St. Venant's Theory of Failure

St. Venant's theory of failure is a theory that explains the failure of ductile materials under stress. It considers the maximum principal strain as the criterion for failure. This theory is also known as the theory of maximum principal strain.

Maximum Principal Strain Theory

According to St. Venant's theory of failure, a ductile material fails when the maximum principal strain exceeds the strain at yield in a uniaxial tension test. The maximum principal strain is the strain that occurs in the direction of the maximum tensile stress.

This theory states that the material fails when the strain at any point in the material reaches a critical value. The critical value of strain is the strain at which the material starts to neck down or elongate in one direction.

Assumptions

The theory assumes that the material is ductile and that it behaves in a linear elastic manner up to the yield point. It also assumes that the material is isotropic, homogeneous, and free of stress concentrations.

Applications

The maximum principal strain theory is used to design structures that are subject to bending and torsion. It is also used to design pressure vessels and pipes.

Limitations

The maximum principal strain theory has some limitations. It does not apply to brittle materials that do not exhibit plastic deformation. It also does not take into account the effects of stress concentrations and loading rates.

Conclusion

In conclusion, St. Venant's theory of failure is a theory that explains the failure of ductile materials under stress. It considers the maximum principal strain as the criterion for failure. This theory has applications in the design of structures subject to bending and torsion, as well as pressure vessels and pipes. However, it has some limitations and does not apply to brittle materials that do not exhibit plastic deformation.