Structural Properties of Bolted Jointshttp://machinedesign.com/print/83207 Published on Machine Design (http://machinedesign.com) Structural Properties of Bolted Joints by Kenneth J. Korane Created 02/17/2010 - 13:28 Engineers need to understand the behavior of bolts, flanges, seals, and gaskets to design reliable connections. Authored by: Moo-Zung Lee West Hills, Calif. Edited by Kenneth J. Korane [email protected] [1] Key points: • Structural properties of bolted joints depend on bolt and clamped-member stiffnesses. • Clamped members can be treated as a sleeve or hollow cylinder. Moo-Zung Lee has a BSME from National Taiwan Univ., MSME from Univ. of Houston, and a Ph.D. from New York State Univ. at Stony Brook. He has nearly 40 years experience in power plant construction and dynamic and stress analyses of nuclearpower-plant piping and aerospace and defense systems. [2] [2]Sound designs of bolted joints rely on a good grasp of their structural behavior, and structural properties of preloaded bolted joints — including the bolt load-sharing ratio, separation load ratio, and joint stiffness — depend only on the stiffnesses of the bolt and clamped members. Nonetheless, bolted joints are rather complicated. Here’s how engineers can approximate bolt and clamped-member stiffnesses and derive structural parameters useful for design. Bolts and clamped members can be modeled as bars connected in series for stiffness calculations. The stiffness of a bar with uniform cross-sectional area A and length L is related to its modulus of elasticity E = σ/ε, the ratio of stress and strain. If a force F elongates a bar by δ, then the bar stiffness is: [3] 1 of 5 11-07-2012 14:13 1-1982) for unified inch screw threads: [6] [6] where D = basic major diameter. [7] [7] 2 of 5 11-07-2012 14:13 . H = √3(P/2). and minimum minor diameter d a 2b 1m = D – 1.1-1989 (revision of ANSI B1. Or calculate it based on the equation from ASME Standard B1. d .5 H. H = height of a sharp V-thread or fundamental triangle. t The tensile-stress area of the screw can be found in handbooks and textbooks. Stiffness of the shank is: [4] where A = πd /4. s 2 The threaded-section stiffness is: [5] [5] where A = tensile-stress area of the screw. calculated from the basic pitch diameter. d .com/print/83207 [3] Bolt stiffness Bolts consist of shank and threaded sections.Structural Properties of Bolted Joints http://machinedesign. as shown. 1/P is the number of threads per inch. The basic pitch diameter d 2b = D – 0. and P = thread pitch.75 H. Or determine the stress area of the screw based on the area of a circle with the average diameter. Because the widths across flats of the bolt head are typically w = 1. c c c c Calculate the clamped member stiffness of a solid structural connection using a double-cone load-path model. Calculate total bolt stiffness. This assumes bolt force diminishes linearly along the height of the bolt head starting at the mean area of the seating surface. The clamped-member stiffness o i is: k = A E /L . Lt. These approximations are judgment calls. the double cone shown is equivalent to the sleeve model. includes one-third of the bolt-head height. The series spring-connection n h method may be extended to bolts with multiple diameters. include one-half of the thread-engagement length in the threaded-section length for stiffness calculations. m Equivalent stiffness of the head in terms of the shank is [8] [8] For studs with or without threaded inserts. 3 of 5 11-07-2012 14:13 . from series connection of the section stiffnesses: [9] [9] Clamped members Clamped members can be treated as a sleeve. of the threaded section is from the interior end to the midpoint of the nut height. kb. the mean diameter of stress area in bolt head is d = (d+w)/2. The stress area of the hollow cylinder is: A = π(d – d )/4 c i 2 o 2 where d and d = outside and inside diameters.Structural Properties of Bolted Joints http://machinedesign. If clamped members have the same modulus of elasticity. Ls. This assumes that bolt tensile force decreases linearly from the seating surface to the free surface of the nut.com/print/83207 The effective length. The effective length of the shank. “Effective area of clamped members. as shown in the graphic.5d. Other methods use d/4 in lieu of both H /2 and H /3.” A 30° cone angle is customarily used in industry. respectively. hollow. then each bolt’s share of the spring rate of the seal is: k = πD f/Nδ. The stress and deflection equations of this plate model and coefficients k and k1 are based on data in Timoshenko (Strength of Materials. For example. if it takes linear force f (force/length) to deform the seal by δ. Part II. 3rd ed.Structural Properties of Bolted Joints http://machinedesign. Advanced Theory and Problems. c s c Flange stiffness A pair of flat flanges with a gasket can be modeled as three hollow cylinders in a series connection. assuming L1<L2. These seals may not be in the structural load path and can be ignored for stiffness calculations. Van Nostrand Reinhold Co. Stepped flanges with a gasket diameter substantially smaller than the bolt-center circle diameter are subject to bending. or other cross sections. and the joint has N bolts equally spaced on the bolt center circle with diameter D . For O-rings with solid. Calculate the stiffness of those flanges using the model shown in the accompanying graphic. [10] Gaskets and seals Some O-rings rely on internal pressure to entrap rubber in the groove for sealing.. New York.” The stiffness of clamped members is calculated from series connections of three hollow cylinders shown in the sleeve model. In other cases an O-ring may dominate the compliance (inverse of stiffness) of clamped members. 1958).com/print/83207 The double-cone model can be modified to accommodate clamped members with different moduli of elasticity and thickness as shown in “Two materials and two thicknesses. stiffness data should be translated to the clamped member stiffness for each bolt. For stress: [11] [12] [12] and deflection: [13] [13] Stiffness of the entire flange as a plate is: 4 of 5 11-07-2012 14:13 . com [2] http://machinedesign. the effects of preload.com/content/flange-stiffness-0217 [12] http://machinedesign.Structural Properties of Bolted Joints http://machinedesign.com/print/83207 [14] [14] The combined clamped member compliance is the sum of compliance of two flanges and one gasket: [15] [15] Stiffness of clamped members for one of the N bolts on the flanges is k = K /N.com/content/equation-10-0217 [15] http://machinedesign. c c In future installments of this series.com/content/bending-constants-0217 [17] http://machinedesign.com/content/equation-5-0217 [8] http://machinedesign. we’ll look at bolted-joint behavior under external load.com/content/equation-1-0217 [4] http://machinedesign.com/content/typical-bolt-dimensions-0217 [3] http://machinedesign.com/content/equation-9-0217 [14] http://machinedesign.com/content/figures-0217 [11] http://machinedesign.com/content/equation-4-0217 [7] http://machinedesign.com/content/equation-8-0217 [13] http://machinedesign.com/content/equation-7-0217 [10] http://machinedesign.com/content/equation-3-0217 [6] http://machinedesign.com/content/nomenclature-0217 5 of 5 11-07-2012 14:13 . loading-plane factors. and reactions to internal loads.com/content/equation-2-0217 [5] http://machinedesign. [16] [17] Source URL: http://machinedesign.com/content/equation-6-0217 [9] http://machinedesign. finite-element models.com/article/structural-properties-of-bolted-joints-0217 Links: [1] mailto:ken.com/content/equation-11-0217 [16] http://machinedesign.korane@penton.