Question

The 45∘ strain rosette is mounted on the surface of a shell. The following readings are obtained for each gage: ϵa=−200(10−6), ϵb=300(10−6), and ϵc=250(10−6)
Determine the in-plane principal strains

Answer 1

Ans) Gicen,

  a = -200 x 10^(-6)

b = 300 x 10^(-6)

  c = 250 x 10^(-6)

Since, the rosette is arranged at 45 degree,

  x = a

   y = c

  xy = 2b - (a + c)

Putting given values,

  x = a = -200 x 10^(-6)

   y = c = 250 x 10^(-6)

  xy = 2b - (a + c) = 2(300) x 10^(-6) - ((-200 + 250) x 10^(-6)) = 550 x 10^(-6)

Now,

tan 2 =   xy / (x - y)

=> tan 2 = 550 / (-200 - 250) = -1.222

=> 2 = arctan(-1.222) = -50.70 degree

=> = -25.35 degree

Hence, ' = 90 + = 90 - 25.35 = 64.65 degree

Also,

   = [(x + y) / 2] + [(x - y) /2] Cos 2 + (xy/2)Sin 2

Putting values,

=> = [(-200 + 250) / 2 + [(-200 - 250)/2] Cos(-50.70) + (550/2)Sin(-50.70)] x 10^(-6)

=> = (25 + 142.51 - 212.80) x 10^(-6)

=> = -45.29 x 10^(-6)

Now, ' = x + y -

=> ' = (-200 + 250 - (-45.29)) x 10^(-6)

=> ' = 95.29 x 10^(-6)