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Torsion_summary - logical r-theta system we find that there...

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Torsion Note that this is not complete. I decided it would be of greater value for you to make your own summaries. However, you may copy and paste equations out of here. Dr. Merrill 1) General Case a) Use the ‘Prandtl Stress Function’ such that. b) b.i)Satisfies equilibrium b.ii) Satisfies compatibility b.iii) Valid for (b.iii.1) uniform bar (ie not changing in the z direction) (b.iii.2) Torque applied at ends (b.iii.3) No constraint in z (warping allowed to develop) 2) Circles (both solid and hollow) a) b) We have stress in the x-y coordinate system. However, if we examine this in the more
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Unformatted text preview: logical r-theta system, we find that there is really only one component of stress, and that is in the theta direction (so no stress in the radial direction). This is written as: 3) Narrow Rectangular Cross sections a) The important condition here is that the top and bottom surfaces are traction free, so . Since, these faces are so close together (t is smll), we will assume that these are zero everywhere in the body. And if tau_yz is zero, so is dphi/dx. b) So. c) Note that warping is 0 along the entire centerline of the sheet....
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