Module 11 Design of Joints for Special Loading. Version 2 ME, IIT Kharagpur

Transcription

1 Module 11 Desgn o Jonts or Specal Loadng Verson ME, IIT Kharagpur

2 Lesson 1 Desgn o Eccentrcally Loaded Bolted/Rveted Jonts Verson ME, IIT Kharagpur

3 Instructonal Objectves: At the end o ths lesson, the students should be able to understand: Meanng o eccentrcty n loadng. Procedure or desgnng a screw/bolted jont n eccentrc loadng. Procedure or desgnng rveted jont under eccentrc loadng. In many applcatons, a machne member s subjected to load such that a bendng moment s developed n addton to drect normal or shear loadng. Such type o loadng s commonly known as eccentrc loadng. In ths lesson desgn methodology wll be dscussed or three derent types o jonts subjected to eccentrc loadng () Screw jont () Rveted jont () Welded jont 1. Eccentrcally loaded screwed jont: Consder a bracket xed to the wall by means o three rows o screws havng two n each row as shown n gure An eccentrc load F s appled to the extreme end o the bracket. The horzontal component, F h, causes drect tenson n the screws but the vertcal component, F v, s responsble or turnng the bracket about the lowermost pont n let (say pont O), whch n an ndrect way ntroduces tenson n the screws. Verson ME, IIT Kharagpur

4 F v F H L Fgure : Eccentrcally loaded bolted jont It s easy to note that the tenson n the screws cannot be obtaned by equatons o statcs alone. Hence, addtonal equatons must be ormed to solve or the unknowns or ths statcally ndetermnate problem. Snce there s a tendency or the bracket to rotate about pont O then, assumng the bracket to be rgd, the ollowng equatons are easly obtaned. θ tanθ y l 1 1 y l y l 3 3 where y elongaton o the -th bolt l dstance o the axs o the -th bolt rom pont O. I the bolts are made o same materal and have same dmenson, then ky where orce n the -th bolt k stness o the bolts Thus l or αl (α proportonalty constant) Verson ME, IIT Kharagpur

5 F v F H L l y L 1 Fgure 11.1.: Determnaton o orces n bolts Usng the moment balance equatons about O, the lowermost pont n the let sde, the ollowng equaton s obtaned. l FhL1+ FvL FL h 1+ FL v.e., α. The actor appears because there are two bolts l n a row. Thus the orce n the -th screw s F L F L h 1 + v Fh l +, where n total number o bolts. l n For sae desgn o the jont t s thereore requred that σ max st A where s t allowable tensle stress o the bolt. Note that F v causes also drect shear n the bolt. Its eect may be gnored or a prelmnary desgn calculaton. Verson ME, IIT Kharagpur

6 . Eccentrcally loaded rveted jont: Consder, now, a bracket, whch carres a vertcal load F. The bracket, n ths case, s connected to the wall by our rvets as shown n gure The orce, Rvet F Centrod L Fgure : Eccentrcally loaded rvet jont n addton to nducng drect shear o magntude 4 F n each rvet, causes the whole assembly to rotate. Hence addtonal shear orces appear n the rvets. Once agan, the problem s a statcally ndetermnate one and addtonal assumptons are requred. These are as ollowng: () magntude o addtonal shear orce s proportonal to the dstance between the rvet center and the centrod o the rvet assembly, whose coordnates are dened as x A x A, y A y A ( A area o the cross-secton o the -th rvet) Verson ME, IIT Kharagpur

7 () drectons o the orce s perpendcular to the lne jonng centrod o the rvet group and the rvet center and the sense s governed by the rotaton o the bracket. Notng that or dentcal rvets the centrod s the geometrc center o the rectangle, the orce n the -th rvet s αl where α proportonal constant l dstance o the -th rvet rom centrod. Takng moment about the centrod l FL FL or α l Thus, the addtonal orce s FL l. l FL F Drect Indrect Fgure : Forces on rvets due to The net orce n the -th rvet s obtaned by parallelogram law o vector addton as ' F + 4 F + 4 cosθ where θ angle between the lnes o acton o the orces shown n the gure. Verson ME, IIT Kharagpur

8 For sae desgnng we must have ' τ max s A where s s allowable shear stress o the rvet. Model questons and answers: s Q. 1. The base o a pllar crane s astened to the oundaton by n bolts equally placed on a bolt crcle o dameter d. The dameter o the pllar s D. Determne the maxmum load carred by any bolt when the crane carres a load W at a dstance L rom the center o the base. W d D L Ans. In ths case the pllar have a tendency to topple about the pont on the outer dameter lyng closest to the pont o applcaton o the load. Choose the lne jonng the center o the base and the pont o applcaton o the load as the reerence lne. In ths case y dstance o the -th bolt rom the tltng pont D d cosθ where θ angular poston o the -th bolt. Snce there are n equally spaced bolts so Verson ME, IIT Kharagpur

9 π θ+ 1 θ n Usng the same consderatons as done n secton-1, the orce n the -th bolt s ( /) W L D D d cosθ y n D d It s easy to see that y +. Hence the maxmum load occurs when θ ± π whereby D D d W L +. n D d + max Q.. A bracket s supported by means o 4 rvets o same sze as shown n gure 6. Determne the dameter o the rvet the maxmum shear stress s 140 MPa. Ans. F 1 The drect shear orce 5 kn per rvet. The maxmum ndrect shear orce occurs n the topmost or bottommost rvet and ts magntude s 0 80 F 45 kn and the drecton s horzontal Verson ME, IIT Kharagpur

10 Thereore the maxmum shear orce on the rvet assembly s 1 F F + F. Hence π 4 whch yelds d 16 mm. d ss F 80 mm 0 kn 30 mm 30 mm 30 mm Verson ME, IIT Kharagpur