Atoa area moment of inertia Calculator App

ATOA Software Technologies Engineering Productivity Apps to ALL! Design on the GO!

AREA

LITE/PRO

Area Moment of Inertia Calculator

by

apps.atoa.com

2 ATOA Software Technologies

ATOA Public

Engineering Productivity Apps to ALL, Design on the GO!

Bending Cross Sectional Shape vs

Load = 1000 N Same Material Same Support Same weight

= Cost

Deflection

= Performance

5 mm vs 30 mm 6X better

?

Area moment of Inertia 1.46 mm4 vs 0.22 mm4


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Bending Cross Sectional Shape vs

Higher Area MI

=

Better Flexural loading performance


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Area Moment of Inertia app Why?

• Area, principal or 2nd moment of inertia (MI) is the sectional properties of 2D shapes

• Useful for structural mechanics and dynamics and s critical for bending stiffness and strength

• MI properties for a standard shapes can be obtained from a table or standard formulas.

• But for irregular shapes and nonstandard sizes, the sectional properties are not readily available.

• This tool allows you to draw any shape and calculate geometric and inertial properties.

Standard Shapes

Arbitrary Shapes


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Area Moment of Inertia App Theory

• A general formula for the moments of arbitrary shape bounded by straight lines is derived leveraging Green’s theorem for transforming domain to boundary integrals. This formula is implemented as an algorithm for computing inertial properties of arbitrary shapes.

• Moment of inertia is calculated w.r.t the centroid. Ix cg and Iy cg

Arbitrary Cross sections (e.g. corroded I beam Section)

dydxA dydxyAx dydxyI xx

2

;

;

;


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areaMILite Tutorial

• Draw by tapping the vertexes

• Tap areaMI to calculate MI

• Default draw window size is 2 mm &snap size is 0.2 mm. Change defaults by tapping settings.

Select a convenient Unit.

Drag and drop vertex to modify Shape

Edit the X,Y coordinates of the vertex

Set the size to the maximum from nano meter (10-9) to giga meter (10+9).

• Tips: Draw and then edit by tap or X, Y input.

Boundary should not cross each other.

For irregular shapes use maximum points

X

ATOA Software Technologies Engineering Productivity Apps to ALL! Design on the GO!

Area Moment of Inertia APP for

Android OS

Validation

and Verification


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Prediction Comparison

MI of each sections were predicted by

1. Analytical Method: Theory of Elasticity/ Roark's Formulas.

2. Numerical Method: Numerical Integration solver/ Comsol Multiphysics.

3. ATOA Area MI app.

Following 5 common sections are compared (Analytical vs Numerical vs Area MI app). Rectangular - Section

T - Section

I - Section

C - Section

Circular - Section

Following 2 artery sections are also compared (Numerical vs Area MI app). Aileron Aero Profile

Eroded I-Beam Cross section


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Rectangular section


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T- Section


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I - Section


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C - Section


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Circular Section


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Aileron aero Profile


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Eroded I-Beam Crossection


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Comparison of Results

• For straight line profiled geometry the prediction accuracy is very high.

• For curved boundary the accuracy can be improved by increasing the number of vertex.

• But for arbitrary shapes such as corroded or damaged members, custom built sections, 3D printed shapes, complex designs, Area MI lite is the only app which will help to cross sectional area and principal Moment of inertia, Ix and Iy.

17 ATOA Software Technologies Engineering Productivity Apps

ATOA Public

Engineering For ALL and to enable Design on the GO!

Lite vs Pro areaMILite areaMIPro

To download your apps and for more Visit

apps.atoa.com

• Free • Maximum Number of

Vertex 24 • Properties: A, Ix, Iy • Open Section: No • Composite Section: No • Import Export data: No • Share DWG/Results: No

• Paid • Maximum Number of

Vertex 1000+ • Properties: A Cx Cy Ix Iy Ixy Z • Open Section: Yes • Composite Section: Yes • Import Export data: Yes • Share DWG/Results: Yes

Date post:	24-Jun-2015
Category:	Design
Upload:	atoa-scientific-technologies
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