MAE156A Midterm Exam Dr. Nordendale Spring 2026
UNIVERSITY OF CALIFORNIA, LOS ANGELES
SCHOOL OF ENGINEERING AND APPLIED SCIENCE
DEPARTMENT OF MECHANICAL AND AEROSPACE ENGINEERING
MAE 156A
Advanced Strength of Materials
Instructor: Dr. Nordendale
Midterm Examination
May 5, 2026
NAME: _______________________________________________________________
UID: _________________________________________________________________
Problem 1 (10 points)
Problem 2 (15 points)
Problem 3 (15 points)
Problem 4 (20 points)
Problem 5 (15 points)
Problem 6 (25 points)
Total (100 points)
It is imperative that you neither talk about nor reveal the contents or nature of the exams you have taken in
this class to anyone including social media, forums, or groups. In addition, if you gain knowledge of the
exams before taking them, from any source, you are required to report to the instructor the source and the
extent of your knowledge. Violators will be reported to the appropriate UCLA office to open an
investigation and to take disciplinary actions for the violation of the academic honor code.
https://www.deanofstudents.ucla.edu/studentconductcode
Department of Mechanical and Aerospace Engineering
University of California, Los Angeles
1
, MAE156A Midterm Exam Dr. Nordendale Spring 2026
Total Score: /100
Problem 1 (10 points)
(a) Determine the principal stresses, 𝜎1,2, and max shear stress, 𝜏𝑚𝑎𝑥 , for a 2D element subjected to the
stresses shown on the diagram below, using Mohr’s circle. (5 points)
C =
z(Tx 5) z) + =
-
5 +
35) =
To
C(t ,
0)
A (Tx ,
-
[xy) = A( -
50, 0)
B(Ty [xy) = B(5t 0) ,
,
IN ⑨
Ymax R= -50)2
R 2 To
S
=
Initial Stress state Tmax IR = =
ZTo
R
has Tx y 0
A(- To 0)
=
, c (to 0) T
⑨ ⑧
,
⑨ > 5
: T = 35 Tz
um
B(35 , %
R
Tz =
To
-
°
Emax
-
(b) Using the same 2D stresses shown in part (a) above, determine the stress state of an element rotated ⑤
20
degrees accele
counterclockwise. Sketch the stresses on the element below. You may use any method you like.
(5 points)
T
N [max
=2
·
A(TX ,
x y)
-
R
&
Txy =
-1 735 Al-50 0) ,
28)Co
.
, T
⑨ ⑨ > T
Tz B(35 , %
- R
S ·
B'(Ty Exy)
-
V &
-
,
-
Lmax
Rcos2
[xy' = Rsin 20 Ty =
C+
T 1 = C-RLos 20
(2to) sin 600
X
: =
(25) cos 60"
=
To -
(25) cos60 =
To +
Exy - 73To =
To + (25) ·
0 5
Jo -(250)
=
0 5
.
.
= .
.
2
T = 0
-neg ative since
coordinate is
Ti
Y
= 25.
of circle
on top
UNIVERSITY OF CALIFORNIA, LOS ANGELES
SCHOOL OF ENGINEERING AND APPLIED SCIENCE
DEPARTMENT OF MECHANICAL AND AEROSPACE ENGINEERING
MAE 156A
Advanced Strength of Materials
Instructor: Dr. Nordendale
Midterm Examination
May 5, 2026
NAME: _______________________________________________________________
UID: _________________________________________________________________
Problem 1 (10 points)
Problem 2 (15 points)
Problem 3 (15 points)
Problem 4 (20 points)
Problem 5 (15 points)
Problem 6 (25 points)
Total (100 points)
It is imperative that you neither talk about nor reveal the contents or nature of the exams you have taken in
this class to anyone including social media, forums, or groups. In addition, if you gain knowledge of the
exams before taking them, from any source, you are required to report to the instructor the source and the
extent of your knowledge. Violators will be reported to the appropriate UCLA office to open an
investigation and to take disciplinary actions for the violation of the academic honor code.
https://www.deanofstudents.ucla.edu/studentconductcode
Department of Mechanical and Aerospace Engineering
University of California, Los Angeles
1
, MAE156A Midterm Exam Dr. Nordendale Spring 2026
Total Score: /100
Problem 1 (10 points)
(a) Determine the principal stresses, 𝜎1,2, and max shear stress, 𝜏𝑚𝑎𝑥 , for a 2D element subjected to the
stresses shown on the diagram below, using Mohr’s circle. (5 points)
C =
z(Tx 5) z) + =
-
5 +
35) =
To
C(t ,
0)
A (Tx ,
-
[xy) = A( -
50, 0)
B(Ty [xy) = B(5t 0) ,
,
IN ⑨
Ymax R= -50)2
R 2 To
S
=
Initial Stress state Tmax IR = =
ZTo
R
has Tx y 0
A(- To 0)
=
, c (to 0) T
⑨ ⑧
,
⑨ > 5
: T = 35 Tz
um
B(35 , %
R
Tz =
To
-
°
Emax
-
(b) Using the same 2D stresses shown in part (a) above, determine the stress state of an element rotated ⑤
20
degrees accele
counterclockwise. Sketch the stresses on the element below. You may use any method you like.
(5 points)
T
N [max
=2
·
A(TX ,
x y)
-
R
&
Txy =
-1 735 Al-50 0) ,
28)Co
.
, T
⑨ ⑨ > T
Tz B(35 , %
- R
S ·
B'(Ty Exy)
-
V &
-
,
-
Lmax
Rcos2
[xy' = Rsin 20 Ty =
C+
T 1 = C-RLos 20
(2to) sin 600
X
: =
(25) cos 60"
=
To -
(25) cos60 =
To +
Exy - 73To =
To + (25) ·
0 5
Jo -(250)
=
0 5
.
.
= .
.
2
T = 0
-neg ative since
coordinate is
Ti
Y
= 25.
of circle
on top
