Baixe Chapter 9 e outras Notas de estudo em PDF para Cultura, somente na Docsity!
TI O CHAPTER 4 PROBLEM 9,1 9.2 through 9,4 For the loading shown, determine (e) the equation of the elastic curve for she cantilever bear 4, (8) the defetio et the free end, () the slopo at th fee y end, My 7 SOLUTION O aa, BÊ Lo, — 9zM,=o «M+M= O Lx=L, y:0) M= Mo 2 fe t58=0] er sy = M= M Mo (Sp ELG: Mx, Aloe, Ext, $=01 O ML+c, C=-ML Ely = AMx'+C x +40, [x=L,y-0] OC AMLU-MLAC C= AML* . Mo (x? > 3 to) Eastic curve ye meg (= Zina d = Me (Lx a ZEF (L-x) = .M - 2. Mb & y8x=0 XE get 0) ser | — . dy. M (4 = — Mott - — Mob ts Bexo Ge Pe(to = Medio) Eee ML Aa EL “gy a q | PROBLEM 9.3 9.1 through 9.4 For the loading shown, determine (a) the equation of the elastic curve for the cantilever beam 4B, (b) the deflection et the fres end, (c) the slope at the free end, y te SOLUTION E Bo» DzM,-o wo + M=o PR Ms -fwx* lx= L, y=0] A, , [x=L, 4$=0] EI ds Meu LU EIH: -Euxt e, =, [x=L,$=0] Oz -fwlº + C, [6d dwlt EIS guns dwl? Ely = want + Ewlix 4 €, Ex-L, y:el O = -awlls fwl!s0 = O Costa Dl! - -Bwl* (a) Elastie curve y eme ( x! = Ursa BL) a - 2 BWUlt O O ul o wb* bl yex=o Mº 287 SEI Nose ma - MZ . wb* egexo $i ter Ager << — o o, 5 mam o PROBLEM 9.4 9.1 through 9,4 For the loading shown, determine (2) the equation of the elastic curve for the cantilever beam 42, (b) the deflection at the fres end, (c) the slope at the free end. SOLUTION tel qzr-o Rc âwl = O ç E ? 4 A RA - Lui io, -0l K Wa ig DIM, : O [a pai TaRa L casa M anca M mofo o a (E 32 M = gu 1 2 z av x v Ju pe — x —+4 ie ul XX DEM,= O am” = dm + a + M= o =. z wo x Mgmt + imlx — qe dy a wa ELSA = -EWol + dwlx —- BE ds qui e quo - MC EI e? ama Lx EM HT , [x=0, +01 0:-0+0-0+ € co 2 3 ua XE Ely * -Em'x + o welx) — qaé C, [x-0,y: 0] 0=-040-0+40 +€, c:o (a) Edastic curve y=-ga- (blocos AE) — y val b) yexl y=- E t-m*no) = cm Er A Mol" Jor Ts Er! - à $ [co ge xel EAR Be (apr A - - 4 eb 3 O q -— —1 — [| O aa PROBLEM 9.6 9.6 For the beam and loading shown, determine (a) the equation of the elastic curve for portion BC vf the beam, (b) the deflection at midspan, (c) the slope at B. SOLUTION Using ABC as a Free body DEMe=o (EYE) - REL +WwLYÉ)- o Re = Ewl wi . é ul kd! For portion BC ondy o
ERÍS- d Sw? = 43 EI Os PROBLEM 9,9 9,9 and 9,10 For the beam and loading shown, (4) express lhe magnitude and location of the maximum deflection in terms of wo, L, E, and 7, (b) Calculate the value of the maximum deflectlon, assuming that beum 42 is a W18 x 50 rolled shape and that v,= 4.5 kips/f, L= 181%, and E=29 x 10º psi. SOLUTION Using entire beam as a Free body DEM,=o -RLaA(imLAG) = = tml Usina AT as a free body DM =D 2, gw es (AÊ) + M=o M= Embx- bx 2, = Ewlr Ex EIS = amo Lx? Atx! + C, Ely = demoLxS o Meyt + Cx + Cs [x=0,y-01 oro-0+0 + €G C,=o . =L,y=0] Os demlio daML!+ CLA O c, - - Tt E Ebastic curve y: Ei get” -LE ol = Lxt Ea tela Lx? Le - 201 E - EL * ca Jo To Find Pocadioa of magimum dellectou ser 4 0 to Vo q isa soam co io SoLtc/Mon rol = UE oem” xes 05193 L a 18) = 3 Fm. = ge SA Llosa ds fesiss do; - B(o.si93 o: = - 000662 Wall or 0.00652 vb y — Data mr ES kps/P = RO = 375 Mbha, L=18Pt= 216 im 1 = 800 in? for WIg=50 (o. 00652 As 75 Ae . mé Apis tas E 0.228 dm - f 5 q 1 DA 1 IL | PROBLEM 9,10 y “my 9.9 and 9,10 For the beam and Íoading shown, (a) express the magnitude and location of the maximum deflection in terms of wo 2, E, and 1. (bh) Calculate the value of the maximum deflection, assuming that beam 45 is a WI8 x 50 rolled shape and that wo = 4.5 kips/f, L = 18 fl, and Ee 29 x 10º psi. x SOLUTION ay - to ge-w = (o) 0, 1,5 We - meoproy tengo) yr cM(lx-fu) + O = GE M= = Mel Ex) 4 Cm + Cu Ex=0, M=0 ] [o] or 0 +08 + Cn=0 [x=L,M=0] [o) W (pu LEA CL Cos GWel ELSE Mme (sy Lex dx + E) ELA - aqu gu e +C, Fry E (GIO LS) eu dC Ix-0, y:º] 0O= 0o-0+0 +04 € Ge=o fx L,9y:0] o WO AUS RS + qa LEA CL+ o C=-e Wed? s: 26 (lê gude dos deixo) dy No 2.2. dee prt (bl Eures dt) To Pinda Pocation E mamimum delhection set 4 = fo Elk - = Let 2: s + Eixo + se - oe tectos aetod to = dl! = 0 gE- -+o + gr? ) y Nevfum - Raphson doa 208 - e a Ds, uses, 0.4807, o.4807 Xm = ods4807 L a = tb elit (o 4307! A(o.4207)! à são (0,4807) — de (0. 4807 % -- .00es2 E ye = 0.00652 Ab, y — Data: w= Skip SÊ: 375 Ablm, Le lBPt = RlG in 1: 8001" fer WigxSo to 00652378 W216 3 0.229 im. a Je (RG x 10º) C 800) ) 57 ) My PROBLEM 9.12 9.12 (a) Determine the lacation and magnitude of the maximum absolute deflection in AB belween 4 and the center ofthe beam. (4) Assuming that bcam 43 is a W460 x 113, Me = 224 KN-m and E = 200 GPa, determine the maximum atlowable length 4 of the beam if the maximum deflection is not to exceed!.2 mm. SOLUTION Dsina AB as a Free body SM: O -2M-RL=-O Me Usina portion AT as a Free body q )y* =ZMy=0 -Ma+ exe M=o ê 8 M k- -L M= de (tax) Ra Ra 2 Me ELSA = (toa) M dy. M x Co E) Erg Me(tuo nt) 46, 2M!L " v Ely EC E) Cx (xo, y-01 0o=0-0+0+€, C=o [xs L y:e] or Me (Ai = SL)+ cl+0 Co EM y- A (die br - Ex) Me Beliso 4) To Find Socatioa of menimom dellechoa st BF -o x wi-Lx-tl=o x, = E-dictéo) Hu-ÊyLeoxsa ld 2 2. x: dl font? - ENO ausat (ENO as + -o.o1co375 Fal - Mott — Ijml = O.OW037S qo NRao . f EI | a Sobuing For L L= faser: Deda: E = 200n0' Pa, 17 556410! mm! - S5exiot im” Iyad= 1Qmm = b2xidtmo, Mo 224 nO! Nm . (aoortoN(sSexio “Lam tt) - t Ra Fio3) 8.04 m PROBLEM 9.13 9.13 and 9.14 For the beam and Inading shown, determine th i int €. Vs E ado Gra g , determine the deflection at point C. SOLUTION wo 193 Reactione: Rc MILT, Pa MM 4 O
