Moment of inertia

University of Babylon
College of Engineering
Department of Architectural Engineering
Lectures of
Structure I
Instructor: Dr. Majid Mohammed Ali
E-mail :eng.majid.mohammed@uobabylon.edu.iq
2 hours per week
Conduct
Quizzes, homework and project Mid-term exam Final exam
10% 30% 60%

Content of the term
Moment of inertia for single and combined areas 3 weeks
Drawings of axial shear forces ,and bending moments in beams 4 weeks
Stresses, their definition and applications. 1 week
Flexural stresses 4 weeks
Shear stresses 3 weeks

References
Beer, F., 2011. Statics and mechanics of materials. McGraw-Hill Higher Education
Gere, J. and Goodno, B., 2009. Mechanics of materials.?

Lec.1
Moment of inertia
Moment of inertia of plane area of second moment of area - is a geometrical property of an area which reflects how its points are distributed with regard to an arbitrary axis. It can be calculated by:
I_x=???y^2 dA, ? I_y=???x^2 dA ?
Parallel-axis theorem for moments of inertia
It gives the relationship between the moment of inertia with respect to a centroidal axis and the moment of inertia with respect to any parallel axis.
I_x=I_(x_c )+Ad_1^2, I_y=I_(y_c )+Ad_2^2
Moment of inertia of composite areas
Consider a composite area A made of several component areas A1, A2, A3, … Since the integral representing the moment of inertia of A can be subdivided into integrals evaluated over A1, A2, A3, . . . , the moment of inertia of A with respect to a given axis is obtained by adding the moments of inertia of the areas A1, A2, A3, . . . , with respect to the same axis.