Introduction to Elasticity/Constitutive example 1

From Wikiversity
Jump to navigation Jump to search

Example 1[edit | edit source]

Take a uniform bar of length "56", cross-section area "6", density "4", Young's modulus "8", and hang it from a rigid, hypothetical ceiling. Calculate how much the bar increases in length due to its own weight. Assume that the acceleration due to gravity is "6" and the bar is fixed rigidly to the ceiling.

Solution[edit | edit source]

The tensile stress at a point P, at a distance from the ceiling is

From Hooke's law

Now,

Integrating,

Applying the boundary conditions, at , we get . Therefore, the increase in length is