Proposed Revisions to 1997

NEHRP Recommended Provisions

for Seismic Regulations for
Precast Concrete Structures
Part 3 – Diaphragms
by

Neil M. Hawkins, Ph.D. S. K. Ghosh, Ph.D.

Professor Emeritus President
Department of Civil Engineering S. K. Ghosh Associates, Inc.
University of Illinois at Northbrook, Illinois
Urbana-Champaign
Urbana, Illinois

This is the third in a series of three papers discussing significant

modifications expected to be included in the 2000 NEHRP Provisions,
dealing with the design of precast, prestressed concrete seismic-
force-resisting systems. The first article presented an historical review
of the development of the NEHRP Provisions while the second article
discussed the proposed revisions for seismic-force-resisting frame
and structural wall systems composed of precast and prestressed
components. This article provides an overview of design issues
concerning untopped diaphragms composed of both double-tee and
hollow-core slab units.

T
he Proposed Revisions to the 1997 NEHRP Provi- and prestressed elements, and the basis for those revisions,
sions that relate to seismic design requirements for were discussed in the September-October 2000 issue.
precast concrete structures have been discussed in The revisions discussed in this article are Proposal 4-15
two prior issues of the PCI JOURNAL. The history of de- and the associated commentary, and that part of Proposal
velopment of the NEHRP Recommended Provisions,1 with 4-37 that deals with diaphragms. Those proposals and
particular emphasis on the requirements for precast and pre- commentary can be viewed on the internet at
stressed concrete structures, was described in the May-June www.bssconline.org.
2000 issue. The proposed revisions for seismic-force-resist- Most designers and suppliers of precast and prestressed
ing frame and structural wall systems composed of precast concrete systems have now become familiar with the con-

50 PCI JOURNAL
cepts and terminology associated with cast concrete design practices in areas structure.
the use of moment frames and struc- east of the Rocky Mountains. A design example for the floor dia-
tural walls to resist seismic forces. Finally, the article describes the phragm of a similar structure as that
However, in general, they do not have content of Proposal 4-15, the part of shown in Fig. 1 is provided in Chap-
the same degree of understanding as Proposal 4-37 that deals with dia- ter 3 of the PCI Design Handbook.4
to how floor and roof systems (dia- phragms, and the commentaries to Architectural and engineering con-
phragms) need to be designed in order those proposals. siderations for design, construction
to resist the same seismic forces. and maintenance, with special em-
To help develop that understand- phasis on proportioning and detailing
BASIC PRINCIPLES
ing, this article first discusses basic requirements, for parking structures
concepts and terminology related to AND TERMINOLOGY are described in Ref. 5.
diaphragm action and then reviews The basic principles and terminol- In Fig. 1, the structure has plan di-
briefly the performance of precast ogy used in diaphragm design are mensions of 180 x 280 ft (54.9 x 85.3
concrete diaphragms in the 1994 discussed here with respect to the m). The central ramp creates an open-
Northridge earthquake. idealized parking structure shown in ing of 60 x 160 ft (18.3 x 48.8 m). In
Next, the article describes how the Fig. 1. The issues raised by examin- the North-South (N-S) direction, the
design provisions in the ACI (Ameri- ing how to design such a structure spacing between interior column lines
can Concrete Institute) 318 standard,2 for seismic forces are typical of those is 60 ft (18.3 m) and in the East-West
the UBC (Uniform Building Code),3 envisaged by code writers when they (E-W) direction the spacing is 30 ft
and the NEHRP (National Earthquake developed Proposal 4-15. The pro- (9.14 m) in the two end bays, and 40
Hazards Reduction Program) Provi- portions of the structure of Fig. 1 ft (12.2 m) in the four central bays.
sions1 have changed in response to the result in major demands being placed Gravity-load-resisting columns at the
performance of precast concrete struc- on the floor diaphragms of the struc- corners of each bay carry the gravity
tures in the Northridge earthquake ture during an earthquake, as well loads of the floors.
and how that performance has in turn as on the vertical elements of the There are stairwells in three corners
raised significant issues related to pre- seismic-force-resisting system of the and an elevator shaft in the fourth

Fig. 1. Plan of typical precast concrete structure with a large diaphragm.

November-December 2000 51
Fig. 2. Cracking of topping slab around interior column and
along junction of double tee. Fig. 3. Fracture of connection of perimeter steel to shear wall.

corner. Key locations in the structure from I to F and from A to O. In ad- spond elastically to the design-basis
are labeled A through U. The lateral dition, because of the central ramp, earthquake of the code are reduced, for
forces are resisted by 20 ft long x 8 in. there are effectively four sub-dia- design purposes, by an R-factor that
thick (6.10 m x 203 mm) cast-in-place phragms, ABMN, BCSR, CEIJ and depends on the inelastic deformability
shear walls extending from E to F UTJM in the flat area, and a fifth sub- of the seismic-force-resisting system.
and N to O in the (N-S) direction and diaphragm, RSTU, that is the ramp Inelastic deformability is the ability
from D to E and K to L in the (E-W) extending between floors. Each sub- of a structural system to continue to
direction. The structure has three lev- diaphragm requires chord, body and sustain gravity loads as it deforms lat-
els above grade with heights of 10.5 ft collector reinforcement for it to func- erally beyond the stage where the lat-
(3.20 m) each. tion properly. eral displacements are recoverable (no
The floors are assumed to be Chord and collector reinforcement residual displacements remain follow-
deep beams in their own plane (di- and boundary elements for the over- ing the passage of an earthquake). If
aphragms), transferring their seis- all diaphragm, and for each sub-dia- the shear walls of Fig. 1 are ordinary
mic forces to the shear walls. The phragm, must be proportioned to resist reinforced walls, not conforming to the
perimeter of each diaphragm must be reversing loads. The chord and collec- requirements of Section 21.6 of ACI
reinforced so that transfer is accom- tor perimeter reinforcement must also 318-99, the R-factor is 4.5.
plished. For example, for N-S forces, be sufficient to satisfy integrity steel Seismic forces are only one of sev-
the edges of the diaphragm from A to requirements of Section 7.13 of ACI eral factors that may control the pro-
E and from I to N must be strength- 318-99. The body reinforcement must portions and reinforcement selected
ened with longitudinal and transverse be sufficient to satisfy the shrinkage for shear walls. Consequently, the
reinforcement (chord reinforcement). and temperature steel requirements of yield strength of the shear walls can
Those reinforcements provide the dia- Section 7.12 of ACI 318-99. be greater than that assumed for the
phragm with boundary elements. If the diaphragm is of uniform specified seismic forces and the forces
The chord reinforcement must pro- proportions throughout the structure acting on the diaphragm will increase
vide a design flexural strength greater and uncracked, then the diaphragm in proportion to those acting on the
than the factored moment acting at is rigid and, for the shear wall layout shear walls until the latter yield. Un-
every location along the length of the shown in Fig. 1, the center of rigid- less, for the seismic forces experi-
diaphragm. Any contribution of the ity will not coincide with the center enced by the structure, the strength of
concrete of the diaphragm in tension, of mass in the E-W direction. Tor- the diaphragm, and that of each of the
and of the reinforcement in the body sional forces will be transferred to the sub-diaphragms, is greater than the
of the diaphragm, to the design flex- shear walls and the diaphragm must yield strength of the shear walls, the
ural strength is normally neglected. be able to resist the resulting combi- diaphragm can fail prematurely.6,7
N-S seismic forces cause N-S and E- nation of shear and torsional effects. Design of the diaphragm requires
W shear stresses in the diaphragm and If the diaphragm is cracked, due to careful assessment of both the mag-
reinforcement must be provided in the temperature, shrinkage or seismic ef- nitude of the seismic forces likely to
body of the diaphragm to resist those fects, then its stiffness will decrease act on it and of its nominal strength at
stresses. significantly and it may even become those forces, relative to the nominal
To drag the seismic shear forces flexible relative to the lateral stiffness strength of the vertical elements of the
transferred to the ends of the dia- of the shear walls. seismic-force-resisting system.
phragm into the shear walls, there Under current code procedures, the
must be collector reinforcement seismic forces that would have been PERFORMANCE OF
provided in drag struts extending induced in a structure if it were to re-

52 PCI JOURNAL
Fig. 4. Local debonding of topping slab and buckling of
chord steel. Fig. 5. Debonding of topping slab on hollow-core slab units.

DIAPHRAGMS IN the ments for shear stress. That shrinkage system. The factor Ωο has a value
1994 NORTHRIDGE steel requirement can be satisfied with of 2.5 for shear walls, and 3.0 for
fabrics that are 6x6-W2.1xW2.1 and frames supporting diaphragms. In the
EARTHQUAKE
4x4-W1.4x1.4. 1997 NEHRP Provisions, this Ωο re-
This section discusses the perfor- quirement was applied to structures
mance of diaphragms supported on in Seismic Design Category (SDC)
precast concrete gravity-load-resist-
POST-NORTHRIDGE CHANGES
C and higher. In the 2000 IBC, it ap-
ing systems in the 1994 Northridge IN DESIGN REQUIREMENTS plies only to structures assigned to
earthquake. The damage that oc- As a result of the damage observed SDC D and higher. The 1997 NEHRP
curred to such diaphragms has been to diaphragms supported on precast Provisions also permitted Ωo times the
well documented8,9 and several studies concrete members in the 1994 North- effects of the prescribed seismic forces
have been made to determine possible ridge earthquake, several design not to exceed the maximum force that
causes for that damage.6,7,10 changes were made in the 1997 UBC,3 can be transferred to the collector by
Fig. 2 shows the cracking observed the 1997 NEHRP Provisions,1 as well the diaphragm and other elements of
around the top of an interior gravity- as in ACI 318-99.2 the seismic-force-resisting system.
load-resisting column, and across the In the 1997 UBC, in the 1997 This provision was not explicitly in-
width of the smaller dimension of the NEHRP Provisions, and, therefore, cluded in the IBC.
diaphragm, on the roof of a three-story also in IBC 2000,20 provisions were In ACI 318-99, for regions of high
parking structure. The diaphragm con- introduced placing restrictions on ei- seismic risk, changes were made in the:
sisted of concrete topping on precast, ther diaphragm proportions or dia- 1. Strength reduction factor φ as-
prestressed concrete double tees. That phragm connections to columns for sociated with the shear design of
topping had cracked along the junction structures having precast concrete diaphragms.
of two double tees and the connectors gravity-load-carrying systems. In the 2. Classification of topping slab
between the tees had ruptured. latter case, the integrity of the dia- diaphragms.
At one end of that crack, the chord phragm at the design displacement 3. Strength and ductility require-
reinforcement extending into the shear was to be ensured by requiring “par- ments for reinforcement for shear in
wall had ruptured (see Fig. 3), and at tially restrained” beam-to-column topping slab diaphragms.
the other end (see Fig. 4), the topping connections throughout the gravity- 4. Use of prestressing steel as chord
had debonded from the tee and the load-resisting system. 12 The design reinforcement.
chord reinforcement had buckled. In displacement is the total lateral dis- The φ -value for shear is specified
another instance (see Fig. 5), where placement expected in the design- as 0.6 if the nominal shear strength
the diaphragm consisted of topping basis earthquake. of a structural element is less than the
on hollow-core units, the topping had In addition, collector elements of shear corresponding to the develop-
cracked along the edges of the units diaphragms, their splices and their ment of its nominal flexural strength.
and debonded from them. connections to seismic-force-resist- Also, the φ­-factor used in the shear
The topping slabs were nominally ing elements were required to be de- design of a diaphragm must be no
2 to 2.5 in. (51 to 63 mm) thick and signed for a factor Ωο times the force larger than the φ-factor used in the
reinforced with welded wire fabric. resulting from an elastic analysis of shear design of the vertical elements
Fabric satisfying the shrinkage and the structure under code-prescribed of the seismic-force-resisting system
temperature steel requirements of Sec- seismic forces, where Ωο is an over- supporting the diaphragm.
tion 7.12.2.1(b) is generally sufficient strength factor dependent on the form In ACI 318-99, two types of top-
to also satisfy structural steel require- of the vertical seismic-force-resisting ping slab diaphragms are recognized,

November-December 2000 53
namely, cast-in-place composite, and slab diaphragms, composite or non- in. (3.2 mm). In Ref. 6, it is recom-
cast-in-place noncomposite. The for- composite, such shear cracking does mended that wire sizes greater than
mer must have a thickness of not less not occur. W4.5 be used and that the ρfy value
than 2 in. (51 mm), and the surface Instead, cracking follows the edges for the reinforcement crossing the
of the precast concrete member on of the precast concrete members (see crack exceed 150 psi (1 MPa).
which the topping is placed must be Fig. 2), and shear strength must be In California, prior to 1994, the con-
clean, free of laitance, and intention- provided across that crack by shear- tinuous chord and collector reinforce-
ally roughened. The topping must be friction reinforcement. Further, be- ment required by codes was some-
reinforced and the diaphragm detailed cause such cracking is likely to pre- times provided by bonded unstressed
so that there can be a complete trans- exist, due to temperature and prestressing strands with the stresses
fer of forces to chords, collectors, and shrinkage effects, the µ-value for pro- in those strands under seismic actions
the vertical elements of the seismic- portioning the shear-friction reinforce- exceeding 60,000 psi (1035 MPa). In
force-resisting system. ment is taken as 1.0 and the maximum ACI 318-99, the use of such strands
Since the topping is bonded to the nominal shear stress is limited to 8 is allowed but with the stress limited
precast concrete member, connec- fc′ . to 60,000 psi (1035 MPa). This is to
tions between precast elements and Welded wire fabric is gener- prevent wide cracking that may result
the chords, as well as other intercon- ally used as the shear reinforcement from high stress (and hence, strains)
necting members, can be used for load in topping slabs. The cold drawing in the bonded reinforcement. How-
transfer. A noncomposite topping slab process used to manufacture wire re- ever, where unbonded stressed strands
diaphragm must have a thickness not sults in its failure strain decreasing are used in the slab, their full effective
less than 2.5 in. (63 mm) and, because as the wire diameter decreases. W1.4 prestress can be utilized.
it does not rely on composite action and W2.1 wires may show as little as While ACI 318-99 requires the use
with the precast members, the load 1.0 percent elongation at fracture. In of a topping slab or monolithic concrete
transfer to the chords, and other mem- welded wire fabric, the anchorage for diaphragms in regions of high seismic
bers, must be made by direct connec- a given wire is provided by the trans- risk, untopped precast concrete ele-
tions into the topping. verse wires welded to it, and there- ments can still be used for diaphragms
Possibly, the most significant fore, in topping slabs, as the spac- in regions of moderate and low seismic
change in ACI 318-99 concerns the ing between the wires paralleling the risk, and therefore, for structures as-
reinforcement of the topping slab for crack decreases, the maximum crack signed to SDCs A, B and C.
shear. For a monolithic diaphragm, width at wire fracture decreases.
shear strength requirements are the For 4 x 4 fabric with W1.4 wires,
same as those for slender walls. It is that width can be as little as 0.04 in. UNRESOLVED SEISMIC
presumed that if shear cracking devel- (1.0 mm). Note that ACI 318-99 re- DESIGN ISSUES FOR
ops, it will extend diagonally across quires a minimum transverse wire DIAPHRAGMS IN REGIONS OF
the diaphragm in the same manner as spacing of 10 in. (254 mm) to provide HIGH SEISMIC RISK
in a deep beam. However, for topping crack widths that can approach 1/8 When the proposed revisions to the
1997 NEHRP Provisions were being
discussed, it was apparent that there
were at least three significant unre-
solved design issues for diaphragms,
in regions of high seismic risk, in-
volving precast concrete members.
Those issues were:
• Is it sufficient to require only in-
tentional roughness for the precast
elements for bonding of the topping
slab to those elements or should the
more stringent roughness require-
ments of the shear-friction provi-
sions of Section 11.7 of ACI 318-99
apply?
• Is there a size effect, rather than
an aspect ratio effect, that needs
to be considered for diaphragms
supported on precast gravity-load-
systems?
• If diaphragms can be designed to
respond in an essentially elastic
Fig. 6. Typical connection between a precast double tee and spandrel beam. manner during severe earthquakes,

54 PCI JOURNAL
 are there likely to be fundamental has yet to be adequately addressed in of diaphragm between inflection
differences between the response the codes. points.
of diaphragms consisting of top- If as required by the 1997 NEHRP
ping slabs on precast members and Size Effects for Diaphragms Provisions the allowable diaphragm
diaphragms composed of untopped Supported on Precast deflection is set at 0.75 percent of the
precast members? Gravity Systems story height in order to limit damage
to attachments, then the required am-
Lateral deformations of a dia-
Interface Shear Strength Between plification in chord steel to meet the
phragm must be limited sufficiently,
Topping and Precast Unit stiffness requirements is:
so that the lateral displacement de-
Chapter 17 of ACI 318-99 deals mands on non-seismic components
with composite precast and cast-in- of the building are not excessive. If a (1)
place concrete flexural members. structure has vertical elements of the
Section 17.5.2.1 permits the nominal seismic-force-resisting system that are  1.0 Leff  2 
 bd than
but not
1 less
interface shear strength between the designed to the drift limits of the 1997 1 + 0.4  
 12   hs    bd  
precast member and the topping slab NEHRP Provisions, demand on the where bd is the diaphragm width  and
to be taken as 80 psi (0.55 MPa) when non-seismic components of the struc- all dimensions are in feet.
the contact surfaces are clean, free of ture can be very large if, as required In Proposal 4-37 of the Proposed
laitance, and intentionally roughened. by the Provisions, appropriate cracked Revisions to the 1997 NEHRP Provi-
Tests on precast concrete double section properties are used for the dia- sions, the foregoing requirement for
tee and hollow-core units with bonded phragm and for the elements of the deflection has been substituted for
topping slabs have shown that a lateral-force-resisting system. the 1997 NEHRP Provisions limita-
shear strength of 80 psi (0.55 MPa) The cracked section flexural stiff- tion of three on the aspect ratio of
can readily be achieved at the flex- ness depends on the amount of chord diaphragms in structures having pre-
ural strength of units with intention- reinforcement and is likely to be in cast gravity-load-carrying systems.
ally roughened surfaces. However, it the range of only 5 to 20 percent of
is also clear that the stiffness of the the uncracked section stiffness. The
composite member and its flexural flexural component of the midspan Response of Diaphragms Utilizing
strength can be reliably increased if deflection of a rectangular diaphragm Precast Concrete Elements
the surface is roughened to the re- is a function of both the span of the It is customary to design concrete
quirements of Section 11.7 of ACI diaphragm and its aspect ratio. How- diaphragms assuming them to be elas-
318-99.18 ever, the shear component is a con- tic and rigid relative to the seismic-
Further, studies of topping slabs stant for a given span. force-resisting system. Therefore, for
on surfaces where roughness was ob- To obtain realistic deflection es- the development of code provisions, it
tained by sand blasting17 have shown timates, the shear component of the is reasonable to ask, if the diaphragm
that debonding is likely to start soon deflection must be included for aspect remains elastic, are there likely to be
after casting in the corner of units and ratios less than 3. For example, at as- fundamental differences in behavior
can extend up to 2 ft (0.61 m) into the pect ratios of 2 and 1.5, the deflection for diaphragms composed of:
unit before equilibrium is established. including shear effects is 1.6 and 2.0, 1. Cast-in-place concrete slabs.
Thus, while an interface shear strength respectively, times the deflection ne- 2. Topping slabs on precast concrete
of 80 psi (0.55 MPa) can be relied glecting such effects. units.
upon for global structural design pur- A diaphragm must satisfy simul- 3. Untopped precast concrete units?
poses, no similar strength value can taneously both strength and stiffness ACI 318-99 recognizes that there
be relied upon locally. requirements. In Ref. 19, it is shown will be fundamental differences be-
A typical connection between a that for most overall diaphragm spans tween the behavior of cast-in-place
precast double tee with topping and encountered in practice, stiffness con- and topping slab diaphragms due to
a spandrel beam is shown in Fig. 6. siderations will control over strength. the presence of precast units below
Bonding of the topping to the precast Because stiffness depends on both the the topping slab. For topping slab dia-
member is essential to prevent buck- amount of chord steel and the aspect phragms, severe earthquakes cause
ling of the chord steel during any load ratio, one possible approach for simul- cracking along the edges of the pre-
reversals that yield the chord steel. taneously satisfying strength and stiff- cast units if prior thermal and shrink-
Further, splicing of the threaded insert ness requirements is to amplify the age stresses have not already caused
steel to the reinforcement of the top- chord steel requirements calculated on such cracking.
ping slab is essential to being able to strength considerations alone. The behavior of the topping slab in
develop the yield strength of the insert The required amount of chord steel shear is affected and, therefore, the
steel if the topping partially debonds amplification is a function of the story manner in which it must be reinforced
at the end of the double tee. How to height, hs, allowable deflection and for shear differs from that for a cast-
deal with the issues of local versus the product of the span, Leff, and the in-place diaphragm. In a diaphragm
global interface shear strength consid- aspect ratio, bd/hs for the diaphragm. utilizing untopped precast units, the
erations in regions of high seismic risk Note that Leff is defined as the length pattern of cracking along the edges of

November-December 2000 55
Fig. 7. Diaphragm utilizing untopped hollow-core slabs.

the units will be the same as that for precast elements are allowed in re- length of about 2 in. (51 mm) and an
topping slab diaphragms. gions of high seismic risk. The de- amplitude of about 0.2 in. (5 mm).
Therefore, if a rational means is velopment of code provisions cover- The profile is produced during the ex-
provided for transferring shears be- ing such diaphragms is, however, a trusion of the slab by a special wheel
tween units that duplicates the role of realistic goal. device.
the topping slab reinforcement, why is In Italy and regions of Central In the full-scale tests validating the
the behavior of an elastic diaphragm America, diaphragms utilizing un- use of this diaphragm, the untopped
utilizing untopped precast units likely topped precast concrete hollow-core slabs were 32.8 ft long, 39.4 in. wide
to differ from that of an elastic top- units are used in regions of high seis- and 11.8 in. deep (10.0 m x 1000 mm
ping slab diaphragm? mic risk. Typical details for such a x 300 mm). The tie beams connecting
The prior section discussed how diaphragm are shown in Fig. 7. The the transverse edges of the slabs were
the 1997 NEHRP Provisions is being longitudinal edges of the slabs are ser- 5.9 in. wide x 11.8 in. deep (150 mm
revised to ensure that diaphragms rated, reinforcement is used to anchor x 300 mm) and the reinforcement in
cracked in flexure have greater stiff- the slabs to full depth perimeter tie those beams was a variable. The dia-
ness. That approach was based on as- beams, and the tie beams are rein- phragm consisted of six parallel units,
suming the diaphragms to be rect- forced to provide chord reinforcement tested as a cantilever with maximum
angular and the ratio of the cracked along with restraint to the transverse moment and shear occurring on the
section stiffness in flexure to that in opening of the longitudinal joints be- full depth grouted joint between the
shear to be the same as the ratio of the tween slabs. fifth and sixth units.
uncracked section stiffness in flexure This diaphragm type is the result These tests showed that it is es-
and to that in shear. of extensive laboratory and field tests sential that the longitudinal joints of
The factors that control the cracked summarized in Ref. 11. The serration such diaphragms be “ductile,” and be
section stiffness in shear, the conse- extends the full length of the slab, is able to “strain-harden.” The profile of
quences of plan irregularities, and, located immediately below the lon- the serration was essential to achiev-
therefore, possible local inelastic be- gitudinal vertical shear key, covers ing that characteristic. An effective
havior, deserve further consideration about one-third of the depth of the system of ties between slabs and tie
before diaphragms utilizing untopped slab, and is a sinusoidal wave with a beams, and within the tie beams, was

56 PCI JOURNAL
also essential to achieving satisfactory such diaphragms in past earthquakes, dependent upon the structural redun-
performance. analytical studies and trial designs. dancy present in the building, Ωο is
Under in-plane lateral loading, the It is desirable that provisions be ap- the overstrength factor for the seis-
forces in the diaphragm were initially plicable to two untopped diaphragm mic-force-resisting system used in the
distributed according to strut-and-tie types, namely, those constructed using building, and C s is the seismic re-
concepts. However, once the longitu- double tees, and those constructed sponse coefficient for the building.
dinal joints started to “yield” at shear using hollow-core slabs. Until hollow- Thus, to ensure elastic response,
stresses as low as about 60 psi (0.41 core slab manufacturers are willing to untopped precast diaphragms used
MPa), the internal force distribution provide slabs with serrated edges, the in conjunction with special moment
changed. A Vierendeel truss pattern same design philosophy must apply frames need to be designed for forces
emerged with the slabs acting as con- to both diaphragm types. The phi- that are up to four and a half times
nectors, the stresses in the tie beams losophy of the Appendix is to require (the multiplier may be even larger in
no longer constant, and shear and that untopped diaphragms be designed certain situations) the seismic design
flexure effects at beam-to-slab con- for loads large enough to ensure that force for a cast-in-place slab on the
nections becoming important. they remain elastic under severe earth- same moment frame system.
Displacements of up to 3 in. (76 quakes and then to require connec- Rational elastic models must be
mm) were achieved along longitudi- tions that exhibit ductility ratios of at used to determine the in-plane shear
nal joints without the diaphragm los- least two for the forces acting on them and tension/compression forces acting
ing its integrity. The shear stress for under the design seismic forces. on connections that cross joints. For
“yielding” of the longitudinal joints To satisfy the criterion that the dia- example, in Fig.1, the shear stresses
depended on the reinforcement in the phragm remain elastic, the provisions and tension/compression stresses act-
tie beams and doubling that reinforce- of the Appendix cannot be applied ing on a joint immediately to the right
ment doubled the stress corresponding to structures with in-plane disconti- of Line BR can be determined from
to “yielding.” nuities in the vertical elements of the beam theory if all the connections
seismic-force-resisting system. For all on that line have the same stiffness
other structural irregularities, analyses characteristics, and are evenly spaced
PROPOSED REVISIONS must specifically consider the effects along that line.
TO 1997 NEHRP of the irregularities. The shear force per unit length will
PROVISIONS For SDCs D, E and F, the Appendix vary parabolically from zero at B to
requires that diaphragms, regardless a maximum at R and the axial stress
Detailed below are the proposed
of type, be designed to resist design per unit length will vary linearly from
revisions to the 1997 NEHRP Provi-
seismic forces as follows: a maximum at B to a minimum at R.
sions requirements for diaphragms
utilizing untopped precast concrete Clearly, the connections chosen for
units. Line BR will have to function satis-
(2)
As explained in the first article factorily for a wide combination of
in this series, Subcommittee TS-4 shear and tension/compression values.
of BSSC proposed additions to the where  n  The Appendix requires that connec-
∑F
Fpx = diaphragm x i  force tors used at joints, such as Line BR,
2000 NEHRP Provisions covering Fpx =  i =ndesign
 w px at Level i
the use of untopped precast concrete Fi = design force applied be shown by analysis and testing to
 ∑ wi 
diaphragms in regions of high seismic  i = x  to Level i
wi = weight tributary be able to develop the strengths re-
risk. However, the Provisions Update wpx = weight tributary to the quired by analysis and have ductilities
Committee (PUC) determined that be- diaphragm at Level x at those strengths equal to or greater
fore such provisions could be added The force determined from Eq. (2) than 2.0. Embedments for connec-
to the NEHRP Provisions, further ad- need not exceed 0.4SDSIwpx but must tions must be governed by steel yield-
vances were needed in understanding not be less than 0.2SDSIwpx, where SDS ing and not by fracture of concrete
the inertial forces required to design is the design (5 percent damped) spec- or welds, and the φ factors used for
such diaphragms, and the ductility tral response acceleration at the site at design of the diaphragm must also be
levels required for diaphragm con- short periods, and I is the occupancy used for design of the connections.
nections in order to provide adequate importance factor. Procedures that should be used for
strength and toughness. Untopped diaphragms must be de- acceptance testing of connections to
The TS-4 proposal on diaphragms signed for either: validate their design strengths are
utilizing untopped precast concrete 1. A design force ρΩο Fpx but not described in the Commentary to the
units is included in the 2000 NEHRP less than ρΩοCswpx, or Appendix. Prior to conducting tests
Provisions in an Appendix to the 2. A design shear force equal to on which design strengths are to be
chapter on concrete. That proposal is 1.25 times that required for yielding based, a design procedure needs to
from here on termed the Appendix. of the vertical elements of the seis- have been developed for prototype
The objective of this Appendix is to mic-force-resisting system calculated connections and that procedure used
provide a framework for laboratory using a φ factor of unity. to proportion the test specimens for
testing, analysis of the performance of Note that ρ is a reliability factor the acceptance testing. Because re-

November-December 2000 57
 high seismic risk.
The provisions of the Appendix
to the concrete chapter of the 2000
NEHRP Provisions on design of dia-
phragms utilizing untopped precast
elements are described, together with
portions of the Commentary to that
Appendix that outline desirable accep-
tance testing procedures for connec-
tions of untopped precast concrete dia-
phragms. The provisions of the above
Appendix impose penalties for the use
of untopped diaphragms because those
Fig. 8. Criteria for acceptance testing of diaphragm connections. provisions must cover diaphragms
composed of both double-tee and hol-
low-core slab units.
sults will be sensitive to connection one and not more than 1.25 times δm. Tests conducted in Italy have shown
details, acceptance testing to establish For the theory used to establish con- that those penalties for hollow-core
design values should be undertaken nection properties to be acceptable, slabs can be significantly reduced if
only after a preliminary test program connections must satisfy, for all de- appropriate detailing of the diaphragm
has been conducted that can be used sign loadings, the conditions shown in and the hollow-core units are used.
to establish a design procedure. Fig. 8. They must develop a strength, Research is needed to develop simi-
Test results for reversed cyclic load- Emax, greater than the calculated nom- lar detailing concepts for pretopped
ing of some typical connections are re- inal strength, E n, and that strength, double-tee diaphragms.
ported in Refs. 13 through 16 and those Emax, must be developed at a displace-
results can be used to establish design ment not greater than 3δm. Further,
procedures for those typical details. for cycling between limiting displace- ACKNOWLEDGMENT
For the acceptance tests, the con- ments of ±3δm or less, the peak force The original proposal leading to the
nections should be not less than two- for the third loading cycle for a given Appendix described in this article was
thirds scale and be subjected to a loading direction must be not less than prepared by a PCI Fast Team consist-
sequence of reversing limiting dis- 0.8Emax for the same loading direc- ing of Ned Cleland, Thomas D’Arcy,
placements of increasing magnitude. tion. Robert Fleischman, S.K. Ghosh, Neil
Three cycles should be applied at Hawkins, Phillip Iverson, Michael
each limiting displacement before the Oliva, Richard Sause and Paul Johal
CONCLUDING
limiting displacement is incremented and for which Ned Cleland was the
and the maximum load for the first REMARKS leader. The contributions of the mem-
sequence of three cycles should equal This article provides an overview bers of that team, and particularly Ned
0.75 times the calculated nominal of design issues for diaphragms uti- Cleland, are gratefully acknowledged
strength, En, of the connection. lizing precast concrete elements and as is also the cooperation of Susan
For calculations of ductility, the proportioned according to the 1997 Nakaki, John Stanton, Sharon Wood
stiffness of the connection is to be NEHRP Provisions, 2000 IBC, and and José Pincheira in the preparation
taken as 0.75En divided by the cor- ACI 318-99 requirements. It also pro- of this article.
responding displacement δm. Subse- vides a compendium of information
quent to the first sequence of three relevant to the design of diaphragms
REFERENCES
cycles, limiting displacements should utilizing untopped precast concrete
be incremented by values not less than elements that are located in regions of 1. FEMA,NEHRPRecommendedProvisions

58 PCI JOURNAL
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November-December 2000 59