Using a Design Margin or a Probability of Failure Approach to Bolted Joint Design Background The root cause of the majority of bolt-joint failures is due to insufficient preload. It is unusual for the bolt to be overloaded. If the preload provided by the bolt is insufficient, joint separation and movement can occur resulting in possible bolt fatigue and self-loosening issues. In order that such problems do not occur it is vital that there is sufficient residual clamp force acting on the joint interface after accounting for the effects of the applied forces and embedding losses. A Preload Requirement Chart graphically illustrates this point as it looks at the forces acting on the joint interface. Such a chart is shown below. I was recently asked the question that if the minimum preload value was equal to the total preload requirement, would the joint be okay. That is, the design margin would be 1, so would the joint be, okay? Most Engineers are familiar with the use of a design margin or factor of safety. Crudely put, if the margin is below 1 the joint will fail, if above 1 it will be okay. It gives that certainty which we crave for, will the joint fail or not, yes or no. Reality is more nuanced. Probability Assessment Instead of being absolute values, preload, applied forces, embedding loss etc. are probability distributions. This means that the answer to the question that if the design margin was 1, would everything be okay, cannot be categorical. There will be a probability, a small one, that the total preload requirement would be greater than the minimum preload. Hence, not okay. A truer picture is what probability of failure is acceptable. This is likely to vary with the application, no one is likely to be happy if a nuclear reactor joint had a failure probability of 1 in 1000. The Normal or Gaussian Distribution A normal, or gaussian, distribution is the famous bell shaped curve that is shown below. The results centre around the mean, away from the mean, the values become less and less likely. Based upon the analysis of many torque-tension tests, as well as torque measurement, the distributions are normal, or usually close to normal. A typical set of results is shown in the image below. Normally, engineering judgement would be used to decide, given the uncertainty about the loading and preload values, what design margin would be acceptable. But just based upon the statistical aspect, if the design margin was just 1, there is a chance that in practice a very low failure rate can be expected assuming that load and preload values are known. To get a failure rate that was insignificant, the design margin needs to be larger than 1. A probability assessment can be used, together with some engineering judgement, to determine how much larger than 1 the design margin needs to be given the implications if failure of the application did occur. Why complete a Probability Assessment A probability assessment of failure is closer to the reality of the situation and offers a refined and data-driven approach compared to a traditional factor of safety. This can be important, here's why: Insight into variability: Probability assessments account for uncertainties in aspects such as the bolt preload, loading conditions, etc. By analysing these variables statistically, you can understand the likelihood of failure more comprehensively. Risk management: In critical applications, even the smallest risk of failure can have catastrophic consequences. Most joints are torque tightened; this approach needs to take account of the variation in the fastener friction which generally follows a normal distribution (the classical bell shaped curve). Due to this, the minimum preload is not an absolute minimum but a level at which just a very small percentage will fall below, such as 0.1%. But in many applications, having a failure rate of 1 in 1000 (which is 0.1%) is unacceptable. Probability assessments help quantify and manage risk, enabling engineers to prioritize safety in a meaningful way. It is difficult to quantify risk when a design margin approach is used. The design margin/factor of safety is simpler and quicker to apply and remains widely used for its conservatism and reliability. However, the choice between these methods often depends on the complexity and criticality of the engineering application. There are practical difficulties in applying the probability approach. In bolting, frequently there are two issues. What is the fastener friction value and hence the bolt preload for the specified tightening torque and secondly, what is the loading being applied to the joint. For a probability approach to be applied, the probability distributions are needed which are usually unknown. Optimized designs: The design margin/factor of safety approach often involves applying a blanket multiplier to ensure safety, which can result in over-design and inefficiency. Probability assessments allow for optimization, balancing safety with cost, weight, or resource constraints. Real-world relevance: Probability assessments align more closely with real-world scenarios, where failure isn't always a black-and-white outcome. This method provides insights into degrees of reliability and helps make informed decisions based on acceptable risk levels. This can be especially useful when a service issue arises in which bolt fatigue or loosening issue is being experienced. Being able to estimate the degree of the problem can be useful in decision making. An example of this is illustrated below. As an example, consider a joint looked at in a previous newsletter, this consisted of several M10 property class 10.9 bolts. The applied force is resolved so that an individual bolt region sustains a shear force of 5 kN. The joint plates have an interface coefficient of static friction of 0.15.As an example, consider a joint looked at in a previous newsletter, this consisted of several M10 property class 10.9 bolts. The applied force is resolved so that an individual bolt region sustains a shear force of 5 kN. The joint plates have an interface coefficient of static friction of 0.15. To prevent joint slip a clamp force of at least 33.3 kN (5 / 0.15) is needed plus any preload loss from embedding. Using the BOLTCALC software to complete the calculations, allows a Preload Requirement Chart to be created. This is shown below: The design margin is 0.67 and so some joints can be anticipated to fail. The actual percentage of assemblies that would fail depends upon the intersections of the preload and applied force statistical distributions. As previously mentioned, the preload variation is likely to be normal, or close to normal. The load distribution in most situations is unlikely to be normal. The calculation to determine the preload was based upon the minimum interface friction value. The maximum would likely to be close to 0.3, with again evidence that it would follow a normal or close to normal distribution. A statistical analysis of the joint showing two scenarios. The first being that all the assemblies must sustain the maximum loading, this gives a failure rate of 8 out of 10. The second, that the loading on the assemblies is random, gives a failure rate of 1 in 10. These charts are shown in the graphic below. Reality is likely to be between these two extremes. It would require a significant amount of testing and analysis to determine a more precise value for the failure rate since the exact forms of the probability distributions would need to be determined. For a service fix for this application it was decided to look at the use of a friction shim. With a shim at the joint interface, the coefficient of static friction is increased to 0.7 reducing the preload requirement from 39 kN to 18 kN. There is now a design margin of 9 kN or 1.48 (as a ratio between the minimum preload to the preload requirement). Whether this is deemed sufficient is an engineering judgement that would consider the likelihood of the loading being as assumed etc. When a friction shim is included, it can be expected that the preload loss from embedding will increase due the extra interface being present and the surface condition. The increase in embedding loss is more than compensated by the reduction in the clamp force needed to prevent slip. Although the above preload requirement clearly shows a design margin greater than 1 (it is 1.48), when a statistical analysis is applied, there will remain a very small chance of failure. This is illustrated in the two statistical charts shown below. Whether such a low failure rate is acceptable will depend upon the criticality of the application, but for your normal bolted joint the answer is likely to be yes. The disadvantage of the probability approach is that it can be disconcerting but is likely to be closer to reality than the design margin approach. It is disconcerting since most people are uncomfortable with a risk of any magnitude. The Design Engineer may well be asked the question, will it fail or not? Replying that there is a failure probability of 0.000006 is likely to raise eyebrows and maybe concern. In practice, even with the randomised loading case, the failure rate is likely to be significantly less than 1 in 170000. The probability value assumes that if joint slip occurred just once, joint failure would result. In practice, although a single slip would likely reduce the preload to some extent, the chance of a subsequent applied dynamic load, slipping the joint again would be remote. The bending stress incurred and potentially fixed into the threads could well however have fatigue consequences. These probability considerations are of importance in applications that are safety critical. To ensure that the probability of failure is negligible, a design margin somewhat greater than 1 is needed. The BOLTCALC program can complete a probability assessment on whether the preload is sufficient so that the probability of failure is negligible. The charts presented here are from the BOLTCALC program. Social Media Links Instagram Linkedin Twitter