Examples

Example 6.3: For the data in Example 6.1, find whether lamina will fail if a) Hoffman and b) Tsai-Wu theory is used.

Solution: The strain transformation and  are as given in Example 6.1.

Hoffman Theory:

For planar stress the Hoffman theory is

Using the strength parameters and stresses we get

Thus, the failure index is greater than unity. Hence, according to this theory, for the given state of strain/stress the lamina fails.

Tsai-Wu Theory:

Using the stresses and strength parameters, for planar stress state the Tsai-Wu theory with term  is given as

The strength parameters are calculated as

Thus, putting the stress values, we get

Since, the value of failure index by Tsai-Wu theory is greater than unity, the lamina will fail.