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

GoFlat Width Ratio of Stiffened Element using Moment of Inertia Formula

GoFlat Width Ratio given Depth of Stiffener Lip 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 = \sqrt{\frac{k \cdot π^{2} \cdot E s}{12 \cdot f cr \cdot (1 - μ^{2})}}

w_t - Flat Width Ratio?k - Local Buckling Coefficient?E_s - Modulus of Elasticity for Steel Elements?f_cr - Elastic Local Buckling Stress?μ - Poission Ratio for Plates?π - Archimedes' constant?

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

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Here is how the Flat Width Ratio of Stiffened Element using Elastic Local Buckling Stress equation looks like with Values.

Here is how the Flat Width Ratio of Stiffened Element using Elastic Local Buckling Stress equation looks like with Units.

Here is how the Flat Width Ratio of Stiffened Element using Elastic Local Buckling Stress equation looks like.

13 = \sqrt{\frac{2 \cdot {3.1416}^{2} \cdot 200000}{12 \cdot 2139.195 \cdot (1 - {0.3}^{2})}}

13 = \sqrt{\frac{2 \cdot {3.1416}^{2} \cdot 200000MPa}{12 \cdot 2139.195MPa \cdot (1 - {0.3}^{2})}}

13 = \sqrt{\frac{2 \cdot {3.1416}^{2} \cdot 200000}{12 \cdot 2139.195 \cdot (1 - {0.3}^{2})}}

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

Follow our step by step solution on how to calculate Flat Width Ratio of Stiffened Element using Elastic Local Buckling Stress?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

w t = \sqrt{\frac{2 \cdot π^{2} \cdot 200000MPa}{12 \cdot 2139.195MPa \cdot (1 - {0.3}^{2})}}

Next Step Substitute values of Constants

∴

w t = \sqrt{\frac{2 \cdot {3.1416}^{2} \cdot 200000MPa}{12 \cdot 2139.195MPa \cdot (1 - {0.3}^{2})}}

Next Step Convert Units

∴

w t = \sqrt{\frac{2 \cdot {3.1416}^{2} \cdot 2E+11Pa}{12 \cdot 2.1E+9Pa \cdot (1 - {0.3}^{2})}}

Next Step Prepare to Evaluate

∴

w t = \sqrt{\frac{2 \cdot {3.1416}^{2} \cdot 2E+11}{12 \cdot 2.1E+9 \cdot (1 - {0.3}^{2})}}

Next Step Evaluate

∴

w t = 13.0000002829223

LAST Step Rounding Answer

∴

w t = 13

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

Variables

Constants

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

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

Elastic Local Buckling Stress

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.

Symbol: f_cr

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Elastic Local Buckling Stress

Poission Ratio for Plates

The Poission Ratio for Plates is defined as the ratio of lateral strain to longitudinal strain.

Symbol: μ

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Poission Ratio for Plates

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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 given Depth of Stiffener Lip

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

Go Flat Width Ratio given Plate Slenderness Factor

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

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 of Stiffened Element using Elastic Local Buckling Stress?

Flat Width Ratio of Stiffened Element using Elastic Local Buckling Stress evaluator 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 evaluate 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 w_t symbol.

How to evaluate Flat Width Ratio of Stiffened Element using Elastic Local Buckling Stress using this online evaluator? To use this online evaluator for Flat Width Ratio of Stiffened Element using Elastic Local Buckling Stress, enter Local Buckling Coefficient (k), Modulus of Elasticity for Steel Elements (E_s), Elastic Local Buckling Stress (f_cr) & Poission Ratio for Plates (μ) and hit the calculate button.

FAQs on Flat Width Ratio of Stiffened Element using Elastic Local Buckling Stress

What is the formula to find Flat Width Ratio of Stiffened Element using Elastic Local Buckling Stress?

The formula of Flat Width Ratio of Stiffened Element using Elastic Local Buckling Stress is expressed as 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))). Here is an example- 42.51611 = sqrt((2*pi^2*200000000000)/(12*2139195000*(1-0.3^2))).

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

With Local Buckling Coefficient (k), Modulus of Elasticity for Steel Elements (E_s), Elastic Local Buckling Stress (f_cr) & Poission Ratio for Plates (μ) we can find Flat Width Ratio of Stiffened Element using Elastic Local Buckling Stress using the 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))). This formula also uses Archimedes' constant and 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((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)

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

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

​GoFlat Width Ratio given Depth of Stiffener Lip Formula

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

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

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

FAQs on Flat Width Ratio of Stiffened Element using Elastic Local Buckling Stress

Variable Name

GoFlat Width Ratio of Stiffened Element using Moment of Inertia Formula

GoFlat Width Ratio given Depth of Stiffener Lip Formula