After breaking the cross section into its composite parts, determine the area, the location of the centroid, and the centroidal moments of inertia for each part.
The centroid and the area of each part were found in the previous section,
Centroid: Composite Parts. The moments of inertia for each part can be found from the tables in the
Sections Appendix.
For the axis system as shown, the properties for part 1 are,
x_{1} = 1 cm y_{1}
= 3.5 cm A_{1} = 6 cm^{2}
I_{x'1} = 1/12 2(3)^{3}
= 54/12 cm^{4}
I_{y'1} = 1/12 3(2)^{3}
= 24/12 cm^{4}
The properties for part 2 are,
x_{2} = 8 cm y_{2}
= 1 cm A_{2} = 32 cm^{2}
I_{x'2} = 1/12 16(2)^{3}
= 128/12 cm^{4}
I_{y'2} = 1/12 2(16)^{3}
= 8192/12 cm^{4}
And the properties for part 3 are,
x_{3} = 15 cm y_{3}
= 7 cm A_{3} = 20 cm^{2}
I_{x'3} = 1/12 2(10)^{3}
= 2000/12 cm^{4}
I_{y'3} = 1/12 10(2)^{3}
= 80/12 cm^{4}
Part 4 is a triangle and its properties are,
x_{4} = 17.33 cm y_{4}
= 10.67 cm A_{4} = 8cm^{2}
I_{x'4} = 1/36 4(4)^{3}
= 256/36 cm^{4}
I_{y'4} = 1/36 4(4)^{3}
= 256/36 cm^{4}
