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Flat Width Ratio given Plate Slenderness Factor Formula

GoFlat Width Ratio of Stiffened Element using Moment of Inertia Formula

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

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Flat Width Ratio is the ratio of width w of a single flat element to the thickness t of the element. Check FAQs

w t = λ \cdot \sqrt{\frac{k \cdot E s}{f emax}} \cdot (\frac{1}{1.052})

w_t - Flat Width Ratio?λ - Plate Slenderness Factor?k - Local Buckling Coefficient?E_s - Modulus of Elasticity for Steel Elements?f_emax - Maximum Compressive Edge Stress?

Flat Width Ratio given Plate Slenderness Factor Example

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Here is how the Flat Width Ratio given Plate Slenderness Factor equation looks like with Values.

Here is how the Flat Width Ratio given Plate Slenderness Factor equation looks like with Units.

Here is how the Flat Width Ratio given Plate Slenderness Factor equation looks like.

12.9797 = 0.326 \cdot \sqrt{\frac{2 \cdot 200000}{228}} \cdot (\frac{1}{1.052})

12.9797 = 0.326 \cdot \sqrt{\frac{2 \cdot 200000MPa}{228MPa}} \cdot (\frac{1}{1.052})

12.9797 = 0.326 \cdot \sqrt{\frac{2 \cdot 200000}{228}} \cdot (\frac{1}{1.052})

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Flat Width Ratio given Plate Slenderness Factor Solution

Follow our step by step solution on how to calculate Flat Width Ratio given Plate Slenderness Factor?

FIRST Step Consider the formula

w t = λ \cdot \sqrt{\frac{k \cdot E s}{f emax}} \cdot (\frac{1}{1.052})

Next Step Substitute values of Variables

∴

w t = 0.326 \cdot \sqrt{\frac{2 \cdot 200000MPa}{228MPa}} \cdot (\frac{1}{1.052})

Next Step Convert Units

∴

w t = 0.326 \cdot \sqrt{\frac{2 \cdot 2E+11Pa}{2.3E+8Pa}} \cdot (\frac{1}{1.052})

Next Step Prepare to Evaluate

∴

w t = 0.326 \cdot \sqrt{\frac{2 \cdot 2E+11}{2.3E+8}} \cdot (\frac{1}{1.052})

Next Step Evaluate

∴

w t = 12.9796933558073

LAST Step Rounding Answer

∴

w t = 12.9797

Flat Width Ratio given Plate Slenderness Factor Formula Elements

Variables

Functions

Flat Width Ratio

Flat Width Ratio is the ratio of width w of a single flat element to the thickness t of the element.

Symbol: w_t

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Flat Width Ratio

Plate Slenderness Factor

Plate Slenderness Factor is a function of the width/thickness (b/t) ratio of a slender plate cross sectional element.

Symbol: λ

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Plate Slenderness Factor

Local Buckling Coefficient

Local Buckling Coefficient is the factor when thin cold form structures are subjected to local buckling.

Symbol: k

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Local Buckling Coefficient

Modulus of Elasticity for Steel Elements

The Modulus of Elasticity for Steel Elements is the measure of the stress–strain relationship on the object.

Symbol: E_s

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Modulus of Elasticity for Steel Elements

Maximum Compressive Edge Stress

Maximum Compressive Edge Stress is defined as the largest compressive stress along the laminar edges of the structural element.

Symbol: f_emax

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Maximum Compressive Edge Stress

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.

Syntax: sqrt(Number)

Other Formulas to find Flat Width Ratio

Go Flat Width Ratio of Stiffened Element using Moment of Inertia

w t = \sqrt{{(\frac{I min}{1.83 \cdot t^{4}})}^{2} + 144}

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

w t = \sqrt{\frac{k \cdot π^{2} \cdot E s}{12 \cdot f cr \cdot (1 - μ^{2})}}

Go Flat Width Ratio given Depth of Stiffener Lip

w t = \sqrt{{(\frac{d}{2.8 \cdot t})}^{6} + 144}

Go Flat Width Ratio for Safe Load Determination

w t = \frac{4020}{\sqrt{f uc}}

Other formulas in Cold Formed or Light Weighted Steel Structures category

Go Allowable Design Strength

R a = \frac{R n}{f s}

Go Nominal Strength using Allowable Design Strength

R n = f s \cdot R a

Go Minimum Allowable Moment of Inertia

I min = 1.83 \cdot (t^{4}) \cdot \sqrt{({w t}^{2}) - 144}

Go Elastic Local Buckling Stress

f cr = \frac{k \cdot π^{2} \cdot E s}{12 \cdot {w t}^{2} \cdot (1 - μ^{2})}

How to Evaluate Flat Width Ratio given Plate Slenderness Factor?

Flat Width Ratio given Plate Slenderness Factor evaluator 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 evaluate 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 evaluate Flat Width Ratio given Plate Slenderness Factor using this online evaluator? To use this online evaluator 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.

FAQs on Flat Width Ratio given Plate Slenderness Factor

What is the formula to find Flat Width Ratio given Plate Slenderness Factor?

The formula of Flat Width Ratio given Plate Slenderness Factor is expressed as Flat Width Ratio = Plate Slenderness Factor*sqrt((Local Buckling Coefficient*Modulus of Elasticity for Steel Elements)/Maximum Compressive Edge Stress)*(1/1.052). Here is an example- 72.30406 = 0.326*sqrt((2*200000000000)/228000000)*(1/1.052).

How to calculate Flat Width Ratio given Plate Slenderness Factor?

With Plate Slenderness Factor (λ), Local Buckling Coefficient (k), Modulus of Elasticity for Steel Elements (E_s) & Maximum Compressive Edge Stress (f_emax) we can find Flat Width Ratio given Plate Slenderness Factor using the formula - Flat Width Ratio = Plate Slenderness Factor*sqrt((Local Buckling Coefficient*Modulus of Elasticity for Steel Elements)/Maximum Compressive Edge Stress)*(1/1.052). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Flat Width Ratio?

Here are the different ways to Calculate Flat Width Ratio-

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)

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: Value
: Unit

Flat Width Ratio given Plate Slenderness Factor Formula

​GoFlat Width Ratio of Stiffened Element using Moment of Inertia Formula

​GoFlat Width Ratio of Stiffened Element using Elastic Local Buckling Stress Formula

Flat Width Ratio given Plate Slenderness Factor Example

Flat Width Ratio given Plate Slenderness Factor Solution

Flat Width Ratio given Plate Slenderness Factor Formula Elements

Other Formulas to find Flat Width Ratio

Other formulas in Cold Formed or Light Weighted Steel Structures category

How to Evaluate Flat Width Ratio given Plate Slenderness Factor?

FAQs on Flat Width Ratio given Plate Slenderness Factor

Variable Name

GoFlat Width Ratio of Stiffened Element using Moment of Inertia Formula

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