80
3 Analysis of Strain
Fig 3.11 Rotation of
coordinate axes
(b) The orientation of the principal strains can be obtained from the following
relation
tan 2θ =
γ xy
ε x − ε y
=
15 × 10
−6
(−13 − 13)10 −6
tan 2θ = −0.577
∴ 2θ = 150
◦
∴ θ = 75
◦
.
Hence, the directions of the principal planes are θ 1 = 75
◦ and θ 2 = 165
◦ .
Example 3.3 Data taken from a 45° strain rosette reads as follows:
ε 0 = 750 µm/m
ε 45 = −110 µm/m
ε 90 = 210 µm/m
Find the magnitudes and directions of principal strains.
Solution: Given
3 Analysis of Strain
Fig 3.11 Rotation of
coordinate axes
(b) The orientation of the principal strains can be obtained from the following
relation
tan 2θ =
γ xy
ε x − ε y
=
15 × 10
−6
(−13 − 13)10 −6
tan 2θ = −0.577
∴ 2θ = 150
◦
∴ θ = 75
◦
.
Hence, the directions of the principal planes are θ 1 = 75
◦ and θ 2 = 165
◦ .
Example 3.3 Data taken from a 45° strain rosette reads as follows:
ε 0 = 750 µm/m
ε 45 = −110 µm/m
ε 90 = 210 µm/m
Find the magnitudes and directions of principal strains.
Solution: Given