cheme130-unknown-mt1-Li-soln

cheme130-unknown-mt1-Li-soln - UNIVERSITY OF CALIFORNIA...

Info iconThis preview shows pages 1–6. 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

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

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5

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

View Full DocumentRight Arrow Icon
Background image of page 6
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: UNIVERSITY OF CALIFORNIA, BERKELEY College of Engineering Mechanics of Materials (CE130—II) The First Mid—term Examination (Spring 2004) Problem 1. Consider the following statically indeterminate system (Fig. 1). Find the reactions forces R1 and R2. Hint: The flexibility is defined as L and relationship between internal force and elongation of a two force bar is P = f A. Figure 1: A Statically Indeterminate System Problem 2 Consider the following two shaft system. Both shafts have circular cross section. Find the maximum shear stress in the system. Assuming T3 = T and To 2 2T. The radius of shaft AB is given as R = C; and the radius of shaft BC is given as R 2 2C. Hints: torsion formula Tp 7d?“ 7' = 1—, for shafts with circular cross section , II) = 2 . (2) p Figure 2: Torsion of a two—shaft system Problem 3 A planar circular three-hinge arch consists of two segments as shown in Fig. Determine the reaction forces at A and B caused by the application of a vertical force F. Problem 4 Consider a long ( 1000 meters in z-direction) concrete block 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, Figure 3: A two-bar truss system the block is subjected biaxial tensile stress load7 namely, anc = 5MPa and cry = 10MPa. This is a typical plane strain state. Let E 2 100MB; and Poisson’s ratio 1/ = 0.3. Find 02, cm, and cy. Hint: The generalized Hooke’s law is e — Lava '7 _ E E E _ _0_z fl_ 2 6y — VE+E 11E (TE 01, 02 : 711......1/4. _ ‘2 E E+E Problem 5. Consider a rectangular block with the dimension dw >< dy >< dz. Uniform shear stress, any, is acting on the surfaces normal to (+/ A) x-axis and uniform shear stress7 Tyz, is acting on the surfaces normal to (+/*) y-axis as shown in Figure 4. Show my 2 Tym. Hint: use moment equilibrium equation about the z—axis M2 = 0). Figure 4: Infinitesimal element in pure shear 4m " + rk +z~l H1 . (15¢ git r Gs,‘+.'un le‘u‘; 3:: iik ,5 ._fiHM . fwd“ ?noH¢m 1. X 15 / L 6') i ’P $ ~ )( + 2L (27C) V X P $ L (f) H/ (R2 SYJJ'ZMI 72:2» — x A”: H +2¥>< fix ~ 47‘ A‘” = O '24? r}? = ~3—FP a») H 0 + 0'3CP='9CP =0 3)” ' P A AU)+ AU’) + — 4 Xszfil 7mb’em Z We 4??”1‘ 4th M‘Ffii‘m‘vo ® © @ l T I 2T / i 2 l @ , @ 2T Tooé’f J I 1‘ 2T 45);?!» 2 Alia NM '- M2 T62): 3T " ‘4 y 5 L’ / /7 / /+ / / / 2 @337: BT'C -: ,4]: :: 2T. 20 "" T g (‘rrC‘U/a WT C3 / 17(2cf/2. 27f C ‘7’}: WNWM slum» 34m; [‘5 ?a blew 3 “Al . ' Jabboel‘f allagrmu of #154: join+ I'; ( waf-e brf'k ACQBC Gré "l‘wo— n1 MmLev-s ) {if PB EV srwuurl‘vr ; 1%, FE ZF = o P r ‘5‘ €o$4f°+ fig Gséfo— P z: 0 ASP; =t> => IFA=F5=NE§ m U! ml— ’9 -7 r '3 : C'ngf-klo' xix‘tf) xw - -I m = o_o7 [admin Rosie“: Kite a Woman-f aha-and -?-aw‘$ 2M0? = o r‘ <4 3‘ . __ r\ Mr vii. W #7“ FT 0m am (ET: {FT}: ...
View Full Document

This note was uploaded on 02/18/2010 for the course CHEME 120A taught by Professor Gilman during the Spring '10 term at Berkeley.

Page1 / 6

cheme130-unknown-mt1-Li-soln - UNIVERSITY OF CALIFORNIA...

This preview shows document pages 1 - 6. Sign up to view the full document.

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