Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
An example problem for determining the neutral axis location (z-axis) and moment of inertia for a given aerospace mechanics of materials profile. The problem involves calculating the centroid and moment of inertia for three sub-areas of the profile using both integration and the parallel axis theorem. The document also includes formulas and calculations for a rectangle as a reference.
Typology: Lecture notes
1 / 9
This page cannot be seen from the preview
Don't miss anything!
1
Aerospace Mechanics of Materials (AE1108-II) – Example Problem
Determine the neutral axis location (z-axis) andmoment of inertia for the following profile
12mm 300mm
80mm
z
y O
150mm
_ y=?
Divide into sub-areas
t=12mm
b=300mm
z
y O
_ y=c
1
_ z=150mm
c^2
_ y^1
_ y^2
_ y^3
3 1
1
3 1
i^
i
i
i i
1
1
2
2
3
3
1
2
3
Centroid^ datum
1
1
2
2
3
3
1
1
2
3
2
1
t=12mm
b=300mm
z
y O
_ y=c
(^1) c^2
_ y^1
_ y^2
_ y^3
datum
_ z=150mm
Centroid
5
Aerospace Mechanics of Materials (AE1108-II) – Example Problem
You can integrate:
2 A I^
y dA ^
or
Use parallel axis theorem
t=12mm b=300mm
2
1
3
z
y O
150mm
18.48mm
For a rectangle:
3
centroid
2
1
i
z^
centroid
i^
i
2
x^
x
Parallel axis theorem:
d = distance from centroid ofA to centroid of overall section
b
h
b/
h/ y O
z
t=12mm
b=300mm
z
y O
d^2
Moment of Inertia
Area 2:
2
2
2
2
2
4
z^
c
I^
A d
mm
2
2
mm
^
(Calculated previously)
3
4
2
c
t h I^
mm
2
1
h 2 d^
c^
mm
c^1
=18. c^2
=61.
t=12mm
b=300mm
z
y O
d^3
Moment of Inertia
Area 3:
Same as Area 2! c^1
=18. c^2
=61.
2
3
3
3
3
4
z^
c
I^
A d
mm
2
3
mm
3
4
3
c
t h I^
mm
3
1
h 2 d^
c^
mm
