cee130-Fall_2006-mt1-Li-exam - UNIVERSITY OF CALIFORNIA,...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: UNIVERSITY OF CALIFORNIA, BERKELEY Coiiege of Engineering Mechanics of Materials (CElBD—I) Fall 2006 The First Mid—term Examination Problem 1. {25 points} Derive the equilibrium equation for a two-dimensional infinitesimal element; in the vertical (Y) direction. Note iliat the thickness of the element (z—direction) is micen as i {unit length), and X,Y are the body forces with the unit; of force per unit volume. Figure 1: A 2D infinitesimal element Problem 2 (25 points} Consider the following twonbar system (Figure 2}. Tile fiexibilities of we eiastic bars are given as f1 and f2, the lengths of the two bars are L1 and L2, and the thermal expansion coefficients of the two bars are given as a; and cm. The right end of the second bar has a distance A from the well. There is a temperature increase of AT. Find the reaction forces as the point A, i.e. RA, and at the point C, i.e. R0, for two different cases: (1) A S {CriLi + GeLalAT; (2)13 > ((11141 + Q2L3)AT . Hints: AP = fl” and AT a: GLAT. Figure 2: A possible statically Indeterminate System Problem 3 (25 points) Two cylindrical shafts are made of different materials, i.e. shear modulus Ga 75 02, but have the same length L. One solid cyiinder of diameter 2:: = d, and the other is a holiow cylinder with outer radius co = R and inner radius ci m 0.51%. They are subjected to the same external torque, T9, as indicated in Figure 3. (I) If the maximum shear stress in botii shafts is the same, find the reiationsiiip between c w R ? (2) If the angieof-twist at the free end (where the external torque is applied) (15 is the some for both shafts, find the relationship of d ~ R ? Hints: . . mi“ For a solid cylinder : J = 73—2— (1) For a hollow cyiinder : J = gum: — {1?}, d9 = 2cm :1,- = 2c1- (2) Tc TL 7mm: = “'3': = a}? {3} B /\ / To L A B /\ In Figure 3: Torsion of two shafts Problem 4 {25 points) Consider a very long ( 1000 meters in z-direction) concrete biock with its both ends fixed. The cross section of the concrete block (section in x-y plane) is a 5 meter square. Suppose that in x—y plane, the block is subjected biaxial tensile stress load, namely, ox: = 5MP“ and orW = 10M Pa. This is a typical plane strain state (Cu 2 0}. Let E = 10011an and Poisson’s ratio V = 0.3. Find on, em, and amp Hints: The equations of the generaiized Hooke’s law are (73:1: 0-511; 47:: = “E”— 73””? .. ‘7“ 52m ‘72: M “ ""5 E”? o o (7.- (,z = -1,__ JEL+_::_ E E E ...
View Full Document

Page1 / 3

cee130-Fall_2006-mt1-Li-exam - UNIVERSITY OF CALIFORNIA,...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online