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Plate Slenderness Factor Formula

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

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

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

Plate Slenderness Factor Example

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Here is how the Plate Slenderness Factor equation looks like with Values.

Here is how the Plate Slenderness Factor equation looks like with Units.

Here is how the Plate Slenderness Factor equation looks like.

0.3265 = (\frac{1.052}{\sqrt{2}}) \cdot 13 \cdot \sqrt{\frac{228}{200000}}

0.3265 = (\frac{1.052}{\sqrt{2}}) \cdot 13 \cdot \sqrt{\frac{228MPa}{200000MPa}}

0.3265 = (\frac{1.052}{\sqrt{2}}) \cdot 13 \cdot \sqrt{\frac{228}{200000}}

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Plate Slenderness Factor Solution

Follow our step by step solution on how to calculate Plate Slenderness Factor?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

λ = (\frac{1.052}{\sqrt{2}}) \cdot 13 \cdot \sqrt{\frac{228MPa}{200000MPa}}

Next Step Convert Units

∴

λ = (\frac{1.052}{\sqrt{2}}) \cdot 13 \cdot \sqrt{\frac{2.3E+8Pa}{2E+11Pa}}

Next Step Prepare to Evaluate

∴

λ = (\frac{1.052}{\sqrt{2}}) \cdot 13 \cdot \sqrt{\frac{2.3E+8}{2E+11}}

Next Step Evaluate

∴

λ = 0.326510024838442

LAST Step Rounding Answer

∴

λ = 0.3265

Plate Slenderness Factor Formula Elements

Variables

Functions

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

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

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

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

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 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 Flat Width Ratio of Stiffened Element using Moment of Inertia

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

How to Evaluate Plate Slenderness Factor?

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

How to evaluate Plate Slenderness Factor using this online evaluator? To use this online evaluator for Plate Slenderness Factor, enter Local Buckling Coefficient (k), Flat Width Ratio (w_t), Maximum Compressive Edge Stress (f_emax) & Modulus of Elasticity for Steel Elements (E_s) and hit the calculate button.

FAQs on Plate Slenderness Factor

What is the formula to find Plate Slenderness Factor?

The formula of Plate Slenderness Factor is expressed as Plate Slenderness Factor = (1.052/sqrt(Local Buckling Coefficient))*Flat Width Ratio*sqrt(Maximum Compressive Edge Stress/Modulus of Elasticity for Steel Elements). Here is an example- 0.32651 = (1.052/sqrt(2))*13*sqrt(228000000/200000000000).

How to calculate Plate Slenderness Factor?

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

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Plate Slenderness Factor Formula

Plate Slenderness Factor Example

Plate Slenderness Factor Solution

Plate Slenderness Factor Formula Elements

Other formulas in Cold Formed or Light Weighted Steel Structures category

How to Evaluate Plate Slenderness Factor?

FAQs on Plate Slenderness Factor

Variable Name