1、25Steel Design GuideFrame Design UsingWeb-Tapered Members25Steel Design GuideAMERICAN INSTITUTE OF STEEL CONSTRUCTIONFrame Design Using Web-Tapered MembersRICHARD C. KAEHLERComputerized Structural Design, S.C.Milwaukee, WisconsinDONALD W. WHITEGeorgia Institute of TechnologyAtlanta, GeorgiaYOON DUK
2、KIMGeorgia Institute of TechnologyAtlanta, Georgia00i-0vi_DG25_TP_acknow_TOC.indd a 6/21/11 1:46 PMAISC 2011byAmerican Institute of Steel ConstructionAll rights reserved. This book or any part thereof must not be reproducedin any form without the written permission of the publisher.The information p
3、resented in this publication has been prepared in accordance with recognized engineering principles and is for general information only. While it is believed to be accurate, this information should not be used or relied upon for any specific application without competent professional examination and
4、 verification of its accuracy, suitability and applicability by a licensed professional engineer, designer or architect. The publication of the material contained herein is not intended as a representation or warranty on the part of the American Institute of Steel Construction, or of any other perso
5、n named herein, that this information is suitable for any general or particular use or of freedom from infringement of any patent or patents. Anyone making use of this information assumes all liability arising from such use.Caution must be exercised when relying upon other specifications and codes d
6、eveloped by other bodies and incorporated by reference herein since such material may be modified or amended from time to time subsequent to the printing of this edition. The Institute bears no responsibility for such material other than to refer to it and incorporate it by reference at the time of
7、the initial publication of this edition.Printed in the United States of America00i-0vi_DG25_TP_acknow_TOC.indd b 6/21/11 1:46 PMAuthorsRichard C. Kaehler, P.E. is a vice president at Computerized Structural Design, S.C. in Milwaukee, WI. He is a member of the AISC Committee on Specifications and its
8、 task committees on Stability and Member Design, and chairs its Editorial task committee.Donald W. White, Ph.D is a Professor at the Georgia Institute of Technology School of Civil and Environ-mental Engineering. He is a member of the AISC Committee on Specifications and its task committees on Membe
9、r Design and Stability.Yoon Duk Kim, Ph.D is a postdoctoral fellow at the Georgia Institute of Technology School of Civil and Environmental Engineering.AcknowledgmentsThe authors express their gratitude to the Metal Building Manufacturers Association (MBMA) and the Amer-ican Iron and Steel Institute
10、 (AISI), who provided the funding for both the preparation of this document and the research required to complete it. The authors also appreciate the guidance of the MBMA Steering Committee:Al Harrold Butler ManufacturingAllam Mahmoud United Structures of AmericaDean Jorgenson Metal Building Softwar
11、eDennis Watson BC Steel BuildingsDuane Becker Chief BuildingsJeff Walsh American BuildingsNorman Edwards QuestwareScott Russell Nucor Building SystemsSteve Thomas Varco Pruden BuildingsDr. Efe Guney of Intel Corporation and Mr. Cagri Ozgur of Georgia Tech provided assistance with several investigati
12、ons of design calculation procedures.The authors also appreciate the efforts of the AISC reviewers and staff members who contributed many excel-lent suggestions.PrefaceThis design guide is based on the 2005 AISC Specification for Structural Steel Buildings. It provides guid-ance in the application o
13、f the provisions of the Specification to the design of web-tapered members and frames composed of web-tapered members. The recommendations of this document apply equally to the 2010 AISC Specification for Structural Steel Buildings, although some section and equation numbers have changed in the 2010
14、 Specification.i00i-0vi_DG25_TP_acknow_TOC.indd i 6/21/11 1:46 PMii00i-0vi_DG25_TP_acknow_TOC.indd ii 6/21/11 1:46 PMiiiCHAPTER 5 MEMBER DESIGN 315.1 KEY TERMINOLOGY .315.2 AXIAL TENSION 315.2.1 Tensile Yielding 315.2.2 Tensile Rupture 31Example 5.1Tapered TensionMember with Bolt Holes 325.3 AXIAL C
15、OMPRESSION .335.3.1 Calculate Elastic Buckling Strength 355.3.2 Calculate Nominal Buckling Stress Without Slender Element Effects, Fn1365.3.3 Calculate Slenderness Reduction Factor, Q, and Locate Critical Section .375.3.4 Calculate Nominal Buckling Stress with Consideration of Slender Elements, Fcr.
16、375.3.5 Strength Ratio 385.3.6 Other Considerations .38Example 5.2Tapered Column with Simple Bracing .385.4 FLEXURE .585.4.1 Common Parameters585.4.2 Compression Flange Yielding 615.4.3 Lateral-Torsional Buckling (LTB) 615.4.4 Compression Flange Local Buckling (FLB) 625.4.5 Tension Flange Yielding (
17、TFY) 635.4.6 Tension Flange Rupture 635.4.7 Strength Ratio 64Example 5.3Doubly Symmetric Section Tapered Beam .645.4.8 Commentary on Example 5.3 825.5 COMBINED FLEXURE AND AXIAL FORCE 825.5.1 Force-Based Combined Strength Equations 835.5.2 Separate In-Plane and Out-of-Plane Combined Strength Equatio
18、ns .835.5.3 Stress-Based Combined Strength Equations 84Example 5.4Combined Axial Compression and Flexure .855.5.4 Commentary on Example 5.4 94Table of ContentsCHAPTER 1 INTRODUCTION .11.1 BASIS FOR RECOMMENDATIONS .11.2 LIMITATIONS .11.3 BENEFITS OF WEB-TAPERED MEMBERS 21.4 FABRICATION OF WEB-TAPERE
19、D MEMBERS .21.5 GENERAL NOTES ON DOCUMENT .3CHAPTER 2 WEB-TAPERED MEMBER BEHAVIOR AND DESIGN APPROACHES .52.1 PREVIOUS RESEARCH .52.2 RELATIONSHIP TO PRIOR AISC PROVISIONS FOR WEB-TAPERED MEMBERS .9CHAPTER 3 DESIGN BASIS 133.1 KEY TERMINOLOGY .133.2 LIMIT STATE DESIGN .143.2.1 LRFD Design Basis .143
20、.2.2 ASD Design Basis .143.2.3 Allowable Stress Design .15CHAPTER 4 STABILITY DESIGN REQUIREMENTS 174.1 KEY TERMINOLOGY .174.2 ASCE 7 AND IBC SEISMIC STABILITY REQUIREMENTS 174.3 AISC STABILITY REQUIREMENTS 194.4 STABILITY DESIGN METHODS .204.4.1 Limits of Applicability .214.4.2 Type of Analysis .21
21、4.4.3 Out-of-Plumbness .214.4.4 Stiffness Reduction .22 4.4.5 Design Constraints 224.5 COMMON ANALYSIS PARAMETERS .224.5.1 Pr224.5.2 PeLor eLPr.234.5.3 2nd/1st244.6 DETAILED REQUIREMENTS OF THE STABILITY DESIGN METHODS .244.6.1 The Effective Length Method (ELM) 244.6.2 The Direct Analysis Method (DM
22、) . 264.6.3 The First-Order Method (FOM) 2900i-0vi_DG25_TP_acknow_TOC.indd iii 6/21/11 1:46 PMiv5.6 SHEAR .955.6.1 Shear Strength of Unstiffened Webs 955.6.2 Shear Strength of Stiffened Webs Without Using Tension Field Action .955.6.3 Shear Strength of Stiffened Webs Using Tension Field Ation 965.6.
23、4 Web-to-Flange Weld 97Example 5.5Shear Strength of a Tapered Member .975.7 FLANGES AND WEBS WITH CONCENTRATED FORCES 1025.8 ADDITIONAL EXAMPLES 102Example 5.6Tapered Column with Unequal Flanges and One-Sided Bracing .102Example 5.7Singly Symmetric Section Tapered Beam with One-Sided Bracing .120Exa
24、mple 5.8Combined Axial Compression and Flexure .132CHAPTER 6 FRAME DESIGN .1396.1 FIRST-ORDER ANALYSIS OF FRAMES .1396.2 SECOND-ORDER ANALYSIS OF FRAMES 1406.2.1 P-Only Analysis 1416.2.2 Analysis Using Elements that Include Both P- and P- Effects in the Formulation .1426.2.3 Alternative Amplified Fi
25、rst-Order Analysis 1436.2.4 Required Accuracy of Second-Order Analysis.1436.2.5 Stiffness Reduction .1446.2.6 Load Levels for Second-Order Analysis.1446.2.7 Notional Loads .1456.2.8 Explicit Out-of-Plumbness 1456.2.9 Lean-on Structures 1466.3 ANALYSIS OF SINGLE-STORY CLEAR-SPAN FRAMES .1486.3.1 Beha
26、vior of Single-Story Clear-Span Frames 1486.3.2 In-Plane Design Length of Rafters 1486.3.3 Sidesway Calculations for Gabled Frames .1486.4 SERVICEABILITY CONSIDERATIONS .149CHAPTER 7 ANNOTATED BIBLIOGRAPHY151APPENDIX A. CALCULATING eLOR PeLFOR TAPERED MEMBERS . 169A.1 EQUIVALMENT MOMENT OF INERTIA .
27、169A.2 METHOD OF SUCCESSIVE APPROXIMATIONS .170A.3 EIGENVALUE BUCKLING ANALYSIS 172APPENDIX B. CALCULATING IN-PLANE eFACTORS FOR THE ELM 173B.1 COLUMNS .173B.1.1 Modified Story-Stiffness Method 173B.1.2 Eigenvalue Buckling Analysis .173B.2 RAFTERS .174B.2.1 Eigenvalue Buckling Analysis .174B.2.2 Met
28、hod of Successive Approximations 175B.3 THE RELATIONSHIP BETWEEN K AND e175APPENDIX C. BENCHMARK PROBLEMS 177C.1 PRISMATIC MEMBERS .177C.2 TAPERED MEMBERS 177C.3 METHOD OF SUCCESSIVE APPROXIMATIONS .184C.3.1 eLand PeLof Simple Web-Tapered Column 184C.3.2 eLof Stepped Web-Tapered Column .187SYMBOLS 1
29、93GLOSSARY 197REFERENCES . 19900i-0vi_DG25_TP_acknow_TOC.indd iv 6/21/11 1:46 PMAISC DESIGN GUIDE 25 / FRAME DESIGN USING WEB-TAPERED MEMBERS / 1This document provides suggested methods for the design of web-tapered I-shaped beams and columns, as well as frames that incorporate web-tapered I-shaped
30、beams and/or columns. Both the requirements for analysis and rules for proportion-ing of web-tapered framing members are addressed. The emphasis is on members and frames with proportions and bracing details commonly used in metal building systems. However, this information is equally applicable to s
31、imilar tapered members used in conventional steel construction.The methods contained herein are primarily interpreta-tions of, and extensions to, the provisions of the 2005 AISC Specification for Structural Steel Buildings (AISC, 2005), hereafter referred to as the AISC Specification. The recom-mend
32、ations of this document apply equally to the 2010 AISC Specification for Structural Steel Buildings, although some section and equation numbers have changed in the 2010 AISC Specification. These recommendations are not intend-ed to apply to structures designed using earlier editions of the AISC Spec
33、ification.The 2005 AISC Specification is a significant departure from past AISC Specifications, particularly the ASD Speci-fications, with which almost all metal buildings have been designed in the United States. Engineers and other users fa-miliar with the previous ASD editions will find significan
34、t changes in the presentation of the AISC Specification, the member design provisions, and the requirements for analy-sis. The AISC Specification contains no provisions specific to tapered members.The methods presented in this document comply with the 2005 AISC Specification and provide additional i
35、nformation needed to apply the Specification to tapered members. In some instances, procedures are provided for situations not addressed by the AISC Specification. These are noted where they occur.The publication of the recommendations in this document is not intended to preclude the use of other me
36、thods that comply with the AISC Specification.1.1 BASIS FOR RECOMMENDATIONSThe following sources were used extensively in the prepa-ration of this document, are referenced extensively herein, and should be used in conjunction with this publication for a fuller understanding of its recommendations:1.
37、 ANSI/AISC 360-05, Specification for Structural Steel Buildings (AISC, 2005) and its commentary2. “A Prototype Application of the AISC (2005) Stability Analysis and Design Provisions to Metal Building Structural Systems” (White and Kim, 2006)The References and Annotated Bibliography sections of this
38、 document provide references to other publications relevant to the design of tapered members and frames composed of tapered members. Additional requirements for seis-mic design and detailing can be found in the ANSI/AISC 341-05, Seismic Provisions for Structural Steel Buildings (AISC, 2005a).A signi
39、ficant research program was conducted as part of the development of this Design Guide. This research was conducted by White, Kim and others at the Georgia Institute of Technology. The focus of this work was the verification and adaptation of the AISC Specification provisions for ta-pered members and
40、 frames composed of tapered members. The researched topics included studies on the following:1. Beam lateral-torsional buckling (LTB)2. Column in-plane and out-of-plane fl exural buckling3. Column torsional and fl exural-torsional buckling4. Infl uence of local buckling on member resistances5. Combi
41、ned infl uence of local buckling and member yielding on overall structure stiffness and strength6. Synthesis of approaches for calculation of second-order forces and moments in general framing systems7. Benchmarking of second-order elastic analysis soft-ware8. Consideration of rotational restraint a
42、t nominally sim-ply supported column bases9. Consideration of general end restraint effects on the LTB resistance of web-tapered membersThe reader is referred to Kim and White (2006a, 2006b, 2007a, 2007b); Kim (2010); Ozgur et al. (2007); and Guney and White (2007) for a detailed presentation of res
43、earch re-sults for these topics.1.2 LIMITATIONSExcept where otherwise noted in the text, these recom-mendations apply to members satisfying the following limits:1. Specifi ed minimum yield strength, Fy 55 ksi.2. Homogeneous members only (hybrid members are not Chapter 1Introduction001-004_DG25_Ch1.i
44、ndd 1 6/21/11 1:46 PM2 / FRAME DESIGN USING WEB-TAPERED MEMBERS / AISC DESIGN GUIDE 25considered); i.e., FFyf yw= , where Fyfand Fyware the fl ange and web minimum specifi ed yield strengths.3. Web taper is linear or piecewise linear.4. Web taper angle is between 0 and 15.5. Thickness of each fl ang
45、e is greater than or equal to the web thickness.6. Flange slenderness ratio is such thatbtff218wherebf= fl ange width, in.tf= fl ange thickness, in.7. Flange width is such thatbhf7throughout each unbraced length, Lb. Exception: if LrEFbty 11.bhf9throughout the unbraced length. In the foregoing equat
46、ions,h = web height, in.rt= radius of gyration of the fl ange in fl exural compression plus one third of the web area in compression due to the application of major axis bending moment alone, calculated using the largest section depth within the length un-der consideration, in.8. Web slenderness (wi
47、thout transverse stiffeners or with stiffeners at a/h 1.5) is such thathtEFwy040260.whereE = modulus of elasticity, ksitw= web thickness, in.9. Web slenderness (with transverse stiffeners at a/h 1.5)is such thathtEFwy 12It is expected that these recommendations can be extended to homogeneous members
48、 with larger yield strengths. How-ever, the background research for these recommendations was focused on Fy= 55 ksi, because the use of larger yield strengths is not common in current practice.In addition, it is expected that the recommendations can be extended to hybrid members. The background rese
49、arch for the recommendations in this Design Guide was focused on homogeneous members and the AISC Specification does not address hybrid members. Comprehensive provisions for flexural design of hybrid members are provided in the American Association of State Highway and Transportation Officials (AASHTO) LRFD Bridge Design Specifications (AASHTO, 2004, 2007).Furthermore, it is expected that the recommendations can be applied to members with parabolic or other tapered web geometries. However, calculation of the elastic buckling re-sistances of the
