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Unformatted text preview: 1.050 Engineering Mechanics Lecture 23: Example – detailed steps 1 Problem statement p Note : p is applied pressure at the top of the soil layer K , G given r Goal: Determine ξ ( x r ), ε ( x r ), σ ( x r ) On the next few slides we will go through steps 1, 2, 3 and 4 to solve this problem. g r ρ H x z Isotropic solid (soil) on a rigid substrate (infinitely large in x-y- directions) rigid substrate (no displacement) 2 1 Reminder: 4-step procedure to solve elasticity problems • Step 1 : Write down BCs (stress BCs and displacement BCs), analyze the problem to be solved (read carefully!) • Step 2 : Write governing equations for stress tensor, strain tensor, and constitutive equations that link stress and strain, simplify expressions • Step 3 : Solve governing equations (e.g. by integration), typically results in expression with unknown integration constants • Step 4 : Apply BCs (determine integration constants) 3 Step 1 : Boundary conditions Write out all BCs in mathematical equations Displacement BCs: At z =H: Displacement specified r ξ d ( z = H ) = (0,0,0) or ξ x d = 0, ξ y d = 0, ξ z d = (no displacement at the interface between the soil layer and the rigid substrate) Stress BCs:...
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This note was uploaded on 11/29/2011 for the course CIVIL 1.018j taught by Professor Markusbuehler during the Fall '08 term at MIT.
- Fall '08