Notes on Nuts and Bolts

A screw thread is a helical groove on a shaft. When used for delivering power, it is called a drive screw. Drive screws aren't really all that efficient, as they loose a significant amount of power to friction. However, this friction can be put to use in the case of threaded fasteners. You might say that a drive screw is an inclined plane wrapped around a post, while a fastener is a wedge wrapped around a post.

Bolt Terms

Nut and Bolt terms

A 1/2-13UNC-2A-3 bolt, with a 2" thread and a 1" shank.

As nuts and bolts are not perfectly rigid, but stretch slightly under load, the distribution of stress on the threads is not uniform. In fact, on a theoretically infinitely long bolt, the first thread takes a third of the load, the first three threads take three-quarters of the load, and the first six threads take essentially the whole load. Beyond the first six threads, the remaining threads are under essentially no load at all. Therefore, a nut or bolt with six threads acts very much like an infinitely long nut or bolt (and it's a lot cheaper).

Stress on threads

Stress on bolt threads. Note how the majority of
the stress is on the first thread to the left.
Image from Spiralock.

      

Thread % %Sum
1 34% 34%
2 23% 55%
3 16% 71%
4 11% 82%
5 9% 91%
6 7% 98%

There is little point in having more than six threads in anything. Nuts with National Coarse threads typically have 5 threads in them, whereas nuts with National Fine threads have about 8 threads. Nuts are usually stronger than the bolts they are on, which is to say that the bolt will usually break before the nut strips.

It is often said that two threads must be exposed above a nut. The reason for this is that the first two threads of a bolt are often poorly formed, and may not engage the nut properly. If they're not doing their share, the other threads in the nut will be overloaded, and the nut may strip.

Thread Terms

Metric and American threads both conform to the same profile, a series of equilateral triangles with the crests chopped off and the roots rounded.

Thread Profile

External Standard Thread Profile

The depth of the threads is 54.127% of the distance between threads, and the radius of the rounded root is 14.434% of the distance between threads. Another way of looking at it would be to say that 1/8 of the height of each equilateral triangle is chopped off the top, and 1/4 of the height off the bottom, leaving only 5/8 of the height available. (The height of an equilateral triangle is equal to the width times half of the square root of three; 5/8 of this is 0.54127.)

The root diameter of the thread is the nominal diameter minus 108.3% of the pitch of the thread. This means that fine threads have larger root diameters than coarse threads, and thus larger tap drill sizes. For threading using a tap or die, most threads are not cut to full depth, but to 75% or so. The resulting threads are not quite as strong, but full depth threading is very hard on the tap or die. Threading on a lathe presents no difficulty cutting to full depth.

Thread Specifications

Thread specifications are written thus:

1/2-13UNC-2

which means:

There are four Fit Classes, ranging from falling-off-loose to scientific-instrument-tight.

The class is followed by an A for external (screw) threads and a B for internal (nut) threads. Most are class 2. 3 is for precision assembly, and 4 is used for things like lathe lead screws and measuring instruments.

In November 1948, NATO issued a new standard for threads, the Unified National system. American bolts had flat-bottomed groves between threads, which interfered with British round-topped threads. Likewise, British bolts wouldn't fit American nuts. The Unified system uses a round-bottom grove to fit the British threads, and a flat-topped thread to fit the American threads, so it not only fit itself, but both existing systems.

American/United National Threads

Size Diameter TPI
Coarse
TPI
Fine
Root Dia.
Coarse
Hex
Head
Size
SAE
Washer
ID
SAE
Washer
OD
SAE
Washer
Thickness
#0 0.0600 - 80 0.0447        
#1 0.0730 64 72 0.0560        
#2 0.0860 56 64 0.0668   3/32" 1/4" 1/32"
#3 0.0990 48 56 0.0771        
#4 0.1120 40 48 0.0813   1/8" 5/16" 1/32"
#5 0.1250 40 44 0.0971        
#6 0.1380 32 40 0.1073   5/32" 3/8" 3/64"
#8 0.1640 32 36 0.1299   3/16" 7/16" 3/64"
#10 0.1900 24 32 0.1570   7/32" 1/2" 1/16"
#12 0.2160 24 28 0.1722   1/4" 9/16" 1/16"
1/4" 0.2500 20 28 0.1850 3/8" 9/32" 5/8" 1/16"
5/16" 0.3125 18 24 0.2400 1/2" 11/32" 11/16" 1/16"
3/8" 0.3750 16 24 0.2940 9/16" 13/32" 13/16" 1/16"
7/16" 0.4375 14 20 0.3440 5/8" 15/32" 15/16" 1/16"
1/2" 0.5000 13 20 0.4000 3/4" 17/32" 1-1/16" 3/32"
9/16" 0.5625 12 18 0.4540 7/8" 19/32" 1-3/16" 3/32"
5/8" 0.6250 11 18 0.5070 15/16" 21/32" 1-5/16" 3/32"
3/4" 0.7500 10 16 0.6200 1-1/8" 13/16" 1-1/2" 1/8"
7/8" 0.8750 9 14 0.7310 1-5/16" 15/16" 1-3/4" 1/8"
1" 1.0000 8 12 0.8370 1-1/2" 1-1/16" 1-3/4" 1/8"

A much more complete table is available here.

Metric Threads

Metric threads use the same thread profile as SAE threads. The biggest difference is that the thread pitch (distance between consecutive threads) is given instead of threads per unit distance.
Diameter Coarse
Pitch
mm
Fine
Pitch
mm
Root Dia.
Coarse
mm
Hex
Head
Size
mm
ISO
Washer
ID
mm
ISO
Washer
OD
mm
ISO
Washer
Thickness
mm
1 0.25   0.7294        
1.1 0.25   0.8294        
1.2 0.25   0.9294        
1.4 0.30   1.075        
1.6 0.35   1.221 3.2      
1.8 0.35   1.421        
2 0.40   1.567 4      
2.2 0.45   1.713        
2.5 0.45   2.013 5      
3 0.50   2.459 5.5 3.4 7.0 0.6
3.5 0.60   2.850        
4 0.70 0.50 3.242 7 4.5 9.0 0.9
4.5 0.75 0.50 3.688        
5 0.80 0.50 4.134 8 5.5 10 11
5.5   0.50          
6 1.00 0.50 4.917 10 6.7 12.5 1.8
7 1.00 0.75 5.917        
8 1.25 0.75 6.647 13 8.7 17 1.8
9 1.25 0.75 7.647        
10 1.50 0.75 8.376 16 10.9 21 2.2
11 1.50 0.75 9.376        
12 1.75 0.75 10.11 18 13.4 24 2.7
14 2.00 1.00 11.83 21      
16 2.00 1.00 13.83 24 17.4 30 3.3
18 2.50 1.00 15.29        
20 2.50 1.00 17.29 30 21.5 37.9 3.3

Bolt Strength

The Society of Automotive Engineering has issued standard J429, which sets forth standards for both strength. The SAE grade of a bolt is marked on it's head in the form of short radial lines, the number of lines being two less than the SAE grade (i.e.. 3 lines for grade 5).
SAE Grade Size Range Strength (psi)
1 1/4" to 1-1/2" 60,000
2 1/4" to 3/4" 74,000
2 7/8" to 1-1/2" 60,000
5 1/4" to 1" 120,000
5 1-1/8" to 1-1/2" 105,000
7 1/4" to 1-1/2" 133,000
8 1/4" to 1-1/2" 150,000

ASTM standards are sometimes used as well; A325 bolts are the equivalent of SAE 5, and A490 bolts are the equivalent of SAE 8.

Preload

A very misunderstood part of bolting stuff together is preload, which is the tension placed on the bolt by the nut (as opposed to the load). A sufficiently high preload will protect the bolt from fatigue as the load changes, as the varying load will change the clamping force on the bolted components, rather than the tension on the bolt. (This is not strictly true, but for a tinkerer like me, it's adequate.) As a rule of thumb, the preload should exceed the maximum load by 15% or so.

In order for this to work, however, the joint must be stiffer than the bolt. For this reason, the shank of high-tech bolts are often necked down to the same diameter of the root of the thread. As long as it isn't thinner than the root of the thread, it isn't any weaker than the thread, and therefore doesn't effect overall bolt strength, but it is significantly less stiff than the original shank.

There are two ways to measure preload on a bolt; a torque wrench, and by measuring the angle the nut has turned. Of the two, the latter is more accurate, as friction plays a significant - and more importantly, indeterminate - role when using a torque wrench.

Torque = K × preload × diameter

K, the so-called Nut Factor, usually varies between 0.3 and 0.1, and is very sensitive to a number of factors, ranging from temperature to thread condition, even to how fast the bolt is tightened.

Measuring the angle the nut has turned is simply measuring how much the bolt is stretching, equal to the pitch (distance between threads) times the number of turns. Using this requires that the components being bolted don't compress much (or compress a known amount), and that the "spring rate" of the bolt be known.

Turns = preload ÷ (spring rate × pitch)

For example, if the "spring rate" of a 1/2-13 bolt is 50,000 pounds per inch (note that I made that up, and that most bolts will yield long before stretching an inch), and you need 500 pounds of preload, you'll need to stretch the bolt 500 ÷ 50000 = 0.01 inch. At 13 threads per inch (0.0769 inches per thread), this would equate to 0.13 turns, or about 45° past snug.

If more than one bolt is used in a joint, and those bolts are closer together than about four diameters, the preload on one bolt will effect the preload on the other bolts by compressing the joint. This effect is called "crosstalk", and then all bets are off. Joints that are significantly less stiff than the bolts, such as joints involving gaskets, suffer much worse from crosstalk. The best way to control crosstalk is to use a carefully thought out tightening sequence (usually a spiral starting at the center, or for circular patterns, alternating bolts), and to tighten the bolts in small steps. Even so, it's a crap shoot.

References

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© 2003 W. E. Johns