Homework_8 (2)
docx
keyboard_arrow_up
School
Purdue University *
*We aren’t endorsed by this school
Course
200
Subject
English
Date
Apr 3, 2024
Type
docx
Pages
4
Uploaded by yonghyunlee8963
AAE 35200 – Structural Analysis I
Homework 8
Fall 2023
Due: 11:59 PM on 10/20/23, uploaded to Gradescope
Problem 1
[25 points]
Consider the closed, two-cell circular section shown in the figure below. The wall thicknesses
are t
1
= 0.1 cm, t
2
= 0.3 cm, and t
12
= 0.2 cm. The material has a shear modulus of G
= 27 GPa.
a)
If the section is subjected to a torque T
that causes a rate of twist of θ
= 3°/m, calculate the
shear flows and the applied torque.
[15 points]
b)
If the maximum allowable shear stress is τ
allow
= 187 MPa, find the maximum allowable
torque and the corresponding rate of twist.
[10 points]
Problem 2 [25 points]
Consider the two-cell, stringer-web section shown in the figure below. The material has a shear
modulus of G
= 27 GPa.
a)
If a torque of T
= 2 × 10
5
Nm is applied to the section, calculate the shear flows and rate of
twist.
[15 points]
b)
If the maximum allowable rate of twist is θ
= 2°/m, calculate the maximum allowable torque
for the section.
[10 points]
Problem 3
[25 points]
For this problem you will need to complete the three-cell torsion tutorial and download the
MATLAB code. The three-cell fuselage section shown in the figure below is subjected to a
torque of 56,500 Nm. The shear modulus of the material is G
= 25,000 N/mm
2
. The wall lengths,
thicknesses, and cell areas are given in the table below.
Wall
Length [mm]
Thickness [mm]
Cell
Area [mm
2
]
12 upper
1084
1.220
I
108,400
12 lower
2160
1.625
II
202,500
14, 23
127
0.915
III
528,000
34 upper
797
0.915
34 lower
797
0.915
a)
Set up the equations needed to solve for the shear flow in each cell. Do not solve the
equations by hand.
[10 points]
b)
Modify the MATLAB code provided to solve the shear flow equations. Attach a PDF of your
code and a screenshot of the shear flows generated by your code.
[10 points]
c)
Calculate the rate of twist of the section. [5 points]
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
Problem 4
[25 points]
For this problem you will need to complete the three-cell torsion tutorial and download the
MATLAB code. The four-cell wing section shown in the figure below is subjected to a torque of
50,000 Nm. The shear modulus of the material is G
= 25,000 N/mm
2
. The wall lengths,
thicknesses, and cell areas are given in the table below.
Wall
Length [mm]
Thickness [mm]
Cell
Area [mm
2
]
12, 78
762
0.915
I
161,500
23, 67
812
0.915
II
291,000
34, 56
812
0.915
III
291,000
45 outer
1525
0.711
IV
226,000
45 inner
356
1.220
36
406
1.625
27
356
1.220
18
254
0.915
a)
Set up the equations needed to solve for the shear flow in each cell. Do not solve the
equations by hand.
[10 points]
b)
Modify the MATLAB code provided to solve the shear flow equations. Attach a PDF of your
code and a screenshot of the shear flows generated by your code.
[10 points]
c)
Calculate the rate of twist of the section. [5 points]