Concrete Slab Collectors SEAOC Blue

SEAOC Blue Book – Seismic Design Recomme Recommendations ndations Concrete Slab Collectors

ASCE 7-05

2006 IBC

Other standa standard rd

reference section(s) 12.4.3 12.8 12.10

reference section(s)

reference section(s) ACI 318-08, 9.3.2, 21.11

Introduction and Background Collector elements (also called drag struts or drag elements) are elements of floor or roof structures that serve to transmit lateral forces from their location of origin to the seismic force-resisting-system (SFRS) of the building. Typically, collectors transfer earthquake forces in axial tension or compression. When a collector is a part of the gravity force-resistin force-resisting g system, it is designed for seismi seismicc axial forces along with the bendin bending g momen momentt and shear force from the applicable gravity loads acting simultaneously with seismic forces. When subjected to lateral forces corresponding to a design earthquake, most buildings are intended to undergo inelastic, nonlinear behavior. Typically, the structural elements of a building that are intended to perform in the nonlinear range are the vertical elements of the SFRS, such as structural walls or moment frames. For the intended seismic seism ic response to occur occur,, other parts of the seismic-force seismic-force path, particularly floor and roof diaphragm collectors collectors and their connections to the SFRS, should have the strength to remain essentially elastic during an earthquake. This is the intent of most building codes and for this reason collectors should be designed for larger seismic forces than those for which walls, braced frames, or moment frames are designed. Traditional seismic design practices prior to the 1997 UBC were generally based on providing discrete collector element elem entss hav having ing spe specif cific ic rein reinfor forcem cement ent to tran transfe sferr the ent entire ire req requir uired ed se seism ismic ic load to the rec receiv eiving ing end of the seismi sei smicc for forcece-res resisti isting ng ver vertica ticall elem element ent.. This practice practice was partly due to, and bas based ed on, the low col collec lector tor forc forcee requirements in the older seismic design codes. In the 1994 Northridge Earthquake, failure of collector elements, which contained insufficient reinforcement, was observed in more than one pre-cast parking structure. Collector elements were observed to have yielded early on, rendering the collector elements unable to transmit the lateral force to the shear walls.

Overstrength ASCE 7-05 section 12.10.2.1 requires collectors, their splices, and their connections to the SFRS to be designed for the special load combinations with the overstrength factor, 0. The overstrength factor represents an upper bound lateral strength and is appropriate for use in estimating the maximum forces developed in non-yielding elements of the lateral system during design basis ground motion. The int intent ention ion of the ove overstr rstreng ength th fac factor, tor, wh when en app applied lied to col collec lector tor ele eleme ments nts,, is to min minimiz imizee the probabilit probability y of diaphragm-to-SFRS connection failure and instead force all the yielding into the building's properly detailed SFRS elements. This requirement perhaps had its genesis in ATC 3-06 (ATC 1978), which recommends embedment of chord reinforcing “sufficient to take the reactions without overstressing the material in any respect.” Applying the overstrength factor effectively increases the collector force demand by approximately 200% to 300%. It often becom becomes es impractical to provid providee a collec collector tor element that is concentric concentric with the shear wall/moment wall/moment frame t hat has adequate strength to resist the full seismic force and transfer it to the ends of the vertical seismic force-resisting element. Additionally, by concentrating all the collector reinforcement in a small region in line with the wall, the elastic stiffness of the adjacent floor slab may be underestimated. This “traditional” methodology can result in a condition where the floor slab having larger area and being stiffer than the collector element would initially resist the collector seismic tension. tension. If the floor slabs are not adequately reinforced reinforced for the seismic tension force, significant significant cracking may occur, until the reinforced collector element starts yielding and reaches its full strength.

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Design Forces ASCE 7-05 (ASCE 2006) Section 12.10.1.1 reads that collectors shall be designed to resist design seismic forces from the structu structural ral analysis, Fx (12.8-11), but shall not be less than that determined in accordance with F x (12.10-1.) Both Fx and F x are amplified by the overstrength factor. When collector design forces are designed for only inertial forces the redundancy factor can be set equal to 1.0 in accordance with section 12.10.1.1. One method used by many practicing engineers to obtain collector design forces is to assume that the diaphragm actss as a sim act simple ple beam wit with h uni uniform form distribu distribution tion of she shear ar in the dire directi ction on nor normal mal to the lateral lateral span and wit with h increasing axial farces in collectors aligned with SFRS elements, as shown in Figure 1. This method neglects any distributed tension or compression in the direction of lateral forces. Figure 2 shows an alternative mechanism of force delivery to the SFRS based on diaphragm shear capacity. Another approach to collector design would be to use the strut and tie model as covered in detail in Appendix A of ACI 318-08 code (ACI 2008). It is the opinion of the SEAOC Seismology Committee that the Seismic Load Effect Including Overstrength Factor of ASCE 7-05 Section 12.4.3 shall apply to the strut and tie model. Any mechanism of force delivery can be assumed in analysis provided the complete load path has adequate strength.

Figure 1. Uniform

distribution of shear normal to lateral span

Figure 2. Forces

delivered to SFRS based on diaphragm shear capacity

Section 12.3.1 of ASCE 7-05 requires that the structural analysis explicitly include consideration of the stiffness of the diaphragm, unless the diaphragm can be idealized as flexible or rigid. By using a semi-rigid assumption for diaphragms diaph ragms in t he analysis model, collector forces, Fx, can be readily found. Analysis software that can model semirigid diaphragms has techniques for cutting sections through diaphragms modeled with horizontal finite elements. Interpre Inte rpretatio tation n of Minim Minimum um Colle Collector ctor Desi Design gn Forc Forces. es. ASCE 7-05 Section 12.10.1.1, Diaphragm Design

Forces, prov Forces, provides ides the equ equatio ation n for ver vertic tical al dis distrib tributi ution on of dia diaphr phragm agm for forces ces,, with the max maximum imum and min minimum imum diaphragm forces of 0.4SDSIw x and 0.2SDSIw x, respectively. When the minimum diaphragm force from Section 12.10.1.1 is used for collector design, it may not be rational to amplify the collector force by 0 as required by Section 12.10.2.1, since the  0 applies to the forces established by R and the seismic force resisting system.

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The SEAOC Seismology Committee therefore recommends E mh (in Section 12.4.3.1) for collectors be set equal to the greater of: 1)

0QE, where QE is the greater of:

F x (12.10-1) ignoring the 0.2SDSIw x minimum or Fx (12.8-11) or 2) 0.2SDSIw

x

Transfer Slabs. In addition to its inertial loads, the diaphragm must also be designed to transfer forces between

vertical elements of the SFRS above and below the floor level in question. This requirement is triggered when the SFRS is discontinuous at the floor level and the load path clearly runs through the diaphragm. But it also applies where the stiffness of the SFRS changes significantly from one story to the next, such as with the introduction of basement walls at the ground level. In both cases the diaphragm d iaphragm forms part of the t he load path between SFRS elements. For collectors of diaphragms that transfer forces between SFRS elements, the Seismology Committee position is that additional design considerations are necessary for two reasons. First, when the diaphragm forms part of the load path between SFRS elements, the forces transferred through it i t (that is, any design forces in i n addition to the prescribed p rescribed F x) are essentially those of the SFRS and are therefore subject to increases for redundancy. Second, if the diaphragm is acting essentially essentially as an element of the SFRS, it should either be as ductil ductilee as the SFRS or remain essentially essentially elastic. elastic. Redundanc Redund ancy y and ove overstr rstreng ength th prov provisi isions ons wer weree not orig origina inally lly inte intende nded d to be imp impose osed d sim simult ultane aneous ously ly on any           than 1.0, then the maximum force it can deliver might be underestimated by  0 alone. Thus, reasonable arguments may be made that transfer diaphragm collectors should be designed for forces increased by both  and 0. As noted in ASCE 7-05 section 12.4.3.1, however, the maximum expected force “need not exceed the maximum force that can develop in the element as determined by a rational, plastic mechanism analysis or nonlinear response analysis utilizing realistic expected values of material properties,” and this statement forms the basis of the following Seismology Committee position. Any portion of a diaphragm that transfers force between vertical elements of the seismic force-resisting system should be designed for the largest transfer force that can be delivered to it by adjacent load path elements, unless the diaphr dia phragm agm’s ’s sec section tion pro proport portion ionss and det details ails are sho shown wn to pro provid videe duc ductili tility ty equ equiva ivalent lent to the adja adjacen centt SFRS elements. In other words, the diaphragm should not inadvertently become a non-ductile weak link in an otherwise ductile system. Thus, consistent with this philosophy as noted in ASCE 12.10.1.1 for transfer forces in diaphragms, a   factor factor equal to the building redundancy factor shall be applied, but only to the portion of the load created by the change in SFRS stiffness. Direct Connection of Diaphragm to SFRS. ASCE 7-05 Figure 12.10-1 clearly indicates that no “collector” is

required when the diaphragm is directly connected required connected to a full-len full-length gth shearwall. The overstrength overstrength factor does not apply to this direct connection.

Illustration of Design Methodology The building industry, specifically the structural engineering profession, has struggled with a reasonable method to construct concrete collector elements in reinforced concrete floor and roof slabs that can accommodate high force demands associated with  0 and other code provisions. Of particular relevance is the ability of the slab section sec tions, s, rath rather er tha than n the beams, to act as col collec lectors tors.. The me metho thods ds des describ cribed ed bel below ow mak makee the design and construction of reinforced concrete collector elements more tenable for certain types of structures.

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This method focuses on the issue of the assumed seismic force distribution used in collector design, and it presents methods of design that the SEAOC Seismology Committee judges to be acceptable. The key aspect of any design method for collectors is that each segment of the seismic force path must be evaluated for adequate strength by checking the free body diagram of forces at all potential critical sections. The purpose of the following discussion is to illustrate an alternative collector design approach where part of the seismic load is resisted by the reinforcement directly in line with the shear wall, which transfers the force directly to the end of the shear wall. The balance of seismic force is resisted by reinforcing bars placed along the sides of the wall and uses the slab shear-friction capacity at the wall-to-slab interface to transfer seismic forces to the wall. See Figure 3. (In this example, "shear wall" represents the vertical seismic force-resisting element; the condition for momentt frames or other systems are similar). momen

Figure 3 . Perspective View of Wall and Collector

Where the slab is adjacent to a shear wall and is used to resist seismic “collector forces,” there is an eccentricity between the resultant of collector force in the slab and shear wall reaction. This eccentricity can create secondary stresses stres ses in the slab transfer region (or “diap “diaphragm hragm segment”) segment”) adjacent to the wall. For a complete and consistent load path design, the effect of seismic force eccentricity in this “diaphragm segment” must be checked to determine that adequate reinforcement is provided to resist the induced stresses. The design examples use a rational load path for collector forces and outline a design process that satisfies code requirements. The buildings used as a basis for the design examples were deliberately selected to be simple and structurally structu rally regular. Two desig design n examp examples les are provid provided. ed. The first example illustrates illustrates t he collector design for a posttensioned roof slab in a building having concrete bearing shear wall seismic force-resisting system. The second example considers the same structure without post-tensioning.

Slab Effective Width A key design issue in this approach is to determine the effective width of slab adjacent to the shear wall that is used to resist collector forces. Where a narrow effective width is assum assumed, ed, eccentric force effects become small, but more reinforcement may be required to drag the collector forces in-line with the wall. On the other hand, if a wide slab

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width is used as collector, more force can be transferred through the slab, reducing reinforcing bar congestion at the end of the wall; however, secondary stresses caused by force eccentricity would be larger. The procedure outlined in these examples proposes to treat the choice of the effective slab width as a design parameter to be selected by the designer. The first example uses an assumed 45-degree influence line to determine the effective slab width; in the second example the effective slab width is arbitrarily selected to be equal to the wall length. For both cases, the resulting force eccentricity should be checked and, if required, additional reinforcement should be provided in the slab transfer region.

Collector Design Procedu Collector Procedure re The following is a suggested outline for collector design. Determine Collector Design Forces. Determine the seismic force distribution to the vertical seismic force-

resisting members by conventional analysis and draw the collector force diagram along the line of seismic forceresisting members (Figure 4). Note that a linear l inear variation of collector force along the line of a vertical seismic force-resisting member assumes a ssumes that the tributary width of the slab is constant and the collector (which, in this case refers to both the element in line with the wall and its adjacent slab section) is stiffer than the other connecting members.

Figure 4 Collector diagram for Wall A .

propose osed d tha thatt the section section of the Determ Det ermine ine the Ste Steel el Are Area a Dir Direct ectly ly in Lin Line e wit with h She Shear ar Wal Wall. l. It is prop collector collec tor tha thatt is dire directly ctly in line with the wall be des design igned ed for all the applicab applicable le gravity gravity loa load d dem demand and plus a reason rea sonabl ablee por portion tion of the tota totall col collec lector tor forc forcee tha thatt the des design igner er can sel select ect considerin considering g the required required num number ber of reinforcing bars and practical limitations of reinforcing bar congestion at the end of the wall. Then, the balance of the collector force will need to be resisted by the adjacent slab section in accordance with the following design procedure. Select Effective Slab Width to Resist Collector Forces. Example No. 1 presents a method to assign the

effective slab width to resist collector forces based on an assumed 45-degree influence line, which originates from the “point of zero force” along the collector collector force diagram (see Figure 5).

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Figure 5 Effective Effective Slab Width as Collector –

Example No. 2 arbitrarily uses the following equation to assign an assumed effective slab width.

B EFFECTIVE

 L  t WALL  n *  WALL   2 

where,, n is the number of sides that slab exists adjacent to the collec where collector. tor. Also, it is prop Also, propose osed d tha thatt the designer designer may choose choose any other sla slab b wid width th that satisfies satisfies the che check ck for secondary secondary eccentric stresses. Determine Required Steel Area to Resist Collector Tension. Determine the net tension force, T NET, and

the required required steel area, AS, at each section section along along the col collec lector. tor. (In these these examples examples the required required steel steel are areaa is calculated only at the maximum force location). For most reinforced concrete slabs the net tension force is equal to the calculated collector tension, FT. For pre-stressed pre-stressed concrete concrete sections, ACI 318-08 section 21.11.7.2 21.11.7.2 allows the use of the slab pre-compression pre-compression force from unbon unbonded ded tendons, F PT, when calculating T NET as it is illustrated in Example No. 1. Hence:

T NET

AS

 F T  O - F PT



T NET

  F

where, FT is the calculated collector tension force,  is system overstrength factor,  is capacity reduction factor as shown in ACI 318-08 Section 9.3.2.1, 9.3.2.1, and Fy is yield strength of reinforcing steel. The reinforcing reinforcing area, AS, represents the total area of the required reinforcing steel. Part of this steel may be placed in the slab element directly in- ine with the wall, and the balance may be distribu distributed ted throughout throughout the effec effective tive slab width adjacent to the wall. The collector reinforcement shall be placed, as much as practicable, symmetrically about the

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centroid centroi d of the con concre crete te sec section tion in ord order er to pre preven ventt add additio itional nal outout-ofof-plan planee sla slab b ben bendin ding g str stress esses. es. Additio Additional nal calcul cal culatio ation n sha shall ll be per perform formed ed to dete determi rmine ne the effe effect ct of col collec lector tor forc forcee ecc eccent entric ricity ity rela relative tive to the she shear ar wall wall reaction and required reinforcement. For pre-stressed concrete sections, the magnitude of pre-compression force, F PT, depends on the assumed effective slab width, which should be selected based on engineering judgment and verified by calculation to determine the required added reinforcement to resist effect of eccentric forces and secondary stresses. Check Chec k Coll Collecto ectorr Comp Compress ression ion Stre Stress. ss. Determine the total compression force, C NET, and check concrete concrete

compressive stress at each section along the collector. (In these examples concrete compressive stress is checked only at the maximum force location). For most reinforced concrete slabs the total compression force is equal to the calculated collector compression, F C. For pre-stressed concrete sections, since pre-compression force, F PT, was used to reduce the net tension, T NET, it must be accounted for in calculating to the total compression force, C NET. Hence:

C NET

 F C  O  F PT

The ACI 318-08 Section 21.11.7.5 design concept for collectors in compression is that transverse reinforcement must be provided where large collector compressive forces exist. Since the collector forces have been increased by the overstrength factor, ACI 318-08 gives:

C NET AC

 0.5  f'c

ACI 318-08 21.11.7.5

where AC is the gross cross-sectional area of the effective concrete section in compression. The magnitude of A C depends depen ds on the assumed effective slab width. Since the resultan resultantt of conc concrete rete compression compression forces would be eccen eccentric tric relative rela tive to the shear wal wall, l, addi addition tional al cal calcul culatio ation n sha shall ll be perf perform ormed ed to det determ ermine ine the eff effect ect of col collect lector or forc forcee eccentricity relative to the shear wall reaction and required reinforcement. conditions itions where all or part of collector reinforcement reinforcement is Check Diaphragm Segments for Eccentricity. For cond placed at the sides of the shear wall, the transfer region (or the diaphragm segment adjacent to the wall) should be designed to resist the seismic shear and in-plane bending moment resulting from the eccentricity of the portion of collector force that is not transferred directly into the end of the shear wall. In keeping with the code intent to design collectors and their connections for the “maximum expected seismic force,” the stresses due to collector eccentricity in that diaphragm segment adjacent to the wall shall be determined using an overstrength amplification factor. The specific diaphragm configurations, such as slab thickness variations, location of framing members, opening patterns, and other local conditions, could produce a complex stress state in the transfer region of eccentric collectors collec tors and affect the required slab reinfo reinforcemen rcement. t. Due to the vast variati variation on of diaphra diaphragm gm configurations configurations in actual design situations, a single all-encompassing design procedure could not be presented to be applicable to all possible cases. Hence, for the discussions in this section only an example of a simple diaphragm segment is provided to illustrate the general design requirements and a simplified rational procedure to satisfy these requirements. Figure 6 shows an idealized partial plan at the edge of a diaphragm with the seismic resisting wall “a-d” and the seismic collector located eccentrically at a distance “e” relative to the wall. The figure also shows the diaphragm segmen seg mentt adja adjacen centt to the wall wit with h int interna ernall for forces ces acting on the free bod body y “ab “abcd, cd,”” (ex (excep ceptt the componen components ts of tension ten sion/com /compre pressi ssion on forc forces es perp perpen endicu dicular lar to the fre freee bod body y dia diagram gram are igno ignored red in this example example for sak sakee of simplicity.) simplic ity.) The collector collector design force is designated designated as F c. In a general sense it consist of a compression and tension collector portions and the portion of diaphragm shear force along Line bc, respectively, designated as (F c) comp, (Fc) tens te ns,, an and d Vd. Con Consid siderin ering g the seis seismic mic amp amplifi lificat cation ion fac factor tor and coll collect ector or ecc eccent entrici ricity, ty, the max maximum imum ecc eccent entric ric moment acting on the free body abcd is calculated as:

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F c = (F c)comp + (F c)tens + V d d M e = (o. F c) . e The applied eccentric moment should be resisted by the combined action of all the diaphragm internal forces, thus:

M 2 a

V e

Me = V e.h + M 1 + M 2 + M 3 where, the magnitude of internal forces, V e, M1, M2, M3, could be calcul cal culate ated d in a rigo rigorou rouss ana analys lysis is in acc accord ordanc ancee with the their ir rela relative tive h stiffness. stiffne ss. However, for practica practicall desig design n purpo purposes, ses, the calcula calculation tion can be greatly simplified by using capacity design concepts. The following discussion presents a possible procedure for determining the diaphragm segment design capacities. For example, the moment capacity of the slab region under direct tension from collector force, i.e. moment M3 in the Figure 6, may be conservatively neglected. Furthermore, Furthe rmore, the shear capac capacity ity Ve shall be calcu calculated lated using only the capacity of shear reinforcing bars and neglecting the contribution of concre con crete te sec section tion un under der ten tension sion.. Hen Hence, ce, the stre strengt ngth h limi limits ts for the shear force Ve, and bending moment M2, are determ determined ined as:

M 2 =  F y . AS2. ( j.e ) V e =  A sv .F y

b

M 1

d

V e M 3

c

V d d

 .F .F

e

Figure 6. Diaphragm Segment Plan

where, AS2 is the reinforcement areas perpendicular to section ab, (j.e) is the effective moment arm, and A sv is the smaller of the reinforcing bar area parallel to sections ab and dc. Then, the required flexural strength, M 1, can be calculated as:

M 1 = M e – ( V e.h + M 2 ) (Alternatively, it may be assumed that the bending moments M 1, M2, and M3 would reach their allowable strength limit and calculate the required shear, Ve, to satisfy the basic equilibrium of forces. A similar procedure may be used for other combinations of bending moments and shear force.) For conditions where the eccentricity is small relative to the dimension h, it is reasonable to assume that the relative stiffness associated with the actions M 1 and Ve is much larger than the other actions; hence, without being too conservative, the contribution of the moments M2 and M3 may be negle neglected, cted, which simplifies the equation for M 1, to the following:

M 1 = M e – V e.h The required moment capacity, M 1, can be computed by taking into account the effect of the slab’s distributed reinf rei nforc orcem emen entt tha thatt is pr prov ovid ided ed fo forr gr grav avity ity lo load ads, s, bu butt is in ex exces cesss of wh what at is ne neede eded d to re resi sist st se seism ismic ic lo load ad combina com bination tions. s. For cas cases es whe where re the available available distribute distributed d rein reinfor forcem cement ent is not ade adequa quate te to sat satisfy isfy the requ required ired strength, supplemental reinforcing steel should be provided at the eccentric force transfer zone. Figure 7 shows an arrangement of various reinforcing bars perpendicular to section bc; and illustrates the terms used in the following computation for moment M1.

M 1 =  Fy {AS1.( j 1.h) + A*S .(j*.h ) }

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where, AS1 is the available area of the distributed slab reinforcement perpendicular to the section b c that can be used for seismic load combination, (j1.h) is its effective moment arm; A*S is the area of supplemental reinforcement, and (j*.h) is the effectiv effectivee moment arm of the suppl supplemental emental steel. steel. Check Diaphragm Segment Shear Strength. The

slab shear stress demand should be checked for the shear force fo rce tra trans nsfe ferr reg regio ion n ad adjac jacen entt to th thee wa wall ll an and, d, wh wher eree required requ ired,, add additio itional nal rein reinfor forcem cement ent sh shall all be pro provid vided. ed. Two Tw o sh shea earr fo forc rcee tr tran ansf sfer er mec echa hani nism smss sh shou ould ld be considered. cons idered. First, slab shear strength strength should be evaluated cons co nsid ider erin ing g th thee co cont ntri ribu buti tion on of al alll av avai aila labl blee sl slab ab reinforcemen reinfo rcement. t. The streng strength th reduct reduction ion facto factor, r,  ,, for shear should be taken as 0.75 according to ACI 318-08 9.3.2.3.

V u



 Acv  c

f' c

  n F y

a

slab reinf.

j1.h F y.As1

added reinf.



j*.h

F y.A*s d

where, Acv is the net area of the concrete section bounded by the slab thickness and length of the wall, wall,  c is the ratio of the width to length of the diaphragm segments, which in this case is equal to effective slab width to the length of    n is th thee ra rati tio o of di dist stri ribu bute ted d sh shea ear r reinforcement perpendicular to the wall.

b

c

Figure 7. Diaphragm Segment Reinforcement

Speciall atte Specia attentio ntion n mus mustt be giv given en to Acv when the ver vertic tical al sei seismi smicc forc force-re e-resis sisting ting mem member ber is not con continu tinuous ously ly connected to the diaphragm. For example, for an exterior wall that is 25 ft long, but is located adjacent to a 10 ft wide stair opening, then the length used in calculating the shear area is 15 ft. Check Shear-Friction at Wall-to-Slab Interface . The strength of transfer mechanism by shear friction at the

face of the supporting wall and/or frame should be checked. For this mechanism the potential sliding plane should be identified; for most practical design cases the potential sliding plane is taken as the vertical plane at the interface between the wall and the slab. The shear-friction reinforcement can include all reinforcement that crosses this plane, as long as it is not used to resist direct tension. Hence, the area of the required shear transfer reinforcement, A VF per foot of wall length is calculated as:

AVF 

V n   fy  Lw

where, Lw is length of interface between the wall and the slab.

Other Considerations for Collector Design Using Gravity Slab Reinforcement. The collector design procedure in these examples assumes that a portion of seismic collector load is resisted by the shear strength along the wall interface with the floor slab. For this load path the slab longitudinal reinforcement parallel to the shear wall can be used to t o transfer the balance of the collector force to the side of the wall. For design efficiency, a portion of the slab reinforcement that is provided for gravity loads, but is in excess of what is needed to resist seismic load combinations, can be used to resist collector or diaphragm forces, provided it meets the special detailing requirements for seismic force-resisting systems. The seismic requirements are more stringent than those of a typical non-seismic slab to reflect the adverse conditions resulting form seismic load reversals.

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The main detailing issues in regard to using slab gravity reinforcement for seismic diaphragm include the following: spacing;  Minimum diaphragm reinforcement ratio and required bar spacing;  Diaphragm reinforcement splices and development length; Symmetric ric distribution distribution of diaphragm reinforcement reinforcement at top and bottom of section to resist seismic net axial  Symmet force without inducing additional slab bending moment. stress con concen centrat tration ion at a fac facee of the SFRS Check Che ck Loc Local al Str Stres ess s Con Conce centr ntrati ation on at fac face e of Wal Wall. l. The stress elements should elements should be stu studie died. d. It is the Seismolog Seismology y Comm Committee ittee's 's opi opinio nion n tha thatt the local fail failure ure will trigger trigger the redistribution of the load and eventually the interface between the SFRS elements and slab will carry most of the load. The local failure will not cause collapse or have significant impact on the load transfer from the strain compatibility of the slab. Planar elem element entss suc such h as she shear ar wal walls ls and diaphragm diaphragm slabs have a bet better ter pos posttDetailing of reinforce reinforcement. ment. Planar cracking behavior if the reinforcing is reasonably distributed over regions of high shear and axial stress rather than being concentrated in narrow groups near the edges of these elements. Distributed reinforcing allows the formation of multiple narrow cracks over the stressed region, while the stiffening effect of concentrated group reinforcing results in a few wide cracks with possible localized spalling. Note that the current shear wall provisions allow and encourage the use of vertical reinforcing distributed over the wall section rather than in concentrated boundary elements. Similarly, provision of distributed steel in an assigned effective width of a collector element can result in better post cracking cr acking performance perfor mance than t han if i f t he collector is made up of large diameter bars i n and closely adjacent adj acent to the vertical lateral force resisting element. Using smaller bars in larger amounts to spread over a wide band of slab will result in a better stress distribution than using smaller quantities of big bars. Since a wide slab band is used in collector design, this check seldom becomes critical. critica l. This idea is suppo supported rted from the study of finite elemen elementt analy analysis sis of examp examples les indicating the stress distribution distribution is spread out in a wide band across the slab section. Even with the existence of shrinkage cracks, the reinforcement in the slab keeps the diaphragm inertia inertia force distributed distributed in a relativ relatively ely wide band until the failure line forms. It is believed that the concentration of bars in collectors changes the force distribution; it attracts the force to the narrow band formed for med by b y these bars and causes early overstress in i n the t he narrow narro w region. regio n.

References ACI (2008). Building code requirements for structural concrete (ACI 318-08)and commentary , American Concrete Institute, Farmington Hills, MI. ASCE (2006). ASCE/SEI 7-05, Minimum design loads for buildings and other structures, including supplement no. 1, American Society of Civil Engineers, Reston, VA. ATC (1978). Tentative provisions for the development of seismic provisions for buildings , ATC-3-06, Applied Technology Council, Redwood City, CA. SEAOC Seismology Committee (1999). Recommended lateral force requirements and commentary , seventh edition, Structural Engineers Association of California, Sacramento, CA. Keywords collectors concrete slab How To Cite This Publication In the writer’s text, the article should be cited as: (SEAOC Seismology Seismology Committee 2008) In the writer’s reference list, the reference should be listed as: SEAOC Seismology Committee (2007). “Concrete slab collectors,” August, 2008, The SEAOC Blue Book: Seismic design recommendations , Structural Engineers Association of California, Sacramento, CA. Accessible via the world wide web at: http://www.seaoc.org/bluebook/index.html at: http://www.seaoc.org/bluebook/index.html

Article 5.02.03 5.02.030 0


August 2008

Concrete Slab Collectors SEAOC Blue

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