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# muddyzm12 - Muddy Card Responses Lecture M12 Just what does...

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Muddy Card Responses Lecture M12 Just what does shear stress do? It pulls/pushes on a face making it want to crack apart? Not really. It is the stress that is generated if you were to put your hand on the face of the cube and try to slide your hand across the face, the friction between your hand and the surface would result in a shear stress. Note there are some lecture notes missing from the online postings, will these be available (preferably before Friday) I am very sorry about this. I had prepared the notes but somehow omitted them to send them to the graduate TA’s to post. They are up on the web site now. Could you expand on how you sum stresses . Not sure what you mean here. I can interpret it in two ways. 1) the stresses at a particular point simply sum, in the same way as any other linear variables. If you apply a stress s and then an additional stress s then the total mn mn stress, at that point, is 2 s 2) The other interpretation is that if you are summing stresses, in mn. the sense of ensuring equilibrium, then you must remember that you need to convert the stresses to forces, by multiplying by the area that they act on, in order to apply equilibrium. When we do equilibrium of forces why does only one of each pair of strains vary? Ê + Á s 11 + ∂s 11 d x 1 ˜ ˆ ( d x 2 d x 3 ) - s 11 ( d x 2 d x 3 ) Ë x 1 ¯ First, we are dealing with stresses not strains. These are two very different quantities and it is important to be precise. Second, we (I) have set this problem up so that there is an arbitrary gradient of stress across the element. So I have chosen there to be a stress of s 11 on the negative x 1 face and Ê Á s 11 + ∂s 11 d x 1 ˜ ˆ on the positive x 1 face. I have also chosen where I place the inifinitessimal Ë x 1 ¯ cuboid relative to the coordinate systems. This is all done to make the analysis easy/convenient. Note that the choice of coordinate system, etc. does not alter the physics of the problem (i.e. that equilibrium must be maintained).

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