moment of inertia of composite shape

STATICS OF RIGID BODIES
General Instructions
Refer to and satisfy the requirement of each question carefully. All solutions and answers must be prepared in sheet of
either short or long bond papers. All solution must be handwritten.
1. consider the irregular beam section on the right, compute for
the centroidal moment of inertia about both centroidal axes.
Compute also the moment of inertia about a horizontal axis
passing through the topmost fiber of the section (36 in from the
bottom). Solutions must be presented in the following order:
a) Individual areas
b) Total area
c) Location of the centroidal x-axis
d) Moment of inertia about the centroidal x-axis
e) Location of the y-axis
f) Moment of inertia about the centroidal y-axis
g) Momen of inertia about the topmost fiber of the section
(36 inches from the bottom).



Solution:
y-axis




Fig.1


Fig.2



Fig.3
x-axis
0




Formulas:
• Area of rectangle: bh
• x = 1/2b
• y = 1/2y
• location of centroidal x-axis = Ax / Atotal
• location of centroidal y-axis = Ay / Atotal