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1、On the Analysis and Design of Bracing Connections William A. Thornton Author Dr. William A. Thornton is chief engineer of Cives Steel Company and president of Cives Engineering Corporation, which are both lo- cated in Roswell, Georgia. He is responsible for all structural design originated by the co
2、mpany and is a consultant to the five divisions of Cives Steel Company in matters relating to connection design and fabrication practices. Dr. Thornton has 30 years experience in teach- ing, research, consulting and prac- tice in the area of structural analysis and design, and is a registered profes
3、sional engineer in 22 states. He has frequently served as an invited lecturer at the American In- stitute of Steel Construction spon- sored seminars on connection design and is author or co-author of a number of recently published papers on connection design and related areas. He is a member of the
4、American Society of Civil En- gineers, American Society of Mechanical Engineers, American Society for Testing Metals, American Welding Society, and the Research Council on Structural Connections. Dr. Thornton currently serves as a member of technical committees of the American Institute of Steel Con
5、struction, American Society of Civil Engineers, American Welding Society, Research Council on Structural Connections and as chairman of the American Institute of Steel Construction Committee on Manuals, Textbooks and Codes. Summary Bracing connections constitute an area in which there has been much
6、disagreement concerning a proper method for design. This paper con- siders three methods for design considered acceptable by the American Institute of Steel Con- struction Task Group on Heavy Bracing Connections and shows that these methods satisfy first prin- ciples from a limit analysis point of v
7、iew, and are consistent with the results of extensive research per- formed on this problem since 1981. The paper includes a number of worked out examples to demonstrate the application of the methods to actual situations. 26-1 2003 by American Institute of Steel Construction, Inc. All rights reserve
8、d. This publication or any part thereof must not be reproduced in any form without permission of the publisher. On the Analysis and Design of Bracing Connections W.A. Thornton, PhD, PE Chief Engineer Cives Corporation Roswell, Georgia USA INTRODUCTION For many years, the methods for the analysis of
9、bracing connections for heavy construction have been a source of controversy between engineers and steel fabricators. Beginning in 1981, the American Institute of Steel Construction sponsored extensive computer oriented research at the University of Arizona (1) to develop a rational analysis method.
10、 Since 1981 physical testing has been performed by Bjorhovde (2) and Gross(3) on full size models of gusset, beam, and column. The results of this work have not yet been distilled into a consistent method of design. It is the purpose of this paper to do so. The AISC has formed a task group with ASCE
11、 to propose a design method (or design methods) for this problem. The recommendations arrived at by this Task Group at a meeting in Kansas City, Missouri, on March 13, 1990 are contained in Appendix A. This paper will attempt to justify the recommended design methods based on Models 2A, 3, and 4, an
12、d will include discussion of certain other possible models, such as Models 1 and 5. It will be noted that the author is co-chairman of this Task Group. This paper, however, is not the work of the Task Group and the author is solely responsible for its content EQUILIBRIUM MODELS FOR DESIGN - CONCENTR
13、IC CONNECTIONS An equilibrium model for concentric connections is defined here as a model of the beam , column, gusset and brace(s) which make up the connection in which the connection interface forces provide equilibrium for the beam, column, gusset, and brace with no forces in the beam and column
14、other than those that would be present in an ideally pin connected braced frame. In other words, there are no couples induced in the beam and column due to the connection components. Figs. 1 through 5 show the interface forces for equilibrium Models 1, 2A, 3, 4, and 5 respectively. Equilibrium model
15、s apply to concentric connections, i.e. those for which all member gravity axes meet at a common “working“ point, and to eccentric connections, i.e. those for which all member gravity axes do not meet at a common point. In this latter case, couples are induced in the frame members which must be cons
16、idered in the design of these members. Model 1 - KISS This is the simplest possible model which is still an equilibrium model. It has been referred to as the “keep it simple, stupid!“ model, or the KISS model. It is simple with respect to calculations but it yields very conservative designs as will
17、be shown. Thus it is easy to use and safe, but yields cumbersome looking and expensive connections. This method is not recommended by the AISC/ASCE Task Group and is included here for comparison purposes. 26-3 2003 by American Institute of Steel Construction, Inc. All rights reserved. This publicati
18、on or any part thereof must not be reproduced in any form without permission of the publisher. Model 2A - AISC This model is a bit more complex computationally but yields less cumbersome designs than Model 1, which are still conservative. It is a generalization of the method presented in the AISC bo
19、ok Engineering for Steel Construction (4) and hence will be referred to as the AISC Model. In Ref. 4, only connections to column webs are considered. This was intentional because the AISC Manual and Textbook Committee, which oversees the production of this book, could not (in 1983) agree on a proper
20、 method for connections to column flanges. Model 2A is a generalization suggested by the author. It will be shown to be conservative. Model 3 - Thornton This method was developed by the author and is capable of producing uniform stress distributions on all connection interfaces. For this reason, it
21、will always produce the greatest capacity for a given connection or the smallest connection for given loads. In the sense of the Lower Bound Theorem of Limit Analysis, it comes closest to giving the true force distribution among the connection interfaces. It will be shown to come extremely close to
22、predicting exactly the failure load of the Chakraborti and Bjorhovde (2) tests. Of the three models thus far considered, it is the most complex computationally, but will yield the most economic and least cumbersome connections. Further discussion of this model can be found in Appendix B of Ref. 3. M
23、odel 4 - Ricker This method was developed by David Ricker, Vice President of Engineering of Berlin Structural Steel Company of Berlin, Connecticut and a member of the AISC/ASCE Task Group. As shown in Fig. 4, the forces at the centroids of the gusset edges are always assumed to be parallel to the br
24、ace force. The method is fairly complex computationally, as can be seen from Fig. 4a, probably about as complex as Model 3. The moment M is required because the resultant force on the gusset to beam interface does not necessarily pass through the centroid of the beam to column connection causing a m
25、oment M on this connection which must be considered in design for this to be a true equilibrium model. Note that the moment M, because it is a free vector, can be applied either to the beam to column interface or the gusset to beam and gusset to column interfaces. The choice is the designers option.
26、 A weakness of this model lies in the “rigidity“ of the assigned directions of the gusset interface forces. When the connection is to a column web, the gusset to column interface force is still parallel to the brace force. This means there is a force component on this interface perpendicular to the
27、column web. Since the column web is very flexible in this direction, this model may require that the column web be stiffened to accomodate the force component perpendicular to the web. It will be shown later that the results of Gross (3) test 3A can not be predicted by this model because the web is
28、not stiffened. Model 5 - Modified Richard Of the five models presented here, this is the only one which is not solely based on first principles, but rather contains empirical coefficients derived by Richard(1) from extensive computer analysis. As originally presented by Richard, this is an equilibri
29、um model only if the 26-4 2003 by American Institute of Steel Construction, Inc. All rights reserved. This publication or any part thereof must not be reproduced in any form without permission of the publisher. force resultants act at some points on the gusset to beam and gusset to column interfaces
30、 other than their centroids. Richard has not defined the interface points where his interface forces act. Since it is standard practice in connection design to refer all forces to the centroid of the connection under consideration, the author has done so and called this method the “Modified Richard“
31、 method. The moments MB and MC of Fig. 5 are required on the gusset edges to transport the Richard interface forces to the interface centroids. As is the case with Model 1, this model was not recommended by the AISC/ASCE Task Group, but is included here for purposes of comparison. ECCENTRIC CONNECTI
32、ONS Eccentric Connections are those with member gravity axes which do not intersect at a common working point. Instead the working point is usually assumed at the face of the flange of the beam or column or both as shown in Fig. 6. This working point is chosen to allow more compact connections to re
33、sult. Fig. 7 shows the gusset interface forces usually assumed. These are shears on the gusset edges. Because these shears intersect the brace line at a common point equilibrium of the gusset can be enforced, and it is a true equilibrium model only if the couples induced in the beam and column are c
34、onsidered in the design of the beam and column. Figs. 6 and 7 call this the “classical“ case because it was a very commonly used method in the past but presently is rejected by many engineers because of the induced beam and column couples. One of the objects of this paper is to investigate the conse
35、quences of use of this method. It should be noted that models 1, 2A, and 3 all reduce to the classical case if eB = eC = 0. Models 4 and 5 do not reduce to the classical case. COMPARISON OF MODEL PREDICTIONS WITH PHYSICAL TEST RESULTS Two sets of data for full scale and scale physical tests are avai
36、lable to assess the accuracy of failure prediction of the five equilibrium models discussed in the previous section. These are the tests of Chakrabarti and Bjorhovde (2) and those of Gross(3). Chakrabarti and Bjorhovde Tests A set of six tests were performed by Chakrabarti and Bjorhovde (2) on the s
37、pecimens of Fig. 8. Fig. 8 was replicated six times, i.e. for each of two gusset thicknesses ( and ) and three brace angles from the horizontal ( = 30, 45, and 60). Only the gusset is treated here because the gusset specimens exceeded the capacity of the testing frame. In the test frame, the specime
38、n was oriented with column horizontal and bolted to the test frame which was in turn bolted to the laboratory floor, and the beam was vertical with top end free. Thus, this setup is roughly equivalent to a situation in a real building where the brace horizontal component ( of Fig. 8) is passed to an
39、 adjacent bay. The force is referred to as a “transfer force“ and denoted In the calculations to predict capacity using the five models, the transfer force for the Chakrabarti/Bjorhovde tests is and this is made up of HC from the gusset to column connection and HB from the beam to column connection.
40、 Thus, the beam to column connection for all models will be subjected to HB (axial) and VB (shear). 26-5 2003 by American Institute of Steel Construction, Inc. All rights reserved. This publication or any part thereof must not be reproduced in any form without permission of the publisher. Tables 1,
41、2, and 3 give the results of predicting Chakrabarti/Bjorhovdes failure loads using the five models. (Appendix A of Ref. 3 contains calculations similar to those required here to produce Tables 1-6). It will be seen from Tables 1-3 that Model 3 very closely predicts the actual failure load. In Tables
42、 1 and 2, it even predicts the correct interface where failure first occurs. Table 3 presents something of an anomoly. In all three tests, the brace to gusset connection was exactly the same and has a predicted capacity (all Models) of 142k. In Tables 1 and 2, the brace to gusset connection failed a
43、t 143k and 148k respectively, but in Table 3, the 60 case with exactly the same brace to gusset connection, it did not fail and a load of 158k was achieved at which the gusset to column connection failed. For some unknown reason, the brace to gusset connection for this 60 case is much stronger than
44、expected. Note that given a brace to gusset connection with an actual capacity (per Chakrabarti/Bjorhovdes test) in excess of 158k, Model 3 correctly predicts that the gusset to column connection will fail first at 155k, about 2% less than the actual failure load of 158k. Further reviewing the data
45、of Tables 1-3, it can be seen that all the models are conservative, Model 3 being barely so, and Model 1 being grossly conservative. The other Models are moderately conservative except that Model 4 sometimes duplicates Model 3s performance. The author believes that the results presented in Tables 1-
46、3 show that all these Models are reasonable for design except Model 1 which is consistently too conservative. Gross Tests Gross (3) performed three essentially full scale (they are referred to as scale in Gross report) tests on the specimens shown in Figs. 9, 10, and 11. These tests differ from the
47、Chakrabarti/Bjorhovdes tests in that the beam and column(s) participate in the tests by frame action. Fig. 12 shows the complete test specimen (specimen 1) and Fig. 13 gives a schematic of the test frame. In the Chakrabarti/Bjorhovde tests, the brace connection is effectively isolated from the frame
48、 action. Therefore, Gross tests are more realistic as compared to a real structure where frame action can not be eliminated, and it will be interesting to see how well the equilibrium models predict failure in this case. Gross tests differ from Chakrabarti/Bjorhovde in another way: Specimens 2 and 3
49、 are eccentric connections. As noted earlier the five equilibrium models can be used for Specimens 2 and 3, but couples of possibly all three types (see Table 7) will be induced in the members for these configurations. Tables 4, 5 and 6 compare the model predictions with Gross actual failure loads. It will be seen that all the equilibrium models are conservative and none, not even Model 3, comes close to predicting the actual failure load of the connection interfaces. The reason for this in the case of Specimens 1 and 2 is due to frame action. This has the effect of