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The National Earthquake Hazards Reduction Program (NEHRP) Technical Briefs are published by the National Institute of Standards and Technology (NIST), as aids to the efficient transfer of NEHRP and other research into practice, thereby helping to reduce the nation’s losses from earthquakes.
The National Institute of Standards and Technology (NIST) is a federal technology agency within the U.S. Department of Commerce that promotes U.S. innovation and industrial competitiveness by advancing measurement science, standards, and technology in ways that enhance economic security and improve our quality of life. It is the lead agency of the National Earthquake Hazards Reduction Program (NEHRP). Dr. John (Jack) R. Hayes is the Director of NEHRP, within NIST’s Engineering Laboratory (EL). Dr. John (Jay) Harris managed the project to produce this Technical Brief for EL.
Thomas A. Sabol, Ph.D., S.E., A.I.A, is Principal with Englekirk & Sabol in Los Angeles, California and Adjunct Professor of Civil and Environmental Engineering at UCLA, teaching classes in steel design, seismic design, and tall buildings design. He is both a registered structural engineer and architect. He has led his firm’s design work on projects such as the Getty Museum and major buildings on the campuses of the University of California at Los Angeles, Riverside, and San Diego. He is a member of the American Institute of Steel Construction Task Committee 9 – Seismic Provisions.
The contributions of the three review panelists for this publication are gratefully acknowledged. James O. Malley, P.E., S.E., is Vice-President of Engineering with Degenkolb Engineers in San Francisco, California. For the Building Seismic Safety Council he has chaired the technical subcommittee responsible for the development of steel provisions. In 2000, AISC presented Mr. Malley its Special Achievement Award. He has served as president of the Structural Engineers Association of California. He was named the 2010 T.R. Higgins Lectureship Award winner for his work on the AISC Seismic Provisions. For the American Institute of Steel Construction, he is the chair of Task Commitee 9 - Seismic Provisions and serves on the Specifications Committee. Dominic J. Kelly, P.E., S.E., is an Associate Principal of Simpson Gumpertz & Heger Inc. in Waltham, MA where he designs, rehabilitates, and investigates building and non-building structures. He is a Fellow of the American Concrete Institute, and has served on ACI Code Committee 318 since 2003. He has served as a member of the Seismic Code Committee of ASCE 7 since 2000. Thomas Sputo, Ph.D., P.E., S.E., SECB is President of Sputo and Lammert Engineering, LLC in Gainesville, FL, designing and investigating buildings and other structures, and is the Technical Director of the Steel Deck Institute. Additionally, he is a Senior Lecturer at the University of Florida, teaching structural design. He is a member of the American Iron and Steel Institute Committee on Specifications, where he chairs the Subcommittee on Test Methods. He is a former chair of the ASCE Committee on Cold-Formed Steel.
This NIST-funded publication is one of the products of the work of the NEHRP Consultants Joint Venture carried out under Contract SB134107CQ0019, Task Order 10253. The partners in the NEHRP Consultants Joint Venture are the Applied Technology Council (ATC) and the Consortium of Universities for Research in Earthquake Engineering (CUREE). The members of the Joint Venture Management Committee are James R. Harris, Robert Reitherman, Christopher Rojahn, and Andrew Whittaker, and the Program Manager is Jon A. Heintz.
Rafael Sabelli, P.E., S.E., is Director of Seismic Design at Walter P Moore, a structural and civil engineering firm with offices nationwide. He is a member of the American Institute of Steel Construction Task Committee 9 – Seismic Provisions, a member of the Building Seismic Safety Council’s 2014 Provisions Update Committee, and of the American Society of Civil Engineers Seismic Subcommittee for ASCE 7-10. W. Samuel Easterling, Ph.D., P.E., is the Montague-Betts Professor of Structural Steel Design and Department Head in the Charles E. Via, Jr. Department of Civil and Environmental Engineering at Virginia Tech. He is a member of the American Institute of Steel Construction Committee on Specifications and the Chair of Task Committee 5 – Composite Design, a member of the American Iron and Steel Institute Committee on Specifications, and a member of the Building Seismic Safety Council 2014 Provisions Update Committee Issue Team 6 – Diaphragm Issues.
these include: • Formed concrete diaphragms on steel members (these are addressed in Seismic Design Technical Brief No. Introduction Building structures are typically composed of horizontal spanning elements. • Out-of-plane wall support and design of subdiaphragms. • Ramp issues in parking garages. ASCE 7-10 is the latest published version of that standard.3. braced frames. This system is typically conceived of as spanning horizontally between the vertical elements of the lateral load-resisting system. • Saw-tooth roofs and similar discontinuities. it is not specifically addressed. Chords. diaphragms serve a number of other functions in providing structural stability and resistance to lateral loads. In order to maximize the utility of this Technical Brief as a stand-alone design reference work. a jurisdiction may reference the previous (2005) edition in its code regulations. This Guide addresses the design of diaphragms composed of steel beams and steel deck with concrete fill. which establishes general regulations for buildings. and Collectors. Seismic design of building systems entails controlling the building displacements.g. Additionally. The forwardlooking approach here in this Guide will facilitate its use over the next several years. Seismic Design of Cast-in-Place Concrete Diaphragms. though in a particular case at the time a reader may consult this Guide. Seismic Design of Composite Steel Deck and Concrete-filled Diaphragms: A Guide for Practicing Engineers 1 . however.1. and thus large movements. The 2012 IBC adoption of ASCE 7-10 has no modifications relevant to composite or concretefilled steel deck diaphragm design. and • Expansion joints and seismic separation issues. which in turn deliver the forces to the foundation. as discussed in Section 2. walls. such as semirigid and flexible diaphragms.3: Seismic Design of Cast-in-Place Concrete Diaphragms. diaphragms are a critical component of seismic design and must be properly designed to ensure adequate performance. includes a great deal of useful information on diaphragm design in general. such as columns and walls. and Collectors).. The design forces and analysis requirements for diaphragms are contained in ASCE/SEI 7-10 Minimum Design Loads for Buildings and Other Structures (ASCE 2010. vertical elements. and foundation elements. but a future Technical Brief devoted entirely to bare steel-deck diaphragms is anticipated. such as beams and floor and roof decks. In passing. typically by providing resistance to the inertial forces generated by the acceleration of the building mass. The National Earthquake Hazards Reduction Program (NEHRP) Seismic Design Technical Brief No. Thus. Chords. this material is integrated with a treatment of conditions beyond the scope of the reinforced concrete diaphragm Technical Brief. because ASCE 7-10 has been adopted into the 2012 edition of the International Building Code (IBC 2012. Items not covered in this document A number of important issues related to diaphragm design are not addressed in this document. would result. Sidebars in the Guide Sidebars are used in this Guide to illustrate key points and to provide additional guidance on good practices and open issues in analysis. The first segment of this load path is composed of the diaphragm system. although many of the diaphragm analysis and design methods described herein are applicable to the design of diaphragms to resist wind forces and provide structural integrity in Seismic Design Category A buildings. • Strut-and-tie analysis methods. Without this element of the load path there would be no resistance to the movement of the distributed building mass. and resistance is composed of a continuous lateral load path from these spanning elements to vertical elements that have lateral resistance (e. • Design of open-web joists as chords or collectors. and construction. the Guide addresses some issues related to the design of diaphragms with non-composite (bare) steel deck. moment frames). Often the great majority of the load is derived from the mass of the roof and floor systems themselves. and perhaps collapse. herein referred to as ACSE 7). design. As Seismic Design Category A is exempt from seismic design. This Guide covers seismic design issues pertaining to Seismic Design Category B up through Seismic Design Category F. some material is duplicated here. herein referred to as IBC). Together these elements comprise an integral system that resists both vertical and lateral loads. • Detailed treatment of steel-deck only systems.
two approaches have commonly been used to calculate the in-plane shear strength. This Guide is intended to address these ambiguities and to provide guidance on the appropriate design of composite deck and steel deck diaphragms. abbreviations. References are listed in Section 10. however IBC recognizes the SDI DDM. This Guide will also be useful to others wishing to apply building code provisions correctly. This Guide was written for practicing structural engineers and is intended to provide guidance in the application of code requirements for the design of diaphragms in steel systems. The attachment of the slab to the steel framing would then need to be addressed using one of the other documents. herein referred to as ACI 318).) Neither is a design code. Section 12 provides credits for figures contained within this document. This Guide begins by generally discussing the role of diaphragms (Section 2).) The specific design information that appears in TI 809-04 for diaphragms does not appear in UFC 3-31004. A consensus standard for steel deck diaphragms that is predominately based on the SDI DDM03 is under development by the American Iron and Steel Institute. The IBC adopts both of these standards. Note that TI 809-04 often called the Tri-Services Manual. and the analysis of the diaphragm itself (Section 6). identifying the components of diaphragms (Section 3). Section 11 contains a list of notations. The design in-plane shear strength of concrete-filled or unfilled steel deck can be determined by calculation. ANSI/AISC 341 Seismic Design Provisions for Structural Steel Buildings (AISC 2010b. and other interpretations may be reasonable. such as educators and students.TI 809-04 (USACE 1998. with SDI DDM03 citing the third edition) and the Seismic Design of Buildings . referred to here as AISC 360) for steel and composite members. referred to here as SDI DDM. this Guide represents only the opinion of the authors on matters not explicitly defined by building codes. Seismic Design for Buildings in 2007 and updated in 2010 (UFC 2010. including limitations and quality requirements. there nevertheless exist ambiguities. and engineering judgment is required in their consistent application. herein referred to as AISC 341) contains additional requirements. or it may be done by testing and subsequent development of an evaluation report. Additional requirements are given in Section 8. and other authorities have been consulted.) Together these documents comprise the building code requirements applicable to composite deck and steel deck diaphragms. or design manuals. Historically. Seismic Design of Composite Steel Deck and Concrete-filled Diaphragms: A Guide for Practicing Engineers 2 . and to those interested in understanding the basis of such code provisions and of common design methods. and a glossary.Component strengths are determined using ANSI/AISC 360 Specification for Structural Steel Buildings (AISC 2010. The Guide proceeds to detailed guidance on the design of diaphragm components (Section 7). While numerous respected practitioners. was superseded by UFC 3-310-04. researchers. design standards. and constructability concerns are discussed in Section 9. (References to the building code in this Guide refer to the editions cited above. as ACI 318 does not explicitly address this condition. Next the Guide describes the building analysis necessary to obtain appropriate diaphragm design forces (Section 5). and proceeding to the behavior of diaphragms (Section 4). such as building officials. In cases where the designer wishes to ignore the presence of steel deck in concrete-filled systems. These approaches are described in the Steel Deck Institute Diaphragm Design Manual (SDI 2004. the in-plane strength of the concrete above the top flange of the deck is evaluated using Building Code Requirements for Structural Concrete and Commentary (ACI 2008. While each of these documents has been developed or revised over numerous cycles to work with the others.
Figure 2-1 illustrates several of these roles for a building with a podium level at grade and with belowgrade levels. • Transfer forces through the diaphragm – As a building responds to earthquake loading. including in-plane and out-of-plane offsets in these elements. and to the basement walls. significant inertial forces can develop in the plane of the diaphragm. Consequently. including those due to tributary portions of walls and columns. the diaphragms complete the three-dimensional framework to resist lateral loads. The largest transfers commonly occur at discontinuities in the vertical elements. by tying together the vertical elements of the lateral force-resisting system. Out-of-plane forces also develop due to wind pressure acting on exposed wall surfaces.2. The main roles include: • Transfer lateral inertial forces to vertical elements of the seismic force-resisting system – The floor system commonly comprises most of the mass of the building. soil pressure bears against the basement walls out-of-plane. through the podium slab. producing compressive reaction forces at the edges of the diaphragms. One of the primary roles of the diaphragm in an earthquake is to transfer these lateral inertial forces. Lateral loads Diaphragm Gravity framing Structural braced frame Transfer (podium) slab Thru st Thru st Gravity loads Moment-resisting frame Basement wall Inclined column Below grade soil pressure Figure 2-1 – Roles of diaphragms.1 Typical Conditions	Diaphragms serve multiple roles to resist gravity and lateral forces in buildings. Seismic Design of Composite Steel Deck and Concrete-filled Diaphragms: A Guide for Practicing Engineers 3 . • Support soil loads below grade – For buildings with subterranean levels. • Resist vertical loads – Most diaphragms are part of the floor and roof framing and therefore support gravity loads. to the vertical elements of the seismic force-resisting system. thereby providing lateral support to resist buckling as well as second-order forces associated with axial forces acting through lateral displacements. The Roles of Diaphragms 2. The tendency is for a majority of the shear in the vertical elements above grade to transfer out of those elements. The basement walls span between diaphragms or between a diaphragm and the foundations. lateral shears often must be transferred from one vertical element of the seismic forceresisting system to another. Large diaphragm transfer forces can occur in this case. They also assist in distributing inertial loads due to vertical response during earthquakes. Furthermore. The diaphragm-to-wall connections provide resistance to these out-of-plane forces. Figure 2-1 illustrates a common discontinuity at a podium slab. • Resist out-of-plane forces – Exterior walls and cladding develop out-of-plane lateral inertial forces as a building responds to an earthquake. • Provide lateral support to vertical elements – Diaphragms connect to vertical elements of the seismic force-resisting system at each floor level.
vertical columns become somewhat inclined when the building undergoes significant drift. Use of building code seismic demands amplified by Ω0 . such as at openings in the diaphragm around its perimeter. the cantilevered diaphragm’s aspect ratio may result in significant horizontal displacements at the extreme edges that are not accurately captured by analytical models that assume essentially rigid body response. Diaphragms also serve a number of specialized functions. The development of these chord members may extend a considerable distance into the main body of the diaphragm. e. • Resist thrust from inclined and offset columns – Architectural configurations sometimes require inclined or offset columns.2 Additional Functions	the response of a diaphragm and must be considered by the designer.2. is one approach to accomplish this goal. and other large openings such as atria. which include: • Redistribution of loads around openings – For buildings with stairway openings. • Redistribution of forces due to torsion – Some architectural configurations result in torsional response due to the application of lateral forces. Additionally. aspect ratios greater than 1. the system overstrength factor. the diaphragm assists in redistributing lateral forces around the openings and to the lateral force-resisting elements. and torsional irregularities that may impact Diaphragm Chord or collector Large opening at diaphragm perimeter resulting in unbraced collector or chord Vertical element of seismic force-resisting system Figure 2-2 – Unbraced collector or chord. Relatively flexible diaphragms generally do not facilitate the distribution of lateral forces due to torsion. may require diaphragm chords to develop the tension component of flexural demand. The thrusts can act either in tension or compression. While designers often attempt to evenly distribute vertical elements of the seismic force-resisting system throughout the footprint of the diaphragm. or as a part of a bridge connection between adjacent segments of diaphragm. aspect ratios associated with flexural behavior.g. due to gravity and overturning actions. elevator shafts. depending on orientation of the column and whether it is in compression or tension. Chapter 12 of ASCE 7 classifies a number of horizontal structural irregularities. Another common condition that demands the attention of the designer is where a chord or collector is laterally unbraced over a significant distance. Although not a code requirement. the effect of the unbraced length on the available compression strength must be considered. diaphragm discontinuities.. the importance of maintaining an integral load path suggests that the magnitude of the chord force assumed in design should be sufficient to maintain elastic behavior under all but the largest earthquakes. The diaphragm or components within it need to be designed to resist these thrusts. In addition.5 to 2. mechanical shafts. as shown in Figure 2-2. In these conditions. Seismic Design of Composite Steel Deck and Concrete-filled Diaphragms: A Guide for Practicing Engineers 4 . portions of the diaphragm without vertical seismic elements may sometimes exist and extend a considerable distance from the main body of the diaphragm. such as reentrant corners. Diaphragms with sufficient strength and stiffness are capable of distributing forces to the lateral force-resisting elements. These diaphragms cantilever horizontally from the bulk of the diaphragm and need to be carefully evaluated by the designer. Generally speaking. which can result in large horizontal thrusts acting within the plane of the diaphragms.
The web of the beam is the deck. or drag struts. Seismic Design of Composite Steel Deck and Concrete-filled Diaphragms: A Guide for Practicing Engineers 5 . referred to as chords. The supports for the beam are the vertical elements of the lateral load-resisting system. chords. moment frames. These components consist of the deck (bare steel deck or composite slab). Collector forces are illustrated in Figure 3. The seam fasteners are important to the shear behavior of the unfilled steel deck. or walls. These collector members must transfer the forces to each other across their connections to the columns. The Glossary in Section 11 defines the specific meanings of these and other terms used in this Guide. the steel deck consists of individual deck sheets. (a) Plan (b) Collector actions Mu Vu Figure 3-2 – Diaphragm collectors. where the beams that are part of the braced or moment frame do not extend the full depth of the diaphragm. Cu compression chord Collectors. In cases where the vertical elements of the lateral load-resisting system are not the full depth of the diaphragm. each of which must be considered as part of the strength determination and response. The remaining spandrel members in Figure 3. They are critical at the construction stage in filled diaphragms. that is. Their role in the filled deck diaphragm is less important. This is illustrated in Figure 3. and structural fasteners at locations of deck support. frame d tension chord Vu Tu (a) Plan (c) Internal moment and shear resistance The diaphragm deck may consist of either an unfilled steel deck (typical for roofs) or a filled steel deck.3.1 at the outer frame lines. or. which provides the shear resistance.1 are attached to the deck through fasteners collecting inertial forces from the deck and in turn delivering those forces to the frame members. seam (or stitch) fasteners at the edges of sheets. More details and design approaches are given in Chapter 7. are made up of the steel framing at the perimeter of the floor. Diaphragm Components Diaphragms consist of several components. they are not the mechanism for load transfer. Given that the diaphragm typically involves multiple bays. such as braced frames. depending on the means by which they are attached to the deck. occur where the deck forces are transferred to a frame line over a partial length. The diaphragm is commonly idealized as a beam spanning horizontally as shown in Figure 3. collectors (also known as drag struts) and fasteners used to attach the deck to the perimeter framing members.2. but after the concrete has cured.1. The chord components must be designed to resist the tension or compression generated from beam behavior. V Mu M Vu (b) Simple beam idealization Figure 3-1 – Diaphragm component idealization. which is achieved through bond of the steel deck to the concrete over essentially the entire diaphragm area. These members may be considered non-composite. the chord members must be tied together through the connections to columns. the designer may wish to consider their composite strength. The top and bottom flanges of the beam. The perimeter fasteners are required to tie the deck to the chords and to the vertical elements of the lateral load-resisting system. or composite steel deck and concrete-filled diaphragm. In all cases. the framing members along the frame line function to “collect” the diaphragm shears and deliver these forces to the frame. This results in an axial component of force through the connection that must be considered.
5 in this design spectrum.1 Dynamic Response of Buildings and Diaphragms	From fundamental studies of structural dynamics (e. Fpx. the term SDS represents the design spectral acceleration for short-period structures. The ratio of the peak response acceleration to the peak ground acceleration is called the response acceleration magnification. Seismic Design of Composite Steel Deck and Concrete-filled Diaphragms: A Guide for Practicing Engineers 6 . Rodriguez et al. because each floor reaches its peak response at a different time during the In addition to resisting inertial forces (tributary mass times floor acceleration). Thus. considering only diaphragm actions due to Fpx is not sufficient.4SDS. Fx. because of higher-mode response. dynamic response. Diaphragm Behavior and Design Principles 4. the diaphragm develops internal forces as it imposes displacement compatibility (Figure 4-3). For buildings responding inelastically. The behavior of multi-story buildings is similar. but it would be overly conservative to design the vertical elements of the seismic force-resisting system for the sum of all the individual peaks. frames and walls acting independently have different displacement profiles under lateral loads. two different sets of design forces commonly are specified for design: • One set of design forces. is applied to the design of the diaphragms. In Figure 4-1. The smooth design response spectrum of ASCE 7 (2010) (Figure 4-1) represents this period dependency. 2007) show response acceleration magnification also is around 2. Each floor should be designed to resist the inertial force corresponding to the peak response acceleration for that floor. diaphragms also must be able to transfer forces between different vertical elements of the seismic force-resisting system. Its value for short-period structures is 2. (a) Isolated frame and wall (b) Frame and wall connected by floor diaphragm Figure 4-3 – Diaphragms develop transfer forces by imposing displacement compatibility between different vertical elements of the seismic force-resisting system. The peak ground acceleration. Shakal et al. the different floors trace out different acceleration histories. For example.g. Figure 4-1 – ASCE 7 design response spectrum showing spectral response acceleration as a function of vibration period. In general. which is the spectral acceleration at T = 0. Almost all buildings have force transfers of this type that should be investigated and considered in design. wn hn w2 h2 Fx Fpx w1 h1 (a) Structure (b) Model (c) Forces for vertical element design (d) Forces for diaphragm design Figure 4-2 – Design forces for vertical elements and diaphragms. is applied to the design of the vertical elements of the seismic force-resisting system.. has a building code-prescribed value of 0.. Chopra 2005) we know that the dynamic response acceleration of an oscillator subjected to earthquake ground motion varies with time and that the peak value will be a function of the vibration period of the structure as compared to the frequency content of the input motion. a lower response acceleration magnification generally is obtained. 1995.g. if interconnected by a diaphragm. Studies of building responses (e.4. One important observation about multi-story buildings is that.5 for buildings responding essentially elastically. Figure 4-2 shows these sets of loads. • A second set of design forces.
. If the diaphragm is modeled as a rigid element in a computer analysis of the building. seismic design of a diaphragm should clearly identify the load paths to the vertical elements. Design of gravity columns needs to accommodate the increased displacements. if it occurs at all. the collector design strengths should be determined using a conservative estimate. 2002). expected materials properties. Seismic joints can relieve this action if provided at every level. and the lateral deformations in these flexible diaphragms can result in diaphragm displacements significantly exceeding displacements of the vertical elements (Fleischman et al. This goal is implied in the design approach contained in ASCE 7.. See the sidebar on nonlinear dynamic analysis for additional guidance. Thus. These segments tend to respond dynamically somewhat independently of the vertical system. a. Some building configurations result in longitudinal splits in the diaphragm (e. which. To achieve this goal. The situation is further complicated when a single column supports sloping diaphragms from two different levels such that the relative stiffness of the vertical elements changes. one of the principles of earthquake-resistant design is to maintain a relatively stiff and damage-free diaphragm that is capable of tying together the vertical elements of the seismic force-resisting system. should be restricted to the vertical elements.” These idealized designations affect the manner in which the designer distributes the design lateral force to be resisted by various vertical elements in the lateral force-resisting system as well as whether the diaphragm is capable of distributing load via 4. causing significant axial load in the diaphragm. for example. the seismic force-resisting system. result in relatively long and narrow diaphragm segments. In addition.3 Diaphragm Classification An appropriate analysis of the lateral system requires the correct assessment of the relative stiffness of the diaphragm compared to the vertical elements of the lateral force-resisting system.” “rigid. Likewise. The model should also reflect a realistic proportioning of the relative stiffness of the column and the diaphragm. See NEHRP Seismic Design Technical Brief No. the inclined ramps can act as unintended diagonal braces. Traditionally. when combined with significant separation of the vertical elements of the seismic force-resisting system. 4. Large diaphragm transfer b. unrealistically large transfer forces might be calculated at the levels of the discontinuities.2 Intended Diaphragm Performance Diaphragms are not intended to be the main source of inelastic deformation in a structure. See SEAOC (2009). diaphragms have been idealized as either “flexible. and sometimes for one or several floors below the discontinuity. an acceptably low probability of failure can be achieved.” or “semirigid. This approach can be acceptable if the analysis and design approach are established to achieve the intent of the code that the collector not be the weak link in the load path. Design approaches for steel deck diaphragms appear to have been relatively effective in limiting diaphragm damage. Vertical element of seismic force-resisting system Nonlinear Dynamic Analysis Guidance Nonlinear response history analysis is sometimes used to determine forces in collectors and their connections as an alternative to using Ω 0 -amplified forces Fx and Fpx. such as the design strength using nominal material properties and the code strength reduction factor. in a parking structure). Figure 4-4 shows a common example involving vertical discontinuities at (a) a setback in the building profile and (b) a podium level at grade.g. 2010). with few cases of observed damage following earthquakes. 4. Large diaphragm transfer Figure 4-4 – Diaphragm transfer forces at irregularities in the vertical elements of the seismic force-resisting system. and should aim to provide diaphragm strength along that load path at least equal to the maximum force that can be developed by the vertical elements. but is not an explicit requirement. At such locations. Collector demands should be determined using an appropriate estimate of the materials properties. They should consider the variability in demands produced by different earthquake ground motions. By appropriate selection of the design demands and strengths. modeling diaphragm flexibility can produce more realistic estimates of design forces in the diaphragms and the vertical elements. shorter) elements that are not always considered by designers. which results in concentrations of lateral force in the stiffer (i. Significant inelastic response in Seismic Design of Composite Steel Deck and Concrete-filled Diaphragms: A Guide for Practicing Engineers 7 . Nonlinear Structural Analysis for Seismic Design (Deierlein et al.Sometimes the largest diaphragm transfer forces are at offsets or discontinuities of the vertical elements of the seismic force-resisting system. it is possible that fully code-compliant designs may not meet this proportioning goal.e.
Seismic Design of Composite Steel Deck and Concrete-filled Diaphragms: A Guide for Practicing Engineers 8 . (a) Translation (b) Translation with rotation (torsion) Figure 4-5 – Plan view of rigid diaphragm.1. The tributary area is considered from a lateral load perspective rather than a vertical load perspective. V. Torsional response can exaggerate the displacement of some edges of a rigid diaphragm (see Figure 4-5b). ASCE 7 § 12.10-1) is constructed from the story forces. As discussed in Section 4. A diaphragm is considered rigid for the purpose of distributing story shear and torsional moment to lateral force-resisting elements when the lateral deformation of the diaphragm is less than or equal to two times the average story drift. Examples of semirigid diaphragms include steel deck diaphragms spanning between moment frames. It is also possible that the prescriptive definition of a rigid diaphragm may not be applicable in situations where relatively large seismic demands need to be transferred through the diaphragm.8). Thus. In real buildings. A rigid diaphragm sustains little in-plane deformation (relative to the walls and frames) due to its dynamic response. In essence.3. These lateral seismic forces represent the overall building design lateral force distribution. (This method does not specifically address variations in drift due to sloping diaphragms or due to the maximum drift being at a location other than diaphragm midspan.1 also requires the diaphragm to be designed for the diaphragm design force.8-12) and thus relates to the design base shear.) ASCE 7 permits concrete-filled steel deck with spanto-depth ratios of three or less to be idealized as rigid.10. Fx. and all points in it experience essentially the same displacement about a given axis (see Figure 4-5a). In a structure with a rigid diaphragm. In these cases. but not all. the structural analysis must explicitly include consideration of the in-plane stiffness of the diaphragm. semirigid modeling of those spans is necessary. An example of a flexible diaphragms is a bare steel deck spanning between braced frames or shear walls. This force is defined by three equations in ASCE 7. otherwise semirigid modeling is necessary.1. the lateral seismic forces. It is possible for a diaphragm to be idealized in different ways depending upon the direction under consideration. do not necessarily reflect the estimated maximum force induced at a particular diaphragm level. spans meet the criteria for flexible diaphragms.1. The lateral seismic forces Fx are determined in the analysis of the vertical elements of the seismic force-resisting system (Figure 4-6a). Fpx (Figure 4-6b). In the flexible case.10 contains the main provisions for diaphragm design. although the Seismic Response History Procedure of ASCE 7 Chapter 16 also can be used. In some cases. The first (Equation 12. They may also have different lateral force-resisting systems. the diaphragm design forces Fpx.4 Building Code Provisions Pertaining to Diaphragms Seismic design of diaphragms is required for all buildings in Seismic Design Category B through F. The definitions of flexible and rigid diaphragms are given in ASCE 7 § 12.10-3) are minima and maxima and relate to the response-spectrum parameter SDS . a diaphragm is idealized as flexible for the purpose of distributing story shear when the computed maximum in-plane deflection of the diaphragm under lateral load is more than two times the average story drift.10-2 and 12. the vertical elements are considered to be significantly more rigid than the diaphragm. the distribution of seismic demand to the walls and frames at a given level generally depends upon the relative rigidity of these elements. and they are not dependant on the system design coefficients R and Ω 0. A diaphragm that is flexible in one direction will not be effective in sharing torsion between the orthogonal systems. A three-dimensional building analysis is necessary to determine the horizontal distribution of forces when diaphragms are rigid or semirigid. Conversely. even if the diaphragm is rigid or semirigid in the orthogonal span. In a structure with a flexible diaphragm. These forces typically are determined from the Equivalent Lateral Force Procedure (ASCE 7 § 12. Where some. the diaphragm is considered to be significantly more rigid than the vertical elements. The second two equations (Equations 12. Diaphragms are always permitted to be treated as semirigid. for a diaphragm to be idealized as rigid it must meet the criteria for both directions.torsion. the sum of which results in the design base shear. and any transfer forces associated with response under the design seismic loading. diaphragms often have multiple spans. ASCE 7 § 12. On the other hand. Fx. The design must consider the lateral seismic forces Fx. the diaphragm in-plane stiffness relative to the vertical elements of the lateral force-resisting system does not permit it to be idealized as either a rigid or a flexible diaphragm. from the Equivalent Lateral Force vertical distribution (Equation 12. 4. and may have very different proportions in orthogonal directions. the distribution of seismic demand to the vertical elements in the lateral force-resisting system generally depends on the tributary area of the diaphragm supported by the vertical element.
a nonlinear response history analysis typically is used. Diaphragm accelerations and the resulting forces can be determined directly from the analysis.10-2 or 12. the selection and scaling procedure needs to properly address those vibration modes.11 apply for the design of the concrete portion of the diaphragm. According to ASCE 7 § 12. such as podium slabs. and D apply to the steel portions. Seismic Design of Composite Steel Deck and Concrete-filled Diaphragms: A Guide for Practicing Engineers 9 . and axial forces. For buildings assigned to Seismic Design Categories B or C. the engineer should exercise good judgment when using the results of a nonlinear response history analysis. and for levels with significant transfers. depending upon the specific condition being evaluated. In such cases. B. including splices and connections to resisting elements. For structures assigned to Seismic Design Categories C through F. Associated design requirements typically are evaluated by applying Fpx to one floor at a time rather than all floors simultaneously. This approach uses the maximum force that can be delivered to a diaphragm by the framing system as the design force. Transfer forces are added to those calculated using § 12. and the reliable resistance as the design strength. whichever produces the larger effect. Where capacity-based design is used. Ground motions sometimes are selected and scaled with a focus on the fundamental period of vibration. (2009). multiple load patterns. section cuts can be used to track diaphragm forces at each time step. However.2. For buildings assigned to Seismic Design Categories D through F. the general requirements in ACI 318 Chapters 1 through 18 and in AISC 360 apply. especially those governed by the minimum diaphragm force of ASCE 7 Equation 12.1 of this Guide) or the overall building model.10-2 or § 12. Diaphragms must also be designed to resist the transfer forces that develop due to framing interaction among different vertical elements.10-1 to determine the governing loading for the component. See Section 5. are required to resist the load combinations.10-3.5 Alternative Approaches There are alternative approaches to determine design forces in diaphragms and collectors. collectors must be capable of transferring the seismic forces originating in other portions of the structure to the element providing the resistance to those forces. and thus multiple ground motions are typically used to analyze the response of structures. In performance-based seismic design. including horizontal offsets or changes in mass and stiffness of the vertical seismic force-resisting system. As with any computer model. but it is overly conservative for other levels. Figure 4-6 – Design forces. The approach may be suitable for roof diaphragms. the diaphragm and its components must be designed to resist all shears. as the forces are not derived from the system response coefficient. those forces need not be amplified by Ω 0. the force from Equation 12. including effects of openings and other discontinuities. moments. Approaches to diaphragm analysis that consider the overall building model are discussed by Sabelli et al. Failure of some connections between concrete diaphragms and concrete shear walls in the 1994 Northridge earthquake triggered code changes for collectors that apply to all diaphragms. multiple failure mechanisms. and AISC 341 Chapters A.1 of this Guide.10. because peak diaphragm accelerations and design forces may be determined by higher vibration modes.10-2. Note that if Fpx is governed by ASCE 7 Equation § 12. 4. The lateral seismic load effect is either Ω 0Fx or Ω 0Fpx. using either simplified models (see Section 6. which are those structures subject to the more stringent seismic design requirements in ASCE 7 due to their occupancy and design earthquake ground motion.10.10-3 should be compared to Ω 0 times the force from ASCE 7 Equation § 12. If diaphragms are modeled as finite elements. and appropriate strength calculation procedures so that the resulting demands and capacities safely cover the range of combinations that can be reasonably expected. Capacity-based design is another way to determine diaphragm design forces.2 and are subject to either the overstrength factor or the redundancy factor. the provisions of ACI 318 § 21. engineers should consider expected material properties. Different ground motions will result in differing degrees of response in a given structure. (a) Vertical elements of the lateral load-resisting system (b) Diaphragms Sections 5 through 9 of this Guide provide guidance on how to analyze and design the diaphragm and different diaphragm related components.Once the forces are determined using the ASCE 7 provisions. R. including overstrength factor Ω 0. collectors.
It begins with a three-dimensional analysis of the building.1 Consistency of Internal Diaphragm Design Forces and Design Forces for the Vertical Elements In limited cases. and there exist multiple load paths for seismic forces from their point of origin to the foundation. and the building’s torsional response all play a role in determining appropriate diaphragm design forces. diaphragms may be determinate with respect to the horizontal distribution of lateral loading. discontinuities. The diaphragm. Nevertheless. the design of the diaphragm should be done consistently with the design approach for the building as a whole. Building Analysis and Diaphragm Forces The seismic forces developed in a diaphragm are dependent on the overall response of the building to the ground motion. Although elastic analysis can be used to determine the relative stiffness of each load path. The procedure for obtaining diaphragm forces from a Modal Response Spectrum Analysis requires additional steps. the condition is indeterminate (Figure 5-1 c and d). In indeterminate cases.2 Diaphragm Classification As mentioned above. the condition is indeterminate. the corresponding forces transferred from the diaphragm to each wall or frame at each level can be obtained for each loading condition. In such cases the design procedure begins with analyzing the diaphragm and applying the reaction forces to the vertical elements. 5. the diaphragm cannot be designed until there is at least some preliminary analysis of the overall building structure. Figure 5-1 shows a number of determinate and indeterminate diaphragm conditions. Determining the appropriate Seismic Design of Composite Steel Deck and Concrete-filled Diaphragms: A Guide for Practicing Engineers 10 . In such cases. and those in which there are only three lines of lateral resistance (corresponding to the three degrees of freedom in the diaphragm plane. Flexible diaphragm Rigid diaphragm (a) Shearwall (typical) (c) Semi-rigid diaphragm (b) Determinate diaphragm conditions (d) Indeterminate diaphragm conditions 5. interaction between frames. During an earthquake the load path may change significantly. In the far more common cases. Thus. From the results of that analysis. being a critical part of the load path. or other dynamic characteristics of the building. As explained in Section 4. and those in which there are only three lines of lateral resistance (corresponding to the three degrees of freedom in the diaphragm plane. the relative stiffness of the vertical elements of the lateral load-resisting system. see Figure 5-1). and to assign the force accordingly. and there exist multiple load paths for seismic forces from their point of origin to the foundation. In the far more common cases. among which is demonstration that there is sufficient strength and stiffness in the structure with respect to design seismic loading. see Figure 5-1b). The building period. In cases in which the diaphragm support condition is indeterminate. the code-prescribed diaphragm design forces are typically larger than the corresponding story force from an Equivalent Lateral Force analysis. the seismic load-resisting system employed. the elastic analysis of the building serves several important purposes. Failure to provide this strength and stiffness is a serious deficiency with respect to fundamental building code requirements. discontinuities in frame stiffness. Additionally. see sidebar. the design sequence is reversed. in certain circumstances the diaphragm is determinate with respect to the horizontal distribution of lateral loading. In most circumstances. must provide sufficient capacity consistent with the load path and force distribution to demonstrate compliance with these strength and stiffness requirements. These forces can be conceived of as the reactions of the diaphragm on its flexible supports. the internal forces used in the design of diaphragm components should be consistent with the forces in the vertical elements to demonstrate code compliance. This typically entails design with the expectation of inelastic demands in the vertical elements of the lateral loadresisting system. the vertical position of the diaphragm in the building. Figure 5-1 – Determinate cases are those in which diaphragms are truly flexible (Figure 5-1a). it should be understood that yielding of the vertical elements of the lateral load-resisting system will have a significant effect on the relative stiffness of these load paths. diaphragms also resist transfer forces as a result of discontinuities in frames. Determinate cases are those in which diaphragms are truly flexible.5. no single load path is absolutely correct. Note that the forces used in the design of diaphragms other than the roof are typically larger than those used for the design of the vertical elements as explained in Section 4.
this procedure would overestimate shears in diaphragms that resist transfer forces. transfer forces in the absence of distinct discontinuities may be considered an artifact of the analysis and not inherent in the building’s response to ground motions. especially at the lower levels of the building. Transfer forces are necessarily large when there are discontinuities in the system. This is sometimes referred to as the “backstay effect.” The analysis might show a shear diagram such as is shown in the figure. the slab will transfer shear consistent with its strength. Forces determined using ASCE 7 Equation 12. this can be achieved through modeling of diaphragm flexibility. because the higher Fpx forces are not to be considered as simultaneous forces. This equation is applied to the story forces obtained from an Equivalent Lateral Force analysis and thus includes the Response Reduction Coefficient. With current commercially available software. a building analysis that does not rely on such transfer forces may be performed. if the design of the horizontal distribution of strength and stiffness among the vertically oriented resisting elements is performed based on such an analysis. R. The lower bound corrects the potential underestimation of forces at diaphragms low in the building due to higher-mode effects. In this case.10-2 and 12. This is especially important for systems with a high Response Modification Coefficient. and diaphragm design must be performed at a higher force level. it is often convenient to amplify the analysis forces for the purposes of diaphragm design by a simple ratio of Fpx to Fx. Such amplification of transfer forces often underestimates the forces in some components and overestimates the forces in others (Sabelli et al. Equivalent Lateral Force building analysis is performed with forces corresponding to the design base shear.Transfer Forces and Building Analysis: The “Backstay Effect” A common example of a building analysis that depends on transfer forces is a shearwall connection to a ground floor slab above a basement (see Figure 5-2). and some shear ductility demands would be expected. the building will have inadequate strength in some vertical elements. The upper bound often governs in systems with a low R. However. These forces are higher than the Equivalent Lateral Force story forces (Fx) at all levels below the roof. As discussed in Chapter 4. This equation is given upper and lower bounds in ASCE 7 Equations 12. even if a Modal Response Spectrum Analysis is ultimately used to design the vertical elements. or concentrated ductility demands in the diaphragm. such as discontinuous walls or frames or abrupt Reaction at ground floor diaphragm Wall elevation Shear diagram Figure 5-2 – Shearwall in building with basement. it is possible that without the ability to transfer forces. as the shearwall might be effectively several stories taller. the building must be analyzed again. R. Failure to provide adequate strength and stiffness in the diaphragm to deliver those transfer forces may invalidate use of that analysis for design. This is often a difficult force to accommodate. the resulting structure may be significantly more flexible. However. 2009). Transfer forces are nearly always present in analyses of multi-story buildings with indeterminate diaphragms. In such Seismic Design of Composite Steel Deck and Concrete-filled Diaphragms: A Guide for Practicing Engineers 11 . larger displacements than anticipated. such a distribution produces appropriate design shears and overturning moments for the walls and frames. and designers are inclined to reduce it by modeling flexibility in that slab or detailing a gap to permit some relative movement of slab and wall. In some cases. Alternatively.10-1 to all diaphragms within a single analysis would overestimate the shear and overturning in the walls and frames. diaphragm forces in such cases is significantly more complicated than it is for flexible diaphragms. but may underestimate diaphragm inertial forces. cases. application of Equation 12. as the reduction in response is more effective in the first mode than in other modes. 5. The degree to which such forces are incorrect depends on the relative magnitude of diaphragm inertial forces and transfer forces. Therefore. However.10-1 (Fpx) reflect the acceleration of a particular diaphragm within the building.10-3. This is always appropriate for determinate structures. Additionally.3 Determination of Design Lateral Forces The typical diaphragm design procedure presupposes that an Equivalent Lateral Force analysis has been performed. which indicates a reaction at the ground floor diaphragm greater than the total shear force in the wall (PEER 2011).
and (c). This would entail modeling these elements so that modal forces.(a) (b) (c) (d) (e) (f) Figure 5-3 – Vertical force distribution with diaphragm force. Story forces. making certain mechanisms difficult to discern in some cases. It should be noted that a set of such reactions for a particular diaphragm will not be statically consistent. In practice. 3. and (f) are the combinations of story forces and diaphragm forces appropriate for evaluating the diaphragms at levels 1. Alternatively. but this is not a concern for most regular buildings. In cases where it is not required. In theory.10-3. Designers may consider using the results of a Modal Response Spectrum Analysis to obtain diaphragm design forces (although such an approach is not formally addressed in ASCE 7). and combinations thereof.101. Additionally. Such an approach would not be in strict compliance with the code. diaphragm reaction forces can be obtained for each loading case being considered. 2. Use of Modal Response Spectrum Analysis has also been proposed for obtaining diaphragm reactions. it is difficult to determine whether the transfer forces are large enough to have a significant effect without performing an appropriate analysis or examining the reactions as described below. and a consistent set of force directions will not be provided. substituting the diaphragm force Fpx for the story force Fx at the level of interest. Designers must consider whether such ambiguities significantly affect the internal diaphragm forces used in design. Forces applied below the diaphragm of interest typically have little or no effect on the forces within the diaphragm. 12. Thus designers must adopt other procedures to obtain the story forces necessary for Equation 12. and 12. there could be significant differences in the load paths determined in the two procedures.10-1. (b) is the set of diaphragm forces Modal Response Spectrum Analysis Modal Response Spectrum Analysis is often required for the building analysis. without applying ASCE 7 Equations 12. the results of Modal Response Spectrum Analysis do not distinguish forces resulting from the acceleration of a diaphragm from transfer forces affecting the diaphragm. For Modal Response Spectrum Analysis. (2009) in which the transfer forces from the building analysis are not amplified but the diaphragm forces are. reactions need to be computed for each mode and combined using an appropriate modal combination procedure. Current commercially available analysis software is typically able to calculate diaphragm reactions for each mode and provide a modal combination. They also can be large in taller buildings and buildings that combine different lateral systems. Such a force distribution is shown in Figure 5-3. This approach explicitly addresses the appropriate combination of transfer and diaphragm inertial forces for each diaphragm. As discussed above. and 4 respectively. do not exist in Modal Response Spectrum Analysis. (e).101. accelerations. where (a) is the Equivalent Lateral Force distribution (Fx). An alternative to this was proposed by Sabelli et al. One approach to analyzing the combination of transfer and inertial forces is to perform a separate building analysis for each diaphragm. it nevertheless provides significant economy due to the reduced base shear and thus is often used. are determined in the analysis.10-2. such as walls and moment frames. An alternative approach is to use the Modal Response Spectrum Analysis directly to determine design forces for diaphragm components of interest. as used in ASCE 7 Equation 12. changes in stiffness. Reactions cannot be meaningfully computed using the difference between Modal Response Spectrum Analysis wall or frame shear at one level and the next. One procedure commonly used is to design the vertical elements of the lateral load-resisting system for Modal Response Spectrum Analysis forces and perform a separate static analysis only for the purposes of obtaining diaphragm design forces. Seismic Design of Composite Steel Deck and Concrete-filled Diaphragms: A Guide for Practicing Engineers 12 . designers have used Modal Response Spectrum Analysis to represent the anticipated diaphragm (Fpx). (d).
In some cases. such as application of accidental torsion in the opposite direction. • Diaphragms that have a significant offset in the center of mass form one level to the next. while simultaneously reducing the principal membrane stiffness of the deck. and the effects of orthogonal frames in resisting torsion on the diaphragm. it is reasonable to include a factor to represent moderate cracking in the slab and other softening mechanisms of the diaphragm. 5. as in the case of semirigid diaphragms. the flexibility of the diaphragm contributes significant additional displacement which should be considered in evaluating these systems in accordance with the deformation compatibility requirements of ASCE 7 § 12. it may be appropriate to model these elements with the axial stiffness of the beams and tributary area of the deck. the additional moment due to accidental eccentricity. and the chord and collector or distributor forces. transfer forces are typically large. and special components such as distributors may be required to resist forces being delivered into the diaphragm by the walls and frames.4 Diaphragms and Discontinuities in the Vertical System There are several types of discontinuities in the walls and frames that require large force transfers through the diaphragm. Such an analysis includes the reactions. In such cases. consistent with the building analysis. as discussed in Section 4. Seismic Design of Composite Steel Deck and Concrete-filled Diaphragms: A Guide for Practicing Engineers 13 . Building Modeling Issues In many cases explicit modeling of the diaphragm as part of a three-dimensional building structure model is advantageous. Research supporting the selection of this factor is lacking.5 (Moehle et al. 5. designers have typically used a modification factor between 0.15 and 0. namely the shear in the deck.12. 2010). will have some effect on the internal diaphragm forces. Such internal diaphragm forces are consistent with the building analysis for the loading case considered. Such a reduction in diaphragm stiffness and the resulting change in horizontal force distribution may have a significant effect on the building response. an analysis of the diaphragm may be performed to obtain internal diaphragm forces. • Walls and frames that have a significant change in shear or overturning stiffness from one level to the next. If such modeling is used to determine chord and collector forces.5 Deformation Compatibility of Gravity System with Flexible and Semirigid Diaphragms	Components of the structural system and nonstructural systems are evaluated considering the expected story drifts of the building to ensure that the deformations imposed on these elements do not cause a loss of their ability to support their gravity loads. It may even be required. and sensitivity studies or design envelopes may be appropriate for the design of walls and frames.Once these reactions are obtained. Such modeling should reasonably reflect the expected behavior and also permit the determination of appropriate design forces. This is especially advantageous in the design of ground floor diaphragms above basements and diaphragms at the top of podium levels. Changes in the loading case. the diaphragm inertial forces. • Walls and frames that terminate at a level below the roof. Where shear in the deck is large. Cases include: • Walls and frames that are supported by columns.5.
In such cases flexible diaphragms may be analyzed similarly. Several analytical methods have been developed. the moment diagram constructed using the methods described above does not close due to the torsional moment resisted by the orthogonal lateral load-resisting system. Cantilever portions of diaphragms. Figure 6-2 – Diaphragm reactions for an indeterminate case. simple-span diaphragms are often analyzed as simple beams. the moment diagram so constructed would not come to zero at one of the diaphragm ends.6. calculated as Fp /L for rectangular diaphragms with uniform mass. L is the diaphragm span between vertical elements of the lateral load-resisting system. 6.2 Equivalent Beam Corrected for Moment Equilibrium	where C is the chord force. can be analyzed as cantilever beams regardless of their rigidity with respect to the supporting frame. the diaphragm loading is in equilibrium with the complete set of reactions at that level. Where the entire depth of the diaphragm is utilized to resist the shear the unit shear may be computed as: v = V / d	(Equation 6-3) where v is the average unit shear along the depth of the diaphragm. the diaphragm analysis method should use diaphragm inertial and transfer forces that are consistent with those in the building analysis. Shear and moment diagrams are used to compute maximum diaphragm shear and chord forces: V = wL / 2	C = wL2 / 8 / d	(Equation 6-1) (Equation 6-2)	6. In other words. with both positive moments in the spans and negative moments at the interior supports. In some cases the diaphragm is continuous with interior walls or frames. d is the distance between chords. This Guide provides some guidance in the selection and application of analytical methods. and w is distributed. for indeterminate diaphragm conditions a building analysis is performed to determine the diaphragm reactions (forces transferred from or to the vertical elements of the lateral load-resisting system). being a simpler case. Figure 6-1 shows a simple-span diaphragm and beam model. Figure 6-1 – Beam analogy for simple diaphragm. including those of the orthogonal lateral load-resisting system that resists some of the torsion. Seismic Design of Composite Steel Deck and Concrete-filled Diaphragms: A Guide for Practicing Engineers 14 . Diaphragm Analysis and Internal Component Forces Once the building is appropriately modeled and diaphragm inertial and transfer forces are determined. and there is little guidance on the selection of a suitable one. As discussed in Section 5. V is the total diaphragm shear adjacent to the line of support at the vertical elements of the lateral load-resisting system. At a minimum.1 Beam Analogy Because diaphragms can be thought of as spanning between the vertical elements of the lateral load-resisting system that act as lateral supports. Thus for a given loading case. an analysis of the internal forces within the diaphragm must be done in order to determine the design forces for the diaphragm components. In such cases.
Seismic Design of Composite Steel Deck and Concrete-filled Diaphragms: A Guide for Practicing Engineers 15 . This creates additional shear between these collector lines and the chord lines. Fp is the inertial force on the diaphragm. R2 is the reaction at one of the shear walls parallel to the force Fp in Figure 6-6. which would have an effect similar to that illustrated in Figure 6-4 . and v2’ is the additional unit shear between the orthogonal collectors. RB is the reaction at one of the shear walls perpendicular to the force Fp in Figure 6-6. Figure 6-3 shows the shear diagram constructed from these unequal reactions. In such cases the chord forces are often significantly smaller than the collector forces for the orthogonal direction of loading. and between the orthogonal collector lines. as is illustrated in Figure 6-5. Figure 6-4 – Moment diagrams for diaphragm (concentrated force). v1’ is the additional unit shear between the orthogonal collector and the chord. Figure 6-2 shows diaphragm reactions for an indeterminate case. the two chord force diagrams would differ as the “Moment Correction” would occur at different points along the chord. Other functions may also be used to represent the pattern of the contribution of orthogonal frames. the walls perpendicular to the direction of the inertial force considered) will be larger than the moment correction force calculated at the diaphragm chord by a factor equal to the ratio of moment arms (d/d ’ ). or they may deliver their force in a more distributed fashion. both between chord line and orthogonal collector lines. Where the orthogonal frames are not on the chord lines. In this case the force R A and RB in the orthogonal walls (that is. they may deliver their forces to the chords in a concentrated length. In this case: Mc = Fp * L / 2 — R2 * L RB = Mc / d ’ (Equation 6-4) (Equation 6-5) (Equation 6-6) (Equation 6-7) Figure 6-3 – Diaphragm shear diagram. Note that if the orthogonal walls did not align. and the moment correction described above may have no effect on the design. the value of this shear is equal to the chord correction force. Figure 6-5 – Moment diagrams for diaphragm (distributed force). Refer to Figure 6-6. this diagram is labeled “Moment. d ’ is the depth between orthogonal collectors resisting the eccentric moment Mc. where the reactions of the two walls parallel to the loading are not equal due to the unequal wall stiffness. The first is the moment diagram constructed from the shear diagram without consideration of the effect of the perpendicular walls. Figure 6-4 presupposes orthogonal walls on the chord lines. which in turn is used to calculate the chord forces. The third diagram (“Corrected Moment”) combines the other two and shows zero moment at the diaphragm ends.In such cases the analysis can be used with a simple adjustment: the moment imparted by the orthogonal lateral load-resisting system should be applied to the moment diagram. there will be some additional shear in the diaphragm. Mc is the eccentric moment required to close the moment diagram. C ’ = Mc / d	v1’ = C ’ / L = Mc / dL	v2’ = [RB — C ’ ] / L = [1 / d ’ — 1 / d ] Mc / L (Equation 6-8) where C ’ is the chord correction force required to close the moment diagram. L is the length of the diaphragm. If orthogonal walls are not on these chord lines.” The second corresponds to the effect that the orthogonal frames impose (“Moment Correction”). Figure 6-4 shows three moment diagrams. d is the diaphragm depth.
forces on individual components must be determined. Figure 6-7 – Uniform shear model. the design in effect relies on some limited ductility in the diaphragm to permit redistribution of forces to account for the simplifications in the assumed distribution. The deck shear may be uniform or non-uniform. The unit shear in the deck and chord. Note that the additional unit shears computed using Equation 6-7 and Equation 6-8 must be combined with the shears computed using the shear from Equation 6-3.Figure 6-6 – Orthogonal collectors eccentric from chord lines.3 Internal Load Paths	To complete the diaphragm analysis. 6. must be calculated so that those components may be designed. In many cases. Seismic Design of Composite Steel Deck and Concrete-filled Diaphragms: A Guide for Practicing Engineers 16 . or concentrated near the vertical elements of the lateral load-resisting system. chord and collector forces may be considered to be concentrated or distributed. the two shears will be additive and in others subtractive. In some areas. the forces calculated in the chords and collectors should be consistent with the assumed shear distribution. At a minimum. There is relatively little guidance in design standards and other publications for the determination or selection of appropriate distributions of shear forces along chords and collectors. such an assumption may require significant shear ductility in the deck to accommodate the deformations consistent with axial deformations in the collector. it is convenient to utilize the orthogonal collectors as chords even when they are not located at the diaphragm boundaries. In the absence of a rigorous analysis that includes both the nonlinear diaphragm properties and the nonlinear behavior of the system. Figure 6-7 shows such a uniform shear distribution and its corresponding linear distributed axial force on a collector. and the collector forces. The shear may be considered to be uniformly distributed along the depth of the diaphragm. Uniform shear distribution along the diaphragm depth typically requires a linear accumulation of the force in a collector to deliver it to a wall or frame. as discussed below. (as well as the full range of possible ground-motion characteristics). For very long collector lengths.
Such a shear distribution is more consistent with concentrated chords at the diaphragm boundaries. as discussed in Section 7. collector forces. An alternative approach is to design components for the larger forces resulting from each assumption. may be concentrated in beams or distributed in a composite deck. For short diaphragm spans and diaphragms with relatively low shear stiffness (e. For composite deck diaphragms. it is necessary to provide some ductility in the components in which the demands may be underestimated. Such a non-uniform shear distribution corresponds to lower collector forces. The shape of the shear force distribution may vary along the span of the diaphragm. For collectors consisting of reinforcement distributed in an area of the composite deck. and there is no clear evidence that such an approach is necessary. uniform or concentrated shear in the deck. Partial-depth collector Secondary distributed collector Chord reinforcement Figure 6-9 – Partial depth collector and secondary collector. For example. resulting in other chord force distributions.g. flexure in the diaphragm is assumed to be resisted in a force couple consisting of axial forces in the beams at the diaphragm boundary. Nonuniform shear is also more consistent with a distributed chord force than with a concentrated chord force at the diaphragm boundary. the width of deck used as the chord is typically selected based on limiting the compressive stress in the deck. as illustrated in Figure 6-9 (Moehle et al 2010). as discussed in NEHRP Seismic Design Technical Brief No. Local reinforcement is required to resolve this eccentricity. That is. Such a mechanism would result in a somewhat smaller effective depth of the section resisting diaphragm forces and some deviation from uniform diaphragm shear. Figure 6-8 shows a non-uniform shear force distribution and the corresponding distributed chord force. Conversely. chord forces may be accommodated in areas of the deck near the diaphragm boundaries. this chord force distribution is consistent with uniform shear in the diaphragm. Seismic Design of Composite Steel Deck and Concrete-filled Diaphragms: A Guide for Practicing Engineers 17 . 2010). non-composite steel deck diaphragms) such an assumption may require significant collector axial ductility to accommodate deformations consistent with the shear deformations. This is not common practice. Alternatively. Little guidance is available on the potential magnitude of these ductility demands. whether they correspond to a uniform shear distribution or not. As discussed in Section 7. 3 (Moehle et al. As neither assumption. engineers typically rely on the basic ductility measures outlined in ACI 318 and AISC 341. the deck or its connections should be detailed to provide ductility. Similarly. a secondary collector and local chords may be used to convert concentrated shear forces near a wall or frame to uniformly distributed shear in the body of the diaphragm. there is an eccentricity from the wall or frame. typically approximately half the collector width. Non-uniform shear distribution Distributed chord forces For non-composite steel deck diaphragms.Alternatively. when uniform shear is assumed.. the chord forces may also be assumed to be resisted in such beams. can be verified in the absence of a rigorous nonlinear building analysis for known loads. In current practice. the shear may be assumed to be concentrated near the vertical elements. when concentrated shear is assumed. the collector load path should be detailed for ductility. As mentioned above. Figure 6-8 – Non-uniform shear and distributed chord forces.
The impact of the reduced area on the portions of the diaphragm that remain must be taken into account as well as the need to transfer forces around the opening. Openings in a diaphragm should be located to preserve as much of the overall diaphragm as possible about any axis. 6. and neither nonlinear behavior in the diaphragm nor in the vertical elements of the lateral load-resisting system is directly addressed. five to ten feet is often used. Thus. See Figure 6-10. diagonal compression and tension may be reported in a finite element analysis. Larger areas of integration may require local shear ductility. unless the chord or collector force is intended to be shared on those lines. Openings in the diaphragm may be idealized similarly to openings in the web of a steel beam. Designers should avoid locating openings in such a way that narrow sections of diaphragm are used to connect different parts of the diaphragm. require consideration by the designer. with the same maximum compressive stress permitted. semirigid diaphragm modeling can be used to determine diaphragm component forces. Generally. While such modeling of the diaphragm is more accurate than the simpler beam analogy models discussed above. and reentrant corners. It may also be necessary to reduce the axial stiffness of nearby parallel beams. clusters of diaphragm openings at reentrant corners or along a single edge of the diaphragm should be avoided. either within a threedimensional building analysis. See Figure 6-11. additional walls or frames may be required in order to prevent isolating one section of the diaphragm from another. In some cases. These stresses may similarly be integrated over moderate widths to permit design of a portion of the deck as a collector.4 Local Effects at Discontinuities Discontinuities in the diaphragm. Stresses corresponding to distributed chord and collector forces in composite decks may also be reported in a finite element analysis. because of the large forces that must be transferred through the small section of remaining diaphragm. Where semirigid modeling is used. using the appropriate diaphragm loading from ASCE 7 § 12. steps. This permits concentrating reinforcement in areas of expected higher demand. For design purposes this stress may be integrated over a limited area. If beams are used as the chords or collectors. Tension and combined shear and tension are more conveniently evaluated in the principal axes of the deck. Seismic Design of Composite Steel Deck and Concrete-filled Diaphragms: A Guide for Practicing Engineers 18 . non-uniform shear stress is likely to be reported. and results should be treated with similar caution. The compression on the diagonal should be treated similarly to compression in the principal axes of the deck. In composite decks.10 combined with the equivalent lateral forces from § 12. It is generally better to locate diaphragm openings so that they are surrounded by substantial portions of the diaphragm or are separated as much as possible. providing moderate ductility in the diaphragm is warranted. only one simplified loading pattern is considered. or as a separate analysis of the diaphragm itself with applied inertial and transfer forces and appropriate reactions from the building model as discussed in Section 5.8. Openings clustered along a single edge of diaphragm Chord or collector Opening clustered at reentrant corner Collector force cannot cross opening Vertical element of seismic force-resisting system Figure 6-10 – Undesirable diaphragm openings clustered along a single edge of the diaphragm or at a reentrant corner.Diaphragm Modeling Issues As discussed in the Sidebar in Section 5. such as openings. it should be noted that it shares some of the same assumptions and limitations. For similar reasons. deck principal membrane stiffness should be modeled as very low to permit determination of beam axial forces.
the steel beam at the step or a downturned concrete slab can be used to transfer the in-plane forces. and walls and frames are remote from the offset. Depending upon the magnitude of the vertical offset. a step in the diaphragm is created. Unless a wall or frame is located at the step. Diaphragm force Displacement at vertical diaphragm offset Figure 6-12 – Elevation view of the displacement at vertical diaphragm offset. When the slab elevation from one section of the diaphragm to another changes abruptly.12. As shown in Figure 6. and the magnitude of the force that needs to be transferred should at least be equal to the demand allocated to the vertical elements aligned with the collector. Seismic Design of Composite Steel Deck and Concrete-filled Diaphragms: A Guide for Practicing Engineers 19 . In this case. Reentrant corners often require extending boundary members into the adjacent section of the diaphragm to adequately transfer loads through the reentrant corner. the stiffness of the out-of-plane load path should be considered in evaluating the effectiveness of transferring forces through the step. when the vertical offset is significant. the designer must ensure that an adequate load path is available to transfer both overturning and chord forces. across the entire diaphragm. preferably. The collector needs to extend at least far enough across the diaphragm to develop this demand or. the extended portion of the diaphragm chord functions as a collector.Opening are seperated as much as possible Openings near reentrant corners still permit extension of chord or collector into the diaphragm and connection to vertical element of seismic force-resisting system Vertical element of seismic force-resisting system Chord or collector Figure 6-11 – Diaphragm openings located to minimize local diaphragm discontinuities.
estimated to be as high as 90 %. 1994b) reported this strength using normalweight concrete as Vn = 3. Calculation-based methods will be presented here.0032 te b √f c ’ (Equation 7-2) Seismic Design of Composite Steel Deck and Concrete-filled Diaphragms: A Guide for Practicing Engineers 20 . 7. is also provided. These include 1) calculation-based methods. The agreement between the calculated and experimental strength of diaphragms in which the experimental strength was controlled by the diagonal shear strength was very good. or some other approach may be selected by the designer..0.3. or a blend of steel and synthetic macro-fibers. The commentary to § I7 of AISC 360 provides general guidance that is presented later in this section. Additionally. 1994b). Calculation procedures for composite diaphragms were also presented by Easterling and Porter (1994a. Easterling and Porter (1994a. thus requiring large numbers of steel headed-stud anchors over a very small length of the steel shape. and only 2 of the 16 tests fell below 1. The composite deck can be evaluated for in-plane. The coefficient 3. Both the significant numbers of steel anchors and additional reinforcement result in additional cost. and 3) results of full-scale in-plane diaphragm tests. Typical composite slab construction consists of embossed composite decks attached to steel framing and filled with either normalweight or structural lightweight concrete. welded-wire reinforcement.2 was based on research findings. following the provisions of AISC 360.1 Composite Deck Steel-framed buildings frequently utilize steel deck composite slabs for the floors. shear using multiple approaches. The vast majority. The secondary reinforcement may be in the form of deformed bars.5 in. but it is traditional and more convenient to design the individual components based on their behavior and the roles they play in the diaphragm system. the mean experimental-to-calculated strength was 1. The AISI document is based extensively on the methodology used in the Steel Deck Institute Diaphragm Design Manual (SDI DDM03. of composite deck slabs are attached to framing members using steel headed-stud anchors. significant steel reinforcement must be placed in the slab to resist the tension components of the composite beam moment in the slab. The detailing of steel anchors is discussed in Section 7. Component Design The individual components described in Section 3 constitute a system. In design of steel decks for gravity loads. steel fibers. synthetic macro-fibers. Rewriting the equation for Vn in the form used in SDI DDM03 results in the following: S n = 0. and that is the shear strength limit state in the concrete. 2) deck manufacturer evaluation reports from agencies such as ICC Evaluation services. No primary or secondary reinforcement was used in the slabs. the American Iron and Steel Institute (AISI) Committee on Specifications is developing and balloting a diaphragm design specification.e. and the behavior is not fully known.) SDI member companies publish diaphragm load tables that are based on calculation methods.84 – 1. nor is it described in detail in design specifications. or diaphragm.1 with a range of 0. i. specific guidance is not provided. these members may be designed as noncomposite beams over their entire length.29. At the time of this writing. This is because the combined load effects from gravity and lateral loads on members that have both negative and positive moments (and thus may be treated as both composite and non-composite) have not been effectively studied. Both beams and girders are typically designed as composite members. The embossed steel deck serves as both the stay-in-place formwork and the tensile reinforcement for gravity load resistance. there is one primary limit state that must be considered for the composite deck. it is common practice to not design negative moment regions in beams to act compositely. Secondary reinforcement. For diaphragms designed with steel headed-stud anchors. The steel headed-stud anchors are detailed to provide the desired composite action between the slab and structural steel member for gravity load resistance. The procedure for the design of the members that are part of a moment or braced frame at the edge of the diaphragm is not entirely clear. This is due to the requirement of having to transfer large shear forces between the steel shape and the slab.7. b is the depth of the diaphragm (inches) and f c ’ is the concrete compressive strength (psi). Although AISC 360 stipulates that composite diaphragms and collectors shall be designed. the length of the negative moment region. Of the 16 diaphragms that exhibited this limit state. or compositely in the positive moment region and non-compositely in the negative moment region. Diaphragm tests conducted as part of the research utilized concrete thickness that varied between 4 and 7. used to constrain cracks in the concrete caused by shrinkage and temperature effects. t e is the effective thickness of the composite slab including a contribution from the steel deck using a transformed section approach.2 te b √f c ’ (Equation 7-1) Where Vn is the shear strength of the diaphragm. and combinations of those two approaches. Thus. test results. There is not a diaphragm design specification presently in place in the United States.
e. the edge fastening along the collectors and chords must be detailed to satisfy the shear transfer demand based on the strength of the field of the diaphragm. additional shear reinforcement may be added to the slab to increase the strength. The work by Easterling and Porter used a contribution of the steel deck through a transformed section approach. 5. 3 (Moehle et al. warping of the deck may result in separation of the deck and concrete. none of the test diaphragms reported by Easterling and Porter contained additional reinforcement (no flexural or secondary reinforcement was used.1-1) Equation 7-3 Where B is the contribution of fasteners that attach deck to steel support members (see definitions for Eq.3-1 in SDI DDM03) and equals 0. Once the strength is determined within the field of the diaphragm. While the two approaches do not take the same form. 2010) provides guidance. but seldom at floors.1 of SDI DDM03. is Sn= BQf ⁄ L + kbdc√f c ’ (SDI DDM03 Eq. Both approaches discussed rely on the steel deck to serve as minimum reinforcement within the field of the diaphragm. The controlling strength is based on the minimum calculated strength based on edge fasteners. Steel deck manufacturers have conducted tests and analyses to develop design load tables. A key point to reiterate is that the strength calculations reviewed pertain to the strength of the field of the diaphragm. The shear stress utilized is 3√f c ’ for normal weight concrete and equations are presented that utilize a concrete thickness of 2. This approach is consistent with the noncomposite steel deck diaphragm calculation model used in SDI DDM03 that will be briefly reviewed later in this section. Therefore. the composite slab properties do not provide adequate resistance. Edge fasteners must be detailed to transfer the strength to the lateral load-resisting frame if that strength is to be utilized.2-4 in SDI DDM03). and dc is concrete cover depth. k is a coefficient that depends on the unit weight of concrete (see definitions for Eq. The behavior of the composite diaphragm near the frame members is very different in these cases. the recommendation is to use the SDI approach. The tests and analyses often utilize proprietary fastening methods that may Seismic Design of Composite Steel Deck and Concrete-filled Diaphragms: A Guide for Practicing Engineers 21 . These load tables are often based on evaluation service reports that were developed by combining test results with various calculation methods. The SDI DDM03 uses a methodology that incorporates a combination of the shear strength of the concrete cover thickness and a contribution of the deck-to-steel framing fasteners within the field (i. As mentioned. the provisions of ACI 318 should be used to determine the strength within the field of the diaphragm. when evaluating the diaphragm demand. As mentioned previously. and extensive design load tables are given in Appendix V. Near the edge of the diaphragm within approximately 36 inches. and one that is covered well in the literature. However. is the approach described in SDI DDM03. b is unit width of the deck (12 in). both use the shear strength of the concrete as the primary mechanism of resistance. If. and 3) results of full-scale in-plane diaphragm tests. A full description of the method is not presented here due to space limitations and the fact that the non-composite diaphragm strength is beyond the scope of this document. 5. and powder-actuated fasteners. In a case such as this. 2. screws.where Sn is the nominal shear strength for diaphragms with structural concrete fill (kips/foot). and the current draft of the AISI diaphragm specification. and corner fasteners. The strength and stiffness of steel deck diaphragms is based on an elastic model that considers the deck. fasteners of the deck to the structural members. These provisions are described in section 2. Q f is the structural fastener strength. and the SDI DDM03 approach utilizes the concrete cover plus a contribution of fasteners that connect the deck to the steel support members. L is the deck panel length.2 Steel Deck Unfilled steel deck diaphragms are often used at roofs. interior panel fasteners.003 for concrete with a unit weight of 145 pcf. NIST Tech Brief No. The interface between the steel deck and the concrete must be utilized to transfer the forces into the framing. 2) deck manufacturer evaluation reports from agencies such as the ICC Evaluation Service. 7. then the edge fasteners are detailed to resist the required shear.5 in and a concrete compressive strength of 3000 psi. but given that the SDI DDM03 approach will likely be included in the AISI Diaphragm Standard. Alternatives to steel headed-stud anchors for transfer of the composite deck diaphragm forces to the framing members include arc-spot welds. and the behavior of the composite deck near the edge of the framing becomes similar to that of a bare steel deck diaphragm. The basic equation used in SDI DDM03. Design load tables appear in the SDI DDM03 that use these limits.. The most detailed of the calculation methods. Both methods give acceptable results. and fasteners of deck sheets at their edges or seams. a brief description of the approach follows. away from the perimeter) of the diaphragm.) The welded wire fabric prescribed in the SDI DDM03 serves to mitigate the effects of shrinkage and temperature-induced cracking. this method forms the basis for the AISI standard that is under development. Steel deck diaphragm strengths are generally determined by one of three methods: 1) calculation-based methods.
In the past few years. and additional reinforcement. These fasteners are less important to composite diaphragms. either arc-spot welds. These are typically deck crimping mechanisms that have been evaluated with both elemental experimental tests and full-size steel diaphragm tests. These include arc-spot (or puddle) welds. The use of steel headed-stud anchors is the most commonly used form of fastening deck to steel support members. The deck-to-structural fasteners do have an influence on the composite diaphragm strength. is deemed to be appropriate. At other times. and steel headedstud anchors. i. steel headed-stud anchors. but evaluation reports developed for the manufacturers reflect the diaphragm strength based on these seam fasteners. Typically. self-tapping/self drilling screws. using Ω0. Design load tables based on the evaluation reports are available for use by the engineering community. The recommendation is to apply ASCE 7 load combinations that recognize reduced demand from live loads if in-plane loads are at a maximum. The strength of steel deck diaphragms is primarily a function of the panel-to-panel fasteners. i. As previously noted. Regardless of the choice of fasteners. powder-actuated fasteners. may provide some guidance to the designer. The seismic provisions in AISC 341 do not contain explicit requirements for dealing with this type of diaphragm. 7. The welding of the steel headed-stud anchors follows. A variety of fasteners can be utilized to accomplish this load transfer. or heavier-gage steel deck are not practical methods to increase the capacity of the diaphragm. The panel-to-panel fasteners have little impact on composite diaphragm strength because the bond between the deck and the concrete is a more complete way to provide panel-to-panel connections. manufacturers test reports.e.. However. the strength of welds. The use of screws or powder-actuated fasteners to attach deck to structural members in composite floor diaphragms is much less common. Diagonal Bracing In some cases it may not be possible to utilize composite deck or steel deck diaphragms to transfer lateral loads around large openings. The direction of shear flow is not uniformly additive for gravity and in-plane loads. As has already been mentioned. The detailed results are not generally available in their basic form. given the prevalent use of composite design for flexural members. the methods in SDI DDM03 are generally applicable if basic fastener strength and stiffness characteristics are available. The question then arises as to how many additional anchors are required to resist the in-plane forces.not be represented in the more general methods described in SDI DDM03. because out-of-plane bracing of the nodes cannot be provided. as well as the interior deckto-structure fasteners. The SDI requires that the floor deck be attached on 12 inch centers and.. screws. either traditional “button-punching” or proprietary seaming. the underlying design intent for diaphragm behavior. powder-actuated fasteners. and the concrete transfers shear between adjacent panels rather than the shear being transferred through the connection. the side seam fastening can be accomplished using welds. and in the AISI diaphragm standard that is under development. Therefore the approach described in the AISC Commentary. Diagonal bracing within the plane of the diaphragm may be a practical way of solving these problems. That said. and screws can be found in AISI S100. a number of proprietary deck seam attachment methods have been developed. additional concrete thickness. and the connections should be capable of developing the tensile strength of the brace member. The commentary of AISC 360 provides guidance on this issue for the first time. or crimping. steel headed-stud anchors have been detailed as part of the gravity composite beams. Arc-spot welds are commonly used to fasten the deck in place when it is first laid out on the frame. as previously discussed and represented in the SDI DDM03 equation for filled diaphragms. and vice-versa. In the typical design scenario. The detailing of steel headed-stud anchors for combined gravity and in-plane (diaphragm) forces has been the subject of much discussion. The members in this diagonally braced diaphragm should be capable of resisting the amplified seismic demand. The selection of the type and number of fasteners depends on the level of force that needs to be transferred and the relative economy of the fastener options. the seam fastening is not particularly important to composite diaphragm behavior and strength. The strength of steel headed-stud anchors can be determined using AISC 360. as well as the design philosophy for concentrically braced frames in AISC 341. The behavior of the steel headed-stud anchors is known to be ductile. the demands in the diaphragm exceed its capacity. and as illustrated in Figure 7-1. half the beam receiving the in-plane forces will experience additive forces and the other half will see forces in opposite directions.e. or a combination of both are typically used.3 Shear Transfer The strength of the diaphragm deck determined for the field of the diaphragm must be adequately transferred to the perimeter framing members if that strength is to be utilized. Additionally. essentially elastic behavior. the side seam fastening has little influence on composite deck diaphragm strength. Seismic Design of Composite Steel Deck and Concrete-filled Diaphragms: A Guide for Practicing Engineers 22 .
A “user note” (guidance similar to commentary placed within the provisions) indicates that the 25 % reduction is not necessary for gravity and collector components in structures with intermediate or special seismic force-resisting systems designed for the amplified seismic load. because the behavior and performance of these elements have not been studied extensively. That information is presented here with the added input of the authors of this Guide. Collectors transfer the deck forces along the edge of the diaphragm when the edge members are not directly part of the lateral frame. Chord members accumulate the tension and compression forces delivering the moment of the “deep beam” model. Diaphragm chords and collectors function as the means by which deck forces are transferred from fasteners to the lateral frame elements.4 Chords and Collectors The AISC 360 Commentary provides guidance for the first time for chord and collector elements.(a) Shear flow due to gravity loads only (b) Shear flow due to gravity and lateral loads in combination Figure 7-1 – Shear flow at collector beams (AISC 360) Copyright © American Institute of Steel Construction Reprinted with Permission. The guidance is not Seismic Design of Composite Steel Deck and Concrete-filled Diaphragms: A Guide for Practicing Engineers 23 . All rights reserved. always definitive. Both of these members can be designed assuming that they behave non-compositely or compositely. AISC 341 requires that the steel headed-stud anchor strength be reduced from the values given in AISC 360 in cases in which composite moment frames. 7. composite braced frames or composite shear walls are used as part of intermediate or special seismic force-resisting systems. The best judgment of the members of the task committee responsible for AISC Chapter I is provided in the AISC commentary.
This ductility is principally achieved from deformations that occur in the mild steel material used to manufacture steel headed-stud anchors.S. The AISC 360 Commentary recommends a simplified approach until such time as research results become available to improve the understanding of these members. The low relative ductility of welded diaphragms. It is recommended that the simplifying assumption of noncomposite axial strength and composite flexural strength be made for the composite beam-column. Beam-to-column connections along the chord or collector must be designed for the combined shear. Combined axial and flexural interaction can be evaluated using the provisions of Chapter H in the AISC Specification. powder-actuated fasteners). Refer to parts 10. Essa et al. on steel headedstud anchors has not included reinforcement within the shear cone breakout area. assuming non-composite action. The flexural strength of the collector and chord members can be evaluated assuming either non-composite or composite action. This is deemed to be good practice because of concerns that the ductility demand may cause failure of the steel anchors if less than 25 % composite action is used. This is deemed to be conservative and is appropriate given the lack of more definitive guidance. AISC 360 addresses the application of stability bracing for beam-columns. The Steel Construction Manual (AISC 2005) and generally available technical literature have addressed a variety of connections that must transfer loads from shear. The beam will behave compositely in the presence of the steel anchors. axial force. the member will respond as a composite beam-column with an eccentric axial load delivered from the plane of the deck. The majority of testing conducted in the U. 2003. This may be attributable to the less than uniform attachment around the circumference of the weld. even if the designer chooses to ignore the flexural composite action. composite diaphragms exhibit ductile behavior.) Ductility of Shear Transfer Devices	The ductility of diaphragms is an important design consideration. when compared to diaphragms constructed with other fastener types.) In cases in which concrete-filled steel deck diaphragms are used and fastened by means other than steel headed-stud anchors. In general. Seismic Design of Composite Steel Deck and Concrete-filled Diaphragms: A Guide for Practicing Engineers 24 . Composite diaphragms typically rely on steel headed-stud anchors for the load transfer from the composite deck to the collector elements. screws. This applies to both the required strength and stiffness of the stability bracing. Tremblay and their colleagues (Rogers and Tremblay 2003. and through warping deformations of the deck profile. ductility is primarily achieved through bearing type deformations in the sheet steel around fasteners (welds. stipulating that the requirement may be addressed by adding the stability bracing required for the axial force (column bracing) to the stability bracing required for the flexural forces (beam bracing). The designer should consider the conclusions of Rogers and Tremblay that screws and powder-actuated fasteners exhibit ductility superior to that of welds without washers. The behavior of these members is complex and has not been the subject of significant research. thus the ductility achieved in these tests has relied only on the steel anchor behavior. Reinforcement is not required by AISC 360 adjacent to the steel headed-stud anchors that are detailed as part of composite beams. has been documented in the work of Rogers. the behavior may be expected to be similar to unfilled steel deck diaphragms. However the fastener configuration used to transfer the diaphragm shears to collector elements can influence the ductility. If non-composite beam action is chosen as the design method.Clearly. and flexure in varying relative magnitudes. they exhibit the least ductile behavior. 12 and 13 in the Steel Construction Manual (AISC 2005. when steel headed-stud anchors are present. In unfilled steel deck diaphragms. There is no clear guidance on how to incorporate the eccentricity. Research has shown that while welds possess the highest strength of typical fasteners. Steel headed-stud anchors possess significant ductility and allow load sharing and redistribution along the length of attachment. the Commentary recommends providing steel anchors at a minimum level of 25 % composite action if the in-plane forces require fewer steel headed-stud anchors. This approach recommends designing the collectors and chords for the axial forces. moment and axial effects delivered to the connection.
For reinforced concrete components. and AISC 341 Tables J6.1 Inspection Composite steel deck diaphragms and their chords and collectors are a part of the seismic force-resisting system.3 Bracing of Columns into Diaphragms Columns spanning more than one floor through openings in the diaphragm are sometimes laterally braced at intermediate levels back to the adjacent diaphragm to reduce the unbraced length of the column. Connections of elements bracing the columns to the adjacent diaphragm must be capable of developing these loads and providing the required level of stiffness. Diaphragms and their elements provide resistance to prescribed seismic forces. Additional Requirements 8. therefore. diaphragms are part of the seismic force-resisting system and should be identified on the statement of special inspections. from IBC Table 1704. stud shear connectors. and steel reinforcing. AISC 360 Chapter N and AISC 341 Chapter J describe inspection tasks for structural steel seismic systems. In addition. IBC Tables 1704.8. The IBC acquires material verification of structural steel components. Periodic inspection is intended to include inspection of all completed reinforcing steel placement. E. Shorter structures of high occupancy categories or Seismic Design Category E also require structural observations. performing slump and air content tests. but observing diaphragm components is recommended.4: • Verifying use of required design mixture. The statement is to include inspection requirements for seismic force-resisting systems in structures assigned to Seismic Design Categories C. or F.3 and 1704. Examples of components that require inspection include structural steel members. the IBC requires continuous special inspection of structural steel welding. connections. welding filler materials. the IBC requires that the size and placement of reinforcing steel be verified with periodic inspections. • Maintenance of specified curing temperature and techniques. and high-strength bolts. In an effort to ensure proper construction.4.10. AISC 360 Chapter C and Appendix 6 contain design requirements for stability bracing of columns. Concrete for diaphragms also requires special inspections. • Concrete placement. Chapter 17 of the IBC requires that the design professional for a building prepare a statement of special inspections identifying the required inspections for construction of the building. 8. including diaphragm steel. Specific required observations for seismic forceresisting systems are not specified. AISC 360 Table N6-1. or F whose height is greater than 75 ft. J8 and J9 list the specific structural steel and reinforced concrete components that require inspection. 8. J7. • Grouting of bonded prestressing tendons that are part of the seismic force-resisting system. Seismic Design of Composite Steel Deck and Concrete-filled Diaphragms: A Guide for Practicing Engineers 25 . with the exception of single-pass fillet welds not exceeding 5/16 inch in size and floor and roof deck welding. concrete fill.2. AISC 360 requires the inspection prior to concrete placement and installation of steel deck and prior to the placement and installation of stud shear connectors. D.2 Quality Assurance According to IBC § 17. and determining concrete temperature at time of placement. • Sampling fresh concrete for strength test specimens. In addition to the requirements in the IBC. inspections are required for most structural steel buildings. Refer to the IBC for current requirements. structural observations by a registered design professional are required for all structures assigned to Seismic Design Category D. Proper construction of diaphragms and their elements is paramount to ensure that the structure will perform as intended during a major earthquake. Inspection of steel frame joint details for compliance with approved construction documents is also required. These special inspections often include the following. E.
5 Location of Construction Joints Construction joints can create weakened planes within the diaphragm. The impacts to the continuity and development of chord and collector reinforcement at construction joints should also be understood. Contract Documents should also require that contractors provide detailed construction joint layout drawings well in advance of concrete placement.4 Protected Zones Testing conducted subsequent to the 1994 Northridge earthquake showed that discontinuities within the protected zone. Detailing and Constructability Issues 9. and connections using only the web of the chord and collector are often not sufficient. and instructions should be clearly detailed in the Contract Documents.1. They can also impact development and splices of reinforcement. instead. § 6. the conduit shall not significantly impair the strength of the construction. it is recommended that conduit not be permitted within the composite deck system and that. The magnitude of the forces along the load path can be significant. The installation of welded stud shear connectors within the protected zone of a moment frame beam or the link in an eccentrically braced frame is not permitted by AISC 341 § I2.2 Penetrations Isolated penetrations. although the ultimate transfer of these forces to the vertical elements of the seismic force-resisting system may result in magnitudes that exceed the capacity of the diaphragm in the vicinity of the vertical element. For that reason. 9. the diaphragm should be analyzed and reinforced as if an opening in the diaphragm existed. such as those caused by welding of stud shear connectors. While construction joints are often detailed carefully on reinforced concrete projects. 9. 9. As a result. and electrical junction boxes. Lastly.1 Detailing of Connections at Chords and Collectors The load path along the length of a collector or chord must be maintained. the conduit run beneath the steel deck. Some engineers use added reinforcement in the slab to resist chord or collector forces. larger than one third of the overall thickness of the slab. connections at column flanges using angles may be flexible enough that deformation in the connection is significant. It also requires that they be spaced no closer than three diameters on center. It is for this reason that a direct load path to the vertical elements using structural steel framing is typically employed. limitations. 9. Although a bolted connection at the web has significant stiffness in the direction of the applied load. such as those for conduits. and fireproofing of the steel deck may be required to establish a reliable fire rating. Arc spot welds as required to secure the decking are permitted because it is believed that the penetration of the weld into the base metal is sufficiently small. Shear-friction reinforcement can be provided across construction joints if necessary to maintain continuity of the diaphragm in shear.3 of ACI 318 addresses items embedded in concrete from the perspective of the strength of the concrete fill. For this reason. even when it is otherwise interrupted by intervening girders or columns.9. These requirements do not address the potential impact on the fire rating of the floor system. welded connections of the chord or collector flanges across the flanges of intervening girders and columns are often used. construction joints in composite deck diaphragms are often overlooked by the designer and located haphazardly by the contractor. It is not uncommon to find these members connected at their flanges and webs to intervening girders and columns. pipes. If conduit within the composite deck cannot be avoided. This section places limits on embedded items with an outside dimension Seismic Design of Composite Steel Deck and Concrete-filled Diaphragms: A Guide for Practicing Engineers 26 . are generally not of significance with respect to the seismic performance of the diaphragm. If a significant number of penetrations are localized in one area. and these evaluation reports are generally silent with respect to conduits within the composite deck and their impact on the performance of the composite deck as a diaphragm or as a fire-rated system. Most manufacturers of steel deck have obtained structural and fire rating approvals through organizations such as ICC-ES and their evaluation reports. have the potential to encourage premature fracture of steel subjected to significant inelastic deformation. typical details.3 Embedded Items in Composite Deck Conduits or other items embedded in composite deck have the potential to introduce an area of reduced structural strength as well as compromise the fire rating of the composite deck system.
R. 3. Washington. Nonlinear structural analysis for seismic design: A guide for practicing engineers. 577-596. 560-576. May 2002. (2007).. PEER (2011). Gaithersburg. (PEER 2010/05).R. and Willford. (1994a). R.. Kelly. References ACI (2008). NIST GCR 10-917-4. and Meyer.S. “Seismic design forces for rigid floor diaphragms in precast concrete building structures.G. Feb. DC. T. Oakland. 4. and Porter. International Building Code. 120 (2). ASCE.A. 133 (11) November 2007.J.” Earthquake Spectra.D.” Journal of Structural Engineering. pp. p.. VA. Washington. and Blandón. Moehle... International Code Council. M. a partnership of the Applied Technology Council and the Consortium of Universities for Research in Earthquake Engineering. 1658-1666. and Porter. (2002). Farmington Hills. L.J. Chopra. ASCE. NIST GCR 10-917-5. DC (in press).. Chicago. produced by the NEHRP Consultants Joint Venture. AISC (2010b). A. Seismic provisions for structural steel buildings (AISC 341-10) and commentary. AISC (2005).Part II. Fleischman.” Journal of Structural Engineering. chords.P.. “Steel-deck-reinforced concrete diaphragms . J. M. 1604-1615. IL. ASCE. Easterling. “Seismic performance of perimeter lateral system structures with highly flexible diaphragms.M. L. “Behavior of roof deck diaphragms under quasistatic cyclic loading. 120(2). C.T. American Iron and Steel Institute. ASCE. Tremblay. J. S. NEHRP Seismic Design Technical Brief No. W. G. (2010). H. M. American Concrete Institute. American Institute of Steel Construction. AISI (2007).K. “ Journal of Structural Engineering. ASCE. MI. Deierlein. Farrow. North American specification for the design of cold-formed steel structural members (AISI S100-2007). Feb. Steel construction manual. Guidelines for performance-based seismic design of tall buildings. and Eastman. Pacific Earthquake Engineering Research Center. M. (2005). Minimum design loads for buildings and other structures (ASCE/SEI 7-10). Restrepo.. 129(12). pp. Rodriguez. Specification for structural steel buildings (AISC 360-10) and commentary. K. 13th Edition. IL. Seismic design of cast-in-place concrete diaphragms. NEHRP Seismic Design Technical Brief No. Hooper. Building code requirements for structural concrete (ACI 318-08) and commentary. Earthquake Engineering Research Institute. 2nd Edition. for the National Institute of Standards and Technology. (2010). IBC (2012). a partnership of the Applied Technology Council and the Consortium of Universities for Research in Earthquake Engineering. produced by the NEHRP Consultants Joint Venture. 129. A. pp.. (1994b). Chicago. 18 (2). D. and Rogers.E. S.B.Part I. and collectors: A guide for practicing engineers. Seismic Design of Composite Steel Deck and Concrete-filled Diaphragms: A Guide for Practicing Engineers 27 .. Berkeley CA. Reinhorn. American Society of Civil Engineers. Essa. “ Journal of Structural Engineering. Chicago.. for the National Institute of Standards and Technology.I. J. ASCE (2010). K..10. Easterling. MD. Gaithersburg. pp. American Institute of Steel Construction. Earthquake dynamics of structures: A primer. (2003). W. AISC (2010a). CA. American Institute of Steel Construction.. “Steel-deck-reinforced concrete diaphragms . Reston. IL. MD. J.
Huang.” Earthquake Spectra 11 (S2). 24-29. (1995). Trifunac... Sabelli R. (2008).. DC. Seismic design of buildings – UFC 3-310-04. E. Brady. J. W. D. UFC (2010).. J. Seismic Design of Composite Steel Deck and Concrete-filled Diaphragms: A Guide for Practicing Engineers 28 . pp. SDI (2004)... Third Edition (SDI DDMO3).S. R. F. Pottebaum. A. C.” Structural Engineer. R. G. “Inelastic seismic response of frame fasteners for steel roof deck diaphragms. Shakal. Darragh. J. “Diaphragms for seismic loading. H.A. T. M. (2003). Diaphragm design manual. D. Steel Deck Institute. A. January. Sacramento. B. 129 (12). Lindvall.” Journal of Structural Engineering. and Mori.Rogers. M. pp. pp. TI 809-04. SEAOC blue book: Seismic design recommendations. Wald. Part 2. 22-23. Directorate of Military Programs. April 1995.. Fox Grove. Department of Defense. 13-96.. 1647-1657. CA. Heaton. Unified Facilities Criteria. C. IL Structural Engineers Association of California (SEAOC) Seismology Committee. U. “Recorded ground and structure motions... February. and Tremblay. and Dean. USACE (1998). J. Army Corps of Engineers Engineering and Construction Division. Part 1. B. Washington. DC. (2009). pp. Washington. ASCE. Seismic Design for Buildings. Structural Engineers Association of California.
height above the base to Level x Seismic Design of Composite Steel Deck and Concrete-filled Diaphragms: A Guide for Practicing Engineers 29 . and all areas where L is greater than 100 psf inertial force on the diaphragm diaphragm design force diaphragm force from ASCE 7 Equations 12.max Fpx.8-12.0 for garages. and 12. and Glossary b	beff B	C Cu Cmax	C’ d dc	d’ D e ex	E Ev fc ’ fy f1 Fp Fpx Fpx	Fpx.10-1. Abbreviations. 12.10-2.8-11 and 12. Notations. taken as 0.10-3 upper limit to the diaphragm design force lower limit to the diaphragm design force story force from ASCE 7 Equations 12.5 except taken as 1. as appropriate) effective width of collector contribution of fasteners that attach deck to steel support chord force factored compressive force at section maximum compression force in a collector element chord correction force required to close the moment diagram diaphragm depth (distance between chords) concrete cover depth depth between orthogonal collectors resisting the eccentric moment Mc effect of dead load eccentricity created by diaphragm step or depression eccentricity of diaphragm design lateral force relative to center of rigidity effect of horizontal seismic (earthquake-induced) forces effect of vertical seismic input specified compressive strength of concrete specified yield strength of reinforcement live load factor.11.min Fx	hx	in-plane depth of diaphragm considered in the calculation of shear strength (unit width of 12 inches or entire diaphragm depth. areas occupied as places of public assembly.
003 for concrete with a unit weight of 145 pcf stiffness of vertical element i span of diaphragm or diaphragm segment diaphragm span between vertical elements of the lateral load-resisting system length of the diaphragm the effect of live load deck panel length eccentric moment required to close the moment diagram factored moment structural fastener strength response modification coefficient reaction force in slab at vertical element i forces in shear walls effect of snow load spectral response pseudo-acceleration. water in soil. spectral response acceleration parameter at short periods elastic section modulus nominal shear strength for diaphragms with structural concrete fill (k/ft) effective thickness of the composite slab including a contribution from the steel deck using a transformed section approach fundamental period of the building Seismic Design of Composite Steel Deck and Concrete-filled Diaphragms: A Guide for Practicing Engineers 30 .H I K k k	ki L	L	L	L	L	Mc	Mu	Qf	R Ri RA. 5. 5. 5 percent damped. R2	S Sa SDS SD1	SDS Sm Sn	te	T effects of soil. g design. 5 percent damped. 5 percent damped.3-1 in SDI DDM03) and equals 0. R1. spectral response acceleration parameter at short periods design.3-1 in SDI DDM03) and equals 0.003 for concrete with a unit weight of 145 pcf distribution exponent for design seismic forces coefficient that depends on the unit weight of concrete (see definitions for Eq. RB. or other materials importance factor coefficient that depends on the unit weight of concrete (see definitions for Eq. spectral response acceleration parameter at a period of 1 second design.
2 SD1 / SDS average unit shear along the depth of the diaphragm factored shear stress additional unit shear between the orthogonal collector and the chord additional unit shear between the orthogonal collectors design base shear total diaphragm shear adjacent to the line of support at the vertical elements of the lateral loadresisting system factored shear force distributed force. or assigned to. calculated as Fp /L for rectangular diaphragms with uniform mass the weight tributary to the diaphragm at Level x portion of effective seismic weight of the building that is located at.TL	Tmax	Ts	T0	v vu	v1’ v2’ V	V	Vu	W	wpx wx long-period transition period maximum tension force in a collector element = SD1 / SDS	= 0. Level x strength reduction factor a redundancy factor based on the extent of structural redundancy present in system overstrength factor φ ρ Ω0	Seismic Design of Composite Steel Deck and Concrete-filled Diaphragms: A Guide for Practicing Engineers 31 .
Third Edition International Building Code International Code Council Steel Deck Institute Structural Engineers Association of California Structural Engineering Institute Glossary The terms used to refer to describe elements of diaphragms and aspects of diaphragm design have not been used consistently in the past. and distributors. This element is considered to collect the force as a distributed shear from the deck and deliver it via axial force or shear to the walls and frames. deck. Steel deck with concrete fill without significant bond. or they may be designated regions of a composite deck with appropriate reinforcement. these terms are presented below with the meaning that they are given in this Guide. The combination of inertial forces and transfer forces. Chords may be distinct members (beams). Collectors may be distinct members (beams). The complete system necessary to deliver diaphragm forces to the walls and frames. A collector is a member or system of members that resists a horizontal force (axial force in the case of a beam). Steel deck with concrete fill with bond such that the steel deck acts as reinforcement. transferring it between the deck and the walls and frame.Abbreviations ACI AISC	AISI	ANSI	ASCE DDM (SDI DDM 03)	IBC ICC	SDI	SEAOC SEI American Concrete Institute American Institute of Steel Construction American Iron and Steel Institute American National Standards Institute American Society of Civil Engineers Steel Deck Institute Diaphragm Design Manual. To avoid confusion. or they may be designated regions of a composite deck with appropriate reinforcement. This includes chords. Forces derived from loads prescribed by ASCE 7 for the design of members and connections. collectors. Chord	Boundary elements in the diaphragm that resist in-plane flexural forces. Collector Composite deck Concrete-filled deck Deck Design forces Diaphragm Diaphragm forces Seismic Design of Composite Steel Deck and Concrete-filled Diaphragms: A Guide for Practicing Engineers 32 . Horizontal bracing is treated as equivalent to deck in this Guide. The element in the diaphragm systems that resists the in-plane shear necessary to deliver diaphragm forces to the collectors or walls and frames (steel deck or composite deck ).
See AISC 341 for more information. braced frames. In-plane rotation of the diaphragm due to lateral load. Following the common convention for the conceptualization of seismic design. or other dynamic characteristics of the building. or other dynamic characteristics of the building. The difference is that in the conceptualization of the load path. The term “drag strut” has been used synonymously with “collector. Steel deck without concrete fill (referred to as “metal deck” in ASCE 7). the distributor takes force away from a wall or frame and delivers it as a distributed force to the deck. interaction between frames. Element providing shear transfer between steel and concrete in a composite member (commonly referred to as a “steel stud”). A distributor is a type of a collector. Diaphragm forces resulting from the acceleration of the mass tributary to the diaphragm. The term “collector” is preferred in this Guide. These include shearwalls. it has been used to denote members transferring lateral forces between discontinuous walls or frames. Plastic hinge regions of beams in moment frames and links in eccentrically braced frames are protected zones. Vertical elements of the lateral load-resisting system.Diaphragm reaction Distributor The force transferred between a diaphragm and a wall or frame. the load path is treated as beginning at the inertial mass of the building and ending with the delivery of the forces to the supporting soil. Diaphragm forces resulting from the acceleration of mass from levels above. While beams and diagonal braces are not oriented vertically. These forces act on the diaphragm as a result of discontinuities in frames.” In some circumstances. Redistribution forces act on the diaphragm as a result of discontinuities in frame stiffness. and moment frames. A type of transfer force not due to the presence of a discontinuous wall or frame.” Drag strut Inertial forces Load path Protected zone Redistribution forces Steel stud anchor Steel deck Torsion Transfer forces Vertical elements Seismic Design of Composite Steel Deck and Concrete-filled Diaphragms: A Guide for Practicing Engineers 33 . Area of a steel member expected to be subject to significant inelastic strain demand during an earthquake and for which the consequence of failure is high. they form part of a frame that is addressed by the term “vertical element. frame stiffness. interaction between frames.
after Moehle et al. 2010 Images courtesy of Jack Moehle Images courtesy of Rafael Sabelli Image courtesy of Jack Moehle and Dominic Kelly Images courtesy of Tom Sabol Image courtesy of the American Institute of Steel Construction. Seismic Design of Composite Steel Deck and Concrete-filled Diaphragms: A Guide for Practicing Engineers 34 . All rights reserved. Credits Cover photo:	Figure 2-1	Figure 2-2	Figures 3-1 and 3-2	Figures 4-1 through 4-4	Figures 4-5 through 6-8	Figure 6-9	Figures 6-10 through 6-12	Figure 7-1	Image courtesy of Patti Harburg-Petrich Image courtesy of Tom Sabol. after Moehle et al. Samuel Easterling. Copyright © 2010 by American Institute of Steel Construction Reprinted with permission.12. 2010 Image courtesy of Tom Sabol Image courtesy of W.

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