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BOLTED AND RIVETED JOINTS 22.24
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FASTENING, JOINING, AND CONNECTING
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Example. Let us assume for our ongoing example that we are concerned only about separation of the joint members. Minimum acceptable clamping force, therefore, is zero. Select an Initial Preload Target. We now, rather arbitrarily, select an initial preload target that is somewhere between the acceptable minimum and acceptable maximum bolt tensions which we computed earlier. Let us try 60 percent of the acceptable maximum of 16.9 kip (75.2 kN) or, in our example, 10.1 103 lb (45.1 kN).
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22.3.3 Estimating Actual Upper Limit on Bolt Tension We must now determine whether or not the tension we will actually develop in any bolt will exceed the maximum acceptable tension, given our preliminary target preload and a consideration of the tools, lubricants, and procedures we are planning to use during assembly. We must also consider the effects of the external tension loads which will be placed on this joint after assembly. Tool Errors. We can select many different types of assembly tools. Each choice carries with it certain accuracy implications; some tools can produce preload in the fasteners with far greater precision than can other tools. Table 22.4 lists some of the many possibilities. We will assume for our example that we are going to use a manual torque wrench and must face a potential scatter in preload for a given torque of 30 percent. Operator Problems. Even if we used perfect tools, we would see some scatter in the resulting preload because of operator problems. Are the operators skilled, properly trained, or tired Do they care about their work Are the bolts readily accessible Let us assume for purposes of our example that the operators will contribute an estimated 10 percent additional scatter in preload. We do not just add this 10 percent to the 30 percent we assigned to the torque wrench when we assess the combined impact of tools and operators. We use the statistician s method for combining the variances of two variables, as follows:
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2 2 2 = T + O
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(22.16)
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In our example this suggests that the combined variance will be 2 = 302 + 102 = 1000 giving us a 3 sigma deviation (square root of the variance) of 31.6 percent. We have selected a target preload of 10.1 103 lb. Consideration of tool and operator scatter gives us FP(max) = FPT + 0.316FPT = 13.3 103 lb (59.2 kN) FP(max) = FPT 0.316FPT = 6.91 103 lb (30.7 kN) Effects of External Tension Load. Now let us see what happens when an external tension load is placed on the preloaded joint. Although it is difficult to do this in
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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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TABLE 22.4 Tool Accuracy
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BOLTED AND RIVETED JOINTS 22.26
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practice, we usually assume that a tension load is applied between the head of the fastener and the nut or tapped hole at the other end. Such a load would have a worstcase effect on the tension in the fasteners and on the clamping force on joint members, so this assumption is a safe and conservative one. Any such tension load, no matter how small, will add to the tension in the bolts, increasing the length of the bolts slightly and thereby reducing the clamping force on the joint interface. Not all the external load applied to the bolt is seen by the bolt, however. Part of the external load merely replaces part of the outward force which the joint initially exerted on the bolts that were clamping it. This can be illustrated by what engineers call a joint diagram, such as that shown in Fig. 22.13. Note that the external load applied to the bolt is equal to the sum of the changes which occur in the bolt and joint. It is equal, in other words, to the increase in tension in the fasteners plus the decrease in compressive load in the joint. We say that one part of the external load has been absorbed by the bolts; the rest has been absorbed by the joint (Ref. [22.6], pp. 199ff ). The relative stiffness or spring rate of bolt and joint determines how much of the load each will absorb. In Fig. 22.13 the joint stiffness is 3.23 times that of the bolt, as determined by our previous calculation of the stiffness ratio RJB for the bolt in Fig. 22.10. The joint, therefore, will absorb approximately seven-tenths of any applied external tension load. We should note in passing that the effects of an external compressive load can also be illustrated by a joint diagram, such as that shown in Fig. 22.14. This time the tension in the bolt is reduced and the compression in the joint is increased simultaneously by the single external load. The portions absorbed by fasteners and joint are again proportional to their relative stiffness.
FIGURE 22.13 Joint diagram for a joint loaded in tension. A joint diagram consists of two force-elongation diagrams, one for the bolt and one for the joint material loaded by that bolt put front-to-front (Ref. [22.6], pp. 199 206). It illustrates the combined elastic behavior of bolt and joint.
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