Strength Properties and Failure Theories

The strength characteristics of a composite orthotropic lamina are much more difficult to dehne than those of an isotropic material. In both cases, the engineer is interested in identifying material strength parameters which can be determined experimentally using simple tests, where the strength parameters are used to define allowable stresses for purposes of design. 

Consider for example, the maximum shear stress (or Tresca) theory of failure with respect to yielding, which can be stated as follows A material subjected to any combination of loads will yield whenever the maximum shear stress at any point in the material exceeds the value of the maximum shear stress in a simple tensile test at yield.  

The maximum shear stress at any point can be expressed in terms of principal stresses by the equation 

Equations 9.1, 9.2 provide the means of putting the Tresca theory of failure in equation form as follows  

Alternatively, introducing a factor of safety t, we obtain the design equation 

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