ME 307
Machine
Design I
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 36 Slide 1
ME 307
Machine
Design I
8-1
8-2
8-3
8-4
8-5
8-6
8-7
8-8
8-9
8-10
8-11
8-12
8-13
8-14
8-15
Thread Standards and Definitions
The Mechanics of Power Screws
Strength Constraints
Joints-Fasteners Stiffness
Joints-Member Stiffness
Bolt Strength
Tension Joints-The External Load
Relating Bolt Torque to Bolt Tension
Statically Loaded Tension Joint with Preload
Gasketed Joints
Fatigue Loading of Tension Joints
Shear Joints
Setscrews
Keys and Pins
Stochastic Considerations
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 36 Slide 2
ME 307
Machine
Design I
8-3
8-4
8-5
8-6
Dr. A. Aziz Bazoune
Strength Constraints
Joints-Fasteners Stiffness
Joints-Member Stiffness
Bolt Strength
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 36 Slide 3
ME 307
Machine
Design I
8-4 Joints: Fastener Stiffness
When a connection is desired that can be disassembled without destructive
methods and that is strong enough to resist external tensile loads, moment
loads, and shear loads, or a combination of these, then the simple bolted joint
using hardened steel washers is a good solution.
 Twisting the nut stretches the
produce the clamping force. This
force is called the pretention
preload.
 This force exists in the connection
nut has been properly tightened.
bolt to
clamping
or bolt
after the
Figure 8-13
A bolted connection loaded in tension by the forces P.
Note the use of two washers. Note how the threads
extend into the body of the connection. This is usual and
is desired. LG is the grip of the connection.
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 36 Slide 4
ME 307
Machine
Design I
Joints: Fastener Stiffness
Figure
8-14 shows
another
tension-loaded connection. This
joint uses cap screws threaded
into one of the members.
Figure 8-14
Section of cylindrical pressure vessel.
Hexagon-head caps crews are used to
fasten the cylinder head to the body.
Note the use of an O-ring seal. LG’ is
the effective length of the connection
(See Table 8-7) .
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 36 Slide 5
ME 307
Machine
Design I
Joints: Fastener Stiffness
 An alternative approach to this problem
(of not using a nut) would be to use studs.
 A stud is a rod threaded on both ends. The
stud is screwed into the lower member
first; then the top member is positioned
and fastened down with hardened washers
and nuts
 Studs are regarded as permanent, and so
the joint can be disassembled merely by
removing the nut and washer.
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 36 Slide 6
ME 307
Machine
Design I
Joints: Fastener Stiffness

Spring Rate : The ratio between the
force applied to the member and the
deflection produced by that force.

The grip LG of a connection is the total
thickness of the clamped material.

Total distance between the underside of
the nut to the bearing face of the bolt
head; includes washer, gasket thickness
etc.
Dr. A. Aziz Bazoune
The grip LG here is the sum
of the thicknesses of both
members and both washers.
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 36 Slide 7
ME 307
Machine
Design I
Table 8-7
Suggested Procedure
fastener Stiffness
for
Finding
To find different parameters use table
8-7
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 36 Slide 8
307
InME joint
under tension the members are under compression and the bolt under
Machine
Design I
tension:
kb = equivalent spring constant of bolt composed of threaded kt and
unthreaded kd parts acting as springs in series.
1
1
1 From Chapter 5


kb kd kt (Springs in series)
kd kt
kb 
kd  kt
For short bolts
A E
AE
kd  d , kt  t
kb= kt
ld
lt
Ad At E
kb 
Adlt  Atld
At: tensile stress area (Tables 8-1, 8-2), lt: length of threaded portion of the
grip; Ad: major diameter area of fastener; ld: length of unthreaded portion in
grip. kb: is the estimated effective stiffness of the bolt or cap screw in the
clamped zone.
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 36 Slide 9
ME 307
Machine
Design I
Dr. A. Aziz Bazoune
8-5 Joints- Member Stiffness
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 36 Slide 10
ME 307
Machine
Design I
8-5 Joints- Member Stiffness
 There may be more than two members included in the grip
of the fastener.
 All together these act like compressive springs in series.
 Equivalent spring constant km
1
1
1
1
1
 

 ....
km k1 k2
k3
ki
 If one of the members is a soft gasket, its stiffness relative
to the other members is usually so small that for all
practical purposes the others can be neglected and only
gasket stiffness used.
 With no gasket, the stiffness of the members is difficult to
obtain, except by experimentation.
 Compression spreads out between the bolt head and the
nut and area is not uniform.
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 36 Slide 11
ME 307
Machine
Design I
8-5 Joints Member Stiffness
Joint pressure distribution theoretical models


Ito used ultrasonic techniques to determine pressure distribution at
the member interface. Results show that pressure stays high out to
about 1.5 bolt radii.
Ito suggested the use of Rotscher’s pressure cone method for stiffness
calculations with a variable cone angle. This method is quite
complicated.
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 36 Slide 12
ME 307
Machine
Design I
8-5 Joints Member Stiffness
Figure 8-15
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 36 Slide 13
ME 307
Machine
Design I


8-5 Joints Member Stiffness
We choose a simpler approach using a fixed
cone angle.
The contraction of an element of the cone of
thickness dx is subjected to a compressive
force P is, from Eq. (5-3),
d 

Pdx
EA
The area of the element is
2
2

D
d  
A   r  ri    x tan       
2
 2  

D  d 
D d 

   x tan  
x
tan


2  
2 


2
0
Dr. A. Aziz Bazoune
2

Figure 8-15b general cone
geometry using a half-apex
angle .
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 36 Slide 14
ME 307
Machine
Design I

8-5 Joints Member Stiffness
Substituting this into the previous equation and integrating the resulting
equation from 0 to t gives.
P
(2t tan   D  d)(D  d)
ln
 Ed tan  (2t tan   D  d)(D  d)
P
 Ed tan 
k 
(8-19)
 ln (2t tan   D  d)(D  d)
(2t tan   D  d)(D  d)
 

For Members made of Aluminum, hardened steel and cast iron 25o<<33o

With =30o, this becomes
Dr. A. Aziz Bazoune
k 
0.574  E d
(1.55 t  D  d)(D  d)
ln
(1.55 t  D  d)(D  d)
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
(8-20)
CH-8 LEC 36 Slide 15
ME 307
Machine
Design I

8-5 Joints Member Stiffness
Substituting this into the previous equation and integrating the resulting
equation from 0 to t gives.
P
(2t tan   D  d)(D  d)
ln
 Ed tan  (2t tan   D  d)(D  d)
P
 Ed tan 
k 
 ln (2t tan   D  d)(D  d) (8-19)
(2t tan   D  d)(D  d)
 

With =30o, this becomes
k 
Dr. A. Aziz Bazoune
0.574  E d
(1.55 t  D  d)(D  d)
ln
(1.55 t  D  d)(D  d)
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
(8-20)
CH-8 LEC 36 Slide 16
ME 307
Machine
Design I
8-5 Joints Member Stiffness
 If members of the joint have the same E with symmetrical frusta (l=2t),
then they act as two identical springs in series km = k/2. For = 30° and
D = dw = 1.5 d, this can be written as,
km 


0.5774  E d
 0.5774 l  0.5d 
2 ln  5

0.5774
l

2.5
d


(8-22)
o
Finite element analysis agree with  = 30 recommendation coinciding
exactly at the aspect ratio d/l = 0.4.
Additionally, FEM offered an exponential curve-fit of the form
km
 Ae(Bd/l)
Ed
(8-23)
where A and B are given in Table 8-8.
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 36 Slide 17
ME 307
Machine
Design I
8-5 Joints Member Stiffness
Figure 8-16
The dimensionless plot
of stiffness versus aspect
ratio of the members of
a bolted joint, showing
the relative accuracy of
method of Rotsher,
Michke and Motosh,
compared to Finite
Element Analysis (FEA)
conducted by Wileman,
Choudury, and Green.
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 36 Slide 18
ME 307
Machine
Design I
Dr. A. Aziz Bazoune
8-5 Joints Member Stiffness
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 36 Slide 19
ME 307
Machine
Design I

8-6 Bolt Strength
Bolt strength is specified by:
1.
2.
3.

minimum proof strength Sp
or minimum proof load Fp,
and minimum tensile strength, Sut
The proof load is the maximum load (force)
that a bolt can withstand without acquiring
a permanent set.

The proof strength is the quotient of the
proof load and the tensile-stress area.

The proof strength is about 90% of the 0.2%
offset yield strength.
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 36 Slide 20
ME 307
Machine
Design I

8-6 Bolt Strength
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.
If Sp not available use:
Sp =0.85 Sy
Fp = At Sp
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 36 Slide 21
ME 307
Machine
Design I
Dr. A. Aziz Bazoune
8-6 Bolt Strength
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 36 Slide 22
ME 307
Machine
Design I
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 36 Slide 23
ME 307
Machine
Design I
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 36 Slide 24