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Minimum Allowable Moment of Inertia Formula

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The Minimum Area Moment of Inertia is the limiting moment of inertia ( quantitative measure of the rotational inertia) for satisfying any structural situation. Check FAQs

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

I_min - Minimum Area Moment of Inertia?t - Thickness of Steel Compression Element?w_t - Flat Width Ratio?

Minimum Allowable Moment of Inertia Example

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Here is how the Minimum Allowable Moment of Inertia equation looks like with Values.

Here is how the Minimum Allowable Moment of Inertia equation looks like with Units.

Here is how the Minimum Allowable Moment of Inertia equation looks like.

7.4E+6 = 1.83 \cdot (30^{4}) \cdot \sqrt{(13^{2}) - 144}

7.4E+6mm⁴ = 1.83 \cdot ({30mm}^{4}) \cdot \sqrt{(13^{2}) - 144}

7.4E+6 = 1.83 \cdot (30^{4}) \cdot \sqrt{(13^{2}) - 144}

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Minimum Allowable Moment of Inertia Solution

Follow our step by step solution on how to calculate Minimum Allowable Moment of Inertia?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

I min = 1.83 \cdot ({30mm}^{4}) \cdot \sqrt{(13^{2}) - 144}

Next Step Convert Units

∴

I min = 1.83 \cdot ({0.03m}^{4}) \cdot \sqrt{(13^{2}) - 144}

Next Step Prepare to Evaluate

∴

I min = 1.83 \cdot ({0.03}^{4}) \cdot \sqrt{(13^{2}) - 144}

Next Step Evaluate

∴

I min = 7.4115E-06m⁴

Next Step Convert to Output's Unit

∴

I min = 7411500mm⁴

LAST Step Rounding Answer

∴

I min = 7.4E+6mm⁴

Minimum Allowable Moment of Inertia Formula Elements

Variables

Functions

Minimum Area Moment of Inertia

The Minimum Area Moment of Inertia is the limiting moment of inertia ( quantitative measure of the rotational inertia) for satisfying any structural situation.

Symbol: I_min

Measurement: Second Moment of AreaUnit: mm⁴

Note: Value should be greater than 0.

Formulas to find Minimum Area Moment of Inertia

Thickness of Steel Compression Element

The Thickness of Steel Compression Element is the thickness of element or plate.

Symbol: t

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Thickness of Steel Compression Element

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

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 Flat Width Ratio of Stiffened Element using Moment of Inertia

w t = \sqrt{{(\frac{I min}{1.83 \cdot t^{4}})}^{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 Minimum Allowable Moment of Inertia?

Minimum Allowable Moment of Inertia evaluator uses Minimum Area Moment of Inertia = 1.83*(Thickness of Steel Compression Element^4)*sqrt((Flat Width Ratio^2)-144) to evaluate the Minimum Area Moment of Inertia, The Minimum Allowable Moment of Inertia of cold form structure is defined as the limiting or at least necessary structural size for considering the compression element as a stiffened compression element. Minimum Area Moment of Inertia is denoted by I_min symbol.

How to evaluate Minimum Allowable Moment of Inertia using this online evaluator? To use this online evaluator for Minimum Allowable Moment of Inertia, enter Thickness of Steel Compression Element (t) & Flat Width Ratio (w_t) and hit the calculate button.

FAQs on Minimum Allowable Moment of Inertia

What is the formula to find Minimum Allowable Moment of Inertia?

The formula of Minimum Allowable Moment of Inertia is expressed as Minimum Area Moment of Inertia = 1.83*(Thickness of Steel Compression Element^4)*sqrt((Flat Width Ratio^2)-144). Here is an example- 7.4E+18 = 1.83*(0.03^4)*sqrt((13^2)-144).

How to calculate Minimum Allowable Moment of Inertia?

With Thickness of Steel Compression Element (t) & Flat Width Ratio (w_t) we can find Minimum Allowable Moment of Inertia using the formula - Minimum Area Moment of Inertia = 1.83*(Thickness of Steel Compression Element^4)*sqrt((Flat Width Ratio^2)-144). This formula also uses Square Root (sqrt) function(s).

Can the Minimum Allowable Moment of Inertia be negative?

No, the Minimum Allowable Moment of Inertia, measured in Second Moment of Area cannot be negative.

Which unit is used to measure Minimum Allowable Moment of Inertia?

Minimum Allowable Moment of Inertia is usually measured using the Millimeter⁴[mm⁴] for Second Moment of Area. Meter⁴[mm⁴], Centimeter⁴[mm⁴] are the few other units in which Minimum Allowable Moment of Inertia can be measured.

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Minimum Allowable Moment of Inertia Formula

Minimum Allowable Moment of Inertia Example

Minimum Allowable Moment of Inertia Solution

Minimum Allowable Moment of Inertia Formula Elements

Other formulas in Cold Formed or Light Weighted Steel Structures category

How to Evaluate Minimum Allowable Moment of Inertia?

FAQs on Minimum Allowable Moment of Inertia

Variable Name