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Unformatted text preview: stress solution for the same infinite plate subjected to the shear loading q shown on the right? 4. A linear elastic rod is subjected to a shear traction σ rz ( θ ) on the lateral boundary that is independent of coordinate z. Also σ r θ = σ rr =0 on that boundary. The two ends are traction free. (a) State the boundary conditions of this problem in cylindrical coordinates . (b) Assume that the solution to such a problem is independent of z (i.e. ∂ / ∂ z=0) and that u=v=0 and w=w(x,y). Simplify the field equations in Cartesian coordinates . State your answer in terms of the function w. Assume that there are no body forces. Do not solve for w in the resulting equations. Note: Such a problem is called anti-plane shear and forms the counter part to plane strain/stress problems, i.e. a shear traction in the axial direction applied on the lateral surface. ! ! q q x y z...
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This note was uploaded on 09/16/2009 for the course AE AE321 taught by Professor Lambros during the Spring '09 term at University of Illinois at Urbana–Champaign.
- Spring '09