Problem 3 (Total 50 marks) A rectangular dam is subjected to pressure My]: 9,, '9' y on the face, where PW is the density of water and g is the free-fall acceleration. The dam is made from concrete, which density p, (and is therefore subjected to a body force f y=pc ' g per unit volume). The goal is find conditions for a and L to avoid failure. The state of stress in the dam can be approximated by the following equations: a:pw'g.y+pw'g'y.x(x2_302] x 2 403 :pw'g.y3'x+pw.g'y.X(_10X2+6 2]_ ' ' 6' 4a3 2003 a pgy :3pw.gly2 4 4l+3pw'g 2 ] 1,9, 8:13 (0 x 200 [a x2 a) Show that the stress state above satises the equilibrium equations; [10 marks] Further assume the following properties: ,0W = 1000 kg/m3; pc = 2400 kg/m3; o'c = 20 MPa; 9.8 mls2 and L = 50 m. b) The concrete fails by crushing when the minimum principal stress reaches 0mm:_'0c . Assuming the greatest principal compressive stress is located at point B, ( x: 'a and y=L ) find that the dam width must satisfy; [15 marks] c) The concrete cannot withstand any tension. Assuming that the greatest tensile stress is located at point A ( X30 and y: L ), find that the dam width must satisfy