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

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 the 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, pdf data are included.

The first two units 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 17,are assigned to :

-Estimation of the Moment of inertia for Right-angled triangle (about X,Y) &Product of inertia &Polar Moment of Inertia, the radius of gyrations, by using two ways of   Estimations, for the two cases of a right-angle triangle.

Units 18 to 21, are assigned to :

-Estimation of the Moment of inertia for a triangle (about X,Y) & Product of inertia &Polar Moment of Inertia, the radius of gyrations,by using two ways of estimations.

Units 22 to 23, are assigned to :

-Estimation of the Moment of inertia for a triangle (about X,Y) & Product of inertia &Polar Moment of Inertia ,radius of gyrations for an isosceles triangle.

Units 24 to 25,are assigned to :

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

Unit 26 is  assigned to :

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

Units 27 to 32,are assigned to :

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

Units 33 to 34, are assigned to :

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

Units 35 to 36, are assigned to :

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

Units 37 to 38, are assigned to :

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

Units 39 to 44, are assigned to :

-Example no.6 Ix>I y and I XY is -ve, and how to evaluate I max ,I min, through both general equation and Mohr circle.

-Estimate Ix,I y,I x y for different directions.

Quizzes are also introduced.