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1、Computer-Aided Design of Steel Structures with Flexible Connections Gregory G. Delerlein Author Gregory G. Deierlein received his bachelor degree from Cornell University and his masters degree from the University of California, at Berkeley. He received a Ph.D.in structural engineering from the Unive
2、rsity of Texas, at Austin and in 1988 he joined the faculty of Cor- nell University as an assistant professor. Deierlein has several years design experience in struc- tural steel, reinforced concrete, and composite structures. He worked with the firm of Leslie E. Robertson and Associates, P.C. in Ne
3、w York on the design of the 72-story Bank of China Building in Hong Kong, and on the Meyerson Symphony Center in Dallas. Deierlein is a registered professional engineer and a member of the American Society of Civil Engineers, American Concrete Institute, Inter- national Association of Bridge and Str
4、uctural Engineers, Earthquake Engineering Research Institute and the Structural Stability re- search Council. Author Shang-Hsien Hsieh is a graduate research assistant in the School of Civil and Environmental Engineer- ing at Cornell University. He received a bachelor of science de- gree in civil en
5、gineering from Na- tional Taiwan University in 1985 and a master of science degree from Cornell University in January 1990. Mr. Hsiehs research for his masters degree included develop- ment and implementation of the computer-aided analysis and design system for steel structures with semi-rigid conne
6、ctions. Mr. Hsieh is studying for Ph.D. at Cor- nell University in the area of parallel processing for nonlinear structural dynamics. Author Yi-Jiun Shen is a graduate re- search assistant in the School of Civil and Environmental Engineer- ing at Cornell University. She received her bachelor of scie
7、nce degree in civil engineering from the National Central University in Taiwan in 1985. Currently, Ms. Shen is studying for a masters de- gree at Cornell University. Her re- search in involved with the application of interactive computer graphics for design studies of steel structures with semi-rigi
8、d connec- tions. Prior to her graduate study, Ms. Shen worked as a structural engineer at China Engineering Consultants, Inc. in Taiwan, where she was involved with the design of highway bridges, tunnels, tanks and drainage structures. Summary The influence of connection flexibility on the behavior
9、of steel framed structures has long been recognized, however, due to the difficulty of accurately modeling connection effects in analysis, these effects are usually not con- sidered explicitly in design. This paper describes the development and application of a computer- aided design system for incl
10、uding semi-rigid connection behavior in the analysis and design of two and three dimensional buildings. The system utilizes interactive com- puter-graphics to provide a con- venient means of defining and characterizing joint behavior for design. Inelastic connection behavior is modeled using nonline
11、ar moment rotation curves that are imple- mented in an analysis and design program which can account for both geometric and material non- linear behavior in framed struc- tures. For design, connection response is characterized using a library of standarized moment-rota- tion curves which are calibra
12、ted to experimental test data for various connection configurations. Two case studies are presented which 9-1 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. demon
13、strate the influence of con- nection flexibility in evaluating strength and serviceability limit states. Also considered is the effect of semi-rigid connections on the ul- timate limit load of the structure considered. The computer-aided analysis and design methodology which is presented provides an
14、 ap- proach for taking reasonable ac- count of connection effects during the design phase, prior to final detailing of the connections. 9-2 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 perm
15、ission of the publisher. COMPUTER-AIDED DESIGN OF STEEL STRUCTURES WITH FLEXIBLE CONNECTIONS The influence of connection flexibility on the behavior of steel framed structures has long been recognized by engineers. However, because of uncertainties in predicting joint response and difficulties assoc
16、iated with incorporating it in analysis, inelastic joint flexibility is usually not considered explicitly in design. Consequently, in spite of much research there is still incomplete understanding of joint effects and their significance, and need for convenient methods for including these in analysi
17、s and design. Several trends in building design and construction are increasing the importance of incorporating joint behavior in design. These include: 1) the development of inelastic limit state design procedures which require more realistic analysis of actual response, 2) growing emphasis for eva
18、luating inelastic structural response to earthquakes and other extreme loadings, and 3) structural challenges posed by innovations in architecture and construction. Advances in computer technology, particularly the availability of low cost engineering workstations, are providing the means for perfor
19、ming more realistic analyses of structures including joint behavior. This paper describes the development and application of a computer-aided system for including semi-rigid connection behavior in the analysis and design of three dimensional building frames. A key aspect of the proposed method is th
20、e introduction of a standardized connection model which facilitates the incorporation of semi-rigid connection behavior during the preliminary and final stages of design. The analytic formulation used for modelling connection response is based on a discrete nonlinear rotational spring which is imple
21、mented in a program for the analysis and design of three dimensional steel structures. The analysis is based on a finite element approach where the structure is discretized into 3-D inelastic beam-column line elements connected by either rigid or semi-rigid connections. The computer-aided analysis a
22、nd design system utilizes interactive menu-driven graphics for definition of the structural geometry and properties, characterization of connection behavior, control of the analysis and design process, and display of structural response. The paper is organized as follows: 1) a description of the mom
23、ent- rotation behavior model used for the connection, 2) a brief description of the beam-column element formulation and the computer-aided analysis and design system, 3) a presentation of two case studies which demonstrate use of the system in the investigation of the influence of partially restrain
24、ed connections on frame behavior, and 4) a summary and conclusions. 9-3 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. STANDARDIZED MOMENT-ROTATION MODEL FOR CONN
25、ECTIONS In the past, many techniques have been proposed for representing the moment-rotation behavior of semi-rigid connections, some based on simple linear approximations and others on more sophisticated nonlinear functions. The model used in this work is based on a nonlinear equation first present
26、ed by Richard and Abbott (1975), and later by Kishi et.al. (1988). Using this model, the moment-rotation relationship of the connection is given by the following equation: In Eq. 1a, M is the moment corresponding to the connection rotation, The parameters, , are independent variables which are relat
27、ed to the moment-rotation behavior as shown in Fig. 1, and n controls the shape of the curve. This model was chosen because it represents observed experimental data well, it is convenient to implement in the computer program described below, and the four parameters are derived from a rational interp
28、retation of response. One advantage of this model is that it encompasses more simple models. For example, Eq. 1a becomes a simple linear model if an elastic-plastic model if = 0, and a bilinear model if n is large. Figure 1. Moment-Rotation Model for Inelastic Connection Response. 9-4 2003 by Americ
29、an 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. To allow for unloading of the connections associated with nonproportional loading and inelastic force redistribution, the unloadi
30、ng curve shown in Fig. 1 was developed (Hsieh 1990). This portion of the moment-rotation curve is given by the following equation, where the peak moments and rotations reached during the initial loading are In practice, a major obstacle to including semi-rigid connection behavior in the overall anal
31、ysis and design is the difficulty of defining the parameters of the moment-rotation curve. Connection behavior is an integration of many effects including the connection type, geometry, materials, detailing, workmanship, etc. In particular, during design of the overall structural system it is diffic
32、ult (if not impossible) to precisely establish the parameters which define the moment-rotation behavior since usually the exact connection is not completely detailed until late in the design process. One solution to this is the development of standardized connection reference curves which are based
33、on experimental test data and normalized to be amenable to design. To generalize Eqs. 1a and 1b for use in design, the moment-rotation expressions are normalized with respect to a reference value of moment which is defined herein as the nominal connection capacity, The normalized expressions are ide
34、ntical to Eqs. la & b except that M, and are replaced by and . An example is presented below to show how the normalized curves are developed for top- and seat-angle connections with double web angles. Using a standard curve fitting technique, Eq. la was calibrated to experimental data for top- and s
35、eat-angle connections with double web angles (TSAW) as shown in Fig. 2. The data in this case are based on tests conducted by Azizinamini which are included in the Kishi and Chen data base (Kishi 1986). The curves shown in Fig. 2 were normalized by a value of equal to the moment resisted at an appli
36、ed rotation of 0.02 radians. This value was chosen after considering several alternate normalization schemes, further details of which are reported by Hsieh (1990). The normalization results in the set of curves shown in Fig. 3. For a given type of connection, this procedure provides a convenient me
37、ans of condensing the data from a large number of tests by eliminating variations due to scale effects. From the normalized curves shown in Fig. 3, the three standard reference curves shown in Fig. 4 were developed. The center (TSAW-Ave) curve in Fig. 4 was obtained by fitting a curve through the av
38、erage of the set of curves in Fig. 3. The upper and lower curves in Fig. 4 reflect a variation from the average curve of plus or minus two standard deviations. Assuming the 9-5 2003 by American Institute of Steel Construction, Inc. All rights reserved. This publication or any part thereof must not b
39、e reproduced in any form without permission of the publisher. Figure 2. Moment-Rotation Behavior for TSAW Connections. Figure 3. Normalized Moment-Rotation Behavior for TSAW Connections. 9-6 2003 by American Institute of Steel Construction, Inc. All rights reserved. This publication or any part ther
40、eof must not be reproduced in any form without permission of the publisher. variation in connection response is random and normally distributed, the region between the upper and lower curves in Fig. 4 encompasses roughly 95% of the sampled data. Currently, similar curves are being developed by the a
41、uthors for additional connection types. Parameters for the three curves shown in Fig. 4 are presented in Table 1. Figure 4. Standardized Moment-Rotation Curves, for TSAV Connections. Table 1 Standard Reference Curve Parameters for TSAW Connections Curve TSAW-Max TSAW-Ave TSAW-Min 1.0 0.9 0.8 430 270
42、 100 2.6 6.9 12.4 n 1.2 1.3 3.3 The aim of this approach is to establish a library of standard reference curves for common connection configurations. Then, for analysis of the overall structure, only the connection type and nominal capacity would need to be defined. As shown in the first example bel
43、ow, standard curves such as 9-7 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. those shown in Fig. 4 can be used to investigate the range of expected structural b
44、ehavior. By establishing realistic upper and lower bounds of response based on the type and strength of the connection, the structure can be reliably designed without unnecessary concern over the precise behavior of the final connection detail. Mcn A remaining question in the proposed method is how
45、to calculate the value of for design of the final connection detail. defined by the moment sustained at a rotation of approximately 0.02 radians, is representative of a nominal capacity which could be calculated based on plastic mechanism design procedures such as those in the AISC Engineering Detai
46、ling Manual. A preliminary investigation of the calculation for shows that the AISC procedures provide a low value for this moment compared to measured test data. Alternative procedures, such as those developed by Wu (1988) and others, are being reviewed and improved models for calculating are curre
47、ntly being studied. COMPUTER-AIDED ANALYSIS AND DESIGN SYSTEM For this research, the semi-rigid connection model was implemented in an analysis and design program for steel structures called CU-STAND. CU-STAND is an interactive-graphics program which is capable of both geometric and material nonline
48、ar analysis of 3 dimensional structures (Ziemian et.al. 1990, Hsieh et.al. 1989, Deierlein et.al. 1989). Geometric nonlinear behavior is modelled through a second order analysis using an updated Lagrangian formulation with geometric element stiffness matrices. Material nonlinear (inelastic) response
49、 is included through a concentrated plasticity model which is based on a three parameter yield surface. The yield surface provides an elastic-plastic model which includes the influence of major- and minor-axis bending and axial loads on member yielding. In the analysis, the zero-length connection springs defined by the model described in the previous section are attached to 3-D beam-column elements. The beam-column elements have 6 degrees of freedom at each end, and the connection implementation allows for definition of two rotational springs at each end, corresponding to the
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