1. Screws, Fasteners, and the Design of Nonpermanent Joints

2. Chapter Outline
8-1 Thread Standards and Definitions 8-2 The Mechanics of Power Screws 8-3 Strength Constraints Joints-Fasteners Stiffness
8-5 Joints-Member Stiffness 8-6 Bolt Strength 8-7 Tension Joints-The External Load 8-8 Relating Bolt Torque to Bolt Tension
8-9 Statically Loaded Tension Joint with Preload
8-10 Gasketed Joints
8-11 Fatigue Loading of Tension Joints
8-12 Shear Joints
8-13 Setscrews
8-14 Keys and Pins
8-15 Stochastic Considerations

3. Announcements HW #5 Ch 18, on WebCT
Due Date for HW #5 is Mon. DEC. 31, 2007
Quiz on Ch. 18, Mon. DEC. 31, 2007

4. LECTURE 33
8-1 Thread Standards and Definitions

5. Introduction
The fundamental operation in manufacture is the creation of shape - this includes assembly, where a number of components are fastened or joined together either permanently by welding (Ch9) for example or detachably (nonpermanent) by screws, nuts and bolts and so on. Since there is such a variety of shapes in engineering to be assembled, it is hardly surprising that there is more variety in demountable fasteners than in any other machine element. Fasteners based upon screw threads are the most common, so it is important that their performance is understood, and the limitations of the fastened assemblies appreciated.

6. Introduction
There are two distinct uses for screw threads and they usually demand different behavior from the threads :
a   power screw such as a lathe leadscrew or the screw in a car lifting jack which transforms rotary motion into substantial linear motion (or vice versa in certain applications), and

7. Fasteners
a   Threaded Fastener similar to a nut and bolt which joins a number of components together again by transforming rotary motion into linear motion, though in this case the translation is small.

8. Thread Profiles
(c)
Thread profiles.
a) Square (b) ACME; (c) UN, ISO

9. Thread Profile Parameters
Figure 8-1
Terminology of screw threads. Sharp Vee Threads shown for clarity; the crests and roots are actually flattened or rounded during the forming operation
Lead=L=n p

10. Threads
(a) Single (STANDARD)-, (b) double-, and (c) triple threaded screws.
Text Reference: Figure 15.2, page 667

11. Thread Systems
A thread 'system' is a set of basic thread proportions which is scaled to different screw sizes to define the thread geometry. Whitworth, Sellers, British Standard Pipe (BSP) are just three of the many systems which proliferated before the adoption of the
ISO Metric thread system.
The American National (Unified) Thread standards is used mainly in the US.
Square and ACME

12. Thread geometry
The basic profile of ISO Metric threads is built up from contiguous equiangular triangles of height  H disposed symmetrically about a pitch line which becomes the   pitch cylinder of diameter   d2 when the profile is rotated about the axis to form the thread. The distance between adjacent triangles - the pitch - is   p = 2 H /√3. The tips of the triangles are truncated by h/8 to form the major diameter ( size ) d of the thread, and the bases are truncated by h/4 to form the minor diameter  d1 . It follows that d1 =  d - 5 h/4 = d p. This leads to the rule of thumb for suitable tapping size

13. Thread Profile For Metric System (M, MJ)
major
H= 0.5(3)1/2 p
pitch
US N= # threads/in
minor
a ISO 68= a American National (Unified) thread standard= 60°

14. Tensile stress area At =p/4(dm+dr)/2 (see footnote T.8.1)
Thread Standards
ISO Metric thread system: Table 8-1 Major diameter (mm),
2a= 60° Standard thread is RH
Specifications: e.g.: M12x1.75 or
M = Basic Metric, J = round root; 12 = nominal major diameter (mm); 1.75 = pitch (mm)
Tensile stress area At =p/4(dm+dr)/2 (see footnote T.8.1)
MJ12x1.75

16. Thread Standards
The American National (Unified) Thread standards is used mainly in the US: Table-8-2 (Size designation) use d
UN=regular thread, UNR=round root (use root radius)
Specifications: 5/8”-18 UN, UNC, UNF
UNR, UNRC, UNRF
5/8”=d 18 = N (thread size)
UN = Unified, F=fine, C=Coarse, R =Round Root

17. Thread Standards
Square (a) and The ACME Threads (b)-used mainly in power screws Table 8.3 gives preferred pitches for ACME threads

18. Power screw thread forms. [Note: All threads shown are external (i. e
Power screw thread forms. [Note: All threads shown are external (i.e., on the screw, not on the nut); dm is the mean diameter of the thread contact and is approximately equal to (d + dr)/2.]

20. ACME Thread Profile
Figure Details of ACME thread profile. (All dimensions are in inches.)
Text Reference: Figure 15.5, page 670

21. ACME Thread PropertiesN
Crest diameters, threads per inch, and stresses for Acme thread.

22. Mechanics of Power Screws
A power screw is a device that is common to tools or machinery that are used to change angular motion into translation. It is also capable of developing a large amount of mechanical advantage. Familiar applications include clamps or vises, presses, lathes lead screws, and jacks.
The joyce warm-gear screw jack

23. Mechanics of Power Screws
Weight supported by three screw jacks. In each screw jack, only the shaded member rotates.

24. Mechanics of Power Screws
Example of catalogue:

25. Vehicle Screw Jack

27. Power Screw with collar
Different types of collars

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29. CH LEC 35 Slide 29

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31. CH LEC 35 Slide 31

32. Chapter Outline
8-1 Thread Standards and Definitions 8-2 The Mechanics of Power Screws 8-3 Strength Constraints Joints-Fasteners Stiffness
8-5 Joints-Member Stiffness 8-6 Bolt Strength 8-7 Tension Joints-The External Load 8-8 Relating Bolt Torque to Bolt Tension
8-9 Statically Loaded Tension Joint with Preload
8-10 Gasketed Joints
8-11 Fatigue Loading of Tension Joints
8-12 Shear Joints
8-13 Setscrews
8-14 Keys and Pins
8-15 Stochastic Considerations
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33. LECTURE 35 8-3 Strength Constraints 8-4 Joints-Fasteners Stiffness
8-5 Joints-Member Stiffness 8-6 Bolt Strength
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34. Example-3
A single-threaded 20 mm power screw is 20 mm in diameter with a pitch of 5 mm. A vertical load on the screw reaches a maximum of 3 kN. The coefficients of friction are 0.06 for the collar and 0.09 for the threads. The frictional diameter of the collar is 45 mm. Find the overall efficiency and the torque to "raise" and "lower" the load.
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35. Example-3
Given
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36. Example-3 (Cont.’d)
Solution
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37. Example-2 (Cont.’d)
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38. Power Screws Stress Analysis
The following stresses should be checked on both the nut and the screw:
Shearing stress in screw body.
Axial stress in screw body
(8-7)
(8-8)
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39. Power Screws Stress Analysis
Thread bearing stress
(8-10)
where nt is the number of engaged threads.
Figure 8-8
Geometry of square thread useful in finding bending and transverse shear stresses at the thread root
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40. Power Screws Stress Analysis
Thread bending stress
The bending stress at the root of the thread is given by
(8-11)
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41. Power Screws Stress Analysis
Transverse shear stress at the center of the thread root
(8-12)
Notice that the transverse shear stress at the top of the root is zero
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42. Power Screws Stress Analysis
The state of stress at top of root “plane” is
Von-Mises Stress at top of root plane is calculated using Eq. (6-14) of Sec. (6-5) and failure criteria applied (see example 8-1).
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43. Power Screws Stress Analysis
The engaged threads cannot share the load equally. Some experiments show that
the first engaged thread carries 0.38 of the load
the second engaged thread carries 0.25 of the load
the third engaged thread carries 0.18 of the load
the seventh engaged thread is free of load
In estimating thread stresses by the equations above, substituting nt to 1 will give the largest level of stresses in the thread-nut combination
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44. Power Screws Buckling
Assuming that the column (screw) is a Johnson column
where
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45. Example-3 (Example 8-1 in Textbook)
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47. Example-3 (Example 8-1 in Textbook)
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48. Example-3 (Example 8-1 in Textbook)
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49. Example-3 (Example 8-1 in Textbook)
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50. CH LEC 35 Slide 50

51. Types of fasteners
Three types of threaded fastener: (a) Screw (b)Bolt and nut; (c) Stud and nut, (d) Threaded rod and nuts
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52. Threaded Fasteners Purpose: Parts: A- BOLTS:
to clamp two or more members together.
Parts:
(1) Head (Square or Hexagonal)
(2) Washer (dw=1.5d)
(3) Threaded part
(4) Unthreaded part
Dimensions of square and hexagonal bolts are given in TABLE A-29
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53. Threaded Fasteners D is the nominal diameter
The diameter of the washer face is the same as the width across the flats of the hexagon. The thread length (LT) is :
D is the nominal diameter
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54. Threaded Fasteners B- NUTS: Same material as that of a screw
Table A-31 gives dimensions of Hexagonal nuts
Good Practice:
Never re-use nuts;
Tightening should be done such that 1 or 2 threads come out of the nut;
Washers should always be used under bolt head to prevent burr stress concentration.
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55. Threaded Fasteners Common Cap screws
Used for clamping members same as bolt except that 1 member should be threaded.
The head of a hexagon-head cup screw H cap is slightly thinner than that of a hexagonal head bot H bolt .
Figure 8-10
Typical cap-screw heads: (a) fillister head; (b) flat head; (c) hexagonal socket head
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56. Figure 8.11: Types of heads used in machine screws
Threaded Fasteners
Figure 8.11: Types of heads used in machine screws
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57. Joints: Fastener Stiffness
In joint under tension the members are under compression and the bolt under tension: kb = equivalent spring constant of bolt composed of threaded (kt) and unthreaded (kd) parts acting as springs in series km
From Ch 5
For short bolts kb= kt
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58. Joints: Fastener Stiffness
To find different parameters use table 8-7
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59. Joints: Member Stiffness
Members act as springs under compression
Frustum m
Compression stress distribution from experimental data
Equivalent spring constant km
Integrating from 0 to l
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60. Joints: Member Stiffness
For Members made of Aluminum, hardened steel and cast iron 25 <a< 33°
For a= 30°
If Members have same E with symmetrical frusta (l= 2t) they act as 2 identical springs km = k/ For a= 30° and D = dw = 1.5d
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61. Joints: Member Stiffness
Other equations
From Finite element analysis results, A and B from table 8.8
for standard washer
Faces and members
Of same material
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62. Bolt Strength
Bolt strength is specified by minimum proof strength Sp or minimum proof load, Fp and minimum tensile strength, Sut
The SAE specifications are given in
Table 8-9 bolt grades are numbered
according to minimum tensile strength
The ASTM Specs for steel bolts (structural) are in Table 8-10.
Metric Specs are in table 8-11.
proof strength
If Sp not available use Sp =0.85 Sy
Fp = At Sp
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63. Tension Joints Static Analysis a) External Load
External Load P is shared by bolt and members
Equilibrium
Compatibility
Relation P-d
(4)
C is the stiffness constant of the joint,
For typical values of C see table 8-12
Most of external Load P is taken by members
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64. Tension Joints Static Analysis
b) Resultant Bolt & member loads: Fb& Fm
Fm<0
Fi is preload; high preload is desirable in tension connections
c) Torque required to give preload Fi
Fi = 0.75 Fp For re-use
Fi = 0.90 Fp For permanent joint
K is torque coefficient
K values are given in table 8-15 (Average Value = 0.2)
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65. Tension Joints Static Analysis d) Joint Safety
Failure of Joint occurs when:
1) Bolt yields
or 2) Joint separates
Let P0 be external load causing separation Fm=0
0 = (1-C) P0-Fi
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66. Tension Joints 3 6 Static Analysis e) Gasketed Joints
If a full gasket is present in joint
The gasket pressure p is:
To maintain uniformity of pressure adjacent bolts should not be placed more than 6 nominal diameters apart on bolt circle. To maintain wrench clearance bolts should be placed at least 3 d apart
0 = (1-C) P0-Fi 3 6
Db is the diameter of the bolt circle
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67. Tension Joints Fatigue AnalysisPb Fi Fm Fa
Fmax=Fb
Fatigue Analysis
In general, bolted joints are subject to 0-Pmax,e.g pressure vessels, flanges, pipes, …
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68. Tension Joints Fatigue Analysis
High Preload is especially important in fatigue. si is a constant the load line at Fi/At has a unit slope, r=1.0
To find sa use Goodman
or Gerber Eq. 8.42
or ASME-elliptic. Eq. 8.43
Safety factor (using Goodman)
for conservative assessment of n:
Check for yielding also using proof strength: Eq. 8.48
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69. Tension Joints Fatigue Analysis
In case of cut threads use the method described in chapter 7 with Kf values of table 8-16.
The fully corrected endurance limit for rolled threads is given in table 8-17
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70. Fig. 8.19
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71. Fig. 8.21
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72. Failure Modes of Riveted Fasteners
Under Shear
Failure modes due to shear loading of riveted fasteners. (a) Bending of member; (b) shear of rivet; (c) tensile failure of member; (e) bearing of rivet on member or bearing of member on rivet.
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73. Shear Joints
Centroid of pins, rivets or bolts
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74. Shear Joints Shear of pins, rivets bolts due to eccentric loading
V & M statically indeterminate problem
4 steps (assuming same diameter bolts, load shared equally)
Direct load F’
Primary Shear
Centroid
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75. Shear Joints Shear of pins, rivets bolts due to eccentric loading
Moment load M
Secondary Load
The force taken by each bolt is proportional to its radial distance from the centroid
Add Vectorially the direct and moment loads
If bolts are not same size only bolts with max. R should be considered
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76. See Examples 8.6 and 8.7
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77. Fig. 8.26
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78. Problem 8-50
½ in-13 UNC SAE 5
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79. Problem 8-50 Direct load F’ Centroid is at O Secondary Load
4)Add Vectorially the direct and moment loads
Is As=Ad?
LT=2d+1/4=1.25”
Hnut+2p+3/8=7/16+2(1/13)+3/8=0.97”<1.25”
So As=At = in2 and tB=12.7 Kpsi; n=4.2
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80. Problem 8-50
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81. Problem 8-50
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