07-02ChapGere.0012 - u 5 60° from the x axis and(b the...

Solution 7.4-4 Biaxial stress
450
CHAPTER 7 Analysis of Stress and Strain
x
60 MPa
y
20 MPa
xy
0
(a) E
LEMENT AT
22.5
(All stresses in MPa)
2 45 22.5
2 R 60 20 80 MPa R 40 MPa
Point C :
Point D :
Point D :
t
x
1
y
1
R sin 2 u 28.28 MPa
s
x
1
R cos 2 u 20 8.28 MPa
t
x
1
y
1
R sin 2 u 28.28 MPa
s
x
1
20 R cos 2 u 48.28 MPa
s
x
1
20 MPa
(b) M
AXIMUM SHEAR STRESSES
Point S
1
:
max
R 40 MPa
Point S
2
:
min
R 40 MPa
aver
20 MPa
u
s
2
45 2 u
s
2
90
u
s
1
45 2 u
s
1
90
D'
D
A
( 0)
40
2
C
S
1
S
2
R
O
x
1
B ( 90 )
x
1
y
1
2
s
1
( 22.5 )
20 20
60
R
x
O
28.28 MPa
22.5
48.28 MPa
8.28 MPa
y
D
D'
x
O
20 MPa
s
1
45
40 MPa
20 MPa
20 MPa
y
S
2
S
1
Problem 7.4-5 An element in biaxial stress is subjected to stresses
x
6000 psi and
y
1500 psi, as shown in the figure.
Using Mohr’s circle, determine (a) the stresses acting on an element
oriented at a counterclockwise angle