Reference no: EM13865771
Question 1:
The state of strain at a point of an elastic solid is given in the x-y-z coordinates by:
a) Using the matrix transformation law, determine the state of strain at the same point for an element rotated about the x-axis (in the y-z plane) 30oclockwise from its original position.
b) Calculate the strain invariants and write the characteristic equation for the original state of strain.
c) Calculate the deviatoric invariants for the original state of strain.
d) Calculate the principal strains and the absolute maximum shear strain at the point.
e) What are the strain invariants and the characteristic equation for the transformed state of strain?
Question 2:
a) Write a matrix giving the components of the hydrostatic (mean) strain tensor.
b) Evaluate the first, second and third invariants of the hydrostatic strain tensor.
Question 3:
Determine the engineering strain e and the true strain ε for each of the following situations:
a) extension from L to 1.02 L.
b) compression from h to 0.98 h.
c) extension from L to 3 L.
d) compression from 3h to h.
e) compression to zero thickness.
Question 4:
A 40-mm diameter forging billet is decreased in height from 100 to 40. Assuming constant volume for plastic deformations:
a) Determine the average axial strain and the true strain in the direction of compression.
b) What is the final diameter of the forging?
c) What are the transverse strains?
Question 5:
A 50-mm thick plate is decreased in thickness according to the following schedule: 25, 10, 5 mm. Calculate the total strain once on the basis of initial and final dimensions and as the summation of the incremental strains, using (i) conventional strain and (ii) true strain.
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