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
s
x
52 60 MPa s
y
5 20 MPa t
xy
5 0
(a) E
LEMENT AT
u 5 22.5 8
(All stresses in MPa)
2 u 5 45 8 u 5 22.5 8
2 R 5 60 1 20 5 80 MPa R 5 40 MPa
Point C :
Point D :
Point D 9 :
t
x
1
y
1
52 R sin 2 u 52 28.28 MPa
s
x
1
5 R cos 2 u 2 20 5 8.28 MPa
t
x
1
y
1
5 R sin 2 u 5 28.28 MPa
s
x
1
52 20 2 R cos 2 u 52 48.28 MPa
s
x
1
52 20 MPa
(b) M
AXIMUM SHEAR STRESSES
Point S
1
:
t
max
5 R 5 40 MPa
Point S
2
:
t
min
52 R 52 40 MPa
s
aver
52 20 MPa
u
s
2
52 45 8 2 u
s
2
52 90 8
u
s
1
5 45 8 2 u
s
1
5 90 8
D'
D
A
( u 5 0)
40
2 u
C
S
1
S
2
R
O
±
x
1
B ( u 5 90 8 )
t
x
1
y
1
2 u
s
1
( u 5 22.5 8 )
20 20
60
R
x
O
28.28 MPa
u 5 22.5 8
48.28 MPa
8.28 MPa
y
D
D'
x
O
20 MPa
u
s
1
5 45 8
40 MPa
20 MPa
20 MPa
y
S
2
S
1
Problem 7.4-5 An element in biaxial stress is subjected to stresses
s
x
5 6000 psi and s
y
52 1500 psi, as shown in the figure.
Using Mohr’s circle, determine (a) the stresses acting on an element
oriented at a counterclockwise angle