ME 5300/6300 Problem Set #1 (+, B, C problems are to be worked M, W, F resp.) lhis week's review problems take some thinkingoutside the box & use, but stretch concepts covered in ME 3300. They may at first glance appear somewhat difficult and are not'oplug and chug". We will start some in class but are all to behanded in. lB=lcpThe liuear springs in the arrangement shown axe unshetched when o = 0. If L = 100rnm and k = 20 N/mm derive and bquation relating P andu. use a computer toplot P versus ?J from o to 100 mm. what P is required to produce displacements of 10, 40 and 50 mm? Can you use superposition to get the force for 50mor by adding thatat 10 nnin to thar at40mm? Wlfy? Anc -J. H;ii*T^f 1B-2 Problem 1.29 from your text. 1B-3 Two thiurings, oneof alurninrmand the other of steel, just fit snugglytogether as shown (no stess) at T = 00C. Whatwouldbethe contqct pressure Uetrnreen ttrem at 1000 C? Ear= 70GPa, a5 14 x l}a fC, B,t= 200 GpA osr =12.x 106fC. LetR : 0:5m and t = l0 mm 1c-1 rThe mernbers of thethree bar truss aro of thcsame steer and havo thesame cross-sectiooa *i" uoiaffrriuot lengths. Determine *.'o"o ' , disqlacgmonr of rhb pir joint D for the followiig cas* i"l ""rv p rt lPPlisd, (b) only Q ii app[e4 and (c) Neitnerp;;-a ir';pl[raut thetempcrartue of alrmimbers if increasedby au*i*tf,i w; wilt workone of thesc in class (your choice). I C-2'A rubber tG = l_09 psi, co6,yE616 = 2500 psi, and t4o,"u5L = 1000 psil cvlinger has an oD ofz inc[is ana .o ro oCu io.frTil, i r."g,t, ' of I' inch. Its oD istightlybondedto art ol c.rr"."Jriffiiiog ana its ID is tightly bonded to-a steelroa ttrat passes completely through it- Thering is assumed fixed and u ffir T or a.tial force F is applied to thcrod. (a) Findthe stress iistribution if onry thetorquc is ' rynqrq. where does it orcurrnaril.i t tn. varues of thestress at thcID and ODof tho rubber? Wnat ma:rimun fi_ Ur.ppUra *irU 6u1 gxsgsrliirg theallowablc stesses? Tbrough wuat angti,0, will tho sh4ft rotatc at hisT? (b) Findtur rurrr oirtrii"d;if ,ilitc'torco p is applied? \vhere aoes, ttris **i*;;;cur and what aro thevarues. of thesress atthc ID and oD "f ,i; il;rr? What ma:rimum p can beapplied with outexceeding trre arowaure stresses? Ttrough what distance, 6, wili the shaft displace .r,fri, pf Can you tniot o?ty praetical applications ofsucf devicesi. - -_- -- 5rr lC-3 Basket-weavo tii1tr-f l*ce th3t, while once quite popular, is not seen puch-anVm9re.- Thefigure shows schematicallv the constnrction of one plank of the-fence. Th;;;;;l.l;d"r. belbw wourd arternate siars oi tt, porrr'oo which contact is made. Deterno.ine the maximum stress i;;[,;;l-'::- ':'1T'lt I rrinuln,r,sti;-ffi :ftH,iTtr;:lT.:,ff '1j:ff_iih:J;*ut cantileverbeao them uie deflectioo ouru, and superposition to determinc the moment and force ", oiu ,oa in terms of thedeflection and slope atthe othen yhT wouro ue thc s*ess if the plurk is of wood with E= 1.5 x t06,psi, r in.rr uriJ-lyT;ilffiffi1*,il;;", , are 4 inches in diameter and spaced 6 ft apant 0*' f1l * =. hp (EJ t^DrAarG, (o) a,,14g{ffi J{<^ftu-l4 a.cI