Question

The state of plane stress in a plate of 100 mm thickness is given as xx = 100 n/mm2, yy = 200 n/mm2, young's modulus = 300 n/mm2 and poisson's ratio = 0.3. The strain developed in the direction of thickness i.E. In zz direction, is ______ mm/mm.

Answer 1

Strain developed in the direction of thickness i.e. in zz - direction

  $e_{zz\\}$   = - 0.3

Explanation:

Given :

Stress in x- direction  σxx = 100 N/mm2

Stress in y- direction  σyy = 200 N/mm2

Young's modulus E = 300 N/mm2 and

Poisson's ratio γ = 0.3

Stress in z- direction  σzz = 0 N/mm2.

Strain developed in the direction of thickness i.e. in zz- direction

  $e_{zz\\}$  = $\frac{1}{E}$(  σzz - γ × σxx  - γ × σyy )

          = - (0.3  × 100 + 0.3  × 200 ) / 300

         = - 0.3

So ,

Strain developed in the z- direction  $e_{zz\\}$  = -0.3

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