Answer to Question #153658 in Mechanical Engineering for Badshah

Question

Explain key assumptions in the theory of simple stress.

Answer 1

The homogeneous term is used here to indicate that the material of the beam will be the same throughout or we can say more specifically that the material composition of the beam will be same throughout the beam i.e. material of the beam will not be changing throughout.

An isentropic term used here to indicate that elastic properties of the material will be the same in all the directions i.e. modulus of elasticity of the material will be the same in X-direction, in Y-direction, and in Z-direction.

Second assumption

Young’s modulus of elasticity of the material of the beam will be the same in tension and compression.

Third assumption

The beam will be straight before loading and will remain straight once the load will be removed.

Fourth assumption

The sections of the beam which were plane before bending must remain plain after bending too.

Fifth assumption

Beam material must be stressed within its elastic limit and therefore beam material must follow the principle of Hooke’s law.

Bending stress developed in the beam, once beam will be loaded, must be within the elastic limit or we can say that there must be elastic deformation in the beam.

Sixth assumption

The radius of curvature, during bending of the beam, will be large as compared with the dimensions of the cross-section of the beam and the beam will have a symmetrical cross-section