# The Three Least Understood Truths in Bolted Joint Design

As in most endeavors, the most common misconceptions relate to the most fundamental principles. These errors are commonly made simply because their universal nature provides the greatest opportunity for making them. For example, the reason that that most auto accidents occur within a small radius of the driver’s home isn’t because those streets are the most dangerous but because they are the ones that the driver travels on most often. Similarly, one of the main reasons these misconceptions exist so widely is because they are so basic to the use the threaded fasteners. Therefore those with less experience that have questions don’t ask them, while those with that experience assume it’s common knowledge. So, what follows is hopefully some what you always wanted to know about bolted joints but were afraid to ask.

1.Tension, rather that torque, is the quantity that should determine how “tight” a structural joint should be.

The tensile capacity, and generally the longevity of bolted joints in structural applications are determined by the force with which the bolt “squeezes” the components being secured, referred to as the clamp load. The pressure exerted by the joint on the bolt, an equal and opposite reaction to the clamp load, is the bolt tension. Tension is generated in the bolt when one set of threads is turned relative to another set. This movement wants to shorten the distance between the bearing surfaces of the two parts (usually the faces under the nut and bolt head). But the stack of components between those faces provides a great deal of resistance to allowing the bearing faces to move closer to one another. So the faces stay in about the same relative position and the length of fastener that lies between them stretches instead, generating both tension in the bolt and the mating clamp load on the joint. So how does this tension relate to the torque needed to rotate the fastener? Actually, it’s a direct relationship most commonly expressed as T = KDF, where T, K, D and F are the torque, friction factor, nominal bolt diameter and the force (or tension), respectively. So for a given size bolt, torque is directly proportional to tension, with a factor K, (often referred to as the nut factor or friction factor), the only variable that must be known to be able to calculate torque from tension or visa-versa. Unfortunately, this K factor is a compilation of several friction components which vary with materials, finishes, pressure and the speed of relative motion. It is therefore quite difficult to predict (even varying during tightening), so assigning a value for a given joint can’t be done accurately without experimentation.

So why not measure tension directly as a way to determine how tight is right? This is in fact a possibility and is done in limited cases. More often, the torque vs. tension relationship is established in the lab with the results used to establishing target torque. However bolt tension is more difficult and expensive to measure than the toque applied to generate that tension. So the most common method of testing involves tensioning the bolt just beyond its yield point in the joint. At yield, bolt tension can be estimated based on the fasteners proof load (similar to yield strength).This provides a method of estimating the relationship between torque and tension without directly measuring tension.

So the take-way from this discussion is that while tension is the quantity of interest, torque is an easier to measure alternative, directly related to tension through a difficult to measure friction factor. Therefore the accuracy with which one can estimate tension from tightening torque can vary widely, with errors often ranging from 10% to 50% or more. It is important to note that this error has nothing to do with the accuracy of the torque wrench itself. The tool error is simply the uncertainty of how close the wrenches torque reading is to the actual torque. The K factor uncertainty represents how well the input torque can determine the bolt tension. This error is in addition to the tool error and is generally much greater. For example, a torque wrench can have less than 1% error but not be able to tighten bolts within 50% of their target tension.

2.When sizing a fastener for a given application, the saying “When in doubt, make it stout” is a guideline you should throw out.

Typically, unless one is designing products where the cost of failure is high, the detailed analysis and testing required to determine joint loading is not performed, and therefore the quantitative basis of how to size fasteners is limited. Even when the best analytical and test techniques are used, there is always uncertainty as to how well the analytical assumptions or the test protocol replicated actual use conditions. It is therefore common to apply some type of safety factor to the assumptions that go into threaded fastener sizing. While they often produce the same result, in some cases the engineer applies a factor to the assumed loads from which bolt sizes will be calculated, while in others the engineer will simply use the next biggest fastener. Often the latter approach is used when there is no load data available and the joint is being designed based on a product currently in the field. In either case, on the surface it seems a reasonable assumption that if big is good, bigger is better and safer. Actually, the opposite is often true.

The primary methods of varying bolt strength are its size and the material from which it is made. For example, a Grade 8 bolt obviously has greater capacity than a Grade 5 bolt of the same size (In the metric system, property classes 10.9 and 8.8 are the near equivalent of Grade 8 and Grade 5, respectively). But what if we don’t need greater bolt strength and simply want to optimize the joint at the existing strength. One option would be to use a higher grade bolt than planned but reduce its size to yield the same capacity. This is the option we will explore in Table 1. The contents of Table 1 reinforce the axiom that one should strive to use the smallest diameter fastener with the largest L/D ratio possible.

 Table 1.– The Impact of Substituting for a Gr 5 (class 8.8) for a Gr 8 (1class 0.9) Threaded Fastener Which is One Standard Size Smaller. Range of baseline Gr 5 / 8.8 size is 5/16″ to 1″ (M8 to M24). Area Impact of Substitution See Figure # 5/16 Gr 8 for 3/8 Gr 5 Overall Better Worse Same/Depends Tensile Strength Strength comparison is based on proof load – the maximum load that does not cause permanent deformation. The proof stresses in the equivalent grades of metric and English systems are very close so the bolt to bolt differences are primarily due to differences in cross-sectional area. The metric system has larger jumps between sizes so decreasing size has a greater impact in strength. Figure 1 5/16 -18 Gr 8 bolt is 95% as strong as the 3/8 -16 Gr 5 English Metric Eight of 10 English sizes show improvement averaging 2%. Five of 7 metric sizes show a decrease averaging 8%. Fine threads would improve relative strength an additional 10%. Weight As density is essentially unaffected by grade, weight comparison is based on the relative volume of the two sizes. That relative volume changes as the bolt length changes because the head height is fixed. These results are based on a Baseline length of 3-D rounded to the next longest standard length. Figure 2 Both Systems The average weight of the smaller size was 72% in the English system and 65% in Metric relative to the baseline. Size The most practical aspect of comparing the impact of comparing two different bolt sizes is the head size, as this generally determines how easily the bolt can be packaged. Don’t forget that the drive style also has a significant impact on the ultimate packaging density as it determines tool clearance. Both Systems Each step down in std. size reduces hex cap head width approx. 20% and height approx. 15% in both systems. Resistance to Vibration Loosening When lateral external forces can overcome the friction generated within the joint, the clamped components and/or mating threads are capable of sliding relative to each other. This relative movement can cause fastener rotation as the thread helix angle allows the tensioned fastener to reduce grip length, and therefore reduce bolt tension. This motion also increases the level of embedment in the joint, further decreasing bolt tension. A smaller diameter bolt tensioned to the same level will elongate more, so a given decrease in stack height due to embedment results in relatively lower loss. Also, a smaller diameter fastener of the same grip length is generally preferable because the shank is less rigid and more capable of flexing, thus transmitting less motion to the threads. We conducted a simple test to illustrate both these effects, bolting two bars together and then fixing one end while flexing the other while real-time bolt tension readings were taken (Figure 3). We also took video of the test in action showing the level of flexure. See Video Figure 3 Figure 4 Figure 5 The average of two runs show 5/16 tension loss at about 50 lb and 3/8 loss at 300 lb from an initial tension of about 4650 lb. This loss was likely more due to embedment than relative thread motion. The level of relaxation in this type of test is dependant on how much relative motion is generated at the free end. In this setup relative motion at the clamped end reduced motion at the free end. Both Systems Due to the wide variety of joint and loading configurations, quoting general estimates of the benefits are impossible. Cost Component cost comparisons are always difficult because the price paid is as dependant on commercial considerations specific to each purchase as it is to the actual manufactured cost of the component. The Figure 6 cost comparison was made by comparing costs from three major distributors. Costs were expressed in relative, rather than absolute terms as this differential cost is less affected by commercial considerations that the absolute cost. Figure 6 Both Systems By coincidence, the average the cost of the smaller, higher grade fastener was 81% of the baseline cost. Figure 1 also shows discontinuities in the cost of substituting 9/16 and M14 sizes. This higher price for somewhat less common sizes is washed out in higher volume purchases. Ductility In this context ductility refers to the amount of strain (elongation) the fastener will exhibit between the point it yields and when it ultimately fails. Within a particular class of materials, increasing strength and hardness comes at the expense of reduced ductility. In most cases higher ductility is desired, all else being equal. Worse The minimum specified elongation at yield for Grade 5 and Class 8.8 bolts are 14% and 12%, respectively. For Grade 8 and Class 10.9 bolts it is 12% and 9%. Susceptibility of Failure Due to Stress Corrosion Cracking (SCC) and Hydrogen Embitterment (HE) Stress corrosion cracking and hydrogen embrittlement are two directly related phenomena that can cause fastener failures at stress levels much lower than calculations would predict failure. Though the failure mechanism is the same, hydrogen embrittlement refers to situations were hydrogen is introduced prior to installation, generally during plating. The source of hydrogen in a failure due to stress corrosion cracking would be a corrosive reaction due to the environment in which the fastener is exposed. In both cases the harder the material, the more susceptible it is to failure of this nature. Worse Understanding the impact of plating methods on hydrogen embrittlement is much better known today than in the recent past. Also, the hardness of a Gr 8 bolt is near the lower limit of what is considered a critical level. Therefore while the possibility of Gr 8 failure is not dangerously high, it’s potential is greater than with the use of Gr 5 fasteners.  Figure 1. — The relative strength of replacing a given fastener with one that is smaller and a higher grade.  Figure 2. — The relative weight of replacing a given fastener with one that is smaller and a higher grade. Figure 3. — Test assembly used to test tension relaxation. See Video Figure 4. — The results of the flexure test on the assembly shown in Figure 3. A video link of the test is contained Table 1.  Figure 5. — The difference in elongation between tensioning a Gr 5 (Class 8.8) bolt to 75% of its proof load and tensioning a Gr 8 (Class 10.9) bolt one size smaller to the same tension.  Figure 6. — The relative cost of replacing a given fastener with one that is smaller and a higher grade. Based on survey of three fastener distributors.

3.When an external tensile load is applied to a joint, that increased load is not directly added to bolt tension

In simple terms, the bolt does not “feel” the entire external load. In fact, in most cases the vast majority of this additional load is absorbed by the clamped joint members because the joint is usually much stiffer than the bolts. This is the reason bolts tensioned at or near yield can often resist significant external tensile loads, such as the head bolts in your car’s engine. At some point, however the external load can be great enough that the clamp load on the joint is unloaded completely. Any additional load from this point will be entirely additive to the existing bolt tension. The balance between the forces acting on the bolt and the joint are generally displayed on a graph called a “joint diagram”. However, these diagrams aren’t clearly understood without some explanation and study, so we put together what we thought was a more easily understood illustration.

Using a component from an assembly on which we recently conducted some torque-tension testing, we performed a simple test showing the impact of external tensile loading on the bolt tension of a pre-loaded bolt. As shown in Figure 7 we modified the existing assembly by replacing half the joint with a circular plate and replacing the eight 5/16 – 18 socket head cap screws four Gr 5 hex head cap screws. These fasteners were prepped with ultrasonic sensors to allow real-time measurement of bolt tension in the joint. Adapters allow the test assembly to be mounted into a tensile tester. Figure 7. — Test joint used to show the effect of external load on bolt tension. Close-up of top plate with sensored bolts and signal pickup (left). View of assembly mounted in tensile tester for external load application (right).

A target preload of 2,500 lb per bolt was set. The four fasteners were tensioned to slightly greater than that level to allow for relaxation. Just before the test was conducted, tension was read on the four bolts and found to total 10,410. The tensile tester was then programmed to apply a 14,000 lb load at a rate of 30,000 lb/min and then return to home. The tension of one bolt and the load applied by the tensile tester were simultaneously monitored on the ultrasonic system’s transient recorder. The graph of bolt tension and external (tester) load vs. time are shown in Figure 8. Note that the preferable basis of this graph would be position (the relative position of the tester’s cross head), but that signal was not available to the transient recorder. However, since the loading was at constant rate after the initial take-up of about 1,500 lb, the relationship shown in Figure 8 would look identical using either basis. Immediately evident is the change in rate of increasing bolt tension. While the load is applied uniformly the bolt tension initially rises very gradually with the slope increasing a bit until an inflection point where it rises steadily in a linear fashion. That point, noted on the graph as Point A, is the load at which the joint is unloaded completely and 100% of the additional applied load goes directly into increasing bolt tension (sometimes called the “critical load”). That inflection point was estimated at to occur at an applied load of 12,364 lb and a bolt tension of 2801 lb. Figure 8. — Graph of bolt tension and applied load. The early take-up loading and the realease of loading after hitting the target load have been trimmed from plot for clarity.

So up to Point A an external load of 3091 lb per bolt (12,364/4) resulted in only a 261 lb (2801-2540) increase in bolt tension. After Point A, the additional bolt tension should equal the added external load on a per-bolt basis. The calculations are close to what was expected, as the additional 389 lb load per bolt [(13,918-12,364)/4] results in 421 lb of increased bolt tension. Selecting the precise beginning of the linear portion of the tension plot is likely the primary source of error. A question concerning Point A that may arise is why the critical load does not equal the total clamp load on the joint before the external load was applied (12,364 lb. vs. 10,410 lb). That difference indicates the joint is stiffer than the bolts, and actually allows us to calculate the relative stiffness. The 12,364 lb critical load is 18.8% greater than the 10,410 lb pre-load. Through analysis it can be shown that the ratio of the bolt and joint stiffness equals the fractional increase in load required to unload the joint relative to the initial preload. Therefore, in this case the joint is estimated to be 5.3 times as stiff as the bolts (1 / 0.188 = 5.3).

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