¼ E x dx þ γ xy dy
Â
Ã
cosθ þ E yy dysinθ
In s direction,
CC
0
Á m ¼ E xx dx þ γ xy dy
À
Á
i þ E y dy j
Â
Ã
i sin θ þ j cos θ
½
Š
¼ À E xx dx þ γ xy dy
À
Á
sinθ þ E yy dy cosθ
From here, we can obtain
E rr ¼
CC
0
Á l
dr
and
E ss ¼
CC
0
Á m
dr
2.7.2.3 Shear Strain in Local (Material) Coordinates
Displacement along axis s is (Fig. 2.26)
E yy dy cosθ À E xx dx þ γ xy
À
Á
sinθ
We can also obtain displacement of point C along s axis from the arc length
(Fig. 2.27).
Fig. 2.26 Shear strain in
local (material) coordinates
2.7 Deformation and Strain
39