Aerospace Engineering - Aerospace Structures

Exercises of the course

Complete course

Strutture esercizi Esercitazione 1nnnnnntyYn✗>ZlllelzABCe ty = ( EFx=oiHa+Ha=0,n,n^^^^fy^SISto+12HbEFy =0:Vb+Vc+toLttta(2-=L ) L=oia2yVb3Si sa,µ. | ,.....+.«+,,/¨,«+a.,..26Vc3 ⑤EMA=o:-Hcd + Vclz =oHc=_po+poiCIHa =-Hcg=-1728N2 dVb+Vc+PoCL+1PoiCL=oVc=Hcd =-1296n2lz(p.. , +poiC LZ +Had=0, { a.=...=.»..2- Hcd +vela=oVb=-Vc-CLPo+ [ Pt=300N n,nn^^^^f,tu^12961728>y☐ay>zg360^"17281728✓1296oa•µ=OaTy=_("to d -2=- poc z-P,C2-= Ty/a)=-576NoL2eMx=_poc-22_poiCZ}Mx(a)=_43s'zoonum2L6AB'n=-1728N• Ty =- | £tydy +1296=-pocz-Pac È 1+1296 Ty/al=720N Ty/b)=360N2L0•Mx=1296(z-le ) -poczl -PacZ}1Mx/B) =o26L7203601728576435.200~(n]T ( n ] m[Nnn ] nnnnnntyYn>z✗eaBC•ty= | , pdx=PC=0,3Nnon a) z. Ty =- | , tyd -2=- ty Z Ty /b)=-750NaMx=-ty2-=Mx(b)=-937.Soonun2750937.500NCN] T(n]m[nnn]•CALCOLOILMOMENTOTORSIONALErispettoa3assiicarichiTORSIONALIESTERNIz•mza=-ty+0,03è alaaTRAPEZIOISOSCELEmzo=oMz=O CASO2• ty = ([Po+Poiz=C | Po+Poi-2)= ( 300+0,2Z)( 0,6.10'>+2.10'?z ) =g.10-8 2-~+1,8- to"2-+ 0,18 zG.IÓS z}+1,8. 10-4 z?- Ty =- | tydz =a+0,182-3☐4.10-&Z"+1,g.io"z}•Mx=g+0,18È 122•mzo=_1-yC2 ESERCIZIO6^0,8-^"',^ I ^lz=3000 i n-94n41421zz£1.×,|1500,✗zlaasta1•ty=0,42-1leZ11. Ty =- |tydz =_,o,c,2- 12 =-0,22- Eleile03•Mx=-0,22-1311. Ty/ 2-a=le) =-300NMx(2-e=le)=- 150.000 nnmasta2^0,8^I/',/^ I ^• ty =0,4t0,4ZZlzI42izz^Ty,°/4Tz,^^41✗zTze2-1.×,MxtTy,MxyZz• Ty = Ty r/2-=le ) - | tydz =-300-0,4Zz-0,2 ZÌ Olz2soeMx=-300Z-0,2Zz-0,2Zz3h2•mzz=Mxy1z=le)o ESERCITAZIONE 2 |TI =- 1-42-1 nnnnnnSR144Mx=-1-y zal 2-z2-122ty, Ty =- ty -22-✗t Ty "(za=0)=-tyZz-✗-tyLa=- tylzzt.la)-✗nnnnSRMxzMMyyyz, | my =,yy zy , yy ,,z,_yz,+µ ,gz ,,,,=ZZTy,2=- tyzz _ /tyLa+× ) zz-ty LÌ 22 STÌ =o STÉ =-1SFe |SMÌ =o STÌ =--22• SLE =oLZ322• {Ld = | ,1-yza+ /tale+× ) zz-1tulaZzdz 224• SLE = SLI :tulatituli +✗ IL} +tuLÌLÌ =o8341-y LE +tyLaLz+tuLÌ +La✗=o✗=-2375N8343 METODO2 Ty =-tyz0EZEla | mx=-tu-22^nnnnn2Sry2- |Ty =-tyz-✗LeiEZElMx=_ty2-2-✗(z-le)2 Ty =o Ty =-1se☐ezela | "¥ez=L1 | Mx=oMx=-1/z-Lei)e SLE =0. SLD = | "/z-"¥Ity2-2+✗(z-le)dz =2LI= | "tyÈ +✗ zlz -ln)-taleÈ -✗La/z-le)dz = | ,",tuz}+✗ È -2✗"¥2--tylyÈ +✗ LÌdz =2222La+✗-ty(1 È -2×11Z+✗ LÌdz == | ,,z2--l==tyz"+✗-tuLIz>-✗la-22+✗LiZ.836-Li--l=tyz}+✗_tyLIÈ -✗la-2+✗LA=.836-Li=1-y (P -la})+✗-tuLI/il - LÌ )-✗Le / L-Le)836-. SLE = SLD :tyIL >-La})-tale(E-LÌ)+1 /E-LÌ )- Lill - 4) '✗=o86.3.AB✗=-2697,5N •struttura2VOLTEIPERSTATICA^^^^^^4YZ✗Tx=-tyz-XnnnnnnSRY" ( ""='" " '""2CALCOLO✗ Stx =-1SF1Smx=-Z. SI @=o• SLD =1 | "tuz>+✗2-=+Yzdz E]20.era.1:tyL"+✗ E +YÈ =otyE +XL+Y=o832932CALCOLOYSty =o1 {smx =-1• SLE =o• SLD =1 po 'ry è +✗2-+× dz E]2 •ecaz:tyL>+✗ è +YL=otyE +✗zLtY=o626tyE +✗L+Yz=ol'4 LZ t § L-l'4 E -XL=o38124 |; a,+,=o | ,=.+, y ,×,tyE +✗62 | ✗=-tuL=-1147,5N2Y=516.375N nn^/I1,^/I/,////^5^',nnSR2I\^42^zz^Tg 1^^n41Tz,^n41Tze42nzz£1.×,✗=2-1.×,^✗MxtTy,Mxy✗z2 Ty n =-1tyr2-1Zy-✗=-l'412-1-✗2La2h1 | µ,=,ra,,-21-✗Z16La2 Ty z =- Ty n Zz-1(tyz -1-41)ZzZzt Tye (za=(1)=- 1-412-2 _+42-l'41Zz-l'41La_✗2Lz2h222 (ma=-tu,za-tua.ru, zio .+a."¥za-✗/¨=-+ anzi .rua.ru, zio .+a."¥+×za2Glz22Glz2Mzz=-M✗1/Z1=(1)=1-41 LÌ +✗(16 ''',''',////ssSF42^-22Tg 141Tz,41Tze42nzzZt.×,✗=2-1.×,1Mxt1Ty,Mxy✗z Styoi =-1 Styz = STye(2-1=11)=-1 | Shin=-Zi Smxz =-Zz |gaza ,_g,, ,z ,,,, , ,e,• SLE =oL1L2-342-• SLD =1 |tua2-e"+✗ ZÌdz + | ,^1-unzz+tua-tuazz+1-unL1+✗zz+EJXEJX2Glz2☐GLI--32+11-41La+✗La dz =GJT643=11-un LÌ '+✗L ? +11-yyLa+tyz-l'41 LÌ +1-41"¥L2t✗ LÌ +EJX303Ejx83063+11-41 LÌLz+✗ LÌ LZGJT6• SLE = SLD :---2✗ Ty =-tyz+✗✗Mx=-tyÈ +✗2-2sa § ✗✗{Sty =eSF1Smx=z• SLE =o• SLD = SLD "a"+ SLD 1-tuz>+✗ Èdz+1.×mia=e# [ =K. SI @= SLD iL}+1✗-tul"=o✗=1569N3.C-JxKSEJx 321SE432-3✗3Tz zTze^MxzMxt1-☐^^~,^^Ty zl'41^Ty zTy t nnn^Tz zTZT^yyY✗YzzMxzM"z,✗2 Ty r =-1Z1to2-1-X=-toz,_✗2La+Lz2/(1+Lz) | ma,=,µ,z , .yz,6/Letlz)2-2 Ty z =-toZz-1ZztoZz-Y=-toZztto zÉ -Y+☐^^^,=Le+Lz2/latlz)nnY | µ,=,, zy ,no zag ,yz,26(Letta) ( " """"""""""""""" " ="°"" "" """"""""=""""""""""""2/La+(2)2=-to(la+Lz)-✗-Y2Mx}=-to ( LttL2)2-3-✗2-3-YZ}2MZ}=nlxz(Zz=Lz)-Mx, / 2-1=Lei)=-to è +to Lis -Ylz+toL ? +✗La=26(Letta)6/Latlz) 2 / L ? + LE )-toL } -Ylz+✗La=to=tog,,,,,z,/La+Lz)/LÌ + LÌ -Lnlz)-toLz-Ylz+✗La=226(Letta)g LÌ -lulz- 2h22 =toCALCOLO✗SFSmxei/2-1=41Sty/2-1=11)STY(2-1=4)1Smxe/2-1=4)1 """="" """=° | """"= & """"""""='^ |Smx ,=-z, |Smxz =o Smx }=-2-3 Smz }= Le • SLE =oL1(31toz,"+✗ ZÌdz +1to ( le+La/z } +✗2- È + YZÌdz +. SLD =ejx ( o6/Letlz)c-Jx ( o2342+1=+to-to"¥(zL1Lz-YleilzttoLa+✗Ladz =gjt | ">26/lrtlz)6/Le+Lz)o533=1toLstla✗+^to ( LatL2)È }+✗L}+YLÌ EJX30/La+lz)3C-Jx633+^- toLILÌ (3ttoLIL ? (3-YULZL3ttoLs"(3+✗ LÌ (3=GJT6111+LZ)6/Le+Lz)3=1.La}-1La}+1 Lidl }✗+1L}-^ Lrilzl }Y+C-Jx3GJTE>×3GJTab53+1toLstto ( LatL2)Lstt-to"¥ LÌ (3tto LILÌ (3ttoLs"(3EJX30/La+Lz)6GJT26/(1+12)6/Le+Lz)c•Jx=it 24 = 201.299 nn"JT=ITR"= 402.578 nn"42 A=0,0112B=1,736.10'>C=2,543•El.1=AX+BYtC=0CALCOLOYSF smxztzz-zlftylzz-l.atTy z/2-2=12)Smxz/2-2=12)11 Sty ,=o Styz =-1 Sty }= Styz/2-2=12)=-1 |su,=. |sua =-za (su>=-z, Smz }=Smxz/2-2=12)=-Lz• SLE =o3• SLD =1 | "toza-to zÉ + Yzèdz +1 | "to ( la+Lz)2- è +✗2- è -1 YZÌdz +C-Jx26((ytlz)E.Jx2o0342+1 | "}tola-tola+Ylz-toL ?L2-✗LaL2d -2=GJT26("¥+(z)6/Lttlz)☐45333=1toLz-tola+LzY+to/La+Lz)L}+L}✗+(3>Y+EJx830/la+Lz)3633("+1to LÌL }-toLz+L?(2)(3+ LÌ L}Y-✗Lslzl}=2GJT6(Letta)3+1 È L} Y +}_1"¥Lzl}✗+1LÌ +13=1(3EJx3gj,EJX3GJTBE453+1toLz-tolatto(Litla)L}+1to LÈ L}-to(LÉ +L?(2)(3c-Jx830/la+Lz)6GJT=6(Letta)F •E=3,839F=5,7 79A=0,0112B=1,736.10'>C=2,543ax+BY+c=o { ✗=-C+BY✗=-C+BYa | a | bx+EY+F=0-B/CTBY)+Et+F=oYE- BZ =BC-FaAa•Y=-1,4 ESERCITAZIONE 3Tx t=-1-Z1 Tx z =-1-Zz-1-La-✗^^^^^^4SRZ✗ | µ,,=,yz,, | µ,,=,µ zng ,y,,z,.,µ,-✗z,222 | Stai=o Styz =-1SF1 Smu =o | Smxz =-zze SLE =0. SLD = | "322+✗2- Edz rZztt(1ZzttL12-222043'l'3LaL2tt LÌLE +1(2º✗=oLztt8432l'La+tLiLatt LÌ +1La✗=0✗=-2375Ng343SPOSTAMENTO^^^^^^4SRZ✗ Styi =-1 Styz = Styne/2-1=11)=-1se1 || Gm ,,=,z, gm ,=,z,,g.µ,,,z,=,,,,,z,,y,• SI e=1. Sy 32• SLD = | "tzu DZ +1 | "¥1-zz+1-Liza+1- LÌ +✗Zz/zz+Li/dz =C-j2EJ2z☐0-433=y,^, ,g ,yy,+,y,y,yy, ,g ,× yg ,ny,y,y yyyy ,n gg,,,yy, gg .E].883436222. -a li '1g/La"+La")+t,L ?La+✗LnLE +✗• Sy =,taLily}+31' LILÌ +t=- 0,078 nn42c-J- nn^///^/////////^5^',nnSR2I\^42^zz^Tg 1^nnn41Tz,n41✗zTze42^zz1£1_×,Zt.×,MxtTy,Mxy✗z Ty r =-tzut2-1=-tzu?2La24 | µ,=,nz , 6h1 Ty z =-1-zzz-1ZztZztTy n(2-1=Lei)=-t2-z-t2- [ -t(y2LzZlz223Mxz=-tZz-tZz-tLsZz2Glz2MZZ=-M✗1(2-1=(n)=1-( 12 ! . Styei =-e''',''',////ssSM✗1=-2-1SF Styz =-142^-22Tg 1 (an ...,41Tz,41Tze42nzz£1.×,✗=2-1.×,Mxt^Ty,Mit1✗z Smzz =La LaL223• Sy =1te342-1"dzttZztt2-a+t"¥zz dz +1rLa=E] | Glie] ( o26h22CJT | "g☐04=11-La"+rLa"ttLa+t(1 LÌ ttt(?La=13,79mmE]308306GJT6 Ox ''',''',i:{Stai =0ssSFSmu=-1 Styz =o42^-22Tg 1^✗aTz,TZ"142^Zz".µ."×. | su ,=o✗z Smzz =13e1-z ?dz+11- LÌd -2=rla+t LÌLz=1,8. IÓ >rad. ② ×=e>× ( o"GJT | "6462460 --__SucuiCnz(13'Fy'Sz=(21(22(23FZ- OZ ..(31(32(33.-WZ_Tz=oTz=oFYTy =- Fy ^ Ty =-1Mx=- Fyz Mx=-ZMz=oMZ=oTz=FzTz=1FzTy =o^ Ty =oMx=oMx=oMz=☐Mz=oTz=oTz=owz Ty =oe Ty =oMx=oMx=oMz=-Wzmz=-1(11• Sy =1 Fy-22d-2=(3 Fy EJ | "3.E]☐•(12=0(21=o•(13=☐[31=o zll È ,mx,MizlelzABCv : Tu tc•ry= | ,pdx =Pc=0,3~mm•N=☐2- Ty ,= | - tyd -2=- tyz oE-2Ele02- | , >=,. g.ma ,=a.µ ,e..z,a.+e,Mx,=-tu ZZ OEz,Elamia | -2=lei)=-486.10>nmm2 { µ,=µ,,.ae,,, µ ,,z, , z.az. y z,o,,,e,µ,,z,e,,,.gg,.gg,nn,4025048623597,5E3540 n,nn^^^^ty'-StrutturaISOSTATICA2.^ ; a'l'g^yOla°lzdz'/C✓-..-CJL•1-y= { -l'laLI=2112Lz2h22 | µ,=.,z,z,., { un=- {è - t.az GLI6h2Mzz=-M✗1I2-=(n)=tg"¥=48Ab?• Jj =2A49È + AÒ +3A25 È =174 AÒ • Jriy =a/-7-b)IGb )+al-7-b)1-Zb)+ al -b)( Gb)+3A/Sb)/-Zb)=-48ABZ o✗=1aatanZJÌY=-0,3261-ad= -18,65°Ji -JiÌ 4--✗ Ì cosa- Ù Sinacosa-sind | =Rcon✗inMODULO=y= È sino+Ìycosasinacosa&E--✗--.-_-'✗1'-È,--2,23✗z- xè '-7, 9 1=r= b =r= b ==-41.. 51 .-3,50-.42.. Ùz ..1,55---_-___-- è }'-~-✗3-6,00✗a +966+97A)=1' 1911+91*1b-192*-91 " la +(qo'+ 9T/b+ gia =Znreot211Gli-_--=1-2Tb+ 29$(atb)-9nFazanoli->a-o-• 02 =^ I92h+942+9sb+93a) =e' 192 '+ 92*1b+ /9g ' +92*12+19s' +92*1b+ (92*-91*1 a=222Gt222Gt----=1-atb-tt 292*1 atb)- 91$ aznrzgt_32_• È = Òz i--_-1-2Tb+ zqila+b)-9nFa=1-atb-tt 292*1 atb)- 9$ azanoli-32_Znrzgt_32.•-2Tb+ zqila+b)-9nFa=-atb-t+ 292*1 atb)- 9T a32322Tbttt 91*(32+26) - 92*(32+26) =o 91*-92 "=-T2b+13232+Zb32 i -T+ 2191*+92*1 =oa*•9È =T-91=522-.•ztbttt/32+zb)291#-T=o9nF=-zb+1Ttt1=13.a22323.atzb222--3-32-3151-a!!14.-35-36 91Jx=Gah?=a ! % 92T=-1500N5×1=5×2=ah5×3=Sxc,=-ah3934T•91"=-tan=-T4am"4hT4h2^• QI =-T2hT2h3T4h"• qig =-TT4hz911q,"9s°"""""""""""""°"""""°"'o= 291×-11-42 a+2191'+9£)zhb+ 2192 '+ 9¥ )zhb393422T•o=-T Zhb -Tzhb+ ITL291 "+ Ghb 9 È4h24z+ith>91#+ Ghbqè •o=-3.1-b--_• Ò ,=1 I9sith- 942h)=1 9TTh- /92*-91*124 =1 9in/ztit)-2h9È'2h1Gli2h1Gli_2h1Gli_.-e•02=^(91b+922h+93b+942h)=2126£--1 191 '+ 92*1b+ 192 ' +92×-124+19 }' +92*1b+ 192*-91*124 =212Gt.- -.=1-Tb-T +292*1btzh)- 91*24212Gt2h---.-.• È = Òz :1 9in/ztit)-2h9È=1-Tb-T +292*1btzh)- 91*242h2ith?Gt.-z.zhbcit--2-.-.•2 9¥hlztit)-2h9È=1-Tb-T +292*1btzh)- 91*24 Ithzb2h----212+it)+hqì +-G-1lb+2h) qÈ =T-^-1itbitbZb2h | a•ath>91"+GhbqÈ =3.1-b2☐EF•A=3,5232B=-2,7732C=-2,516791"=4,49☐=SOZSITE=90.000F=67500092$=6,62 3922911Jx=6A 22 =3 AAZ C,2949395965×1=5×2--5×3=Aaz5×4--5×5=5×6=-Aa4562e91"=-Ty=-T3722=A@232•92'=-2T3232T322T321Ta• qi ,=-Ta42T325T326•9s'=-2T32I•9g=-T323922911•EQUIVALENZAallerotazioni:poco6-94939596456•o=291'ab+ 2192 '+9")ab+ 2194 '+9"/zab-29"ab2222•o=-T-2T-2T+9#+29*-9*3.a32a•9*=3T22 35T622T3213ST622T321T223T22T223T224ST625T3A64ST625T3A64zeTz n=oTy pTze.Ty r=-Ta=-TMxt222•miattaz+5Tzaz=oMxy=-Tz-STz=-GTzzaga22632•Tz z=o3T22Ty zTzeTz z•Ty z=-T+3Ta=T""^Ty,Mxz2ziaS-GTbt3Ta2-t2Tza-Tz=GT•Mxz=zg(z-b)3za322TT24Tb3 AqBDC-c-caviVA L E N Z AALLERotazioni:pocoaiF.ZR=2199=F.22=F=4,7 7NmmZITRZITR"""""""""""""""""""" ( """=+"""+"""°•SERVE1EQ.:PLVCVaTi•Ne=-9asinotVasinorrn1ma"..Ti=-9r/1-COSO)-Vacoso•Ma=-2219-VasinoR=-9 è/0-Simo)-Varsino•In= tèO_1r asino = R2(0-Sing)21T22Ne/IT2)=-9r+VA | te,,a)=-qrMaIN2)=- 922(it2-1)-var FMIv1'.'ti•nz=-Te/it2)sin0+ne/it2)COSOtFCOSO-92sin@i0, e ',•TZ=T1(it2)COSO+v1(it2)sino+f-Sino-9r/1-COSO)eNzTzLM2•Mz=ma/it2)-zR?IO-si-0)+Te(it2)COSOasino+tu/it2)sinoa/1-COSO)+2-----_un/IT2)tF.COSOr/1-COSO/t.nu(it2)tF.Sinorsino=--=mi/it2)- è10-Simo)+Te(it2)asinot.nu(it2)tF.r / 1-COSO)•Ma=- 922(it2-1)-Var- è/0-Simo)-9èsino+ I -92+Va+F)r/1-coso)==-9è/it2-1)-Var- è/0-Simo)- QRZSINO -9 è + 922coso+Var-varcoso +FR/1-coso)==- 9£ ita_ è/0-Simo)- 922sino-9è + 9£COSO-VA R C O S OtFa/1-coso)==- 922 ITtsino+1-coso_ è/0-Simo)-varcoso+Fa / 1-COSO)2•Il=it è9_^resina= è10-Simo)21T22SISTEMAFittizio•nn=sin@-t,.t,=-coso-rN1ma..Ma=-Simor/1-COSO)-COSOasino=-Esin0-r'.".°Nz=COSO0,•Tz=sinon,M2•Ma=-r+ esisto _ è/1-coso)=- è PLVCit/2-_•SLD=1.9 è/0-sino/tvarsino.asinodo+EJ(o33+192"ittsino+1-coso+r"(0-Simo)+varcoso-Fa / 1-COSO/doe> { "