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BOLTED AND RIVETED JOINTS 22.18
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FASTENING, JOINING, AND CONNECTING
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lier example illustrated in Fig. 22.2. The shear area of bolt 5, therefore, is (see Sec. 22.1.2 for the equations) 0.793 in2 (511 mm2). We can now compute the shear stress within this bolt: = FR5 12 750 = = 16 078 psi A5 0.793
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This is less than the maximum shear stress allowed for A325 steel bolts (see Table 22.1), and so the design is acceptable. It is informative to compare these results with those obtained in Sec. 22.1.3, where we analyzed a joint having similar dimensions, the same input load, and one less bolt.The axial load in the earlier case created a shear stress of only 9646 psi (66.5 MPa) in each bolt. When the same load is applied eccentrically, passing 5.5 in from the centroid, it creates 16 078/9646 times as much stress in the most distant bolts, even though there are more bolts this time to take the load. Be warned!
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22.3 TENSION-LOADED JOINTS: PRELOADING OF BOLTS
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In the joints discussed so far, the bolts or rivets were loaded in shear. Such joints are usually encountered in structural steel work. Most other bolted joints in this world are loaded primarily in tension with the applied loads more or less parallel to the axis of the bolts. The analysis of tension joints usually centers on an analysis of the tension in the fasteners: first with the initial or preload in the fasteners when they are initially tightened, and then with the working loads that exist in the fasteners and in the joint members when external forces are applied to the joint as the product or structure is put into use. These working loads consist of the preload plus or minus some portion of the external load seen by the joint in use. Because clamping force is essential when a joint has to resist tension loads, rivets are rarely used. The following discussion, therefore, will focus on bolted joints. The analytical procedure described, however, could be used with riveted joints if the designer is able to estimate the initial preload in the rivets.
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22.3.1 Preliminary Design and Calculations Estimate External Loads. The first step in the design procedure is to estimate the external loads which will be seen by each bolted joint. Such loads can be static, dynamic, or impact in nature. They can be created by weights such as snow, water, or other parts of the structure. They can be created by inertial forces, by shock or vibration, by changes in temperature, by fluid pressure, or by prime movers. Fastener Stiffness. The next step is to compute the stiffness or spring rate of the fasteners using the following equation: kB = AS ABE LS AB + LB AS (22.10)
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Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.
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BOLTED AND RIVETED JOINTS 22.19
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Example. With reference to Fig. 22.10, AS = 0.232 in2 (150 mm2), LB = 2.711 in (68.9 mm), AB = 0.307 in2 (198 mm2), E = 30 (10)6 psi (207 GPa), and LS = 1.024 in (26 mm). Thus kB = 0.232(0.307)(30 106) = 2.265 106 lb/in (0.396 N/mm) 1.024(0.307) + 2.711(0.232)
Stiffness of a Nongasketed Joint. The only accurate way to determine joint stiffness at present is by experiment. Apply an external tension load to a fastener in an actual joint. Using strain gauges or ultrasonics, determine the effect which this external load has on the tension in the bolt. Knowing the stiffness of the bolt (which must be determined first), use joint-diagram techniques (which will be discussed soon) to estimate the stiffness of the joint. Although it is not possible for me to give you theoretical equations, I can suggest a way in which you can make a rough estimate of joint stiffness. This procedure is based on experimental results published by Motosh [22.7], Junker [22.8], and Osgood [22.9], and can be used only if the joint members and bolts are made of steel with a modulus of approximately 30 106 psi (207 GPa). First compute the slenderness ratio for the bolt (lG/d). If this ratio is greater than 1/1, you next compute a stiffness ratio RJB using the empirical equation RJB = 1 + 3(lG) 7d (22.11)
The final step is to compute that portion of the stiffness of the joint which is loaded by a single bolt from kJ = RJBkB
FIGURE 22.10 Computing the stiffness of a bolt. The dimensions given are those used in the example in the text. This is a 5 8 12 4, SAE J429 Grade 8 hexagon-head bolt with a 3.25-in (82.6-mm) grip. Other dimensions shown are in inches. Multiply them by 25.4 to convert to millimeters.
Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.
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