SCREWS, FASTERNERS, AND THE DESIGN
OF NON PERMANENT JOINTS
Shigley 8th ed.: Chapter 8
Outline
I.
General
a. Threaded Fasteners

Provides clamping force

Temporary – allows disassembly

Examples
1. Bolt (with nut)
2. Machine screw
b. Power screws
II.

Transmit force over some distance

Examples: House jack, Tensile testing machine
Thread Basics
a. Thread Terminology

Pitch, p

Lead, l

Major diameter, d

Minor (root) diameter, d1 (dr )

Mean diameter (pitch diameter), dm

Multiple start thread: double, triple

Class : 1 (loose fit)  3 (snug fit)

Lead angle,  tan  =l/( dm )
b. Fastener Threads

Unified National

Metric

Coarse or Fine

Thread Designation
Examples: 1” 8 UNC A1 or M12X1.75 (See tables 8-1 & 8-2)
Rev. 3/13/07
1
c. Threaded Fastener Mechanical Advantage (1” 8 UNC)
Inclined plane  5.5X
Lever Arm of Wrench  12X
Typical Total Mech. Ad. = 50X to 100X
This is a huge mechanical advantage – the main reason threaded
connections are so common.
III.
Power Screw
a. Power Screw Thread Forms (1/2 the included thread angle = )

Square  = 0

Acme  = 14.5

Buttress  = 7
From a force balance on the thread:
b. Raising torque (with thrust collar friction negligible)
TR 
Fd m
2
 l  fd m sec  n 

 Eqn. 8-1 modified [ = 0 for square thread]
 d m  fl sec  n 
Where tan  n  tan  (cos  ) accounts for normal force
orientation with respect to the thread in force balance calculations.
c. Lowering torque (with thrust collar friction negligible)
TL 
Fd m
2
 fd m sec  n  l 

 Eqn. 8-2 modified [ = 0 for square thread]
 d m  fl sec  n 

 fd m

l cos  n 
If TL  0 => 
Self Locking Equation
 l  or  f 
d m 

 cos  n

Also, can be written: f  tan  (cos  n )
Note: tan  n  tan  (cos  )
Nominally this gives the friction coefficient to provide a self locking
thread. Note: vibration has a huge affect on the requirement of self
locking. Usually, mechanical devices must be used to prevent loosening
in an environment with vibration (shaft rotation, etc). Example are
lock washers and lock nuts: nylon insert nuts, castellated nut, nut
tapered and swaged, etc.
Rev. 3/13/07
2

d. Thrust Collar (often required for power screws)
{with Thrust Collar: TR  TR  TC or TL TL  TC }
TC  Ffc dc 2
e. Efficiency
e
Fl
cos  n  f tan 
workout


workin
2TR
cos  n  f tan 
f. For acme threads: tan  n  tan(14.5 0 )(cos  ) [See handout for acme
efficiency vs. lead angle]
IV.
Static Bolt Stresses
a. Thread loading – upper threads (nearest the bolt head) take the highest
load. Normally, the nut is softer than the bolt to allow some minor
yielding in the nut to help distribute the load on the threads.
b. Nut height (thickness)

Nut height needs to be equal to 0.5 times the bolt diameter for
full strength connection (assumes nut and bolt are the same
material).

Nut is usually made of a softer material than the bolt.
Standard nut height is 7/8ths of the bolt diameter.
V.

Bolt Tightening
a. Proof load, Fp
Fp  At S p [ S p in tables 8-9,10,11 and At is the tensile area table 8-1,2]
b. Preload, Fi
Fi = 0.75 Fp non-permanent fastener
Fi = 0.9 Fp (semi) permanent fastener
c. Loosening

Self locking thread condition (TL  0):
f 

Rev. 3/13/07
l (cos  n )
 tan  cos  n
d m
Vibration is a significant factor in bolt loosening
3

Locking mechanism usually are required: see examples
d. Bolt torque for desired preload (with standard washer)
T  [(
d m tan   f sec  n
)(
)  0.625 f c ]Fi d
2d 1  f tan  sec  n
or T  KFi d
for f  f c  0.15 K  0.2
VI.
Separation in a Bolted Connection with an external force P
a. Bolt stiffness, kb – see handout or text pages 410 to 413
b. Member stiffness km – see handout or text pages 413-416
c. Force in the bolt, Fb
Fb 
kb
P  Fi
kb  km
Fm  0
d. Force in the member, Fm
Fm 
km
P  Fi
kb  km
Fm  0
e. Example: km = 8 kb ; Fi = 1000 lb ; P = 1100 lb (P is the external load)
Fb 
kb
(1100)  (1000) 1122lb f
k b  8kb
Fm 
8k b
(1100) (1000)  22lb f
kb  8k b
Note Fm is still negative (Compressive)
VII.
Bolt Fatigue Strength
a. See text pages 429 to 435
b. Advantages of high initial bolt tension for fatigue resistance:

The dynamic load on the bolt is reduced because the effective
area of the clamped members is larger.

The maximum protection against external loads which can
cause joint separation

Rev. 3/13/07
There is a maximum protection against thread loosening
4
Rev. 3/13/07
5