… The second case is for very thick clamping areas. The issues include bending loads, torsional loads, and fatigue. As can be seen in Figure 9, the methods are very similar for "thick" clamped joints when there is a significant fraction of soft material (i.e. Try this one: This page provides details on the design and analysis of bolted joints. American Society for Testing and Materials. Diameter of the load bearing area between the bolt head and the clamped material (Figure 1), The effective diameter of an assumed cylindrical stress geometry in the clamped material. This series of eight articles will cover all the design guideline of the ACI code with the help of the following concrete anchor foundation bolt design calculation example: Problem statement of the design example. The remainder of this chapter is devoted to various methods of estimating the stiffness of the clamped material and comparing the various methods. Downloads When various factors are typed into the Input cells, Excel will calculate … NASA [11] chose X = 2 and Y = 3 and Bickford [5] states these are the accepted aerospace values. Figure 6 shows the correlation and how it matches to the finite element data. For constant amplitude cyclic loading, there are multiple theories to define stress-life curves in terms of the alternating stress, σalt, the mean stress, σmean, the endurance limit, Se, and the true fracture stress, σfracture [3]. When considering factors (or margins) of safety for bolted joints, it must be realized that part of the load on the joint (the preload and resulting clamping forces) should NOT be scaled by the applied loads to account for the factors of safety, they are fixed. 1. The actual value of dh that really should be used is the start of the stress frustum and not the diameter of the bolt head and/or washer. this does not produce conservative results). Shigley’s Mechanical Engineering Design. The methods of Pulling [13], and the associated Excel spreadsheet, can still be used and reasonable results obtained, but it is important to understand the theory, the limitations, and the deficiencies in it. // -->, Bolt Threads, Grade, Bolt Strength, Excel Spreadsheet Calculator, Bolt Pattern Group Pullout Excel Spreadsheet Calculator, Engineering Fundamentals of Threaded Fastener Design and Analysis, Calculating Assembly Torque per ISO 68 & ISO 724, Bolt Elongation Equation and Calculator while under Axial Stress, Fastener / Thread Tensile Area of External Thread Formula, Fastener / Threaded Pitch Circle Diameter Formula and Calculation, Fastener / Threaded  Shear Area Formula and Calculation, Minimum Thread Engagement Formula and Calculation ISO, BS EN 20898-2 Proof load values - Coarse thread, Minimum Length of Thread Engagement Formula and Calculations Per FED-STD-H28/2B, Shear Area Internal and External Thread  Formula and Calculation Per FED-STD-H28/2B, ANSI, ISO Thread Designations and References, Strength Grade Designation System of Steel Bolts and Screws, Self Tapping Screw Pull-Out and Torque Calculator, Torque Table Standard Bolt Sizes SAE Grades 1 - 8, Torque Values Stainless Steel Bolt Table Chart, Bolt Preload Tension Equation and Calculator, Torque vs Tension Bolts Table Chart SAE J429 Bolts, Torque Wrench Adapter Reduced Arm Calculation, Torque Wrench Adapter Extended Calculation, Guide to Design Criteria for Bolted and Riveted Joints, Hydraulic & Pneumatic Torque Wrenches Application Review, Fastener Thermal Expansion / Contraction Application and Equation, Press Fit Engineering and Design Equations, Bolt or Pin In Single Shear Equation and Calculator, Bolt or Pin In Double Shear Equation and Calculator, Single-Riveted Lap-Joint Formulas for Stress and Strength Design Equations and Calculator, Double-Riveted Lap-Joint Formulas and Calculator for Stress and Strength Design, Single-Riveted Lap-Joint with Inside Cover Plate Formulas and Calculator for Stress and Strength Design, Double-Riveted Lap-Joint with Inside Cover Plate Formulas and Calculator, Loading Capacities of Ordinary Bolts per. The bolt meets the factor of safety for the combined load if the following inequality is met. In the latest form, this method has been shown to be applicable to most commercial metals (including Steel, Aluminum, Brass and Titanium) and a wide range of geometries including two-material joints. The work of Wileman [17], Musto [10] and Morrow [9] are all based on this method and each is an extension of the previous work. Although not shown, this significant difference begins at roughly an l/db ratio of about 2.0. Metric Bolts - Minimum Ultimate Tensile and Proof Loads US Bolts … For the case where the bolt head diameter (or washer diameter) is greater than the joint "diameter" of the material being clamped, the entire area is used so, where DJ is the diameter of the joint. Several methods for the design and analysis of bolted joint connections are presented. BOLTED CONNECTIONS – II Job No: Sheet 1 of 1 Rev Structural Steel Job Title: Eccentrically Loaded Bolt Group Design Project Worked Example – 1 Made by Date 01-10-00 SRSK Checked by VK Date Calculation Sheet Design Example 1: Design a bolted connection between a bracket 8 mm Remarks thick and the flange of an ISHB 400 column using HSFG bolts… Subscripts will be described in the text. Hardware Supplier Manufacturer … Additional information on nut factors can be found in Bickford [4] and the Machinery's Handbook [12]. Figure 2 identifies important geometric parameters for a thread joint. Otherwise, the Shigley method is recommended. Units are given in terms of length (L), force (F), radians (rad) and temperature (T). The positives of this method include the overall simplicity of the application of the method, the simplicity with which the effect of clearance holes can be accounted for, and that an extension to including bending to the factor of safety calculations may be included (although they should be used with great care since the underlying assumptions are based on beam theory accurately portraying the joint). Roach, R. A, Working Draft of "Design & Analysis Guidelines for Satellite Fasteners & Flexures", 2007. He derived the same expressions for axial loading that were shown above (except he did not include qi to account for clearance) and provided the following guidance for Q (actually he provided guidance for the area of the cylinder which implies Q). Durbin, Samuel, Charles Morrow, and Jason Petti, "Review of Bolted Joints near Material Edges", Internal Sandia Memo, 2007. Pulling, E. M., S. Brooks, C. Fulcher, K. Miller, Guideline for Bolt Failure Margins of Safety Calculations, Internal Sandia Report, December 7, 2005. From the springs in parallel assumptions, we know the total extension of the bolt equals the total extension of the layers which can be written as, From static equilibrium, the force in the bolt is equal and opposite to the force in each layer which can be written as, The force can be related to the constrained displacement for each layer (and similarly for the bolt) as. The differences are likely due to the fact that Morrow's data covers multiple materials in addition to various geometries and Wilemans's data is for a single material. The joint must demonstrate a separation factor of safety at limit load. Figure 1 contains a cross section of a typical through-bolted joint. BS449: Part 2 Bolt Grade 8.8, Loading Capacities of Ordinary Bolts per. If an estimate can be obtained for the stiffness of the bolt (which is trivial) and the clamped material (which is difficult), then externally applied axial loads can be partitioned appropriately between the two and factors of safety can be computed to determine if the joint design is sufficient. 2 / DESIGN GUIDE 1, 2ND EDITION / BASE PLATE AND ANCHOR ROD DESIGN The vast majority of building columns are designed for axial compression only with little or no uplift. Safety factors need only be applied to external loads. Fig.1: Anchor Bolt design Example Plan View . Miller, Keith, private conversations, 2007. Thermal effects are important in many bolted applications. The trends of Morrow [9] seem to be more physically intuitive and are backed up by finite element analysis. Bannantine [3] also notes that tests using random histories with several stress levels show very good correlation with Miner's rule. Their data is based on multiple sources. axial) compression (see Shigley [16] for the complete derivation), the stiffness of a layer can be computed as. Actual test data tend to fall between the Goodman and Gerber curves. This report provides a guideline for designing and analyzing bolted joints. Bending loads can come from two primary sources. Engineering Forum In contrast, a complicated joint or one with small margins may require additional analysis. For such col-umns, the simple column-base-plate connection detail shown in Figure 1.1 is sufficient. Design of bolted beam-column connections Bolt capacity of force resistance needs to be calculated in most of the connections except some seated connections as shown in The general procedure of bolted beam-column connection design is: Fig.2.4 and Fig.2.5 (bolts … To get a quantitative comparison of the various analytic method relative to one another, consider the case of 5/8" bolt with a bolt head diameter of 15/16" (1.5 times the bolt diameter) clamping two "plates" of the same material. at n = 0.5) at the bounds. nd is used to denote non-dimensional quantities. The bending load will be primarily seen by the bolts as axial load (tensile on one side and compression on the other). They followed the methodology of Musto [10] that was described in the previous section and looked at both edge effects and corner effects. The guidelines NASA [11] used for bolted joints on the space shuttle are generally applicable and are adopted here. The thermal load that increases the tensile load will be added to the maximum preload when computing the factor of safety of the bolt. ANSI Hardware Engineering Data  No effort has been made to ensure this is still 'state of the art' so an interested reader may want to pursue a literature search. }, Fastener, Bolt and Screw Design Torque and Force Calculations, ISO Hardware Engineering Data It is based on a standard spring stiffness model for the overall joint that was previously discussed. … { Two of those methods are presented here. The external axial load applied to separate clamped materials. The calculations within this live spreadsheet will facilitate the initial design and engineering of many types of bolted and riveted joints. The methods produce very similar results. As such, small errors in Q become large errors in the member stiffness. Miner's rule for determining failure due to fatigue can be written simply in the form, where ni is the number of cycles at the ith stress amplitude level and Ni is the number of cycles to failure at the ith stress amplitude. Subscripts will be described in the text. Preliminary analysis indicates a joint with a single threaded fastener can resist torque loads on the order of the applied preload torque. First, there must be 'symmetric' frustums across the entire joint regardless of the number of materials (otherwise static equilibrium would not be met). Figure 8 shows the results for an l/db ratio of 0.75 (this represents a "thin" clamped joint) and Figure 9 shows the results for an l/db ratio of 5.0 (this represents a "thick" clamped joint). As expected, the Wileman [17] and Morrow [9] methods produce similar results since Morrow's fit is based on extensions to Wileman's work. As can be seen in Figure 8 the methods produce very similar results for "thin" clamped joints. A linear analysis allows for accurate geometric representation and loading effects and limited contact effect can also be incorporated. color: #000000; - You can calculate the shear strength or the tensile strength of a bolt • Simple connection: If the line of action of the force acting on the connection passes through the center of gravity of the connection, … document.write(''); If this is done, a hand calculation of the shear load on the bolts can done and that load added directly into the loads on the bolt (it is desirable to have the shear load taken by frictional capacity in which case the actual load the bolt would see is zero). There are a number of additional issues that will be discussed here. Joint Design Joint Design Loads can be applied to bolted joints in a number of different ways, each of which produces unique effects on the joint. •The diameter of this unthreaded rod is the average of the ... Head Type of Bolts ... C indicates the proportion of external load P that the bolt will carry. At this point, the recommended method is to use a pre-computed nut factor from Table 4 until the analytic methods are better understood, compared to the known methods, and confidence is gained in the accuracy of the method. His equations are modified here to account for qi so that it can be compared to the work of Pulling [13]. These can include off center holes, deformation due to the preload causing bending (e.g., pipe flanges bending due to the gap between them when preloaded), or other geometric effects. 1357-1360. A table of nut factors was given in Table 4. Bickford [5] suggests that in general the shear ultimate strength for steels is between 0.55 (for stainless steels and aluminum) to 0.60 (for carbon steels) times the tensile ultimate strength. A low nut factor gives a higher preload and clamping force but puts the bolt closer to yield while a high nut factor gives a lower preload and clamping force but the capacity of the joint to resist external tensile loads has been reduced. This is the manufacturer specified axial load the bolt must withstand without permanent set. Axial loads, shear loads, thermal loads, and thread tear out are used in factor of safety calculations. The data shown in Figure 7 indicates that Q can reasonably vary from 1.6 to 2.6 depending on the geometry. the edge of the assumed loaded material) are free (i.e. See the instructions within the documentation for more details on performing this analysis. Where possible, the description identifies a figure or equation that further defines the parameter. BS: 449: Part 2, GD&T Training Geometric Dimensioning Tolerancing. Any consistent set of units may be used. Bolt proof load. For cases with a small alternating stress compared to the mean stress, there is little data. the surrounding joint contains material to at least three times the bolt diameter). This document provides general guidance for the design and analysis of bolted joint connections. Online Books & Manuals For hard steels (i.e., brittle) where the ultimate strength approaches the true fracture stress, the Morrow and Goodman lines are essentially the same. The general approach is to idealize a bolted joint into a pair of springs in parallel. Based on this, it is recommended to use the Morrow method whenever only 2 layers of material are being clamped and the l/db ratio is within their recommended bounds. This is a major concern and great care must be taken when considering bending loads on bolted joints with this method. By assuming a 1D (i.e. Fig.2: Anchor Bolt design … Bickford's [4] and Pulling's [13] work is based on this assumption. These include Soderberg. From this data we can see there is a large variation in Q depending on the thickness of the joint relative to the bolt diameter and the joint diameter (i.e. According to the following calculation formulas, the program calculates geometric dimensions of the bolt from the specified nominal bolt diameter: Minimum diameter of the nut thread D 1 = d - 1.082531 p … the two "plates"). Factor used in the computation of thread tear out, Length of engaged threads needed to avoid tear-out in using high tensile strength bolts. An applied axial load, F, will produce a displacement, δ. Need a bolted joint calculator? An unconstrained object will expand due to a change in temperature as, where ΔL is the change in length due to thermal effects, αL is the coefficient of thermal expansion, L is the length, and ΔT is the change in temperature. The approach is based on beam theory and as such they are assuming the ends (i.e. The first stage is based on idealized models to provide an initial estimate useful for design. In these cases, any analysis should be done using a range of nut factors to bound the results. Disclaimer ; A factor, Q, is defined as the ratio between the actual bolt diameter and the idealized cylindrical stress field, By considering the layer as a one dimensional spring, the stiffness of the ith layer can be computed as, The area of the ith layer can be computed, assuming the inner diameter is qidb (where qi ≥ 1 and is used to allow for clearance between the clamped material and the bolt) and the outer diameter is Qdb, as, The addition of qi is a logical extension to account for clearance holes that were included in the work of Pulling, et. It is not recommended to use these equations. For ductile steels, the Morrow line predicts less sensitivity to mean stress. The reasons for recommending the DMP method are 1) it matches very well with finite element analysis and Shigley's frustum approach for standard cases, 2) it doesn't have the subtleties and the unknown accuracy for differing materials with different thickness (but matches extremely well for identical thicknesses where Shigley is known to be accurate) and 3) it is the easiest to apply and gives the same results in cases where both are equally applicable. document.write('') These loads can be significant and should be accounted for but there is no general approach to handle the cases so the engineer must determine how to account for them and to ensure the design meets all the criteria when considering these loads. Musto [10] extended this approach to two materials by introducing two new variables, where ms denotes the 'more stiff' material and ls denotes the 'less stiff' material. The accuracy of this method is highly dependent on the choice of Q. This set of equations yields the additional loads due to the thermal effects. BS449: Part 2 Bolt Grade 10.9, Loading Capacities of Ordinary Bolts per. The results of this work produce a clamped material stiffness for commercial metals of. if (document.getElementById("tester") != undefined) The following two tables list variables used throughout this document. Part of the load will be taken up by the bolt, Fb, and part will be taken up by the clamped material, Fm. Additionally, limited guidance is provided for fatigue considerations. In addition to the yield limit equations for dowel-type connections, application of spacing, end, and edge distance requirements for connections and provisions related to bolt design … Durbin, Morrow and Petti [6] examined boundary effects of bolted joints when the bolt head diameter (or washer) is 1.5 times larger than the bolt diameter and in the restricted db/l range of 0.167 to 1.786. ; There are N equations of the type of Equation (32) (one for each layer). In cases, where it is not, it is recommended that the hollow frustum approach of Shigley [16] be used. Axial loads, shear loads, thermal loads, and thread tear out are used in factor of safety calculations. If we have N layers of clamped materials, we have 2*N+2 unknowns (N+1 forces and N+1 extensions, the +1 is for the bolt). BS449: Part 2 Bolt Grade 12.9, Excel Spreadheet Design Calculator per. As such, it can be used for both combined and tensile only in cases to judge if the joint meets the factor of safety requirements. For cases with a small mean stress in relationship to the alternating stress, there is little difference in the theories. Applied shear stress in a stress field. A change in temperature can cause an increase or a decrease in the preload of the bolt. This source of this page is Brown et al., "Guideline for Bolted Joint Design and Analysis: Version 1.0," Sandia Report SAND2008-0371, Sandia National Laboratories, 2008. The correlation has a standard error of 0.065. where E is the Young's modulus of the material, db is the diameter of the bolt and l is the thickness of the clamped materials (i.e. Equation (31) is one additional equation. where dbmm is the minimum major diameter of the external threads, di is the maximum pitch diameter of the internal threads. Applied tensile or compressive stress in a stress field. This data is shown in Figure 7. A discussion of them is beyond the scope of this document and the reader is referred to a reference on fatigue such as Bannantine [3]. They implemented an iterative solve for Q and incorporated that into an updated spreadsheet based on the original work of Pulling [13]. Bickford [5] uses these same equations for the case where the internal threads are stronger than the external, and this is the practice recommended here. We know the bolt and the clamped material act as springs in parallel so we can solve for the total displacement (assuming the joint is not loaded to the point where the material is no longer clamped which is complete failure of the joint) as, The stiffness constant, C, of the joint is defined to be the ratio of the load taken by the bolt to that of the joint as a whole and can be computed as, The part of externally applied load that is taken up by the bolt can be computed as, and the load in the clamped material can be computed as. For example, in the design of bolted … For the cases where these methods are applicable, this guide should be sufficient as an initial design and analysis guideline. Now that an estimate for the bolt stiffness, kb, and the clamped material stiffness, km, has been obtained, we can examine how an externally applied tensile load is partitioned between them. They assumed that the same material is loading in bending as was loaded axially. } In this article on mechanical design tutorial today I will talk about design … There is no one right answer or way to approach all the cases. } Used in Pulling's method (Equation 13), Diameter of a bolted joint. See. The following design resources are for design screws and bolts for the proper torque, stress, strain, preload and other engineering critical design parameters. While there are subtleties to applying the method, it has been used successfully since the 1960's for designing and analyzing bolted joints and it is general enough to apply to any axisymmetric geometry (although the accuracy is unknown at best or questionable at worst for anything but simple geometries). As such, how to consider factors of safety must be considered. Should you find any errors omissions broken links, please let us know -, Do you want to contribute to this section? It consists of a bolt, two washers, two materials, and a nut. For variable amplitude loading, Miner's rule can be used to estimate fatigue life [1]. A., J. J. Comer and J. L. Handrock. There is an additional concern with this method because it is probable that the actual load on the bolt due to bending will be higher than what this theory predicts (i.e. … The basic philosophy is to use a staged approach. Any of the methods can be used successfully if the engineer is aware of the assumptions and limitations and applies the theory correctly. All of the analytic or empirical approaches presented in this chapter make assumptions and are quite good in many cases but none applies in every case. The Soderberg method is very conservative and seldom used. Nowadays lots of software tools are available in market to take care about the lengthy calculations. Engineering News The following design resources are for design screws and bolts for the proper torque, stress, strain, preload and other engineering critical design parameters. document.write(''); BS449: Part 2 Bolt Grade 6.8, Loading Capacities of Ordinary Bolts per. The second term accounts for additional material based on the thickness, l, of the joint. For the purposes of this version of the document, washers can either be considered part of the bolt or as individual layers of clamped material. 45 degrees is often used but this often over estimates the clamping stiffness. The first primary source of bending loads is direct bending applied to the bolt during the preload phase due to geometric effects. These analytic methods seem to produce nut factors that are much larger than the experimentally accepted values. For the case of a bolted flange of a pipe with the bending applied to the neutral axis of the pipe, the actual load on the bolt will be more like an axial load and less like a bending load. This section outlines how to account for the thermal loads. This is the value Shigley used in the 1st edition of Mechanical Engineering Design. They are here to give some perspective to what goes into the nut factor. Calculations must use exact lengths of both the unthreaded portion of the bolt and the remaining length of the unengaged threaded portion of the bolt … Based on the pros and cons of each method, it is recommended that the empirical method of Morrow [9] be used as the preferred method when it is applicable. In general, it is highly recommended that any torsional load be carried through shear by having multiple bolts and/or shear pins rather than by a single bolt. A plot of Q for various thicknesses and DJ/dh ratios is shown in Figure 4. Oberg, E., F. D. Jones, L. H. Holbrook, and H. H. Ryffel, Machinery's Handbook, 27. As such, the methods described in the previous section should be applicable to most bolted joints. Additional work will be done to understand the differences in a future revision of this document. All of the analytic approaches presented in this section implicitly assume an axisymmetic stress field. That assumption is valid throughout this section as well given that the expansion (or contraction) is only axial (i.e. Bickford [4] noted that spheres, cylinders and frustums could all be used. A summary of analytic approaches to compute a nut factor are given in Appendix A. This is equivalent to a nut factor of. Again consider the case of 5/8" bolt with a bolt head diameter of 15/16" (1.5 times the bolt diameter) clamping two "plates". | Contact, Home [13] and is adopted here. (Equation 50), Dimensionless joint geometry parameter, or aspect ratio, used in the DMP method (equation 24). The data was generated assuming a 5/8" diameter bolt, d, with a bolt head diameter of 15/16" (1.5 time the bolt diameter), dh. The third method is based on using finite element analysis of bolted joints and fitting the results with empirical equations. Young's modulus for the less stiff (ls) material in a two material bolted joint. It should be pointed out that Shigley [16] suggests that the work of Wileman [17] is the preferred method (when it is applicable) to the frustum approach presented here. A ratio of applied stress, factoring in the required factors of safety, to allowable stress (this applies to both yield and ultimate strengths) is defined independently for the tensile load (Rt) and the shear load (Rs) as. Wileman [17] used finite element analysis to determine the clamped material stiffness for two "plates" made of the same material. floodproofing, and construction of a floodwall in a … This can lead to over-stressing the bolt or reducing the clamping load and therefore reducing the frictional capacity of the joint. The Machinery's Handbook [12] and the NASA guide [11] give estimates for the accuracy of bolt preload based on application method. These include better guidelines for choosing a pre-computed nut factor or using a method to compute a more accurate nut factor, bending effects (both globally applied that result in axial loads on the bolt and local bending on the bolt due to geometric effects such as bolting a pipe flange that has a gap between materials), fatigue analysis, extending the DMP method [9] to more than two materials and how to include thermal effects with it, and guidelines on designing bolted joints to carry shear load (including frictional capacity, shear pins, shear load applied to the bolts, etc.). There is no one right choice for the preload or torque. document.write(' ') He also chose to use a cylinder. These fasteners literally hold the world around us together. For rolled threads, he suggests an average stress concentration factor of 2.2 for SAE grades 0 to 2 and a factor of 3.0 for SAE grades 4 to 8. The design bearing strength at the bolt hole is φRn. A brief overview of the various options for assessing fatigue life are provided here but ultimately the engineer must use his/her judgment when assessing fatigue life of bolted joints. In the long term, it is planned to look at pressure vessel design codes where this issue is addressed to see if they can be applied in a general way. These tools definitely help to drastically reduce the design time. Register . This was the original assumption made by Shigley in his first edition mechanical engineering design book [8] and is what is chosen by Bickford [4]. Unless identified below, subscripts will be identified in the text. In this method it is assumed the true 'barrel shaped' stress field can be approximated as a cylinder of diameter dc (see Figure 3, dc equals Qd). The next comparison that can be made is using two materials for Shigley's method [16] and the extension of Wileman [17] by Musto [10] and then Morrow [9]. Physically, this parameter could be different for every clamped layer but for the equations presented in this document, it is assumed to be the same value for all layers. The second primary source of bending loads is a bending load applied to the structure that must be transmitted through the bolted joint. In this method, the stiffness in a layer is obtained by assuming the stress field looks like a frustum of a hollow cone (See Figure 5). Bickford's [4] method is dramatically different than the other 2 and in comparison will produce much lower clamped material stiffness. The divergence in the methods occurs as the clamped material gets thick compared to the bolt diameter. where X and Y are chosen dependent on how much conservatism is desired. else the extension that would be physically measured) and ΔLconstrained is the extension caused by the constraint. If the bolt is in a threaded hole, the starting point for the frustum at the threaded end should be at the bolt threads and this is typically assumed to be at the midpoint of the engaged threads and dh is typically used instead of db. Thread Stress Area Calculator and Equation, Torque Design Guidelines and Considerations. As will be shown by comparing the different methods in a later section, the value of Q is variable and depends on the geometry of the joint. While this joint includes washers on both ends, many bolted joints do not use washers and the methodologies presented in this document apply to bolted joints with or without washers. To determine if the internal threads will strip out before the bolt break, first compute the factor J as, where Sy,ET is the tensile strength of the external thread material and Su,IT is the tensile strength of the internal material and the shear areas of the external and internal threads are computed as. An analytic expression for the nut factor, K [12], can be written as, where P is the screw thread pitch, μt is the coefficient of friction between the threads, μB is the coefficient of friction between the bearing surfaces, DB is the equivalent diameter of the friction torque bearing surfaces and can be computed when the contact area is circular as. In many cases, additional work will be needed to assess the quality of current practices and provide guidance. Alternative design bolts use design features that indirectly indicate tension. It appears it is overly conservative and will not be considered further in this document. BS449: Part 2 Bolt Grade 4.6, Loading Capacities of Ordinary Bolts per. This implies a Q factor of. By combining the torque-angle curves with a few simple calculations … This section provides a comprehensive list of symbols used in equations and figures in subsequent sections. As can be seen by examining the data, there can be large ranges of potential nut factors and as such, it is recommended in the Standard Handbook of Machine Design [15] to only use nut factors when approximate preload is sufficient for the design. Connection Calculator Provides users with a web-based approach to calculating capacities for single bolts, nails, lag screws and wood screws per the 2015 NDS . For the case of equal tensile strengths of the internal and external threads, the length of engagement of the threads to prevent the threads stripping out should be more than, where Le is the minimum length of engagement, At is the tensile stress area of the screw head (given below), n is the number of threads per inch, dmt is the maximum minor diameter of the internal threads, and dbmp is the minimum pitch diameter of the external threads. Using it implies the need to have a very accurate solution due to small margins, designing into the non-linear regime, and/or other non-traditional design spaces. As will be shown, the results for the frustum approach and the Wileman approach produce very similar results for joints with only one material. $$ {1 \over k_m} = {1 \over k_1} + {1 \over k_2} + ... + {1 \over k_i} $$, $$ A_i = { \pi \over 4 } \left[ (Q d_b)^2 - (q_i d_b)^2 \right] = { \pi \over 4 } ~d_b^2 ~(Q^2 - q_i^2) $$, $$ k_{axial} = { \pi ~d_b^2 \over 4 } \sum_{i} { E_i (Q^2 - q_i^2) \over L_i } $$, $$ k_{bending.i} = { E_i I_i \over L_i } $$, $$ I_i = { \pi \over 64 } \left[ (Q d_b)^4 - (q_i d_b)^4 \right] $$, $$ k_{bending} = { \pi ~d_b^4 \over 64 } \sum_{i} { E_i (Q^4 - q_i^4) \over L_i } $$, $$ A = { \pi \over 4 } \left[ D_J^{~2} - (q d_b)^2 \right] = { \pi \over 4 } \left[ (Q d_b)^2 - (q d_b)^2 \right] ~~\text{when}~~ d_h \ge D_J $$, $$ Q = { D_J \over d } ~~\text{when}~~ d_h \ge D_J $$, $$ A = { \pi \over 4 } \left[ d_h^2 - (q d_b)^2 \right] + {\pi \over 8} \left( {D_J \over d_h} - 1 \right) \left( {d_h l \over 5} + {l^2 \over 100} \right) ~~\text{when}~~ d_h \lt D_J \le 3 d_h $$, $$ Q = {1 \over d} \sqrt{ d_h^2 + \left( {D_J \over d_h} - 1 \right) \left( {d_h l \over 10} + {l^2 \over 200} \right) } ~~\text{when}~~ d_h \lt D_J \le 3 d_h $$, $$ A = {\pi \over 4} \left[ \left( d_h + {l \over 10} \right)^2 - (q d_b)^2 \right] ~~\text{when}~~ D_J \gt 3 d_h ~~\text{and}~~ l \le 8 d_h $$, $$ Q = {1 \over d_b} \left( d_h + {l \over 10} \right) ~~\text{when}~~ D_J \gt 3 d_h ~~\text{and}~~ l \le 8 d_h $$, $$ k_i = { \pi ~E ~d_b \tan(\alpha) \over \ln \left({ (2 l \tan(\alpha) + d_h - d_b)(d_h + d_b) \over (2 l \tan(\alpha) + d_h + d_b)(d_h - d_b) }\right) } $$, $$ k_m = 0.78952 ~E ~d_b ~e^{ 0.62914 ~d_b / l } $$, $$ E_{eff} = { 1 \over {1 \over E_{ms} } + n \left( {1 \over E_{ls}} - {1 \over E_{ms}} \right) } $$, $$ k_m = E_{eff} ~d_b \left[ m \left( {d_b \over l} \right) + b \right] $$, $$ k_m = E_{eff} ~d_b ~( 0.9991 ~x_G + 0.2189 ~n + 0.5234 ) $$, $$ x_G = { d_b \over l } \left({ d_h^2 - d_c^2 \over 1.25 ~d_b^2 }\right) $$, $$ \Delta L_{bolt} = \sum_{i} \Delta L_{layer_i} $$, $$ L_e = { 2 ~A_t \over \pi ~d_{mt} ~[ 0.5 + n ~(d_{bmp} - d_{mt}) ~\tan(30^{\circ}) ] } $$, $$ A_t = {\pi \over 4} \left( d_b - {0.9743 \over n} \right)^2 $$, $$ A_t = {\pi \over 4} \left( {d_{bmp} \over 2} - {0.16238 \over n} \right)^2 $$, $$ A_t = {\pi \over 4} ( d_b - 0.9382 \cdot P)^2 $$, $$ J = { A_s ~S_{y,ET} \over A_n ~S_{u,IT} } $$, $$ {\sigma_{alt} \over S_e} + {\sigma_{mean} \over S_y} = 1 $$, $$ {\sigma_{alt} \over S_e} + {\sigma_{mean} \over S_u} = 1 $$, $$ {\sigma_{alt} \over S_e} + \left( {\sigma_{mean} \over S_u} \right)^2 = 1 $$, $$ {\sigma_{alt} \over S_e} + {\sigma_{mean} \over S_{fracture}} = 1 $$, $$ R_T = { (F_{preload.max} + F_{thermal} + FOS \cdot C \cdot F) / A_T \over S_{tensile} } $$, $$ R_s = { FOS \cdot \tau_{applied} \over S_{shear} } $$, $$ K = {1 \over 2 d_b} \left( {P \over \pi} + \mu_t d_2 \sec \alpha' + \mu_B D_B \right) $$, $$ D_B = {2 \over 3} \left({ D_0^{~3} - D_i^{~3} \over D_0^{~2} - D_i^{~2} }\right) $$, $$ F_P = { T \over R_o \left( \tan \alpha + { \mu_t \over \cos \beta } \right) + R_e \mu_b } $$, $$ K_{NASA} = {1 \over d_b} \left[ R_t \left( \tan \alpha + { \mu_t \over \cos \beta } \right) + R_e \mu_b \right] $$, Affordable PDH credits for your PE license, Tensile Area of a bolt used for thread tear out calculations (See Section 8.1), Integrated joint stiffness constant. 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