Flat Width Ratio of Stiffened Element using Elastic Local Buckling Stress Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)))
wt = sqrt((k*pi^2*Es)/(12*fcr*(1-μ^2)))
This formula uses 1 Constants, 1 Functions, 5 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
Flat Width Ratio - Flat Width Ratio is the ratio of width w of a single flat element to the thickness t of the element.
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.
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.
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)
Elastic Local Buckling Stress: 2139.195 Megapascal --> 2139195000 Pascal (Check conversion here)
Poission Ratio for Plates: 0.3 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
wt = sqrt((k*pi^2*Es)/(12*fcr*(1-μ^2))) --> sqrt((2*pi^2*200000000000)/(12*2139195000*(1-0.3^2)))
Evaluating ... ...
wt = 13.0000002829223
STEP 3: Convert Result to Output's Unit
13.0000002829223 --> No Conversion Required
FINAL ANSWER
13.0000002829223 13 <-- Flat Width Ratio
(Calculation completed in 00.004 seconds)

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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

Flat Width Ratio of Stiffened Element using Elastic Local Buckling Stress Formula

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)))
wt = sqrt((k*pi^2*Es)/(12*fcr*(1-μ^2)))

What is Local Buckling?

The Local buckling is a failure mode commonly observed in thin-walled structural steel elements. Even though its effect on their behavior at ambient temperature conditions is well documented and incorporated in current design codes, this is not the case when such elements are exposed to fire.

How to Calculate Flat Width Ratio of Stiffened Element using Elastic Local Buckling Stress?

Flat Width Ratio of Stiffened Element using Elastic Local Buckling Stress calculator uses 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))) to calculate the Flat Width Ratio, The Flat Width Ratio of Stiffened Element using Elastic Local Buckling Stress is the ratio of width of the cold formed plate to the thickness of the plate element. Flat Width Ratio is denoted by wt symbol.

How to calculate Flat Width Ratio of Stiffened Element using Elastic Local Buckling Stress using this online calculator? To use this online calculator for Flat Width Ratio of Stiffened Element using Elastic Local Buckling Stress, enter Local Buckling Coefficient (k), Modulus of Elasticity for Steel Elements (Es), Elastic Local Buckling Stress (fcr) & Poission Ratio for Plates (μ) and hit the calculate button. Here is how the Flat Width Ratio of Stiffened Element using Elastic Local Buckling Stress calculation can be explained with given input values -> 42.51611 = sqrt((2*pi^2*200000000000)/(12*2139195000*(1-0.3^2))).

FAQ

What is Flat Width Ratio of Stiffened Element using Elastic Local Buckling Stress?
The Flat Width Ratio of Stiffened Element using Elastic Local Buckling Stress is the ratio of width of the cold formed plate to the thickness of the plate element and is represented as wt = sqrt((k*pi^2*Es)/(12*fcr*(1-μ^2))) or 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))). 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, 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 & The Poission Ratio for Plates is defined as the ratio of lateral strain to longitudinal strain.
How to calculate Flat Width Ratio of Stiffened Element using Elastic Local Buckling Stress?
The Flat Width Ratio of Stiffened Element using Elastic Local Buckling Stress is the ratio of width of the cold formed plate to the thickness of the plate element is calculated using 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))). To calculate Flat Width Ratio of Stiffened Element using Elastic Local Buckling Stress, you need Local Buckling Coefficient (k), Modulus of Elasticity for Steel Elements (Es), Elastic Local Buckling Stress (fcr) & 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, Elastic Local Buckling Stress & 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.
How many ways are there to calculate Flat Width Ratio?
In this formula, Flat Width Ratio uses Local Buckling Coefficient, Modulus of Elasticity for Steel Elements, Elastic Local Buckling Stress & Poission Ratio for Plates. We can use 5 other way(s) to calculate the same, which is/are as follows -
  • Flat Width Ratio = sqrt((Minimum Area Moment of Inertia/(1.83*Thickness of Steel Compression Element^4))^2+144)
  • Flat Width Ratio = sqrt((Depth of Stiffener Lip/(2.8*Thickness of Steel Compression Element))^6+144)
  • Flat Width Ratio = Plate Slenderness Factor*sqrt((Local Buckling Coefficient*Modulus of Elasticity for Steel Elements)/Maximum Compressive Edge Stress)*(1/1.052)
  • Flat Width Ratio = 4020/sqrt(Computed Unit Stress of Cold formed Element)
  • Flat Width Ratio = 5160/sqrt(Computed Unit Stress of Cold formed Element)
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