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1.1 SCOPE
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2 Chapter 1 Introduction
and a detailed Commentary that provides insights into the source and application of the provisions. The reader interested in additional background on the provisions discussed in this book is encouraged to investigate the materials cited in the appropriate sections of the Commentary. The Specification contains 14 chapters and 8 appendices. To provide a concise guide to the use of the Specification, a brief description is given here.
Chapter A: General Provision. This chapter provides the scope of the Specification and summarizes all referenced specifications, codes, and standards. It also provides the requirements for materials to be used in structural steel design and the design documents necessary to communicate that design. Chapter B: Design Requirements. This chapter gives the general requirements for analysis and design that are applicable throughout the entire Specification. It provides the charging language needed for application of the subsequent chapters. Chapter C: Design for Stability. This chapter, along with Appendix 7, addresses the requirements for the design of structures to ensure stability. It details those factors that must be taken into consideration in any analysis and design. Chapter D: Design of Members for Tension. This chapter applies to the design of members subjected to axial tension resulting from forces acting through the centroidal axis. Chapter E: Design of Members for Compression. This chapter addresses members subjected to axial compression resulting from forces applied at the centroidal axis. Chapter F: Design of Members for Flexure. This chapter applies to members loaded in a plane parallel to a principal axis that passes through the shear center or is restrained against twisting. This is referred to as simple bending about one axis. Chapter G: Design of Members for Shear. This chapter addresses webs of singly or doubly symmetric members subject to shear in the plane of the web. It also addresses other shapes such as single angles and hollow structural sections. Chapter H: Design of Members for Combined Forces and Torsion. This chapter addresses design of members subject to an axial force in combination with flexure about one or both axes, with or without torsion. It also applies to members subjected to torsion only. Chapter I: Design of Composite Members. This chapter addresses the design of members composed of steel shapes and concrete working together as a member. It addresses compression, flexure, and combined forces. Chapter J: Design of Connections. This chapter addresses the design of connections, including the connecting elements, the connectors, and the connected portions of members. Chapter K: Additional Requirements for HSS and Box Section Connections. This chapter addresses requirements in addition to those given in Chapter J for the design of connections to hollow structural sections and built-up box sections of uniform thickness and connections between HSS and box members. Chapter L: Design for Serviceability. This chapter summarizes the performance requirements for the design of a serviceable structure.
Introduction Chapter 1 3
Chapter M: Fabrication and Erection. This chapter addresses the requirements for shop drawings, fabrication, shop painting, and erection. Chapter N: Quality Control and Quality Assurance. This chapter addresses the requirements for ensuring quality of the constructed project. Appendix 1: Design by Advanced Analysis. The body of the Specification addresses design based on an elastic analysis. This appendix addresses design by alternative methods generally referred to as advanced methods. It includes the classical plastic design method and design by direct modeling of imperfections. Appendix 2: Design for Ponding. This appendix provides methods for determining whether a roof system has sufficient strength and stiffness to resist the influence of water collecting on the surface and forming a pond. Appendix 3: Fatigue. This appendix provides requirements for addressing the influence of high cycle loading on members and connections that could lead to cracking and progressive failure. For most building structures, fatigue is not an issue of concern. Appendix 4: Structural Design for Fire Conditions. This appendix provides the criteria for evaluation of structural steel subjected to fire conditions, including (1) the prescriptive approach provided for in the model building code and most commonly used in current practice and (2) the engineered approach. Appendix 5: Evaluation of Existing Structures. This appendix provides guidance on the determination of the strength and stiffness of existing structures by load tests or a combination of tests and analysis. Appendix 6: Member Stability Bracing. This appendix details the criteria for ensuring that column, beam and beam-column bracing has sufficient strength and stiffness to meet the requirements for member bracing assumed in the provisions of the Specification for design of those members. Appendix 7: Alternative Methods of Design for Stability. This appendix, along with Chapter C, provides methods of designing structures to ensure stability. Two alternative methods are provided here, including the method most commonly used in past practice. Appendix 8: Approximate Second-Order Analysis. This appendix provides a method for obtaining second-order effects by an amplified first-order analysis. The provisions are limited to structures supporting load primarily through vertical columns.
Each chapter of this book will identify those chapters of the Specification that are
pertinent to that chapter. The reader is encouraged to become familiar with the organization of the Specification.
1.3 THE MANUAL
The AISC Steel Construction Manual, 15th edition, is the latest in a series of manuals published to assist the building industry in designing safe and economical steel building structures. The first edition was published in 1928 and the ninth edition in 1989. These manuals addressed design by the allowable stress method. In 1986 the first edition of the load and resistance factor design
4 Chapter 1 Introduction
method manual was published, with the third edition published in 1999. The next in this unbroken string of manuals published in support of steel design and construction was the first manual to unify these two design methods and was published in 2005 as the 13th edition. The current edition of the Manual is the 15th. Students who purchase the Manual through the AISC Student Discount Program also have an opportunity to apply for a free AISC Student Membership at the same time. Students are encouraged to become AISC Student Members in order to take full advantage of all free member benefits.
As is the case for the Specification, AISC has two resources to assist in addressing the historic aspects of steel design and construction. The first is, again, AISC Design Guide 15, AISC Rehabilitation and Retrofit Guide: A Reference for Historic Shapes and Specifications. This Guide provides properties of beam and column sections as old as the wrought iron shapes produced as early as 1873. The second resource is the electronic AISC Shapes Database. This database is available through the AISC web site www.aisc.org. It is a searchable database with properties for all shapes produced since 1873, consistent with the printed data in Design Guide 15. Access to the electronic shapes database is free to AISC members.
The Manual is presented in 17 parts as follows: Part 1: Dimensions and Properties Part 2: General Design Considerations Part 3: Design of Flexural Members Part 4: Design of Compression Members Part 5: Design of Tension Members Part 6: Design of Members Subject to Combined Forces Part 7: Design Considerations for Bolts Part 8: Design Considerations for Welds Part 9: Design of Connecting Elements Part 10: Design of Simple Shear Connections Part 11: Design of Partially Restrained Moment Connections Part 12: Design of Fully Restrained Moment Connections Part 13: Design of Bracing Connections and Truss Connections Part 14: Design of Beam Bearing Plates, Column Base Plates, Anchor Rods, and Column Splices Part 15: Design of Hanger Connections, Bracket Plates, and Crane-Rail Connections Part 16: Specifications and Codes Part 17: Miscellaneous Data and Mathematical Information
Introduction Chapter 1 5
Each chapter of this book identifies those parts of the Manual that will be used with the material to be addressed. In many instances, the user will need to look in several parts of the Manual to fully understand the topics or solve the problems presented.
1.4 AISC WEB SITE RESOURCES
Another primary resource is the AISC web site, where there is information that is free to all visitors and additional electronic resources that are free to members only. Students will find a great deal of useful information on the AISC publications web site, www.aisc.org/epubs. The primary resources include electronic versions of the Specification, the Shapes Database, the Steel Construction Manual References, and the Steel Construction Manual Design Examples. The Specification, as described in Section 1.2 and the historic Shapes Database, as mentioned in Section 1.3, are available free to all through the web site. The 15th edition Steel Construction Manual Shapes Database is also available free to all. The AISC web site also includes an extensive array of journal and proceedings papers. All of the references cited in the Commentary and the Manual, for which AISC owns the copyright, are accessible under Steel Construction Manual Resources; Interactive Reference List.
Probably the most valuable aspect of the AISC web site for readers of this book is the complete set of the 15th edition Steel Construction Manual Design Examples. These examples are presented in four sections.
Section I: Examples Based on the AISC Specification. This section contains examples demonstrating the use of the specific provisions of the Specification, organized by Specification chapter. Section II: Examples Based on the AISC Steel Construction Manual. This section contains examples of connection design using the Specification and the tables found in the Manual. Section III: System Design Examples. This section contains examples associated with the design of a specific building and the application of the system-wide requirements. Section IV: Additional Resources. This section provides design tables for higher-strength steels than published in the printed Manual.
Although the topics covered in this book are supported by calculated example problems,
the reader might find the electronic Steel Construction Manual Design Examples helpful for further understanding of some of the specific provisions or design aids described in the book. In addition, some of the Design Examples go beyond the coverage in this book and provide additional useful information regarding typical design or detailing. The reader is encouraged to investigate what the AISC web site has to offer through both free and member only publications.
1.5 PRINCIPLES OF STRUCTURAL DESIGN
From the time an owner determines a need to build a building, through the development of conceptual and detailed plans, to completion and occupancy, a building project is a multi-faceted task that involves many professionals. The owner and the financial analysis team evaluate the basic economic criteria for the building. The architects and engineers form the design team and prepare the initial proposals for the building, demonstrating how the users’ needs will be met. This teamwork continues through the final planning and design stages, where the design drawings, specifications, and contract documents are readied for the construction phase. During this process, input may also be provided by the individuals who will transform the plans into a
6 Chapter 1 Introduction
real-life structure. The steel detailer, fabricator and erector all have a role in that process, and add their respective expertise to make the design constructible. Thus, those responsible for the construction phase of the project often help improve the design by taking into account the actual on-site requirements for efficient construction.
Once a project is completed and turned over to the owner, the work of the design teams is normally over. The operation and maintenance of the building, although major factors in the life of the structure, are not usually within the scope of the designer’s responsibilities, except when significant changes in building use are anticipated. In such cases, a design team should verify that the proposed changes can be accommodated.
The basic goals of the design team can be summarized by the words safety, function, and economy. The building must be safe for its occupants and all others who may come in contact with it. It must neither fail locally nor overall, nor exhibit behavioral characteristics that test the confidence of rational human beings. To help achieve that level of safety, building codes and design specifications are published that outline the minimum criteria that any structure must meet.
The building must also serve its owner in the best possible way to ensure that the functional criteria are met. Although structural safety and integrity are of paramount importance, a building that does not serve its intended purpose will not have met the goals of the owner.
Last, but not least, the design, construction, and long-term use of the building should be economical. The degree of financial success of any structure will depend on a wide range of factors. Some are established prior to the work of the design team, whereas others are determined after the building is in operation. Nevertheless, the final design should, within all reasonable constraints, produce the lowest combined short- and long-term expenditures.
The AISC Specification follows the same principles. The mission of the AISC Committee on Specifications is to “develop the practice-oriented specification for structural steel buildings that provide for life safety, economical building systems, predictable behavior and response, and efficient use.” Thus, this book emphasizes the practical orientation of this Specification.
1.6 PARTS OF THE STEEL STRUCTURE
All structures incorporate some or all of the following basic types of structural components:
1. Tension members 2. Compression members 3. Bending members 4. Combined force members 5. Connections The first four items represent structural members. The fifth, connections, represents the
contact regions between the structural members, which ensure that all components work together as a structure.
Detailed evaluations of the strength, behavior, and design criteria for these members are presented in the following chapters:
Tension members: Chapter 4 Compression members: Chapter 5
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4 Building S
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ng Corporation
e most commosed by wind rete cores. Thnt because of rpose in this vertical conduircases, electrtion are also cirection of theee-dimensionentation of s
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ures with lonlong distanc
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rigid frameshe frame, suc
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he vertical er bracing referred to aped cross viding the ure for all
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1 1.7.4 Highh-Rise Const
High-rise cin Figure structures addition, omulti-story
Pasystem in hthe analysirise buildicrucial to t
Soquantified are presenwhen a streccentricitwind loadconsiderinwill be ma
Frresistance.quite succeChicago, IYork City,Center in Cthe Willis
truction
construction 1.12. The lwarrant treat
over the past y frame desigarticular care high-rise conis of lower-risngs but havethe proper desome of these
through a not in all structructure is dis
ty of the columds, the resultng the secondaking a seriouraming system Thus, attempessful. This tIllinois, shown, shown in FiChicago, showTower in Chi
refers to mularge heights ting them ind40 years sev
gn, such as themust be exe
struction. It isse structures,
e significantlysign of the hieffects may b
ormal, linearlytures, they masplaced lateramn loads. Whting effects m-order effects
us and perhapsms for high-ripts at makingtube may be in in Figure 1gure 1.13b; awn in Figure icago (former
lti-story buildand unique
dependently fveral designere super compoercised in thes not just a mbecause man
y less impactgh-rise structbe referred toy elastic analyay be more sially, additionhen added to tmay be signs. A designers unconservatise buildings
g the perimetein the form o.13a, or a fram
a solid wall tu1.13c; or sev
rly known as
dings of signiproblems en
from typical rs have develosite column
e choice and matter of extrany effects playt on frames oture. as second-orysis of the fraignificant in
nal moment ithe moments nificantly larr who does notive error. reflect the in
er of a buildinof a truss, asme, as in the
ube with cutouveral interconthe Sears Tow
FigurStructPhoto Corpo
Introdu
ificant heightncountered ibeam-and-co
loped a numband the steel design of the
apolating fromy a major roleof smaller he
rder effects, bame. Althoughigh-rise struis induced inand shears pr
rger than thoot incorporat
ncreased impng act as a unwith the Johnformer Worlduts for windo
nnected or bunwer), shown i
re 1.12 Highture courtesy Doug
oration
uction Chap
; an examplein the designolumn constrber of new coplate shear w
e lateral loadm the principle in the desigight. These e
because they gh second-orductures. Forn a column droduced by grose computedte both types
portance of lanit or tube havn Hancock Bd Trade Cent
ows, as used indled tubes, sin Figure 1.13
h-Rise Buildin
glas Steel Fabr
pter 1 15
e is shown n of such ruction. In oncepts in wall. d resisting les used in gn of high-effects are
cannot be der effects r example, due to the ravity and d without of effects
ateral load ve proven uilding in
ter in New n the Aon such as in 3d.
ng
ricating
1
1
16 Chapter 1
1.7.5 Gabl
1 Introduct
Figure 1.1(c) the AonPhoto (b) co
le-Frame Co
Many desiThese struengineeredof frames fand similais seen in F
ion
13 High-Risn Center; (d) ourtesy Leslie
onstruction
igners incluductures lend d building indfor storage wr types of struFigure 1.14.
(a)
(c) se Buildings (the Willis ToE. Robertson A
de the single-themselves
dustry has capwarehouses, in
uctures. An ex
(a) the John Hower. Associates, RL
-story frame particularly
pitalized on thndustrial buildxample of a p
(b)
(d)
Hancock Cent
LLP
as part of thwell to full
he use of thisdings, temporpre-engineere
ter; (b) the W
he long-span ly welded cs system throurary and permed metal build
World Trade Ce
construction construction. ugh fine-tune
manent office ding with a ga
enter;
category. The pre-
ed designs buildings,
able frame
1 1.8 DESIG
Figure 1.1Photo court
GN PHILOS
A successfdesign loais economithe primarlabor and impossibletask of thepublished consideratiby the desbusiness cl
Toloads that termed thethe materistrength or
In corresponddegree to wfor accomp
Alexact magnthe structustandards those magn
Asthe behavigiven by twhole. Faito have ocfailure is t
14 Pre-engintesy Metal Buil
SOPHIES
ful structural ds without ovical to build ary concern of
materials we to design a e designer is by the Amerions that predsigner will dlimate. o perform a swill be exert
e load effect oial and the sr capacity of t
its simplest ding connectiwhich this is plishing this glthough past nitude of the
ural elements, and, althoughnitudes. Loads is the case fior and strengthe magnitudeilure may eithccurred if defthe result of
neered Metal lding Manufac
design resulverstressing aand operate fof an owner, swill vary fromstructure thatto produce arican Institutdict structuraldictate the ec
structural dested on each eor the requirehapes that cothe element.form, structu
ons, so that thaccomplished
goal have beeexperience mloads that withis is usuall
h the values ds, load factorfor loading, sgth of structure of the loadher occur as tflections, for a lack of str
Building cturers Associa
lts in a structany componenor its intendedafety must bem one geogt is equally eca safe and serte of Steel Cl behavior anonomy of a
ign, it is necelement throued strength. Itompose these
ural design ihe strength ofd is often termen used over tmight seem toill be appliedly not the casgiven are spers, and load cosignificant unral members.that causes t
the physical cinstance, exc
rength (colla
ation
ture that is sants, does not d life span. Ae the primary
graphic locaticonomical in rviceable stru
Construction and material re
particular so
cessary to quaughout the lifet is also necese elements. T
is the determf the structuremed the margthe years. o indicate thad to the structe. Design loaecific, signifiombinations
ncertainty is a The true indthe failure ofcollapse of paceed certain p
apse) or stiffn
Introdu
afe for its oct deform or vAlthough econy concern of ion to anothall locations.
ucture, designare based on sponse. The u
olution in a p
antify the caufe of the strucssary to accoThis is referr
mination of me is greater thgin of safety.
at the structurture, and the ads are providicant uncertaiare discussed
associated witdication of loaf a componenart of the builpredetermineness (deflecti
uction Chap
ccupants, can ibrate excessnomy may apthe engineer
her, making . Because the
n criteria suchtechnical m
use of these pparticular loc
uses and effecture. This is unt for the bered to as the
member sizes han the load e
Numerous ap
ral designer kexact strength
ded by many inty is associ
d in Chapter 2th the determad-carrying cnt or the strulding, or be ced values. Whion), these ph
pter 1 17
carry the ively, and pear to be . Costs of it almost
e foremost h as those
models and provisions cation and
ects of the generally
ehavior of e nominal
and their effect. The pproaches
knows the h of all of codes and iated with
2. mination of capacity is cture as a
considered hether the henomena
18 Chapter 1 Introduction
reflect the limits of acceptable behavior of the structure. Based on these criteria, the structure is said to have reached a specific limit state. A strength failure is termed an ultimate limit state, whereas a failure to meet operational requirements, such as deflection, is termed a serviceability limit state.
Regardless of the approach to the design problem, the goal of the designer is to ensure that the load on the structure and its resulting load effect, such as bending moment, shear force, and axial force, in all cases are sufficiently below each of the applicable limit states. This ensures that the structure meets the required level of safety or reliability.
Three approaches to the design of steel structures are permitted by the AISC Specification:
1. Allowable strength design (ASD) 2. Load and resistance factor design (LRFD) 3. Design by inelastic analysis
The design approaches represent alternative ways of formulating the same problem, and all have the same goal. All three are based on the nominal strength of the element or structure. The nominal strength, most generally expressed as Rn, is determined in exactly the same way, from the exact same equations, whether used in ASD or LRFD. Some formulations of design by inelastic analysis, such as plastic design, also use these same nominal strength equations whereas other approaches to inelastic design model in detail every aspect of the structural behavior and do not rely on the equations provided through the Specification. The use of a single nominal strength expression for both ASD and LRFD permits the unification of these two design approaches. It will become clear throughout this book how this approach has simplified steel design for those who have struggled in the past with comparing the two available philosophies. The following sections describe these three design approaches, any one of which is an acceptable approach to structural steel design according to the AISC Specification.
1.9 FUNDAMENTALS OF ALLOWABLE STRENGTH DESIGN (ASD)
Prior to 2005, allowable strength design was referred to as allowable stress design. It is the oldest approach to structural design in use today and has been the foundation of AISC Specifications since the original provisions of 1923. Allowable stress design was based on the assumption that under actual load, stresses in all members and elements would remain elastic. To meet this requirement, a safety factor was established for each potential stress-producing state. Although historically ASD was thought of as a stress-based design approach, the allowable strength was always obtained by using the proper combination of the allowable stress and the corresponding section property, such as area or elastic section modulus.
The current allowable strength design approach is based on the concept that the required strength of a component is not to exceed a certain permitted or allowable strength under normal in-service conditions. The required strength is determined on the basis of specific ASD load combinations and an elastic analysis of the structure. The allowable strength incorporates a factor of safety, Ω, and uses the nominal strength of the element under consideration. This strength could be presented in the form of a stress if the appropriate section property is used. As a result of doing this, the resulting stresses will most likely again be within the elastic range, although this is not a preset requirement of the Specification.
The magnitude of the factor of safety and the resulting allowable strength depend on the particular governing limit state against which the design must produce a certain margin of safety.
Introduction Chapter 1 19
Safety factors are obtained from the Specification. This requirement for ASD is provided in Section B3.2 of the Specification as
na
RR ≤Ω
(AISC B3-2)
which can be stated as
Nominal StrengthRequired Strength (ASD) Allowable StrengthSafety Factor
≤ =
The governing strength depends on the type of structural element and the limit states
being considered. Any single element can have multiple limit states that must be assessed. The safety factor specified for each limit state is a function of material behavior and the limit state being considered. Thus, it is possible for each limit state to have its own unique safety factor. For example, the limit state of yielding of a tension member is given by
n y gP F A=
where Fy is the steel yield strength and Ag is the gross area of the member. The safety factor is
1.67.Ω= Thus, for steel with a yield strength of 50 ksi, the allowable strength is
50.030
1.67gn
gAP A= =
Ω
Design by ASD requires that the allowable stress load combinations of the building code
be used. Loads and load combinations are discussed in detail in Chapter 2.
1.10 FUNDAMENTALS OF LOAD AND RESISTANCE FACTOR DESIGN (LRFD)
Load and resistance factor design explicitly incorporates the effects of the random variability of both strength and load. Because the method includes the effects of these random variations and formulates the safety criteria on that basis, it is expected that a more uniform level of reliability, and thus safety, for the structure and all of its components will be attained.
LRFD is based on the concept that the required strength of a component under LRFD load combinations is not to exceed the design strength. The required strength is obtained by increasing the load magnitude by load factors that account for load variability and load combinations. The design strength is obtained by reducing the nominal strength by a resistance factor that accounts for the many variables that impact the determination of member strength. Load factors for LRFD are obtained from the building codes for strength design and will be discussed in Chapter 2. As for ASD safety factors, the resistance factors are obtained from the Specification.
The basic LRFD provision is provided in Section B3.1 of the Specification as
u nR R≤ φ (AISC B3-1)
which can be stated as
Required Strength (LRFD) Resistance Factor Nominal Strength=Design Strength≤ ×
20 Chapter 1 Introduction
Again considering the limit state of yielding of a tension member, n y gP F A=
and the resistance factor is 0.90φ = . For steel with a yield strength of 50 ksi, the design strength is
0.90(50) 45n g gP A Aφ = =
LRFD has been a part of the AISC Specifications since it was first issued in 1986.
1.11 INELASTIC DESIGN
The Specification permits a wide variety of formulations for the inelastic analysis of steel structures through the use of Appendix 1. Any inelastic analysis method will require that the structure and its elements be modeled in sufficient detail to account for all types of behavior. An analysis of this type must be able to track the structure’s behavior from the unloaded condition through every load increment to complete structural failure. The only inelastic design approach that will be discussed in this book is plastic design (PD).
Plastic design is an approach that has been available as an optional method for steel design since 1961, when it was introduced as Part 2 of the then current Specification. The limiting condition for the structure and its members is attainment of the load that would cause the structure to collapse, usually called the ultimate strength or the plastic collapse load. For an individual structural member this means that its plastic moment capacity has been reached. In most cases, due to the ductility of the material and the member, the ultimate strength of the entire structure will not have been reached at this stage. The less stressed members can take additional load until a sufficient number of members have exhausted their individual capacities so that no further redistribution or load sharing is possible. At the point where the structure can take no additional load, the structure is said to have collapsed. This load magnitude is called the collapse load and is associated with a particular collapse mechanism.
The collapse load for plastic design is the service load times a certain load factor. The limit state for a structure that is designed according to the principles of plastic design is therefore the attainment of a mechanism. For this to occur, all of the structural members must be able to develop the yield stress in all fibers at the most highly loaded locations.
There is a fine line of distinction between the load factor of PD and the safety factor of ASD. The former is the ratio between the plastic collapse load and the service or specified load for the structure as a whole, whereas the latter is an empirically developed, experience-based term that represents the relationship between the elastic strength of the elements of the structure and the various limiting conditions for those components. Although numerically close, the load factor of plastic design and the factor of safety of allowable stress design are not the same parameter.
1.12 STRUCTURAL SAFETY AND INTEGRITY
The preceding discussions of design philosophies indicate that although the basic goal of any design process is to ensure that the end product is a safe and reliable structure, the ways in which this is achieved may vary substantially.
In the past, the primary goal for safety was to provide an adequate margin against the consequences of overload. Load factor design and its offshoots were developed to take these considerations into account. In real life, however, many other factors also play a role. These include, but are not limited to the following:
1. Variations of material strength
2. 3. 4. 5. 6. 7.
These factcomponenthe fact tha
Thload variasolution, thand resistaevaluated own specifThis methfailure wilthis probab
In parameterssafety varithought ofmore unifoelement inHowever, varies undrather, theothers.
FoR, are assuby the beresistance mean valufull represe
Variati
Accura
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Presenc
Lack of
Variati
tors consider nts. An even gat different tyhus, a methodability will bherefore, is toance factor dand the resufic factor in e
hod recognizell actually ocbility. No spe
ASD, the vs. They are luies with eachf as LRFD wform level of n an LRFD dea detailed an
der different loe goal is to s
or the developumed to each ll-shaped curis greater tha
ues, Qm and Rentation of th
ons of cross-s
acy of method
nce of workma
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f member stra
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only some ofgreater sourceypes of load hd of design thbe burdened o deal with sadesign, wherlting safety m
each combinates that there icur. Howeve
ecific level of variabilities oumped togethh strength lim
with a single lreliability th
esign will be nalysis of relioad combinatsimply have a
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sectional size
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anship in sho
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aightness
ons of load ap
f the sources e of variation
have different hat does not awith unaccou
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of load and her through thmit state but load factor. L
han ASD desthe same, regability under tions. In ASDa safe structu
FD, load effebility that canre 1.15. Strufect, R > Q. I
be relatively ean area wher
e and shape
op and field
al stresses
pplication poi
of variation on is the loadin
variational chattempt to incunted-for soubabilistic con
bilistic characrmined statisth material limfinite, though
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strength are he use of a si
does not vaLRFD designigns. That isgardless of ththe LRFD p
D there is no aure, although
ect (member fn be describeductures can bf it were appreasy to ensurere the two cur
Introdu
ints
of the strengtng, which is fharacteristics
corporate the urces of uncncept. This is cteristics of tically. Each
mit state is alsh very small, attempt to attaiven or implie
not treated ingle factor oary with loadns are generals, the probabihe type of loarovisions shoattempt to att
h some eleme
force), Q, andd by the normbe consideredropriate to coe a structure’rves overlap.
uction Chap
th of a structufurther comp
s. effects of str
certainty. Thethe foundatioload and strload type is
so given its owchance that
ach a specificed by the Spec
explicitly asof safety. Thed source. ASlly expected ility of failurd or load com
ows that reliatain uniform rents will be s
d resistance (mal distributiod safe as lon
oncentrate sols safety. How
pter 1 21
ure and its licated by
rength and e realistic on of load rength are s given its wn factor. structural
c value to cification. s separate e factor of D can be to have a
re of each mbination. ability still reliability; safer than
(strength), ons shown ng as the ely on the wever, the
2
22 Chapter 11 Introduct
Figure 1.1
Figure 1.1 This area occurrenceThe smalle
Anand load ecases wheris positiveleft of the value, (R –shown in Fof (R – Q)
A presented amore usefuof the resireliability and load emeans and
Thcarried outfactors, anwhereas re
Figure 1.1
ion
15 Probabili
16 Probabili
represents caes of failure. er the region onother approaffect. Figure re (R – Q) < 0, the structureorigin represe– Q)m, must bFigure 1.16 as. third represe
as ln(R/Q). Tul in the derivistance and lindex β. Unfeffect compo
d standard devhe statistical at by the appro
nd safety factoesistance facto
17 Probabili
ity Distributio
ity Distributio
ases where thSafety of theof overlap is, ach to presen1.16 shows th
0, the structure is considereents the probabe maintaineds βσ(R–Q), whe
entation of thThe logarithmi
vation of the load effect dafortunately, wonents. Thus, viations. analyses requopriate specifors have beenors and safety
ity Distributio
on, R and Q
on, (R – Q)
he load effecte structure is the lower the
nting the datahe same data re is said to haed safe. In thiability of failud at an approere β is the rel
he data is shic form of thefactors requi
ata, the probwe know the
we must rel
uired to establfication commn established. y factors for e
on, ln(R/Q)
t exceeds thea function o
e probability oa is to look a
as Figure 1.1ave failed, anis presentationure. To limit
opriate distancliability index
hown in Figue data is a weired in LRFD
bability of faiactual distribly on other c
lish an appromittees, and tLoad factors
each limit stat
e resistance af the size of of failure.
at the differen15 but presennd for all casen of the data,that probabilce from the ox and σ(R–Q) is
ure 1.17. In ell-conditioneD. If we knowilure can be butions for recharacteristic
opriate level othe resulting ls are presentedte are given in
and therefore this region o
nce between nts it as (R – Qes where this d, the shaded aity of failure,origin. This ds the standard
this case, thed representatw the exact di
directly relatelatively few s of the data
of reliability hload factors, d in the buildn the Specific
identifies of overlap.
resistance Q). For all difference area to the , the mean distance is d deviation
he data is tion and is istribution ted to the resistance
a, such as
have been resistance
ding codes cation.
Introduction Chapter 1 23
Since the load combinations and resistance and safety factors have been established, the
reliability can be determined for specific design situations. The reliability index, β, is given in the Specification Commentary as
( )
2 2
ln m m
R Q
R Q
V Vβ =
+ (AISC C-B3-2)
where Rm is the mean resistance, Qm is the mean load effect, as discussed earlier, and VR and VQ are the coefficients of variation of resistance and load effect respectively. Design according to LRFD is given by
u nR R≤ φ (AISC B3-1) where the required strength, Ru is another term for the load effect, Q, Rn is the nominal strength and ϕ is the resistance factor. The reliability of design is determined when the required strength is exactly equal to the available strength. Thus, Equation B3-1 can be rewritten as nQ R= φ . The load effect will depend on the load combination being considered. Thus, for the LRFD live load plus dead load combination, written in terms of the live-to-dead load ratio, L/D,
( )( )1.2 1.6 1.2 1.6 nQ D L L D D R= + = + = φ (1) From Ravindra and Galambos1 the mean resistance is given by
m n m m mR R M F P= (2)
and the coefficient of variation of the resistance is given by
2 2 2R m F PV V V V= + + (3)
Mm is the mean of the ratio of the actual yield stress to the specified yield stress and VM is
the coefficient of variation; Fm is the mean of the ratio of the actual section property to the Manual value and VF is the coefficient of variation; and Pm is the mean of the ratio of the test specimen strength to the predicted strength using the Specification equations and the actual material and geometric properties and VP is the coefficient of variation.
Solving Equation 1 for Rn and substituting into Equation 2 yields
( )( )1.2 1.6m m m m
L D DR M F P
+=
φ (4)
Rearranging Equation 2 yields
mm m m
n
RM F PR
= (5)
1 Ravindra, M.K. and Galambos, T.V. (1978), “Load and Resistance Factor Design for Steel,” Journal of the Structural
Division, American Society of Civil Engineers, Vol. 104, No. ST9, September, pp. 1,337–1,353.
24 Chapter 1 Introduction
Thus, combining Equations 4 and 5 gives
( )( )1.2 1.6 mm
n
RR D L DR
⎛ ⎞= + ⎜ ⎟φ⎝ ⎠
(6)
From Ravindra and Galambos the mean load effect for dead load plus live load is
m m mQ D L= + (7)
which can, with some manipulation, be rewritten as
( )( )( )m m m m mQ D L D D L L L D D= + = + (8) They also give the coefficient of variation of the load effect which can be written as a
function of the live-to-dead load ratio as
( )( ) ( )( )( )2 2m D m L
Qm
D D V L L L D VV
Q
+= (9)
If Equations 6 and 8 are substituted into Equation C-B3-2 the reliability index, β, will be
given in terms of the live-to-dead load ratio, L D , and the resistance factor, ϕ. Thus,
( )( ) ( )( )2 2
1.2 1.61 ln m
n m mR Q
L DRR D D L L L DV V
⎡ ⎤⎛ ⎞+β = ⎢ ⎥⎜ ⎟⎜ ⎟φ ++ ⎢ ⎥⎝ ⎠⎣ ⎦
(10)
For LRFD, the live plus dead load combinations are 1.4D and (1.2D + 1.6L). The
effective dead load factor as a function of the live-to-dead-load ratio can be taken as
( )LRFD
1.4max
1.2 1.6i
iL D
⎡ ⎤γ = ⎢ ⎥+⎣ ⎦
(11)
and the mean load effect dead load multiplier as
( )( )im m m i
Q D D L L L D= + (12) Thus, Equation 10 can be generalized to address other LRFD load combinations as
follows: ( )
( ) ( )( )LRFD
2 2 2 2
1.2 1.61 1ln ln i
ii
m m
n m m n mR Q R Q
L DR RR D D L L L D R QV V V V
⎡ ⎤⎛ ⎞ ⎡ ⎤+ ⎛ ⎞γβ = =⎢ ⎥⎜ ⎟ ⎢ ⎥⎜ ⎟⎜ ⎟φ + φ+ +⎢ ⎥ ⎝ ⎠⎣ ⎦⎝ ⎠⎣ ⎦
(13)
where LRFDiγ is the effective LRFD load factor for the load combination under consideration, imQis the mean load effect multiplier for that load combination, and
iQV is the coefficient of variation of the load effect, all as a function of the varying load ratio as indicated by the subscript i.
Introduction Chapter 1 25
To convert Equation 13 for use with ASD load combinations, LRFDiγ is replaced by ASDiγand nRφ is replaced by nR Ω . Thus, Equation 13 becomes
( )ASD
2 2
1 ln i
ii
m
n mR Q
RR QV V
⎡ ⎤⎛ ⎞γβ = ⎢ ⎥⎜ ⎟Ω⎢ ⎥+ ⎝ ⎠⎣ ⎦
(14)
Based on extensive studies for A992 steel (Bartlett et al.2) and the original work for the
development of the 1986 AISC Specification by Ravindra and Galambos, the following values can be used:
Mm = 1.055; VM = 0.058 Fm = 1.00; VF = 0.05 Pm = 1.02; VP = 0.06
Thus, ( )( )( )
( ) ( ) ( )2 2 2
1.055 1.00 1.02 1.076
0.058 0.05 0.06 0.097
m n n
R
R R R
V
= =
= + + =
Based on Galambos et al.3 (1982), the ratio of mean to code specified dead and live loads
can be taken as, for dead load Dm/D = 1.05; VD = 0.10
and for live load
Lm/L = 1.00; VL = 0.25
The values for imQ and imV will be functions of the live-to-dead load ratio. The reliability index, β, based on Equations 13 and 14, for a live-to-dead load ratio from
1.0 to 5.7 is presented in Figure 1.18 for a compact wide-flange beam under uniform moment for both LRFD and ASD. The figure is based on the load combination of live load plus dead load and statistical variations consistent with those used in the development of the Specification. It is seen that the reliability of design by LRFD is somewhat more uniform for this condition than design by ASD and that at a live to dead load ratio of approximately 3, the two approaches yield the same reliability. The higher the reliability index is, the safer the structure. Regardless of the numerical value of β, any structure that meets the requirements of the Specification will be sufficiently safe. A more detailed discussion of the statistical basis of steel design is available in Load and Resistance Factor Design of Steel Structures.4 Since the introduction of the 2005 AISC Specification, design by ASD and LRFD have essentially been equivalent and differ only by the effect of load combinations.
2 Bartlett, R.M., Dexter, R.J., Graeser, M.D., Jelinek, J.J., Schmidt, B.J. and Galambos, T.V. (2003), “Updating Standard
Shape Material Properties Database for Design and Reliability,” Engineering Journal, American Institute of Steel Construction, Vol. 40, No. 1, pp. 2–14.
3 Galambos, T.V., Ellingwood, B., MacGregor, J.G. and Cornell, C.A. (1982), “Probability-Based Load Criteria: Assessment of Current Design Practice,” Journal of the Structural Division, American Society of Civil Engineers, Vol. 108, No. ST5, May, pp. 959–977.
4 Geschwindner, L. F., Disque, R. O., and Bjorhovde, R. Load and Resistance Factor Design of Steel Structures. Englewood Cliffs, NJ: Prentice Hall, 1994.
26 Chapter 1 Introduction
Figure 1.18 Reliability Index vs Live-to-Dead Load Ratio for Compact Simply Supported Wide-Flange Beams with Uniform Moment
General structural integrity requires a continuous load path to the ground for resisting all
gravity and lateral loads that might be applied to the structure. With the introduction of the 2016 AISC Specification, provisions that address structural integrity beyond these general requirements have been introduced. The requirements in Section B3.9 are beyond normal strength requirements and are intended to improve the connectivity of the structure and thus the performance of the structure under undefined extraordinary events. These requirements apply only to a small set of structures where additional structural integrity is mandated.
1.13 LIMIT STATES
Regardless of the design approach, ASD or LRFD, or the period in history of the design’s execution, 1923 or 2018, all design is based on the ability of a structure or its elements to resist load. This ability is directly related to how an element carries that load and how it might be expected to fail, which is referred to as the element’s limit state. Each structural element can have multiple limit states, and the designer is required to determine which of these limit states will actually limit the structure’s strength.
There are two types of limit states to be considered: strength limit states and serviceability limit states. Strength limit states are those limiting conditions that, if exceeded, will lead to collapse of the structure or a portion of the structure, or to such serious deformations that the structure can no longer be expected to resist the applied load. Strength limit states are identified by the Specification, and guidance is provided for determination of the nominal strength, Rn, the safety factor, Ω, and the resistance factor, φ. Examples of the more common strength limit states found in the Specification are yielding, rupture, and buckling.
Serviceability limit states are not as well defined as strength limit states. If a serviceability limit state is exceeded, it usually means that the structure has reached some performance level that someone would find objectionable. The Specification addresses design for serviceability in Chapter L and defines serviceability in Section L1 as “a state in which the function of a building, its appearance, maintainability, durability, and the comfort of its occupants are preserved under typical usage.” Chapter L lists deflections, drift, vibration, wind-induced motion, thermal expansion and contraction, and connection slip as items to be considered, although no specific limitations are given for any of these limit states.
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Introduction Chapter 1 27
Strength and serviceability limit states will be addressed throughout this book as appropriate for the elements or systems being considered.
1.14 BUILDING CODES AND DESIGN SPECIFICATIONS
The design of building structures is regulated by a number of official, legal documents that are known commonly as building codes. These cover all aspects of the design, construction, and operation of buildings and are not limited to just the structural design aspects.
The model code currently in use in the United States is the ICC International Building Code. Model codes are published by private organizations and have been adopted, in whole or in part, by state and local governments as the legal requirements for buildings within their area of jurisdiction. In addition to the model codes, cities and other governmental entities have written their own local building codes. Unfortunately, since the adoption of a building code is in great part a political activity, the regulations in use across the country are not uniform. A new International Building Code is published every 3 years but not adopted as quickly as issued. Thus, building codes with effective dates from 2003 to 2015 are still in use. In addition, governmental bodies will often adopt a model code with local amendments. Because of the technical nature of the AISC Specification, local amendments normally do not affect those aspects of steel design but they often do modify the loading definitions and thus do ultimately affect steel design.
To the structural engineer, the most important sections of a building code deal with the loads that must be used in the design, and the requirements pertaining to the use of specific structural materials. The load magnitudes are normally taken from Minimum Design Loads for Buildings and Other Structures, a national standard published by the American Society of Civil Engineers (Structural Engineering Institute) as ASCE/SEI 7. The loads presented in ASCE/SEI 7 may be altered by the model code authority or the local building authority upon adoption, although this practice adds complexity for designers who may be called upon to design structures in numerous locations under different political entities. Throughout this book, ASCE/SEI 7 will be referred to simply as ASCE 7 as it is most commonly referred to in the profession.
The AISC Specification is incorporated into the model building code by reference. The Specification, therefore, becomes part of the code, and thus part of the legal requirements of any locality where the model code is adopted. Locally written building codes also exist and the AISC Specification is normally adopted within those codes by reference also. Through these adoptions the AISC Specification becomes the legally binding standard by which all structural steel buildings must be designed. However, regardless of the Specification rules, it is always the responsibility of the engineer to ensure that their structure can carry the intended loads safely, without endangering the occupants.
1.15 INTEGRATED DESIGN PROJECT
This section introduces a building to be used in subsequent chapters of this book as an integrated design project. It is a relatively open-ended design project in that only a limited set of design parameters are set at this point. Several options will be presented in subsequent chapters so that the project can be tailored at the desire of the instructor.
The building is a four-story office building with one story below grade. It is located in Downers Grove, Illinois, at approximately 42°N latitude and 88°W longitude. This is a 102,000 ft2 building with approximately 25,500 ft2 per above-grade floor. For the first three floors, the floor-to-floor height is 13 ft 6 in. For the top floor, the floor-to-roof height is 14 ft 6 in. The below-grade floor-to-floor height is 15 ft 6 in. The façade is a lightweight metal curtain wall that extends 2.0 ft above the roof surface, and there is a 6.0 ft screen wall around the middle bay at the roof to conceal mechanical equipment and roof access. All steel will receive spray-applied fireproofing as necessary.
2
28 Chapter 11 Introduct
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Introduction Chapter 1 31
12. Describe the difference between a strength limit state of a structure and a serviceability limit state. 13. Give a description of both the LRFD and ASD design approaches. What is the fundamental difference between the methods? 14. Provide a brief description of plastic design (PD).
15. Identify three sources of variation in the strength of a structure and its components. 16. Provide three examples of strength limit states. 17. Provide three examples of serviceability limit states.