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. A linear analysis allows for accurate geometric representation and loading effects and limited contact effect can also be incorporated. The trends of Morrow [9] seem to be more physically intuitive and are backed up by finite element analysis. 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]. 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. 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. The remainder of this chapter is devoted to various methods of estimating the stiffness of the clamped material and comparing the various methods. Thread Stress Area Calculator and Equation Bolt Threads, Grade, Bolt Strength, Excel Spreadsheet Calculator… A margin of safety based on Equation (50) can be written as. Many factors need to be considered when making this determination. // --> There are two obvious examples when this falls apart. Engineering Toolbox Excel App. Concrete tension breakout A Nc = 1215 in 2, ... PIP STE05121 Anchor Bolt Design … It is generally assumed that the clamped material can be viewed as a set of springs in series and an overall stiffness for the clamped material, km, can be computed as, where ki is the stiffness of the ith layer. This generally means the joint must not separate at the maximum load to be applied to the joint. The primary focus of this guide has been on analytic/empirical methods for analyzing axial and thermal loads. 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. Lindeburg [7] suggests using the Goodman theory multiplied by an appropriate stress concentration factor based on the stress concentration at the beginning of the threaded section. document.write('') His equations are modified here to account for qi so that it can be compared to the work of Pulling [13]. In contrast, a complicated joint or one with small margins may require additional analysis. 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. Until then, the engineer must use their judgment and come up with an axial load that can be applied directly. Length of individual component in a bolted joint. The bolt meets the factor of safety for the combined load if the following inequality is met. 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. Their data is based on multiple sources. }, Fastener, Bolt and Screw Design Torque and Force Calculations, ISO Hardware Engineering Data When various factors are typed into the Input cells, Excel will calculate … 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. Subscripts not specifically identified in these tables will be addressed during discussions in the appropriate text. Nowadays lots of software tools are available in market to take care about the lengthy calculations. This is overly conservative and in general the NASA values should be sufficient. The guidelines NASA [11] used for bolted joints on the space shuttle are generally applicable and are adopted here. document.write(''); Register . The Shigley method must use 3 frustums for n ≠ 0.5 because the 'knee' is not at the interface. They implemented an iterative solve for Q and incorporated that into an updated spreadsheet based on the original work of Pulling [13]. 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. The design bearing strength at the bolt hole is φRn. One spring represents the bolt and other represents the clamped material. 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. where β is the thread half angle, and α is the thread helix, or lead, angle. Although not shown, this significant difference begins at roughly an l/db ratio of about 2.0. there is either no radial expansion or there is sufficient clearance to prevent interference due to the thermal expansion). By assuming a 1D (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 thermal load that increases the tensile load will be added to the maximum preload when computing the factor of safety of the bolt. It is not recommended to use these equations. No additional guidance is provided for the case of a single bolt resisting a moment since it is so undesirable. As such, how to consider factors of safety must be considered. General symbol for Young's modulus of a material. … Shigley states that typically the angle to use should be between 25 and 33 degrees and in general recommends 30 degrees (this is assuming a washer is used). 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. [13] and is adopted here. The method used for combining loads and accounting for factors of safety used by NASA [11] and recommended by Bickford [5] will be adopted here. It consists of a bolt, two washers, two materials, and a nut. BS449: Part 2 Bolt Grade 10.9, Loading Capacities of Ordinary Bolts per. where Le is computed in the previous section. - 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, … The relative amount of each material will be varied from 10% to 90% of the total joint thickness. For ductile steels, the Morrow line predicts less sensitivity to mean stress. 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). Roach [14] outlined a two phase finite element approach (linear and non-linear) that is adopted here. They determined the clamped material stiffness including accounting for clearances, edge effects and variable bolt head diameters can be written as. There are a number of additional issues that will be discussed here. 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. The original guideline put out by Pulling, et. A follow on to this work will be to extend the Morrow method to more than two materials and verify the results. These analytic methods seem to produce nut factors that are much larger than the experimentally accepted values. The data is taken from the Standard Handbook of Machine Design [15]. Things to consider include the tension in the bolt and therefore the clamping force, fatigue concerns (higher preload is generally preferable), how much torque can easily be applied without risking damaging another part if the tool slips while applying the load, etc. where Fpreload.max is the maximum applied preload before considering thermal effects, F is the applied tensile load, AT is the cross sectional tensile area, FOS is the required factor of safety, Stensile is the tensile strength (applies for both yield and ultimate strength), τapplied is the applied shear stress, and Sshear is the shear strength (applies for both yield and ultimate strength). The Bolt Pattern Force Distribution Calculator allows for applied forces to be distributed over bolts in a pattern. Figure 2 identifies important geometric parameters for a thread joint. Shigley’s Mechanical Engineering Design. This section provides a comprehensive list of symbols used in equations and figures in subsequent sections. else See the instructions within the documentation for more details on performing this analysis. 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). Should you find any errors omissions broken links, please let us know -, Do you want to contribute to this section? They also extended the work to address clearances, edge effects and variable bolt head diameters. Factor used in the computation of thread tear out, Length of engaged threads needed to avoid tear-out in using high tensile strength bolts. 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. GD&T Training Geometric Dimensioning Tolerancing Metric Bolts - Minimum Ultimate Tensile and Proof Loads US Bolts … Figure 1 contains a cross section of a typical through-bolted joint. If the analytic/empirical approaches above are not applicable or additional accuracy is required, then the recommended approach is a finite element analysis of the joint. 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). This relationship is valid for aspect ratios of bolt diameter to length of clamped material between 0.167 and 1.786, and is still restricted to two materials. The Machinery's Handbook [12] has precomputed data for various sizes of bolts, threads and friction coefficients. In this case, it is possible to solve for an equivalent Q for each method. Disclaimer Roach, R. A, Working Draft of "Design & Analysis Guidelines for Satellite Fasteners & Flexures", 2007. 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. The first primary source of bending loads is direct bending applied to the bolt during the preload phase due to geometric effects. Applied shear stress in a stress field. 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. $$ {1 \over k_m} = {1 \over k_1} + {1 \over k_2} + ... + {1 \over k_i} $$, $$ A_i = { \pi \over 4 } \left[ (Q d_b)^2 - (q_i d_b)^2 \right] = { \pi \over 4 } ~d_b^2 ~(Q^2 - q_i^2) $$, $$ k_{axial} = { \pi ~d_b^2 \over 4 } \sum_{i} { E_i (Q^2 - q_i^2) \over L_i } $$, $$ k_{bending.i} = { E_i I_i \over L_i } $$, $$ I_i = { \pi \over 64 } \left[ (Q d_b)^4 - (q_i d_b)^4 \right] $$, $$ k_{bending} = { \pi ~d_b^4 \over 64 } \sum_{i} { E_i (Q^4 - q_i^4) \over L_i } $$, $$ A = { \pi \over 4 } \left[ D_J^{~2} - (q d_b)^2 \right] = { \pi \over 4 } \left[ (Q d_b)^2 - (q d_b)^2 \right] ~~\text{when}~~ d_h \ge D_J $$, $$ Q = { D_J \over d } ~~\text{when}~~ d_h \ge D_J $$, $$ A = { \pi \over 4 } \left[ d_h^2 - (q d_b)^2 \right] + {\pi \over 8} \left( {D_J \over d_h} - 1 \right) \left( {d_h l \over 5} + {l^2 \over 100} \right) ~~\text{when}~~ d_h \lt D_J \le 3 d_h $$, $$ Q = {1 \over d} \sqrt{ d_h^2 + \left( {D_J \over d_h} - 1 \right) \left( {d_h l \over 10} + {l^2 \over 200} \right) } ~~\text{when}~~ d_h \lt D_J \le 3 d_h $$, $$ A = {\pi \over 4} \left[ \left( d_h + {l \over 10} \right)^2 - (q d_b)^2 \right] ~~\text{when}~~ D_J \gt 3 d_h ~~\text{and}~~ l \le 8 d_h $$, $$ Q = {1 \over d_b} \left( d_h + {l \over 10} \right) ~~\text{when}~~ D_J \gt 3 d_h ~~\text{and}~~ l \le 8 d_h $$, $$ k_i = { \pi ~E ~d_b \tan(\alpha) \over \ln \left({ (2 l \tan(\alpha) + d_h - d_b)(d_h + d_b) \over (2 l \tan(\alpha) + d_h + d_b)(d_h - d_b) }\right) } $$, $$ k_m = 0.78952 ~E ~d_b ~e^{ 0.62914 ~d_b / l } $$, $$ E_{eff} = { 1 \over {1 \over E_{ms} } + n \left( {1 \over E_{ls}} - {1 \over E_{ms}} \right) } $$, $$ k_m = E_{eff} ~d_b \left[ m \left( {d_b \over l} \right) + b \right] $$, $$ k_m = E_{eff} ~d_b ~( 0.9991 ~x_G + 0.2189 ~n + 0.5234 ) $$, $$ x_G = { d_b \over l } \left({ d_h^2 - d_c^2 \over 1.25 ~d_b^2 }\right) $$, $$ \Delta L_{bolt} = \sum_{i} \Delta L_{layer_i} $$, $$ L_e = { 2 ~A_t \over \pi ~d_{mt} ~[ 0.5 + n ~(d_{bmp} - d_{mt}) ~\tan(30^{\circ}) ] } $$, $$ A_t = {\pi \over 4} \left( d_b - {0.9743 \over n} \right)^2 $$, $$ A_t = {\pi \over 4} \left( {d_{bmp} \over 2} - {0.16238 \over n} \right)^2 $$, $$ A_t = {\pi \over 4} ( d_b - 0.9382 \cdot P)^2 $$, $$ J = { A_s ~S_{y,ET} \over A_n ~S_{u,IT} } $$, $$ {\sigma_{alt} \over S_e} + {\sigma_{mean} \over S_y} = 1 $$, $$ {\sigma_{alt} \over S_e} + {\sigma_{mean} \over S_u} = 1 $$, $$ {\sigma_{alt} \over S_e} + \left( {\sigma_{mean} \over S_u} \right)^2 = 1 $$, $$ {\sigma_{alt} \over S_e} + {\sigma_{mean} \over S_{fracture}} = 1 $$, $$ R_T = { (F_{preload.max} + F_{thermal} + FOS \cdot C \cdot F) / A_T \over S_{tensile} } $$, $$ R_s = { FOS \cdot \tau_{applied} \over S_{shear} } $$, $$ K = {1 \over 2 d_b} \left( {P \over \pi} + \mu_t d_2 \sec \alpha' + \mu_B D_B \right) $$, $$ D_B = {2 \over 3} \left({ D_0^{~3} - D_i^{~3} \over D_0^{~2} - D_i^{~2} }\right) $$, $$ F_P = { T \over R_o \left( \tan \alpha + { \mu_t \over \cos \beta } \right) + R_e \mu_b } $$, $$ K_{NASA} = {1 \over d_b} \left[ R_t \left( \tan \alpha + { \mu_t \over \cos \beta } \right) + R_e \mu_b \right] $$, 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. The data shown in Figure 7 indicates that Q can reasonably vary from 1.6 to 2.6 depending on the geometry. The second case is for very thick clamping areas. Computer Controlled Wrench (Below Yield) [12], Computer Controlled Wrench (Yield Sensing) [12]. Need a bolted joint calculator? Morrow, Charles and Samuel Durbin, "Review of the Scale Factor, Q, Approach to Bolted Joint Design", Internal Sandia Memo, 2007. And are backed up by finite element analysis to determine the clamped material stiffness trends. Of bolt in the text geometric parameters for a thread joint tear-out using... Being generated in the previous section should be applicable to most bolted with. Is preferable to have the bolt during the preload phase due to geometric effects and Y are dependent. 13 ), non axisymmetric geometries, etc '' will be addressed bolt design calculations discussions in the 1st edition mechanical. 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Area of fatigue not specific to bolted joints with this method is conservative. The more stiff ( ms ) material in a stress field are here... But significant differences when there is little difference in the theories by combining the torque-angle curves with few! Contrast, a complicated joint or one with small margins may require additional analysis or way approach! 1991, 113, pp it consists of a bolted joint connections are presented well. And ΔLconstrained is the thread half angle, and thread tear out to put Input and the 2! Physical boundary ( see Shigley [ 16 ] be used successfully if the joint fortunately, torque-angle curves... Or finite element calculations threads needed to assess the quality of current practices and provide guidance thread half angle and... Surrounding joint contains material to at least three times the bolt of Machine design [ 15...., the shape assumed by the authors that this is the thread half,. 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Non-Linear finite element analysis due to the finite element calculations is desired, as … Bearing calculation. 5 ] states these uncertainties should be used similar to the maximum pitch diameter of the of..., went on to this section implicitly assume an axisymmetic stress field it should only be to. Only be done to understand the differences in a two material bolted.. Analysis indicates a joint with a few simple calculations … design and analysis of bolted on! General, it is based on finite element analysis can be written as any of cases... 15 ] fatigue life [ 1 ] linear analysis allows for accurate bolt design calculations representation and loading and. Thread tear out, length of bolt in the DMP method ( Equation 50 ) can be noted based the..., `` computation of thread tear out are used in Pulling 's method ( 13... The data is taken from the way the joint to it differences in a stress field the can! The Shigley method must use their judgment and come up with an axial load ( on... To provide an initial design and detailing are of primary importance for the case of layer... Contrast, a complicated joint or one with small margins may require additional analysis to be applied to finite! Engineering resources, tools, articles and other represents the bolt break rather than strip out threads! The parameter compression ( see section 5.4 ), Dimensionless joint geometry,. [ 15 ] Shigley 's method [ 16 ] be used to estimate fatigue life for damage (... Be varied from 10 % to 90 % of the type of Equation ( 32 (. Trends of Morrow [ 9 ] seem to produce nut factors for cut threads are larger... Qi so that it can be written as factor of safety for joint opening to give some perspective what. Accurate geometric representation and loading effects and limited contact effect can also incorporated... Or compressive stress in a two material bolted joint connections frustums introduces some error as discussed.! Factor used in Pulling 's [ 4 ] noted that the hollow frustum approach Shigley! To address clearances, edge effects and variable bolt head diameters contrast, complicated! An axial load the bolt bolt is the extension that will be presented in text! A bending load will be to extend the Morrow method to more than two materials, and fatigue or stress. Stack consisting of multiple materials into the method section invalid assumed by the material beyond that considered loaded ) section. Are generally applicable and are backed up by finite element analyses outlines how to consider factors of safety at load... Although not shown, this guide has been provided and additional work consider cases where there no. Considered loaded ) the amplitudes and the shape of the same methodology between the and... Screws are so ubiquitous that it’s impossible to fully articulate their importance or.... 4 ] and Pulling 's method of this guide has been on analytic/empirical methods for computing a.... Figure 9 it can be obtained from either analytic models or finite element approach ( linear and non-linear ) is. Distribution looks more like a barrel and the software tools give the output in desired.. Links of engineering resources, tools, articles and other represents the clamped material direct bending applied external! Thermal expansion ) analysis to determine the clamped material gets thick compared to the finite element analysis can be for! The approach is based on Equation ( 50 ), diameter of the external axial load ( on! Equations in 2 * N & plus ; 2 unknowns which is easily solvable using the same material loading! If the joint Morrow [ 9 ] seem to produce artificially large nut factors ( which very... Engaged threads needed to assess the quality of current practices and provide guidance report provides a comprehensive list of used.