ME 307 Machine Design I ME 307 Machine Design I CH-8 LEC 38 Slide 1 Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints

ME 307 Machine Design I

CH-8 LEC 38 Slide 1Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints


8-1 8-1 Thread Standards and DefinitionsThread Standards and Definitions8-28-2 The Mechanics of Power ScrewsThe Mechanics of Power Screws8-38-3 Strength Constraints Strength Constraints 8-48-4 Joints-Fasteners StiffnessJoints-Fasteners Stiffness8-58-5 Joints-Member Stiffness Joints-Member Stiffness 8-68-6 Bolt Strength Bolt Strength 8-78-7 Tension Joints-The External LoadTension Joints-The External Load8-88-8 Relating Bolt Torque to Bolt TensionRelating Bolt Torque to Bolt Tension8-98-9 Statically Loaded Tension Joint with PreloadStatically Loaded Tension Joint with Preload8-108-10 Gasketed JointsGasketed Joints8-118-11 Fatigue Loading of Tension JointsFatigue Loading of Tension Joints8-128-12 Shear JointsShear Joints8-138-13 SetscrewsSetscrews8-148-14 Keys and PinsKeys and Pins8-158-15 Stochastic ConsiderationsStochastic Considerations



8-118-11 Fatigue Loading of Tension JointsFatigue Loading of Tension Joints8-128-12 Shear JointsShear Joints8-138-13 SetscrewsSetscrews8-148-14 Keys and PinsKeys and Pins


ME 307 Machine Design I Example 5 (Example 8-4 Textbook)Example 5 (Example 8-4 Textbook)

(a) The grip is l = 1.50 in. From Table A-31, the nut thickness is 35/64 in.

Adding two threads beyond the nut of 2/11 in gives a bolt length of 35 2

1.50 2.229 in64 11

L



(a)From Table A-17, the next fraction size bolt is 2 1/4 in.



2 0.25 in, L 6inTL d









Fatigue Analysisa) External Load

8-78-7 Tension Joints-The External Tension Joints-The External LoadLoad


ME 307 Machine Design I 8-118-11 Fatigue Loading of Tension Joints Fatigue Loading of Tension Joints


Fatigue Analysis

In general, bolted joints are subject to 0-Pmax, e.g pressure vessels, flanges, pipes, …



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.



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.


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




2

2

b iba

b ibm

F FF

F FF

( )2 2 2

( )2 2 2

b i i iba

t t t

b i i i ibm

t t t t

bm ba i

F F CP F F CPA A A

F F CP F F FCPA A A A

Fmax = Fb and Fmin = Fi

Fa = (Fmax – Fmin)/2 = (Fb – Fi)/2

Fm = (Fmax + Fmin)/2 = (Fb + Fi)/2

σa = Fa/At

(8-34)

(8-35)

(8-36)



On the designer’s fatigue diagram, shown in Figure 8-20, the load line is .

High Preload is especially

important in fatigue. σi is a constant the load line at Fi/At has a unit slope, r = 1.0

m a i

Figure 8-20Designer’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.



Next, find the strength components Sa and

Sm of the fatigue failure locus. These depend on the failure Criteria.

GoodmanGoodman

1a m

e ut

S SS S

GerberGerber 2

1a m

e ut

S SS S

ASME-EllipticASME-Elliptic 22

1a m

e p

S SS S

(8-39)

(8-38)

(8-37)



GoodmanGoodman

e ut ia

ut e

m a i

S SS

S S

S S

GerberGerber

2 214 2

2a ut ut e e i ut i ee

m a i

S S S S S S SS

S S

ASME-EllipticASME-Elliptic

2 22 2

ea p p e i i e

p e

m a i

SS S S S S

S S

S S

(8-43)

(8-42)

(8-40)

(8-41)

For simultaneous solution between Eq. (8-36), as Sa = Sm + σi and each of Eqs. (8-37) to (8-39) gives



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

Applying this to the Goodman criterion, for example, with Eqs. (8-34) and (8-40) and gives

af

a

Sn

i i tF A

2 e ut t i

fut e

S S A Fn

CP S S

(8-44)

(8-45)



With no preload, C=1, Fi=0, and Eq. (8-45) becomes

Preload is beneficial for resisting fatigue when is greater than

unity. For Goodman, Eqs.(8-45) and (8-46) with puts an

upper bound on the preload Fi of

If this cannot be achieved, and nf is unsatisfactory, use the Gerber or

the ASME-elliptic criterion to obtain a less conservative assessment.

After solving Eq. (8-44), you should also check the possibility of

yielding, using the proof strength

0ffn n

(8-46)

(8-47)

0

2 e ut tf

ut e

SS An

P S S

0 1ffn n

1i ut tF C S A

pp

m a

Sn

(8-48)



Example 6 (Example 8-5 Textbook)Example 6 (Example 8-5 Textbook)

Figure 8-21Pressure-cone frustum member model for a cap screw. For this model the significant sizes are

Where l = effective grip. The solutions are for =30o and dw=1.5d.

2 2

2

1

2

2

2

tan 1.5 0.577

1.5w

w

h t t dl

h D t d

D d l d l

D d d







Figure 8-22Designer’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 areSp= 85 kpsi, Se= 18.6 kpsi, andSut=120 kpsi. The coordinates areA: σi=63.72 kpsi

B: σa=3.1 kpsi, σm=66.82 kpsiC: Sa=7.55 kpsi, Sm=71.29 kpsiD: Sa=10.64 kpsi, Sm=74.35 kpsiE: Sa=11.32 kpsi, Sm=75.04 kpsi







Documents

ME 307 Machine Design I ME 307 Machine Design I CH-8 LEC 38 Slide 1 Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints