Flat Width Ratio of Stiffened Element using Moment of Inertia Calculator

✖The Minimum Area Moment of Inertia is the limiting moment of inertia ( quantitative measure of the rotational inertia) for satisfying any structural situation.ⓘ Minimum Area Moment of Inertia [I_min]			+10% -10%
✖The Thickness of Steel Compression Element is the thickness of element or plate.ⓘ Thickness of Steel Compression Element [t]			+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 of Stiffened Element using Moment of Inertia [w_t]

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Formula

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Flat Width Ratio of Stiffened Element using Moment of Inertia

Formula

`"w"_{"t"} = sqrt(("I"_{"min"}/(1.83*"t"^4))^2+144)`

Example

`"12.99702"=sqrt(("7.4E^6mm⁴"/(1.83*("30mm")^4))^2+144)`

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Flat Width Ratio of Stiffened Element using Moment of Inertia Solution

STEP 0: Pre-Calculation Summary

Formula Used

Flat Width Ratio = sqrt((Minimum Area Moment of Inertia/(1.83*Thickness of Steel Compression Element^4))^2+144)
w_t = sqrt((I_min/(1.83*t^4))^2+144)
This formula uses 1 Functions, 3 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.
Minimum Area Moment of Inertia - (Measured in Meter⁴) - The Minimum Area Moment of Inertia is the limiting moment of inertia ( quantitative measure of the rotational inertia) for satisfying any structural situation.
Thickness of Steel Compression Element - (Measured in Meter) - The Thickness of Steel Compression Element is the thickness of element or plate.

STEP 1: Convert Input(s) to Base Unit

Minimum Area Moment of Inertia: 7400000 Millimeter⁴ --> 7.4E-06 Meter⁴ (Check conversion here)
Thickness of Steel Compression Element: 30 Millimeter --> 0.03 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

w_t = sqrt((I_min/(1.83*t^4))^2+144) --> sqrt((7.4E-06/(1.83*0.03^4))^2+144)

Evaluating ... ...

w_t = 12.9970180446904

STEP 3: Convert Result to Output's Unit

12.9970180446904 --> No Conversion Required

FINAL ANSWER

12.9970180446904 ≈ 12.99702 <-- Flat Width Ratio

(Calculation completed in 00.004 seconds)

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NSS College of Engineering (NSSCE), Palakkad

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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 of Stiffened Element using Moment of Inertia Formula

Flat Width Ratio = sqrt((Minimum Area Moment of Inertia/(1.83*Thickness of Steel Compression Element^4))^2+144)
w_t = sqrt((I_min/(1.83*t^4))^2+144)

What is Stiffened Compression Member?

A structural element, subject to compressive forces, that has been reinforced or stiffened, along a line perpendicular to its weak axis of bending, in order to provide additional strength against buckling is called as stiffened compression member.

How to Calculate Flat Width Ratio of Stiffened Element using Moment of Inertia?

Flat Width Ratio of Stiffened Element using Moment of Inertia calculator uses Flat Width Ratio = sqrt((Minimum Area Moment of Inertia/(1.83*Thickness of Steel Compression Element^4))^2+144) to calculate the Flat Width Ratio, The Flat Width Ratio of Stiffened Element using Moment of Inertia is defined as the width to thickness ratio of the compression member which is qualified as the stiffened compression member. Flat Width Ratio is denoted by w_t symbol.

How to calculate Flat Width Ratio of Stiffened Element using Moment of Inertia using this online calculator? To use this online calculator for Flat Width Ratio of Stiffened Element using Moment of Inertia, enter Minimum Area Moment of Inertia (I_min) & Thickness of Steel Compression Element (t) and hit the calculate button. Here is how the Flat Width Ratio of Stiffened Element using Moment of Inertia calculation can be explained with given input values -> 12 = sqrt((7.4E-06/(1.83*0.03^4))^2+144).

FAQ

What is Flat Width Ratio of Stiffened Element using Moment of Inertia?

The Flat Width Ratio of Stiffened Element using Moment of Inertia is defined as the width to thickness ratio of the compression member which is qualified as the stiffened compression member and is represented as w_t = sqrt((I_min/(1.83*t^4))^2+144) or Flat Width Ratio = sqrt((Minimum Area Moment of Inertia/(1.83*Thickness of Steel Compression Element^4))^2+144). The Minimum Area Moment of Inertia is the limiting moment of inertia ( quantitative measure of the rotational inertia) for satisfying any structural situation & The Thickness of Steel Compression Element is the thickness of element or plate.

How to calculate Flat Width Ratio of Stiffened Element using Moment of Inertia?

The Flat Width Ratio of Stiffened Element using Moment of Inertia is defined as the width to thickness ratio of the compression member which is qualified as the stiffened compression member is calculated using Flat Width Ratio = sqrt((Minimum Area Moment of Inertia/(1.83*Thickness of Steel Compression Element^4))^2+144). To calculate Flat Width Ratio of Stiffened Element using Moment of Inertia, you need Minimum Area Moment of Inertia (I_min) & Thickness of Steel Compression Element (t). With our tool, you need to enter the respective value for Minimum Area Moment of Inertia & Thickness of Steel Compression Element 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 Minimum Area Moment of Inertia & Thickness of Steel Compression Element. We can use 5 other way(s) to calculate the same, which is/are as follows -

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 = Plate Slenderness Factor*sqrt((Local Buckling Coefficient*Modulus of Elasticity for Steel Elements)/Maximum Compressive Edge Stress)*(1/1.052)
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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