96
3 Analysis of Strain
ε x = −0.000832
ε y = −0.000832
ε z = 0.001664
γ xy = 0
γ yz = 0.00145
γ xz = 0
Find the principal strains.
13. The components of strain at a point in a body are
ε x = 0.01
ε y = −0.05
ε z = 0.05
γ xy = 0.03 γ yz = 0.01
γ xz = 0.008
Find the principal strains.
14. At a point in a material, the state of strain is represented by
ε x = 0.00233
ε xy = −0.00152
ε y = 0.00091
ε yz = 0.00085
ε z = 0.00125
ε zx = 0.00110
Find the direction cosines of the principal strains.
15. The principal strains at a point are given by
ε 1 = 2 × 10
−3
ε 2 = −3 × 10
−3
ε 3 = −4 × 10
−3
Calculate the octahedral normal and shearing strains.
16. The strain components at a point are given by
ε x = 10x y + 12z; γ xy = 4x y
2
ε y = 6x y
2
+ 2yz; γ yz = 2yz
2
ε z = 2x
2 z + 2y; γ xz = 2xz
2
Verify whether the compatibility equations are satisfied or not at the point (1,
−1, 2).
17. For the given displacement field,
u = c
x
2
+ 2z
, v = c
4x + 2y
2
+ z
, w = 4cz
2
,
where c is a very small constant, determine the strain at (2, 1, 3) in the direction.
0, −
1
√
2
,
1
√
2
.
18. A state of plane strain in a steel plate is defined by the following data
ε x = 0.00050
ε y = 0.00014
ε z = 0.00036