cee130-fa05-mt1-Li-exam - UNIVERSITY OF CALIFORNIA BERKELEY...

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Unformatted text preview: UNIVERSITY OF CALIFORNIA. BERKELEY millage of Engineering Mechanics of Materials (CEBU—I) Fall 2005 The First Mid-term Examination \u flifl/‘Effl/Z é’flaflw é: Pro em 1. A circu stepped shaft has the dimensions shown in the figure. Use energy methof to determine the angina of twist at the loaded and. Shear modulus G is given. Figure l: A 2]) infinitesimml eiemem Hint: _ . , mi“ For a 5011:! cyhuder : II, = a? [l] . l . . T21; . W, _ 551.50. L — 20.1? (2} Prabkz‘m 2. Derive he equilibrium equation fixr a; tMJ-djluunsimml infinitesinml clement in the hurizoutal {w} directimn'. Note that the thickness of the filament {zad‘mionj is La.an as 1 (unit length), and X,Y are the body forces with the unit (force per unit volume). [20 points] Figure-2; A 2D infinitesimal element Problem 3 mymu Drama: 15 constructed as snow: m me figure .3. ALI 101nm my me cuxwluumu pm wu- lected'NI‘here is an external force P = 8kN acting at point E. Find the reactions. at point 0. (20 mints] \ Figure 3: A two-bar bracket system Prol‘fiqu 4 Consider a three elastic bar system (statically indeterminate) with external forces. Both the engfl] a1 [(1 the Hexil‘fity of each bar an;- 5|nuwn in Figure 4. Them is a temperature rise, 59.} flu! (0°), md the coefficient of thunnul expansion is n, and the thermal strum can be calcuiamd by the formula :7- : nAL Find the reaction forces 3;. H2. {20 points) f=;-—- and AT=(TL {3} Pro m5 Couside ~11 cloned cylind’rical steel presure vase! under internal pressure p = 1.0M Pn as shown 'I the figure. a {1} Find hoop stress a; and longitfdinal stress a: (2} Find the hoop strain (1. The average radius of the cylinder is. rm“. = 1.0m. and its thickness is t = 10mm. Let E = DOE—1'1“:I and u = 0.25. Figure 5: A cylindrical pressure rm] under internal pressure p. Mint: 0': = g E a? _ 2t. md the generalized Houke’s law are I _ a Pay I!” r __ _ _ _ _ w E E E a, a“ cr, e], = -PE 4‘ *E-J: - PE You may neglect. the pressure in thickness direction. (*1) (5} (6) {7) (8} ...
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cee130-fa05-mt1-Li-exam - UNIVERSITY OF CALIFORNIA BERKELEY...

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