# 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.

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

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).

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.

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