HW #1
1. The following data were collected from a 12 mm diameter
test specimen of magnesium :
F /( / 4)(12 mm) 2 F / 113 .1
( 30) / 30
Load
(N)
0
Gage Length
(mm)
30.0000
Stress Strain
(MPa)
(mm/mm)
0
0.0
5000
30.0296
44.2
0.000987
1000
0
30.0592
88.4

Ch 4. Concept of stress
1. Notation of stress components
ij
= normal stress along j-direction
on i surface (in this case i = j)
ij
: shear stress along j direction
on i surface (in this case i j)
z
rewrite using stress tensor
xy
xx
xx xy xz
yy
yx

HW #5
1. A block of aluminum in the form of a rectangular
parallelepiped (see figure) of dimensions a = 125mm, b =
100mm, and c = 75mm is subjected to triaxial stresses x = 75
MPa, y = -35 MPa and z = -10 MPa acting on the x, y and z
max
faces, respecti

Ch 5. Strain and Material Relation
Purpose : Detailed explanation of strain
Hookes low in 3-D
5.1 Strain
normal strain ()
shear strain ( )
Normal strain
L
A
B
x
x
P : Normal load
B
A
u
u+du
P
L
Deformation of a prismatic bar
where = axial deformation
L

HW #3
1. A bar ABC having two different cross-sectional areas is loaded by and
axial force P (see figure). parts AB and BC are circular in cross section
with diameters 50 , and 38mm, respectively. If the normal stress in AB is
40 MPa, what is the normal

HW #4
1. A two-dimensional condition of stress at a point in y 2MPa
y
a loaded structure is shown in Fig. Compute
xy with between 0 180 in 5 increments for
x
= 7 MPa, y
= 2 MPa, and
xy
= 5 MPa. Plot
x
and
x
and
xy versus .
xy 5MPa
x 7MPa
x
2. An el

HW #2
1. Identify the lip plane and the slip step in Fig.(Note) for plastic
deformation by motion of a screw dislocation
2. Cold working a metal by rolling it to a lesser thickness or
hammering it introduces a large number of dislocations into the
crysta