1 determi’le the slop e at point D Using the met hod of work and energy, decima l places_) 1 points eBook H int Print A __ __ __ __. D 2E I L ‘ 11 I I I L/ 2- — — –L /2 ,- –, .- The slop e at end B is I ~-~ MoL ~ . EI 1 caused by the couple Mo- (Round the fina l ans wer to thre e 2 g E = 72 GP a, um a llo y. Us in d urin g a ten sile tes t of an alu min ed ain obt a le nu mbe r:) dat from wn dra n has bee l ans we rs t o th e n e are st wh o fina the und (Ro y_ The stress-strain diag ram sho wn allo the of the mo dul us of tou ghn ess th e mod ulus of resi lien ce and dete rmine u (MPa) point s 600 eBoo k H int Print 300 150 I I I \ 0.006 I I I I I I I I I I I I I I 0.14 0.18 I I I I I I I I I I I The modulus of resilie nce of the ~- – ~ ] kJ/m3_ alloy is/,- The mod ulus of toug hne ss of the allo y is [ ] M J/ m3_ 3 Determin e the modulus of resilien ta) Stai nles s stee l AISI 302 tann eale d): £=1 90 GPa: poi nts ce for eac h of the follo win g met ‘ ay= 260 MPa I eSool< Hint Prim als: tb) Stai nles s stee l AISI 302 tcold -roll ed): E= 190 GPa l I, : ay= 520 MPa le) Mall eabl e cast iron : E= 165 GPa : ay= ~O MPa (Round the final answ ers to one dec ima l plac e.) The mod ulus of resil ienc e for AISI 302 tann eale d) stee l is\ The mod ulus of resil ienc e for AISI 302 tcol d-ro lled ) stee l is\ The mod ulus of resil ienc e for mal leab le cas t iron is\ \ kJt m 3 . \ kJ/ m3. \ kJ/m3_ 4 1 points eBook Determ ine the modulu s of resilien ce for each of the followi ng alloys: 6 (a) Titanium: E= 16.5 x 10 psi: ay= 120 ksi 6 (b) Magne sium: E= 6.5 x 10 psi: ay= 29 ksi 6 (c) Coppe r nickel (annealed): E= 20 x 10 psi: ay= 16 ksi (Round the final answers to one decimal pla.ce1.) Hint Print 3 The modulu s of resilience for titanium is ~I- – ~ llin.-lb! in . The modulu s of resilience for magnesium is I~–~I in.-lb/in3 . The modulus of resilience for copper nickel (annealed) is ~I–~I in.-lb/in3. 5 of the = 6 m/s whe n it strik es a sma ll plate attac hed to end A AB and has a spee d rod rm unifo the along s move O collar g A 3.5-k d iame te r that can be use d rod is 250 MPa , dete rmin e the sma llest the in s stres able allow the that ing know rod. Using E = 200 GPa and al place .) for the rod. (Round the final answ er t o one decim vo points Vo A eBook H ,nt P rint G I I it 7 D 1.2 m ·1 I The small est diam eter that can be used for the rod is I I .__—‘ mm . 6 points eBook Hint Prim rgy of the pris mat al stres se s, dete rmin e the stra in ene Taking into acco unt only the effec t of norm es_) plac answ e r t o thre e deci mal shown.Given: wo = 6w . (Round the final ~} 1111 r1 tJ t B ~ – L —-i►I h The strain ener gy for the b eam is re- –]- ~f ic bea m AB for the loa din g 7 show n. Take P= 7.6 kips_ (For S8 x due to bend ing for the steel beam and load ing Using E= 29 >< 106 psi. deter mine the strain energ y whole num ber.) 4 stresses.) (Roun d the final answ er to the near est ~8-4, I= 57.5 in .)(Neglect the effec t of shear ing p palms eBook Hint Print ” . [,,, L • J X D •·’ L (if1 _ \_3l1 S’S X \ !,;A .-\b. The strain energ y due to bend ing is \~_ _ _.\ in 8 points n ing th e ex pr es sio ifo rm thi ck ne ss _ Us un nno of on cti of a se th th e le ng irc ula r cro ss er AB , wh e re ds is mb er AB ha s a no n-c me mb al me ric of ind cyl ist w tw llo of ho fin al a n s we r ne the an gle The thin-walled cti on _ (R ou nd th e erg y de ns ity, de ter mi se -en s ain os cr str ll the wa for e th on e of ~ and the ex pre ssi T se d by the ce nte r lin 2 an d A is the are a en clo on cti se ss cro ll wa the , small element of .) to three decimal places = T’ eBook Hin t Prin t ~ ~/’ < els , ].~✓ \~ ~ Th p .:inn Ip nf twi ,t of th – – -7 J l J,’ ~ rP mP rn hP r AR is 1 X 8 :, ::.e LLIU I I UI I IUI I-LI i LU Id I LI u::,: 11e1 11ue 1 MD I Id::. d \I I t:::.: :,. u::,1 1 1y LI It: e.11.µ1 e::,: :,1u 1 I the len gth of a of me mb er AB, wh ere ds is st twi of gle an the e min ter ain-energy density, de the fin al an sw er and the expression for the str wa ll cro ss se ctio n. (Round the of line r nte ce the by enclosed ss section and A is the area small element of the wall cro to three decimal places.) , , ,e ll 1111 -VVd llt:U I IUII UVV Lym IUI ILd l I ,- . 2;A T’ 1 I IUI 1- UI IIIU I 111 LI IILI poin ts eBo ok H int Prin t X The ang le of twi st of the me mb er AB is I T I TL2 :r,t tds . ‘-·- – – ‘ GA 9 of th e bra ss owing tha t po rti on CD Kn a). GP 39 = G ( 8D to the bra ss rod TA = 76 0 N -m. = 26 GPa) is bo nd ed of the tw o rod s. Ta ke y erg en The aluminum rod AB (G ain str al tot 40 mm. de ter mi ne the has an inn er dia me ter of points eBook Hi-l t Prin t 37 5 mm / A 40 0m m / Th e tot al str ain e ne rgy of the tw o rod s is lr’—-_ -~ ___,] J _ ro d is ho llo w an d 9 s rod po rtio n CD of the b ras 39 GP a). Kn ow ing tha t = (G BD rod ss bra the N-m . 26 GPa) is bo nd ed to o rod s. Ta ke TA = 76 0 The aluminum rod AB (G = al str ain en erg y of the tw tot the ine erm det , mm 40 has an inn er dia me te r of poin ts eBo ok Hint Prin t 375 mm / A 40 0m m / The total stra in e ne rgy of t he tw . o rod s 1s [___ J ___, J . is ho llo w an d 10 ing E = t ruc tura l ste eL Us t o f a sp eci me n of s tes sile ten a g rin du dat a ob tain ed tw o de c i m a l w n has bee n dra wn fro m h e fin a l an sw ers to sho t m nd gra ou dia (R L train tee ss-s s e stre h t The e s s of the mo dul us of tou gh n 6 mo dul us of res ilie nce and 29 x 10 psi, det erm ine the places.) points
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