CONTINUUM MECHANICS ESS 411
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This 2 page Study Guide was uploaded by Miss Jeanette Keebler on Wednesday September 9, 2015. The Study Guide belongs to ESS 411 at University of Washington taught by Kenneth Creager in Fall. Since its upload, it has received 39 views. For similar materials see /class/192643/ess-411-university-of-washington in Earth And Space Sciences at University of Washington.
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Date Created: 09/09/15
Earth and Space Sciences 411511 Geophysical Continuum Mechanics Fall 2008 Midterm Study Questions The Mid Term will be a takehome test with a limit of 2 hours It should be taken without access to notes or other people or books except for our text by Mase and Mase The exam will consist of 4 questions that will be selected from the questions below perhaps after slight modi cations Problems 1 5 Mase and Mase 34 316 319 322 329 Problem 6 Mohr s circles for stress Explain in prose use of diagrams to illustrate your prose is OK a what Mohr s circles for stress represent about a stress state b how they can be constructed and 0 why they are useful for investigating fault failures Problem 7 Tensors and Index notation a Using index notation show that the dot product of two vectors p and qJ is independent of the coordinate system b Show that a stress state is a pureshear state if its rst and third invariants are zero Find the magnitude 0390 of the stresses in this pure shear state in terms of the second stress invariant HT Hint consider the characteristic equation for eigenvalues Problem 8 More Mohr s circles Assume that 0391 and 0393 are both negative 0392 is halfway between 0391 and 537 0391 gt 0393 engineering convention in Mase and Mase and internal friction exists a Use Mohr circles to show why 0 rocks at depth do not fracture under lithostatic pressure alone and 0 the deviatoric stress needed for fracture increases at greater depth b Suppose a rock under compression in all directions e g deep in the Earth is stressed close to its brittle limit Show graphically which change is more likely to make the rock fracture 0 decreasing the magnitude of 0391 or 0 increasing the magnitude of 0393 by the same amount quotwin anisntrnpic racks Heat ow q m w m 2 rs grver by 11 191 where 160 rs the thermalrconducnmty tensor w m deg and 74 15 the temperature gradnent 37m The bulk therma1 emduetamty can be wd the plane othe layenng the rocks
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