^2))
fcr = (k*pi^2*Es)/(12*wt^2*(1-μ^2))

What is Poisson's Ratio?

The Poisson's Ratio is defined as the ratio of the change in the width per unit width of a material, to the change in its length per unit length, as a result of strain.

How to Calculate Elastic Local Buckling Stress?

Elastic Local Buckling Stress calculator uses Elastic Local Buckling Stress = (Local Buckling Coefficient*pi^2*Modulus of Elasticity for Steel Elements)/(12*Flat Width Ratio^2*(1-Poission Ratio for Plates^2)) to calculate the Elastic Local Buckling Stress, The Elastic Local Buckling Stress of structural profiles is typically considered by individually examining the stability of the isolated plates that make up the cross-section. Elastic Local Buckling Stress is denoted by fcr symbol.

How to calculate Elastic Local Buckling Stress using this online calculator? To use this online calculator for Elastic Local Buckling Stress, enter Local Buckling Coefficient (k), Modulus of Elasticity for Steel Elements (Es), Flat Width Ratio (wt) & Poission Ratio for Plates (μ) and hit the calculate button. Here is how the Elastic Local Buckling Stress calculation can be explained with given input values -> 0.002139 = (2*pi^2*200000000000)/(12*13^2*(1-0.3^2)).

FAQ

What is Elastic Local Buckling Stress?
The Elastic Local Buckling Stress of structural profiles is typically considered by individually examining the stability of the isolated plates that make up the cross-section and is represented as fcr = (k*pi^2*Es)/(12*wt^2*(1-μ^2)) or Elastic Local Buckling Stress = (Local Buckling Coefficient*pi^2*Modulus of Elasticity for Steel Elements)/(12*Flat Width Ratio^2*(1-Poission Ratio for Plates^2)). Local Buckling Coefficient is the factor when thin cold form structures are subjected to local buckling, The Modulus of Elasticity for Steel Elements is the measure of the stress–strain relationship on the object, Flat Width Ratio is the ratio of width w of a single flat element to the thickness t of the element & The Poission Ratio for Plates is defined as the ratio of lateral strain to longitudinal strain.
How to calculate Elastic Local Buckling Stress?
The Elastic Local Buckling Stress of structural profiles is typically considered by individually examining the stability of the isolated plates that make up the cross-section is calculated using Elastic Local Buckling Stress = (Local Buckling Coefficient*pi^2*Modulus of Elasticity for Steel Elements)/(12*Flat Width Ratio^2*(1-Poission Ratio for Plates^2)). To calculate Elastic Local Buckling Stress, you need Local Buckling Coefficient (k), Modulus of Elasticity for Steel Elements (Es), Flat Width Ratio (wt) & Poission Ratio for Plates (μ). With our tool, you need to enter the respective value for Local Buckling Coefficient, Modulus of Elasticity for Steel Elements, Flat Width Ratio & Poission Ratio for Plates and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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