1in
4.5in
Y
7in
6in
12in
5in
7in
9.5in
7in
Moment of Inertia of Areas:
y
8.5in
y
A2
A1
x
x
12in
y
6in
A3
x
1.5in
5in
7in
X
9.5in
Z
A1:
Ixc=1/3bh^3+Ad^2 = 5472+114(6-6.15)^2
=5474.565in^4
Iyc=1/3b^3h+Ad^2 = 3429.5+114(4.75-3.19)^2
=3706.9304in^4
A2:
Ixc=1/3bh^3+Ad^2=360+30(4.5-6.15)^2
=441.675in^4
Iyc=1/3b^3h+Ad^2=250+30(7-3.19)^2
=685.483in^4
A3:
Ixc=1/12*b*h^3+Ad^2=7.59375+2.25(9-6.15)^2
=25.869375in^4
Iyc=1/12*b^3*h+Ad^2=0.375+2.25(8.833-3.19)^2
=72.0303785in^4
Centroid:
Ix=Ix1-Ix2-Ix3=5474.565-441.675-25.869375
=4441.455625in^4
Iy=Iy1-Iy2-Iy3=3706.9304-685.483-71.77276025
=2949.67464in^4
A1:
Ixc=1/12bh^3+Ad^2=1368+114(6-6.15)^2
=1370.565
Iyc=1/12b^3h+Ad^2=857.375+114(4.75-3.19)^2
=1134.8054
Area moment inertial with respect to the centroidal axis:
Ix=Ix1-Ix2-Ix3
Ix1=1/12*b*h^3=1368in^4
Ix2=1/36*b*h^3=2.53125in^4
Ix3=1/12b*h^3=90in^4
Iy=Iy1-Iy2-Iy3
Iy1=1/12*b^3*h=857.375in^4
Iy2=1/36*b^3*h=0.125in^4
Iy3=1/12*b^3*h=12.5in^4
Ix=1275.46875in^4
Iy=844.75in^4
A2:
Ixc=1/12bh^3+Ad^2=90+30(4.5-6.15)^2
=171.675
Iyc=1/12b^3h+Ad^2=62.5+30(7-3.19)^2
=497.983
A3:
Ixc=1/36bh^3+Ad^2=2.53125+2.25(9-6.15)^2
=20.806875
Ixy=1/36b^3h+Ad^2=0.125+2.25(8.833-3.19)^2
=71.78122415
Ix=Ix1-Ix2-Ix3=1370.565-171.675-20.806875
=1178.083125in^4
Iy=Iy1-Iy2-Iy3=1134.8054-497.983-71.78122415
=565.0411759in^4