An 18-m-long steel wire of S-mm diameter is to be used in the manufacture of a prestressed conerete beam. It is observed that the wire stretches 45 mm when a tensile force P is applied. Knowing that £ = 200 GPa, determine (a) the magnitude of the force P, (b) the corresponding normal stress in the wire. @ aL : Pp. EAA EA a . Pe 2000 © «YG (SY mye US win sO \BRIO™ mys « Pe 437.4370) -/Pe 9.32 1) © £-P . TwiFYaN NMG eye Seo Wra (1) Wy m !PROBLEM 2.7 2.7 A steel rod is 2.2 m long and must not stretch more than 1.2 mm when a 8.5 KN load is applied to it. Knowing that E = 200 GPa, determine (a) the smallest diameter rod which should be used, (b) the corresponding normal stress caused by the load. @, _ PL ” ER > P © 6-f- _ &: Sx) ¥ 2- 2x0 min Zeopid PD. oy a mn™ AZ 9-16 mm SHO A) “Wy (7 9) mm? < 2mm 109-| HP (7)PROBLEM 2.15 A single axial load of magnitude P =58 kN is applied at end C of the brass rod ABC. Knowing that £ = 105 GPa, determine the diameter d of portion BC for which the deflection of point C will be 3 mm. SB IEN) $= 53K) j ’ ac 5 > 2m ogm D ae —> go ‘ > > Ben | —> Pa, = 53 ta) a A B > °s c= Bejy = Legtb wa =+3inm 3 4 53x10 x Foo . SBxI0 % 1200 co /05x1OxtA* BRIO 30° pd = 16.52 mmr=4¢p) PROBLEM 219 Both portions of the rod ABC are made of an aluminum for which £ =70 GPa. Knowi neat he rms ar KN, determine (the ae of Q 30 hat the deflect 0, (b) th reter DO ter 2 | Yii-O) 9 @ am Boje- Maye rd, Ble sth, =+ nee 18 wo \ (CO pins ae WT 29|Q = 32-3 Vf (4-9) 2 _ ( 4-323) y0x >) P= 4-9) © 4g Bee PonsbT bot =- 0.073 mm i.e. |Op- 0-073 mm (| )(Ghrlenia) | bea) = ae RfPROBLEM 2.23 Members 4B and BC are, made of steel (E = 200 GPa) with cross- ectional areas of 516 mm” and 412 mm’, respectively. For the loading shown, determine the elongation of (a) member AB, (5) member BC. => Vne= 195-260 (1) * joi, “B's ZY¥x=° BIAS > Ve = Wee Fy iB) oA) es => Vee- (5om() 19S an6ae (58 122 | * 2 200,00 T x Sib mn ER Jag 20000 ox Slim SOR Don. 1s I B x00 mn Oe be. Zeon TH mt | rN @Lhoe O4ec- _. . ef se s r Ze => 195 = Tag cs) . VS __ Tes Dd 4/4 mn =(incresein teenth) =| 3-23 mm Cee)PROBLEM 2.27 A D P=5kN Each of the links 4B and CD is made of aluminum (E = 75 GPa) and has Te a cross-sectional area of 258 mm’, Knowing that they support the rigid E member BC, determine the deflection of point £. Fd nam —° 0.20 m he Ska) 3 Ze ‘ - => Fan(o-z+0-4u) B = S(O) => Sap 2 344K CY Z¥ge0 => Kep 2 2-344 = 1-56 ke (7) Ap = Ap ems = 2-064 mm (4) he = hep, (gp bipasies Sas) = 0-024 mm (J) o-2m o-44mm E ca BSp-Ac - Ag-Ae é f Bp-A 6 >A, (ABB oa 4Ag =| 0-053 mm aN o2m E o-44mPROBLEM 2.61 ‘A 20-mm-diameter rod made of an experimental plastic is subjected to a tensile force of magnitude P = 6 KN. Knowing that an elongation of 14 mm and a decrease in diameter of 0.85 mm are observed in a 150-mm length, determine the modulus of elasticity, the modulus ot iy, and Poisson’ ratio for the material. 9 _. Lien) SA ‘a0 mn mn — OL +l mm. 32 ~)0 > wm te TD /g01r0m ¥ I8-32790 mein Ze _ Sd ~~ O:3Sm S425 KJ" rom ym ~ “dy zoom" _ Ct 865 =|0.455 -e - "93-33% yp bxion) = (9. 6) 2 YA 7 Wy (os nn? A 1 MR (1) ba EG = [el SIN popes : ‘7 9333x0° | He Ble E_ 2 2046S Wh —— - , Z(H) 27+ 0-455) ae ° ooA line of slope 4:10 has been scribed on a cold-rolled yellow-brass 20. wow | 150 mum | plate, 150:mm wide and 6 mm thick. Knowing that £ = 105 GPa and ————*__ y= 0.34, determine the slope of the line when the plate is subjected to a 200-KN centric axial load as shown. J Zoo cn 2g —_ "Ihe = wm jo 200 x10 1) orem - — = 222.22 TT * Tmt Wa (1) Gye 222122 WW 4712. K10° vam, Cx = Ee yosx07 Pa hey -( Mn) Layo = (14 2:l2ni’) 10 = 10.021 by = -U x= — 034 (+212x0°) =- 042) x0 mys Lyye(regyhy,o = (I4(-0-721 x0) W=3z > ple Slope = a S9AF mo 10-02[ mm —=_ arPROBLEM 2.69 A 30-mm square was scribed on the side of a large steel pressure vessel. After pressurization, the biaxial stress condition at the square is as shown. For £ = 200 GPa and v =0.30, determine the change in length of (a) side AB, (b) side BC, (c) diagnonal AC. bye + 30 Ra, byae yo Wea , &z=0 Wa ene 56 -ulbys th. = {a- 03(40-+0)f Zp Expat 034 HS? wren ain incyease “5 Ey = AAO Nya 20mm (0:34x06°) =}+J0-2X/0 mm] L460 eye [os veal) Lf yo-05(erra)f => ey =+ 0.03 re ono Knenease. -a\ |Y.,, 4 Gy = Bee = WA ef 0 mm (0-08) 2210 Le, i Lacie [Ladct bac .= | 30430 = 42-4264 Lac, [Legge bee, Re | 30. 102 + 30.0024"= 424353 wn [ML ad = 4D-43$3-A2 YHA T Axo mmPROBLEM 2.75 The plastic block shown is i \ded to a rigid support and to a vertical plate to which a 240-kN load P is applied. Knowing that for the plastic us G=1080 MPa, determine the deflection ofthe plate. 5D mm i __ 2K) | 25 MP, 2 plskic~ Fpo(goyrme Sp boskc “oo Splshe- Doloshic = a N\A = 235 BIx 7 ple SO MPa rad | 5 M40 Bolaheo= & — am Az 50%233IN0- ao Ss] K =14 wld) J SSR NANA — USEach of the four vertical links connecting the two rigid hori zontal. members is os a aluminum (E=70 GPa) and has rectangular tere of 10 x 40 mm. te the loading shown, determine the deflectio of (a) point E, ro 7 (c) point G. a c dD, 4 EFG: J | Za N e7° aoe a > Lleg (4o0)=24 (652) “ 25emm Yoomm AZXy-2 > Fee + 2(19:5) -24=° > Yep= 7-5 = ZOKN) ©) LL ) End asomn NS eN OD mn eels -&) FOpO IE (Yox'0) on Oe x fom a snl yet oS650 mm oom => Kee O> ZaAG mm xO mm