ME 323 – Mechanics of Materials
Final Exam
May 5, 2025
Name (Print) solution
(Last) (First)
PROBLEM #1 (25 Points): A material point is subjected to the 2D stress state ( , , ), and its stresses
along the x’ and y’ directions are shown below.
’
30º
a) Draw the 3D Mohr’s circle in the following diagram. Clearly label the three principal stresses and the
absolute maximum shear stress.
Tpl
2omp Tpz
tomp
qo.T
tompaa os 20Mpa
Takax 5 Mpa
, ME 323 – Mechanics of Materials
Final Exam
May 5, 2025
Name (Print)
(Last) (First)
b) Determine the values of ( , , ).
Tx 20 Mpa Jy toMPa Exy 0
Tx 119 11 cos 60
20 20 12.5MPa
Exy 128 sin 1 60 2011 E 12.99 Mpa
51 5 cos 20 5 15 1 2.5M
Ty
c) Draw the maximum in-plane shear stress element. Show the stress components and its orientation relative
to the x-axis.
ImmP R 15hPa Jane 118 sapa
1194150
have
R
I
d) If the normal strains in the x and x’ directions are to be measured, what should their values be? Assuming
Young’s modulus = 10 GPa and Poisson’s ratio = 0.3.
Final Exam
May 5, 2025
Name (Print) solution
(Last) (First)
PROBLEM #1 (25 Points): A material point is subjected to the 2D stress state ( , , ), and its stresses
along the x’ and y’ directions are shown below.
’
30º
a) Draw the 3D Mohr’s circle in the following diagram. Clearly label the three principal stresses and the
absolute maximum shear stress.
Tpl
2omp Tpz
tomp
qo.T
tompaa os 20Mpa
Takax 5 Mpa
, ME 323 – Mechanics of Materials
Final Exam
May 5, 2025
Name (Print)
(Last) (First)
b) Determine the values of ( , , ).
Tx 20 Mpa Jy toMPa Exy 0
Tx 119 11 cos 60
20 20 12.5MPa
Exy 128 sin 1 60 2011 E 12.99 Mpa
51 5 cos 20 5 15 1 2.5M
Ty
c) Draw the maximum in-plane shear stress element. Show the stress components and its orientation relative
to the x-axis.
ImmP R 15hPa Jane 118 sapa
1194150
have
R
I
d) If the normal strains in the x and x’ directions are to be measured, what should their values be? Assuming
Young’s modulus = 10 GPa and Poisson’s ratio = 0.3.
