630_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

624
CHAPTER 7 Analysis of Stress and Strain
Solution 7.7-3 Square plate in biaxial stress
(a) I
NCREASE IN LENGTH OF DIAGONAL
¢ d â
x
1
L
d
0.00458 in. ;
For u f 45°: â
x
1
270 * 10
6
â
x
1
â
x
+ â
y
2
+
â
x
â
y
2
cos 2 u +
g
xy
2
sin 2 u
L
d
b 1 2 16.97 in.
f 45° g
xy
0
â
y
113 * 10
6
b 12.0 in. â
x
427 * 10
6
(b) C
HANGE IN ANGLE
Minus sign means line rotates clockwise (angle
decreases.)
(c) S
HEAR STRAIN BETWEEN DIAGONALS
(Negative strain means angle increases)
g 314 * 10
6
rad ;
ced
For u f 45°: g
x
1
y
1
314 * 10
6
rad
Eq. (7-71b):
g
x
1
y
1
2
â
x
â
y
2
sin 2 u +
g
xy
2
cos 2 u
¢ f 157 * 10
6
rad (decrease) ;
f Od
For u f 45°: a 157 * 10
6
rad
Eq. (7-68): a ( â
x
â
y
) sin u cos u g
xy
sin
2
u
f
Problem 7.7-4 Solve the preceding problem if , and P
y
211 * 10
6
. b 225 mm, P
x
845 * 10
6
Solution 7.7-4 Square plate in biaxial stress