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- 1. Steel Frame Design Manual AISC ASD-2001, AIS ASD-1989, AISC LRFD-1999 AISC LRFD-1993, BS 5950-2000, BS 5950-1990, CISC 1994, Eurocode 3-1992, UBC ASD-1997 and UBC LRFD-1997 For SAP2000® and ETABS® ISO SAP022811M7 Rev. 0 Version 15 Berkeley, California June 2011
- 2. COPYRIGHT Copyright ã Computers and Structures, Inc., 1978-2011. All rights reserved. The CSI Logo®, SAP2000®, ETABS® and SAFE® are registered trademarks of Computers and Structures, Inc. Watch & LearnTM is a trademark of Computers and Structures, Inc. The computer programs SAP2000® and ETABS® and all associated documentation are proprietary and copyrighted products. Worldwide rights of ownership rest with Computers and Structures, Inc. Unlicensed use of these programs or reproduction of documentation in any form, without prior written authorization from Computers and Structures, Inc., is explicitly prohibited. No part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior explicit written permission of the publisher. Further information and copies of this documentation may be obtained from: Computers and Structures, Inc. 1995 University Avenue Berkeley, California 94704 USA Tel: (510) 649-2200 Fax: (510) 649-2299 E-mail: info@csiberkeley.com (for general questions) E-mail: support@csiberkeley.com (for technical supports questions) Web: www.csiberkeley.com
- 3. DISCLAIMER CONSIDERABLE TIME, EFFORT AND EXPENSE HAVE GONE INTO THE DEVELOPMENT AND DOCUMENTATION OF ETABS AND SAP2000. THE PROGRAMS HAVE BEEN THOROUGHLY TESTED AND USED. IN USING THE PROGRAMS, HOWEVER, THE USER ACCEPTS AND UNDERSTANDS THAT NO WAR- RANTY IS EXPRESSED OR IMPLIED BY THE DEVELOPERS OR THE DISTRIBUTORS ON THE ACCURACY OR THE RELIABIL- ITY OF THE PROGRAMS. ETABS AND SAP2000 ARE VERY PRACTICAL TOOL FOR THE DESIGN OF REINFORCED CONCRETE STRUCTURES. HOW- EVER, THE USER MUST THOROUGHLY READ THE MANUAL AND CLEARLY RECOGNIZE THE ASPECTS OF REINFORCED CONCRETE DESIGN THAT THE PROGRAM ALGORITHMS DO NOT ADDRESS. THE USER MUST EXPLICITLY UNDERSTAND THE ASSUMP- TIONS OF THE PROGRAMS AND MUST INDEPENDENTLY VER- IFY THE RESULTS.
- 4. Table of Contents CHAPTER I Introduction 1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Recommended Reading . . . . . . . . . . . . . . . . . . . . . . . . . 4 CHAPTER II Design Algorithms 5 Design Load Combinations. . . . . . . . . . . . . . . . . . . . . . . . 6 Design and Check Stations . . . . . . . . . . . . . . . . . . . . . . . . 8 P-D Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Element Unsupported Lengths . . . . . . . . . . . . . . . . . . . . . . 9 Effective Length Factor (K) . . . . . . . . . . . . . . . . . . . . . . . 11 Choice of Input Units . . . . . . . . . . . . . . . . . . . . . . . . . . 14 CHAPTER III Check/Design for AISC-ASD01 15 Design Loading Combinations . . . . . . . . . . . . . . . . . . . . . 18 Classification of Sections . . . . . . . . . . . . . . . . . . . . . . . . 22 Special Seismic Provisions of Member Design . . . . . . . . . . . . . 24 Ordinary Moment Frames (OMF) . . . . . . . . . . . . . . . 24 Intermediate Moment Frames (IMF) . . . . . . . . . . . . . 25 Special Moment Frames (SMF) . . . . . . . . . . . . . . . . 25 Ordinary Concentrically Braced Frames (OCBF) . . . . . . . 28 Special Concentrically Braced Frames (SCBF) . . . . . . . . 28 Eccentrically Braced Frames (EBF) . . . . . . . . . . . . . . 29 Calculation of Stresses . . . . . . . . . . . . . . . . . . . . . . . . . 32 Calculation of Allowable Stresses . . . . . . . . . . . . . . . . . . . 33 Allowable Stress in Tension . . . . . . . . . . . . . . . . . . . . 33 Allowable Stress in Compression . . . . . . . . . . . . . . . . . 34 Flexural Buckling . . . . . . . . . . . . . . . . . . . . . . . 34 i
- 5. Flexural-Torsional Buckling. . . . . . . . . . . . . . . . . . 36 Allowable Stress in Bending . . . . . . . . . . . . . . . . . . . . 38 I-sections. . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 Channel sections . . . . . . . . . . . . . . . . . . . . . . . . 42 T-sections and Double angles . . . . . . . . . . . . . . . . . 43 Box Sections and Rectangular Tubes . . . . . . . . . . . . . 43 Pipe Sections. . . . . . . . . . . . . . . . . . . . . . . . . . 44 Round Bars . . . . . . . . . . . . . . . . . . . . . . . . . . 45 Rectangular and Square Bars . . . . . . . . . . . . . . . . . 45 Single-Angle Sections. . . . . . . . . . . . . . . . . . . . . 45 General Sections . . . . . . . . . . . . . . . . . . . . . . . . 48 Allowable Stress in Shear . . . . . . . . . . . . . . . . . . . . . 48 Calculation of Stress Ratios . . . . . . . . . . . . . . . . . . . . . . . 49 Axial and Bending Stresses. . . . . . . . . . . . . . . . . . . . . 49 Shear Stresses. . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 Joint Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 Design of Continuity Plates . . . . . . . . . . . . . . . . . . . . 52 Design of Doubler Plates . . . . . . . . . . . . . . . . . . . . . . 56 Weak Beam Strong Column Measure . . . . . . . . . . . . . . . 59 Evaluation of Beam Connection Shears . . . . . . . . . . . . . . 61 Evaluation of Brace Connection Forces . . . . . . . . . . . . . . 63 CHAPTER IV Check/Design for AISC-ASD89 65 Design Loading Combinations . . . . . . . . . . . . . . . . . . . . . 68 Classification of Sections . . . . . . . . . . . . . . . . . . . . . . . . 68 Calculation of Stresses . . . . . . . . . . . . . . . . . . . . . . . . . 72 Calculation of Allowable Stresses . . . . . . . . . . . . . . . . . . . 73 Allowable Stress in Tension . . . . . . . . . . . . . . . . . . . . 73 Allowable Stress in Compression . . . . . . . . . . . . . . . . . 73 Flexural Buckling . . . . . . . . . . . . . . . . . . . . . . . 73 Flexural-Torsional Buckling. . . . . . . . . . . . . . . . . . 75 Allowable Stress in Bending . . . . . . . . . . . . . . . . . . . . 80 I-sections. . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 Channel sections . . . . . . . . . . . . . . . . . . . . . . . . 83 T-sections and Double angles . . . . . . . . . . . . . . . . . 84 Box Sections and Rectangular Tubes . . . . . . . . . . . . . 85 Pipe Sections. . . . . . . . . . . . . . . . . . . . . . . . . . 86 Round Bars . . . . . . . . . . . . . . . . . . . . . . . . . . 86 Rectangular and Square Bars . . . . . . . . . . . . . . . . . 86 Single-Angle Sections. . . . . . . . . . . . . . . . . . . . . 87 General Sections . . . . . . . . . . . . . . . . . . . . . . . . 89 Allowable Stress in Shear . . . . . . . . . . . . . . . . . . . . . 89 Calculation of Stress Ratios . . . . . . . . . . . . . . . . . . . . . . . 91 Axial and Bending Stresses. . . . . . . . . . . . . . . . . . . . . 91 Shear Stresses. . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 ii CSI Steel Design Manual
- 6. CHAPTER V Check/Design for AISC-LRFD99 95 Design Loading Combinations . . . . . . . . . . . . . . . . . . . . . 98 Classification of Sections . . . . . . . . . . . . . . . . . . . . . . . 102 Calculation of Factored Forces . . . . . . . . . . . . . . . . . . . . 103 Special Seismic Provisions of Member Design . . . . . . . . . . . . 105 Ordinary Moment Frames (OMF) . . . . . . . . . . . . . . 105 Intermediate Moment Frames (IMF) . . . . . . . . . . . . . 108 Special Moment Frames (SMF) . . . . . . . . . . . . . . . 108 Ordinary Concentrically Braced Frames (OCBF) . . . . . . 109 Special Concentrically Braced Frames (SCBF) . . . . . . . 109 Eccentrically Braced Frames (EBF) . . . . . . . . . . . . . 112 Calculation of Nominal Strengths . . . . . . . . . . . . . . . . . . . 114 Compression Capacity . . . . . . . . . . . . . . . . . . . . . . 115 Flexural Buckling . . . . . . . . . . . . . . . . . . . . . . 115 Flexural-Torsional Buckling . . . . . . . . . . . . . . . . . 117 Torsional and Flexural-Torsional Buckling . . . . . . . . . 117 Tension Capacity . . . . . . . . . . . . . . . . . . . . . . . . . 119 Nominal Strength in Bending . . . . . . . . . . . . . . . . . . . 120 Yielding . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 Lateral-Torsional Buckling. . . . . . . . . . . . . . . . . . 120 Doubly Symmetric Shapes and Channels . . . . . . . . . . 120 T-sections and Double Angles . . . . . . . . . . . . . . . . 122 Single Angles. . . . . . . . . . . . . . . . . . . . . . . . . 123 Pipe and Circular sections . . . . . . . . . . . . . . . . . . 124 General and SD Sections . . . . . . . . . . . . . . . . . . . 124 Flange Local Buckling . . . . . . . . . . . . . . . . . . . . 124 I Shapes, Channels, Double Channels . . . . . . . . . . . . 126 Boxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 T-sections and Double Angles . . . . . . . . . . . . . . . . 127 Single Angles. . . . . . . . . . . . . . . . . . . . . . . . . 128 Pipe Sections . . . . . . . . . . . . . . . . . . . . . . . . . 128 Circular, Rectangular, General Sections, and SD-Sections . 129 Web Local Buckling . . . . . . . . . . . . . . . . . . . . . 129 I Shapes, Channels, Double-Channels, and Boxes . . . . . 129 T-sections and Double Angles . . . . . . . . . . . . . . . . 132 Single Angles. . . . . . . . . . . . . . . . . . . . . . . . . 132 Pipe Sections . . . . . . . . . . . . . . . . . . . . . . . . . 132 Circular, Rectangular, General Sections, and SD Sections. . 132 Shear Capacities. . . . . . . . . . . . . . . . . . . . . . . . . . 132 Major Axis of Bending . . . . . . . . . . . . . . . . . . . . 133 Minor Axis of Bending. . . . . . . . . . . . . . . . . . . . 133 Calculation of Capacity Ratios . . . . . . . . . . . . . . . . . . . . 134 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 Axial and Bending Stresses . . . . . . . . . . . . . . . . . . . . 134 Axial, Bending, Shear and Torsion Stresses . . . . . . . . . 135 Shear Stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 iii Table of Contents
- 7. Joint Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 Design of Continuity Plates . . . . . . . . . . . . . . . . . . . . 136 Design of Doubler Plates . . . . . . . . . . . . . . . . . . . . . 140 Weak Beam Strong Column Measure. . . . . . . . . . . . . . . 143 Evaluation of Beam Connection Shears. . . . . . . . . . . . . . 145 Evaluation of Brace Connection Forces. . . . . . . . . . . . . . 147 CHAPTER VI Check/Design for AISC-LRFD93 149 Design Loading Combinations. . . . . . . . . . . . . . . . . . . . . 152 Classification of Sections . . . . . . . . . . . . . . . . . . . . . . . 152 Calculation of Factored Forces . . . . . . . . . . . . . . . . . . . . 156 Calculation of Nominal Strengths . . . . . . . . . . . . . . . . . . . 158 Compression Capacity . . . . . . . . . . . . . . . . . . . . . . 158 Flexural Buckling . . . . . . . . . . . . . . . . . . . . . . 158 Flexural-Torsional Buckling . . . . . . . . . . . . . . . . . 162 Torsional and Flexural-Torsional Buckling . . . . . . . . . 162 Tension Capacity . . . . . . . . . . . . . . . . . . . . . . . . . 164 Nominal Strength in Bending . . . . . . . . . . . . . . . . . . . 165 Yielding . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 Lateral-Torsional Buckling. . . . . . . . . . . . . . . . . . 165 Flange Local Buckling . . . . . . . . . . . . . . . . . . . . 169 Web Local Buckling . . . . . . . . . . . . . . . . . . . . . 173 Shear Capacities. . . . . . . . . . . . . . . . . . . . . . . . . . 176 Calculation of Capacity Ratios . . . . . . . . . . . . . . . . . . . . 177 Axial and Bending Stresses . . . . . . . . . . . . . . . . . . . . 178 Shear Stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . 178 CHAPTER VII Check/Design for BS 5950-2000 181 Design Loading Combinations. . . . . . . . . . . . . . . . . . . . . 184 Classification of Sections . . . . . . . . . . . . . . . . . . . . . . . 185 Calculation of Factored Forces . . . . . . . . . . . . . . . . . . . . 185 Calculation of Section Capacities . . . . . . . . . . . . . . . . . . . 189 Compression Resistance . . . . . . . . . . . . . . . . . . . . . 189 Tension Capacity . . . . . . . . . . . . . . . . . . . . . . . . . 191 Moment Capacity . . . . . . . . . . . . . . . . . . . . . . . . . 191 Plastic and Compact Sections . . . . . . . . . . . . . . . . 191 Semi-compact Sections. . . . . . . . . . . . . . . . . . . . 193 Lateral-Torsional Buckling Moment Capacity . . . . . . . . . . 193 Shear Capacities. . . . . . . . . . . . . . . . . . . . . . . . . . 195 Calculation of Capacity Ratios. . . . . . . . . . . . . . . . . . . . . 197 Local Capacity Check . . . . . . . . . . . . . . . . . . . . . . . 197 Under Axial Tension . . . . . . . . . . . . . . . . . . . . . 197 Under Axial Compression . . . . . . . . . . . . . . . . . . 197 Overall Buckling Check. . . . . . . . . . . . . . . . . . . . . . 198 iv CSI Steel Design Manual
- 8. Shear Capacity Check . . . . . . . . . . . . . . . . . . . . . . . 198 CHAPTER VIII Check/Design for BS 5950-1990 199 Design Loading Combinations. . . . . . . . . . . . . . . . . . . . . 202 Classification of Sections . . . . . . . . . . . . . . . . . . . . . . . 203 Calculation of Factored Forces . . . . . . . . . . . . . . . . . . . . 205 Calculation of Section Capacities . . . . . . . . . . . . . . . . . . . 207 Compression Resistance . . . . . . . . . . . . . . . . . . . . . 207 Tension Capacity . . . . . . . . . . . . . . . . . . . . . . . . . 209 Moment Capacity . . . . . . . . . . . . . . . . . . . . . . . . . 209 Plastic and Compact Sections . . . . . . . . . . . . . . . . 209 Semi-compact Sections. . . . . . . . . . . . . . . . . . . . 210 Lateral-Torsional Buckling Moment Capacity . . . . . . . . . . 210 Shear Capacities. . . . . . . . . . . . . . . . . . . . . . . . . . 213 Calculation of Capacity Ratios. . . . . . . . . . . . . . . . . . . . . 213 Local Capacity Check . . . . . . . . . . . . . . . . . . . . . . . 215 Under Axial Tension . . . . . . . . . . . . . . . . . . . . . 215 Under Axial Compression . . . . . . . . . . . . . . . . . . 215 Overall Buckling Check. . . . . . . . . . . . . . . . . . . . . . 215 Shear Capacity Check . . . . . . . . . . . . . . . . . . . . . . . 216 CHAPTER IX Check/Design for CISC94 217 Design Loading Combinations. . . . . . . . . . . . . . . . . . . . . 220 Classification of Sections . . . . . . . . . . . . . . . . . . . . . . . 221 Calculation of Factored Forces . . . . . . . . . . . . . . . . . . . . 221 Calculation of Factored Strengths . . . . . . . . . . . . . . . . . . . 224 Compression Strength. . . . . . . . . . . . . . . . . . . . . . . 224 Tension Strength . . . . . . . . . . . . . . . . . . . . . . . . . 225 Bending Strengths. . . . . . . . . . . . . . . . . . . . . . . . . 225 I-shapes and Boxes . . . . . . . . . . . . . . . . . . . . . . 226 Rectangular Bar . . . . . . . . . . . . . . . . . . . . . . . 227 Pipes and Circular Rods . . . . . . . . . . . . . . . . . . . 227 Channel Sections . . . . . . . . . . . . . . . . . . . . . . . 228 T-shapes and double angles . . . . . . . . . . . . . . . . . 228 Single Angle and General Sections. . . . . . . . . . . . . . 229 Shear Strengths . . . . . . . . . . . . . . . . . . . . . . . . . . 229 Calculation of Capacity Ratios. . . . . . . . . . . . . . . . . . . . . 231 Axial and Bending Stresses . . . . . . . . . . . . . . . . . . . . 231 Shear Stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . 234 CHAPTER X Check/Design for EUROCODE 3-92 235 Design Loading Combinations. . . . . . . . . . . . . . . . . . . . . 238 Classification of Sections . . . . . . . . . . . . . . . . . . . . . . . 239 Calculation of Factored Forces . . . . . . . . . . . . . . . . . . . . 243 v Table of Contents
- 9. Calculation of Section Resistances . . . . . . . . . . . . . . . . . . 244 Tension Capacity . . . . . . . . . . . . . . . . . . . . . . . . . 245 Compression Resistance . . . . . . . . . . . . . . . . . . . . . 245 Shear Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . 247 Moment Resistance . . . . . . . . . . . . . . . . . . . . . . . . 248 Lateral-torsional Buckling . . . . . . . . . . . . . . . . . . . . 249 Calculation of Capacity Ratios. . . . . . . . . . . . . . . . . . . . . 251 Bending, Axial Compression, and Low Shear . . . . . . . . . . 251 Bending, Axial Compression, and High Shear . . . . . . . . . . 252 Bending, Compression, and Flexural Buckling . . . . . . . . . . 252 Bending, Compression, and Lateral-Torsional Buckling . . . . . 253 Bending, Axial Tension, and Low Shear . . . . . . . . . . . . . 254 Bending, Axial Tension, and High Shear . . . . . . . . . . . . . 254 Bending, Axial Tension, and Lateral-Torsional Buckling . . . . 255 Shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255 CHAPTER XI Check/Design for UBC-ASD97 257 Design Loading Combinations. . . . . . . . . . . . . . . . . . . . . 259 Member Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260 Classification of Sections . . . . . . . . . . . . . . . . . . . . . 260 Calculation of Stresses . . . . . . . . . . . . . . . . . . . . . . 262 Calculation of Allowable Stresses . . . . . . . . . . . . . . . . 262 Calculation of Stress Ratios . . . . . . . . . . . . . . . . . . . . 263 Axial and Bending Stresses . . . . . . . . . . . . . . . . . 263 Shear Stresses . . . . . . . . . . . . . . . . . . . . . . . . 265 Seismic Requirements. . . . . . . . . . . . . . . . . . . . . . . 266 Ordinary Moment Frames . . . . . . . . . . . . . . . . . . 266 Special Moment-Resisting Frames . . . . . . . . . . . . . . 266 Braced Frames . . . . . . . . . . . . . . . . . . . . . . . . 267 Eccentrically Braced Frames . . . . . . . . . . . . . . . . . 268 Special Concentrically Braced Frames . . . . . . . . . . . . 271 Joint Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272 Design of Continuity Plates . . . . . . . . . . . . . . . . . . . . 273 Design of Doubler Plates . . . . . . . . . . . . . . . . . . . . . 276 Beam/Column Plastic Moment Capacity Ratio . . . . . . . . . . 278 Evaluation of Beam Connection Shears. . . . . . . . . . . . . . 279 Evaluation of Brace Connection Forces. . . . . . . . . . . . . . 281 CHAPTER XII Check/Design for UBC-LRFD97 283 Design Loading Combinations. . . . . . . . . . . . . . . . . . . . . 285 Member Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286 Classification of Sections . . . . . . . . . . . . . . . . . . . . . 286 Calculation of Factored Forces . . . . . . . . . . . . . . . . . . 288 Calculation of Nominal Strengths. . . . . . . . . . . . . . . . . 289 Calculation of Capacity Ratios . . . . . . . . . . . . . . . . . . 290 vi CSI Steel Design Manual
- 10. Axial and Bending Stresses . . . . . . . . . . . . . . . . . 290 Shear Stresses . . . . . . . . . . . . . . . . . . . . . . . . 291 Seismic Requirements. . . . . . . . . . . . . . . . . . . . . . . 292 Ordinary Moment Frames . . . . . . . . . . . . . . . . . . 292 Special Moment-Resisting Frames . . . . . . . . . . . . . . 292 Braced Frames . . . . . . . . . . . . . . . . . . . . . . . . 293 Eccentrically Braced Frames . . . . . . . . . . . . . . . . . 294 Special Concentrically Braced Frames . . . . . . . . . . . . 297 Joint Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299 Design of Continuity Plates . . . . . . . . . . . . . . . . . . . . 299 Design of Doubler Plates . . . . . . . . . . . . . . . . . . . . . 303 Weak Beam Strong Column Measure. . . . . . . . . . . . . . . 306 Evaluation of Beam Connection Shears. . . . . . . . . . . . . . 307 Evaluation of Brace Connection Forces. . . . . . . . . . . . . . 308 CHAPTER XIII Design Output 311 Overview. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311 Graphical Display of Design Output . . . . . . . . . . . . . . . . . 312 Tabular Display of Design Output . . . . . . . . . . . . . . . . . . . 313 Member Specific Information . . . . . . . . . . . . . . . . . . . . . 314 References 317 Index 319 vii Table of Contents
- 11. C h a p t e r I Introduction Overview SAP2000 and ETABS feature powerful and completely integrated modules for de- sign of both steel and reinforced concrete structures. The program provides the user with options to create, modify, analyze and design structural models, all from within the same user interface. The program is capable of performing initial mem- ber sizing and optimization from within the same interface. The program provides an interactive environment in which the user can study the stress conditions, make appropriate changes, such as revising member properties, and re-examine the results without the need to re-run the analysis. A single mouse click on an element brings up detailed design information. Members can be grouped together for design purposes. The output in both graphical and tabulated formats can be readily printed. The program is structured to support a wide variety of the latest national and inter- national design codes for the automated design and check of concrete and steel frame members. The program currently supports the following steel design codes: • U.S. AISC 360-2005/IBC 2006 • U.S. AISC ASD-2001, • U.S. AISC LRFD-1999, Overview 1
- 12. • U.S. AISC ASD-1989, • U.S. AISC-LRFD-1994, • UBC ASD-1997, • UBC LRFD-1997, • Canadian CAN/CSA-S16.1-1994, • British BS 5950-2200, • British BS 5950-1990, and • Eurocode 3 (ENV 1993-1-1). The design is based upon a set of user-specified loading combinations. However, the program provides a set of default load combinations for each design code sup- ported in the program. If the default load combinations are acceptable, no definition of additional load combination is required. In the design process the program picks the least weight section required for strength for each element to be designed, from a set of user specified sections. Dif- ferent sets of available sections can be specified for different groups of elements. Also several elements can be grouped to be designed to have the same section. In the check process the program produces demand/capacity ratios for axial load and biaxial moment interactions and shear. The demand/capacity ratios are based on element stress and allowable stress for allowable stress design, and on factored loads (actions) and factored capacities (resistances) for limit state design. The checks are made for each user specified (or program defaulted) load combina- tion and at several user controlled stations along the length of the element. Maxi- mum demand/capacity ratios are then reported and/or used for design optimization. All allowable stress values or design capacity values for axial, bending and shear actions are calculated by the program. Tedious calculations associated with evalu- ating effective length factors for columns in moment frame type structures are auto- mated in the algorithms. The presentation of the output is clear and concise. The information is in a form that allows the designer to take appropriate remedial measures if there is member over- stress. Backup design information produced by the program is also provided for convenient verification of the results. When using 1997 UBC-ASD or UBC-LRFD design codes, requirements for conti- nuity plates at the beam to column connections are evaluated. The program per- forms a joint shear analysis to determine if doubler plates are required in any of the 2 Overview CSI Steel Design Manual
- 13. joint panel zones. Maximum beam shears required for the beam shear connection design are reported. Also maximum axial tension or compression values that are generated in the member are reported. Special 1997 UBC-ASD and UBC-LRFD seismic design provisions are imple- mented in the current version of the program. The ratio of the beam flexural capaci- ties with respect to the column reduced flexural capacities (reduced for axial force effect) associated with the weak beam-strong column aspect of any beam/column intersection, are reported for special moment resisting frames. Capacity require- ments associated with seismic framing systems that require ductility are checked. Special requirements for seismic design are not implemented in the current version of SAP2000. English as well as SI and MKS metric units can be used to define the model geome- try and to specify design parameters. Organization This manual is organized in the following way: Chapter II outlines various aspects of the steel design procedures of the program. This chapter describes the common terminology of steel design as implemented in the program. Each of eleven subsequent chapters gives a detailed description of a specific code of practice as interpreted by and implemented in the program. Each chapter de- scribes the design loading combinations to be considered; allowable stress or ca- pacity calculations for tension, compression, bending, and shear; calculations of demand/capacity ratios; and other special considerations required by the code. • Chapter III gives a detailed description of the AISC ASD code (AISC 2001) as implemented in the program. • Chapter IV gives a detailed description of the AISC ASD steel code (AISC 1989) as implemented in the program. • Chapter V gives a detailed description of the AISC LRFD code (AISC 1999) as implemented in the program. • Chapter VI gives a detailed description of the AISC LRFD steel code (AISC 1993) as implemented in the program. • Chapter VII gives a detailed description of the British code BS 5950 (BSI 2000) as implemented in the program. Organization 3 Chapter I Introduction
- 14. • Chapter IIIV gives a detailed description of the British code BS 5950 (BSI 1990) as implemented in the program. • Chapter IX gives a detailed description of the Canadian code (CISC 1994) as implemented in the program. • Chapter X gives a detailed description of the Eurocode 3 (CEN 1992) as imple- mented in the program. • Chapter XI gives a detailed description of the UBC ASD (UBC 1997) as imple- mented in the program. • Chapter XII gives a detailed description of the UBC (UBC 1997) as imple- mented in the program. Chapter XIII outlines various aspects of the tabular and graphical output from the program related to steel design. Recommended Reading It is recommended that the user read Chapter II “Design Algorithms” and one of eleven subsequent chapters corresponding to the code of interest to the user. Finally the user should read “Design Output” in Chapter XIII for understanding and inter- preting the program output related to steel design. 4 Recommended Reading CSI Steel Design Manual
- 15. C h a p t e r II Design Algorithms This chapter outlines various aspects of the steel check and design procedures that are used by the program. The steel design and check may be performed according to one of the following codes of practice. • American Institute of Steel Construction’s “Allowable Stress Design and Plas- tic Design Specification for Structural Steel Buildings”, AISC-ASD (AISC 2001). • American Institute of Steel Construction’s “Allowable Stress Design and Plas- tic Design Specification for Structural Steel Buildings”, AISC-ASD (AISC 1989). • American Institute of Steel Construction’s “Load and Resistance Factor De- sign Specification for Structural Steel Buildings”, AISC-LRFD (AISC 1999) • American Institute of Steel Construction’s “Load and Resistance Factor De- sign Specification for Structural Steel Buildings”, AISC-LRFD (AISC 1994). • British Standards Institution’s “Structural Use of Steelwork in Building”, BS 5950 (BSI 2000). • British Standards Institution’s “Structural Use of Steelwork in Building”, BS 5950 (BSI 1990). 5
- 16. • Canadian Institute of Steel Construction’s “Limit States Design of Steel Struc- tures”, CAN/CSA-S16.1-94 (CISC 1995). • European Committee for Standardization’s “Eurocode 3: Design of Steel Structures C Part 1.1: General Rules and Rules for Buildings”, ENV 1993-1-1 (CEN 1992). • International Conference of Building Officials’ “1997 Uniform Building Code: Volume 2: Structural Engineering Design Provisions” Chapter 22 Divi- sion III “Design Standard for Specification for Structural Steel Buildings ¾ Allowable Stress Design and Plastic Design”, UBC-ASD (ICBO 1997). • International Conference of Building Officials’ “1997 Uniform Building Code: Volume 2: Structural Engineering Design Provisions” Chapter 22 Divi- sion II “Design Standard for Load and Resistance factor Design Specification for Structural Steel Buildings”, UBC-LRFD (ICBO 1997). Details of the algorithms associated with each of these codes as implemented and interpreted in the program are described in subsequent chapters. However, this chapter provides a background which is common to all the design codes. It is assumed that the user has an engineering background in the general area of structural steel design and familiarity with at least one of the above mentioned de- sign codes. For referring to pertinent sections of the corresponding code, a unique prefix is as- signed for each code. For example, all references to the AISC-LRFD code carry the prefix of “LRFD”. Similarly, – References to the AISC-ASD code carry the prefix of “ASD” – References to the Canadian code carry the prefix of “CISC” – References to the British code carry the prefix of “BS” – References to the Eurocode carry the prefix of “EC3” – References to the UBC-ASD code carry the prefix of “UBC Design Load Combinations The design load combinations are used for determining the various combinations of the load cases for which the structure needs to be designed/checked. The load com- bination factors to be used vary with the selected design code. The load combina- tion factors are applied to the forces and moments obtained from the associated 6 Design Load Combinations CSI Steel Design Manual
- 17. load cases and the results are then summed to obtain the factored design forces and moments for the load combination. For multi-valued load combinations involving response spectrum, time history, moving loads and multi-valued combinations (of type enveloping, square-root of the sum of the squares or absolute) where any correspondence between interacting quantities is lost, the program automatically produces multiple sub combinations using maxima/minima permutations of interacting quantities. Separate combina- tions with negative factors for response spectrum cases are not required because the program automatically takes the minima to be the negative of the maxima for re- sponse spectrum cases and the above described permutations generate the required sub combinations. When a design combination involves only a single multi-valued case of time his- tory or moving load, further options are available. The program has an option to re- quest that time history combinations produce sub combinations for each time step of the time history. Also an option is available to request that moving load combi- nations produce sub combinations using maxima and minima of each design quan- tity but with corresponding values of interacting quantities. For normal loading conditions involving static dead load, live load, wind load, and earthquake load, and/or dynamic response spectrum earthquake load, the program has built-in default loading combinations for each design code. These are based on the code recommendations and are documented for each code in the corresponding chapters. For other loading conditions involving moving load, time history, pattern live loads, separate consideration of roof live load, snow load, etc., the user must define design loading combinations either in lieu of or in addition to the default design loading combinations. The default load combinations assume all static load cases declared as dead load to be additive. Similarly, all cases declared as live load are assumed additive. How- ever, each static load case declared as wind or earthquake, or response spectrum cases, is assumed to be non additive with each other and produces multiple lateral load combinations. Also wind and static earthquake cases produce separate loading combinations with the sense (positive or negative) reversed. If these conditions are not correct, the user must provide the appropriate design combinations. The default load combinations are included in design if the user requests them to be included or if no other user defined combination is available for concrete design. If any default combination is included in design, then all default combinations will Design Load Combinations 7 Chapter II Design Algorithms
- 18. automatically be updated by the program any time the user changes to a different design code or if static or response spectrum load cases are modified. Live load reduction factors can be applied to the member forces of the live load case on an element-by-element basis to reduce the contribution of the live load to the factored loading. The user is cautioned that if moving load or time history results are not requested to be recovered in the analysis for some or all the frame members, then the effects of these loads will be assumed to be zero in any combination that includes them. Design and Check Stations For each load combination, each element is designed or checked at a number of lo- cations along the length of the element. The locations are based on equally spaced segments along the clear length of the element. The number of segments in an ele- ment is requested by the user before the analysis is made. The user can refine the design along the length of an element by requesting more segments. The axial-flexure interaction ratios as well as shear stress ratios are calculated for each station along the length of the member for each load combination. The actual member stress components and corresponding allowable stresses are calculated. Then, the stress ratios are evaluated according to the code. The controlling com- pression and/or tension stress ratio is then obtained, along with the corresponding identification of the station, load combination, and code-equation. A stress ratio greater than 1.0 indicates an overstress or exceeding a limit state. P-D Effects The program design algorithms require that the analysis results include the P-D ef- fects. The P-D effects are considered differently for “braced” or “nonsway” and “unbraced” or “sway” components of moments in frames. For the braced moments in frames, the effect of P-D is limited to “individual member stability”. For un- braced components, “lateral drift effects” should be considered in addition to indi- vidual member stability effect. In the program, it is assumed that “braced” or “non- sway” moments are contributed from the “dead” or “live” loads. Whereas, “un- braced” or “sway” moments are contributed from all other types of loads. For the individual member stability effects, the moments are magnified with mo- ment magnification factors as in the AISC-LRFD code is considered directly in the design equations as in the Canadian, British, and European codes. No moment magnification is applied to the AISC-ASD code. 8 Design and Check Stations CSI Steel Design Manual
- 19. For lateral drift effects of unbraced or sway frames, the program assumes that the amplification is already included in the results because P-D effects are considered for all but AISC-ASD code. The users of the program should be aware that the default analysis option in the program is turned OFF for P-D effect. The default number of iterations for P-D analysis is 1. The user should turn the P-D analysis ON and set the maximum number of iterations for the analysis. No P-D analysis is required for the AISC- ASD code. For further reference, the user is referred to CSI Analysis Reference Manual (CSI 2005). Element Unsupported Lengths To account for column slenderness effects, the column unsupported lengths are re- quired. The two unsupported lengths are l33 and l22 . See Figure II-1. These are the lengths between support points of the element in the corresponding directions. The length l33 corresponds to instability about the 3-3 axis (major axis), and l22 corre- sponds to instability about the 2-2 axis (minor axis). The length l22 is also used for lateral-torsional buckling caused by major direction bending (i.e., about the 3-3 axis). See Figure II-2 for correspondence between the program axes and the axes in the design codes. Normally, the unsupported element length is equal to the length of the element, i.e., the distance between END-I and END-J of the element. See Figure II-1. The pro- gram, however, allows users to assign several elements to be treated as a single member for design. This can be done differently for major and minor bending. Therefore, extraneous joints, as shown in Figure II-3, that affect the unsupported length of an element are automatically taken into consideration. Element Unsupported Lengths 9 Chapter II Design Algorithms
- 20. In determining the values for l22 and l33 of the elements, the program recognizes various aspects of the structure that have an effect on these lengths, such as member connectivity, diaphragm constraints and support points. The program automati- cally locates the element support points and evaluates the corresponding unsup- ported element length. Therefore, the unsupported length of a column may actually be evaluated as being greater than the corresponding element length. If the beam frames into only one di- rection of the column, the beam is assumed to give lateral support only in that direc- tion. The user has options to specify the unsupported lengths of the elements on an element-by-element basis. 10 Element Unsupported Lengths CSI Steel Design Manual l33 l22 Axis 1 Axis 3 Axis 2 End I End j Figure II-1 Major and Minor Axes of Bending
- 21. Effective Length Factor (K) The column K-factor algorithm has been developed for building-type structures, where the columns are vertical and the beams are horizontal, and the behavior is ba- sically that of a moment-resisting nature for which the K-factor calculation is rela- tively complex. For the purpose of calculating K-factors, the elements are identi- fied as columns, beams and braces. All elements parallel to the Z-axis are classified as columns. All elements parallel to the X-Y plane are classified as beams. The rest are braces. Effective Length Factor (K) 11 Chapter II Design Algorithms 2 33 2 SAP2000 EUROCODE 3 z z y y ASD89, LRFD95 & AASHTO y y x x CISC95 y y x x y y x x BS5950 Figure II-2 Correspondence between the program Axes and Code Axes
- 22. The beams and braces are assigned K-factors of unity. In the calculation of the K-factors for a column element, the program first makes the following four stiff- ness summations for each joint in the structural model: S = E I L cx c c c x æ è çç ö ø ÷÷å S = E I L bx b b b x æ è çç ö ø ÷÷å S = E I L cy c c c y æ è çç ö ø ÷÷å S = E I L by b b b y æ è çç ö ø ÷÷å where the x and y subscripts correspond to the global X and Y directions and the c and b subscripts refer to column and beam. The local 2-2 and 3-3 terms EI l22 22 and EI l33 33 are rotated to give components along the global X and Y directions to form the( / )EI l x and( / )EI l y values. Then for each column, the joint summations at END-I and the END-J of the member are transformed back to the column local 1-2-3 coordinate system and the G-values for END-I and the END-J of the member are calculated about the 2-2 and 3-3 directions as follows: 12 Effective Length Factor (K) CSI Steel Design Manual Figure II-3 Unsupported Lengths are Affected by Intermediate Nodal Points
- 23. G = S S I I c I b 22 22 22 G = S S J J c J b 22 22 22 G = S S I I c I b 33 33 33 G = S S J J c J b 33 33 33 If a rotational release exists at a particular end (and direction) of an element, the corresponding value is set to 10.0. If all degrees of freedom for a particular joint are deleted, the G-values for all members connecting to that joint will be set to 1.0 for the end of the member connecting to that joint. Finally, if G I andG J are known for a particular direction, the column K-factor for the corresponding direction is calcu- lated by solving the following relationship for a: a a a 2 I J I J 36 6( + ) = tan G G G G - from which K = p / a. This relationship is the mathematical formulation for the evaluation of K factors for moment-resisting frames assuming sidesway to be unin- hibited. For other structures, such as braced frame structures, trusses, space frames, transmission towers, etc., the K-factors for all members are usually unity and should be set so by the user. The following are some important aspects associated with the column K-factor algorithm: • An element that has a pin at the joint under consideration will not enter the stiff- ness summations calculated above. An element that has a pin at the far end from the joint under consideration will contribute only 50% of the calculated EI value. Also, beam elements that have no column member at the far end from the joint under consideration, such as cantilevers, will not enter the stiffness summation. • If there are no beams framing into a particular direction of a column element, the associated G-value will be infinity. If the G-value at any one end of a col- umn for a particular direction is infinity, the K-factor corresponding to that di- rection is set equal to unity. • If rotational releases exist at both ends of an element for a particular direction, the corresponding K-factor is set to unity. • The automated K-factor calculation procedure can occasionally generate artifi- cially high K-factors, specifically under circumstances involving skewed beams, fixed support conditions, and under other conditions where the pro- gram may have difficulty recognizing that the members are laterally supported and K-factors of unity are to be used. Effective Length Factor (K) 13 Chapter II Design Algorithms
- 24. • All K-factors produced by the program can be overwritten by the user. These values should be reviewed and any unacceptable values should be replaced. Choice of Input Units English as well as SI and MKS metric units can be used for input. But the codes are based on a specific system of units. All equations and descriptions presented in the subsequent chapters correspond to that specific system of units unless otherwise noted. For example, AISC-ASD code is published in kip-inch-second units. By de- fault, all equations and descriptions presented in the chapter “Check/Design for AISC-ASD89” correspond to kip-inch-second units. However, any system of units can be used to define and design the structure in the program. 14 Choice of Input Units CSI Steel Design Manual
- 25. C h a p t e r III Check/Design for AISC-ASD01 This chapter describes the details of the structural steel design and stress check al- gorithms that are used by the program when the user selects the AISC-ASD01 de- sign code (AISC 2001). Various notations used in this chapter are described in Table IV-1. For referring to pertinent sections and equations of the original ASD code, a unique prefix “ASD” is assigned. However, all references to the “Specifications for Al- lowable Stress Design of Single-Angle Members” carry the prefix of “ASD SAM”. The design is based on user-specified loading combinations. But the program pro- vides a set of default load combinations that should satisfy requirements for the de- sign of most building type structures. In the evaluation of the axial force/biaxial moment capacity ratios at a station along the length of the member, first the actual member force/moment components and the corresponding capacities are calculated for each load combination. Then the ca- pacity ratios are evaluated at each station under the influence of all load combina- tions using the corresponding equations that are defined in this chapter. The con- trolling capacity ratio is then obtained. A capacity ratio greater than 1.0 indicates overstress. Similarly, a shear capacity ratio is also calculated separately. 15
- 26. 16 CSI Steel Design Manual A = Cross-sectional area, in 2 Ae = Effective cross-sectional area for slender sections, in 2 Af = Area of flange , in 2 Ag = Gross cross-sectional area, in 2 A Av v2 3, = Major and minor shear areas, in 2 Aw = Web shear area, dtw , in 2 Cb = Bending Coefficient Cm = Moment Coefficient Cw = Warping constant, in 6 D = Outside diameter of pipes, in E = Modulus of elasticity, ksi Fa = Allowable axial stress, ksi Fb = Allowable bending stress, ksi F Fb b33 22, = Allowable major and minor bending stresses, ksi Fcr = Critical compressive stress, ksi Fe33 ¢ = ( ) 12 23 2 33 33 33 2 E K l r p Fe22 ¢ = ( ) 12 23 2 22 22 22 2 E K l r p Fv = Allowable shear stress, ksi Fy = Yield stress of material, ksi K = Effective length factor K K33 22, = Effective length K-factors in the major and minor directions M M33 22, = Major and minor bending moments in member, kip-in Mob = Lateral-torsional moment for angle sections, kip-in P = Axial force in member, kips Pe = Euler buckling load, kips Q = Reduction factor for slender section, = Q Qa s Qa = Reduction factor for stiffened slender elements Qs = Reduction factor for unstiffened slender elements S = Section modulus, in 3 S S33 22, = Major and minor section moduli, in 3 Table III-1 AISC-ASD Notations
- 27. 17 Chapter III Check/Design for AISC-ASD01 S Seff eff, ,,33 22 = Effective major and minor section moduli for slender sections, in 3 Sc = Section modulus for compression in an angle section, in 3 V V2 3, = Shear forces in major and minor directions, kips b = Nominal dimension of plate in a section, in longer leg of angle sections, b tf w-2 for welded and b tf w-3 for rolled box sections, etc. be = Effective width of flange, in bf = Flange width, in d = Overall depth of member, in fa = Axial stress either in compression or in tension, ksi fb = Normal stress in bending, ksi f fb b33 22, = Normal stress in major and minor direction bending, ksi fv = Shear stress, ksi f fv v2 3, = Shear stress in major and minor direction bending, ksi h = Clear distance between flanges for I shaped sections ( )d tf-2 , in he = Effective distance between flanges less fillets, in k = Distance from outer face of flange to web toe of fillet , in kc = Parameter used for classification of sections, [ ] 4.05 0.46 h tw if h tw >70 , 1 if h tw £70 . l l33 22, = Major and minor direction unbraced member lengths, in lc = Critical length, in r = Radius of gyration, in r r33 22, = Radii of gyration in the major and minor directions, in rz = Minimum Radius of gyration for angles, in t = Thickness of a plate in I, box, channel, angle, and T sections, in tf = Flange thickness, in tw = Web thickness, in bw = Special section property for angles, in Table III-1 AISC-ASD Notations (cont.)
- 28. English as well as SI and MKS metric units can be used for input. But the code is based on Kip-Inch-Second units. For simplicity, all equations and descriptions pre- sented in this chapter correspond to Kip-Inch-Second units unless otherwise noted. Design Loading Combinations The design load combinations are the various combinations of the load cases for which the structure needs to be checked. For the AISC-ASD01 code, if a structure is subjected to dead load (DL), live load (LL), wind load (WL), and earthquake in- duced load (EL), and considering that wind and earthquake forces are reversible, then the following load combinations may have to be defined (ASD A4). The DLmultiplier and r factors are specified in ASCE 7-02: 1.0 DL (ASCE 2.4.1-1) 1.0 DL + 1.0 LL (ASCE 2.4.1-2) 1.0 DL ± 1.0 WL (ASCE 2.4.1-5) 0.6 DL ± 1.0 WL (ASCE 2.4.1-7) 1.0 DL + 0.75 (1.0 LL ± 1.0 WL) (ASCE 2.4.1-6) 1.0 DL (0.6 - 0.7 DLmultiplier ) ± 0.7 r EL (ASCE 2.4.1-8) 1.0 DL (1 + 0.7 DLmultiplier ) ± 1.0 r EL (ASCE 2.4.1-5) 1.0 DL + 0.75 (0.7 DLmultiplier + 1.0 LL ± 0.7 r EL) (ASCE 2.4.1-6) It is noted here that whenever special seismic loading combinations are required by the code for special circumstances, the program automatically generates those load combinations internally. The following additional seismic load combinations are frequently checked for specific types of members and special circumstances. (0.9-0.2SDS) DL ± W0 EL (ASCE 9.5.2.7.1, 2.3, LRFD SEISMIC 4.1) (1.2 + 0.2SSDS) DL + 1.0 LL ± W0 EL where, W0 is the seismic force amplification factor which is required to account for structural overstrength. The default value of W0 is taken as 3.0 in the program. If the user defines one or more auto-seismic loads, then the value of W0 defined for each auto-seismic load cases. Also if special seismic data is defined by the user, the user specifies an W0 value, and the user requests the program to include the special seismic design data, then the user specified W0 takes precedence over the default 18 Design Loading Combinations CSI Steel Design Manual
- 29. Design Loading Combinations 19 Chapter III Check/Design for AISC-ASD01 Figure III-1 AISC-ASD Definition of Geometric Properties
- 30. 20 Design Loading Combinations CSI Steel Design Manual Section Description Ratio Checked Compact Section Noncompact Section Slender Section I-SHAPE b tf f2 ( rolled) £ Fy65 £ Fy95 No limit b tf f2 (welded) £ Fy65 £ 95 F ky c/ No limit d tw For f Fa y £ 0.16 £ - 640 1 F f Fy a y ( )3.74 , For f Fa y/ > 0.16 £ 257 / Fy . No limit No limit h tw No limit If compression only, £ Fy253 otherwise £ Fb760 ( ) £ + £ 14000 16.5 260 F Fy y BOX b t f £ Fy190 £ Fy238 No limit d tw As for I-shapes No limit No limit h tw No limit As for I-shapes As for I-shapes Other t tw f³ 2 , d bw f£ 6 None None CHANNEL b t f As for I-shapes As for I-shapes No limit d tw As for I-shapes No limit No limit h tw No limit As for I-shapes As for I-shapes Other No limit No limit If welded b df w £ 0.25, t tf w £ 3.0 If rolled b df w £ 0.5, t tf w £ 2.0 Table III-2 Limiting Width-Thickness Ratios for Classification of Sections Based on AISC-ASD
- 31. values and those defined for the auto-seismic load cases. Moreover, W0 can be overwritten for each individual member. The overwritten W0 gets the highest pre- cedence. The guidelines for selecting a reasonable value for W0 can be found in ANSI/AISC 341 SEISMIC section 4.1 and Table I-4-1. These are also the default design load combinations in the program whenever the AISC-ASD01 code is used. The user should use other appropriate loading combi- Design Loading Combinations 21 Chapter III Check/Design for AISC-ASD01 Section Description Ratio Checked Compact Section Noncompact Section Slender Section T-SHAPE b tf f2 £ Fy65 £ Fy95 No limit d tw Not applicable £ Fy127 No limit Other No limit No limit If welded b df w ³ 0.5, t tf w ³ 1.25 If rolled b df w ³ 0.5, t tf w ³ 1.10 DOUBLE ANGLES b t Not applicable £ Fy76 No limit ANGLE b t Not applicable £ Fy76 No limit PIPE D t £ Fy3 300, £ Fy3 300, £ Fy13,000 (Compression only) No limit for flexure ROUND BAR ¾ Assumed Compact RECTANGLE ¾ Assumed Noncompact GENERAL ¾ Assumed Noncompact Table III-2 Limiting Width-Thickness Ratios for Classification of Sections Based on AISC-ASD (Cont.)
- 32. nations if roof live load is separately treated, if other types of loads are present, or if pattern live loads are to be considered. When designing for combinations involving earthquake and Wind loads, allowable stresses are NOT increased by the 4/3 factor per the ASD Supplement No. 1 which references ASCE7. For seismic combinations, the allowable stresses are increased by 1.7 factor in accordance with ANSI/AISC 341 Seismic Section 4.2. Live load reduction factors can be applied to the member forces of the live load case on an element-by-element basis to reduce the contribution of the live load to the factored loading. Classification of Sections The allowable stresses for axial compression and flexure are dependent upon the classification of sections as either Compact, Noncompact, Slender, or Too Slender. The program classifies the individual members according to the limiting width/thickness ratios given in Table III-2 (ASD B5.1, F3.1, F5, G1, A-B5-2). The definition of the section properties required in this table is given in Figure III-1 and Table III-1. If the section dimensions satisfy the limits shown in the table, the section is classi- fied as either Compact, Noncompact, or Slender. If the section satisfies the criteria for Compact sections, then the section is classified as Compact section. If the sec- tion does not satisfy the criteria for Compact sections but satisfies the criteria for Noncompact sections, the section is classified as Noncompact section. If the sec- tion does not satisfy the criteria for Compact and Noncompact sections but satisfies the criteria for Slender sections, the section is classified as Slender section. If the limits for Slender sections are not met, the section is classified as Too Slender. Stress check of Too Slender sections is beyond the scope of the program. In general the design sections need not necessarily be Compact to satisfy ANSI/AISC 341-02 codes. However, for certain special seismic cases they have to be Compact and have to satisfy special slenderness requirements. See subsection “Seismic Requirements” later in this manual. The sections which do satisfy these additional requirements are classified and reported as “SEISMIC” in the program. These special requirements for classifying the sections as “SEISMIC” in the pro- gram are given in Table III-3 (ANSI/AISC 341SEISMIC 8.2, Table I-8-1). If these criteria are not satisfied, when the code requires them to be satisfied, the user must modify the section property. In this case the program gives an error message in the output file. 22 Classification of Sections CSI Steel Design Manual
- 33. Classification of Sections 23 Chapter III Check/Design for AISC-ASD01 Description of Section Width- Thickness Ratio (l) COMPACT (SEISMIC ZONE) (l ps) NONCOMPACT (Uniform Compression) (M M22 33 0» » ) (lr ) I-SHAPE b tf f2 (rolled) £ E Fy 0 3. £ E Fy056. b tf f2 (welded) £ E Fy 0 3. £ E Fy056. h tc w For P Pu b yj £ 0.125, £ æ è ç ç ö ø ÷ ÷314 1. E F - P Py u b y 1.54 j For P Pu b yj > 0.125 £ æ è ç ç ö ø ÷ ÷ ³ ì í ï îï ü ý ï þï 112 1 49. . E F - P P E Fy u b y y 2.33 j £ E Fy1 49. BOX b t f h tc w 0 64. E Fy Not applicable £ E Fy0 64. £ E Fy1 49. CHANNEL, DOUBLE CHANNEL b tf f h tc w As for I-shapes As for I-shapes As for I-shapes As for I-shapes T-SHAPE b tf f2 d tw Not applicable Not applicable As for I-shapes £ E Fy075. ANGLE b t 0 3. E Fy £ E Fy0 45. DOUBLE-ANGLE (Separated) b t 0 3. E Fy £ E Fy0 45. Table III-3 Limiting Width-Thickness Ratios for Classification of Sections (Special Cases) based on AISC-LRFD
- 34. In classifying web slenderness of I-shapes, Box, and Channel sections, it is as- sumed that there are no intermediate stiffeners (ASD F5, G1). Double angles are conservatively assumed to be separated. Special Seismic Provisions of Member Design When using the AISC-ASD01 option, the following Framing Systems are recog- nized (ANSI/AISC 341 SEISMIC 9, 10, 11, 12, 13, 14, 15): • Ordinary Moment Frame (OMF) • Intermediate Moment Frame (IMF) • Special Moment Frame (SMF) • Ordinary Concentrically Braced Frame (OCBF) • Special Concentrically Braced Frame (SCBF) • Eccentrically Braced Frame (EBF) • Special Truss Moment Frame (STMF) By default the frame type is taken as Special Moment-Resisting Frame (SMRF) in the program. However, the frame type can be overwritten in the Preference form to change the default and in the Overwrites form on a member by member basis. If any member is assigned with a frame type, the change of the frame type in the Prefer- ence will not modify the frame type of the individual member for which it is as- signed. Currently the program does not apply any special requirement for STMF. The special seismic requirements checked by the program for member design are dependent on the type of framing used and are described below for each type of framing. Thus special provisions for buildings are only applied if the building frame is classified as seismic design category (SDC) D or E. (ANSI/AISC 341 SEISMIC 1). No special requirement is checked for frames with seismic design category A, B, or C. Ordinary Moment Frames (OMF) For this framing system, the following additional requirements are checked and re- ported (ANSI/AISC 341 SEISMIC 11): • When P P u nj in columns due to prescribed loading combinations without consid- eration of amplified seismic load is greater than 0.4, the axial compressive and tensile strengths are checked in absence of any applied moment and shear for 24 Special Seismic Provisions of Member Design CSI Steel Design Manual
- 35. the following Special Seismic Load Combinations (ANSI/AISC 341 SEISMIC 8.3, 4.1, ASCE 9.5.2.7.1, 2.3). ( )0 9 0 2 0. .- ±S DL ELDS W ( )12 0 2 10 0. . .+ + ±S DL LL ELDS W Intermediate Moment Frames (IMF) For this framing system, the following additional requirements are checked and re- ported (ANSI/AISC 341 SEISMIC 10): • When P P u nj in columns due to prescribed loading combinations without consid- eration of amplified seismic load is greater than 0.4, the axial compressive and tensile strengths are checked in absence of any applied moment and shear for the following Special Seismic Load Combinations (ANSI/AISC 341 SEISMIC 8.3, 4.1, ASCE 9.5.2.7.1, 2.3.2). ( )0 9 0 2 0. .- ±SDS DL ELW ( )12 0 2 10 0. . .+ + ±SDS DL LL ELW Special Moment Frames (SMF) For this framing system, the following additional requirements are checked or re- ported (ANSI/AISC 341 SEISMIC 9): • When P P u nj in columns due to prescribed loading combinations without consid- eration of amplified seismic load is greater than 0.4, the axial compressive and tensile strengths are checked in absence of any applied moment and shear for the following Special Seismic Load Combinations (AISC SEISMIC 8.3, 4.1, ASCE 9.5.2.7.1, 2.3.2). ( )0 9 0 2 0. .- ±S DL ELDS W ( )12 0 2 10 0. . .+ + ±S DL LL ELDS W Special Seismic Provisions of Member Design 25 Chapter III Check/Design for AISC-ASD01
- 36. 26 Special Seismic Provisions of Member Design CSI Steel Design Manual Section Type Reduction Factor for Unstiffened Slender Elements (Qs) Equation Reference I-SHAPE [ ]Q if b t F k b t F k if Fs f f y c f f y c y= £ - 1.0 95 1.293 0.00309 95 2 2 , [ ]{ } k b t F k k b t F if b t F k c f f y c c f f y f f y c < < ³ ì 2 2 2 2 195 26,200 195 , . í ïï î ï ï ASD A-B5-3, ASD A-B5-4 BOX Qs =1 ASD A-B5.2c CHANNEL As for I-shapes with b tf f2 replaced by b tf f . ASD A-B5-3, ASD A-B5-4 T-SHAPE For flanges, as for flanges in I-shapes. For web see below. [ ]Q if d t F d t F if F d ts w y w y y w£ £ - < 1.0 , 127 1.908 0.00715 127 , , [ ]{ } < ³ ì í ïï î ï ï 176 20,000 176 F d t F if d t F y w y w y , , . 2 ASD A-B5-3, ASD A-B5-4, ASD A-B5-5, ASD A-B5-6 DOUBLE- ANGLE [ ]Q if b t F b t F if F b ts y y y= £ - < < 1.0 , 76 1.340 0.00447 76 155 , , [ ]{ } F b t F if b t F y y y , , .15,500 155 2 ³ ì í ïï î ï ï ASD A-B5-1, ASD A-B5-2, SAM 4-3 ANGLE [ ]Q if b t F b t F if F b ts y y y= £ - < < 1.0 , 76 1.340 0.00447 76 155 , , [ ]{ } F b t F if b t F y y y , , .15,500 155 2 ³ ì í ïï î ï ï ASD A-B5-1, ASD A-B5-2, SAM 4-3 PIPE Qs =1 ASD A-B5.2c ROUND BAR Qs =1 ASD A-B5.2c RECTAN- GULAR Qs =1 ASD A-B5.2c GENERAL Qs =1 ASD A-B5.2c Table III-4 Reduction Factor for Unstiffened Slender Elements, Qs
- 37. Special Seismic Provisions of Member Design 27 Chapter III Check/Design for AISC-ASD01 Section Type Effective Width for Stiffened Sections Equation Reference I-SHAPE h h if h t f t f h t f if h t e w w w w = £ - é ë ê ù û ú > , , ( ) , 195.74 253 44.3 1 195.74 f . ì í ï ï î ï ï (compression only, f P Ag = ) ASD A-B5-8 BOX h h if h t f t f h t f if h t e w w w w = £ - é ë ê ù û ú > , , ( ) , 195.74 253 44.3 1 195.74 f . ì í ï ï î ï ï (compression only, f P Ag = ) b b if b t f t f h t f if b t e f f f = £ - é ë ê ê ù û ú ú , , ( ) , 183.74 253 50.3 1 > ì í ï ï î ï ï 183.74 f . (compr., flexure, f Fy= 0.6 ) ASD A-B5-8 ASD A-B5-7 CHANNEL h h if h t f t f h t f if h t e w w w w = £ - é ë ê ù û ú > , , ( ) , 195.74 253 44.3 1 195.74 f . ì í ï ï î ï ï (compression only, f P Ag = ) ASD A-B5-8 T-SHAPE b be = ASD A-B5.2c DOUBLE- ANGLE b be = ASD A-B5.2c ANGLE b be = ASD A-B5.2c PIPE Qa = 1, (However, special expression for allowable axial stress is given.) ASD A-B5-9 ROUND BAR Not applicable ¾ RECTAN- GULAR b be = ASD A-B5.2c GENERAL Not applicable ¾ Table III-5 Effective Width for Stiffened Sections
- 38. • The I-, Channel-, and Double-Channel Shaped beams and columns are addi- tionally checked for compactness criteria as described in Table VI-1 (AISC SEISMIC 9.4, 8.2, Table I-8-1). If this criteria is satisfied the section is re- ported as SEISMIC as described earlier under section classifications. If this cri- teria is not satisfied the, the program issues an error message. • The program checks the laterally unsupported length of beams to be less than ( )0 08. E Fy yr . If this criteria is not satisfied, the program issues an error mes- sage.(ANSI/AISC 341 SEISMIC 9.8) • The program checks the slenderness ratio, L®, for columns to be less than 60 (ANSI/AISC 341 SEISMIC 9.7.b(2)). If the criteria is not satisfied, the pro- gram issues an error message. Ordinary Concentrically Braced Frames (OCBF) For this framing system, the following additional requirements are checked or re- ported (ANSI/AISC 341 SEISMIC 14): • The columns and beams (NOT braces) are designed for the following special amplified seismic load combinations (AISC/ANSI 341 SEISMIC 14.2, ASCI 9.5.2.7.1, 2.3.2.1, 2.3.2). ( )0 9 0 2 0. .- ±S DL ELDS W ( )12 0 2 10 0. . .+ + ±S DL LL ELDS W • The maximum Kl r ratio of the braces for V or inverted-V configurations is checked not to exceed 4 23. E Fy (ANSI/AISC 341 SEISMIC 14.2). If this crite- ria is not met, an error message is reported in the output. Special Concentrically Braced Frames (SCBF) For this framing system, the following additional requirements are checked or re- ported (ANSI/AISC 341 SEISMIC 13): • When P P u nj in columns due to prescribed loading combinations without consid- eration of amplified seismic load is greater than 0.4, the axial compressive and tensile strengths are checked in absence of any applied moment and shear for 28 Special Seismic Provisions of Member Design CSI Steel Design Manual
- 39. the following Special Seismic Load Combinations (ANSI/AISC 341 SEISMIC 8.34.1, ASCE 9.5.2.7.1, 2.3.2). ( )0 9 0 2 0. .- ±S DL ELDS W ( )12 0 2 10 0. . .+ + ±S DL LL ELDS W • All beam, columns and brace members are checked to be Compact according to Table V-2(ANSI/AISC 341 SEISMIC 13.5, 13.2d, 8.2, Table I-8-1). If this cri- teria is satisfied the section is reported as SEISMIC as described earlier under section classifications. If this criteria is not satisfied the program issues an error message. This special criteria is only checked for I, Channel, Double-Channel, Angle, Double-Angle, Box and Pipe sections. • The compressive strength for braces is taken as j c nP . P Pu c n£ j (ANSI/AISC 341 SEISMIC 13.26) • The maximum K l r ratio of the braces is checked not to exceed 5.87 F E y . If this check is not met, the program issues an error message. Note: Beams intersected by Chevron (V or inverted-V) braces are NOT cur- rently checked to have a strength to support loads for the following two condi- tions (ANSI/AISC 341 SEISMIC 13.4a): a A beam that is intersected by braces shall be designed to support the effects of all tributary dead and live loads form load combinations stipulated by the code, assuming the bracings are not present, and b A beam that is intersected by braces shall be designed to resist the effects of load combinations stipulated by the code, except that a loadq b shall be substi- tuted for the term E. q b is given by the difference of R F Ay y for the tension brace and 0 3. j c nP for the compression brace. Users need to check for this requirement independently. Eccentrically Braced Frames (EBF) For this framing system, the program looks for and recognizes the eccentrically braced frame configurations shown in Figure VI-II. The following additional re- Special Seismic Provisions of Member Design 29 Chapter III Check/Design for AISC-ASD01
- 40. quirements are checked or reported for the beams, columns and braces associated with these configurations (ANSI/AISC 341 SEISMIC 15). • When P P u nj in columns due to prescribed loading combinations without consid- eration of amplified seismic load is greater than 0.4, the axial compressive and tensile strengths are checked in absence of any applied moment and shear for the following Special Seismic Load Combinations (ANSI/AISC 341 SEISMIC 8.3, 4.1, ASCE 9.5.2.7.1, 2.3.2). ( )0 9 0 2 0. .- ±S DL ELDS W ( )12 0 2 10 0. . .+ + ±S DL LL ELDS W • The I-shaped, Channel-shaped, and Double-Channel Shaped beams are addi- tionally checked for compactness criteria as described in Table VI-III (ANSI/AISC 341 SEISMIC 15.2, 8.2, Table I-8-1). If this criteria is satisfied the section is reported as SEISMIC as described earlier under section classifi- cations. If this criteria is not satisfied the user must modify the program issues an error message. • The link beam yield strength, Fy , is checked not to exceed the following (AISC SEISMIC 15.2): Fy £ 50 ksi (ANSI/AISC 341 SEISMIC 15.2) If the check is not satisfied, the program issue an error message. • The shear strength for link beams is taken as follows (AISC SEISMIC 15.2): V Vu v n£ j , (ANSI/AISC 341 SEISMIC 15.2) where, ( )j j jV V M en pa pa= min , 2 , (ANSI/AISC 341 SEISMIC 15.2) V V P P pa p u y = - æ è ç ç ö ø ÷ ÷ 1 2 , (ANSI/AISC 341 SEISMIC 15.1) M M P P pa p u y = - é ë ê ù û ú1.18 1 , (ANSI/AISC 341 SEISMIC 15.2) 30 Special Seismic Provisions of Member Design CSI Steel Design Manual
- 41. V F d t tp y f w= -0.6 ( )2 , (ANSI/AISC 341 SEISMIC 15.2) M Z Fp y= , (ANSI/AISC 341 SEISMIC 15.2) j j= v (default is 0.9) , (ANSI/AISC 341 SEISMIC 15.2) P A Fy g y= . (ANSI/AISC 341 SEISMIC 15.2) • If P A Fu g y> 0.15 , the link beam length, e, is checked not to exceed the follow- ing (ANSI/AISC 341 SEISMIC 15.2): e A A M V if A A w g p p w g £ - ¢ é ë ê ù û ú é ë ê ù û ú ¢ ³1.15 0.5 1.6 0.3 , 1 r r .6 0.3 , M V if A A p p w g é ë ê ù û ú ¢ < ì í ï ï î ï ï r (ANSI/AISC 341 SEISMIC 15.2) where, A d t tw f w= -( )2 , and (ANSI/AISC 341 SEISMIC 15.2) ¢ =r P Vu u . (ANSI/AISC 341 SEISMIC 15.2) If the check is not satisfied, the program reports an error message. • The link beam rotation,q, of the individual bay relative to the rest of the beam is calculated as the story drift DM times bay length divided by the total lengths of link beams in the bay. The link beam rotation, q, is checked as follows (ANSI/AISC 341 SEISMIC 15.2). q £ 0.08 radian , where link beam clear length, e M Vs s£1.6 , q £ 0.03 radian , where link beam clear length, e M Vs s³ 2.6 , and q £ value interpolated between 0.08 and 0.02 as the link beam clear length varies from 1.6 M Vs s to 2.6 M Vs s . • The beam strength outside the link is checked to be at least 1.1 times the beam forces corresponding to the controlling link beam shear strength (ANSI/AISC 341 SEISMIC 15.6). The controlling link beam nominal shear strength is taken as follows: ( )min ,V M epa pa2 , (ANSI/AISC 341 SEISMIC 15.6, 15.2) Special Seismic Provisions of Member Design 31 Chapter III Check/Design for AISC-ASD01
- 42. The values of Vpa and M pa are calculated following the procedure described above (ANSI/AISC 341SEISMIC 15.2). The correspondence between brace force and link beam force is obtained from the associated load cases, whichever has the highest link beam force of interest. All braces are checked to be at least compact per regular ANSI/AISC 341code (ANSI/AISC 341 SEISMIC 15.6). If this criteria is not satisfied, the program issues an error message. The brace strength is checked for 1.25Ry times the brace forces corresponding to the controlling link beam nominal shear strength (ANSI/AISC 341 SEIS- MIC 15.6). The controlling link beam nominal shear strength and the corre- sponding forces are obtained by the process described earlier. The I-, Channel-, and Double-Channel- shaped column sections are checked to be at least compact per regular ANSI/AISC 341 code (ANSI/AISC 341 SEIS- MIC 8.2, Table I-8-1, LRFD B.5.1). If this criterion is not satisfied, the pro- gram issues an error message. • The column strength is checked for 1.1Ry times the column forces correspond- ing to the controlling link beam nominal shear strength (ANSI/AISC 341 SEISMIC 15.8). The controlling link beam nominal shear strength and the cor- responding forces are obtained by the process described above. Note: Axial forces in the beams are included in checking the beams. The user is re- minded that using a rigid diaphragm model will result in zero axial forces in the beams. The user must disconnect some of the column lines from the diaphragm to allow beams to carry axial loads. It is recommended that only one column line per eccentrically braced frame be connected to the rigid diaphragm or a flexible dia- phragm model be used. Calculation of Stresses The stresses are calculated at each of the previously defined stations. The member stresses for non-slender sections that are calculated for each load combination are, in general, based on the gross cross-sectional properties.: f = P/Aa f = M /Sb33 33 33 f = M /Sb22 22 22 f = V /Av v2 2 2 f = V /Av v3 3 3 32 Calculation of Stresses CSI Steel Design Manual
- 43. If the section is slender with slender stiffened elements, like slender web in I, Chan- nel, and Box sections or slender flanges in Box, effective section moduli based on reduced web and reduced flange dimensions are used in calculating stresses. f = P/Aa (ASD A-B5.2d) f = M /Sb eff33 33 33, (ASD A-B5.2d) f = M /Sb eff22 22 22, (ASD A-B5.2d) f = V /Av v2 2 2 (ASD A-B5.2d) f = V /Av v3 3 3 (ASD A-B5.2d) The flexural stresses are calculated based on the properties about the principal axes. For I, Box, Channel, T, Double-angle, Pipe, Circular and Rectangular sections, the principal axes coincide with the geometric axes. For Single-angle sections, the de- sign considers the principal properties. For general sections it is assumed that all section properties are given in terms of the principal directions. For Single-angle sections, the shear stresses are calculated for directions along the geometric axes. For all other sections the shear stresses are calculated along the geometric and principle axes. Calculation of Allowable Stresses The allowable stresses in compression, tension, bending, and shear are computed for Compact, Noncompact, and Slender sections according to the following sub- sections. The allowable flexural stresses for all shapes of sections are calculated based on their principal axes of bending. For the I, Box, Channel, Circular, Pipe, T, Double-angle and Rectangular sections, the principal axes coincide with their geo- metric axes. For the Angle sections, the principal axes are determined and all com- putations related to flexural stresses are based on that. If the user specifies nonzero allowable stresses for one or more elements in the de- sign over write form, these values will override the above mentioned calculated values for those elements as defined in the following subsections. The specified al- lowable stresses should be based on the principal axes of bending. Allowable Stress in Tension The allowable axial tensile stress value Fa is assumed to be 0.60 Fy . F = Fa y0.6 (ASD D1, ASD SAM 2) Calculation of Allowable Stresses 33 Chapter III Check/Design for AISC-ASD01
- 44. It should be noted that net section checks are not made. For members in tension, if l r is greater than 300, a message to that effect is printed (ASD B7, ASD SAM 2). For single angles, the minimum radius of gyration, rz , is used instead of r22 and r33 in computing l r . Allowable Stress in Compression The allowable axial compressive stress is the minimum value obtained from flex- ural buckling and flexural-torsional buckling. The allowable compressive stresses are determined according to the following subsections. For members in compression, if Kl r is greater than 200, a warning message is printed (ASD B7, ASD SAM 4). For single angles, the minimum radius of gyra- tion, rz , is used instead of r22 and r33 in computing Kl r . Flexural Buckling The allowable axial compressive stress value, Fa , depends on the slenderness ratio Kl r based on gross section properties and a corresponding critical value, Cc , where Kl r K l r K l r = ì í î ü ý þ max ,33 33 33 22 22 22 , and C c = 2 2 p E Fy . (ASD E2, ASD SAM 4) For single angles, the minimum radius of gyration, rz , is used instead of r22 and r33 in computing Kl r . For Compact or Noncompact sections Fa is evaluated as follows: ( ) F = Kl/r C F + Kl/r C K a c y c 1.0 - ì í î ü ý þ - ( )2 2 2 5 3 3 8 ( )l/r Cc 3 3 8 , if Kl r Cc£ , (ASD E2-1, SAM 4-1) F = E Kl r a 12 23 2 2 p ( ) , if Kl r Cc> . (ASD E2-2, SAM 4-2) 34 Calculation of Allowable Stresses CSI Steel Design Manual
- 45. If Kl r is greater than 200, then the calculated value of Fa is taken not to exceed the value of Fa calculated by using the equation ASD E2-2 for Compact and Noncom- pact sections (ASD E1, B7). For Slender sections, except slender Pipe sections, Fa is evaluated as follows: ( ) F = Q Kl/r C F + Kl/r C a c y1.0 - ì í ï îï ü ý ï þï¢ ( )2 2 2 5 3 3 8 ( ) c c Kl/r C ¢ ¢ - 3 3 8 , if Kl r Cc£ ¢ , (ASD A-B5-11, SAM 4-1) F = E Kl r a 12 23 2 2 p ( ) , if Kl r Cc> ¢ .(ASD A-B5-12, SAM 4-2) where, C E Q F c y ¢ = 2 2 p . (ASD A-B5.2c, ASD SAM 4) For slender sections, if Kl r is greater than 200, then the calculated value of Fa is taken not to exceed its value calculated by using the equation ASD A-B5-12 (ASD B7, E1). For slender Pipe sections Fa is evaluated as follows: F = D t Fa y 662 0.40+ (ASD A-B5-9) The reduction factor,Q, for all compact and noncompact sections is taken as 1. For slender sections, Q is computed as follows: Q Q Qs a= , where (ASD A-B5.2.c, SAM 4) Qs = reduction factor for unstiffened slender elements, and (ASD A-B5.2.a) Qa = reduction factor for stiffened slender elements. (ASD A-B5.2.c) The Qs factors for slender sections are calculated as described in Table III-4 (ASD A-B5.2a, ASD SAM 4). The Qa factors for slender sections are calculated as the ratio of effective cross-sectional area and the gross cross-sectional area. Calculation of Allowable Stresses 35 Chapter III Check/Design for AISC-ASD01
- 46. Q A A a e g = (ASD A-B5-10) The effective cross-sectional area is computed based on effective width as follows: ( )A A b b te g e= - -å be for unstiffened elements is taken equal to b, and be for stiffened elements is taken equal to or less than b as given in Table III-5 (ASD A-B5.2b). For webs in I, box, and Channel sections, he is used as be and h is used as b in the above equation. Flexural-Torsional Buckling The allowable axial compressive stress value, Fa , determined by the limit states of torsional and flexural-torsional buckling is determined as follows (ASD E3, C-E3): ( ) ( ) F = Q Kl/r C F + Kl/r C a e c y e 1.0 - ì í ï îï ü ý ï þï ¢ 2 2 2 5 3 3 8 ( ) c e c Kl/r C ¢ ¢ - 3 3 8 , if ( )Kl/r C e c£ ¢ , (E2-1, A-B5-11) ( ) F = E Kl/r a e 12 23 2 2 p , if ( )Kl/r C e c> ¢ . (E2-2, A-B5-12) where, C E Q F c y ¢ = 2 2 p , and (ASD E2, A-B5.2c, SAM 4) ( )Kl/r E Fe e = p2 . (ASD C-E2-2, SAM 4-4) ASD Commentary (ASD C-E3) refers to the 1986 version of the AISC-LRFD code for the calculation of Fe. The 1993 version of the AISC-LRFD code is the same as the 1986 version in this respect. Fe is calculated in the program as follows: • For Rectangular, I, Box, and Pipe sections: 36 Calculation of Allowable Stresses CSI Steel Design Manual
- 47. ( ) F EC K l GJ I I e w z z = + é ë ê ê ù û ú ú + p2 2 22 33 1 (LRFD A-E3-5) • For T-sections and Double-angles: F = F F H F F H F F e e ez e ez e ez 22 22 22 2 2 1 1 4+æ è çç ö ø ÷÷ - - + é ( )ë ê ê ù û ú ú (LRFD A-E3-6) • For Channels: F = F F H F F H F F e e ez e ez e ez 33 33 33 2 2 1 1 4+æ è çç ö ø ÷÷ - - + é ( )ë ê ê ù û ú ú (LRFD A-E3-6) • For Single-angle sections with equal legs: F = F F H F F H F F e e ez e ez e ez 33 33 33 2 2 1 1 4+æ è çç ö ø ÷÷ - - + é ( )ë ê ê ù û ú ú (ASD SAM C-C4-1) • For Single-angle sections with unequal legs, Fe is calculated as the minimum real root of the following cubic equation (ASD SAM C-C4-2, LRFD A-E3-7): ( )( )( ) ( ) (F F F F F F F F F x r Fe e e e e ez e e e e- - - - - -33 22 2 22 0 2 0 2 2 F F y r e e- =33 0 2 0 2 0) , where, x y0 0, are the coordinates of the shear center with respect to the centroid, x0 0= for double-angle and T-shaped members (y-axis of symme- try), r x y I I Ag 0 0 2 0 2 22 33 = + + + = polar radius of gyration about the shear center, H x y r = - +æ è ç ç ö ø ÷ ÷1 0 2 0 2 0 2 , (LRFD A-E3-9) ( ) F E K l r e33 2 33 33 33 2 = p , (LRFD A-E3-10) Calculation of Allowable Stresses 37 Chapter III Check/Design for AISC-ASD01
- 48. ( ) F E K l r e22 2 22 22 22 2 = p , (LRFD A-E3-11) ( ) F EC K l GJ Ar ez w z z = + é ë ê ê ù û ú ú p2 2 0 2 1 , (LRFD A-E3-12) K K22 33, are effective length factors in minor and major directions, Kz is the effective length factor for torsional buckling, and it is taken equal to K 22 in the program, l l22 33, are effective lengths in the minor and major directions, lz is the effective length for torsional buckling, and it is taken equal to l22 . For angle sections, the principal moment of inertia and radii of gyration are used for computing Fe (ASD SAM 4). Also, the maximum value of Kl, i.e, max( , )K l K l22 22 33 33 , is used in place of K l22 22 or K l33 33 in calculating Fe22 and Fe33 in this case. Allowable Stress in Bending The allowable bending stress depends on the following criteria: the geometric shape of the cross-section, the axis of bending, the compactness of the section, and a length parameter. I-sections For I-sections the length parameter is taken as the laterally unbraced length, l22 , which is compared to a critical length, lc . The critical length is defined as l b F A d F c f y f y = ì í ï îï ü ý ï þï min , ,76 20 000 , where (ASD F1-2) Af is the area of compression flange, 38 Calculation of Allowable Stresses CSI Steel Design Manual
- 49. Major Axis of Bending If l22 is less than lc , the major allowable bending stress for Compact and Noncompact sections is taken depending on whether the section is welded or rolled and whether fy is greater than 65 ksi or not. For Compact sections: F = Fb y33 0.66 if fy £ 65 ksi , (ASD F1-1) F = Fb y33 0.60 if fy >65 ksi , (ASD F1-5) For Noncompact sections: F = b t F Fb f f y y33 2 0.79 0.002- æ è ç ç ö ø ÷ ÷ , if rolled and fy £ 65 ksi, (ASD F1-3) F = b t F k Fb f f y c y33 2 0.79 0.002- æ è ç ç ö ø ÷ ÷ , if welded and fy £ 65 ksi, (ASDF1-4) F = Fb y33 0.60 if fy >65 ksi.. (ASD F1-5) If the unbraced length l22 is greater than lc , then for both Compact and Non- compact I-sections the allowable bending stress depends on the l rT22 ratio. For l r C FT b y 22 102 000 £ , , F Fb y33 =0.60 , (ASD F1-6) for 102 000 510 00022, ,C F l r C F b y T b y < £ , F F l r C F Fb y T b y y33 22 2 2 3 1530 000 = - é ë ê ê ù û ú ú £ ( / ) , 0.60 , and (ASD F1-6) for l r C FT b y 22 510 000 > , , Calculation of Allowable Stresses 39 Chapter III Check/Design for AISC-ASD01
- 50. F C l r Fb b T y33 22 2 170 000 0= é ë ê ù û ú £ , ( / ) 0.6 , (ASD F1-7) and Fb33 is taken not to be less than that given by the following formula: ( ) F C l d A Fb b f y33 22 12 000 = 0.6 , / £ (ASD F1-8) where, rT is the radius of gyration of a section comprising the compression flange and 1 3 the compression web taken about an axis in the plane of the web, C = + M M + M M b a b a b 1.75 1.05 0.3 æ è çç ö ø ÷÷ æ è çç ö ø ÷÷ £ 2 2.3, where (ASD F1.3) M Ma band are the end moments of any unbraced segment of the member and Ma is numerically less than Mb ; M Ma b being positive for double curvature bending and negative for single curvature bending. Also, if any moment within the segment is greater than Mb , Cb is taken as 1.0. Also, Cb is taken as 1.0 for cantilevers and frames braced against joint translation (ASD F1.3). The program defaults Cb to 1.0 if the unbraced length, l22 , of the member is rede- fined by the user (i.e. it is not equal to the length of the member). The user can overwrite the value of Cb for any member by specifying it. The allowable bending stress for Slender sections bent about their major axis is determined in the same way as for a Noncompact section. Then the following additional considerations are taken into account. If the web is slender, then the previously computed allowable bending stress is reduced as follows: F R R Fb PG e b33 33 ¢ = , where (ASD G2-1) R A A h t F PG w f b = - - é ë ê ê ù û ú ú £1.0 0.0005 1.0 760 33 , (ASD G2) ( ) R A A A A e w f w f = + - + £ 12 12 2 1.0 3 3 a a , (hybrid girders) (ASD G2) 40 Calculation of Allowable Stresses CSI Steel Design Manual
- 51. Re =1.0 , (non-hybrid girders) (ASD G2) Aw = Area of web, in2 , Af = Area of compression flange, in2 , a = £ 0.6 1.0 F F y b33 (ASD G2) Fb33 = Allowable bending stress assuming the section is non-compact, and Fb33 ¢ = Allowable bending stress after considering web slenderness. In the above expressions, Re is taken as 1, because currently the program deals with only non-hybrid girders. If the flange is slender, then the previously computed allowable bending stress is taken to be limited as follows. ( )F Q Fb s y33 ¢ £ 0.6 , where (ASD A-B5.2a, A-B5.2d) Qs is defined earlier. Minor Axis of Bending The minor direction allowable bending stress Fb22 is taken as follows: For Compact sections: F = Fb y22 0.75 if fy £ 65 ksi , (ASD F2-1) F = Fb y22 0.60 if fy >65 ksi , (ASD F2-2) For Noncompact and Slender sections: F = b t F Fb f f y y22 2 1.075 0.005- æ è ç ç ö ø ÷ ÷ , if fy £ 65 ksi, (ASD F2-3) F = Fb y22 0.60 if fy >65 ksi.. (ASD F2-2) Calculation of Allowable Stresses 41 Chapter III Check/Design for AISC-ASD01
- 52. 42 Calculation of Allowable Stresses
- 53. If the web is slender, then the previously computed allowable bending stress is reduced as follows: F R R Fb e PG b33 33 ¢ = (ASD G2-1) If the flange is slender, the previously computed allowable bending stress is taken to be limited as follows: ( )F Q Fb s y33 ¢ £ 0.6 (ASD A-B5.2a, A-B5.2d) The definition for rT ,Cb , Af , Aw , Re, RPG ,Qs , Fb33 , and Fb33 ¢ are given earlier. Minor Axis of Bending The minor direction allowable bending stress Fb22 is taken as follows: F = Fb y22 0.60 (ASD F2-2) T-sections and Double angles For T sections and Double angles, the allowable bending stress for both major and minor axes bending is taken as, F = Fb y0.60 . Box Sections and Rectangular Tubes For all Box sections and Rectangular tubes, the length parameter is taken as the laterally unbraced length, l22 , measured compared to a critical length, lc . The critical length is defined as l M /M b F , b F c a b y y = + ì í î ü ý þ max ( )1950 1200 1200 (ASD F3-2) where Ma and Mb have the same definition as noted earlier in the formula for Cb . If l22 is specified by the user, lc is taken as 1200 b Fy in the program. Major Axis of Bending If l22 is less than lc , the allowable bending stress in the major direction of bending is taken as: Calculation of Allowable Stresses 43 Chapter III Check/Design for AISC-ASD01
- 54. F = Fb y33 0.66 (for Compact sections) (ASD F3-1) F = Fb y33 0.60 (for Noncompact sections) (ASD F3-3) If l22 exceeds lc , the allowable bending stress in the major direction of bend- ing for both Compact and Noncompact sections is taken as: F = Fb y33 0.60 (ASD F3-3) The major direction allowable bending stress for Slender sections is deter- mined in the same way as for a Noncompact section. Then the following addi- tional consideration is taken into account. If the web is slender, then the previ- ously computed allowable bending stress is reduced as follows: F R R Fb e PG b33 33 ¢ = (ASD G2-1) The definition for Re, RPG , Fb33 , and Fb33 ¢ are given earlier. If the flange is slender, no additional consideration is needed in computing al- lowable bending stress. However, effective section dimensions are calculated and the section modulus is modified according to its slenderness. Minor Axis of Bending If l22 is less than lc , the allowable bending stress in the minor direction of bend- ing is taken as: F = Fb y22 0.66 (for Compact sections) (ASD F3-1) F = Fb y22 0.60 (for Noncompact and Slender sections) (ASD F3-3) If l22 exceeds lc , the allowable bending stress in the minor direction of bend- ing is taken, irrespective of compactness, as: F = Fb y22 0.60 (ASD F3-3) Pipe Sections For Pipe sections, the allowable bending stress for both major and minor axes of bending is taken as F = Fb y0.66 (for Compact sections), and (ASD F3-1) F = Fb y0.60 (for Noncompact and Slender sections). (ASD F3-3) 44 Calculation of Allowable Stresses CSI Steel Design Manual
- 55. Round Bars The allowable stress for both the major and minor axis of bending of round bars is taken as, F = Fb y0.75 . (ASD F2-1) Rectangular and Square Bars The allowable stress for both the major and minor axis of bending of solid square bars is taken as, F = Fb y0.75 . (ASD F2-1) For solid rectangular bars bent about their major axes, the allowable stress is given by F = Fb y0.60 , And the allowable stress for minor axis bending of rectangular bars is taken as, F = Fb y0.75 . (ASD F2-1) Single-Angle Sections The allowable flexural stresses for Single-angles are calculated based on their prin- cipal axes of bending (ASD SAM 5.3). Major Axis of Bending The allowable stress for major axis bending is the minimum considering the limit state of lateral-torsional buckling and local buckling (ASD SAM 5.1). The allowable major bending stress for Single-angles for the limit state of lateral- torsional buckling is given as follows (ASD SAM 5.1.3): F = F F Fb major ob y ob, 0.55 0.10- é ë ê ù û ú , if F Fob y£ (ASD SAM 5-3a) F = F F F Fb major y ob y y, 0.95 0.50 0.66- é ë ê ê ù û ú ú £ , if F Fob y> (ASD SAM 5-3b) where, Fob is the elastic lateral-torsional buckling stress as calculated below. Calculation of Allowable Stresses 45 Chapter III Check/Design for AISC-ASD01
- 56. The elastic lateral-torsional buckling stress, Fob , for equal-leg angles is taken as F C l t ob b= 28,250 , (ASD SAM 5-5) and for unequal-leg angles Fob is calculated as F C I S l lt rob b major w w= + +é ë ù û 143,100 0.052min min2 2 2 b b( ) , (ASD SAM 5-6) where, ( )t t tw f= min , , ( )l l l= max ,22 33 , Imin = minor principal moment of inertia, Imax = major principal moment of inertia, Smajor = major section modulus for compression at the tip of one leg, rmin = radius of gyration for minor principal axis, bw AI z w z dA z= + é ë ê ù û ú -ò 1 22 2 0 max ( ) , (ASD SAM 5.3.2) z = coordinate along the major principal axis, w = coordinate along the minor principal axis, and z0 = coordinate of the shear center along the major principal axis with respect to the centroid. bw is a special section property for angles. It is positive for short leg in compres- sion, negative for long leg in compression, and zero for equal-leg angles (ASD SAM 5.3.2). However, for conservative design in the program, it is always taken as negative for unequal-leg angles. In the above expressions Cb is calculated in the same way as is done for I sections with the exception that the upper limit of Cb is taken here as 1.5 instead of 2.3. C = + M M + M M b a b a b 1.75 1.05 0.3 æ è çç ö ø ÷÷ æ è çç ö ø ÷÷ £ 2 1.5 (ASD F1.3, SAM 5.2.2) 46 Calculation of Allowable Stresses CSI Steel Design Manual
- 57. The allowable major bending stress for Single-angles for the limit state of local buckling is given as follows (ASD SAM 5.1.1): F = Fb major y, 0.66 , if b t Fy £ 65 , (ASD SAM 5-1a) F = Fb major y, 0.60 , if 65 76 F b t Fy y < £ , (ASD SAM 5-1b) ( )F = Q Fb major y, 0.60 , if b t Fy > 76 , (ASD SAM 5-1c) where, t = thickness of the leg under consideration, b = length of the leg under consideration, and Q = slenderness reduction factor for local buckling. (ASD A-B5-2, SAM 4) In calculating the allowable bending stress for Single-angles for the limit state of local buckling, the allowable stresses are calculated considering the fact that either of the two tips can be under compression. The minimum allowable stress is consid- ered. Minor Axis of Bending The allowable minor bending stress for Single-angles is given as follows (ASD SAM 5.1.1, 5.3.1b, 5.3.2b): F = Fyb,minor 0.66 , if b t Fy £ 65 , (ASD SAM 5-1a) F = Fyb,minor 0.60 , if 65 76 F b t Fy y < £ , (ASD SAM 5-1b) ( )F = Q Fyb,minor 0.60 , if b t Fy > 76 , (ASD SAM 5-1c) In calculating the allowable bending stress for Single-angles it is assumed that the sign of the moment is such that both the tips are under compression. The minimum allowable stress is considered. Calculation of Allowable Stresses 47 Chapter III Check/Design for AISC-ASD01
- 58. General Sections For General sections the allowable bending stress for both major and minor axes bending is taken as, F = Fb y0.60 . Allowable Stress in Shear The shear stress is calculated along the geometric axes for all sections. For I, Box, Channel, T, Double angle, Pipe, Circular and Rectangular sections, the principal axes coincide with their geometric axes. For Single-angle sections, principal axes do not coincide with the geometric axes. Major Axis of Bending The allowable shear stress for all sections except I, Box and Channel sections is taken in the program as: F Fv y= 0.40 (ASD F4-1, SAM 3-1) The allowable shear stress for major direction shears in I-shapes, boxes and chan- nels is evaluated as follows: F Fv y= 0.40 , if h t Fw y £ 380 , and (ASD F4-1) F C F Fv v y y= £ 2.89 0.40 , if 380 260 F h ty w < £ . (ASD F4-2) where, ( )C k F h t if h t k F h t k F if h t v v y w w v y w v y = ³ 45 000 2 , , , , 56,250 190 w v y k F < ì í ï ï î ï ï 56,250 , (ASD F4) 48 Calculation of Allowable Stresses CSI Steel Design Manual
- 59. ( ) ( ) k a h if a h a h if a h v = + £ + > ì í ï ï î ï ï 4.00 5.34 5.34 4.00 2 2 1 1 , , , , (ASD F4) tw = Thickness of the web, a = Clear distance between transverse stiffeners, in. Currently it is taken conservatively as the length, l22 , of the member in the pro- gram, h = Clear distance between flanges at the section, in. Minor Axis of Bending The allowable shear stress for minor direction shears is taken as: F Fv y= 0.40 (ASD F4-1, SAM 3-1) Calculation of Stress Ratios In the calculation of the axial and bending stress capacity ratios, first, for each sta- tion along the length of the member, the actual stresses are calculated for each load combination. Then the corresponding allowable stresses are calculated. Then, the capacity ratios are calculated at each station for each member under the influence of each of the design load combinations. The controlling capacity ratio is then ob- tained, along with the associated station and load combination. A capacity ratio greater than 1.0 indicates an overstress. During the design, the effect of the presence of bolts or welds is not considered. Also, the joints are not designed. Axial and Bending Stresses With the computed allowable axial and bending stress values and the factored axial and bending member stresses at each station, an interaction stress ratio is produced for each of the load combinations as follows (ASD H1, H2, SAM 6): • If fa is compressive and f Fa a > 0.15, the combined stress ratio is given by the larger of Calculation of Stress Ratios 49 Chapter III Check/Design for AISC-ASD01
- 60. f F + C f f F' F + C fa a m b a e b m b33 33 33 33 22 22 1 1- æ è çç ö ø ÷÷ f F' Fa e b- æ è çç ö ø ÷÷ 22 22 , and (ASD H1-1, SAM 6.1) ( ) f F f F f F a y b b b bQ 0.60 + +33 33 22 22 , where (ASD H1-2, SAM 6.1) fa , fb33 , fb22 , Fa , Fb33 , and Fb22 are defined earlier in this chapter, Cm33 and Cm22 are coefficients representing distribution of moment along the member length. Cm = 1.00 , if length is overwritten, 1.00 , if tension member, 0.85 , if sway frame, 0.6 0.4 if- M a M b , nonsway, no transverse loading, 0.85 , if nonsway, trans. load, end restrained, 1.00 , if nonsway, trans. load, end unrestrained. ì í ï ï ï ï î ï ï ï ï (ASD H1) For sway frame Cm =0.85 , for nonsway frame without transverse load C M Mm a b= -0.6 0.4 , for nonsway frame with transverse load and end re- strained compression member Cm =0.85 , and for nonsway frame with trans- verse load and end unrestrained compression member Cm =1.00 (ASD H1), where M Ma b is the ratio of the smaller to the larger moment at the ends of the member, M Ma b being positive for double curvature bending and negative for single curvature bending. When Mb is zero, Cm is taken as 1.0. The program defaults Cm to 1.0 if the unbraced length factor, l, of the member is redefined by either the user or the program, i.e., if the unbraced length is not equal to the length of the member. The user can overwrite the value ofCm for any member. Cm assumes two values,Cm22 andCm33 , associated with the major and minor di- rections. Fe ¢ is given by F E Kl r e ¢ = 12 23 2 2 p ( / ) . (ASD H1) • If fa is compressive and f Fa a £ 0.15, a relatively simplified formula is used for the combined stress ratio. 50 Calculation of Stress Ratios CSI Steel Design Manual
- 61. f F + f F + f F a a b b b b 33 33 22 22 (ASD H1-3, SAM 6.1) • If fa is tensile or zero, the combined stress ratio is given by the larger of f F f F f F a a b b b b + +33 33 22 22 , and (ASD H2-1, SAM 6.2) f F f F b b b b 33 33 22 22 + , where fa , fb33 , fb22 , Fa , Fb33 , and Fb22 are defined earlier in this chapter. However, ei- ther Fb33 or Fb22 need not be less than 0.6Fy in the first equation (ASD H2-1). The second equation considers flexural buckling without any beneficial effect from axial compression. For circular and pipe sections, an SRSS combination is first made of the two bend- ing components before adding the axial load component, instead of the simple ad- dition implied by the above formulae. For Single-angle sections, the combined stress ratio is calculated based on the prop- erties about the principal axis (ASD SAM 5.3, 6.1.5). For I, Box, Channel, T, Dou- ble-angle, Pipe, Circular and Rectangular sections, the principal axes coincide with their geometric axes. For Single-angle sections, principal axes are determined in the program. For general sections no effort is made to determine the principal direc- tions. Shear Stresses From the allowable shear stress values and the factored shear stress values at each station, shear stress ratios for major and minor directions are computed for each of the load combinations as follows: f F v v 2 , and f F v v 3 . For Single-angle sections, the shear stress ratio is calculated for directions along the geometric axis. For all other sections the shear stress is calculated along the principle axes which coincide with the geometric axes. Calculation of Stress Ratios 51 Chapter III Check/Design for AISC-ASD01
- 62. Joint Design When using AISC-ASD01 design code, the structural joints are checked and/or de- signed for the following: • Check for the requirement of continuity plate and determination of its area • Check for the requirement of doubler plate and determination of its thickness • Check for the ratio of beam flexural strength to column flexural strength • Reporting the beam connection shear • Reporting the brace connection force Design of Continuity Plates In a plan view of a beam/column connection, a steel beam can frame into a column in the following ways: • The steel beam frames in a direction parallel to the column major direction, i.e. the beam frames into the column flange. • The steel beam frames in a direction parallel to the column minor direction, i.e. the beam frames into the column web. • The steel beam frames in a direction that is at an angle to both of the principal axes of the column, i.e. the beam frames partially into the column web and par- tially into the column flange. To achieve a proper beam/column moment connection strength, continuity plates such as shown in are usually placed on the column, in line with the top and bottom flanges of the beam, to transfer the compression and tension flange forces of the beam into the column. For connection conditions described in the last two steps above, the thickness of such plates is usually set equal to the flange thickness of the corresponding beam. However, for the connection condition described by the first step above, where the beam frames into the flange of the column, such continuity plates are not always needed. The requirement depends upon the magnitude of the beam-flange force and the properties of the column. This is the condition that the program investi- gates. Columns of I-sections only are investigated. The program evaluates the con- tinuity plate requirements for each of the beams that frame into the column flange (i.e. parallel to the column major direction) and reports the maximum continuity plate area that is needed for each beam flange. The continuity plate requirements 52 Joint Design SAP2000 Steel Design Manual
- 63. are evaluated for moment frames (OMF, IMF, SMF) only. No check is made for braced frames (OCBC, SCBF, EBF). The program first evaluates the need for continuity plates. Continuity plates will be required if any of the following four conditions are not satisfied: • The column flange design strength in bending must be larger than the beam flange force, i.e., jR = t F Pn fc yc bf(0.9)6.25 2 ³ if not at top story (LRFD K1-1) jR t F Pn fc yc bc= ³( . )( . ) .0 5 0 9 6 25 2 if at top story (LRFD K1-2) • The design strength of the column web against local yielding at the toe of the fillet must be larger than the beam flange force, i.e., jR k +t F t Pn c fb yc wc bf= (1.0) (5.0 ) ³ , if not at top story (LRFD K1-2) jR k t F t Pn c fb yc wc bf= + ³( . )( . )10 2 5 , if at top story (LRFD K1-3) • The design strength of the column web against crippling must be larger than the beam flange force, i.e., jR t + t d t t n wc fb c wc fc = (0.75) 0.80 2 1 3 æ è ç ç ö ø ÷ ÷ æ è ç ç ö ø ÷ ÷ é ë ê ê ù û ú ú ³ 1.5 EF t t Pyc fc wc bf , if not at top story (LRFD K1-4) jR t + t d t t n wc fb c wc fc = æ è ç ç ö ø ÷ ÷ æ è ç ç ö ø ( . )( . )075 0 40 1 32 ÷ ÷ é ë ê ê ù û ú ú ³ 1.5 EF t t Pyc fc wc bf , it at top story (LRFD K1-5a) • The design compressive strength of the column web against buckling must be larger than the beam flange force, i.e., jR t EF d Pn wc yc c bf= (0.9) 24 3 ³ , if not at top story (LRFD K1-8) jR t EF d Pn wc yc c bf= (0.9) 12 3 ³ , if at top story (LRFD K1.9, E2) Joint Design 53 Chapter III Check/Design for AISC-ASD01

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