ME 5300/6300 Problem Set #1 (+, B, C problems are to be worked M, W, F resp.)

lhis week's review problems take some thinking outside the box & use, but stretch concepts covered in ME 3300. They may atfirst glance appear somewhat difficult and are not'oplug and chug". We will start some in class but are all to be handed in.

lB=lcpThe liuear springs in the arrangement shown axe unshetchedwhen o = 0. If L = 100rnm and k = 20 N/mm derive and bquationrelating P and u. use a computer to plot P versus ?J from o to 100mm. what P is required to produce displacements of 10, 40 and 50mm? Can you use superposition to get the force for 50 mor byadding that at 10 nnin to thar at 40 mm? Wlfy?

Anc -J. H;ii*T^f1B-2 Problem 1.29 from your text.

1B-3 Two thiurings, one of alurninrm and the other of steel, just fit snuggly together asshown (no stess) at T = 00 C. What would be the contqct pressure Uetrnreen ttrem at 1000 C?Ear= 70 GPa, a5 14 x l}a fC, B,t= 200 GpA osr =12.x 106fC. Let R : 0:5 m and t = l0 mm1c-1 rThe mernbers of the three bar truss aro of thc same steer and havothe same cross-sectiooa *i" uoiaffrriuot lengths. Determine

*.'o"o ' ,disqlacgmonr of rhb pir joint D for the followiig cas* i"l ""rv

p rtlPPlisd, (b) only Q ii app[e4 and (c) Neitnerp;;-a ir';pl[rautthetempcrartue of alr mimbers if increasedby au *i*tf,i w;wilt work one of thesc in class (your choice).I C-2'A rubber tG = l_09 psi, co6,yE616 = 2500 psi, and t4o,"u5L = 1000psil cvlinger has an oD of z inc[is ana .o ro oCu io.frTil, i r."g,t,' of I' inch. Its oD istightlybondedto art ol c.rr"."Jriffiiiog anaits ID is tightly bonded to-a steelroa ttrat passes completely throughit- The ring is assumed fixed and u ffir T or a.tial force F isapplied to thc rod. (a) Find the stress iistribution if onry the torquc is' rynqrq. where does it orcur rnaril.i t tn. varues of the stress atthc ID and OD of tho rubber? Wnat ma:rimun fi_ Ur.ppUra *irU6u1 gxsgsrliirg the allowablc stesses? Tbrough wuat angti, 0, will thosh4ft rotatc at his T? (b) Find tur rurrr oirtrii"d;if ,ilitc'torco pis applied? \vhere aoes, ttris **i*;;;cur and what aro the varues.of the sress at thc ID and oD

"f ,i; il;rr? What ma:rimum p canbe applied with out exceeding trre arowaure stresses? Ttrough whatdistance, 6, wili the shaft displace .r,fri, pf Can you tniot o?typraetical applications ofsucf devicesi.

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lC-3 Basket-weavo tii1tr-f l*ce th3t, while once quite popular, isnot seen puch-anVm9re.- The figure shows schematicallv theconstnrction 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 Irrinuln,r,sti;-ffi :ftH,iTtr;:lT.:,ff '1j:ff_iih:J;*ut

cantileverbeao them uie deflectioo ouru, and superposition todeterminc the moment and force ", oiu ,oa in terms of the deflectionand slope at the othen yhT wouro ue thc s*ess if the plurk is ofwood 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{ff i

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