Exam 1 Solutions - CEN 302 — Mechanics of Materials...

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Unformatted text preview: CEN 302 — Mechanics of Materials Section Exam #1 S O LUTt o (of Name : Problem 1. (30 points) A rigid bar (ABD) is supported at B by an 2014—T6 aluminum flexible rod (BC). (a) Calculate the lateral deflection of points B and D based on the loading shown in the figure below. Aluminum has a modulus of'elasticity E=73 ,1 GPa and a square cross section of 1cm by lcm‘, (b) If Poisson’s ratio is v=—0H35 and modulus of Rigidity G=27GPa calculate the change of the cross sectional area (Indicate if it expands or contracts) (0) If the yielding stress for the 2014—T6 aluminum is ayie1d=400MPa, and we use for our design a factor of safety of Fsit=fiifl§i will the cross section be adequate? (Material behaves the same in compression and tension) (d) Do ygflr calculations hold true if'the bar is made of 606 l—T6 aluminum that has a ayield=245 MPa (Assume same E,G,V as 2014-T6)? (If'no, please explain in detail which calculations are wrong) 12L; . O ‘ E <- gc w it? be .Eulaizzckd Co mg»? 33a 0% <39 91,53 Km, i {)0 i / I t) 6“ : I.— “ —: p 15 ()JQQQ’QQQ) Pa ;,;130 MPa I A 0.01 {0.91 \ 8% ‘34; C 0 1} V — F , g g} ' 8 p % fi min/73490 — " 0:003‘ta‘2 OR 933:” gfwwwflw flCM/‘A {YMQQHY‘ ‘ff’zctvhrwg?‘&$§ my : g #1:, it b (b7 fig; :fi‘:r J o;3§’ :fi? :; i<3,3S :flb &&%g r w O’zg aéww $9 5201} : (OWZSx-UYOOBVQ “5+0; 00419:; (Qt/ayafiwbléw QMM “Mm”? 1/7, fry»: filbzaf I a L, 75:0 9’) 91m NW :D 83%} «:2 among? w: 0.0% :3 0,996,253”? W») K N Q {,1 {ya 53 k ‘ng 3% wk :24 rag; iii _ , aauq : o,[email protected]& n O-Q' ’3, 2f AQ‘ACN? @floOOOOOaiW‘ as; »/’—\- 颮mfiq : fiflmaaim _/ S 5M A (1Q 5%QQ _ F S : WWW :v (.3 2 400- 2w away 504.4%; I fiat/“£310 9.) 51/7, W Adm} sham :- gmMPa flaw SO 49% X'33 0H0” is Ndfigy $412,: ({9}) S .— \ — A f mav— mm- :':b (Two: O‘flflg w {5%149 m 33’" y W Pw: few «5*? 1" 2"“31 r aflcm \ {T w @5231; M {Q Problem 2. (20 points) The four element pin—jointed planar truss in Figure supports a single downward load P. at joint C. All members have the same cross—sectional area, A1=1000 inz, and the same length L, The allowable stress in tension is (0’1)anow=20ksi, and the allowable stress in compression is (O'C)anow=10ksi. Determine the allowable load: Pallow FEW; flifl‘lsfip (TEEMSMH?) A l (Te/(Afime «_ o fl). ,1»: ‘ w 4. 5:215?“ i a?" imw ‘lE‘MSim : 53393.9 3 “if” a a w :9 w 0;,» y Problem 3. (25 points) The three part axially loaded member shown in the following Figure consists of a tubular segment (1) with outer diameter dol = 1.,00in and inner diameter d“ = 0..75in., a solid circular rod segment (2) with diameter d2 = 1.00in. and another circular segment (3) with diameter 075 in. The line of action of the three applied loads is along the centroidal axis of the member. Determine the mormal stresses 0'], 0'2 and 03 in each of the three respective segments. ! [1 fix a s. 71er #17 an”: a" we: W» w? M Problem 4. (20 points) The steel bar shown below has a cross sectional area of 003 in by 0,3 in. and a length of 10 in. The properties of the material are shown in the stress — strain curve shown below. a. Determine the required load in order the length of the bar to reach 10.06 in. (10 points) b. After the application, the above stated load is removed. Is there any permanent deformation? If yes how much? (10 points) (unknown values can be taken from the graph) PE <———~———————————> L=10 in Stress-Strain Curve 80 3-1 , 0 0001 0002 0003 f 0004 0005 0006 0007 0008 0009 001 O gogfiqstrainfin/in) L£~Lf Mow/a : . /0,0‘ g : Wm : 0,605 Ne w 6 A / Q f a) 5 1”‘“~‘eas;>f:) (’5‘ : k 93 (fig : 1:;9 I 1:; 32., (:93 pl till/fl 6 M, ” 36/09:) Mn 7 l v ,i ~I : / ‘6 O 002‘ firm I 19 _ e‘e’m’lc; p % W V 22. 1 I " M t‘ “"1 ~ .— 0 9‘»,// t if 3,” r I. Gil} f ...
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