4 Threads and Their Strength
4.7 THE STRENGTH OF THREADS
There’s a surprising amount of disagreement on what parameters determine the strength of a thread and on how best to evaluate the quality—including the strength—of a threaded fastener before use. Let’s take a look at some conventional wisdom concerning thread strength and then look at some recent thoughts and concerns about thread strength and quality.
4.7.1 BASICCONSIDERATIONS
As we saw in Chapter 1, one of our principal design goals is ‘‘a fastener strong enough to support the maximum preload it might receive during assembly, plus the maximum additional loads it might see in service, as a result of forces applied to the joint, differential thermal expansion, etc.’’ The larger the nominal diameter of a fastener, of course, the stronger it will be. As far as static loads are concerned, therefore, we’d like the shank or body of the bolt to be the full, basic, or nominal diameter of the thread, or at least to be greater than the root diameter of the threads [2].
We must then specify a length of thread engagement capable of developing the full strength of that body. This is just another way of saying that we want the body to break before the threads strip, because a broken bolt is easier to detect than a stripped thread.
When the threads strip they do so by shearing in one of three ways. If the nut material is stronger than the material from which the bolt is made, the threads will strip at the roots of the bolt teeth. If the bolt material is stronger, stripping will occur at the roots of the nut threads. If the materials have equal strengths, both nut and bolt threads will strip simultan-eously, at their pitch diameters.
Studies made at the National Bureau of Standards many years ago showed that the shear strength for most common fastener materials varied between 50% and 60% of their ultimate tensile strengths. As a result, the stripping areas (ATS), defined in the formulas below (on which the recommended lengths of thread engagement are based) are set at twice the tensile stress area (As) of the same thread [5].
If the fastener is to be subjected to fatigue or impact loads, we’d like it to be more resilient than a fastener subjected to static loads. Some recommend a shank (body) diameter about 60% of that used for static loads if the fastener will see impact loads, or a shank diameter of 90% of the static diameter if it will experience fatigue loads (repeated load cycles) [2].
4.7.2 THREADSTRENGTH EQUATIONS
You’ll find both long form and short form thread strength equations in earlier editions of this book. Those equations are complete and accurate but they’re not convenient to use because each requires input data for various thread parameters: the maximum inner diameter of the nut threads or the minimum pitch diameter of the bolt threads, for example. Such things are tabulated in long tables in Machinery’s Handbook or ANSI=ASME B1.1, or FED-STND-H28, each of which also includes a group of thread strength equations. Since you have to go
to one of these sources for the data it makes sense to go to them for your thread strength equations as well.
You’ll find that the equations allow you to compute two different factors: ATS of the threads and the length of thread engagement (Le) required to develop the full strength of the fastener. You’ll also find that these two are, understandably, directly proportional to each other. Longer engagement means more threads to strip, which means a larger stripping area. You can’t compute ATS without knowing or assuming an Le or compute length of engagement without making assumptions about ATSsince each is a function of the other.
One of my goals is to give you all of the data you need to deal with most on-the-job, everyday questions and to answer the problems at the end of each chapter. In pursuit of this goal I have included Tables 4.5 through 4.7. They will give you the thread-stripping areas for a length of thread engagement equal to one nominal diameter of the bolt. This is the common length for thick or heavy hex nuts; which are stronger than thinner, regular hex nuts. You can use an ATSfrom one of these tables to compute the force required to strip that length of thread, using Equation 4.1 below. You can then compare that with the force required to break your bolt (using Equation 3.1). Remember, nuts are usually made of material weaker than the bolt material but, in an apparent contradiction, you want the bolt to fail before the nut. If your calculations show that the threads would strip before the bolt would break then you’ll have to change something: probably increase the length of thread engagement.
In a minute I’ll show you how to deal with lengths of engagement greater or less than one diameter. But first, here’s the basic procedure.
4.7.3 THREAD STRENGTHCOMPUTATIONSWHENLe5D
Le¼ D, where Le¼ length of thread engagement (in., mm) and D ¼ nominal diameter of the bolt (in., mm).
First we compute the force required to strip the threads:
FSt¼ SuATS (4:1)
where
Su ¼ ultimate shear strength (psi, MPa) of the nut or bolt materials (from Table 2.7 in Chapter 2)
ATS¼ cross-sectional area (in.2, mm2) through which the shear occurs for a length of engagement equal to D (from Tables 4.5 through 4.7)
FSt ¼ the force (lb, N) required to strip that length of threads of a bolt or nut
Next we compute the tensile force required to break the bolt (FTen) and compare it to the force required to strip the threads:
FTen¼ UTS AS (3:1B)
You can find ASin Tables 4.5 through 4.7, or can compute it from
AS¼ 0:7895[D (0:9743=n)]2 (3:1A)
In Equations 3.1A and 3.1B
UTS¼ ultimate tensile strength of the bolt material (psi, MPa) AS ¼ the tensile stress area of the bolt (in.2, mm2)
D ¼ nominal diameter of the bolt (in., mm)
n ¼ number of threads per inch
FTen ¼ the tensile force required to break the bolt (lb, N)
If the computed FST is greater than FTen you’re finished. If not, or if the difference in strength is unnecessarily large (too much length of engagement) proceed as suggested later.
First, though, let’s look at an example of the basic procedure.
4.7.4 BASICPROCEDURE—ANEXAMPLE Let’s assume that we have the following:
Bolts:5=8in. diameter fasteners with 0.625–11UNC Class 2A threads (see Table 4.3) made from ASTM F2281 GR 600 material having a UTS of 130 ksi (see Chapter 2; Section 5).
Joint material: SAE J414 GR 1035 having a shear strength of 54 ksi (see Table 2.7). We’ll tighten the bolts in tapped holes in this material rather than in nuts in this example.
From Table 4.6
ATSof a 0.625–11 Class 2A thread¼ 0.891 in.2if Le¼ D AS ¼ 0.226 in.2
FSt ¼ Su ATS¼ 54,000 0.891 ¼ 48,114 lbs FTen¼ UTS AS¼ 130,000 0.226 ¼ 29,380 lbs
So the bolt will break before the threads will strip if Le¼ D ¼ 0.625 in. That’s the desirable outcome so we may be done. But that’s a very large difference between thread and bolt strengths, and suggests that we’ve asked for a greater length of thread engagement that required. This also suggests ‘‘more nut threads than we need’’ which, in turn, might lead to a slight possibility of pitch interference. In any event, it’s useful to know what to do next if we don’t like the results of the preceding calculation.
4.7.5 THREADSTRENGTH CALCULATIONSWHENLe=/ D
As mentioned earlier the Le and the ATS are directly proportional to each other. It is, therefore, very easy to compute stripping areas for engagement lengths other than nominal diameter, D:
ATS0¼ (Desired Le=D) ATS (4:2)
where ATSis the value found in Tables 4.4 through 4.6. It is 0.891 in.2in the present example, for a 0.625–11, Class 2A thread (in.2, mm2).
ATS0 ¼ Recalculated stripping area for a length of thread engagement greater to or less than the nominal diameter of the fastener (D) (in.2, mm2).
For example, what if the joint plate in the previous example were only1=2in. thick rather than5=8in. thick?
ATS0¼ (0:5=0:625) 0:891 ¼ 0:7128 in:2 and
FSt¼ 54,000 0:7128 ¼ 38,491 lbs
The bolt will still break before the threads tapped in a1=2in. plate will strip, so we could stop here. What if the plate is only1=4in. thick?
FSt¼ 54,000 (0:250=0:625) 0:891 ¼ 19,245 lbs
Now the threads will strip before our5=8–11 bolt would break, which is not a good idea. In this case we should use a regular or heavy nut to tighten the bolts, rather than tapping the holes in the plate.
4.7.6 OTHERSTRESSAREAFORMULAS
In Chapter 3, we were introduced to the most common formula for the thread stress area (Equation 3.1A). We will usually use this expression when computing the strength of a thread and, in fact, have been using it in Section 4.7.3. It could be important for you to know, however, that different expressions must be used for some of the other thread forms illus-trated in Figures 4.1 and 4.2. Here are some examples [27].
TABLE 4.4
Selected UNC=UNF=8UN Tread Stress and Shear Areas
Bolt Tread Strip Area, Le 1 1 Diameter
Nut Thread Strip Area, Le 5 1 Diameter
Thread Tensile Stress Area 2A=2B 3A=3B 2A=2B 3A=3B
0.1900–24UNC 0.0175 0.050 0.053 0.076 0.080
0.1900–32UNF 0.0200 0.052 0.055 0.074 0.078
0.2500–20UNC 0.0318 0.092 0.096 0.135 0.141
0.2500–28UNF 0.0364 0.093 0.101 0.130 0.137
0.3125–18UNC 0.0524 0.147 0.157 0.213 0.222
0.3750–16UCN 0.0775 0.216 0.232 0.310 0.322
0.3750–24UNF 0.0878 0.217 0.242 0.299 0.314
0.4375–14UFC 0.0163 0.296 0.321 0.428 0.443
0.5000–13UFC 0.1419 0.389 0.427 0.562 0.581
0.5000–20UNF 0.1599 0.400 0.444 0.541 0.567
0.5625–12UNC 0.182 0.503 0.548 0.717 0.741
0.6250–11UNC 0.226 0.624 0.683 0.891 0.919
0.6250–18UNF 0.256 0.624 0.708 0.853 0.892
0.7500–10UNC 0.334 0.910 1.00 1.29 1.33
0.7500–16UNF 0.373 0.924 1.04 1.24 1.30
0.8750–9UNC 0.462 1.24 1.38 1.77 1.83
0.8750–14UNF 0.509 1.26 1.43 1.71 1.78
1.0000–8UNC 0.606 1.66 1.82 2.33 2.40
1.1250–8UN 0.790 1.92 2.14 2.95 3.04
1.2500–8UN 1.000 2.65 2.91 3.65 3.75
1.3750–8UN 1.233 3.22 3.55 4.41 4.54
1.5000–8UN 1.492 3.86 4.26 5.25 5.41
1.6250–8UN 1.78 4.55 5.03 6.17 6.35
1.7500–8UN 2.08 5.30 5.87 7.15 7.36
1.8750–8UN 2.41 6.10 6.76 8.20 8.45
2.0000–8UN 2.77 6.96 7.72 9.32 9.61
2.2500–8UN 3.56 8.85 9.83 11.78 12.16
2.5000–8UN 4.44 10.96 12.19 14.53 15.01
2.7500–8UN 5.43 13.30 14.80 17.57 18.16
3.0000–8UN 6.51 15.85 17.67 20.88 21.59
3.2500–8UN 7.69 18.62 20.79 24.47 25.32
3.5000–8UN 8.96 21.63 24.16 28.37 29.36
3.7500–8UN 10.34 24.83 27.78 32.51 33.67
4.0000–8UN 11.81 28.28 31.65 36.96 38.30
Note: All areas are given in square inches.
UNJ threads rolled after heat treatment:
AS¼ 0:7854(d2 max)2 (4:3)
UNJ and MJ threads rolled before heat treatment or not rolled at all:
AS¼ 0:7854[0:5(d2 maxþ d3 max)]2 (4:4) M-form metric threads:
AS¼ 0:7854(D 0:9382P)2 (4:5)
Metric MJ threads rolled after heat treatment:
AS¼ 0:7854(d3 max)2[2 d3 max=d2 max)2] (4:6) where
D ¼ basic pitch diameter (in., mm) P ¼ thread pitch (in., mm)
d2max¼ maximum pitch diameter (in., mm) d3max¼ maximum rounded root minor diameter
TABLE 4.5
Selected Metric M Series Thread Stress and Shear Areas
Bolt Thread Strip Area, Le 5 1 Diameter
Nut Thread Strip Area, Le 5 1 Diameter Thread Tensile Stress Area 6H=6g 6H=4g6g 6H6g and H=4g6g
M5 0.8 14.183 35.366 37.085 49.994
M6 1 20.123 51.875 54.174 73.145
M8 1.25 36.609 97.290 100.74 134.63
M10 1.5 57.990 155.80 160.73 214.77
M12 1 84.267 227.72 234.86 313.41
M14 2 115.44 313.94 323.24 434.47
M16 2 156.67 417.55 429.92 569.12
M20 2.5 244.79 665.58 682.06 907.76
M22 2.5 303.40 814.67 — 1,100.3
M24 3 352.50 971.10 994.23 1,320.2
M27 3 459.41 1,246.7 — 1,674.3
M30 3.5 560.59 1,549.2 1,582.5 2,086.5
M36 4 816.72 2,271.5 2,315.8 3,026.2
M42 4.5 1,120.9 3,120.2 3,175.2 4,168.3
M48 5 1,473.2 4,119.5 4,187.3 5,482.0
M56 5.5 2,030.0 5,680.3 5,769.4 7,510.2
M64 6 2,676.0 7,483.6 7,596.4 9,847.3
M72 6 3,459.8 9,574.2 9,718.5 12,478
M80 6 4,344.1 11,922 12,101 15,419
M90 6 5,590.8 15,217 15,446 19,534
100 6 6,994.7 18,856 19,170 24,059
Note: All areas given in square millimeters.