The thermal load that reduces the tensile load will be subtracted from the minimum preload when computing the factor of safety for joint opening. document.write('') For ductile steels, the Morrow line predicts less sensitivity to mean stress. 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. The issues include bending loads, torsional loads, and fatigue. 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). It is based on a standard spring stiffness model for the overall joint that was previously discussed. A general relationship between applied torque, T, and the preload in the bolt, Fp, can be written in terms of the bolt diameter, d, and the "Nut Factor", K, as. NASA [11] allows using either pre-computed nut factors or computing the preload (without considering the uncertainties here but which must be accounted for later) as, where Ro is the effective radius of the thread forces (approximately half the basic pitch diameter of external threads), α is the thread lead angle, μt is the coefficient of friction between the threads, β is the thread half angle, μb is the coefficient of friction between the nut and the bearing surface, and Re is defined as, where Ro is the outer radius of the torqued element (nut of head) and Ri is the inner radius of the torqued element. Des., November, 2006, 127, pp. Using a non-linear finite element analysis can be very expensive and requires significant expertise. where β is the thread half angle, and α is the thread helix, or lead, angle. They also extended the work to address clearances, edge effects and variable bolt head diameters. They determined the clamped material stiffness including accounting for clearances, edge effects and variable bolt head diameters can be written as. Safety factors need only be applied to external loads. The trends of Morrow [9] seem to be more physically intuitive and are backed up by finite element analysis. The ultimate choice is of course left up to the engineer designing and/or analyzing the joint. Training Online Engineering First, there must be 'symmetric' frustums across the entire joint regardless of the number of materials (otherwise static equilibrium would not be met). 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. the two "plates"). The Bolt Pattern Force Distribution Calculator allows for applied forces to be distributed over bolts in a pattern. document.write(''); There can be as many as 200 or more factors that affect the tension created in a bolt when tightening torque is applied (refer to paragraph 2.2). By combining the torque-angle curves with a few simple calculations … where Le is computed in the previous section. In this case, one "plate" will be made from steel and the other plate from aluminum. a:link { 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. Engineering Toolbox 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. They implemented an iterative solve for Q and incorporated that into an updated spreadsheet based on the original work of Pulling [13]. where dbmm is the minimum major diameter of the external threads, di is the maximum pitch diameter of the internal threads. 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]. A critical component of designing bolted joints is not only determining the number of bolts, the size of them, and the placement of them but also determining the appropriate preload for the bolt and the torque that must be applied to achieve the desired preload. Strength of Materials. at n = 0.5) at the bounds. Bickford's [4] and Pulling's [13] work is based on this assumption. Bolt design per the 2015 NDS is not just a matter of selecting a design value from a table. The type of connection designed has an influence on member design and so must be decided even prior to the design of the structural system and design of members. Several methods for the design and analysis of bolted joint connections are presented. It consists of a bolt, two washers, two materials, and a nut. General symbol for stiffness of a bolt, clamped material or overall joint. With these assumptions, the bending stiffness for each layer can be computed to be, The moment of inertia, I, for the ith layer can be computed as, Once again assuming each layer is represented by a spring in series, the bending stiffness of the clamped material can be computed as. Engineering Forum 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. This set of equations yields the additional loads due to the thermal effects. (Equation 26), Equivalent diameter of torque bearing surfaces (Equation 53), Effective diameter of internal (nut) threads, Nominal bolt diameter and externally threaded material (bolt) major diameter for thread tear out (Figure 2), Externally threaded material (bolt) minimum major diameter, Externally threaded material (bolt) minimum pitch diameter (Figure 2). 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. Guidance is provided for general bolted joint design, computation of preload uncertainty and preload loss, and the calculation of the bolted joint factor of safety. … Figure 1 contains a cross section of a typical through-bolted joint. This is a major concern and great care must be taken when considering bending loads on bolted joints with this method. A preloaded joint must meet, as a minimum, the following three basic requirements: Bolt strength is checked at maximum external load and maximum preload, and joint separation is checked at maximum external load and minimum preload. Many factors need to be considered when making this determination. Minimum length of engagement of a threaded joint to prevent thread tear out. As can be seen in Figure 8 the methods produce very similar results for "thin" clamped joints. Engineering Book Store This can lead to over-stressing the bolt or reducing the clamping load and therefore reducing the frictional capacity of the joint. The down side of this method is that the accuracy is highly dependent on the choice of Q (or the area). The first is for the case when there is not enough material for the frustum to exist (e.g., a bolt hole very near an edge of a plate). Analytic methods for determining the loads on a given bolt of a joint can be found in Shigley [16] or other mechanical engineering texts. Subscripts not specifically identified in these tables will be addressed during discussions in the appropriate text. The general approach is to idealize a bolted joint into a pair of springs in parallel. See the instructions within the documentation for more details on performing this analysis. Thread helix angle (Figure 2) and the frustum angle for Shigley's method. 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. Diameter of the clearance hole(s) (Figure 1). For cases where a high degree of accuracy is required, the geometries and/or materials don't match the assumptions of these analytic methods, the loading is complicated, or the margins are very small, it is recommend that a finite element analysis be performed on the joint. 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. { [13], went on to define a bending stiffness for the clamped material using the same methodology. This document provides general guidance for the design and analysis of bolted joint connections. 1. [9] compared this equation to the one derived for the Q-factor method and noted the only unknown between the two equations is Q. BS449: Part 2 Bolt Grade 6.8, Loading Capacities of Ordinary Bolts per. It is planned for follow on work to extend the work of Morrow [9] to cases of more than two materials and perhaps to expand the range of geometries that it is applicable to. For real loads, this is non-trivial and multiple methods have been recommended. Shigley [16] used a similar methodology but made a different assumption about the shape of the stress field to better correlate with experimental data. Also Check Bolt Value Overview : https://youtu.be/dIXXSs3Zt5s Detailing of joint Pitch End distance : https://youtu.be/RgegCGg_F6o The bolt must have adequate fracture and fatigue life. Bending loads can come from two primary sources. Musto, J. C. and N. R. Konkle, "Computation of Member Stiffness in the Design of Bolted Joints", ASME J. Mech. Hardware Supplier Manufacturer If the joint is simple enough and the margins are large enough, this may be all that is required. 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… steel in this case). This can include bolts very close together, bolts near a physical boundary (see section 5.4), non axisymmetric geometries, etc. The value of D used for a given layer must take into account the frustum of the previous layer and not just the bolt or washer diameter. Unless identified below, subscripts will be identified in the text. The accuracy of this method is highly dependent on the choice of Q. Sample Design Calculations. Bearing strength calculation applies to both bearing-type and slip-critical connections. Thread Stress Area Calculator and Equation Bolt Threads, Grade, Bolt Strength, Excel Spreadsheet Calculator… Design recommendations are provided for both allowable stress design and load factor design… The classic example would be a pipe with a bending load applied to it. An overview of the current methods used to analyze bolted joint connections is given. Any of the methods can be used successfully if the engineer is aware of the assumptions and limitations and applies the theory correctly. 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. Column Base Plate Design - Online Calculation Report Checked By Date CN 16.04.2014 per EN 1992-1-1, EN 1993-1-1 and EN 1993-1-8 ... Bolt design strength f yd = f y / g M2 : Numerical values for … design and detailing are of primary importance for the economy of the structure. 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. For hard steels (i.e., brittle) where the ultimate strength approaches the true fracture stress, the Morrow and Goodman lines are essentially the same. Oberg, E., F. D. Jones, L. H. Holbrook, and H. H. Ryffel, Machinery's Handbook, 27. BS449: Part 2 Bolt Grade 8.8, Loading Capacities of Ordinary Bolts per. The use of 3 frustums introduces some error as discussed previously. There are N+1 equations of the type of Equation (33) (N for the clamped material and 1 for the bolt). Guidance is provided for general bolted joint design, computation of preload uncertainty and preload loss, and the calculation of the bolted joint factor of safety. a) The design bearing strength is for service load when deformation is a design … The third method is based on using finite element analysis of bolted joints and fitting the results with empirical equations. In this article on mechanical design tutorial today I will talk about design … It should be noted that this analysis requires the stiffness of each material so it can not be used for the FEA based empirical approaches that just define the total member stiffness. 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. The results of this work produce a clamped material stiffness for commercial metals of. There are two obvious examples when this falls apart. 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 . Used in Bickford method, Internally threaded material (nut) maximum minor diameter (Figure 2), Internally threaded material (nut) maximum pitch diameter (Figure 2). Roach [14] outlined a two phase finite element approach (linear and non-linear) that is adopted here. Also used as the length of bolt in the joint. 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. These include Soderberg. It is not recommended to use these equations. Bannantine [3] makes the following generalizations about these relationships for the general area of fatigue NOT specific to bolted joints. 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 … These calculations require knowing the tensile yield and ultimate strength, which is easy to obtain, as well as the shear yield and ultimate strengths, which are not generally known. Metric Bolts - Minimum Ultimate Tensile and Proof Loads US Bolts … 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. Due to the complexity of this type of analysis, it should only be done by experienced analysts. Fortunately, torque-angle signature curves can be obtained for most bolted joints. The book is intended to provide a comprehensive source of information on bolted and riveted structural joints as well as an explanation of their behavior under various load conditions. Figure 2 identifies important geometric parameters for a thread joint. Figure 10 shows the results for n = 0.5 across the range of l/d ratios. 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. the edge of the assumed loaded material) are free (i.e. Two of those methods are presented here. The following two tables list variables used throughout this document. Bannantine [3] also notes that tests using random histories with several stress levels show very good correlation with Miner's rule. Shigley’s Mechanical Engineering Design. Units are given in terms of length (L), force (F), radians (rad) and temperature (T). Example Calculation Calculation Example – Design bolted … A basic guideline given in the Machinery's Handbook [12] is to use 75% of the proof strength (or 75% of 85% of the material yield strength if the proof strength is not known) for removable fasteners and 90% of the proof strength for permanent fasteners. 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. For example, in the design of bolted … His equations are modified here to account for qi so that it can be compared to the work of Pulling [13]. 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. Bolt torque (Nm, lb f ft): 1213 Note that standard dry torques are normally calculated to produce a tensile stress - or axial force or clamp load - in the bolt that equals to 70% of minimum tensile strength or 75% of proof strength. Usually subscripted. 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". It is a linear theory because it is assumed that sum of the ratios of cycles at a given amplitude to the fatigue life at that amplitude can be summed to get the total effect of the variable loading, and it is independent of the order of the loading. } He then proposed the clamped material stiffness to be, and computed valued of m and b based on different materials stiffness ratios between materials and ratios of bolt diameter to clamped material length. For variable amplitude loading, Miner's rule can be used to estimate fatigue life [1]. Axial loads, shear loads, thermal loads, and thread tear out are used in factor of safety calculations. The actual point of where one frustum begins and the other ends must be computed for each layer. Pulling, E. M., S. Brooks, C. Fulcher, K. Miller, Guideline for Bolt Failure Margins of Safety Calculations, Internal Sandia Report, December 7, 2005. The design … Bannantine [3] notes that Miner's rule can be non-conservative for two level tests where the initial level is a high amplitude and the second level is a low amplitude. For unified screw threads and steels of up to 100 ksi ultimate tensile strength, the Machinery's Handbook recommends using, and for steels over 100 ksi ultimate tensile strength recommends using, For M-form metric threads, Bickford [5] recommends using. Choice is of course left up to the bolt must have adequate fracture and fatigue life 1! Done to understand the differences in a two phase finite element approach ( linear and non-linear ) that required... 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