Example 6.4: For the data in Example 6.2, find the maximum value of  if a) Hoffman and b) Tsai-Wu theory is used.

Solution:

Hoffman Theory:

For planar stress the Hoffman theory is rearranged as

Using the stresses and strength parameters,

Thus, we get

Solving this quadratic equation for  we get .

Tsai-Wu Theory:

For planar stress state the Tsai-Wu theory with term  is given as

The strength parameters are as given in Example 6.3. Putting the stresses, we get

Solving this for , we get .