Minimum Allowable Moment of Inertia Calculator

✖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 [w_t]			+10% -10%

✖The Minimum Area Moment of Inertia is the limiting moment of inertia ( quantitative measure of the rotational inertia) for satisfying any structural situation.ⓘ Minimum Allowable Moment of Inertia [I_min]

⎘ Copy

👎

Formula

✖

Minimum Allowable Moment of Inertia

Formula

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

Example

`"7.4E^6mm⁴"=1.83*(("30mm")^4)*sqrt((("13")^2)-144)`

Calculator

LaTeX

Reset

👍

Download Cold Formed or Light Weighted Steel Structures Formulas PDF PDF Image

Minimum Allowable Moment of Inertia Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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

STEP 1: Convert Input(s) to Base Unit

Thickness of Steel Compression Element: 30 Millimeter --> 0.03 Meter (Check conversion here)
Flat Width Ratio: 13 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

I_min = 1.83*(t^4)*sqrt((w_t^2)-144) --> 1.83*(0.03^4)*sqrt((13^2)-144)

Evaluating ... ...

I_min = 7.4115E-06

STEP 3: Convert Result to Output's Unit

7.4115E-06 Meter⁴ -->7411500 Millimeter⁴ (Check conversion here)

FINAL ANSWER

7411500 ≈ 7.4E+6 Millimeter⁴ <-- Minimum Area Moment of Inertia

(Calculation completed in 00.004 seconds)

You are here -

Home » Engineering » Civil » Design of Steel Structures » Cold Formed or Light Weighted Steel Structures » Minimum Allowable Moment of Inertia

Credits

Created by Chandana P Dev

NSS College of Engineering (NSSCE), Palakkad

Chandana P Dev has created this Calculator and 500+ more calculators!

Verified by Mithila Muthamma PA

Coorg Institute of Technology (CIT), Coorg

Mithila Muthamma PA has verified this Calculator and 700+ more calculators!

< 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

Minimum Allowable Moment of Inertia Formula

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

What are Cold Form Structures?

The Cold-formed steel structures are steel structural products that are made by bending flat sheets of steel at ambient temperature into shapes which will support more than the flat sheets themselves. They have been produced for more than a century since the first flat sheets of steel were produced by the steel mills.

How to Calculate Minimum Allowable Moment of Inertia?

Minimum Allowable Moment of Inertia calculator uses Minimum Area Moment of Inertia = 1.83*(Thickness of Steel Compression Element^4)*sqrt((Flat Width Ratio^2)-144) to calculate 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 calculate Minimum Allowable Moment of Inertia using this online calculator? To use this online calculator for Minimum Allowable Moment of Inertia, enter Thickness of Steel Compression Element (t) & Flat Width Ratio (w_t) and hit the calculate button. Here is how the Minimum Allowable Moment of Inertia calculation can be explained with given input values -> 7.4E+18 = 1.83*(0.03^4)*sqrt((13^2)-144).

FAQ

What is Minimum Allowable 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 and is represented as I_min = 1.83*(t^4)*sqrt((w_t^2)-144) or Minimum Area Moment of Inertia = 1.83*(Thickness of Steel Compression Element^4)*sqrt((Flat Width Ratio^2)-144). The Thickness of Steel Compression Element is the thickness of element or plate & Flat Width Ratio is the ratio of width w of a single flat element to the thickness t of the element.

How to calculate Minimum Allowable 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 is calculated using Minimum Area Moment of Inertia = 1.83*(Thickness of Steel Compression Element^4)*sqrt((Flat Width Ratio^2)-144). To calculate Minimum Allowable Moment of Inertia, you need Thickness of Steel Compression Element (t) & Flat Width Ratio (w_t). With our tool, you need to enter the respective value for Thickness of Steel Compression Element & Flat Width Ratio and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

Home

FREE PDFs

🔍 Search