# Statics -Moment of Inertia for Plane Shapes- 1 of 2

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Publisher : Maged M Kamel

Course Language : English

For this Statics  Lectures , these lectures  will cover part of Statics Subject  for passing  the Fundamentals of Engineering Examination,Complete proof for the tabulated values of moment of inertia Ix,Iy,Ixy  and polar moment of inertia for  various shapes,The total number of units for this course are 42 units.

The first two unites are assigned to :

A-Introduction to the concept of Moment of inertia ,difference between  2nd moment of area and mass moment of Inertia.

B-Parallel  axes Theroem proof .

c-How to estimate the Moment of inertia , what is the radius of gyration ?

Units 3 to 6 are assigned to :

- Moment of Inertia for Rectangular section (about x,Y) &Product of inertia & Polar Moment of Inertia ,by using two ways of   Estimations.

Units 7 to 8,solved examples1&2  are assigned to :

- How to determine the moment of inertia for a rectangle section also  for L section.

Units 9 to 15,are assigned to :

-Estimation of the Moment of inertia for Isosceles triangle (about X,Y) &Product of inertia &Polar Moment of Inertia ,radius of gyrations ,by using two ways of   Estimations,first by parallel theorem , by integration,also the moments of inertias and product of inertia at the centroid directley.

Units 16 to 21,are assigned to :

-Estimation of the Moment of inertia for Right angled  triangle (about X,Y) &Product of inertia &Polar Moment of Inertia ,radius of gyrations ,by using two ways of   Estimations,first by parallel theorem , by integration,also the moments of inertias and product of inertia at the centroid directley.

Units 22 to 23,are assigned to :

-Pure bending, stress equation due to bending moment ,why it is necessary to evaluate the product of inertia.?

Unit 24 is  assigned to :

-Derive the exprssion for Maximum&minimum moments of inertia,for any section.

Units 25 to 30,are assigned to :

-Mohr circle different cases,moment of inertia at x is bigger or smaller than Iy and the value of Product of ineria  when +ve or -ve ,how to get the values and directions.

Units 31 to 32,are assigned to :

-Example no.3 Ix>Iy and IXY is +ve, and how to evaluate Imax ,Imin,through both general equation and Mohr circle.

Units 33 to 34,are assigned to :

-Example no.4 Ix<Iy and IXY is +ve, and how to evaluate Imax ,Imin,through both general equation and Mohr circle.

Units 35 to 36,are assigned to :

-Example no.5 Ix<Iy and IXY is -ve, and how to evaluate Imax ,Imin,through both general equation and Mohr circle.

Units 36 to 42,are assigned to :

-Example no.6 Ix>Iy and IXY is -ve, and how to evalue Imax ,Imin,through both general equation and Mohr circle.

-Estimate Ix,Iy,Ixy for different directions.

Quizzes are also introduced.