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1525 Wilson Boulevard, Suite 600, Arlington, VA 22209

Aluminum Design Manual 2005

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  1. 1. 1525 Wilson Boulevard, Suite 600, Arlington, VA 22209
  2. 2. Copyright June 2005, The Aluminum Association, Inc. All rights reserved No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form, or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of The Aluminum Association, Inc.
  3. 3. TABLE OF CONTENTS
  4. 4. Aluminum Design Manual Table of Contents PART TITLE IA Specication for Aluminum Structures Allowable Stress Design IB Specication for Aluminum Structures Building Load and Resistance Factor Design IIA Commentary on Specication for Aluminum Structures Allowable Stress Design IIB Commentary on Specication for Aluminum Structures Building Load and Resistance Factor Design III Design Guide IV Materials V Material Properties VI Section Properties VII Design Aids VIII Illustrative Examples of Design IX Guidelines for Aluminum Sheet Metal Work in Building Construction Appendix 1 Metric Guide for Aluminum Structural Design Index
  5. 5. FOREWORD
  6. 6. FOREWORD The Aluminum Design Manual includes aluminum structural design specications and accompanying commentary, a supplemental design guide, material properties, section properties, design aid tables and graphs, illustrative design examples and guidelines for aluminum sheet metal work in building construction. This edition of the Aluminum Design Manual is the product of the efforts of the Aluminum Association Engineering and Design Task Force, whose members are listed below. The Aluminum Association Engineering and Design Task Force Steve Sunday, Alcoa Inc., chair Frank Armao, Lincoln Electric Co. Randy Killian, Conservatek Industries, Inc. Randy Kissell, The TGB Partnership Greg McKenna, Kawneer Company, Inc. Craig C. Menzemer, University of Akron George Olive, Larson Engineering of Missouri Gerald Orrison, Temcor Teoman Pekz, Cornell University Frank Shoup, Alcoa Inc. Mike Skillingberg, The Aluminum Association, Inc.
  7. 7. Check www.aluminum.org for ADM 2005 updates.
  8. 8. Aluminum Design Manual PART I-A Specication for Aluminum Structures Allowable Stress Design The Aluminum Association, Inc. 1525 Wilson Boulevard, Suite 600, Arlington, VA 22209 Eighth Edition, January 2005
  9. 9. January 2005 I-A-3 FOREWORD The rst edition of the Specication for Aluminum Structures was published in November, 1967, followed by subsequent edi- tions in 1971, 1976, 1982, 1986, 1994, and 2000. This eighth edition of the allowable stress design Specication, developed as a consensus document, includes new or revised provisions concerning shear yield strengths welded strengths adding 6063-T52, 6351-T6, and 7005-T53 materials for screws used to connect aluminum parts factors on welded tensile ultimate strength and compressive yield strength welded connections (groove, llet, plug and slot, and stud welds) screw pull-over revision of Section 1.2, Materials revision of Section 5, Mechanical Connections revision of Section 6, Fabrication and Erection a new Section 8, Castings weighted average strengths design stresses for wind loads fatigue strength for welds with permanent backing net effective areas for channels, I beams, zees, angles, and tees single angles in exure tapered thickness element strength web crippling of extrusions compressive strength of complex cross sections strength of elements in bending in their own plane unbraced length in bending These improvements and additions are the result of studies sponsored by the Aluminum Association and others. The Aluminum Association gratefully acknowledges the efforts of the Engineering and Design Task Force in drafting this Specication and the Engineering Advisory Committee in reviewing it. The Aluminum Association Engineering and Design Task Force Steve Sunday, Alcoa Inc., chair Frank Armao, Lincoln Electric Co. Randy Killian, Conservatek Industries, Inc. Randy Kissell, The TGB Partnership Greg McKenna, Kawneer Company, Inc. Craig C. Menzemer, University of Akron George Olive, Larson Engineering of Missouri Gerald Orrison, Temcor Teoman Pekz, Cornell University Frank Shoup, Alcoa Inc. Mike Skillingberg, The Aluminum Association, Inc. The Aluminum Association Engineering Advisory Committee Includes the members of the Engineering and Design Task force and the following persons: Robert E. Abendroth, Iowa State University Francisco Castano, Geometrica, Inc. Terence Cavanagh, Terrapin Testing, Inc. Karen C. Chou, Minnesota State University, Mankato Cynthia Ebert, Larson Engineering of Missouri
  10. 10. I-A-4 November 2005 Andrew J. Hinkle, S & K Technologies Dimitris Kosteas, Technical University of Munich LeRoy Lutz, Computerized Structural Design Brian Malloy, Alcoa Engineered Products Ray Minor, Hapco American Flag Carl Wagus, American Architectural Manufacturers Association Robert W. Walton, Texas Wall Systems Guidelines for the Preparation of Technical Inquiries on the Specication for Aluminum Structures Technical inquiries to obtain an interpretation or request a revision to the Specication for Aluminum Structures should be directed to: VP, Technology The Aluminum Association 1525 Wilson Blvd. Suite 600 Arlington, VA 22209 Fax: 703-358-2961 email: [email protected] Comments on other parts of the Aluminum Design Manual are also welcome. Inquiries should be typewritten and include the inquirers name, afliation, and address. Each inquiry should address a single section of the Specication unless the inquiry involves two or more interrelated sections. The section and edition of the Speci- cation should be identied. Requests for interpretations should be phrased, where possible, to permit a yes or no answer and include the necessary background information, including sketches where appropriate. Requests for revisions should include proposed wording for the revision and technical justication. Inquiries are considered at the rst meeting of the Engineering and Design Task Force following receipt of the inquiry.
  11. 11. January 2005 I-A-5 IA Specication for Aluminum StructuresAllowable Stress Design TABLE OF CONTENTS Section 1. General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9 1.1 Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9 1.2 Materials. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9 1.3 Safety Factors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9 1.3.1 Building Type Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9 1.3.2 Bridge Type Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9 1.3.3 Other Type Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9 Section 2. Design Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10 2.1 Section Properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10 2.2 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10 2.3 Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10 Section 3. General Design Rules. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.1 Material Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11 3.2 Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11 3.3 Tables Relating to Mechanical Properties and Buckling Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .14 3.4 Allowable Stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23 3.4.1 Tension, Axial. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .26 3.4.2 Tension in Extreme Fibers of BeamsFlat Elements In Uniform Tension . . . . . . . . . . . . . . . . . . . . . . . .26 3.4.3 Tension in Extreme Fibers of BeamsRound or Oval Tubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .26 3.4.4 Tension in Extreme Fibers of BeamsFlat Elements In Bending in Their Own Plane . . . . . . . . . . . . . . . 26 3.4.5 Bearing on Rivets and Bolts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .26 3.4.6 Bearing on Flat Surfaces and Pins and on Bolts in Slotted Holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.4.7 Compression in Columns, Axial, Gross Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .26 3.4.7.1 Sections Not Subject to Torsional or Torsional-Flexural Buckling. . . . . . . . . . . . . . . . . . . . . . . . 26 3.4.7.2 Doubly or Singly Symmetric Sections Subject to Torsional or Torsional-Flexural Buckling. . . . 26 3.4.7.3 Nonsymmetric Sections Subject to Torsional or Torsional-Flexural Buckling . . . . . . . . . . . . . . . 27 3.4.8 Uniform Compression in Elements of Columns Whose Buckling Axis is an Axis of Symmetry Flat Elements Supported On One Edge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .27 3.4.8.1 Uniform Compression in Elements of Columns Whose Buckling Axis is not an Axis of SymmetryFlat Elements Supported On One Edge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .27 3.4.9 Uniform Compression in Elements of ColumnsFlat Elements Supported on Both Edges . . . . . . . . . . . 28 3.4.9.1 Uniform Compression in Elements of ColumnsFlat Elements Supported on One Edge and With Stiffener on Other Edge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .28 3.4.9.2 Uniform Compression in Elements of ColumnsFlat Elements Supported on Both Edges and With an Intermediate Stiffener . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .30 3.4.10 Uniform Compression in Elements of ColumnsCurved Elements Supported on Both Edges. . . . . . . . . 32 3.4.11 Compression in Beams, Extreme Fiber, Gross SectionSingle Web Shapes . . . . . . . . . . . . . . . . . . . . . .32 3.4.12 Compression in Beams, Extreme Fiber, Gross SectionRound or Oval Tubes . . . . . . . . . . . . . . . . . . . . .32 3.4.13 Compression in Beams, Extreme Fiber, Gross SectionSolid Rectangular and Round Sections . . . . . . . 32 3.4.14 Compression in Beams, Extreme Fiber, Gross SectionTubular Shapes. . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.4.15 Uniform Compression in Elements of BeamsFlat Elements Supported on One Edge. . . . . . . . . . . . . . . 33 3.4.16 Uniform Compression in Elements of BeamsFlat Elements Supported on Both Edges . . . . . . . . . . . . .34 3.4.16.1 Uniform Compression in Elements of BeamsCurved Elements Supported on Both Edges . . 34 3.4.16.2 Uniform Compression in Elements of BeamsFlat Elements Supported on One Edge and With Stiffener on Other Edge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .34 3.4.16.3 Uniform Compression in Elements of BeamsFlat Elements Supported on Both Edges and With an Intermediate Stiffener . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .34 3.4.17 Compression in Elements of Beams (Element in Bending in Own Plane)Flat Elements Supported on Tension Edge, Compression Edge Free . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .35
  12. 12. I-A-6 January 2005 3.4.18 Compression in Elements of Beams (Element in Bending in Own Plane) Flat Elements Supported on Both Edges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .35 3.4.19 Compression in Elements of Beams (Element in Bending in Own Plane) Flat Elements Supported on Both Edges and With a Longitudinal Stiffener . . . . . . . . . . . . . . . . . . . . . . . 35 3.4.20 Shear in ElementsUnstiffened Flat Elements Supported on Both Edges. . . . . . . . . . . . . . . . . . . . . . . . 36 3.4.21 Shear in ElementsStiffened Flat Elements Supported on Both Edges . . . . . . . . . . . . . . . . . . . . . . . . . . 36 Section 4. Special Design Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .37 4.1 Combined Axial Load and Bending. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .37 4.1.1 Combined Compression and Bending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .37 4.1.2 Combined Tension and Bending. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .37 4.2 Torsion and Shear in Tubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .37 4.3 Torsion and Bending in Open Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .37 4.4 Combined Shear, Compression, and Bending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .37 4.5 Longitudinal Stiffeners for Webs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .38 4.6 Transverse Stiffeners for Webs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .38 4.6.1 Stiffeners for Web Shear. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .38 4.6.2 Bearing Stiffeners. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .38 4.7 Effects of Local Buckling on Member Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .39 4.7.1 Local Buckling Stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .39 4.7.2 Weighted Average Axial Compressive Stress. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 4.7.3 Weighted Average Bending Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .39 4.7.4 Effect of Local Buckling on Column Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .40 4.7.5 Effect of Local Buckling on Beam Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .40 4.7.6 Effective Width for Calculation of Bending Deection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .40 4.7.7 Web Crippling of Flat Webs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .41 4.7.8 Combined Web Crippling and Bending for Flat Webs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 4.8 Fatigue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .41 4.8.1 Constant Amplitude Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .41 4.8.2 Variable Amplitude Loading. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .41 4.9 Compression in Single Web Beams Including Single Web Beams With Tubular Portions . . . . . . . . . . . . . . . . . . .47 4.9.1 Doubly Symmetric Sections and Sections Symmetric About the Bending Axis . . . . . . . . . . . . . . . . . . . . .47 4.9.2 Singly Symmetric Sections Unsymmetric about the Bending Axis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 4.9.3 Singly Symmetric Sections Symmetric or Unsymmetric about the Bending Axis, Doubly Symmetric Sections and Sections Without an Axis of Symmetry. . . . . . . . . . . . . . . . . . . . . . . . . . 47 4.9.4 Lateral Buckling Coefcients. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .48 4.9.4.1 Doubly Symmetric Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .48 4.9.4.2 Singly Symmetric Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .48 4.9.4.3 Special CasesDoubly or Singly Symmetric Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .48 4.9.4.4 Cantilever Beams. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .49 4.10 Compression in Elastically Supported Flanges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .49 4.11 Single Angles in Flexure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .49 4.11.1 Bending About Geometric Axes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .50 4.11.2 Bending About Principal Axes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .50 4.12 Tapered Thickness Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .51 4.13 Compressive Strength of Beam Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .51 4.13.1 Compressive Strength of Beam ElementsFlat Elements in Uniform Compression . . . . . . . . . . . . . . . . . 51 4.13.2 Compressive Strength of Beam ElementsFlat Elements in Bending In Their Own Plane. . . . . . . . . . . . 51 Section 5. Mechanical Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .52 5.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .52 5.1.1 Minimum Edge Distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .52 5.1.2 Maximum Spacing of Fasteners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .52 5.1.3 Block Shear Rupture. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .52 5.1.4 Net Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .52 5.1.5 Effective Net Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .52 5.1.6 Long Grips . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .52
  13. 13. January 2005 I-A-7 5.1.7 Strength and Arrangement of Connections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .53 5.1.8 Countersunk Holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .53 5.2 Bolted Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .53 5.2.1 Bolt Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .53 5.2.2 Holes and Slots for Bolts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .53 5.2.3 Bolt Tension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .53 5.2.4 Bolt Shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .53 5.2.5 Bolt Bearing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .53 5.2.6 Minimum Spacing of Bolts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .54 5.2.7 Lockbolts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .54 5.2.8 Slip-Critical Bolted Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .54 5.2.8.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .54 5.2.8.2 Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .54 5.2.8.3 Holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .54 5.2.8.4 Design for Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .54 5.2.8.5 Design for Slip Resistance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .54 5.2.8.6 Washers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .54 5.2.8.7 Installation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .55 5.3 Riveted Connections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .55 5.3.1 Rivet Material. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .55 5.3.2 Holes for Cold-Driven Rivets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .55 5.3.3 Rivet Tension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .55 5.3.4 Rivet Shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .55 5.3.5 Rivet Bearing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .56 5.3.6 Minimum Spacing of Rivets. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .56 5.3.7 Blind Rivets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .56 5.3.8 Hollow-End (Semi-tubular) Rivets. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .56 5.4 Tapping Screw Connections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .56 5.4.1 Screw Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .57 5.4.2 Screw Tension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .57 5.4.2.1 Pull-Out . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .57 5.4.2.2 Pull-Over . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .57 5.4.3 Screw Shear and Bearing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .57 5.4.4 Minimum Spacing of Screws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .58 5.5 Building Sheathing Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .58 5.5.1 Endlaps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .58 5.5.2 Sidelaps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .58 5.5.3 Fasteners in Laps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .58 5.5.4 Flashing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .58 Section 6. Fabrication and Erection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .59 6.1 Layout. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .59 6.1.1 Punch and Scribe Marks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .59 6.1.2 Temperature Correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .59 6.2 Cutting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .59 6.2.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .59 6.2.2 Edge Quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .59 6.2.3 Re-entrant Corners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .59 6.2.4 Oxygen Cutting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .59 6.3 Heating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .59 6.4 Holes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .60 6.4.1 Fabrication Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .60 6.4.2 Hole Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .60 6.5 Riveting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .60 6.5.1 Driven Head . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .60 6.5.1.1 Flat Heads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .60 6.5.1.2 Cone-Point Heads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
  14. 14. I-A-8 January 2005 6.5.2 Hole Filling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .60 6.5.3 Defective Rivets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .60 6.6 Finishes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .60 6.6.1 Where Painting Is Required . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .60 6.6.2 Surface Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .60 6.7 Contact with Dissimilar Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .60 6.7.1 Steel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .60 6.7.2 Wood, Fiberboard, or Other Porous Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 6.7.3 Concrete or Masonry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .60 6.7.4 Runoff From Heavy Metals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .61 6.8 Mechanical Finishes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .61 6.9 Fabrication Tolerances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .61 6.10 Bending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .61 6.11 Erection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .61 6.11.1 Erection Tolerances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .61 6.11.2 Bolt Installation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .61 Section 7. Welded Construction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .62 7.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .62 7.2 Welded Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .62 7.2.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .62 7.2.2 Members with Part of the Cross Section Weld-Affected . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .62 7.2.3 Columns or Beams with Transverse Welds Away from Supports and Cantilevers with Transverse Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .62 7.3 Welded Connections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .62 7.3.1 Groove Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .62 7.3.1.1 Complete Penetration and Partial Penetration Groove Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 7.3.1.2 Effective Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .64 7.3.1.3 Design Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .64 7.3.2 Fillet Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .64 7.3.2.1 Effective Throat and Effective Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .64 7.3.2.2 Design Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .65 7.3.3 Plug and Slot Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .65 7.3.3.1 Effective Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .65 7.3.3.2 Design Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .65 7.3.4 Stud Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .65 7.4 Post-Weld Heat Treating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .66 Section 8. Castings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .67 8.1 Materials. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .67 8.2 Mechanical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .67 8.3 Design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .68 8.4 Welding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .68 Section 9. Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .70 9.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .70 9.2 Test Loading and Behavior. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .70 9.3 Number of Tests and the Evaluation of Test Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .70 9.3.1 Tests for Determining Mechanical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .70 9.3.2 Tests for Determining Structural Performance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .70 9.4 Testing Roong and Siding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .71 9.4.1 Test Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .71 9.4.2 Different Thicknesses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .71 9.4.3 Allowable Loads from Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .71 9.4.4 Deections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .71
  15. 15. January 2005 I-A-9 Section 1. General 1.1 Scope This Specication shall apply to the design of aluminum alloy load-carrying members. 1.2 Materials This Specication applies to the aluminum alloys listed in Tables 3.3-1, 5.2.3-1, and 5.3.4-1 and produced to the following ASTM specications: B 209 Aluminum and Aluminum-Alloy Sheet and Plate B 210 Aluminum and Aluminum-Alloy Drawn Seam- less Tubes B 211 Aluminum and Aluminum-Alloy Bar, Rod, and Wire B 221 Aluminum and Aluminum-Alloy Extruded Bars, Rods, Wire, Proles, and Tubes B 241 Aluminum and Aluminum-Alloy Seamless Pipe and Seamless Extruded Tube B 247 Aluminum and Aluminum-Alloy Die Forgings, Hand Forgings, and Rolled Ring Forgings B 308 Aluminum-Alloy 6061-T6 Standard Structural Proles B 316 Aluminum and Aluminum-Alloy Rivet and Cold-Heading Wire and Rods B 429 Aluminum Alloy Extruded Structural Pipe and Tube B 632 Aluminum Alloy Rolled Tread Plate B 928 High Magnesium Aluminum-Alloy Sheet and Plate for Marine Service F 468 Nonferrous Bolts, Hex Cap Screws, and Studs for General Use This Specication also applies to castings that meet the requirements of Section 8.1. 1.3 Safety Factors 1.3.1 Building Type Structures Basic allowable tensile stresses for buildings, structural supports for highway signs, luminaires, trafc signals, and similar structures shall be the lesser of the minimum yield strength divided by a factor of safety of 1.65, or the mini- mum ultimate tensile strength divided by a factor of safety of 1.95. Other allowable stresses for buildings and similar structures shall be based upon the factors of safety shown in Table 3.4-1. 1.3.2 Bridge Type Structures Basic allowable tensile stresses for bridge type structures shall be the lesser of the minimum yield strength divided by a factor of safety of 1.85, or the minimum ultimate tensile strength divided by a factor of safety of 2.2. Other allow- able stresses for bridge and similar structures shall be based upon the factors of safety shown in Table 3.4-1. 1.3.3 Other Type Structures Where it is customary or standard practice to use factors of safety other than those given in Sections 1.3.1 or 1.3.2, the general formulas in Table 3.4-3 shall be permitted to be used with the desired factors of safety substituted for nu, ny, or na.
  16. 16. I-A-10 January 2005 Section 2. Design Procedure 2.1 Section Properties Section properties such as cross-sectional area, moment of inertia, section modulus, radius of gyration, and torsion and warping constants shall be determined using nominal dimensions. Cross section dimensions shall not vary by more than the tolerances given in Aluminum Standards and Data. 2.2 Procedure Computations of forces, moments, stresses, and deec- tions shall be in accordance with accepted methods of elas- tic structural analysis and engineering design. The formu- las and methods for determining allowable stresses in this Specication have been simplied in many cases for ease of computation but are not intended to preclude the use of more rigorous analysis. 2.3 Loads Building-type structures shall be designed for the nomi- nal loads given in the applicable building code or perfor- mance specication. Nominal loads shall be factored and combined in accordance with the applicable building code or performance specication. In the absence of a code or performance specication, ASCE 7-02, Minimum Design Loads for Buildings and Other Structures, shall be used. Bridge-type structures shall be designed for the loads given in AASHTOs Standard Specications for Highway Bridges. Other structures shall be designed for the loads given in the performance specication.
  17. 17. January 2005 I-A-11 Section 3. General Design Rules 3.1 Material Properties Minimum mechanical properties used for non-welded material shall be as listed in Table 3.3-1. Minimum mechanical properties used for welded material shall be as listed in Table 3.3-2. The following properties shall be used unless more pre- cise values are specied: Coefcient of thermal expansion 13 10-6 /o F (23 10-6 /o C) Density 0.1 lb/in3 (2.7 103 kg/m3 ) Poissons ratio 0.33 3.2 Nomenclature A consistent set of units shall be used throughout this Specication. a = detail dimension parallel to the direction of stress ae = equivalent width of rectangular panel al = shorter dimension of rectangular panel a2 = longer dimension of rectangular panel A = cross sectional area Ac = area of compression element (compression ange plus 1 /3 of area of web between compression ange and neutral axis) Ah = gross area of cross section of longitudinal stiffener As = area of the stiffener Asn = thread stripping area of internal thread per unit length of engagement Aw = the portion of area of cross section A lying within 1.0 in. (25 mm) of a weld b = width of section or element be = effective width of at element to be used in deection calculations bo = width of element with an intermediate stiffener as shown in Fig. 3.4.9.2-1 b/t = width to thickness ratio of a at element of a cross section B = buckling formula intercept with the following subscripts: c-compression in columns p-compression in at elements t-compression in curved elements tb-bending in curved elements br-bending in at elements s-shear in at elements c = distance from neutral axis to extreme ber C = buckling formula intersection (see B for subscripts) C = coefcient which depends on screw location Cb = coefcient which depends on moment gradient Cf = constant to be determined from Table 4.8.1-1 and Figure 4.8.1-1 Cm = 0.6 - 0.4(M1/M2) for members whose ends are prevented from sway = 0.85 for members whose ends are not prevented from swaying CP = correction factor Cw = torsional warping constant of the cross section Cwa = t2 sin (0.46Fcy + 0.02 ____ EFcy) Cwb = Cw3 + Ri (1cos) Cw1 = 5.4 in. (140 mm) Cw2 = 1.3 in. (33 mm) Cw3 = 0.4 in. or 10 mm consistent with other units used C1 = coefcient dened in Section 4.9.4 C2 = coefcient dened in Section 4.9.4 d = depth of section or beam df = distance between ange centroids ds = at width of lip stiffener shown in Fig. 3.4.9.1-1 d1 = clear distance from the neutral axis to the compression ange D = buckling formula slope (see B for subscripts) D = diameter Dh = nominal hole diameter Dn = nominal dead load Ds = dened in Fig. 3.4.9.1-1 Dw = nominal washer diameter Dws = larger of the nominal washer diameter and the screw head e = base for natural logarithms 2.72 E = compressive modulus of elasticity (See Table 3.3-1) f = calculated stress fa = average stress on cross section produced by axial load fb = maximum bending stress produced by transverse loads and/or bending moment fs = shear stress caused by torsion or transverse shear loads F = allowable stress Fa = allowable compressive stress for a member con- sidered as an axially loaded column according to Sections 3.4.7 through 3.4.10 Fao = allowable compressive stress of axially loaded member considered as a short column according to Section 4.7.2. Fb = allowable bending stress for members subjected to bending only Fc = allowable compressive stress Fcr = local buckling stress for element from Section 4.7.1 Fcy = compressive yield strength Fcyw = compressive yield strength across a groove weld (0.2% offset in 2 in. (50 mm) gage length) Fe = elastic buckling stress divided by nu = 2 E_______ nu(kL/r)2
  18. 18. I-A-12 January 2005 Feb = elastic lateral buckling stress of beam calculated using Eq. 3.4.11-3 or Section 4.9 with ny = 1.0 Fec = elastic critical stress Fec = allowable elastic lateral buckling stress of beam calculated assuming that the elements are not buckled Fef = elastic torsional-exural buckling stress Fet = elastic torsional buckling stress Fet = 1____ Ar 2 O (GJ + 2 ECw______ (KtLt)2 ) Fex = 2 E______ (kxLb____ rx )2 Fm = mean value of the fabrication factor Fn = allowable stress for cross section 1.0 in. (25 mm) or more from weld Fpw = allowable stress on cross section, part of whose area lies within 1.0 in. (25 mm) of a weld Frb = allowable stress for beam with buckled elements Frc = allowable stress for column with buckled elements Fs = allowable shear stress for members subjected only to torsion or shear FST = allowable stress according to Section 3.4.9.1 or 3.4.16.2 Fsu = shear ultimate strength Fsuw = shear ultimate strength within 1.0 in. (25 mm) of a weld Ft = allowable tensile stress for the member loaded only axially according to Section 3.4.1 Ftu = tensile ultimate strength Ftuw = tensile ultimate strength across a groove weld Ftul = tensile ultimate strength of member in contact with the screw head Ftu2 = tensile ultimate strength of member not in contact with the screw head Fty = tensile yield strength Ftyw = tensile yield strength across a groove weld (0.2% offset in 2 in. (50 mm) gage length) FUT = allowable stress according to Section 3.4.9.1 or 3.4.16.2 Fw = allowable stress on cross section if entire area were to lie within 1.0 in. (25 mm) of a weld Fy = either Fty or Fcy, whichever is smaller g = spacing of rivet or bolt holes perpendicular to direction of load go = distance from shear center to the point of application of load G = shear modulus Gf = grip of rivet or bolt h = clear height of shear web I = moment of inertia Ib = required moment of inertia of bearing stiffener Icy = moment of inertia of compression ange about web Ih = moment of inertia of longitudinal stiffener Io = moment of inertia of the stiffener about the cen- troidal axis of the stiffener parallel to the at element that is stiffened Is = moment of inertia of transverse stiffener to resist shear buckling Ix = moment of inertia of a beam about axis perpendicular to web Iy = moment of inertia of a beam about axis parallel to web Iyc = moment of inertia of compression element about axis parallel to vertical web j = parameter dened by Eq. 4.9.3-5 or -6 J = torsion constant k = the effective length factor. k shall be taken larger than or equal to unity unless rational analysis justies a smaller value kt = coefcient for tension members kx = effective length coefcient for buckling about the x-axis ky = effective length coefcient for buckling about the y-axis kl = coefcient for determining slenderness limit S2 for sections for which the allowable compressive stress is based on ultimate strength k2 = coefcient for determining allowable compres- sive stress in sections with slenderness ratio above S2 for which the allowable compressive stress is based on ultimate strength Ks = coefcient in Section 5.4.2.1 Kt = effective length coefcient for torsional buckling. Kt shall be taken larger than or equal to unity unless rational analysis justies a smaller value L = unsupported length in the plane of bending Lb = unbraced length for bending Ln = nominal live load Ls = length of tube between circumferential stiffeners Lt = unbraced length for twisting m = constant to be determined from Table 4.8.1-1 M = bending moment applied to the member Ma = allowable bending moment for the member if bending moment alone is applied to the member MA = absolute value of moment at quarter-point of the unbraced beam segment MB = absolute value of moment at mid-point of the unbraced beam segment MC = absolute value of moment at three-quarter point of the unbraced beam segment Me = elastic critical moment Mi = bending strength of member with intermediate thickness Mm = mean value of the material factor MMAX = absolute value of maximum moment in the unbraced beam segment M1 = bending strength of member of thinnest material M2 = bending strength of member of thickest material
  19. 19. January 2005 I-A-13 M1/M2 = ratio of end moments where M2 is the larger of the two end moments and M1/M2 is positive when the member is bent in reverse curvature, negative when bent in single curvature n = number of tests n = number of threads per unit length for a screw na = factor of safety on appearance of buckling ns = factor of safety for screw connections nu = factor of safety on ultimate strength ny = factor of safety on yield strength N = length of bearing at reaction or concentrated load N = number of cycles to failure Ns = number of stress ranges in the spectrum P = applied interior reaction or concentrated load per web for at webs Pas = allowable shear force per screw Pat = allowable tensile force per screw Pbs = concentrated load on bearing stiffener Pc = allowable reaction or concentrated load per web Pnot = nominal pull-out strength per screw Pnov = nominal pull-over strength per screw Pns = nominal shear strength per screw Pnt = nominal tensile strength per screw q = uniform design load r = radius of gyration ro = _______________ r 2 x + r 2 y + x 2 o + y 2 o rs = radius of gyration of the stiffener rx , ry = radii of gyration of the cross-section about the cen- troidal principal axes (see Section 4.9.2 for rye of singly symmetric sections unsymmetric about the bending axis) rye = effective radius of gyration R = transition radius, the radius of an attachment of the weld detail Rb = mid-thickness radius of a round element or maxi- mum mid-thickness radius of an oval element Ri = bend radius at juncture of ange and web measured to inside surface of bend Rs = stress ratio, the ratio of minimum stress to maximum stress s = spacing of transverse stiffeners (clear distance between stiffeners for stiffeners consisting of a pair of members, one on each side of the web, center-to-center distance between stiffeners con- sisting of a member on one side of the web only); spacing of rivet or bolt holes parallel to direction of load S = 1.28 ___ E___ Fcy Sc = section modulus of a beam, compression side Sra = the applied stress range Srd = allowable stress range Sre = equivalent stress range Sri = the ith stress range in the spectrum St = section modulus of a beam, tension side Sw = size of a weld Sx = standard deviation of the test results S1, S2 = slenderness limits t = thickness of element tavg = the average thickness of the element tc = depth of full thread engagement of screw into t2 not including tapping or drilling point ti = thickness of the intermediate thickness material tested tmax = thickness of thickest material tested tmax = greater thickness of a tapered thickness element tmin = thickness of thinnest material tested tmin = lesser thickness of a tapered thickness element t1 = thickness of member in contact with the screw head t2 = thickness of member not in contact with the screw head U = parameter dened by Eq. 4.9.3-8 V = shear force on web at stiffener location VF = coefcient of variation of the fabrication factor VM = coefcient of variation of the material factor VP = coefcient of variation of the ratio of the observed failure loads divided by the average value of all the observed failure loads VQ = coefcient of variation of the loads xo = x - coordinate of the shear center Xa = strength at which 99% of the material is expected to conform at a condence level of 95% Xi = failure load of ith test Xm = mean of the test results yo = y - coordinate of the shear center = Dn /Ln i = number of cycles in the spectrum of the ith stress range divided by the total number of cycles s = a factor equal to unity for a stiffener consisting of equal members on both sides of the web and equal to 3.5 for a stiffener consisting of a mem- ber on one side only = 1 (xo /ro)2 o = the target reliability index s = spring constant (transverse force applied to the compression ange of the member of unit length divided by the deection due to the force) = (tmax tmin)_________ tmin for tapered thickness elements s = equivalent slenderness ratio for an intermediate stiffener st = ratio dened in Section 3.4.9.1 and 3.4.16.2 = angle between plane of web and plane of bearing surface ( 90)
  20. 20. I-A-14 January 2005 3.3 Tables Relating to Mechanical Properties and Buckling Constants This Section consists of the following tables concerning formulas for determining allowable stresses and constants and coefcients needed for these formulas: 3.3-1 Minimum Mechanical Properties for Alumi- num Alloys 3.3-1M Minimum Mechanical Properties for Alumi- num Alloys 3.3-2 Minimum Mechanical Properties for Welded Aluminum Alloys 3.3-2M Minimum Mechanical Properties for Welded Aluminum Alloys 3.3-3 Formulas for Buckling Constants for Prod- ucts Whose Temper Designation Begins With -O, -H, -T1, -T2, T3, or -T4 3.3-4 Formulas for Buckling Constants for Prod- ucts Whose Temper Designation Begins With -T5, -T6, -T7, -T8, or -T9
  21. 21. January 2005 I-A-15 Table 3.3-1 MINIMUM MECHANICAL PROPERTIES FOR ALUMINUM ALLOYS ALLOY AND TEMPER PRODUCT THICKNESS RANGE in. Ftu ksi Fty ksi Fcy ksi Fsu ksi COMPRESSIVE MODULUS OF ELASTICITY2 E (ksi) 1100-H12 -H14 Sheet, Plate, Drawn Tube, Rolled Rod & Bar All All 14 16 11 14 10 13 9 10 10,100 10,100 2014-T6 -T651 -T6, T6510, T6511 -T6, T651 Sheet Plate Extrusions Cold Finished Rod & Bar, Drawn Tube 0.040 to 0.249 0.250 to 2.000 All All 66 67 60 65 58 59 53 55 59 58 52 53 40 40 35 38 10,900 10,900 10,900 10,900 Alclad 2014-T6 -T6 -T651 Sheet Sheet Plate 0.025 to 0.039 0.040 to 0.249 0.250 to 0.499 63 64 64 55 57 57 56 58 56 38 39 39 10,800 10,800 10,800 3003-H12 -H14 -H16 -H18 -H12 -H14 -H16 -H18 Sheet & Plate Sheet & Plate Sheet Sheet Drawn Tube Drawn Tube Drawn Tube Drawn Tube 0.017 to 2.000 0.009 to 1.000 0.006 to 0.162 0.006 to 0.128 All All All All 17 20 24 27 17 20 24 27 12 17 21 24 12 17 21 24 10 14 18 20 11 16 19 21 11 12 14 15 11 12 14 15 10,100 10,100 10,100 10,100 10,100 10,100 10,100 10,100 Alclad 3003-H12 -H14 -H16 -H18 -H14 -H18 Sheet & Plate Sheet & Plate Sheet Sheet Drawn Tube Drawn Tube 0.017 to 2.000 0.009 to 1.000 0.006 to 0.162 0.006 to 0.128 0.025 to 0.259 0.010 to 0.500 16 19 23 26 19 26 11 16 20 23 16 23 9 13 17 19 15 20 10 12 14 15 12 15 10,100 10,100 10,100 10,100 10,100 10,100 3004-H32 -H34 -H36 -H38 -H34 -H36 Sheet & Plate Sheet & Plate Sheet Sheet Drawn Tube Drawn Tube 0.017 to 2.000 0.009 to 1.000 0.006 to 0.162 0.006 to 0.128 0.018 to 0.450 0.018 to 0.450 28 32 35 38 32 35 21 25 28 31 25 28 18 22 25 29 24 27 17 19 20 21 19 20 10,100 10,100 10,100 10,100 10,100 10,100 Alclad 3004-H32 -H34 -H36 -H38 -H131, H241, H341 -H151, H261, H361 Sheet Sheet Sheet Sheet Sheet Sheet 0.017 to 0.249 0.009 to 0.249 0.006 to 0.162 0.006 to 0.128 0.024 to 0.050 0.024 to 0.050 27 31 34 37 31 34 20 24 27 30 26 30 17 21 24 28 22 28 16 18 19 21 18 19 10,100 10,100 10,100 10,100 10,100 10,100 3005-H25 -H28 Sheet Sheet 0.013 to 0.050 0.006 to 0.080 26 31 22 27 20 25 15 17 10,100 10,100 3105-H25 Sheet 0.013 to 0.080 23 19 17 14 10,100 5005-H12 -H14 -H16 -H32 -H34 -H36 Sheet & Plate Sheet & Plate Sheet Sheet & Plate Sheet & Plate Sheet 0.017 to 2.000 0.009 to 1.000 0.006 to 0.162 0.017 to 2.000 0.009 to 1.000 0.006 to 0.162 18 21 24 17 20 23 14 17 20 12 15 18 13 15 18 11 14 16 11 12 14 11 12 13 10,100 10,100 10,100 10,100 10,100 10,100 5050-H32 -H34 -H32 -H34 Sheet Sheet Cold Fin. Rod & Bar Drawn Tube Cold Fin. Rod & Bar Drawn Tube 0.017 to 2.000 0.009 to 0.249 All All 22 25 22 25 16 20 16 20 14 18 15 19 14 15 13 15 10,100 10,100 10,100 10,100 For all footnotes, see last page of this Table. ( )
  22. 22. Table 3.3-1 MINIMUM MECHANICAL PROPERTIES FOR ALUMINUM ALLOYS ALLOY AND TEMPER PRODUCT THICKNESS RANGE in. Ftu ksi Fty ksi Fcy ksi Fsu ksi COMPRESSIVE MODULUS OF ELASTICITY2 E (ksi) 5052-O -H32 -H34 -H36 Sheet & Plate Sheet & Plate Cold Fin. Rod & Bar Drawn Tube Sheet 0.006 to 3.000 All All 0.006 to 0.162 25 31 34 37 9.5 23 26 29 9.5 21 24 26 16 19 20 22 10,200 10,200 10,200 10,200 5083-O -H111 -H111 -O -H116 -H32, H321 -H116 -H32, H321 Extrusions Extrusions Extrusions Sheet & Plate Sheet & Plate Sheet & Plate Plate Plate up thru 5.000 up thru 0.500 0.501 to 5.000 0.051 to 1.500 0.188 to 1.500 0.188 to 1.500 1.501 to 3.000 1.501 to 3.000 39 40 40 40 44 44 41 41 16 24 24 18 31 31 29 29 16 21 21 18 26 26 24 24 24 24 23 25 26 26 24 24 10,400 10,400 10,400 10,400 10,400 10,400 10,400 10,400 5086-O -H111 -H111 -O -H112 -H112 -H112 -H112 -H116 -H32 -H34 Extrusions Extrusions Extrusions Sheet & Plate Plate Plate Plate Plate Sheet & Plate Sheet & Plate Drawn Tube Sheet & Plate Drawn Tube up thru 5.000 up thru 0.500 0.501 to 5.000 0.020 to 2.000 0.025 to 0.499 0.500 to 1.000 1.001 to 2.000 2.001 to 3.000 All All All 35 36 36 35 36 35 35 34 40 40 44 14 21 21 14 18 16 14 14 28 28 34 14 18 18 14 17 16 15 15 26 26 32 21 21 21 21 22 21 21 21 24 24 26 10,400 10,400 10,400 10,400 10,400 10,400 10,400 10,400 10,400 10,400 10,400 5154-H38 Sheet 0.006 to 0.128 45 35 33 24 10,300 5454-O -H111 -H111 -H112 -O -H32 -H34 Extrusions Extrusions Extrusions Extrusions Sheet & Plate Sheet & Plate Sheet & Plate up thru 5.000 up thru 0.500 0.501 to 5.000 up thru 5.000 0.020 to 3.000 0.020 to 2.000 0.020 to 1.000 31 33 33 31 31 36 39 12 19 19 12 12 26 29 12 16 16 13 12 24 27 19 20 19 19 19 21 23 10,400 10,400 10,400 10,400 10,400 10,400 10,400 5456-O -H116 -H32, H321 -H116 -H32, H321 -H116 -H32, H321 Sheet & Plate Sheet & Plate Sheet & Plate Plate Plate Plate Plate 0.051 to 1.500 0.188 to 1.250 0.188 to 1.250 1.251 to 1.500 1.251 to 1.500 1.501 to 3.000 1.501 to 3.000 42 46 46 44 44 41 41 19 33 33 31 31 29 29 19 27 27 25 25 25 25 26 27 27 25 25 25 25 10,400 10,400 10,400 10,400 10,400 10,400 10,400 6005-T5 Extrusions up thru 1.000 38 35 35 24 10,100 6061-T6, T651 -T6, T6510, T6511 -T6, T651 -T6 -T6 Sheet & Plate Extrusions Cold Fin. Rod & Bar Drawn Tube Pipe 0.010 to 4.000 All up thru 8.000 0.025 to 0.500 All 42 38 42 42 38 35 35 35 35 35 35 35 35 35 35 27 24 25 27 24 10,100 10,100 10,100 10,100 10,100 6063-T5, -T52 -T5 -T6 Extrusions Extrusions Extrusions Extrusions & Pipe up thru 0.500 up thru 1.000 0.500 to 1.000 All 22 22 21 30 16 16 15 25 16 16 15 25 13 13 12 19 10,100 10,100 10,100 10,100 6066-T6, T6510, T6511 Extrusions All 50 45 45 27 10,100 6070-T6, T62 Extrusions up thru 2.999 48 45 45 29 10,100 6105-T5 Extrusions up thru 0.500 38 35 35 24 10,100 6351 6351 -T5 -T6 Extrusions Extrusions up thru 1.000 up thru 0.750 38 42 35 37 35 37 24 27 10,100 10,100 6463-T6 Extrusions up thru 0.500 30 25 25 19 10,100 7005-T53 Extrusions up thru 0.750 50 44 43 28 10,500 1. Ftu and Fty are minimum specied values (except Fty for 1100-H12, H14 Cold Finished Rod and Bar and Drawn Tube, Alclad 3003-H18 Sheet and 5050-H32, H34 Cold Finished Rod and Bar which are minimum expected values); other strength properties are corresponding minimum expected values. 2. Typical values. For deection calculations an average modulus of elasticity is used; this is 100 ksi lower than values in this column. ( ) I-A-16 May 2005
  23. 23. January 2005 I-A-17 Table 3.3-1M MINIMUM MECHANICAL PROPERTIES FOR ALUMINUM ALLOYS ALLOY AND TEMPER PRODUCT THICKNESS RANGE mm Ftu MPa Fty MPa Fcy MPa Fsu MPa COMPRESSIVE MODULUS OF ELASTICITY2 E (MPa) 1100-H12 -H14 Sheet, Plate, Drawn Tube, Rolled Rod & Bar All All 95 110 75 95 70 90 62 70 69,600 69,600 2014-T6 -T651 -T6, T6510, T6511 -T6, T651 Sheet Plate Extrusions Cold Finished Rod & Bar, Drawn Tube 1.00 to 6.30 6.30 to 50.00 All All 455 460 415 450 400 405 365 380 405 400 360 365 275 275 240 260 75,200 75,200 75,200 75,200 Alclad 2014-T6 -T6 -T651 Sheet Sheet Plate 0.63 to 1.00 1.00 to 6.30 6.30 to 12.50 435 440 440 380 395 395 385 400 385 260 270 270 74,500 74,500 74,500 3003-H12 -H14 -H16 -H18 -H12 -H14 -H16 -H18 Sheet & Plate Sheet & Plate Sheet Sheet Drawn Tube Drawn Tube Drawn Tube Drawn Tube 0.40 to 50.00 0.20 to 25.00 0.15 to 4.00 0.15 to 3.20 All All All All 120 140 165 185 120 140 165 185 85 115 145 165 85 115 145 165 70 95 125 140 75 110 130 145 75 85 95 105 75 85 95 105 69,600 69,600 69,600 69,600 69,600 69,600 69,600 69,600 Alclad 3003-H12 -H14 -H16 -H18 -H14 -H18 Sheet & Plate Sheet & Plate Sheet Sheet Drawn Tube Drawn Tube 0.40 to 50.00 0.20 to 25.00 0.15 to 4.00 0.15 to 3.20 0.63 to 6.30 0.25 to 12.50 115 135 160 180 135 180 80 110 140 160 110 160 62 90 115 130 105 140 70 85 95 105 85 105 69,600 69,600 69,600 69,600 69,600 69,600 3004-H32 -H34 -H36 -H38 -H34 -H36 Sheet & Plate Sheet & Plate Sheet Sheet Drawn Tube Drawn Tube 0.40 to 50.00 0.20 to 25.00 0.15 to 4.00 0.15 to 3.20 0.45 to 11.50 0.45 to 11.50 190 220 240 260 220 240 145 170 190 215 170 190 125 150 170 200 165 185 115 130 140 145 130 140 69,600 69,600 69,600 69,600 69,600 69,600 Alclad 3004-H32 -H34 -H36 -H38 -H131, H241, H341 -H151, H261, H361 Sheet Sheet Sheet Sheet Sheet Sheet 0.40 to 6.30 0.20 to 6.30 0.15 to 4.00 0.15 to 3.20 0.60 to 1.20 0.60 to 1.20 185 215 235 255 215 235 140 165 185 205 180 205 115 145 165 195 150 195 110 125 130 145 125 130 69,600 69,600 69,600 69,600 69,600 69,600 3005-H25 -H28 Sheet Sheet 0.32 to 1.20 0.15 to 2.00 180 215 150 185 140 170 105 115 69,600 69,600 3105-H25 Sheet 0.32 to 2.00 160 130 115 95 69,600 5005-H12 -H14 -H16 -H32 -H34 -H36 Sheet & Plate Sheet & Plate Sheet Sheet & Plate Sheet & Plate Sheet 0.40 to 50.00 0.20 to 25.00 0.15 to 4.00 0.40 to 50.00 0.20 to 25.00 0.15 to 4.00 125 145 165 120 140 160 95 115 135 85 105 125 90 105 125 75 95 110 75 85 95 75 85 90 69,600 69,600 69,600 69,600 69,600 69,600 5050-H32 -H34 -H32 -H34 Sheet Sheet Cold Fin. Rod & Bar Drawn Tube Cold Fin. Rod & Bar Drawn Tube 0.40 to 6.30 0.20 to 6.30 All All 150 170 150 170 110 140 110 140 95 125 105 130 95 105 90 105 69,600 69,600 69,600 69,600 For all footnotes, see last page of this Table. ( )
  24. 24. I-A-18 January 2005 Table 3.3-1M MINIMUM MECHANICAL PROPERTIES FOR ALUMINUM ALLOYS ALLOY AND TEMPER PRODUCT THICKNESS RANGE mm Ftu MPa Fty MPa Fcy MPa Fsu MPa COMPRESSIVE MODULUS OF ELASTICITY2 E (MPa) 5052-O -H32 -H34 -H36 Sheet & Plate Sheet & Plate Cold Fin. Rod & Bar Drawn Tube Sheet 0.15 to 80.00 All All 0.15 to 4.00 170 215 235 255 65 160 180 200 66 145 165 180 110 130 140 150 70,300 70,300 70,300 70,300 5083-O -H111 -H111 -O -H116 -H32, H321 -H116 -H32, H321 Extrusions Extrusions Extrusions Sheet & Plate Sheet & Plate Sheet & Plate Plate Plate up thru 13.00 up thru 12.70 12.70 to 130.00 1.20 to 6.30 4.00 to 40.00 4.00 to 40.00 40.00 to 80.00 40.00 to 80.00 270 275 275 275 305 305 285 285 110 165 165 125 215 215 200 200 110 145 145 125 180 180 165 165 165 165 160 170 180 180 165 165 71,700 71,700 71,700 71,700 71,700 71,700 71,700 71,700 5086-O -H111 -H111 -O -H112 -H112 -H112 -H116 -H32 -H34 Extrusions Extrusions Extrusions Sheet & Plate Sheet & Plate Plate Plate Sheet & Plate Sheet & Plate Drawn Tube Sheet & Plate Drawn Tube up thru 130.00 up thru 12.70 12.70 to 130.00 0.50 to 50.00 4.00 to 12.50 12.50 to 40.00 40.00 to 80.00 1.60 to 50.00 All All 240 250 250 240 250 240 235 275 275 300 95 145 145 95 125 105 95 195 195 235 95 125 125 95 115 110 105 180 180 220 145 145 145 145 150 145 145 165 165 180 71,700 71,700 71,700 71,700 71,700 71,700 71,700 71,700 71,700 71,700 5154-H38 Sheet 0.15 to 3.20 310 240 230 165 71,700 5454-O -H111 -H111 -H112 -O -H32 -H34 Extrusions Extrusions Extrusions Extrusions Sheet & Plate Sheet & Plate Sheet & Plate up thru 130.00 up thru 12.70 12.70 to 130.00 up thru 130.00 0.50 to 80.00 0.50 to 50.00 0.50 to 25.00 215 230 230 215 215 250 270 85 130 130 85 85 180 200 85 110 110 90 85 165 185 130 140 130 130 130 145 160 71,700 71,700 71,700 71,700 71,700 71,700 71,700 5456-O -H116 -H32, H321 -H116 -H32, H321 -H116 -H32, H321 Sheet & Plate Sheet & Plate Sheet & Plate Plate Plate Plate Plate 1.20 to 6.30 4.00 to 12.50 4.00 to 12.50 12.50 to 40.00 12.50 to 40.00 40.00 to 80.00 40.00 to 80.00 290 315 315 305 305 285 285 130 230 230 215 215 200 200 130 185 185 170 170 170 170 180 185 185 170 170 170 170 71,700 71,700 71,700 71,700 71,700 71,700 71,700 6005-T5 Extrusions up thru 25 260 240 240 165 69,600 6061-T6, T651 -T6, T6510, T6511 -T6, T651 -T6 -T6 Sheet & Plate Extrusions Cold Fin. Rod & Bar Drawn Tube Pipe 0.25 to 100.00 All up thru 200 0.63 to 12.50 All 290 260 290 290 260 240 240 240 240 240 240 240 240 240 240 185 165 170 185 165 69,600 69,600 69,600 69,600 69,600 6063-T5, -T52 -T5 -T6 Extrusions Extrusions Extrusions Extrusions & Pipe up thru 12.50 up thru 25.00 12.50 to 25.00 All 150 150 145 205 110 110 105 170 110 110 105 170 90 90 85 130 69,600 69,600 69,600 69,600 6066-T6, T6510, T6511 Extrusions All 345 310 310 185 69,600 6070-T6, T62 Extrusions up thru 80.00 330 310 310 200 69,600 6105-T5 Extrusions up thru 12.50 260 240 240 165 69,600 6351-T5 Extrusions up thru 25.00 260 240 240 165 69,600 6351-T6 Extrusions up thru 20.00 290 255 255 185 69,600 6463-T6 Extrusions up thru 12.50 205 170 170 130 69,600 7005-T53 Extrusions up thru 20.00 345 305 295 195 72,400 1. Ftu and Fty are minimum specied values (except Fty for 1100-H12, H14 Cold Finished Rod and Bar and Drawn Tube, Alclad 3003-H18 Sheet and 5050-H32, H34 Cold Finished Rod and Bar which are minimum expected values); other strength properties are corresponding minimum expected values. 2. Typical values. For deection calculations an average modulus of elasticity is used; this is 700 MPa lower than values in this column. ( )
  25. 25. January 2005 I-A-19 Table 3.3-2 MINIMUM MECHANICAL PROPERTIES FOR WELDED ALUMINUM ALLOYS ALLOY AND TEMPER PRODUCT THICKNESS RANGE in. TENSION COMPRESSION Fcyw 2 ksi SHEAR Fsuw ksi Ftuw 1 ksi Ftyw 2 ksi 1100-H12, H14 All 11 3.5 3.5 8 3003-H12, H14, H16, H18 All 14 5 5 10 Alclad 3003-H12, H14, H16, H18 All 13 4.5 4.5 10 3004-H32, H34, H36, H38 All 22 8.5 8.5 14 Alclad 3004-H32, H34, H36, H38 All 21 8 8 13 3005-H25 Sheet 17 6.5 6.5 12 5005-H12, H14, H32, H34 All 15 5 5 9 5050-H32, H34 All 18 6 6 12 5052-O, H32, H34 All 25 9.5 9.5 16 5083- 5083- 5083- O, H111 O, H116, H32, H321 O, H116, H32, H321 Extrusions Sheet & Plate Plate 0.188-1.500 1.501-3.000 39 40 39 16 18 17 15 18 17 23 24 24 5086- 5086- 5086- O, H111 H112 O, H32, H34, H116 Extrusions Plate Sheet & Plate 0.250-2.000 35 35 35 14 14 14 13 14 14 21 21 21 5154-H38 Sheet 30 11 11 19 5454- 5454- 5454- O, H111 H112 O, H32, H34 Extrusions Extrusions Sheet & Plate 31 31 31 12 12 12 11 12 12 19 19 19 5456- 5456- O, H116, H32, H321 O, H116, H32, H321 Sheet & Plate Plate 0.188-1.500 1.501-3.000 42 41 19 18 18 17 25 25 6005-T5 Extrusions up thru 0.250 24 13 13 15 6061- 6061- T6, T651, T6510, T65113 T6, T651, T6510, T65114 All All over 0.375 24 24 15 11 15 11 15 15 6063-T5, T52, T6 All 17 8 8 11 6351- 6351- T5, T63 T5, T64 Extrusions Extrusions over 0.375 24 24 15 11 15 11 15 15 6463-T6 Extrusions 0.125-0.500 17 8 8 11 7005-T53 Extrusions up thru 0.750 40 24 24 22 1. Filler wires are listed in Table 7.1-1. Values of Ftuw are AWS D1.2 weld qualication values. 2. 0.2% offset in 2 in. gage length across a groove weld. 3. Values when welded with 5183, 5356, or 5556 alloy ller wire, regardless of thickness. Values also apply to thicknesses less than or equal to 0.375 in. when welded with 4043, 5554, or 5654 alloy ller wire. 4. Values when welded with 4043, 5554, or 5654 alloy ller wire.
  26. 26. I-A-20 January 2005 Table 3.3-2M MINIMUM MECHANICAL PROPERTIES FOR WELDED ALUMINUM ALLOYS ALLOY AND TEMPER PRODUCT THICKNESS RANGE mm TENSION COMPRESSION Fcyw 2 MPa SHEAR Fsuw MPa Ftuw 1 MPa Ftyw 2 MPa 1100-H12, H14 All 75 25 25 55 3003-H12, H14, H16, H18 All 95 35 35 70 Alclad 3003-H12, H14, H16, H18 All 90 30 30 70 3004-H32, H34, H36, H38 All 150 60 60 95 Alclad 3004-H32, H34, H36, H38 All 145 55 55 90 3005-H25 Sheet 115 45 45 85 5005-H12, H14, H32, H34 All 105 35 35 62 5050-H32, H34 All 125 40 40 85 5052-O, H32, H34 All 170 65 65 110 5083- 5083- 5083- O, H111 O, H116, H32, H321 O, H116, H32, H321 Extrusions Sheet & Plate Plate 6.30-38.00 38.00-80.00 270 270 270 110 115 115 110 115 115 160 165 165 5086- 5086- 5086- O, H111 H112 O, H32, H34, H116 Extrusions Plate Sheet & Plate 6.30-50.00 240 240 240 95 95 95 85 95 95 145 145 145 5154-H38 Sheet 205 75 75 130 5454- 5454- 5454- O, H111 H112 O, H32, H34 Extrusions Extrusions Sheet & Plate 215 215 215 85 85 85 85 85 85 130 130 130 5456- 5456- O, H116, H32, H321 O, H116, H32, H321 Sheet & Plate Plate 6.30-38.00 38.00-80.00 285 285 125 125 125 120 170 170 6005-T5 Extrusions up thru 12.50 165 90 90 105 6061- 6061- T6, T651, T6510, T65113 T6, T651, T6510, T65114 All All over 9.50 165 165 105 80 105 80 105 105 6063-T5, T52, T6 All 115 55 55 75 6351- 6351- T5, T63 T5, T64 Extrusions Extrusions over 9.50 165 165 105 80 105 80 105 105 6463-T6 Extrusions 3.20-12.50 115 55 55 75 7005-T53 Extrusions up thru 20.00 275 165 165 155 1. Filler wires are listed in Table 7.1-1. Values of Ftuw are AWS D1.2 weld qualication values. 2. 0.2% offset in 50 mm gage length across a groove weld. 3. Values when welded with 5183, 5356, or 5556 alloy ller wire, regardless of thickness. Values also apply to thicknesses less than or equal to 9.5 mm when welded with 4043, 5554, or 5654 alloy ller wire. 4. Values when welded with 4043, 5554, or 5654 alloy ller wire.
  27. 27. January 2005 I-A-21 Table 3.3-3 FORMULAS FOR BUCKLING CONSTANTS FOR PRODUCTS WHOSE TEMPER DESIGNATION BEGINS WITH -O, -H, -T1, -T2, -T3, OR -T4 Type of Member and Stress Intercept ksi Intercept MPa Slope Intersection Compression in Columns and Beam Flanges Bc = Fcy [1 + ( Fcy_____ 1000) 1/2 ] Bc = Fcy [1 + ( Fcy_____ 6900) 1/2 ] Dc = Bc___ 20 (6Bc___ E ) 1/2 Cc = 2Bc____ 3Dc Axial Compression in Flat Elements Bp = Fcy [1 + (Fcy )1/3 ______ 7.6 ] Bp = Fcy [1 + (Fcy )1/3 ______ 14.5 ] Dp = Bp___ 20 (6Bp___ E )1/2 Cp = 2Bp____ 3Dp Axial Compression in Curved Elements Bt = Fcy [1 + (Fcy )1/5 ______ 5.8 ] Bt = Fcy [1 + (Fcy )1/5 ______ 8.5 ] Dt = Bt___ 3.7 (Bt__ E ) 1/3 Ct* Bending Compression in Flat Elements Bbr = 1.3Fcy [1 + (Fcy )1/3 ______ 7 ] Bbr = 1.3Fcy [1 + (Fcy )1/3 _____ 13.3 ] Dbr = Bbr___ 20 (6Bbr____ E ) 1/2 Cbr = 2Bbr____ 3Dbr Bending Compression in Curved Elements Btb = 1.5Fy [1 + (Fy )1/5 ______ 5.8 ] Btb = 1.5Fy [1 + (Fy )1/5 _____ 8.5 ] Dtb = Btb___ 2.7 (Btb___ E ) 1/3 Ctb =(Btb Bt_______ Dtb Dt ) 2 Shear in Flat Elements Bs = Fty___ __ 3 [1 + (Fty / __ 3 )1/3 _________ 6.2 ] Bs = Fty___ __ 3 [1 + (Fty / __ 3 )1/3 _________ 11.8 ] Ds = Bs___ 20 (6Bs___ E ) 1/2 Cs = 2Bs____ 3Ds Ultimate Strength of Flat Elements in Compression or Bending k1 = 0.50, k2 = 2.04 *Ct shall be determined using a plot of curves of limit state stress based on elastic and inelastic buckling or by trial and error solution.
  28. 28. I-A-22 January 2005 Table 3.3-4 FORMULAS FOR BUCKLING CONSTANTS FOR PRODUCTS WHOSE TEMPER DESIGNATION BEGINS WITH -T5, -T6, -T7, -T8, OR -T9 Type of Member and Stress Intercept ksi Intercept MPa Slope Intersection Compression in Columns and Beam Flanges Bc = Fcy [1 + ( Fcy_____ 2250) 1/2 ] Bc = Fcy [1 + ( Fcy______ 15510) 1/2 ] Dc = Bc___ 10 (Bc__ E ) 1/2 Cc = 0.41 Bc___ Dc Axial Compression in Flat Elements Bp = Fcy [1 + (Fcy )1/3 ______ 11.4 ] Bp = Fcy [1 + (Fcy )1/3 ______ 21.7 ] Dp = Bp___ 10 (Bp__ E ) 1/2 Cp = 0.41 Bp___ Dp Axial Compression in Curved Elements Bt = Fcy [1 + (Fcy )1/5 ______ 8.7 ] Bt = Fcy [1 + (Fcy )1/5 ______ 12.8 ] Dt = Bt___ 4.5 (Bt__ E ) 1/3 Ct* Bending Compression in Flat Elements Bbr = 1.3Fcy [1 + (Fcy )1/3 _____ 7 ] Bbr = 1.3Fcy [1 + (Fcy )1/3 _____ 13.3 ] Dbr = Bbr___ 20 (6Bbr____ E ) 1/2 Cbr = 2Bbr____ 3Dbr Bending Compression in Curved Elements Btb = 1.5Fy [1 + (Fy )1/5 _____ 8.7 ] Btb = 1.5Fy [1 + (Fy )1/5 _____ 12.8 ] Dtb = Btb___ 2.7 (Btb___ E ) 1/3 Ctb = (Btb Bt_______ Dtb Dt ) 2 Shear in Flat Elements Bs = Fty___ __ 3 [1 + (Fty / __ 3 )1/3 _________ 9.3 ] Bs = Fty___ __ 3 [1 + (Fty / __ 3 )1/3 _________ 17.7 ] Ds = Bs___ 10 (Bs__ E ) 1/2 Cs = 0.41 Bs___ Ds Ultimate Strength of Flat Elements in Compression k1 = 0.35, k2 = 2.27 Ultimate Strength of Flat Elements in Bending k1 = 0.50, k2 = 2.04 *Ct shall be determined using a plot of curves of limit state stress based on elastic and inelastic buckling or by trial and error solution.
  29. 29. January 2005 I-A-23 3.4 Allowable Stresses Allowable stresses shall be determined in accordance with provisions of this Specication. In the following subsections: The factors nu, ny, and na shall be taken from Table 3.4-1. Values of coefcient kt shall be taken from Table 3.4-2. Table 3.4-1 SAFETY FACTORS Building and similar type structures Bridge and similar type structures nu 1.95 2.20 ny 1.65 1.85 na 1.20 1.35 Other safety factors are given throughout this Specification. Table 3.4-2 COEFFICIENT kt Alloy and Temper Non-welded or Regions Farther than 1.0 in. (25 mm) from a Weld Regions Within 1.0 in. (25 mm) of a Weld 2014-T6, -T651, -T6510, -T6511 Alclad 2014-T6, -T651 1.25 6066-T6, -T6510, -T6511 1.1 6070-T6, -T62 1.1 All Others Listed in Table 3.3-1 1.0 1.0 kt is used in Sections 3.4.1, 3.4.2, 3.4.3, and 3.4.4. Values of k1 and k2 shall be taken from Tables 3.3-3 and 3.3-4. The formulas of this Section are also listed in Table 3.4-3.
  30. 30. I-A-24 March 2005 TypeofStressTypeofMemberorElement Sub- Sec. AllowableStress Table3.4-3 GENERALFORMULASFOR DETERMININGALLOWABLESTRESS FROMSECTION3.4 TENSION,axial Anytensionmember grosssection netsection 1 Fty/ny Ftu/(ktnu) TENSIONIN BEAMS, extremeber, netsection Flatelementsinuniformtension(anges)2F= Fty___ ny orF= Ftu____ ktnu Roundorovaltubes3F= 1.17Fty______ ny orF= 1.24Ftu______ ktnu Flatelementsinbendingin theirownplane(webs) 4 forsymmetricshapes: F= 1.3Fty_____ ny orF= 1.42Ftu______ ktnu forunsymmetricshapes seeSection3.4.4Fortubeswithcircumferentialwelds,equationsofSections3.4.10, 3.4.12,and3.4.16.1applyforRb/t20. BEARING Onrivetsandbolts52Ftu/nu Onatsurfacesandpinsandonboltsinslotted holes 62Ftu/(1.5nu) TypeofStressTypeofMemberorElement Sub- Sec. Allowable Stress SlendernessS1 Slenderness LimitS1 AllowableStress S1
  31. 31. January 2005 I-A-25 TypeofStressTypeofMemberorElement Sub- Sec. Allowable Stress SlendernessS1 Slenderness LimitS1 AllowableStress S1
  32. 32. I-A-26 January 2005 3.4.1 Tension, Axial Axial tensile stress shall not exceed F = Fty/ny (Eq. 3.4.1-1) on the gross area and F = Ftu/(kt )(nu ) (Eq. 3.4.1-2) on the effective net area (see Section 5.1.5). Values of nu and ny are listed in Table 3.4-1. Values of kt are listed in Table 3.4-2. Block shear rupture strength provisions for the end con- nections of tension members are given in Section 5.1.3. 3.4.2 Tension in Extreme Fibers of Beams Flat Elements In Uniform Tension The allowable stress is the lesser of: F = Fty___ ny and F = Ftu___ ktnu 3.4.3 Tension in Extreme Fibers of Beams Round or Oval Tubes The allowable stress is the lesser of: F = 1.17Fty______ ny (Eq. 3.4.3-1) and F = 1.24Ftu______ kt nu (Eq. 3.4.3-2) 3.4.4 Tension in Extreme Fibers of Beams Flat Elements In Bending in Their Own Plane a. For elements symmetric about the bending axis, the allowable stress is the lesser of: F = 1.3Fty_____ ny (Eq. 3.4.4-1) and F = 1.42Ftu______ kt nu (Eq. 3.4.4-2) b. For elements unsymmetric about the bending axis, the extreme ber stress of the element shall not exceed the limiting value from a. and the stress at midheight of the element shall not exceed the stress given in Sec- tion 3.4.2. 3.4.5 Bearing on Rivets and Bolts F = 2Ftu /nu (Eq. 3.4.5-1) This value shall be used for a ratio of edge distance to fas- tener diameter of 2 or greater. For smaller ratios this allow- able stress shall be multiplied by the ratio: (edge distance)/ (2 fastener diameter). Edge distance is the distance from the center of the fastener to the edge of the material in the direction of the applied load and shall not be less than 1.5 times the fastener diameter to extruded, sheared, sawed, rolled, or planed edges. 3.4.6 Bearing on Flat Surfaces and Pins and on Bolts in Slotted Holes F = 2Ftu /(1.5nu ) (Eq. 3.4.6-1) (See Section 5.2.2 for limits on slot lengths.) 3.4.7 Compression in Columns, Axial, Gross Section For members in axial compression, the allowable stress is the lesser of that determined from this Section and Sec- tions 3.4.8 through 3.4.10. a. Fc = Fcy___ ny (Eq. 3.4.7-1) for kL___ r S1 b. Fc = (Bc Dc kL_____ r )__________ nu (Eq. 3.4.7-2) for S1 < kL___ r < S2 c. Fc = 2 E_______ nu (kL___ r )2 (Eq. 3.4.7-3) for kL___ r S2 where S1 = Bc nuFcy_____ ny________ Dc (Eq. 3.4.7-4) S2 = Cc (Eq. 3.4.7-5) k = the effective length factor by rational analysis. k shall be taken larger than or equal to unity unless rational analysis justies a smaller value. L = the unsupported length r = radius of gyration of the column about the axis of buckling 3.4.7.1 Sections Not Subject to Torsional or Torsional-Flexural Buckling For closed sections and other sections that are not sub- ject to torsional or torsional-exural buckling, kL___ r shall be the largest slenderness ratio for exural buckling of the column. 3.4.7.2 Doubly or Singly Symmetric Sections Subject to Torsional or Torsional- Flexural Buckling For doubly or singly symmetric sections subject to tor- sional or torsional-exural buckling kL___ r shall be the larger of the largest slenderness ratio for exural buckling and the equivalent slenderness ratio determined for torsional-exural buckling as follows:
  33. 33. January 2005 I-A-27 (kL___ r )e = ___ E__ Fe (Eq. 3.4.7.2-1) where Fe is the elastic critical stress determined as follows: For torsional buckling: Fe = Fet (Eq. 3.4.7.2-2) For torsional-exural buckling: Fe = Fef = 1___ 2 [(Fex + Fet ) __________________ (Fex + Fet )2 4FexFet ] (Eq. 3.4.7.2-3) Alternatively, for torsional-exural buckling, a conservative estimate of Fe shall be permitted to be obtained as follows: Fe = Fef = FexFet_______ Fex + Fet (Eq. 3.4.7.2-4) In the above equations x-axis is the centroidal symmetry axis A = cross-sectional area Cw = torsional warping constant of the cross-section E = compressive modulus of elasticity (See Table 3.3-1) Fex = 2 E______ (kxLb____ rx )2 (Eq. 3.4.7.2-5) Fet = 1____ Ar 2 O (GJ + 2 ECw______ (KtLt)2 ) (Eq. 3.4.7.2-6) G = shear modulus = 3E/8 (Eq. 3.4.7.2-7) J = torsion constant kx = effective length coefcient for buckling about the x-axis Kt = effective length coefcient for torsional buckling. Kt shall be taken larger than or equal to unity unless rational analysis justies a smaller value. Lt = unbraced length for twisting Lb = unbraced length for bending about the x-axis ro = ___________ r 2 x + r 2 y + x 2 o (Eq. 3.4.7.2-8) polar radius of gyration of the cross-section about the shear center. rx, ry = radii of gyration of the cross-section about the centroidal principal axes xo = x - coordinate of the shear center = 1 (xo /ro )2 (Eq. 3.4.7.2-9) 3.4.7.3 Nonsymmetric Sections Subject to Torsional or Torsional-Flexural Buckling For nonsymmetric sections subject to torsional or torsional-exural buckling kL___ r shall be determined by rational analysis. 3.4.8 Uniform Compression in Elements of Columns Whose Buckling Axis is an Axis of SymmetryFlat Elements Supported On One Edge a. Fc = Fcy___ ny (Eq. 3.4.8-1) for b/t S1 b. Fc = 1__ nu [Bp 5.1Dp b__ t ] (Eq. 3.4.8-2) for S1 < b/t < S2 c. Fc = k2 ____ BpE________ nu(5.1b/t) (Eq. 3.4.8-3) for b/t S2 where S1 = Bp nu__ ny Fcy _________ 5.1Dp (Eq. 3.4.8-4) S2 = k1Bp_____ 5.1Dp (Eq. 3.4.8-5) b = distance from unsupported edge of element to toe of the llet or bend, except if the inside corner radius exceeds 4 times the thickness; then the inside radius shall be assumed equal to 4 times the thickness in calculating b. Element width b is illustrated in Figure 3.4.8-1. 3.4.8.1 Uniform Compression in Elements of Columns Whose Buckling Axis is not an Axis of SymmetryFlat Elements Supported On One Edge a. Fc = Fcy___ ny (Eq. 3.4.8.1-1) for b/t S1 b. Fc = 1__ nu [Bp 5.1Dp b__ t ] (Eq. 3.4.8.1-2) for S1 < b/t < S2 c. Fc = 2 E_________ nu(5.1b/t)2 (Eq. 3.4.8.1-3) for b/t S2 where S1 = Bp nu__ ny Fcy _________ 5.1Dp (Eq. 3.4.8.1-4) S2 = Cp___ 5.1 (Eq. 3.4.8.1-5) b = distance from unsupported edge of element to toe of the llet or bend, except if the inside corner radius exceeds 4 times the thickness; then the inside radius shall be assumed equal to 4 times the thickness in calculating b. Element width b is illustrated in Figure 3.4.8-1.
  34. 34. I-A-28 January 2005 3.4.9 Uniform Compression in Elements of ColumnsFlat Elements Supported on Both Edges a. Fc = Fcy___ ny (Eq. 3.4.9-1) for b/t S1 b. Fc = 1__ nu [Bp 1.6Dp b__ t ] (Eq. 3.4.9-2) for S1 < b/t < S2 c. Fc = k2 ____ BpE________ nu(1.6b/t) (Eq. 3.4.9-3) for b/t S2 where S1 = Bp nu__ ny Fcy _________ 1.6Dp (Eq. 3.4.9-4) S2 = k1Bp_____ 1.6Dp (Eq. 3.4.9-5) b = distance from unsupported edge of element to toe of the llet or bend, except if the inside corner radius exceeds 4 times the thickness; then the inside radius shall be assumed equal to 4 times the thickness in calculating b. Element width b is illustrated in Figure 3.4.9-1. 3.4.9.1 Uniform Compression in Elements of ColumnsFlat Elements Supported on One Edge and With Stiffener on Other Edge The provisions of this Section apply when Ds /b 0.8. The allowable stress is the lesser of Fc = Fcy___ ny (Eq. 3.4.9.1-1) and Fc = FUT + (FST FUT )ST FST (Eq. 3.4.9.1-2) Figure 3.4.8-1 FLAT ELEMENTS SUPPORTED ON ONE EDGE If r > 4t, then use r = 4t to calculate b.
  35. 35. January 2005 I-A-29 For a simple straight lip edge stiffener of constant thick- ness, Fc shall not exceed the allowable stress for the stiffener according to Section 3.4.8. In the above equations Ds = dened in Figure 3.4.9.1-1 and -2 FUT = allowable stress according to Section 3.4.8 neglecting the stiffener FST = allowable stress according to Section 3.4.9 ST = ratio to be determined as follows: ST = 1.0 for b/t S/3 (Eq. 3.4.9.1-3) ST = rs_________ 9t(b/t___ S 1__ 3) 1.0 for S/3 < b/t S (Eq. 3.4.9.1-4) ST = rs___________ 1.5t (b/t___ S + 3) 1.0 for 2S > b/t > S (Eq. 3.4.9.1-5) rs = radius of gyration of the stiffener determined as follows: - For simple straight lip stiffeners of con- stant thickness similar to that shown in Figure 3.4.9.1-1, rs shall be calculated as: rs = ds sin ______ __ 3 - for other stiffeners, rs shall be calculated about the mid-thickness of the element being stiffened ds = at width of lip stiffener shown in Figure 3.4.9.1-1 S = 1.28 ___ E___ Fcy b = distance from unsupported edge of element to toe of llet or bend, except if the inside corner radius exceeds 4 times the thickness; then the inside radius shall be assumed to equal 4 times the thickness in calculating b. Element width b is illustrated in Figures 3.4.9.1-1. and 3.4.9.1-2 Figure 3.4.9-1 FLAT ELEMENTS SUPPORTED ON BOTH EDGES If r > 4t, then use r = 4t to calculate b.
  36. 36. I-A-30 January 2005 3.4.9.2 Uniform Compression in Elements of ColumnsFlat Elements Supported on Both Edges and With an Intermediate Stiffener a. Fc = Fcy___ ny (Eq. 3.4.9.2-1) for s S1 b. Fc = (Bc Dcs)_________ nu (Eq. 3.4.9.2-2) for S1 < s < S2 c. Fc = 2 E____ nus 2 (Eq. 3.4.9.2-3) for s S2 The allowable stress Fc obtained above shall not be more than the allowable stress according to Section 3.4.9 for the sub-elements of the intermediately stiffened element. The allowable stress Fc obtained above shall not be less than that determined according to Section 3.4.9 ignoring the intermediate stiffener. Figure 3.4.9.1-1 EDGE STIFFENED ELEMENTS If r > 4t, then use r = 4t to calculate b. Figure 3.4.9.1-2 EDGE STIFFENED ELEMENTS If r > 4t, then use r = 4t to calculate b.
  37. 37. January 2005 I-A-31 In the above equations: As = area of the stiffener Io = moment of inertia of a section comprising the stiff- ener and one half of the width of the adjacent sub- elements and the transition corners between them taken about the centroidal axis of the section parallel to the element that is stiffened (Figure 3.4.9.2-1). S1 = Bc nuFcy_____ ny_____ Dc (Eq. 3.4.9.2-4) S2 = Cc (Eq. 3.4.9.2-5) s = 4.62(b__ t ) _______________ 1 + As / bt_______________ 1 + __________ 1 + 10.67Io_______ bt3 (Eq. 3.4.9.2-6) Figure 3.4.9.2-1 FLAT ELEMENTS WITH AN INTERMEDIATE STIFFENER Line o-o is the neutral axis of the stiffener and plate of width b/2 on each side of the stiffener. Io is the moment of inertia of the portion shown in the partial section. If r > 4t, then use r = 4t to calculate b.
  38. 38. I-A-32 March 2006 3.4.10 Uniform Compression in Elements of ColumnsCurved Elements Supported on Both Edges a. Fc = Fcy___ ny (Eq. 3.4.10-1) for Rb/t S1 b. Fc = 1__ nu [Bt Dt ___ Rb__ t ] (Eq. 3.4.10-2) for S1 < Rb/t < S2 c. Fc = 2 E__________________ 16nu (Rb__ t )(1 + ____ Rb /t_____ 35 ) 2 (Eq. 3.4.10-3) for Rb/t S2 where S1 = (Bt nu__ ny Fcy ________ Dt ) 2 (Eq. 3.4.10-4) S2 = Ct (Eq. 3.4.10-5) For tubes with circumferential welds, the equations of this Section apply for Rb/t 20. 3.4.11 Compression in Beams, Extreme Fiber, Gross SectionSingle Web Shapes For single web shapes not subject to lateral buckling (bent about the strong axis with continuous lateral support or bent about the weak axis), determine the compressive allowable stress Fc from Sections 3.4.15 through 3.4.19 as applicable. For single web shapes subject to lateral buckling (bent about the strong axis without continuous lateral support), the compressive allowable stress Fc is the lesser of that determined from Sections 3.4.15 through 3.4.19 as appli- cable and the following: a. Fc = Fcy___ ny (Eq. 3.4.11-1) for Lb_____ ry ___ Cb S1 b. Fc = (Bc DcLb________ 1.2ry ___ Cb )____________ ny (Eq. 3.4.11-2) for S1 < Lb_____ ry ___ Cb < S2 c. Fc = Cb2 E________ ny ( Lb____ 1.2ry ) 2 (Eq. 3.4.11-3) for Lb_____ ry ___ Cb S2 where S1 = 1.2 (Bc Fcy )___________ Dc (Eq. 3.4.11-4) S2 = 1.2Cc (Eq. 3.4.11-5) ry = radius of gyration of the shape (about an axis parallel to the web) (For beams that are unsym- metrical about the horizontal axis, ry shall be calculated as though both anges were the same as the compression ange). Lb = length of the beam between bracing points or between a brace point and the free end of a cantilever beam. Bracing points are the points at which the compression ange is restrained against lateral movement or the cross section is restrained against twisting. Cb = coefcient that depends on moment variation over the unbraced length. Cb shall be as given in Section 4.9.4 or taken as 1. Alternatively, Fc may be calculated by replacing ry by rye given in Section 4.9. 3.4.12 Compression in Beams, Extreme Fiber, Gross SectionRound or Oval Tubes a. Fc = 1.17Fcy______ ny (Eq. 3.4.12-1) for Rb/t S1 b. Fc = 1__ ny (Btb Dtb ___ Rb__ t ) (Eq. 3.4.12-2) for S1 < Rb/t < S2 c. For Rb/t S2, the allowable bending stress shall be determined from the formulas for tubes in compres- sion in Section 3.4.10 using the formula that is appro- priate for the particular value of Rb /t. In the above equations Rb = mid-thickness radius of a round element or max- imum mid-thickness radius of an oval element S1 = (Btb 1.17Fcy__________ Dtb ) 2 (Eq. 3.4.12-3) S2 = ( nu__ ny Btb Bt _________ nu__ ny Dtb Dt ) 2 (Eq. 3.4.12-4) For tubes with circumferential welds, the equations of this Section apply for Rb/t 20. 3.4.13 Compression in Beams, Extreme Fiber, Gross SectionSolid Rectangular and Round Sections For rectangular sections bent about the weak axis, rod, and square bar: Fc = 1.3Fcy_____ ny For rectangular sections bent about the strong axis: a. Fc = 1.3Fcy_____ ny (Eq. 3.4.13-1) for d__ t ____ Lb____ Cb d S1
  39. 39. January 2005 I-A-33 b. Fc = 1__ ny (Bbr 2.3Dbr d__ t ____ Lb____ Cbd ) (Eq. 3.4.13-2) for S1 < d__ t ____ Lb____ Cbd < S2 c. Fc = 2 E___

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