Question

A long steel bar (length L-100 m, elastic modulus E = 2x 1011 N/m2, density ρ 7850 kgm3) of unit cross section is held at one end while hanging freely inside a deep pit and you are asked to estimate the longitudinal stress and displacement along the length of the bar Assuming linear elastic behavior, the internal elastic energy U of the hanging bar is given by the expression where z is the distance from the top of the pit and v is the longitudinal virtual displacement Moreover, the load potential W due to the weight of the bar is given by where f-pg is the body force in the bar due to its own weight and g-9.81 m/s2 įs the gravitational constant. The total potential energy of the bar associated with the virtual displacement v is given by the following functional Consider now the family of virtual displacements v given by the expression 2E where c is a numerical constant yet to be determined.

Answer 1