1、Steel Design Guide SeriesSteel and Composite Beams withWeb OpeningsSteel Design Guide SeriesSteel andComposite Beamswith Web OpeningsDesign of Steel and Composite Beams with Web OpeningsDavid DarwinProfessor of Civil EngineeringUniversity of KansasLawrence, KansasAMERICAN INSTITUTE OF STEEL CONSTRUC
2、TION 2003 by American Institute of Steel Construction, Inc. All rights reserved.This publication or any part thereof must not be reproduced in any form without permission of the publisher.Copyright 1990byAmerican Institute of Steel Construction, Inc.All rights reserved. This book or any part thereof
3、must not be reproduced in any form without thewritten permission of the publisher.The information presented in this publication has been prepared in accordance with rec-ognized engineering principles and is for general information only. While it is believedto be accurate, this information should not
4、 be used or relied upon for any specific appli-cation without competent professional examination and verification of its accuracy,suitablility, and applicability by a licensed professional engineer, designer, or architect.The publication of the material contained herein is not intended as a represen
5、tationor warranty on the part of the American Institute of Steel Construction or of any otherperson named herein, that this information is suitable for any general or particular useor of freedom from infringement of any patent or patents. Anyone making use of thisinformation assumes all liability ar
6、ising from such use.Caution must be exercised when relying upon other specifications and codes developedby other bodies and incorporated by reference herein since such material may be mod-ified or amended from time to time subsequent to the printing of this edition. TheInstitute bears no responsibil
7、ity for such material other than to refer to it and incorporateit by reference at the time of the initial publication of this edition.Printed in the United States of AmericaSecond Printing: September 1991Revision: October 2003 2003 by American Institute of Steel Construction, Inc. All rights reserve
8、d.This publication or any part thereof must not be reproduced in any form without permission of the publisher.TABLE OF CONTENTSINTRODUCTION . 1DEFINITIONS AND NOTATION . 32.1 Definitions . 32.2 Notation. 3DESIGN OF MEMBERS WITH WEB OPENINGS 73.1 General 73.2 Load and Resistance Factors 73.3 Overview
9、 of Design Procedures . 73.4 Moment-Shear Interaction 83.5 Equations for Maximum Moment Capacity,Mm. 83.6 Equations for Maximum Shear Capacity, Vm . 103.7 Guidelines for Proportioning and DetailingBeams with Web Openings 123.8 Allowable Stress Design 16DESIGN SUMMARIES AND EXAMPLEPROBLEMS. 174.1 Gen
10、eral 174.2 Example 1: Steel Beam with UnreinforcedOpening . 224.3 Example 1A: Steel Beam with UnreinforcedOpeningASD Approach 234.4 Example 2: Steel Beam with ReinforcedOpening. 244.5 Example 3: Composite Beam withUnreinforced Opening . 274.6 Example 4: Composite Girder withUnreinforced and Reinforc
11、ed Openings 30BACKGROUND AND COMMENTARY 375.1 General 375.2 Behavior of Members with Web Openings . 375.3 Design of Members with Web Openings 405.4 Moment-Shear Interaction 415.5 Equations for Maximum Moment Capacity 425.6 Equations for Maximum Shear Capacity 445.7 Guidelines for Proportioning and D
12、etailingBeams with Web Openings . 485.8 Allowable Stress Design 50DEFLECTIONS 516.1 General. . 516.2 Design Approaches 516.3 Approximate Procedure . 516.4 Improved Procedure . 526.5 Matrix Analysis. 53REFERENCES 55ADDITIONAL BIBLIOGRAPHY . 57APPENDIX A 59INDEX 63 2003 by American Institute of Steel
13、Construction, Inc. All rights reserved.This publication or any part thereof must not be reproduced in any form without permission of the publisher.PREFACEThis booklet was prepared under the direction of the Com-mittee on Research of the American Institute of Steel Con-struction, Inc. as part of a se
14、ries of publications on specialtopics related to fabricated structural steel. Its purpose is toserve as a supplemental reference to the AISC Manual ofSteel Construction to assist practicing engineers engaged inbuilding design.The design guidelines suggested by the author that are out-side the scope
15、of the AISC Specifications or Code do notrepresent an official position of the Institute and are not in-tended to exclude other design methods and procedures. Itis recognized that the design of structures is within the scopeof expertise of a competent licensed structural engineer, ar-chitect or othe
16、r licensed professional for the application ofprinciples to a particular structure.The sponsorship of this publication by the American Ironand Steel Institute is gratefully acknowledged.The information presented in this publication has been prepared in accordance with recognized engineer-ing princip
17、les and is for general information only. While it is believed to be accurate, this information shouldnot be used or relied upon for any specific application without competent professional examination and verifi-cation of its accuracy, suitability, and applicability by a licensed professional enginee
18、r, designer or archi-tect. The publication of the material contained herein is not intended as a representation or warranty onthe part of the American Institute of Steel Construction, Inc. or the American Iron and Steel Institute, orof any other person named herein, that this information is suitable
19、 for any general or particular use or offreedom infringement of any patent or patents. Anyone making use of this information assumes all liabilityarising from such use. 2003 by American Institute of Steel Construction, Inc. All rights reserved.This publication or any part thereof must not be reprodu
20、ced in any form without permission of the publisher.Chapter 1INTRODUCTIONHeight limitations are often imposed on multistory buildingsbased on zoning regulations, economic requirements and es-thetic considerations, including the need to match the floorheights of existing buildings. The ability to mee
21、t these restric-tions is an important consideration in the selection of a fram-ing system and is especially important when the framing sys-tem is structural steel. Web openings can be used to passutilities through beams and, thus, help minimize story height.A decrease in building height reduces both
22、 the exterior sur-face and the interior volume of a building, which lowers oper-ational and maintenance costs, as well as construction costs.On the negative side, web openings can significantly reducethe shear and bending capacity of steel or composite beams.Web openings have been used for many year
23、s in structuralsteel beams, predating the development of straightforwarddesign procedures, because of necessity and/or economic ad-vantage. Openings were often reinforced, and compositebeams were often treated as noncomposite members at webopenings. Reinforcement schemes included the use of bothhori
24、zontal and vertical bars, or bars completely around theperiphery of the opening. As design procedures were devel-oped, unreinforced and reinforced openings were often ap-proached as distinct problems, as were composite and non-composite members.In recent years, a great deal of progress has been made
25、in the design of both steel and composite beams with webopenings. Much of the work is summarized in state-of-the-art reports (Darwin 1985, 1988 seeEqs. 5-19 and 5-20Vertical forces at ends of a beam elementYield strength of opening reinforcementShear modulus =Moment of inertia of a steel tee, withsu
26、bscript b or tMoment of inertia of bottom steel teeMoment of inertia of unperforated steelbeam or effective moment of inertia ofunperforated composite beamMoment of inertia of perforated beamMoment of inertia of teeMoment inertia of top steel teeTorsional constantShape factor for shearElements of be
27、am stiffness matrix, i, j = 1, 6Stiffness matrix of a beam elementLength of a beamUnbraced length of compression flangeBending moment at center line of openingSecondary bending moment at high and lowmoment ends of bottom tee, respectively.Maximum nominal bending capacity at thelocation of an opening
28、Nominal bending capacityPlastic bending capacity of an unperforatedsteel beamPlastic bending capacity of an unperforatedcomposite beamSecondary bending moment at high and lowmoment ends of top tee, respectivelyFactored bending momentMoments at ends of a beam elementNumber of shear connectors between
29、 thehigh moment end of an opening and thesupportNumber of shear connectors over anopeningAxial force in top or bottom teeForce vector for a beam elementAxial force in bottom teeAxial force in concrete for a section underpure bending2.2 NOTATION3 2003 by American Institute of Steel Construction, Inc.
30、 All rights reserved.This publication or any part thereof must not be reproduced in any form without permission of the publisher.Minimum value of for which Eq. 3-10 isaccurate =Axial force in concrete at high and lowmoment ends of opening, respectively, for asection at maximum shear capacityPlastic
31、neutral axisAxial force in opening reinforcementAxial force in top teeIndividual shear connector capacity, includ-ing reduction factor for ribbed slabsRatio of factored load to design capacity atan opening =Strength reduction factor for shear studs inribbed slabsRequired strength of a weldClear spac
32、e between openingsTensile force in net steel sectionDisplacement vector for a beam elementShear at openingShear in bottom teeCalculated shear carried by concrete slab =which-ever is lessMaximum nominal shear capacity at thelocation of an openingMaximum nominal shear capacity of bottomand top tees, r
33、espectivelyPure shear capacity of top teeNominal shear capacityPlastic shear capacity of top or bottom teePlastic shear capacity of unperforated beamPlastic shear capacity of bottom and toptees, respectivelyShear in top teeFactored shearPlastic section modulusLength of openingDepth of concrete compr
34、essive blockProjecting width of flange or reinforcementEffective width of concrete slabSum of minimum rib widths for ribs that liewithin for composite beams with longitu-dinal ribs in slabWidth of flangeDepth of steel sectionDistance from top of steel section to cen-troid of concrete force at high a
35、nd lowmoment ends of opening, respectively.Distance from outside edge of flange to cen-troid of opening reinforcement; may havedifferent values in top and bottom teesEccentricity of opening; always positive for steelsections; positive up for composite sectionsCompressive (cylinder) strength of concr
36、eteDepth of openingDistance from center of gravity of unper-forated beam to center of gravity of a teesection, bottom tee, and top tee, respectively.Length of extension of reinforcement beyondedge of openingDistance from high moment end of openingto adjacent supportDistance from low moment end of op
37、eningto adjacent supportDistance from support to point at whichdeflection is calculatedDistance from high moment end of openingto point at which deflection is calculatedOpening parameter =Ratio of midspan deflection of a beam withan opening to midspan deflection of a beamwithout an openingDepth of a
38、 tee, bottom tee and top tee,respectivelyEffective depth of a tee, bottom tee and toptee, respectively, to account for movementof PNA when an opening is reinforced; usedonly for calculation ofThickness of flange or reinforcementEffective thickness of concrete slabThickness of flangeTotal thickness o
39、f concrete slabThickness of concrete slab above the ribThickness of webHorizontal displacements at ends of a beamelementVertical displacements at ends of a beamelementUniform loadFactored uniform loadDistance from top of flange to plastic neu-tral axis in flange or web of a compositebeamDistance bet
40、ween points about which sec-ondary bending moments are calculatedVariables used to calculateRatio of maximum nominal shear capacityto plastic shear capacity of a tee,Term in stiffness matrix for equivalent beamelement at web opening; see Eq. 6-12Net reduction in area of steel section due topresence
41、of an opening and reinforcement =4 2003 by American Institute of Steel Construction, Inc. All rights reserved.This publication or any part thereof must not be reproduced in any form without permission of the publisher.Dimensionless ratio relating the secondarybending moment contributions of concrete
42、and opening reinforcement to the product ofthe plastic shear capacity of a tee and thedepth of the teeRatio of length to depth or length to effec-tive depth for a tee, bottom tee or top tee,respectively =Poissons ratioAverage shear stressResistance factorBottom teeMaximum or meanNominalTop teeFactor
43、edMaximum deflection due to bending of abeam without an openingMaximum deflection of a beam with anopening due to bending and shearDeflection through an openingBending deflection through an openingShear deflection through an openingComponents of deflection caused by pres-ence of an opening at a poin
44、t between highmoment end of opening and supportMaximum deflection due to shear of a beamwithout an openingRotations of a beam at supports due to pres-ence of an opening = see Eq.6-12Rotations used to calculate beam deflectionsdue to presence of an opening; see Eq. 6-3Rotations at ends of a beam elem
45、entConstant used in linear approximation ofvon Mises yield criterion; recommendedvalue5 2003 by American Institute of Steel Construction, Inc. All rights reserved.This publication or any part thereof must not be reproduced in any form without permission of the publisher.Chapter 3DESIGN OF MEMBERS WI
46、TH WEB OPENINGS3.1 GENERALThis chapter presents procedures to determine the strengthof steel and composite beams with web openings. Compos-ite members may have solid or ribbed slabs, and ribs maybe parallel or perpendicular to the steel section. Openingsmay be reinforced or unreinforced. Fig. 3.1 il
47、lustrates therange of beam and opening configurations that can be han-dled using these procedures. The procedures are compatiblewith the LRFD procedures of the American Institute of SteelConstruction, as presented in the Load and Resistance Fac-tor Design Manual of Steel Construction (AISC 1986a). W
48、ithminor modifications, the procedures may also be used withAllowable Stress Design techniques (see section 3.8).Design equations and design aids (Appendix A) based onthese equations accurately represent member strength witha minimum of calculation. The derivation of these equationsis explained in C
49、hapter 5.The design procedures presented in this chapter are limitedto members with a yield strength 65 ksi meeting theAISC criteria for compact sections (AISC 1986b). Otherlimitations on section properties and guidelines for detail-ing are presented in section 3.7. Design examples arepresented in Chapter 4.3.2 LOAD AND RESISTANCE FACTORSThe load factors for structural steel members with web open-ings correspond to those used in the AISC Load and Resis-tance Factor Design Specifications for Structural Steel Build-ings (AISC 1986b).Resistance factors, 0.90 for steel members and 0.85f
