Transcript Mechanical Engineering Design Chapter 8

ME 307
Machine
Design I
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 38 Slide 1
ME 307
Machine
Design I
8-1 Thread Standards and Definitions
8-2 The Mechanics of Power Screws
8-3 Strength Constraints
8-4 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
CH-8
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
LEC 38 Slide 2
ME 307
Machine
Design I
8-11
8-12
8-13
8-14
Fatigue Loading of Tension Joints
Shear Joints
Setscrews
Keys and Pins
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 38 Slide 3
ME 307
Machine
Design I
Example 5 (Example 8-4 Textbook)
(a) The grip is l = 1.50 in. From Table A31, the nut thickness is 35/64 in.
Adding two threads beyond the nut
of 2/11 in gives a bolt length of
 35 
2
L     1.50     2.229 in
 64 
 11 
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 38 Slide 4
ME 307
Machine
Design I
(a) From Table A-17, the next fraction size bolt is 2 1/4 in.
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 38 Slide 5
ME 307
Machine
Design I
LT  2d  0.25 in, L  6in
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 38 Slide 6
ME 307
Machine
Design I
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 38 Slide 7
ME 307
Machine
Design I
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 38 Slide 8
ME 307
Machine
Design I
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 38 Slide 9
ME 307
Machine
Design I
8-7 Tension Joints-The External Load
Fatigue Analysis
a) External Load
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 38 Slide 10
ME 307
Machine
Design I
8-11 Fatigue Loading of Tension Joints
Fatigue Analysis
 In general, bolted joints are subject to 0Pmax, e.g pressure vessels, flanges, pipes, …
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 38 Slide 11
ME 307
Machine
Design I
8-11 Fatigue Loading of Tension Joints

Table 8-16 lists average fatigue stress-concentration factors for the fillet under
the bolt head and also at the beginning of the threads on the bolt shank.

These are already corrected for notch sensitivity and for surface finish.

Use of rolled threads is the predominant method of thread-forming in screw
fasteners, where Table 8-16 applies.
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 38 Slide 12
ME 307
Machine
Design I

8-11 Fatigue Loading of Tension Joints
In thread-rolling the amount of cold-work and strain strengthening is unknown to
the designer; therefore, fully corrected (including Kf) axial endurance strength is
reported in Table 8-17.
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 38 Slide 13
ME 307
Machine
Design I
8-11 Fatigue Loading of Tension Joints
 Fatigue-loaded bolted joints subjected to
Fatigue action can be analyzed directly by
the methods of Chapter 7.
 Fatigue loading is the one in which the
externally applied load fluctuates between
zero and some maximum force P.
 Fmax = Fb and Fmin = Fi
 Fa = (Fmax – Fmin)/2 = (Fb – Fi)/2
 σa = Fa/At
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 38 Slide 14
ME 307
Machine
Design I
8-11 Fatigue Loading of Tension Joints
 Fmax = Fb and Fmin = Fi
 Fa = (Fmax – Fmin)/2 = (Fb – Fi)/2
 Fm = (Fmax + Fmin)/2 = (Fb + Fi)/2
 σa = Fa/At
F  Fi
Fba  b
2
F  Fi
Fbm  b
2
Dr. A. Aziz Bazoune
 ba
Fb  Fi (CP  Fi )  Fi
CP



2 At
2 At
2 At
 bm 
(8-34)
Fb  Fi (CP  Fi )  Fi
F
CP


 i
2 At
2 At
2 At At
 bm   ba   i
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
(8-35)
(8-36)
CH-8 LEC 38 Slide 15
307 the designer’s fatigue
ME On
Machine
Design I
diagram, shown in Figure 8-20,
the load line is .
 m   a  i
 High Preload is especially
important in fatigue. σi is a
constant the load line at Fi/At has
a unit slope, r = 1.0
Figure 8-20
Designer’s fatigue diagram showing a Goodman
failure locus and how a load line is used to define
failure and safety in preloaded bolted joints in
fatigue.
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 38 Slide 16
ME 307
Machine
Design I
8-11 Fatigue Loading of Tension Joints
 Next, find the strength components Sa and Sm of
the fatigue failure locus. These depend on the
failure Criteria.
 Goodman
Sa Sm

1
Se Sut
 Gerber
2
Sa  Sm 

 1
Se  Sut 
 ASME-Elliptic
Dr. A. Aziz Bazoune
(8-37)
2
(8-38)
2
 Sa   Sm 
      1
 Se   Sp 
(8-39)
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 38 Slide 17
ME 307

For simultaneous solution between Eq. (8-36), as Sa = Sm + σi and each of Eqs. (8-37) to (8-39)
Machine
gives
Design I
 Goodman
Se  Sut   i 
Sa 
Sut  Se
Sm  Sa   i
(8-40)
(8-41)
 Gerber
Sa 
1 
2
2
Sut Sut
 4Se  Se   i   Sut
 2 iSe 

2Se 
(8-42)
Sm  Sa   i
 ASME-Elliptic
Sa 

Se
2
2
S
S

S
p
p
e   i   i Se
2
2
Sp  Se

(8-43)
Sm  Sa   i
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 38 Slide 18
ME 307
Machine
Design I
 When using relations of this section, be sure to use Kf for both σa and σm.
Otherwise, the slope of the load line will not remain 1 to 1.
 The factor of safety guarding against fatigue is given by
nf 
Sa
(8-44)
a
 Applying this to the Goodman criterion, for example, with Eqs. (8-34) and
(8-40) and  i  Fi At gives
nf 
Dr. A. Aziz Bazoune

2Se Sut At  Fi
CP  Sut  Se 

Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
(8-45)
CH-8 LEC 38 Slide 19
 With no preload, C=1, Fi=0, and Eq. (8-45) becomes
ME 307
Machine
Design I
nf 0 
2SeSut At
P  Sut  Se 
(8-46)
 Preload is beneficial for resisting fatigue when nf nf 0 is greater than unity. For
Goodman, Eqs.(8-45) and (8-46) with nf nf 0  1 puts an upper bound on the
preload Fi of
Fi  1  C  Sut At
(8-47)
 If this cannot be achieved, and nf is unsatisfactory, use the Gerber or the ASMEelliptic criterion to obtain a less conservative assessment.
 After solving Eq. (8-44), you should also check the possibility of yielding, using
the proof strength
np 
Dr. A. Aziz Bazoune
Sp
m  a
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
(8-48)
CH-8 LEC 38 Slide 20
ME 307
Machine
Design I
Example 6 (Example 8-5 Textbook)
Figure 8-21
Pressure-cone frustum member model for a
cap screw. For this model the significant sizes
are
h  t2 2 t2  d
l
h  D 2 t2  d
D1  dw  l tan   1.5d  0.577l
D2  dw  1.5d
Where l = effective grip. The solutions are for
=30o and dw=1.5d.
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 38 Slide 21
ME 307
Machine
Design I
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 38 Slide 22
ME 307
Machine
Design I
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 38 Slide 23
ME 307
Machine
Design I
Figure 8-22
Designer’s fatigue diagram for
preloaded bolts, dr showing the
modified Goodman locus, the
Gerber locus and the Langer proof
strength locus, with an exploded
view of the area of interest, The
strengths used are
Sp= 85 kpsi, Se= 18.6 kpsi, and
Sut=120 kpsi. The coordinates are
A: σi=63.72 kpsi
B: σa=3.1 kpsi, σm=66.82 kpsi
C: Sa=7.55 kpsi, Sm=71.29 kpsi
D: Sa=10.64 kpsi, Sm=74.35 kpsi
E: Sa=11.32 kpsi, Sm=75.04 kpsi
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 38 Slide 24
ME 307
Machine
Design I
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 38 Slide 25
ME 307
Machine
Design I
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 38 Slide 26
ME 307
Machine
Design I
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 38 Slide 27