lecture 1

Theories of Elastic Failure:
There are number of machine components, which are subjected to several types of loads simultaneously. When the components is subjected to several types of loads, combined stresses are induced. The design of machine parts subjected to combined loads should be related to experimentally determined properties of material under similar conditions. However, it is not possible to conduct such tests for different possible combinations of loads and obtain mechanical properties. In practice, the mechanical properties are obtained from simple tensile test. In tensile test, the specimen is axially loaded in tension. It is not subjected to either bending moment or torsional moment or a combination of loads.
The theories of elastic failure provide a relationship between the strength of the machine component subjected to complex state of stresses with mechanical properties obtained in tension test. With the help of these theories, the data obtained in tension test can be used to determine the dimensions of the component, irrespective of nature of stresses induced in the component due to complex loads. Several theories have been proposed, each assuming a different hypothesis of failure.
failure of ductile materials under static loading

The principal theories are as follows:
Maximum principal stress theory;
Maximum shear stress theory; and
Distortion energy theory.
Let us assume ?_1,?_2,and ?_3 as the principal stresses induced at a point on the machine part as a result of several types of loads. We will apply the theories of failure to obtain the relationship between