A one dimensional problem of a prismatic bar (see the following figure) loaded under its own weight can be modeled by the stress field x x (x), y z xy yz zx 0, with body forces F x g, F y F z 0, where r is the mass density and g are the local acceleration of gravity Using the equilibrium equations,...

A one-dimensional problem of a prismatic bar (see the following figure) loaded under its own weight can

Question:

A one-dimensional problem of a prismatic bar (see the following figure) loaded under its own weight can be modeled by the stress field σ_x = σ_x(x), σ_y = σ_z = τ _xy = τ _yz = τ _zx= 0, with body forces F_x = ρg, F_y = F_z = 0, where r is the mass density and g are the local acceleration of gravity. Using the equilibrium equations, show that the nonzero stress will be given by σ_x = ρg(l – x), where l is the length of the bar.