Verify the validity of the transformation relations given in Table 7.1 by:

(a) Transforming the plane strain Hooke’s law (7.1.3) into the corresponding plane stress results given in Exercise 7.6 .

(b) Transforming the plane stress Hooke’s law (7.2.2) into the corresponding plane strain results given in Exercise 7.1 .

Table 7.1

Equation 7.1 .3

Data from exercise 7.6 Invert the plane stress form of Hooke’s law (7.2.2) and express the stresses in terms of the strain components:

Equation 7.2 .2

Data from exercise 7.1 Invert the plane strain form of Hooke’s law (7.1.3) and express the strains in terms of the stresses as:

Equation 7.13

Transcribed Image Text:

Table 7.1 Elastic moduli transformation relations for conversion between plane stress and plane strain problems. E Plane stress to plane strain Plane strain to plane stress E 1- E(1+2v) (1 + v) V 1-v V 1+v