Editorial Reviews From the Back Cover Unified ASD and LRFD design AISC building design specifications ASCE07 standard loadings data AASHTO bridge design specifications AN INVALUABLE WORKING TOOL FOR STEEL DESIGN If it has anything to do with the design of steel structures, youll find it in the Structural Steel Designers Handbook. The Fourth Edition of the oneofa kind reference updates descriptions and examples to reflect the latest code provisions of AISC, AASHTO, and AISI, as well as current loadings published by ASCE and adopted by the IBC (International Building Code). The text provides this essential data and demonstrates its application. This massive field manual for engineering professionals also includes the latest developments and trends in materials and methods. Handy tables, charts, formulas, and illustrations make decisions easier for both routine and exceptional structures. Each of the 15 chapters is the work of outstanding engineering experts. From bolted and welded connections to member selection for building floors and roofs, from plate girders and trusses to cablesuspended bridges, this essential guide gives you examples of leadingedge steel design. Easy to follow and use, the Structural Steel Designers Handbook is the tool of choice for both experienced engineers and those just launching their careers. UPDATED TO INCLUDE: AISC combined ASD and LRFD design standard for building frames AASHTO specifications, applicable to virtually all highway bridges AISI specifications for coldformed members, now in force all over North America ASCE07 gravity, seismic, and wind loads, now part of the IBC Alterations in the IBC ASTM material standards, for selection of shapes, plates, bridge steels, sheets, tubing, and cable 30 percent new or revised illustrations Numerous new examples Concentrated text, trimmed and focused on the newest design methods Full coverage of members and connections for buildings and bridges, fabrication and erection, welding and bolting, codes, structural theory and standards, and properties of materials THE TOOLKIT FOR STEEL DESIGN Properties of Structural Steels and Effects of Steelmaking and Fabrication Fabrication and Erection Connections Building Codes, Loads, and Fire Protection Criteria for Building Design Design of Building Members Floor and Roof Systems Lateral Force Design ColdFormed Steel Design Highway Bridge Design Criteria Railroad Bridge Design Criteria Beam and Girder Bridges Truss Bridges Arch Bridges CableSuspended Bridges About the Author Roger L. Brockenbrough (Pittsburgh, PA) is an engineering consultant working in the areas of product design and the development of technical information to facilitate improved steel designs. Formerly he was a Senior Research Consultant for U. S. Steel, involved in research studies on bridge girders (heat curving), pressure vessels, laminar imperfections, bolted connections (weathering steel), connections in HSS, corrugated metal pipe, and coldformed steel. He is the author of numerous technical papers, is the editor of two current McGrawHill books, Structural Steel Designers Handbook and Highway Engineering Handbook, and contributor to a third, Standard Handbook for Civil Engineers. He is a member of the AISC Specifications Committee (Chair of Subcommittee on Materials, Fabrication, and Inspection), Chair of the AISI Committee on Specifications for the Design of ColdFormed Steel Structural Members, member of the AASHTO Flexible Pipe Liaison Committee, member of the Transportation Research Board Committee on Subsurface SoilStructure Interaction, Chair of ASTM A05.17.2 section on Design and Installation of Corrugated Steel Pipe, and a Fellow and Life Member of ASCE. Frederick S. Merritt (deceased) was a consulting engineer for many years, with experience in building and bridge design, structural analysis, and construction management. A Fellow of the American Society of Civil Engineers and a Senior Member of ASTM, he was a former senior editor of Engineering NewsRecord and an authoreditor of many books, including McGrawHills Standard Handbook for Civil Engineers and Structural Steel Designers Handbook.
http://72.3.142.35/mghdxreader/jsp/FinalDisplay.jsp;jsessionid=a2xizE Cataloging-in-Publication Data is on file with the Library of Congress Copyright © 2006, 1999, 1994, 1972 by The McGraw-Hill Companies, Inc All rights reserved Printed in the United States of America Except as permitted under the United States Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a data base or retrieval system, without the prior written permission of the publisher DOC/DOC ISBN 0-07-143218-3 The sponsoring editor for this book was Larry S Hager, the editing supervisor was Stephen M Smith, and the production supervisor was Richard C Ruzycka It was set in Times Roman by International Typesetting and Composition The art director for the cover was Handel Low Printed and bound by RR Donnelley McGraw-Hill books are available at special quantity discounts to use as premiums and sales promotions, or for use in corporate training programs For more information, please write to the Director of Special Sales, McGraw-Hill Professional, Two Penn Plaza, New York, NY 10121-2298 Or contact your local bookstore This book is printed on acid-free paper Information contained in this work has been obtained by The McGraw-Hill Companies, Inc (“McGraw-Hill”), from sources believed to be reliable However, neither McGraw-Hill nor its authors guarantee the accuracy or completeness of any information published herein, and neither McGraw-Hill nor its authors shall be responsible for any errors, omissions, or damages arising out of use of this information This work is published with the understanding that McGraw-Hill and its authors are supplying information but are not attempting to render engineering or other professional services If such services are required, the assistance of an appropriate professional should be sought Copyright © 2006, 1999, 1994, 1972 by The McGraw-Hill Companies, Inc., McGRAW-HILL of 10/30/2007 4:21 PM Brockenbrough_Ch01.qxd 9/29/05 4:59 PM Page 1.1 Source: STRUCTURAL STEEL DESIGNER'S HANDBOOK CHAPTER PROPERTIES OF STRUCTURAL STEELS AND EFFECTS OF STEELMAKING AND FABRICATION Roger L Brockenbrough, P.E President R L Brockenbrough & Associates, Inc Pittsburgh, Pennsylvania This chapter presents and discusses the properties of structural steels that are of importance in design and construction Designers should be familiar with these properties so that they can select the most economical combination of suitable steels for each application and use the materials efficiently and safely In accordance with contemporary practice, the steels described in this chapter are given the names of the corresponding specifications of ASTM, 100 Barr Harbor Dr., West Conshohocken, PA 19428 For example, all steels covered by ASTM A588, “Specification for High-Strength Low-Alloy Structural Steel,” are called A588 steel Most of them can also be furnished to a metric designation such as A588M 1.1 STRUCTURAL STEEL SHAPES AND PLATES Steels for structural uses may be classified by chemical composition, tensile properties, and method of manufacture as carbon steels, high-strength low-alloy (HSLA) steels, heat-treated carbon steels, and heattreated constructional alloy steels A typical stress-strain curve for a steel in each classification is shown in Fig 1.1 to illustrate the increasing strength levels provided by the four classifications of steel The availability of this wide range of specified minimum strengths, as well as other material properties, enables the designer to select an economical material that will perform the required function for each application Some of the most widely used steels in each classification are listed in Table 1.1 with their specified strengths in shapes and plates These steels are weldable, but the welding materials and procedures for each steel must be in accordance with approved methods Welding information for each of the steels is available in publications of the American Welding Society 1.1.1 Carbon Steels A steel may be classified as a carbon steel if (1) the maximum content specified for alloying elements does not exceed the following: manganese—1.65%, silicon—0.60%, copper—0.60%; (2) the specified minimum for copper does not exceed 0.40%; and (3) no minimum content is specified for other elements added to obtain a desired alloying effect 1.1 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Brockenbrough_Ch01.qxd 9/29/05 4:59 PM Page 1.2 PROPERTIES OF STRUCTURAL STEELS AND EFFECTS OF STEELMAKING AND FABRICATION 1.2 CHAPTER ONE FIGURE 1.1 Typical stress-strain curves for structural steels (Curves have been modified to reflect minimum specified properties.) A36 steel has been the principal carbon steel for bridges, buildings, and many other structural uses This steel provides a minimum yield point of 36 ksi in all structural shapes and in plates up to in thick In structural steel framing for building construction, A36 steel has been largely replaced by the higher-strength A992 steel (Art 1.1.2) A529 is a carbon-manganese steel for general structural purposes, available in shapes and plates of a limited size range It can be furnished with a specified minimum yield point of either 50 ksi (Grade 50) or 55 ksi (Grade 55) A573, another carbon steel listed in Table 1.1, is available in three strength grades for plate applications in which improved notch toughness is important 1.1.2 High-Strength Low-Alloy Steels Those steels which have specified minimum yield points greater than 40 ksi and achieve that strength in the hot-rolled condition, rather than by heat treatment, are known as HSLA steels Because these steels offer increased strength at moderate increases in price over carbon steels, they are economical for a variety of applications A242 steel is a weathering steel, used where resistance to atmospheric corrosion is of primary importance Steels meeting this specification usually provide a resistance to atmospheric corrosion at least four times that of structural carbon steel However, when required, steels can be selected to provide a resistance to atmospheric corrosion of five to eight times that of structural carbon steels A specified minimum yield point of 50 ksi can be furnished in plates up to 3/4 in thick and the lighter structural shapes It is available with a lower yield point in thicker sections, as indicated in Table 1.1 A588 is the primary weathering steel for structural work It provides a 50-ksi yield point in plates up to in thick and in all structural sections; it is available with a lower yield point in thicker plates Several grades are included in the specification to permit use of various compositions developed by Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Brockenbrough_Ch01.qxd 9/29/05 4:59 PM Page 1.3 PROPERTIES OF STRUCTURAL STEELS AND EFFECTS OF STEELMAKING AND FABRICATION STRUCTURAL STEELS, STEELMAKING, AND FABRICATION 1.3 TABLE 1.1 Specified Minimum Properties for Structural Steel Shapes and Plates* Elongation, % ASTM designation A36 A529 Grade 50 Grade 55 A573 Grade 58 Grade 65 Grade 70 Structural shape flange or leg thickness range, in Plate thickness range, in Yield stress, ksi† Tensile strength, ksi† In in‡ In in maximum Over All All 36 32 58–80 58–80 23–21 23 20 20 maximum maximum 11/2 max 11/2 max 50 55 70–100 70–100 21 20 18 17 11/2 maximum 11/2 maximum 11/2 maximum ¶ ¶ ¶ 32 35 42 58–71 65–77 70–90 24 23 21 21 20 18 50 46 42 50 46 42 70 67 63 70 67 63 21 21 21 21 21 21 18 18 18 18 — — 42 50 55 60 65 50–65 60 65 70 75 80 65 24 21 20 18 17 21 20 18 17 16 15 18 High-strength low-alloy steels A242 A588 A572 Grade 42 Grade 50 Grade 55 Grade 60 Grade 65 A992 /4 maximum Over 3/4 to 11/2 max Over 11/2 to max maximum Over to max Over to max 11/2 max Over 11/2 to Over All All All maximum maximum maximum 11/4 maximum 11/4 maximum ¶ All All All max max All Heat-treated carbon and HSLA steels A633 Grade A Grade C, D Grade E A678 Grade A Grade B Grade C Grade D A852 A913 maximum 21/2 maximum Over 21/2 to max maximum Over to max ¶ ¶ ¶ ¶ ¶ 42 50 46 60 55 63–83 70–90 65–85 80–100 75–95 23 23 23 23 23 18 18 18 18 18 11/2 maximum 21/2 maximum /4 maximum Over 3/4 to 11/2 max Over 11/2 to max maximum maximum ¶ ¶ ¶ ¶ ¶ ¶ ¶ ¶ ¶ ¶ ¶ All All All All 50 60 75 70 65 75 70 50 60 65 70 70–90 80–100 95–115 90–110 85–105 90–110 90–110 65 75 80 90 22 22 19 19 19 18 19 21 18 17 16 — — — — — — — 18 16 15 14 (Continued) Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Brockenbrough_Ch01.qxd 9/29/05 4:59 PM Page 1.4 PROPERTIES OF STRUCTURAL STEELS AND EFFECTS OF STEELMAKING AND FABRICATION 1.4 CHAPTER ONE TABLE 1.1 Specified Minimum Properties for Structural Steel Shapes and Plates* (Continued) Elongation, % ASTM designation Structural shape flange or leg thickness range, in Plate thickness range, in Yield stress, ksi† Tensile strength, ksi† In in‡ In in 110–130 100–130 18 16 — — Heat-treated constructional alloy steels A514 /2 maximum Over 21/2 to max ¶ ¶ 100 90 *The following are approximate values for all the steels: Modulus of elasticity—29 × 103 ksi Shear modulus—11 × 103 ksi Poisson’s ratio—0.30 Yield stress in shear—0.57 times yield stress in tension Ultimate strength in shear—2/3 to 3/4 times tensile strength Coefficient of thermal expansion—6.5 × 10−6 in per in per °F for temperature range −50 to +150°F Density—490 lb/ft3 † Where two values are shown for yield stress or tensile strength, the first is minimum and the second is maximum ‡ The minimum elongation values are modified for some thicknesses in accordance with the specification for the steel Where two values are shown for the elongation in in, the first is for plates and the second for shapes ¶ Not applicable steel producers to obtain the specified properties This steel provides about four times the resistance to atmospheric corrosion of structural carbon steels These relative corrosion ratings are determined from the slopes of corrosion-time curves and are based on carbon steels not containing copper (The resistance of carbon steel to atmospheric corrosion can be doubled by specifying a minimum copper content of 0.20%.) Typical corrosion curves for several steels exposed to industrial atmosphere are shown in Fig 1.2 FIGURE 1.2 Corrosion curves for structural steels in an industrial atmosphere (From R L Brockenbrough and B G Johnston, USS Steel Design Manual, R L Brockenbrough & Associates, Inc., Pittsburgh, Pa., with permission.) Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Brockenbrough_Ch01.qxd 9/29/05 4:59 PM Page 1.5 PROPERTIES OF STRUCTURAL STEELS AND EFFECTS OF STEELMAKING AND FABRICATION STRUCTURAL STEELS, STEELMAKING, AND FABRICATION 1.5 For methods of estimating the atmospheric corrosion resistance of low-alloy steels based on their chemical composition, see ASTM Guide G101 The A588 specification requires that the resistance index calculated according to Guide 101 shall be 6.0 or higher A588 and A242 steels are called weathering steels because, when subjected to alternate wetting and drying in most bold atmospheric exposures, they develop a tight oxide layer that substantially inhibits further corrosion They are often used bare (unpainted) where the oxide finish that develops is desired for aesthetic reasons or for economy in maintenance Bridges and exposed building framing are typical examples of such applications Designers should investigate potential applications thoroughly, however, to determine whether a weathering steel will be suitable Information on baresteel applications is available from steel producers A572 specifies columbium-vanadium HSLA steels in five grades with minimum yield points of 42 to 65 ksi Grade 42 in thicknesses up to in and Grade 50 in thicknesses up to in are used for welded bridges All grades may be used for bolted construction and for welded construction in most applications other than bridges A992 steel, introduced in 1998, is now the main specification for rolled wide flange shapes for building framing All other hot-rolled shapes, such as channels and angles, can be furnished to A992 It provides a minimum yield point of 50 ksi, a maximum yield point of 65 ksi, and a maximum yield to tensile ratio of 0.85 These maximum limits are considered desirable attributes, particularly for seismic design To enhance weldability, a maximum carbon equivalent is also included, equal to 0.47% or 0.45%, depending on thickness A supplemental requirement can be specified for an average Charpy V-notch toughness of 40 ft ⋅ lb at 70°F 1.1.3 Heat-Treated Carbon and HSLA Steels Both carbon and HSLA steels can be heat treated to provide yield points in the range of 50 to 75 ksi This provides an intermediate strength level between the as-rolled HSLA steels and the heat-treated constructional alloy steels A633 is a normalized HSLA plate steel for applications where improved notch toughness is desired Available in four grades with different chemical compositions, the minimum yield point ranges from 42 to 60 ksi depending on grade and thickness A678 includes quenched-and-tempered plate steels (both carbon and HSLA compositions) with excellent notch toughness It is also available in four grades with different chemical compositions; the minimum yield point ranges from 50 to 75 ksi, depending on grade and thickness A852 is a quenched-and-tempered HSLA plate steel of the weathering type It is intended for welded bridges and buildings and similar applications where weight savings, durability, and good notch toughness are important It provides a minimum yield point of 70 ksi in thickness up to in The resistance to atmospheric corrosion is typically four times that of carbon steel A913 is a high-strength low-allow steel for structural shapes, produced by the quenching and selftempering (QST) process It is intended for the construction of buildings, bridges, and other structures Four grades provide a minimum yield point of 50 to 70 ksi Maximum carbon equivalents to enhance weldability are included as follows: Grade 50, 0.38%; Grade 60, 0.40%; Grade 65, 0.43%; and Grade 70, 0.45% Also, the steel must provide an average Charpy V-notch toughness of 40 ft ⋅ lb at 70°F 1.1.4 Heat-Treated Constructional Alloy Steels Steels that contain alloying elements in excess of the limits for carbon steel and are heat treated to obtain a combination of high strength and toughness are termed constructional alloy steels Having a yield strength of 100 ksi, these are the strongest steels in general structural use A514 includes several grades of quenched and tempered steels, to permit use of various compositions developed by producers to obtain the specified strengths Maximum thickness ranges from 11/4 to in depending on the grade Minimum yield strength for plate thicknesses over 21/2 in is 90 ksi Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Brockenbrough_Ch01.qxd 9/29/05 4:59 PM Page 1.6 PROPERTIES OF STRUCTURAL STEELS AND EFFECTS OF STEELMAKING AND FABRICATION 1.6 CHAPTER ONE Steels furnished to this specification can provide a resistance to atmospheric corrosion up to four times that of structural carbon steel depending on the grade Constructional alloy steels are also frequently selected because of their ability to resist abrasion For many types of abrasion, this resistance is related to hardness or tensile strength Therefore, constructional alloy steels may have nearly twice the resistance to abrasion provided by carbon steel Also available are numerous grades that have been heat treated to increase the hardness even more TABLE 1.2 Charpy V-Notch Toughness for A709 Bridge Steelsa Test temperature, °F Grade Maximum thickness, in, inclusive Joining/ fastening method Minimum average energy, ft ⋅ lb Zone Zone Zone Non-fracture-critical members 36T 50T,b 50WTb, 50ST 70WTc 100T, 100WT HPS50WT HPS50WT Mech./weld Mech./weld 15 15 70 40 10 to to 21/2 21/2 to 21/2 to 21/2 21/2 to 21/2 to 4 Mechanical Welded Mech./weld Mechanical Welded Mech./weld Mechanical Welded Mech./weld Mech./weld 15 20 20 20 25 25 25 35 20 25 70 40 10 50 20 −10 30 −30 10 −10 10 −10 10 −10 70 70 70 70 50 50 50 30 30 30 10 −10 40 40 40 40 20 20 20 0 10 −10 10 10 10 10 −10 −10 −10 −30 −30 NA 10 −10 Fracture-critical members 36F 50F,b 50WFb 70WFc 100F, 100WF HPS50WF HPS50WF 2 to to 21/2 21/2 to 21/2 to 21/2 21/2 to 21/2 to 4 Mech./weld.d Mech./weld.d Mechanicald Weldede Mech./weld.e Mechanicale Welded f Mech./weld.f Mechanicalf Weldedg Mech./weld Mech./weld 25 25 25 30 30 30 35 35 35 45 30 35 a Minimum service temperatures: Zone 1, 0°F; Zone 2, below to −30°F; Zone 3, below −30 to −60°F If yield strength exceeds 65 ksi, reduce test temperature by 15°F for each 10 ksi above 65 ksi c If yield strength exceeds 85 ksi, reduce test temperature by 15°F for each 10 ksi above 85 ksi d Minimum test value energy is 20 ft-lb e Minimum test value energy is 24 ft-lb f Minimum test value energy is 28 ft-lb g Minimum test value energy is 36 ft-lb b Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Brockenbrough_Ch01.qxd 9/29/05 4:59 PM Page 1.7 PROPERTIES OF STRUCTURAL STEELS AND EFFECTS OF STEELMAKING AND FABRICATION STRUCTURAL STEELS, STEELMAKING, AND FABRICATION 1.7 1.1.5 Bridge Steels Steels for application in bridges are covered by A709, which includes steel in several of the categories mentioned above Under this specification, grades 36, 50, 70, and 100 are steels with yield strengths of 36, 50, 70, and 100 ksi, respectively Similar AASHTO grades are designated M270 The grade designation is followed by the letter W, indicating whether ordinary or high atmospheric corrosion resistance is required An additional letter, T or F, indicates that Charpy V-notch impact tests must be conducted on the steel The T designation indicates that the material is to be used in a non-fracture-critical application as defined by AASHTO; the F indicates use in a fracturecritical application There is also a Grade 50S, where the S indicates the steel must be killed A trailing numeral, 1, 2, or 3, indicates the testing zone, which relates to the lowest ambient temperature expected at the bridge site (See Table 1.2.) As indicated by the first footnote in the table, the service temperature for each zone is considerably less than the Charpy V-notch impact-test temperature This accounts for the fact that the dynamic loading rate in the impact test is more severe than that to which the structure is subjected The toughness requirements depend on fracture criticality, grade, thickness, and method of connection High-performance steels (HPS) are the newest additions to the family of bridge steels They are being used increasingly to improve reliability and reduce cost, with approximately 200 bridges in service in 2005 The initial grade, HPS70W, with a specified minimum yield stress of stress of 70 ksi, has been used most HPS50W, with a specified minimum yield stress of 50 ksi, has also become popular HPS100W, with a specified minimum yield stress of stress of 100 ksi, is available to reduce thickness where members are highly loaded 1.2 STEEL-QUALITY DESIGNATIONS Steel plates, shapes, sheetpiling, and bars for structural uses—such as the load-carrying members in buildings, bridges, ships, and other structures—are usually ordered to the requirements of ASTM A6 and are referred to as structural-quality steels (A6 does not indicate a specific steel.) This specification contains general requirements for delivery related to chemical analysis, permissible variations in dimensions and weight, permissible imperfections, conditioning, marking and tension and bend tests of a large group of structural steels (Specific requirements for the chemical composition and tensile properties of these steels are included in the specifications discussed in Art 1.1.) All the steels included in Table 1.1 are structural-quality steels Steel plates for pressure vessels are usually furnished to the general requirements of ASTM A20 and are referred to as pressure-vessel-quality steels Generally, a greater number of mechanicalproperty tests and additional processing are required for pressure-vessel-quality steel 1.3 STEEL SHEET AND STRIP FOR STRUCTURAL APPLICATIONS Steel sheet and strip are used for many structural applications, particularly for cold-formed structural members for residential and light commercial building construction (Chap 9) The facade of many high-rise structures is supported by cold-formed sheet steel systems and interior partitions are often built with steel C-sections The stressed skin of transportation equipment is another application of such material Tensile properties of several sheet steels are presented in Table 1.3 Many of them are available in several strength levels, with a specified minimum yield point from 25 to 80 ksi Some grades may not be suitable for all applications, depending on the ratio of tensile strength to yield point and other considerations (Chap 9) ASTM A606 covers high-strength low-alloy, hot- and cold-rolled steel sheet and strip with enhanced corrosion resistance This material, available in cut lengths or coils, is intended for structural and other uses where savings in weight and improved durability are important It may be ordered as Type or Type 4, with atmospheric corrosion resistance approximately two or four times, Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Brockenbrough_Ch01.qxd 9/29/05 4:59 PM Page 1.8 PROPERTIES OF STRUCTURAL STEELS AND EFFECTS OF STEELMAKING AND FABRICATION 1.8 CHAPTER ONE TABLE 1.3 Specified Minimum Mechanical Properties for Steel Sheet and Strip for Structural Applications ASTM designation Type of product A606 Hot rolled (as rolled) Hot rolled (annealed or normalized) Cold rolled Grade Yield point, ksi Tensile strength, ksi Elongation in in, %a Fu /Fy — 50 70 22 1.40 — 45 65 22 1.44 — 45 65 22 1.44 A653b Galvanized or galvannealed SS 33 SS 37 SS 40 SS 50, Cl SS 50, Cl SS 80 HSLAS 40 HSLAS 50 HSLAS 60 HSLAS 70 HSLAS 80 33 37 40 50 50 80 40 50 60 70 80 45 52 55 65 70 82 50 60 70 80 90 20 18 16 12 12 — 22–24 20–22 16–18 12–14 10–12 1.36 1.41 1.38 1.30 1.40 1.03 1.25 1.20 1.17 1.14 1.12 A792 55% aluminum-zinc alloy coated SS 33 SS 37 SS 40 SS 50, Cl SS 50, Cl SS 80 33 37 40 50 50 80 45 52 55 65 60 82 20 18 16 12 12 — 1.36 1.41 1.38 1.30 1.20 1.03 A1003 Sheet for framing members ST33H ST37H ST40H ST50H ST33L ST37L ST40L ST50L 33 37 40 50 33 37 40 50 — — — — — — — — 10 10 10 10 3 3 1.08c 1.08c 1.08c 1.08c — — — — A1008 Cold rolled SS 25 SS 30 SS 33, Type SS 33, Type SS 40, Type SS 40, Type SS 80 HSLAS 45, Cl HSLAS 50, Cl HSLAS 55, Cl HSLAS 60, Cl HSLAS 65, Cl HSLAS 70, Cl HSLAS 45, Cl HSLAS 50, Cl HSLAS 55, Cl HSLAS 60, Cl HSLAS 65, Cl HSLAS 70, Cl HSLAS-F 50 25 30 33 33 40 40 80 45 50 55 60 65 70 45 50 55 60 65 70 50 42 45 48 48 52 52 82 60 65 70 75 80 85 55 60 65 70 75 80 60 26 24 22 22 20 20 — 22 20 18 16 15 14 22 20 18 16 15 14 22 1.68 1.50 1.45 1.45 1.30 1.30 1.03 1.33 1.30 1.27 1.25 1.23 1.21 1.22 1.20 1.18 1.17 1.15 1.14 1.20 (Continued) Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Brockenbrough_Ch15.qxd 9/29/05 5:43 PM Page 15.78 CABLE-SUSPENDED BRIDGES 15.78 CHAPTER FIFTEEN Mi = W − ξx W e (cos ξx − sin ξx ) = ηm 4ξ 4ξ (15.56) where ηm = e − ξx (cos ξx + sin ξx ) (W Podolny, Jr., and J B Scalzi, Construction and Design of Cable-Stayed Bridges, 2d ed., John Wiley & Sons, Inc., New York.) 15.17 AERODYNAMIC ANALYSIS OF CABLE-SUSPENDED BRIDGES The wind-induced failure on November 7, 1940, of the Tacoma Narrows Bridge in the state of Washington shocked the engineering profession Many were surprised to learn that failure of bridges as a result of wind action was not unprecedented During the slightly more than 12 decades prior to the Tacoma Narrows failure, 10 other bridges were severely damaged or destroyed by wind action (Table 15.12) As can be seen from Table 15.12a, wind-induced failures have occurred in bridges with spans as short as 245 ft up to 2800 ft Other “modern” cable-suspended bridges have been observed to have undesirable oscillations due to wind (Table 15.12b) 15.17.1 Required Information on Wind at Bridge Site Prior to undertaking any studies of wind instability for a bridge, engineers should investigate the wind environment at the site of the structure Required information includes the character of strong TABLE 15.12 Long-Span Bridges Adversely Affected by Wind (a) Severely damaged or destroyed Bridge Dryburgh Abbey Union Nassau Brighton Chain Pier Montrose Menai Straits Roche-Bernard Wheeling Niagara–Lewiston Niagara–Clifton Tacoma Narrows I Location Scotland England Germany England Scotland Wales France USA USA USA USA Designer Span, ft John and William Smith Sir Samuel Brown Lossen and Wolf Sir Samuel Brown Sir Samuel Brown Thomas Telford Le Blanc Charles Ellet Edward Serrell Samuuel Keffer Leon Moisseiff Failure date 260 449 245 255 432 580 641 1010 1041 1260 2800 1818 1821 1834 1836 1838 1839 1852 1854 1864 1889 1940 (b) Oscillated violently in wind Bridge Fyksesund Golden Gate Thousand Island Deer Isle Bronx–Whitestone Long’s Creek Location Year built Span, ft Norway USA USA USA USA Canada 1937 1937 1938 1939 1939 1967 750 4200 800 1080 2300 713 Type of stiffening Rolled I beam Truss Plate girder Plate girder Plate girder Plate girder Source: After F B Farquharson et al., “Aerodynamic Stability of Suspension Bridges,” University of Washington Bulletin 116, parts I through V, 1949–1954 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Brockenbrough_Ch15.qxd 9/29/05 5:43 PM Page 15.79 CABLE-SUSPENDED BRIDGES CABLE-SUSPENDED BRIDGES 15.79 wind activity at the site over a period of years Data are generally obtainable from local weather records and from meteorological records of the U.S Weather Bureau However, caution should be used, because these records may have been attained at a point some distance from the site, such as the local airport or federal building Engineers should also be aware of differences in terrain features between the wind instrumentation site and the structure site that may have an important bearing on data interpretation Data required are wind velocity, direction, and frequency From these data, it is possible to predict high wind speeds, expected wind direction, and probability of occurrence The aerodynamic forces that wind applies to a bridge depend on the velocity and direction of the wind and on the size, shape, and motion of the bridge Whether resonance will occur under wind forces depends on the same factors The amplitude of oscillation that may build up depends on the strength of the wind forces (including their variation with amplitude of bridge oscillation), the energystorage capacity of the structure, the structural damping, and the duration of a wind capable of exciting motion The wind velocity and direction, including vertical angle, can be determined by extended observations at the site They can be approximated with reasonable conservatism on the basis of a few local observations and extended study of more general data The choice of the wind conditions for which a given bridge should be designed may always be largely a matter of judgment At the start of aerodynamic analysis, the size and shape of the bridge are known Its energy-storage capacity and its motion, consisting essentially of natural modes of vibration, are determined completely by its mass, mass distribution, and elastic properties and can be computed by reliable methods The only unknown element is that factor relating the wind to the bridge section and its motion This factor cannot, at present, be generalized but is subject to reliable determination in each case Properties of the bridge, including its elastic forces and its mass and motions (determining its inertial forces), can be computed and reduced to model scale Then, wind conditions bracketing all probable conditions at the site can be imposed on a section model The motions of such a dynamic section model in the properly scaled wind should duplicate reliably the motions of a convenient unit length of the bridge The wind forces and the rate at which they can build up energy of oscillation respond to the changing amplitude of the motion The rate of energy change can be measured and plotted against amplitude Thus, the section-model test measures the one unknown factor, which can then be applied by calculation to the variable amplitude of motion along the bridge to predict the full behavior of the structure under the specific wind conditions of the test These predictions are not precise but are about as accurate as some other features of the structural analysis 15.17.2 Criteria for Aerodynamic Design Because the factors relating bridge movement to wind conditions depend on specific site and bridge conditions, detailed criteria for the design of favorable bridge sections cannot be written until a large mass of data applicable to the structure being designed has been accumulated But, in general, the following criteria for suspension bridges may be used A truss-stiffened section is more favorable than a girder-stiffened section Deck slots and other devices that tend to break up the uniformity of wind action are likely to be favorable The use of two planes of lateral system to form a four-sided stiffening truss is desirable because it can favorably affect torsional motion Such a design strongly inhibits flutter and also raises the critical velocity of a pure torsional motion For a given bridge section, a high natural frequency of vibration is usually favorable: • For short to moderate spans, a useful increase in frequency, if needed, can be attained by increased truss stiffness (Although not closely defined, moderate spans may be regarded as including lengths from about 1000 to about 1800 ft.) • For long spans, it is not economically feasible to obtain any material increase in natural frequency of vertical modes above that inherent in the span and sag of the cable Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Brockenbrough_Ch15.qxd 9/29/05 5:43 PM Page 15.80 CABLE-SUSPENDED BRIDGES 15.80 CHAPTER FIFTEEN • The possibility should be considered that for longer spans in the future, with their unavoidably low natural frequencies, oscillations due to unfavorable aerodynamic characteristics of the cross section may be more prevalent than for bridges of moderate span At most bridge sites, the wind may be broken up; that is, it may be nonuniform across the site, unsteady, and turbulent So a condition that could cause serious oscillation does not continue long enough to build up an objectionable amplitude However, bear in mind: • There are undoubtedly sites where the winds from some directions are unusually steady and uniform • There are bridge sections on which any wind, over a wide range of velocity, will continue to build up some mode of oscillation An increase in stiffness arising from increased weight increases the energy-storage capacity of the structure without increasing the rate at which the wind can contribute energy The effect is an increase in the time required to build up an objectionable amplitude This may have a beneficial effect much greater than is suggested by the percentage increase in weight, because of the sharply reduced probability that the wind will continue unchanged for the greater length of time Increased stiffness may give added structural damping and other favorable results Although more specific design criteria than the above cannot be given, it is possible to design a suspension bridge with a high degree of security against aerodynamic forces This involves calculation of natural modes of motion of the proposed structure, section design with an effort to separate first vertical and torsional modes by at least a factor of 2, performance of dynamic-section-model tests to determine the factors affecting behavior, and application of these factors to the prototype by suitable analysis Most long-span bridges built since the Tacoma Bridge failure have followed the above procedures and incorporated special provisions in the design for aerodynamic effects Designers of these bridges usually have favored stiffening trusses over girders The second Tacoma Narrows, Forth Road, and Mackinac Straits bridges, for example, incorporate deep stiffening trusses with both top and bottom bracing, constituting a torsion space truss The Forth Road and Mackinac Straits bridges have slotted decks The Severn Bridge, however, has a streamlined, closed-box stiffening girder and inclined suspenders Some designs incorporate longitudinal cable stays, tower stays, or even transverse diagonal stays (Deer Isle Bridge) Some have unloaded backstays Others endeavor to increase structural damping by frictional or viscous means All have included dynamic-model studies as part of the design 15.17.3 Wind-Induced Oscillation Theories Several theories have been advanced as models for mathematical analysis to develop an understanding of the process of wind excitation Among these are the following Negative-Slope Theory When a bridge is moving downward while a horizontal wind is blowing (Fig 15.61a), the resultant wind is angled upward (positive angle of attack) relative to the bridge If the lift coefficient CL, as measured in static tests, shows a variation with wind angle α such as that illustrated by curve A in Fig 15.61b, then, for moderate amplitudes, there is a wind force acting downward on the bridge while the bridge is moving downward The bridge will therefore move to a greater amplitude than it would without this wind force The motion will, however, be halted and reversed by the action of the elastic forces Then, the vertical component of the wind also reverses The angle of attack becomes negative, and the lift becomes positive, tending to increase the amplitude of the rebound With increasing velocity, the amplitude will increase indefinitely or until the bridge is destroyed A similar, though more complicated situation, would apply for torsional or twisting motion of the bridge Vortex Theory This attributes aerodynamic excitation to the action of periodic forces having a certain degree of resonance with a natural mode of vibration of the bridge Vortices, which form around the trailing edge of the airfoil (bridge deck), are shed on alternating sides, giving rise to periodic forces and oscillations transverse to the deck Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Brockenbrough_Ch15.qxd 9/29/05 5:43 PM Page 15.81 CABLE-SUSPENDED BRIDGES CABLE-SUSPENDED BRIDGES 15.81 FIGURE 15.61 Wind action on a cable-stayed bridge (a) Downward bridge motion develops upward wind component (b) Lift coefficient CL depends on angle of attack α of the wind Flutter Theory The phenomenon of flutter, as developed for airfoils of aircraft and applied to suspension-bridge decks, relates to the fact that the airfoil (bridge deck) is supported so that it can move elastically in a vertical direction and in torsion, about a longitudinal axis Wind causes a lift that acts eccentrically This causes a twisting moment, which, in turn, alters the angle of attack and increases the lift The chain reaction becomes catastrophic if the vertical and torsional motions can take place at the same coupled frequency and in appropriate phase relation F Bleich presented tables for calculation of flutter speed vF for a given bridge, based on flat-plate airfoil flutter theory These tables are applicable principally to trusses But the tables are difficult to apply, and there is some uncertainty as to their range of validity A Selberg has presented the following formula for flutter speed: 2 ω v vF = 0.88ω b 1 − ω µ (15.57) where v = mass distribution factor for specific section = 2r2/b2 (varies between 0.6 and 1.5, averaging about 1) µ = 2πρb2/m (ranges between 0.01 and 0.12) m = mass per unit length b = half width of bridge ρ = mass density of air ω1 = circular vertical frequency ω1 = circular torsional frequency r = mass radius of gyration Selberg has also published charts, based on tests, from which it is possible to approximate the critical wind speed for any type of cross section in terms of the flutter speed Applicability of Theories The vortex and flutter theories apply to the behavior of suspension bridges under wind action Flutter appears dominant for truss-stiffened bridges, whereas vortex action seems to prevail for girder-stiffened bridges There are mounting indications, however, these are, at best, estimates of aerodynamic behavior Much work has been done and is being done, particularly in the spectrum approach and the effects of nonuniform, turbulent winds 15.17.4 Design Indices Bridge engineers have suggested several criteria for practical design purposes O H Ammann, for example, developed two analytical-empirical indices that were applied in the design of the VerrazanoNarrows Bridge, a vertical-stiffness index and a torsional-stiffness index Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Brockenbrough_Ch15.qxd 9/29/05 5:43 PM Page 15.82 CABLE-SUSPENDED BRIDGES 15.82 CHAPTER FIFTEEN Vertical-Stiffness Index Sv This is based on the magnitude of the vertical deflection of the suspension system under a static downward load covering one-half the center span The index includes a correction to allow for the effect of structural damping of the suspended structure and for the effect of different ratios of side span to center span W I L Sv = 8.2 + 0.14 1 − 0.6 f L L (15.58) where W = weight of bridge, lb/lin ft f = cable sag, ft I = moment of inertia of stiffening trusses and continuous stringers, in2 by ft2 L = length of center span, in thousands of feet L1 = length of side span, in thousands of feet Torsional-Stiffness Index St This is defined as the maximum intensity of sinusoidal loads, of opposite sign in opposite planes of cables, on the center span and producing 1-ft deflections at quarter points of the main span This motion simulates deformations similar to those in the first asymmetric mode of torsional oscillations π2 W B St = + 1 A f where A = B= (15.59) b Hw E 2bd ( AvUv AhUh ) (b/d ) AvUv + ( d/b) AhUh W = weight of bridge, lb/lin ft f = cable sag, ft Hw = horizontal component of cable load due to dead load (half bridge), kips b = distance between centerlines of cables, or centerlines of pairs of cables, ft d = vertical distance between top and bottom planes of lateral bracing, ft E = modulus of elasticity of truss steel, ksf Av = area of the diagonals in one panel of vertical truss, ft2 Ah = area of the diagonals in one panel of horizontal lateral bracing (two members for X or K bracing), ft2 Uv = sin2 γv cos γv Uh = sin2 γh cos γh γh = angle between diagonals and chord of horizontal truss γv = angle between diagonals and chord of vertical truss Typical values of these indices are listed in Table 15.13 for several bridges Other indices and criteria have been published by D B Steinman In connection with these, Steinman also proposed that, unless aerodynamic stability is otherwise assured, the depth, ft, of stiffening girders and stiffening trusses should be at least L/120 + (L/1000)2, where L is the span, ft Furthermore, EI of the stiffening system should be at least bL4 /120 f , where b is the width, ft, of the bridge and f the cable sag, ft 15.17.5 Natural Frequencies of Suspension Bridges Dynamic analyses require knowledge of the natural frequencies of free vibration, modes of motion, energy-storage relationships, magnitude and effects of damping, and other factors Two types of vibration must be considered: bending and torsion Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website 1,215 650 650 1,125 1,125 1,100 4,260 3,500 3,500 4,200 4,200 2,800 L1, ft 232 475 475 326 319 390 f, ft 5,700 22,800+ 21,300 40,000 28,570 36,650 W, lb/ft 2,567 88,000 88,000 66,000 168 180,000 I, in2 ft2 39 90 90 106 106 101.25 b, ft — 25 — 30 — 24 d, ft — 51.3 — 126.5 — 130.8 A, ft4 — 75.5 — 163.7 — 144.5 B, ft4 158 364 342 950 654 702 8.0 5.6 5.6 6.7 6.7 6.2 Frequency, cycles per 61 292 111 694 221 448 Stiffness index 10.0 11.0 7.0 13.2 8.2 11.9 Frequency, cycles per Torsional motions 5:43 PM Source: From M Brumer, H Rothman, M Fiegen, and B Forsyth, “Verrazano-Narrows Bridge: Design of Superstructure,” Journal of the Construction Division, vol 92, no CO2, March 1966, American Society of Civil Engineers Verrazano-Narrows Bridge George Washington Bridge, 8-lane single deck complete George Washington Bridge, 14-lane double deck complete Golden Gate Bridge with upper lateral system only Golden Gate Bridge with double lateral system Tacoma Narrows original with 2-lane single deck (very unfavorable aerodynamic characteristics) L, ft Stiffness index Vertical motions 9/29/05 Bridge Structural parameters TABLE 15.13 Stiffness Indices and First Asymmetric Mode Natural Frequencies Brockenbrough_Ch15.qxd Page 15.83 CABLE-SUSPENDED BRIDGES 15.83 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Brockenbrough_Ch15.qxd 9/29/05 5:43 PM Page 15.84 CABLE-SUSPENDED BRIDGES 15.84 CHAPTER FIFTEEN Bending The fundamental differential equation [Eq (15.22)] and cable condition [Eq (15.26)] of the suspension bridge in Fig 15.41 can be transformed into EIη′′′′ − Hη′′ = ω mη + H p y ′′ H p Lc Ec Ac L + y ′′ ∫ η dx = (15.60) (15.61) where ω = circular natural frequency of the bridge η = deflection of stiffening truss or girder m = bridge mass = w/g y = vertical distance from cable to the line through the pylon supports w = dead load, lb per lin ft g = acceleration due to gravity = 32.2 ft/s2 From these equations, the basic Rayleigh energy equation for bending vibrations can be derived: ∫ EIη′′2 dx + H ∫ η′ dx + ( Ec Ac y ′′ ∫ η dx Lc ) = ω ∫ m η2 dx (15.62) Symbols are defined in “Torsion,” following After ω has been determined from this, the natural frequency of the bridge ω/2π, Hz, can be computed Torsion The Rayleigh energy equations for torsion are ( b2 H Ec Ac ECs ∫ φ′′ dx + GIT + y ′′b ∫ φ dx φ′ dx + ∫ Lc ) + EI y yM ∫ η′′ φ′′dx = ω I p ∫ φ2 dx EI y yM ∫ φ′′η′′dx + EI y ∫ η′′ dx = ω m ∫ η2 dx (15.63) (15.64) where φ = angle of twist, rad E = modulus of elasticity of stiffening girder, ksf G = modulus of rigidity of stiffening girder, ksf IT = polar moment of inertia of stiffening girder cross section, ft4 Ip = mass moment of inertia of stiffening girder per unit of length, kips ⋅s2 Iv = moment of inertia of stiffening girder about its vertical axis, ft4 Cs = warping resistance of stiffening girder relative to its center of gravity, ft6 b = horizontal distance between cables, ft H = horizontal component of cable tension, kips Ac = cross-sectional area of cable, ft2 Ec = modulus of elasticity of cable, ksf Lc = ∫ sec3 adx a = angle cable makes with horizontal, radians yM = ordinate of center of twist relative to the center of gravity of stiffening girder cross, section, ft ω = circular frequency, rad/sec m = m(x) = mass of stiffening girder per unit of length, kips ⋅ s2/ft2 Solution of these equations for the natural frequencies and modes of motion is dependent on the various possible static forms of suspension bridges involved (see Fig 15.9) Numerous lengthy tabulations of solutions have been published Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Brockenbrough_Ch15.qxd 9/29/05 5:43 PM Page 15.85 CABLE-SUSPENDED BRIDGES CABLE-SUSPENDED BRIDGES 15.85 15.17.6 Damping Damping is of great importance in lessening of wind effects It is responsible for dissipation of energy imparted to a vibrating structure by exciting forces When damping occurs, one part of the external energy is transformed into molecular energy, and another part is transmitted to surrounding objects or the atmosphere Damping may be internal, due to elastic hysteresis of the material or plastic yielding and friction in joints, or Coulomb (dry friction), or atmospheric, due to air resistance 15.17.7 Aerodynamics of Cable-Stayed Bridges The aerodynamic action of cable-stayed bridges is less severe than that of suspension bridges, because of increased stiffness due to the taut cables and the widespread use of torsion box decks However, there is a trend towards the use of the composite steel-concrete superstructure girders (Fig 15.16) for increasingly longer spans and to reduce girder dead weight This configuration, because of the long spans and decreased mass, can be relatively more sensitive to aerodynamic effects as compared to a torsionally stiff box 15.17.8 Stability Investigations It is most important to note that the validation of stability of the completed structure for expected wind speeds at the site is mandatory However, this does not necessarily imply that the most critical stability condition of the structure occurs when the structure is fully completed A more dangerous condition may occur during erection, when the joints have not been fully connected and, therefore, full stiffness of the structure has not yet been realized In the erection stage, the frequencies are lower than in the final condition and the ratio of torsional frequency to flexural frequency may approach unity Various stages of the partly erected structure may be more critical than the completed bridge The use of welded components in pylons has contributed to their susceptibility to vibration during erection Because no exact analytical procedures are yet available, wind-tunnel tests should be used to evaluate the aerodynamic characteristics of the cross section of a proposed deck girder, pylon, or total bridge More importantly, the wind-tunnel tests should be used during the design process to evaluate the performance of a number of proposed cross sections for a particular project In this manner, the wind-tunnel investigations become a part of the design decision process and not a postconstruction corrective action If the wind-tunnel evaluations are used as an after-the-fact verification and they indicate an instability, there is the distinct risk that a redesign of a retrofit design will be required that will have undesirable ramifications on schedules and availability of funding (F Bleich and L W Teller, “Structural Damping in Suspension Bridges,” ASCE Transactions, vol 117, pp 165–203, 1952; F Bleich, C B McCullough, R Rosecrans, and G S Vincent, “The Mathematical Theory of Vibration of Suspension Bridges,” Bureau of Public Roads, Government Printing Office, Washington, D.C; F B Farquharson, “Wind Forces on Structures Subject to Oscillation,” ASCE Proceedings, ST4, July, 1958; A Selberg, “Oscillation and Aerodynamic Stability of Suspension Bridges,” Acta Polytechnia Scandinavica, Civil Engineering and Construction Series 13, Trondheim, 1961; D B Steinman, “Modes and Natural Frequencies of Suspension Bridge Oscillations,” Transactions Engineering Institute of Canada, vol 3, no 2, pp 74–83, 1959; D B Steinman, “Aerodynamic Theory of Bridge Oscillations,” ASCE Transactions, vol 115, pp 1180–1260, 1950; D B Steinman, “Rigidity and Aerodynamic Stability of Suspension Bridges,” ASCE Transactions, vol 110, pp 439–580, 1945; “Aerodynamic Stability of Suspension Bridges,” 1952 Report of the Advisory Board on the Investigation of Suspension Bridges, ASCE Transactions, vol 120, pp 721–781, 1955; R L Wardlaw, “A Review of the Aerodynamics of Bridge Road Decks and the Role of Wind Tunnel Investigation,” U S Department of Transportation, Federal Highway Administration, Report No FHWA-RD-72-76; A G Davenport, “Buffeting of a Suspension Bridge by Storm Winds,” ASCE Journal of the Structural Division, vol 115, ST3, June 1962; “Guidelines for Design of Cable-Stayed Bridges,” ASCE Committee on Cable-Stayed Bridges; W Podolony, Jr., and J B Scalzi, Construction and Design of Cable-Stayed Bridges, Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Brockenbrough_Ch15.qxd 9/29/05 5:43 PM Page 15.86 CABLE-SUSPENDED BRIDGES 15.86 CHAPTER FIFTEEN 2d ed., John Wiley & Sons, Inc., New York; E Murakami and T Okubu, “Wind-Resistant Design of a Cable-stayed Bridge,” International Association for Bridge and Structural Engineering, Final Report, 8th Congress, New York, September 9–14, 1968.) 15.17.9 Rain-Wind–Induced Vibration Well-known mechanisms of cable vibration are vortex and wake galloping Starting in approximately the mid-1980s, a new phenomenon of cable vibration has been observed that occurs during the simultaneous presence of rain and wind; thus, it is given the name “rain-wind vibration,” or rain vibration The excitation mechanism is the formation of water rivulets, at the top and bottom, that run down the cable oscillating tangentially as the cables vibrate, thus changing the aerodynamic profile of the cable (or the enclosing HDPE pipe) The formation of the upper rivulet appears to be the more dominant factor in the origin of the rain-wind vibration In the current state of the art, three basic methods of rain-wind vibration suppression are being considered or used: • Rope ties interconnecting the cable stays in the plane of the stays, Fig 15.62a • Modification of the external surface of the enclosing HDPE pipe, Fig 15.62b • Providing external damping FIGURE 15.62 Methods of rain-wind vibration suppression (a) Rope ties (b) Modification of external surface Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Brockenbrough_Ch15.qxd 9/29/05 5:43 PM Page 15.87 CABLE-SUSPENDED BRIDGES CABLE-SUSPENDED BRIDGES 15.87 The interconnection of stays by rope ties produces node points at the point of connection of the secondary tie to the cable stays The purpose is to shorten the free length of the stay and modify the natural frequency of vibration of the stay The modification of the surface may be such as protuberances that are axial, helical, elliptical or circular or grooves or dimples The intent is to discourage the formation of the rivulets and/or its oscillations Various types of dampers such as viscous, hydraulic, tuned mass, and rubber have also been used to suppress the vibration The rain-wind vibration phenomenon has been observed during construction prior to grout injection which then stabilizes after grout injection This may be as a result of the difference in mass prior to and after grout injection (or not) It also has been noticed that the rain-wind vibration may not manifest itself until some time after completion of the bridge This may be the result of a transition from initial smoothness of the external pipe to a roughness, sufficient to hold the rivulet, resulting from an environmental or atmospheric degradation of the surface of the pipe The interaction of the various parameters in the rain-wind phenomenon is not yet well understood and an optimum solution is not yet available It should also be noted that under similar conditions of rain and wind, the hangars of arch bridges and suspenders of suspension bridges can also vibrate (Hikami, Y., and Shiraishi, N., “Rain-Wind Induced Vibrations of Cable in Cable Stayed Bridges,” Journal of Wind Engineering and Industrial Aerodynamics, 29 (1988), pp 409–418, Elsevier Science Publishers B V., Amsterdam; Matsumoto, M., Shiraishi, N., Kitazawa, M., Knisely, C., Shirato, H., Kim, Y and Tsujii, M., “Aerodynamic Behavior of Inclined Circular Cylinders—Cable Aerodynamics,” Journal of Wind Engineering (Japan), no 37, October 1988, pp 103–112; Matsumoto, M., Yokoyama, K., Miyata, T., Fujno, Y and Yamaguchi, H., “Wind-Induced Cable Vibration of Cable-Stayed Bridges in Japan,” Proc of Canada-Japan Workshop on Bridge Aerodynamics, Ottawa, 1989, pp 101–110; Matsumoto, M., Hikami, Y and Kitazawa, M., “Cable Vibration and its Aerodynamic/Mechanical Control,” Proc Cable-Stayed and Suspension Bridges, Deauville, France, October 12–15, 1994, vol 2, pp 439–452; Miyata, T., Yamada, H and Hojo, T., “Aerodynamic Response of PE Stay Cables with Pattern-Indented Surface,” Proc Cable-Stayed and Suspension Bridges, Deauville, France, October 12–15, 1994, vol 2, pp 515–522 15.18 SEISMIC ANALYSIS OF CABLE-SUSPENDED STRUCTURES For short-span structures (under about 500 ft) it is commonly assumed in seismic analysis that the same ground motion acts simultaneously throughout the length of the structure In other words, the wavelength of the ground waves are long in comparison to the length of the structure In long-span structures, such as suspension or cable-stayed bridges, however, the structure could be subjected to different motions at each of its foundations Hence, in assessment of the dynamic response of long structures, the effects of traveling seismic waves should be considered Seismic disturbances of piers and anchorages may be different at one end of a long bridge than at the other The character or quality of two or more inputs into the total structure, their similarities, differences, and phasings, should be evaluated in dynamic studies of the bridge response Vibrations of cable-stayed bridges, unlike those of suspension bridges, are susceptible to a unique class of vibration problems Cable-stayed bridge vibrations cannot be categorized as vertical (bending), lateral (sway), and torsional; almost every mode of vibration is instead a threedimensional motion Vertical vibrations, for example, are introduced by both longitudinal and lateral shaking in addition to vertical excitation In addition, an understanding is needed of the multimodal contribution to the final response of the structure and in providing representative values of the response quantities Also, because of the long spans of such structures, it is necessary to formulate a dynamic response analysis resulting from the multi-support excitation A threedimensional analysis of the whole structure and substructure to obtain the natural frequencies and seismic response is advisable A qualified specialist should be consulted to evaluate the earthquake response of the structure Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Brockenbrough_Ch15.qxd 9/29/05 5:43 PM Page 15.88 CABLE-SUSPENDED BRIDGES 15.88 CHAPTER FIFTEEN (“Guide Specifications for Seismic Design of Highway Bridges,” American Association of State Highway and Transportation Officials; “Guidelines for the Design of Cable-Stayed Bridges,” ASCE Committee on Cable-Stayed Bridges; A M Abdel-Ghaffar, and L I Rubin, “Multiple-Support Excitations of Suspension Bridges,” Journal of the Engineering Mechanics Division, ASCE, vol 108, no EM2, April, 1982; A M Abdel-Ghaffar, and L I Rubin, “Vertical Seismic Behavior of Suspension Bridges,” The International Journal of Earthquake Engineering and Structural Dynamics, vol 11, January–February, 1983; A M Abdel-Ghaffar, and L I Rubin, “Lateral Earthquake Response of Suspension Bridges,” Journal of the Structural Division, ASCE, vol 109, no ST3, March, 1983; A M Abdel-Ghaffar, and J D Rood, “Simplified Earthquake Analysis of Suspension Bridge Towers,” Journal of the Engineering Mechanics Division, ASCE, vol 108, no EM2, April, 1982.) 15.19 ERECTION OF CABLE-SUSPENDED BRIDGES The ease of erection of suspension bridges is a major factor in their use for long spans Once the main cables are in position, they furnish a stable working base or platform from which the deck and stiffening truss sections can be raised from floating barges or other equipment below, without the need for auxiliary falsework For the Severn Bridge, for example, 60-ft box-girder deck sections were floated to the site and lifted by equipment supported on the cables Until the 1960s, the field process of laying the main cables had been by spinning (Art 15.8.3) (This term is actually a misnomer, for the wires are neither twisted nor braided, but are laid parallel to and against each other.) The procedure (Fig 15.63) starts with the hanging of a catwalk at each cable location for use in construction of the bridge An overhead cableway is then installed above each catwalk Loops of wire (two or four at a time) are carried over the span on a set of grooved spinning wheels These are from an endless hauling rope of the cableway until arrival at the far anchorage There, the loops are pulled off the spinning wheels manually and placed around a semicircular strand shoe, which connects them by an eyebar or bolt linkage to the anchorage (Fig 15.28) The wheels then start back to the originating anchorage At the same time, another set of wheels carrying wires starts out from that anchorage The loops of wire on the latter set of wheels are also placed manually around a strand shoe at their anchorage destination Spinning proceeds as the wheels shuttle back and forth across the span A system of counterweights keeps the wires under continuous tension as they are spun The wires that come off the bottom of the wheels (called dead wires) and that are held back by the originating anchorage are laid on the catwalk in the spinning process The wires passing over the wheels from the unreelers and moving at twice the speed of the wheels, are called live wires As the wheels pass each group of wire handlers on the catwalks, the dead wires are temporarily clipped down The live wires pass through small sheaves to keep them in correct order Each wire is adjusted for level in the main and side spans with come-along winches, to ensure that all wires will have the same sag The cable is made of many strands, usually with hundreds of wires per strand (Art 15.8) All wires from one strand are connected to the same shoe at each anchorage Thus, there are as many anchorage shoes as strands At saddles and anchorages, the strands maintain their identity, but throughout the rest of their length, the wires are compacted together by special machines The cable usually is forced into a circular cross section of tightly bunched parallel wires The usual order of erection of suspension bridges is substructure, pylons and anchorages, catwalks, cables, suspenders, stiffening trusses, floor system, cable wrapping, and paving Cables are usually coated with a protective compound The main cables are wrapped with wire by special machines, which apply tension, pack the turns tightly against one another, and at the same time advance along the cable Several coats of protective material, such as paint, are then applied for alternative wrapping (see Art 15.10) Typical cable bands are illustrated in Figs 15.34 and 15.35 These are usually made of paired, semicylindrical steel castings with clamping bolts, over which the wire-rope or strand suspenders are looped or attached by socket fittings Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Brockenbrough_Ch15.qxd 9/29/05 5:43 PM Page 15.89 FIGURE 15.63 Scheme for spinning four wires at a time for the cables of the Forth Road Bridge CABLE-SUSPENDED BRIDGES 15.89 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Brockenbrough_Ch15.qxd 9/29/05 5:43 PM Page 15.90 CABLE-SUSPENDED BRIDGES 15.90 CHAPTER FIFTEEN FIGURE 15.64 Erection procedure used for the Strömsund Bridge (a) Girder, supported on falsework, is extended to the pylon pier (b) Girder is cantilevered to the connection of cable (c) Derrick is retracted to the pier and the girder is raised, to permit attachment of cables and to the girder (d) Girder is reseated on the pier and cable is attached (e) Girder is cantilevered to the connection of cable ( f ) Derrick is retracted to the pier and cable is connected (g) Preliminary stress is applied to cable Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Brockenbrough_Ch15.qxd 9/29/05 5:43 PM Page 15.91 CABLE-SUSPENDED BRIDGES CABLE-SUSPENDED BRIDGES 15.91 FIGURE 15.64 (Continued) (h) Girder is cantilevered to midspan and spliced to its other half (i) Cable is given its final stress ( j) The roadway is paved, and the bridge takes its final position (Reprinted with permission from H J Ernst, “Montage Eines Seilverspannten Balkens im Grossbrucken-bau,” Stahlbau, vol 25, no 5, May 1956.) Cable-stayed structures are ideally suited for erection by cantilevering into the main span from the piers Theoretically, erection could be simplified by having temporary erection hinges at the points of cable attachment to the girder, rendering the system statically determinate, then making these hinges continuous after dead load has been applied The practical implementation of this is difficult, however, because the axial forces in the girder are larger and would have to be concentrated in the hinges Therefore, construction usually follows conventional tactics of cantilevering the girder continuously and adjusting the cables as necessary to meet the required geometrical and statical constraints A typical erection sequence is illustrated in Fig 15.64 Erection should meet the requirements that, on completion, the girder should follow a prescribed gradient; the cables and pylons should have their true system lengths; the pylons should be vertical, and all movable bearings should be in a neutral position To accomplish this, all members, before erection, must have a deformed shape the same as, but opposite in direction to, that which they would have under dead load The girder is accordingly cambered, and also lengthened by the amount of its axial shortening under dead load The pylons and cable are treated in similar manner Erection operations are aided by raising or lowering supports or saddles, to introduce prestress as required All erection operations should be so planned that the stresses during the erection operations not exceed those due to dead and live load when the structure is completed; otherwise, loss of economy will result Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Brockenbrough_Ch15.qxd 9/29/05 5:43 PM Page 15.92 CABLE-SUSPENDED BRIDGES Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website ... PROPERTIES OF STRUCTURAL STEELS AND EFFECTS OF STEELMAKING AND FABRICATION STRUCTURAL STEELS, STEELMAKING, AND FABRICATION 1.3 TABLE 1.1 Specified Minimum Properties for Structural Steel Shapes and Plates*... 4:59 PM Page 1.7 PROPERTIES OF STRUCTURAL STEELS AND EFFECTS OF STEELMAKING AND FABRICATION STRUCTURAL STEELS, STEELMAKING, AND FABRICATION 1.7 1.1.5 Bridge Steels Steels for application in bridges... PROPERTIES OF STRUCTURAL STEELS AND EFFECTS OF STEELMAKING AND FABRICATION STRUCTURAL STEELS, STEELMAKING, AND FABRICATION 1.9 TABLE 1.3 Specified Minimum Mechanical Properties for Steel Sheet and Strip