CEE C30 - Spring 2010 - Zohdi - Midterm 2

CEE C30 - Spring 2010 - Zohdi - Midterm 2 - \ PROBLEM 1 (...

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\ PROBLEM 1 (15 points) A general structure (not shown) deforms under some applied loading. Given the foliowing displacement field at a point in a structre (r,y,,z): ur: A(r2 + y3) ua : B(r - 2')' (1) u"--0 where A, B and C are constants that are not a function of position. (a) Determine the components'of the strain and put them in matrix ([e]) form. (b) For the values of. (r,U, z) : (1, 1, 1), determine the components of the stress and put them in matrix ([o]) form (c) For the stress computed in part (b), determine the (polynomial) equa- tion for the eigenvalues. Do not solve it. t"$ 44
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PROBLEM 2 (20 Points) u(0)=O u(L)=0 Figure 1: Problem 2. ,, Consider the bar in Figure 1 experiencing the giv.en'axial'loads and ZERO- displacement boundary dlsplacements. It is statically INDETERMINANT' The material properties (constant thioughout the bar) are E, u and a. -The bar has a uniform, circular, cross-sectional oftarea A. The bar has a uniform loading along its length of / (Newtonsfmeter). The entire system is also
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This note was uploaded on 03/28/2012 for the course C 85 taught by Professor Papadopoulos during the Spring '08 term at University of California, Berkeley.

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CEE C30 - Spring 2010 - Zohdi - Midterm 2 - \ PROBLEM 1 (...

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