To compute the strains in a new direction, Mohr's circle can again be used. For strains in a direction 60° clockwise with the x axis, rotate the x axis two times 60° (i.e., 120°) as shown with line FG. The strain at that direction are,
ε_{x}^{*} = {50 - 31.62 cos(180 - 120 - 18.43)}×10^{-6}
= (50 - 23.66) ×10^{-6} m/m
= 26.34 ×10^{-6} m/m
To compute the strain in a direction 90° with this line, it can be rotated two times 90° or 180°, which is diametrically opposite to it.
ε_{y}^{*} = {50 + 31.62 cos(180 - 120 - 18.43)}×10^{-6
}= (50 + 23.66) ×10^{-6} m/m
= 73.66 ×10^{-6} m/m
Corresponding shear strain is,
γ_{xy}^{*} = 2 {31.62 sin(180 - 120 - 18.43)}×10^{-6}
= 41.96×10^{-6} rad
The new strains are represented as point F and G on the diagram at the left. |