Flat Width Ratio given Plate Slenderness Factor Calculator

✖Plate Slenderness Factor is a function of the width/thickness (b/t) ratio of a slender plate cross sectional element.ⓘ Plate Slenderness Factor [λ]			+10% -10%
✖Local Buckling Coefficient is the factor when thin cold form structures are subjected to local buckling.ⓘ Local Buckling Coefficient [k]			+10% -10%
✖The Modulus of Elasticity for Steel Elements is the measure of the stress–strain relationship on the object.ⓘ Modulus of Elasticity for Steel Elements [E_s]			+10% -10%
✖Maximum Compressive Edge Stress is defined as the largest compressive stress along the laminar edges of the structural element.ⓘ Maximum Compressive Edge Stress [f_emax]			+10% -10%

✖Flat Width Ratio is the ratio of width w of a single flat element to the thickness t of the element.ⓘ Flat Width Ratio given Plate Slenderness Factor [w_t]

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Formula

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Flat Width Ratio given Plate Slenderness Factor

Formula

`"w"_{"t"} = "λ"*sqrt(("k"*"E"_{"s"})/"f"_{"emax"})*(1/1.052)`

Example

`"12.97969"="0.326"*sqrt(("2"*"200000MPa")/"228MPa")*(1/1.052)`

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Flat Width Ratio given Plate Slenderness Factor Solution

STEP 0: Pre-Calculation Summary

Formula Used

Flat Width Ratio = Plate Slenderness Factor*sqrt((Local Buckling Coefficient*Modulus of Elasticity for Steel Elements)/Maximum Compressive Edge Stress)*(1/1.052)
w_t = λ*sqrt((k*E_s)/f_emax)*(1/1.052)
This formula uses 1 Functions, 5 Variables

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.
Plate Slenderness Factor - Plate Slenderness Factor is a function of the width/thickness (b/t) ratio of a slender plate cross sectional 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.
Maximum Compressive Edge Stress - (Measured in Pascal) - Maximum Compressive Edge Stress is defined as the largest compressive stress along the laminar edges of the structural element.

STEP 1: Convert Input(s) to Base Unit

Plate Slenderness Factor: 0.326 --> No Conversion Required
Local Buckling Coefficient: 2 --> No Conversion Required
Modulus of Elasticity for Steel Elements: 200000 Megapascal --> 200000000000 Pascal (Check conversion here)
Maximum Compressive Edge Stress: 228 Megapascal --> 228000000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

w_t = λ*sqrt((k*E_s)/f_emax)*(1/1.052) --> 0.326*sqrt((2*200000000000)/228000000)*(1/1.052)

Evaluating ... ...

w_t = 12.9796933558073

STEP 3: Convert Result to Output's Unit

12.9796933558073 --> No Conversion Required

FINAL ANSWER

12.9796933558073 ≈ 12.97969 <-- 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 given Plate Slenderness Factor Formula

What is effective width concept?

The effects of local buckling can be evaluated by using the concept of effective width.
Lightly stressed regions at center are ignored, as these are least effective in resisting the
applied stresses. Regions near the supports are far more effective and are taken to be fully effective. The section behavior is modelled on the basis of the effective width

How to Calculate Flat Width Ratio given Plate Slenderness Factor?

Flat Width Ratio given Plate Slenderness Factor calculator uses Flat Width Ratio = Plate Slenderness Factor*sqrt((Local Buckling Coefficient*Modulus of Elasticity for Steel Elements)/Maximum Compressive Edge Stress)*(1/1.052) to calculate the Flat Width Ratio, The Flat Width Ratio given Plate Slenderness Factor relates the parameters, buckling coefficient, width to thickness ratio of section, compressive edge stress and modulus of elasticity. Flat Width Ratio is denoted by w_t symbol.

How to calculate Flat Width Ratio given Plate Slenderness Factor using this online calculator? To use this online calculator for Flat Width Ratio given Plate Slenderness Factor, enter Plate Slenderness Factor (λ), Local Buckling Coefficient (k), Modulus of Elasticity for Steel Elements (E_s) & Maximum Compressive Edge Stress (f_emax) and hit the calculate button. Here is how the Flat Width Ratio given Plate Slenderness Factor calculation can be explained with given input values -> 72.30406 = 0.326*sqrt((2*200000000000)/228000000)*(1/1.052).

FAQ

What is Flat Width Ratio given Plate Slenderness Factor?

The Flat Width Ratio given Plate Slenderness Factor relates the parameters, buckling coefficient, width to thickness ratio of section, compressive edge stress and modulus of elasticity and is represented as w_t = λ*sqrt((k*E_s)/f_emax)*(1/1.052) or Flat Width Ratio = Plate Slenderness Factor*sqrt((Local Buckling Coefficient*Modulus of Elasticity for Steel Elements)/Maximum Compressive Edge Stress)*(1/1.052). Plate Slenderness Factor is a function of the width/thickness (b/t) ratio of a slender plate cross sectional element, 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 & Maximum Compressive Edge Stress is defined as the largest compressive stress along the laminar edges of the structural element.

How to calculate Flat Width Ratio given Plate Slenderness Factor?

The Flat Width Ratio given Plate Slenderness Factor relates the parameters, buckling coefficient, width to thickness ratio of section, compressive edge stress and modulus of elasticity is calculated using Flat Width Ratio = Plate Slenderness Factor*sqrt((Local Buckling Coefficient*Modulus of Elasticity for Steel Elements)/Maximum Compressive Edge Stress)*(1/1.052). To calculate Flat Width Ratio given Plate Slenderness Factor, you need Plate Slenderness Factor (λ), Local Buckling Coefficient (k), Modulus of Elasticity for Steel Elements (E_s) & Maximum Compressive Edge Stress (f_emax). With our tool, you need to enter the respective value for Plate Slenderness Factor, Local Buckling Coefficient, Modulus of Elasticity for Steel Elements & Maximum Compressive Edge Stress 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 Plate Slenderness Factor, Local Buckling Coefficient, Modulus of Elasticity for Steel Elements & Maximum Compressive Edge Stress. 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((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 = sqrt((Depth of Stiffener Lip/(2.8*Thickness of Steel Compression Element))^6+144)
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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