cheme130-unknown-mt1-Li-soln

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

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

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