Plate Slenderness Factor Calculator

✖Local Buckling Coefficient is the factor when thin cold form structures are subjected to local buckling.ⓘ Local Buckling Coefficient [k]			+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 [w_t]			+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%
✖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%

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

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Formula

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Plate Slenderness Factor

Formula

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

Example

0.32651 = (\frac{1.052}{\sqrt{2}}) \cdot 13 \cdot \sqrt{\frac{228 MPa}{200000 MPa}}

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Plate Slenderness Factor Solution

STEP 0: Pre-Calculation Summary

Formula Used

Plate Slenderness Factor = (1.052/sqrt(Local Buckling Coefficient))*Flat Width Ratio*sqrt(Maximum Compressive Edge Stress/Modulus of Elasticity for Steel Elements)
λ = (1.052/sqrt(k))*w_t*sqrt(f_emax/E_s)
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

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

STEP 1: Convert Input(s) to Base Unit

Local Buckling Coefficient: 2 --> No Conversion Required
Flat Width Ratio: 13 --> No Conversion Required
Maximum Compressive Edge Stress: 228 Megapascal --> 228000000 Pascal (Check conversion here)
Modulus of Elasticity for Steel Elements: 200000 Megapascal --> 200000000000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

λ = (1.052/sqrt(k))*w_t*sqrt(f_emax/E_s) --> (1.052/sqrt(2))*13*sqrt(228000000/200000000000)

Evaluating ... ...

λ = 0.326510024838442

STEP 3: Convert Result to Output's Unit

0.326510024838442 --> No Conversion Required

FINAL ANSWER

0.326510024838442 ≈ 0.32651 <-- Plate Slenderness Factor

(Calculation completed in 00.004 seconds)

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Created by Chandana P Dev

NSS College of Engineering (NSSCE), Palakkad

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Meerut Institute of Engineering and Technology (MIET), Meerut

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< Cold Formed or Light Weighted Steel Structures Calculators

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)

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

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 Plate Slenderness Factor?

Plate Slenderness Factor calculator 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 calculate 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 calculate Plate Slenderness Factor using this online calculator? To use this online calculator 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. Here is how the Plate Slenderness Factor calculation can be explained with given input values -> 0.32651 = (1.052/sqrt(2))*13*sqrt(228000000/200000000000).

FAQ

What is 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 and is represented as λ = (1.052/sqrt(k))*w_t*sqrt(f_emax/E_s) or Plate Slenderness Factor = (1.052/sqrt(Local Buckling Coefficient))*Flat Width Ratio*sqrt(Maximum Compressive Edge Stress/Modulus of Elasticity for Steel Elements). Local Buckling Coefficient is the factor when thin cold form structures are subjected to local buckling, Flat Width Ratio is the ratio of width w of a single flat element to the thickness t of the element, Maximum Compressive Edge Stress is defined as the largest compressive stress along the laminar edges of the structural element & The Modulus of Elasticity for Steel Elements is the measure of the stress–strain relationship on the object.

How to calculate 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 is calculated using Plate Slenderness Factor = (1.052/sqrt(Local Buckling Coefficient))*Flat Width Ratio*sqrt(Maximum Compressive Edge Stress/Modulus of Elasticity for Steel Elements). To calculate Plate Slenderness Factor, you need Local Buckling Coefficient (k), Flat Width Ratio (w_t), Maximum Compressive Edge Stress (f_emax) & Modulus of Elasticity for Steel Elements (E_s). With our tool, you need to enter the respective value for Local Buckling Coefficient, Flat Width Ratio, Maximum Compressive Edge Stress & Modulus of Elasticity for Steel Elements and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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