ME 307 Machine Design I. Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints

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1 Dr.. zz Bazoune Chapter 8: Screws, Fasteners and the Desgn of Nonpermanent Jonts

2 Dr.. zz Bazoune Chapter 8: Screws, Fasteners and the Desgn of Nonpermanent Jonts CH-8 LEC 35 Slde 2

3 Dr.. zz Bazoune Chapter 8: Screws, Fasteners and the Desgn of Nonpermanent Jonts CH-8 LEC 35 Slde 3

4 Dr.. zz Bazoune Chapter 8: Screws, Fasteners and the Desgn of Nonpermanent Jonts CH-8 LEC 35 Slde 4

5 Dr.. zz Bazoune Chapter 8: Screws, Fasteners and the Desgn of Nonpermanent Jonts CH-8 LEC 35 Slde 5

6 8-1 Thread Standards and Defntons 8-2 The Mechancs of Power Screws 8-3 Strength Constrants 8-4 Jonts-Fasteners Stffness 8-5 Jonts-Member Stffness 8-6 Bolt Strength 8-7 Tenson Jonts-The External Load 8-8 Relatng Bolt Torque to Bolt Tenson 8-9 Statcally Loaded Tenson Jont wth Preload 8-10 Gasketed Jonts 8-11 Fatgue Loadng of Tenson Jonts 8-12 Shear Jonts 8-13 Setscrews 8-14 Keys and Pns 8-15 Stochastc Consderatons Dr.. zz Bazoune Chapter 8: Screws, Fasteners and the Desgn of Nonpermanent Jonts CH-8 LEC 35 Slde 6

7 8-3 Strength Constrants 8-4 Jonts-Fasteners Stffness 8-5 Jonts-Member Stffness 8-6 Bolt Strength Dr.. zz Bazoune Chapter 8: Screws, Fasteners and the Desgn of Nonpermanent Jonts CH-8 LEC 35 Slde 7

8 Example-3 sngle-threaded 20 mm power screw s 20 mm n dameter wth a ptch of 5 mm. vertcal load on the screw reaches a maxmum of 3 kn. The coeffcents of frcton are 0.06 for the collar and 0.09for the threads. The frctonal dameter of the collar s 45 mm. Fnd the overall effcency and the torque to "rase" and "lower" the load. Dr.. zz Bazoune Chapter 8: Screws, Fasteners and the Desgn of Nonpermanent Jonts CH-8 LEC 35 Slde 8

9 Example-3 Gven Dr.. zz Bazoune Chapter 8: Screws, Fasteners and the Desgn of Nonpermanent Jonts CH-8 LEC 35 Slde 9

10 Example-3 (Cont. d) Soluton Dr.. zz Bazoune Chapter 8: Screws, Fasteners and the Desgn of Nonpermanent Jonts CH-8 LEC 35 Slde 10

11 Example-2 (Cont. d) Dr.. zz Bazoune Chapter 8: Screws, Fasteners and the Desgn of Nonpermanent Jonts CH-8 LEC 35 Slde 11

12 Power Screws Stress nalyss The followng stresses should be checked on both the nut and the screw: 1. Shearng stress n screw body. 2. xal stress n screw body 16T τ (8-7) 3 πd r F σ 4 F πd 2 r (8-8) Dr.. zz Bazoune Chapter 8: Screws, Fasteners and the Desgn of Nonpermanent Jonts CH-8 LEC 35 Slde 12

13 Power Screws Stress nalyss 3. Thread bearng stress σ F 2F B πd n p/2 πd n p (8-10) m t m t where n t s the number of engaged threads. Fgure 8-8 Geometry of square thread useful n fndng bendng and transverse shear stresses at the thread root Dr.. zz Bazoune Chapter 8: Screws, Fasteners and the Desgn of Nonpermanent Jonts CH-8 LEC 35 Slde 13

14 Power Screws Stress nalyss 4. Thread bendng stress The bendng stress at the root of the thread s gven by I C ( 112)( πdrnt)( p2) ( P ) π dnp r t / σ Fp M 4 b M Fp 24 6F 2 Ic 4 πdr np t πdr np t (8-11) Dr.. zz Bazoune Chapter 8: Screws, Fasteners and the Desgn of Nonpermanent Jonts CH-8 LEC 35 Slde 14

15 Power Screws Stress nalyss 5. Transverse shear stress at the center of the thread root 3V 3 F 3F τ (8-12) 2 2 πd n p 2 πd n p m t m t Notce that the transverse shear stress at the top of the root s zero τ 0 Dr.. zz Bazoune Chapter 8: Screws, Fasteners and the Desgn of Nonpermanent Jonts CH-8 LEC 35 Slde 15

16 Power Screws Stress nalyss The state of stress at top of root plane s 6F σx τxy 0 πd np σ y r t 0 τ yz 16 T π d 3 r Von-Mses Stress at top of root plane s calculated usng Eq. (6-14) of Sec. (6-5) and falure crtera appled (see example 8-1). 4 F σ z τ 0 2 zx π dr 1 σ ' σ σ 2 σ σ 2 σ σ 2 6 τ 2 τ 2 τ 2 { ( } 12 ) ( ) ( ) ( ) x y y z z x xy yz zx 2 { } Dr.. zz Bazoune Chapter 8: Screws, Fasteners and the Desgn of Nonpermanent Jonts CH-8 LEC 35 Slde 16

17 Power Screws Stress nalyss The engaged threads cannot share the load equally. Some experments show that the frst engaged thread carres 0.38 of the load the second engaged thread carres 0.25 of the load the thrd engaged thread carres 0.18 of the load the seventh engaged thread s free of load In estmatng thread stresses by the equatons above, substtutng tng n t to 1 wll gve the largest level of stresses n the thread-nut combnaton Dr.. zz Bazoune Chapter 8: Screws, Fasteners and the Desgn of Nonpermanent Jonts CH-8 LEC 35 Slde 17

18 Power Screws Bucklng ssumng that the column (screw) s a Johnson column F S y l 1 S y crt 2π k CE where l L L' ' 2 Dr.. zz Bazoune Chapter 8: Screws, Fasteners and the Desgn of Nonpermanent Jonts CH-8 LEC 35 Slde 18

19 Example-3 (Example 8-1 n Textbook) Dr.. zz Bazoune Chapter 8: Screws, Fasteners and the Desgn of Nonpermanent Jonts CH-8 LEC 35 Slde 19

20 Dr.. zz Bazoune Chapter 8: Screws, Fasteners and the Desgn of Nonpermanent Jonts CH-8 LEC 35 Slde 20

21 Example-3 (Example 8-1 n Textbook) Dr.. zz Bazoune Chapter 8: Screws, Fasteners and the Desgn of Nonpermanent Jonts CH-8 LEC 35 Slde 21

22 Example-3 (Example 8-1 n Textbook) Dr.. zz Bazoune Chapter 8: Screws, Fasteners and the Desgn of Nonpermanent Jonts CH-8 LEC 35 Slde 22

23 Example-3 (Example 8-1 n Textbook) Dr.. zz Bazoune Chapter 8: Screws, Fasteners and the Desgn of Nonpermanent Jonts CH-8 LEC 35 Slde 23

24 Dr.. zz Bazoune Chapter 8: Screws, Fasteners and the Desgn of Nonpermanent Jonts CH-8 LEC 35 Slde 24

25 Types of fasteners Three types of threaded fastener: (a) Screw (b)bolt and nut; (c) Stud and nut, (d) Threaded rod and nuts Dr.. zz Bazoune Chapter 8: Screws, Fasteners and the Desgn of Nonpermanent Jonts CH-8 LEC 35 Slde 25

26 Threaded Fasteners - BOLTS: Purpose: to clamp two or more members together. Parts: (1) Head (Square or Hexagonal) (2) Washer (d w 1.5d) (3) Threaded part (4) Unthreaded part Dmensons of square and hexagonal bolts are gven n TBLE -29 Dr.. zz Bazoune Chapter 8: Screws, Fasteners and the Desgn of Nonpermanent Jonts CH-8 LEC 35 Slde 26

27 Threaded Fasteners The dameter of the washer face s the same as the wdth across the flats of the hexagon. The thread length (L T ) s : Englsh 1 2 n L 6 n D 4 L T 1 2D n L> 6 n 2 Metrc (n mm) m) 2D 6 L 125 D 48 LT 2D < L 200 2D2525 L > 200 D s the nomnal dameter Dr.. zz Bazoune Chapter 8: Screws, Fasteners and the Desgn of Nonpermanent Jonts CH-8 LEC 35 Slde 27

28 Threaded Fasteners B- NUTS NUTS: Same materal as that of a screw Table -31 gves dmensons of Hexagonal nuts Good Practce: 1. Never re-use nuts; 2. Tghtenng should be done such that 1 or 2 threads come out of the nut; 3. Washers should always be used under bolt head to prevent burr stress concentraton. Dr.. zz Bazoune Chapter 8: Screws, Fasteners and the Desgn of Nonpermanent Jonts CH-8 LEC 35 Slde 28

29 Threaded Fasteners Common Cap screws Used for clampng members same as bolt except that 1 member should be threaded. The head of a hexagon-head cup screw H cap s slghtly thnner than that of a hexagonal head bot H bolt. Fgure 8-10 Typcal cap-screw heads: (a) fllster head; (b) flat head; (c) hexagonal socket head Dr.. zz Bazoune Chapter 8: Screws, Fasteners and the Desgn of Nonpermanent Jonts CH-8 LEC 35 Slde 29

30 Threaded Fasteners Fgure 8.11: Types of heads used n machne screws Dr.. zz Bazoune Chapter 8: Screws, Fasteners and the Desgn of Nonpermanent Jonts CH-8 LEC 35 Slde 30

31 Jonts: Fastener Stffness In jont under tenson the members are under compresson and the bolt under tenson: k b equvalent sprng constant of bolt composed of threaded (k t ) and unthreaded (k d ) parts actng as sprngs n seres 1 k k k k b b d b 1 k d 1 k k d k t k k d l d E Dr.. zz Bazoune d d l t d t t k t t E l t E l Chapter 8: Screws, Fasteners and the Desgn of Nonpermanent Jonts t d t For short bolts k b k t CH-8 LEC 35 Slde 31 k m

32 Jonts: Fastener Stffness To fnd dfferent parameters use table 8-7 Dr.. zz Bazoune Chapter 8: Screws, Fasteners and the Desgn of Nonpermanent Jonts CH-8 LEC 35 Slde 32

33 Jonts: Member Stffness Members act as sprngs under compresson Frustum m Compresson stress dstrbuton from expermental data Pdx Equvalent sprng constant k m d δ E Integratng from 0 to l... k m k1 k 2 k 3 k P (2t tan α D d )( D δ ln πed tan α (2t tan α D d )( D Dr.. zz Bazoune k P δ (2t (2t πed tan α tan α Chapter 8: Screws, Fasteners and the Desgn of Nonpermanent Jonts ln tan α D d )( D D d )( D d ) d ) CH-8 LEC 35 Slde 33 d ) d )

34 Jonts: Member Stffness For Members made of lumnum, hardened steel and cast ron 25 <a< 33 For a 30 k ln πEd (1.155t D d )( D d ) ( t D d )( D d ) (8 20) If Members have same E wth symmetrcal frusta (l 2t) they act as 2 dentcal sprngs k m k/2 For a 30 and Dd w 15d 1.5d π Ed k m ( l 0.5 d 2 ln l 2.5 d ( ) ln (8 22 ) Dr.. zz Bazoune Chapter 8: Screws, Fasteners and the Desgn of Nonpermanent Jonts CH-8 LEC 35 Slde 34

35 Jonts: Member Stffness Other equatons From Fnte element analyss results, and B from table 8.8 k m for standard washer Faces and members Ed exp( Bd / l ) Of same materal (8 23 ) Dr.. zz Bazoune Chapter 8: Screws, Fasteners and the Desgn of Nonpermanent Jonts CH-8 LEC 35 Slde 35

36 Bolt Strength Bolt strength s specfed by mnmum proof strength S p or mnmum proof load, F p and mnmum tensle strength, Sut The SE specfcatons are gven n Table 8-9 bolt grades are numbered accordng to mnmum tensle strength The STM Specs for steel bolts (structural) are n Table Metrc Specs are n table proof strength If S p not avalable use S p 0.85 S y F p t S p Dr.. zz Bazoune Chapter 8: Screws, Fasteners and the Desgn of Nonpermanent Jonts CH-8 LEC 35 Slde 36

37 Tenson Jonts Statc nalyss a) External Load External Load P s shared by bolt and members Equlbrum Compatblty P P δ δ b b P δ m m ( 1 ) (2) k b P b P k b k m b Pm Pb Pb km δ & Pm ( 3 ) k b km kb k C b k b k C s the stffness constant of the jont, For typcal values of C see table 8-12 Most of external Load P s taken by members Relaton P-δ P m k k m k m m P CP ( 1 C ) P (4) Dr.. zz Bazoune Chapter 8: Screws, Fasteners and the Desgn of Nonpermanent Jonts CH-8 LEC 35 Slde 37

38 Tenson Jonts Statc nalyss b) Resultant Bolt & member loads: F b &F m F b Pb F CP F F m <0 F P F (1 C ) P F m m F s preload; hgh preload s desrable n tenson connectons c) Torque requred to gve preload F F d m l πfd m sec α F f cd c T 2 πd fl m sec α 2 l Fd m tan λ f sec α F f cd c tan λ T πd m 2 l f tan λ sec α 2 d c ( d d w ) / 2 ( d 1.5d ) / d [ ] d m tan λ f sec α T f c F d 2d l f tan λ sec α d m tan λ f sec α Dr. K. zz Bazoune f T KF d 2d l f tan λ sec α F 0.75 F p For re-use F 0.90 F p For permanent jont Chapter 8: Screws, Fasteners cand the Desgn of Nonpermanent Jonts K s torque coeffcent K values are gven n table 8-15 (verage Value 0.2) CH-8 LEC 35 Slde 38

39 Tenson Jonts σ Statc nalyss d) Jont Safety Falure of Jont occurs when: 1) Bolt yelds F CP b b t t Falure starts C ( np ) t F Load factor For N t Bolts Dr.. zz Bazoune S F σ P t b S P S P t F n CP S P t F n CP / N or 2) Jont separates Let P 0 be external load causng separaton F m 0 F F m m n For (1 C ) P 0 P F ( 1 C ) bolts Chapter 8: Screws, Fasteners and the Desgn of Nonpermanent Jonts n n F P F / N 0(1C) (1-C) P 0 -F ( 1 C ) CH-8 LEC 35 Slde 39

40 Tenson Jonts Statc nalyss e) Gasketed Jonts If a full gasket s present n jont The gasket pressure p s: Fm p To unformty pressure g / N mantan of e adjacent bolts should not be placed more than 6 nomnal Wth load factor n dameters apart on bolt crcle. To mantan wrench F (1 C ) np F clearance bolts should be placed 0 at (1-C) least P3 0 -F d apart m p [ F np (1 C )] N πd g b 3 Nd 6 D b s the dameter of the bolt crcle Dr.. zz Bazoune Chapter 8: Screws, Fasteners and the Desgn of Nonpermanent Jonts CH-8 LEC 35 Slde 40

41 Tenson Jonts Fatgue nalyss F max Fb F a F a F F m P b F F ba bm In general, bolted jonts are subject to 0-P max, e.g pressure vessels, flanges, ppes, F b F F 2 F 2 σ ba Fb F 2 t ( CP F ) F 2 b b bm ba 2 t 2 t 2 t t Dr.. zz Bazoune t F F ( CP F ) F CP F σ σ σ CP 2 Chapter 8: Screws, Fasteners and the Desgn of Nonpermanent Jonts t CH-8 LEC 35 Slde 41

42 Tenson Jonts Fatgue nalyss Hgh Preload s especally mportant n fatgue. σ s a constant the load lne at F / t has a unt slope, r1.0 Dr.. zz Bazoune a e ut t f σ CP( Sut Se) Chapter 8: Screws, Fasteners and the Desgn of Nonpermanent Jonts Safety factor (usng Goodman) To fnd s a use Goodman S S for conservatve a m 1 assessment of n: S e S u S a Se( Sut σ ) S S ut or Gerber Eq or SME-ellptc. Eq S 2S ( S F ) n wth σ Check for yeldng also usng proof strength: Eq e F t CH-8 LEC 35 Slde 42

43 Tenson Jonts Ft Fatgue nalyss In case of cut threads use the method descrbed n chapter 7 wth K f values of table The fully corrected endurance lmt for rolled threads s gven n table 8-17 Dr.. zz Bazoune Chapter 8: Screws, Fasteners and the Desgn of Nonpermanent Jonts CH-8 LEC 35 Slde 43

44 Fg Dr.. zz Bazoune Chapter 8: Screws, Fasteners and the Desgn of Nonpermanent Jonts CH-8 LEC 35 Slde 44

45 Fg Dr.. zz Bazoune Chapter 8: Screws, Fasteners and the Desgn of Nonpermanent Jonts CH-8 LEC 35 Slde 45

46 Falure Modes of Rveted Fasteners Under Shear Falure modes due to shear loadng of rveted fasteners. (a) Bendng of member; (b) shear of rvet; (c) tensle falure of member; (e) bearng of rvet on member or bearng of member on rvet. Dr.. zz Bazoune Chapter 8: Screws, Fasteners and the Desgn of Nonpermanent Jonts CH-8 LEC 35 Slde 46

47 Shear Jonts Centrod of pns, rvets or bolts x x x x x x Σ x x x x x x x Σ Σ ' Σ y y y y y y y Σ Σ ' Dr.. zz Bazoune Chapter 8: Screws, Fasteners and the Desgn of Nonpermanent Jonts CH-8 LEC 35 Slde 47

48 Shear Jonts Shear of pns, rvets bolts due to eccentrc c loadng V & M statcally ndetermnate problem 4 steps (assumng same dameter bolts, load shared equally) 1) Drect load F Prmary Shear F ' V N 2) Centrod x ' y ' Σ x Σ Σ y Σ Dr.. zz Bazoune Chapter 8: Screws, Fasteners and the Desgn of Nonpermanent Jonts CH-8 LEC 35 Slde 48

49 Shear Jonts Shear of pns, rvets bolts due to eccentrc loadng 3) Moment load M Secondary Load M F " r 1 F" r FB " rb FC " rc The force taken by each bolt s proportonal to ts radal dstance from the centrod F r F " F r B B " F r M C C " 1 " n n 2 2 r 2 rb rc 4) dd Vectorally the drect and moment loads If bolts are not same sze only bolts wth max. R should be consdered Dr.. zz Bazoune r D F r D D D "... Chapter 8: Screws, Fasteners and the Desgn of Nonpermanent Jonts CH-8 LEC 35 Slde 49

50 See Examples 8.6 and 8.7 Dr.. zz Bazoune Chapter 8: Screws, Fasteners and the Desgn of Nonpermanent Jonts CH-8 LEC 35 Slde 50

51 Problem 8-50 ½n13 n-13 UNC SE 5 Dr.. zz Bazoune Chapter 8: Screws, Fasteners and the Desgn of Nonpermanent Jonts CH-8 LEC 35 Slde 51

52 Problem ) Drect load F V F ' N 4)dd Vectorally the drect and moment loads F lb 150 lb 2 F B lb 2) Centrod s at O 3) Secondary Load M 1 r " F B 2 r r F " 2 B Dr.. zz Bazoune 4950 x lb Is sd? L T 2d1/41.25 H nut 2p3/87/162(1/13)3/80.97 <1.25 So st n 2 and t B 12.7 Kps; Chapter 8: Screws, Fasteners and the Desgn of Nonpermanent Jonts CH-8 LEC 35 Slde 52 n4.2

53 Problem 8-50 Dr.. zz Bazoune Chapter 8: Screws, Fasteners and the Desgn of Nonpermanent Jonts CH-8 LEC 35 Slde 53

54 Problem 8-50 Dr.. zz Bazoune Chapter 8: Screws, Fasteners and the Desgn of Nonpermanent Jonts CH-8 LEC 35 Slde 54

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