lecture10 - Lecture Date: 04.11.2009 Prepared By: (01) Anas...

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1 Lecture Date : 04.11.2009 Prepared By : (01) Anas Abdulrahim (02) Engin Usta 2-D PROBLEMS IN STRESS ANALYSIS In stress or strain analysis we can model most the problems as 2-D, instead of 3-D analysis it is oftentimes better to use 1-D or 2-D representations of the actual stress or strain case.We can categorize the models as in the following diagram and we apply can employ these models under appropriate conditions. Fundamental 2-D Stress-Strain Models Plane stress : Assume infinitely thin plate (x-y plane), loading is uniformly distrubuted over the thickness parallel to the plane of stress. Plane strain: Assume element infinitely thin along z (x-y plane),all cross sections experience same deformation. Axisymetric: Axisymmetric geometry and loads (r-z plane),at a constant radii load or strain conditions are the same along the circumference.In this problems polar coordinates are used. PLANE STRESS PROBLEMS σ zz = 0 σ yz = 0 σ xz = 0 PLANE STRAIN PROBLEMS Є zz = 0 Є yz = 0 Є xz = 0 ∂/∂z= 0 AXISYMMETRIC PROBLEMS ∂/∂θ= 0
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2 (Axisymmetric figure) PLANE STRESS PROBLEMS The body has dimensions are such that h << a, b Thus, the plate is thin enough such that there is no variation of displacement (and temperature) with respect to z, it depends on x and y.Also the stresses in z direction are zero. Equilibrium Equations
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lecture10 - Lecture Date: 04.11.2009 Prepared By: (01) Anas...

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