(Solved): A cross-section of the wall of a dam is shown in Fig.1.36. The pressure of water on face \\( O ...

A cross-section of the wall of a dam is shown in Fig.1.36. The pressure of water on face \\( O B \\) is also shown. The stresses at any point \\( (x, y) \\) are given by the following expressions \\[ \\begin{array}{l} \\sigma_{x}=-\\gamma y \\\\ \\sigma_{y}=\\left(\\frac{\\rho}{\\tan \\beta}-\\frac{2 \\gamma}{\\tan ^{3} \\beta}\\right) x+\\left(\\frac{\\gamma}{\\tan ^{2} \\beta}-\\rho\\right) y \\\\ \\tau_{x y}=\\tau_{y x}=-\\frac{\\gamma x}{\\tan ^{2} \\beta} \\\\ \\tau_{y z}=\\tau_{z x}=\\sigma_{z}=0 \\end{array} \\] where \\( \\gamma \\) is the specific weight of water and \\( \\rho \\) the specific weight of the dam material. Consider an element \\( O C D \\) and show that this element is in equilibrium under the action of the external forces (water pressure and gravity force) and the internally dis- Fig. 1.36 Problem 1.6 tributed forces across the section \\( C D \\).