Design of Precast Concrete Seismic Bracing Systems · PDF fileResisting Ductile Frame Systems...

34-1

34Design of PrecastConcrete SeismicBracing Systems

Robert E. Englekirk, Ph.D., S.E.*

34.1 Introduction ......................................................................34-134.2 Basic Concepts...................................................................34-2

The Development of a Strength Criterion • Creating an Effective Moment Transfer • Creating an Effective Shear Transfer

34.3 Precast Concrete Seismic Moment-Resisting Ductile Frame Systems......................................34-7Bolted Assemblages • Post-Tensioned Assemblages • Interior Beam–Column Joints

34.4 The Conceptual Design Process.....................................34-18Bolted Systems • Post-Tensioned Systems

34.5 Concluding Remarks.......................................................34-24References ...................................................................................34-24

34.1 Introduction

The precasting of concrete offers a wide variety of fabrication and assembly options. Economical seismicsolutions are, to a large extent, dependent on the fabricator’s capabilities and the contractor’s comfortwith the manner in which a particular precast component or system is integrated into the building. Asa consequence, innovation is the key to creating a successful solution because the options are many. Froma design perspective, options can be placed in two categories: those that emulate cast-in-place concreteconstruction and those that provide connections between components that are capable of sustainingpost-yield deformations. We will refer to these design alternatives as emulative and yielding, respectively.The term jointed precast is also used to identify precast concrete elements designed to yield at the precastinterface (Ghosh and Hawkins, 2001). These two approaches are shown in Figure 34.1. Systems a, b, andd of Figure 34.1 are emulative, for post-yield rotations are expected to occur in the concrete beam awayfrom the point at which precast members are connected. Yielding systems similar to that described inFigure 34.1c are the exclusive focus of this chapter.

* Chairman Emeritus of Englekirk Companies and Adjunct Professor of Structural Engineering at the University ofCalifornia, San Diego, where he actively participates in structural engineering research and teaches graduate coursesin reinforced and prestressed concrete design.

© 2008 by Taylor & Francis Group, LLC

34-2 Concrete Construction Engineering Handbook

34.2 Basic Concepts

The cost-effective development of a yielding connector requires a simple yet effective mechanism fortransferring both shear and moment as well as a suitable means of developing a strength-based loadingcriterion. Accordingly, these basic design and load transfer mechanisms are discussed before we explorethe design of component and building systems.

34.2.1 The Development of a Strength Criterion

The introduction of a yield limit state at the point where the demand is expected to be a maximum(Figure 34.1) suggests that limit-state design procedures should be used to develop objective levels ofsystem strength. Further, adjusting the level of provided strength is much more difficult in precastassemblies where the transfer mechanisms have established capacities that are large and do not allowmodest changes in provided strength. Accordingly, a mechanism approach should be used to define thestrength limit state for a precast concrete system. The mechanism approach should have as its primaryobjective entirely discounting the impact of dead and live loads on seismic bracing programs. Themechanism approach was introduced as plastic design in the 1950s and then was exclusively applied toindeterminate steel systems. The mechanism approach recognizes that system strength is based on theload required to produce a mechanism in the system and that first yield, as a limit state, does not produceconsistent factors of safety.

FIGURE 34.1 Classification of precast ductile frames according to component connector location. (From Englekirk,R.E., Reinforced and Precast Concrete Buildings, John Wiley & Sons, New York, 2003. Reprinted with permission ofJohn Wiley & Sons, Inc.)

Precast unit cast so as to locate precast joint at

points of least moment demand. This system is

often referred to as a “tree column” for the beam

and column are usually cast as one piece.

Precast joints (moment resistant) are located at

points of maximum moment but hinging will not

occur at the precast joint.

Precast joints are located at point of maximum

moment and point at which a plastic hinge is

expected to form.

Precast connections occur in member at point of

maximum moment but hinge location is not

anticipated at the precast joint.

Strong, nonyielding connection joining precast members.

Ductile, energy-dissipating connection joining precast members.“Hinged”, free but guided connection joining precast members or point of inflection (M ≅ 0).

Plastic hinge location (first yield).

(a)

(c)

ℓ

(d)

ℓ2

(b)

ℓh2

h2


Design of Precast Concrete Seismic Bracing Systems 34-3

Consider the frame and extracted subassembly described in Figure 34.2. The strength limit state isdefined by one of the mechanisms shown in Figure 34.3. Observe that dead and live loads only impactmechanisms of Figure 34.3a and Figure 34.3b because, in the mechanism of Figure 34.3c, dead and liveloads create no external work. Our seismic design objective should be to ensure that the mechanismdescribed in Figure 34.3c precedes that described in Figure 34.3b. This objective is accomplished bycomparing the lateral loads required to create the two mechanisms described in Figures 34.3b and 34.3c:

Mechanism of Figure 34.3c

(34.1)

where Mp is assumed to be the nominal strength of the connecting assembly.

Mechanism of Figure 34.3b

(34.2)

where Mp1 is the internal strength of the beam, assumed to be critical at midspan.

FIGURE 34.2 Frame elevation. (From Englekirk, R.E., Reinforced and Precast Concrete Buildings, John Wiley & Sons,New York, 2003. Reprinted with permission of John Wiley & Sons, Inc.)

FIGURE 34.3 Subassembly mechanisms. (From Englekirk, R.E., Reinforced and Precast Concrete Buildings, JohnWiley & Sons, New York, 2003. Reprinted with permission of John Wiley & Sons, Inc.)

(a) System (b) SubassemblyReference: (b)

Point of

inflection

Ve

wD wL

wD wL

Ve

Hi

VeVi

Vi

Ve

hX

ℓ ℓ

VuE

2

VuE

2

VuE

MpMp

2

VuE

2

VuE

Wu

Mp

hx

2

Mnn

Mnn

Mp1 Mp1

Wu

(a) Vertical Deformation (b) Vertical and Lateral Deformation

(c) Lateral Deformation

θ

θ

θ

2θ

2θ

2θ

Plastic

hinge

Analytical hinge

External Work = Internal Work

V h MuE x pθ θ= 2


V h w wuE x uD uθ+ +2 LL p pM M( )

= +� �2 4

2 2 1θ θ θ



The design objective is to determine the strength relationship between the internally provided flexuralstrength (Mp1) and that provided at the ends of the beam (Mp) that would cause the mechanism of Figure34.3c to be critical. If we define A as:

(34.3)

then Mp1, the strength provided in the interior of the beam, must be greater than AMp to attain ourobjective—the dominance of the side-sway mechanism (Figure 34.3c). Accordingly,

(34.4)

Thus, if the strength of the internal plastic hinge (AMp) exceeds (wuD + wuL)�2/8 and the provided momentcapacity at the support is equivalent to or larger than Mp as developed by the mechanism of Figure 34.3c([VuEhx]/2), the impact of vertical loads on the design strength provided in the yielding connector maybe neglected.

Example

The 24-foot internal bay of the frame of Figure 34.2 is shown in Figure 34.4:

(34.5)

Use Equation 34.5 to solve for the minimum value of Mp1 if Mp is 825 ft-kips:

Observe that the design objective can be obtained by the direct application of Equation 34.2 because itis understood that Equation 34.1 must be satisfied.

Conclusion: The side-sway mechanism described in Figure 34.3b can be avoided if the strength of thebeam (Mp1) is enough to satisfy the demand suggested by unconstrained support rotations.

FIGURE 34.4 Internal mechanism. (From Englekirk, R.E., Reinforced and Precast Concrete Buildings, John Wiley &Sons, New York, 2003. Reprinted with permission of John Wiley & Sons, Inc.)

Analytical hinge

VE

2= 100 kips

VE2

9 ft

Mp

Wu = 2.22 kips/ft

Bay Mechanism

Mp1

24 ft

θ

θ

2θ

θ

θ

AM

Mp

p

= 1

A M w wV h

p uD uLuE x=( ) > +( ) +1

8 2

2�


22

22

Vh wE

x uθ+ �

= +�4

2 2 1θ θ θM Mp p

200 92 22 24

42 825 2 235

2

1 1( ). ( )

( ) ,+ = + >M Mp p ft-kipss

AM

Mp

p

= = =1 235

8250 28.



34.2.2 Creating an Effective Moment Transfer

What makes a yielding connection different from a plastic hinge in a cast-in-place beam? The answerlies in the strain distribution in the region where the post-yield rotation will take place. The post-yieldrotation in a cast-in-place beam will occur over a plastic hinge region (Figure 34.5). The strain in theconcrete and reinforcing steel in this plastic hinge region will be essentially constant, for it will tend todistribute itself over a region that extends some distance past the plastic hinge region and into and oftenthrough the beam–column joint. When a precast beam and column are joined at the face of the column,a weakened plane is created (Figure 34.6). This causes a large portion of the rotation to occur at thisdiscontinuity, a condition that will impact the strain state in the flexural connection where flexuralcontinuity is provided by grouted reinforcing. Debonding must be addressed by the designer, and it willusually occur over a much smaller region adjacent to the gap created between the precast beam andcolumn (θp) (Figure 34.6). If, for example, the flexural reinforcement is placed in corrugated tubes andthen grouted, the length of debond appears to be on the order of the diameter of the bar (db), becausethe tubes provide confinement and promote wedging action. To mitigate this strain concentration, adebond length is often provided, and it should be clear that the ultimate strain imposed on the tensionreinforcement will be significantly greater in the precast system than that imposed on the tensionreinforcement in the cast-in-place system.

FIGURE 34.5 Beam 43 after failure. (From Englekirk, R.E., Reinforced and Precast Concrete Buildings, John Wiley &Sons, New York, 2003. Reprinted with permission of John Wiley & Sons, Inc.)

FIGURE 34.6 Rotation at beam–column interface. (From Englekirk, R.E., Reinforced and Precast Concrete Buildings,John Wiley & Sons, New York, 2003. Reprinted with permission of John Wiley & Sons, Inc.)

Center of

rotation

Column

High-strength grout

Mild steel

Mild steel

PT steel

tg

δs

δp

θp

c

d΄

d΄

h

h/2



34.2.3 Creating an Effective Shear Transfer

Shear transfer in cast-in-place concrete regions of discontinuity, such as the beam–column interfacedescribed in Figure 34.7, relies on the toe region of the beam to transfer both compression and shear. Thisshear transfer mechanism is often referred to as shear friction. Essentially, the yielding of the flexural tensionreinforcing of the beam is assumed to create a frictional resistance by its equilibrating compressive coun-terpart. The basic shear transfer strength as developed in design standards implies a shear friction factor(µ) of 0.6 to 1.4. This large range of codified friction factors is attributed to the condition of the interfacewhere shear must be transferred. Figure 34.8 describes the interface when applied shear acts in one direction.Seismic cyclings cause the actions to reverse, and tension cracks in the top of the beam described in Figure34.8 will close and be subjected to shear. The deterioration described in Figure 34.5, exacerbated by thebuckling of the bars, will occur and create a deformation limit state. Accordingly, the shear transfer limitstate is not, given a cyclic deformation, a function of the initial interface surface but rather the propensityof the interface to deteriorate. Yielding precast systems will rely on friction to transfer shear and endeavorto minimize cyclic deterioration. Yielding precast joints will often rely on a steel-to-steel or a steel-to-concreteinterface, for they are also capable of transferring shear forces when the frictional demand is reasonable.The steel-to-concrete friction factor is on the order of 0.7; structural steel design procedures allow a steel-to-steel friction factor of 0.35 for clean mill-surfaced finishes based on a factor safety of between 1.4 and 1.5.

FIGURE 34.7 Shear transfer mechanisms at the beam–column interface. (From Englekirk, R.E., Reinforced andPrecast Concrete Buildings, John Wiley & Sons, New York, 2003. Reprinted with permission of John Wiley & Sons, Inc.)

FIGURE 34.8 Compression fan at interior support of the beam, monotonic loading. (From McGregor, J., ReinforcedConcrete: Mechanics and Design, 3rd ed., Pearson Education, Upper Saddle River, NJ, 1997. With permission.)

Compression fan

Compression field

of uniformly sloped

compressive struts

s

Av fd

s

W

θ θ



Conclusion: The use of a nominal friction coefficient of 0.5 for steel-to-steel and 1.0 for concrete-to-concrete regardless of the type of surface finish seems reasonable. A strength reduction factor of 0.85 isoften recommended but probably excessive in this case, for the compressive force is passively activatedand always proportional to shear demand. This constant relationship between moment and shear obviatesthe need to consider overstrength factors.

34.3 Precast Concrete Seismic Moment-Resisting Ductile Frame Systems

Two basics systems are developed in this section. They have both been used successfully to constructmajor buildings in regions of high seismicity and represent two approaches to creating precast concretebuildings that will perform well when subjected to seismic excitations. The described approaches differprimarily in the means by which the frame beam and column are connected. They are categorized hereinas bolted and post-tensioned, but it is important to realize that the concepts developed are not limitingin their potential application, for variants have been and will continue to be produced.

34.3.1 Bolted Assemblages

The development of the assemblage described in Figure 34.9 was motivated by a desire to improve post-yield behavior of concrete ductile frames, because the ultimate post-yield rotation capability of thesubassembly is increased by 50%. The adaptation of the ductile connection concept to precast concreteis logical, because it allows post-yield deformations to be accommodated where members are joined(Figure 34.1c). Direct-thread alternatives have been used in both cast-in-place systems and compositeprecast concrete systems. The desired behavior is accomplished through a merging of steel technologywith the basic objectives of seismic-load-limiting principles essential to the development of ductilebehavior in structural systems that must survive earthquakes. The basic component is the ductile rod(Figure 34.10), which is capable of attaining strain states in excess of 30%. The assemblage described inFigure 34.9 allows tolerance in all directions and ensures proper seating of the connecting high-strength

FIGURE 34.9 Isometric view of the Dywidag Ductile Connector (DDC©) system. (From Englekirk, R.E., Reinforcedand Precast Concrete Buildings, John Wiley & Sons, New York, 2003. Reprinted with permission of John Wiley &Sons, Inc.)



bolts. The manufacture and distribution of the system is controlled by Dywidag Systems Internationalunder the name of Dywidag Ductile Connector (DDC®). System capacity is developed directly fromaccepted load transfer mechanisms and conditions of equilibrium. The strength reduction factors andoverstrength factors are consistent with values used in the design of concrete ductile frames. The keyelement in the assembly described in Figure 34.9 is the ductile rod (Figure 34.10). This ductile rod is theyielding element. The function of the ductile rod is to accommodate post-yield system deformations.

Our analytic understanding of system behavior, then, logically starts from the ductile rod and movesfirst to the beam and then into the column. When a moment couple is developed between two sets of Nrods separated by a distance d – d′ (Figure 34.11), the nominal moment capacity (Mn) developed is:

(34.6)

where Ty is the nominal tensile strength of one ductile rod. The nominal capacity of the set of ductilerods must be developed in the beam. Because the adopted design objective for the rest of the system iselastic behavior, an overstrength factor (λo) must be introduced.

The first load transfer point proceeding toward the beam is the beam–column interface, where theappropriate level of shear and moment must be transferred. High-strength (1-1/2-in. φ-A490SC) boltsare used to accomplish this transfer. The nominal tensile strength provided by this bolt is on the orderof 210 kips, which exceeds the nominal tension strength of the ductile rod by more than 25%:

The shear load (VnE) induced by the ductile rod mechanism at the beam-to-column interface is:

FIGURE 34.10 Prototypical forged ductile rod. (From Englekirk, R.E., Reinforced and Precast Concrete Buildings,John Wiley & Sons, New York, 2003. Reprinted with permission of John Wiley & Sons, Inc.)

6" Ø

3" Ø

(approx.)

1"

15

"

3"

2.2

5"

1.75" Ø

ℓ p =

9"

Forged

ductile rod

M NT d dn y= − ′( )

TM

d d

NAT

F

bn on

Bbn

t

=− ′( )

=

λ

φ



where �c is the clear span of the beam. The nominal shear capacity required of the connector is:

(34.7)

Comment: Because the design objective is code compliance, factored dead and live loads are appropriatelyused. Concerns relative to attaining shear transfer in the plastic hinge region of a cast-in-place framebeam (Vc = 0) do not apply because the plastic hinge region is no longer in the beam.

The shear transfer mechanism between beam and column is friction. The load proceeds from the faceof the ductile rod to the beam transfer block (see Figure 34.11) through a set of shim plates that providelongitudinal tolerance. The normal load that activates this friction load path is the larger of the boltpretension (Tp) or flexurally induced compression (M/d – d′). The ability of the connector described inFigure 34.11 to transfer load will depend on the level of pretensioning (2NTp) and applied moment (M).The level of applied moment (M) must at some instant be zero. At this instant, both the upper and lowerconnections will participate in the transfer of shear. Accordingly,

(34.8)

where f is the friction factor allowed by the load and resistance factor design (LRFD) specifications.As moment is applied to the connection, the effective level of pretensioning on the tensile bolt group

will be relieved. Observe that the force applied to the ductile rods is unaffected by the level of boltpreload, for the bolts serve only to clamp the beam transfer block to the ductile rod. When the preload(NTp) has been relieved, however, the ability of the compression face connector to transfer shear willcontinue to increase, for the compression (C) crossing the surface described in Figure 34.11 will nowbe entirely a function of the level of moment imposed on the connection. Hence, C will be the larger

FIGURE 34.11 DDC© connection, shear transfer mechanism (friction: steel to steel). (From Englekirk, R.E., Rein-forced and Precast Concrete Buildings, John Wiley & Sons, New York, 2003. Reprinted with permission of John Wiley& Sons, Inc.)

CL Symmetrical

Load transfer ties

Joint development ties

Load transfer ties

Column confinement tiesShim plates

Reference

Figure 34.9

Ductile rod

C

V

VM

nEo n

c

= 2λ�

V V V VnE D L= + +

V V NT fD L p+ < 2



of NTp or (M/d – d′). Accordingly, the nominal capacity of the shear transfer mechanism is the largerof these values:

(34.9)

where f, the friction factor used, should be 0.35 when dead and live loads are the concern (Equation34.8) or 0.5 when seismic limit state shears are considered (Equation 34.7) because a shear slip will notresult in a system failure. Beam component design should logically proceed based on the adoption of avariable overstrength factor (λo). The required capacity of each element should be modified (λoφ) toapproximately account for uncertainties associated with each of the considered load transfer mechanisms.

The yield strength of Threadbars® (high-strength threaded bars manufactured by Dywidag) that extendinto the beam (Figure 34.9) is guaranteed. The assembly has been tested to ensure that yielding does infact occur exclusively in the ductile rod (Figure 34.10). Alternatives for connecting the Threadbars® inthe beam include reverse threads in the transfer block, couplers, or splice bars. Shear reinforcement isdeveloped from Equation 34.7, and high-strength shear reinforcement (fy = 75 ksi) may also be used herebecause post-yield behavior in the stirrups is guarded against by the use of a capacity-based design. Theload path from the ductile rod to the column is by bearing (Figure 34.12). Shear loads are equilibratedby bearing stresses under the compression side rod ends at the face of the column. The bearing stressallowed for confined concrete may appropriately be used because the shear load is only transferredthrough the compressed zone of the frame beam, and the shim plates provide a significant normal orconfining pressure in this part of the column.

The internal bearing at the rod end when two rods abut (Figure 34.12) is subjected to a tensile loadfrom the ductile rod on one side and a compressive load from the rod on the opposite side, at least untilthe post-yield strain imposed on the ductile rod has been recovered. The tensile load will at some pointexceed Tyi, and the yield strength of the rod is accordingly factored to account for probable overstrength.The worst-case bearing load imposed on the anchor end of a ductile rod is 2λoTyi, but this will not berealized because any overstrength compression side demand will be resisted by bearing on the face of thecolumn. The concrete within the core of the column that resists this load is well confined, and thesupporting surface is wider than the bearing area on all sides. The design bearing stress may conservativelybe presumed to be 0.85φ(2)fc′, according to ACI 318-05, Section 10.17.1 (ACI Committee 318, 2005),and this is 1.2fc′.

A set of compressive struts distributes bearing stresses imposed on the rod ends to joint reinforcementlocated above, below, and alongside the ductile rod assembly (Figure 34.12). The internal load transfer

FIGURE 34.12 DDC© connection, shear transfer mechanism (concrete bearing: confined region). (From Englekirk,R.E., Reinforced and Precast Concrete Buildings, John Wiley & Sons, New York, 2003. Reprinted with permission ofJohn Wiley & Sons, Inc.)

Confining plate

fb

fb = 1.2fc

Compressive struts

´

VM

d dNT fn p=

− ′( )

or



mechanism within the joint itself, with the exception of the load transfer ties, is much the same as thatwhich occurs in the panel zone of a concrete ductile frame. It is discussed in considerably more detailin Section 34.4. The bracing tower of Figure 34.13 was built using the DDC® system.

34.3.2 Post-Tensioned Assemblages

Post-tensioned assemblages consisting of precast beams and columns were first tested in the early 1970s.Early rejections of the concept were based on the fact that no energy was dissipated by the system anda concern that anchorage systems would fail. In the 1990s, these problems were overcome with thedevelopment of what is now referred to as the hybrid system (Cheok and Lew, 1993; Englekirk, 2003).The system was then used to construct the building shown in Figure 34.14. A comprehensive test programin support of the design of this building was conducted by Professor Stanton at the University ofWashington. The exterior subassembly shown in Figure 34.15 describes the post-yield behavior of thebeam for the capacity of the column, and the joint in the subassembly significantly exceeds the demandimposed on them by the beam. The fact that post-yield deformation occurred almost exclusively in thebeam was confirmed by the test program.

Flexural strength in the hybrid beam (Figure 34.16) is provided by a combination of unbonded post-tensioning strands and bonded mild steel. Nine 1/2-in. 270-ksi strands stressed to 162 ksi were used inthe system described in Figure 34.15 to provide an effective concentric post-tensioning force of 223.1kips. Three #6 (GR60) reinforcing bars were placed in the top and bottom of the beam in tubes that weresubsequently grouted with high-strength grout. These bars provide energy dissipation, an attribute notprovided by the unbonded post-tensioning. The strength provided by the 16 × 21-in.-deep beam isdefined by the size of the grout pad, which for this test was 16 × 20 in.

The design of the exterior subassembly of Figure 34.15 assumed that the stress in the mild steelcompression reinforcement reached yield. Accordingly, the flexural strength provided by the mild steel(Mns) was:

(34.10)

The flexural strength provided by the unbonded post-tensioning (Mnps) is developed as follows (see Figure34.16):

FIGURE 34.13 Precast concrete bracing tower. (Photograph courtesy of Englekirk Partners, Los Angeles, CA.)

M T d dns ns= − ′( ) = =3 0 44 60 16 5 1307( . )( )( . ) in.-kipss



(34.11a)

(34.11b)

The nominal moment capacity of the hybrid frame beam of Figure 34.15 is:

(34.12)

This corresponds to a beam load or shear of:

The associated column shear or applied test frame force (Fcol) is:

FIGURE 34.14 Paramount Apartments, San Francisco, CA. (Photograph courtesy of David Wakely Photography,San Francisco, CA.)

T A f

T

aT

nps ps pse

nps

=

= =

=

9 0 153 162 223 1( . )( ) . kips

nnps

cf b0 85

223 1

0 85 5 163 3

.

.

. ( )( ).

′= = in.

M Th a

nps nps= −

= −( ) =2 2

223 1 10 1 65 1865. . in.--kips

M M Mn ns nps= + = + =1307 1865 3172 in.-kips

VM

nbn

c

= = =�

3172

6251 2. kips

V F Vh

c col nbx

= =

=

=�51 2

72

117 531 4.

.. kkips



Figure 34.17a describes the behavior of the test specimen. Figure 34.17b identifies critical behaviormilestones. The stresses imposed on the post-tensioning strands are shown in Figure 34.18, where theyare related to test specimen drift. Observe that the predicted nominal strength of 31.4 kips (Vc) is not

FIGURE 34.15 Exterior subassembly. (From Englekirk, R.E., Reinforced and Precast Concrete Buildings, John Wiley& Sons, New York, 2003. Reprinted with permission of John Wiley & Sons, Inc.)

FIGURE 34.16 Beam and column cross-sections, hybrid subassembly test program. (From Englekirk, R.E., Reinforcedand Precast Concrete Buildings, John Wiley & Sons, New York, 2003. Reprinted with permission of John Wiley &Sons, Inc.)

CLine fixture

Tubes continuous forconstruction onlyTypical at beamtop and bottom

Typical9" × 9" blockout

6'-

0"

2 ' -3"5'-2"

1'-

0"

1'-

6"

1"

(5) #3 centerabout fixture

(10) #3 double ties@ 3"o.c.

Outer hoop tiesonly @ 6" o.c.

(6) #4 @strand anchor

2 1

/2"

4'-

9 1

/2"

20"

CL Tube

CL Duct

Typicaldebond #6 bars6" each side ofcolumn face

Anchoragetendon

Typicalgrout joint(fc = 8 ksi)

Typical1/2" chamfer

Base plateand dowels

2"´

(3) #6 @ 3" o.c.in 1-1/2" Ø tubesgrouted




(2) #8 T & Balternatetop & bottom

#4 @ 4" o.c.double hoops

(3) 1/2" Ø strands(fsu = 270 ksi)

16" 20"

18

"

21

"

#8 (16 total)

Beam Section

Beam Section

Joint Region

Column Section

3/4" clr.typical

21

"

20"

#8 (16 total)

18

"

14"

8" Typical#3 hook ties

#5 outer and #4 innerfull hoops(4 required)



reached until a drift ratio of almost 2% is attained (Figure 34.17b). This is at least in part explained bythe fact that the initially delivered post-tensioning force was only 216 kips, or 4% less than the specified223.1 kips. A story drift of 1% was required to develop the assumed design force in the post-tensioning(Tnps = 223.1 kips).

Subassembly stiffness as predicted by idealized member stiffness is developed as follows (Englekirk,2003):

FIGURE 34.17 Test specimen behavior. (From Englekirk, R.E., Reinforced and Precast Concrete Buildings, John Wiley& Sons, New York, 2003. Reprinted with permission of John Wiley & Sons, Inc.)

Fmax (34.8 kips)

.75Fmax (26.1 kips)

.75Fmax (–29.6 kips)

Fmax (–39.5 kips)

–5 –4 –3 –2 –1 0 1 2 3 4 5

50

40

30

20

10

0

–10

–20

–30

–40

–50

Drift Ratio (%)

(a) Full Hysteretic Behavior

Co

lum

n Sh

ear (kip

s)

Mark Event

A

A B C D

B

C

D

E

F

G

Grout cracking interface

Grout lift-off interface

Surface cracking joint

Surface cracking beam

Bar yield, continuity bar

Bar fracture, continuity bar

Concrete spalling-beam

Set Drift Ratio

4

5

5

6

10

17

16

0.10

0.15

0.15

0.20

0.75

4.0

3.5

(31.4, 0.47)Idealizedbehavior F G

0 1 2 3 4 5

Drift Ratio (%)

(b) Critical Behavior Milestones

50

40

30

20

10

0

–10

–20

Co

lum

n Sh

ear (kip

s)



The associated drift ratio (∆/hx) is 0.47%. This drift ratio might be accepted as an idealized representationof stiffness to a column shear of about 50% of the nominal column shear (31.4 kips) but not as a goodidealization for the behavior described in Figure 34.17. The hybrid subassembly appears to be considerablysofter than a cast-in-place system (Englekirk, 2003).

Probable flexural strength and ultimate strain states should be predicted during the system analysisphase, as opposed to the conceptual design phase of the project. The process begins by estimating thestrain states in the reinforcing at a selected level of drift. Consider a 4% post-yield drift ratio (θp), ourobjective drift, and realize that any elastic component of story drift will be small (Figure 34.17). Theplastic hinge length (�p) initially will be the debonded length of the mild steel, in this case 6 in.:

FIGURE 34.18 Post-tensioning (PT) force vs. drift relationship. (From Englekirk, R.E., Reinforced and Precast Con-crete Buildings, John Wiley & Sons, New York, 2003. Reprinted with permission of John Wiley & Sons, Inc.)

318 kips

(nominal yield)

320

310

300

290

280

270

260

250

240

230

220

210

220

–5 –4 –3 –2 –1 0 1 2 3 4 5

Drift (%)

PT

Force

(kips)

∆xc x

b

x

c

x

V h

E I

h

I

h

= +

=

=

2

6 2

117 5

72

�

�

. in.

in.

II

I I

ce g

be

= = =

=

0 710 7 18 20

128400

0 35

34.

. ( )( )

.

in.

gg

x

= =

=

0 35 16 21

124322

31 4 117 5

6

34

2

. ( )( )

. ( . )

in.

∆(( )

..

4000

72

4322

117 5

84000 55+

= in.



Further, assume that all of the post-yield rotation will occur at the beam–column interface (Figure 34.6).The elongations of the tensile reinforcement components, (δp and δs) are best made using an iterativeprocess, for the stress levels in the reinforcement will dictate the location of the neutral axis. Begin theiterative process by assuming a neutral axis depth (c) of 6 in.:

The intentional mild steel debond length (Figure 34.15) was 6 in. but can reasonably be expanded toinclude some adjacent debonding. Hence, the effective debond length (�d) is on the order of:

and the post-yield strain state in the debond region (εsp) is:

This corresponds to a stress in the bar of (Englekirk, 2003):

The elongation of the post-tensioning strand (δpsp) is:

The overall length of the strand (Figure 34.15) is on the order of 100 in.; hence,

The total tensile force in the post-tensioning steel at a joint rotation (θp) of 0.04 radian is (theoretical):

Comment: Observe that the projected force in the post-tensioning is consistent with that measured (onthe positive cycle) at a drift angle of 4% (Figure 34.18).

The tensile force provided by the mild reinforcing is:

θ φy y ph c

= =−( ) =

−

≅�0 002

60 002

20 46 0

.( )

.( ) .000075 radian

c

d cs p

=

= − = − =

6

18 25 6 0 04 0 49

in.

in.δ θ( ) ( . )( . ) .

�d bd= + ( ) =6 2 7 5. in.

ε δsp

s

d

= = =�

0 49

7 50 065

.

.. in./in.

λo yf ≅ 86 ksi

δ θpsp p

hc= −

= − =2

10 6 0 04 0 16( ) . . in.

∆

∆ ∆

ε

ε

psp

ps psp psf E

= =

= =

0 16

1000 0016

0

..

.

in./in.

00016 28 000 45

162 45 207

( , ) =

= + = + =

ksi

f f fps se psp∆ kksi ksi< ≅f py 230

∆ ∆T A f

T

ps sp psp

ps

= = =

= +

9 0 153 45 61 7

223 1

( . ) .

.

kips

661 7 286. = kips

Ts = =3 0 44 86 114( . )( ) kips



The depth to the neutral axis may now be estimated:

Conclusion: A neutral axis depth of 6 in. was reasonably presumed.

Strain levels in the concrete are quite high. If we assume a plastic hinge length (�p) equivalent to thedebond length (�d):

(34.13)

It was for this reason that the developers of the hybrid system armored beam corners with angles duringthe NIST tests (Cheok and Lew, 1993). The University of Washington test specimens were not armored.Beam corners did exhibit surface cracking early, but beam strength did not begin to deteriorate untildrifts exceeded 4% (see Figure 34.17b). The plasticity of high-strength grout probably absorbs a dispro-portionate amount of the post-yield concrete strain because these grouts are usually quite ductile.

Comment: The fact that one of the mild steel bars fractured at a drift angle of 2.5% is disconcertingbecause the apparent strain in this bar is below that normally associated with fracture. Seven identicalbeams were tested, and this bar was the only one that fractured. A conservative selection of the debondlength based on a fracture strain of 5% is suggested.

The probable moment capacity (Mpr) at a drift angle of 4% discounting the ruptured #6 bar is:

(34.14)

This corresponds to a column shear force of:

This predicted column shear force is consistent with the test results (Figure 34.17).

34.3.3 Interior Beam–Column Joints

34.3.3.1 Post-Tensioned Assemblies (Hybrid System)

Joint shear stress analysis procedures are developed as they are for conventionally reinforced cast-in-placeconcrete beam–column joints. The shear imposed on the beam–column joint (Vjh,prob) is shown in Figure34.19:

T T C

a

ps s sy+ − = + − =

=

286 114 79 320

320

0 85 5 1

kips

. ( )( 664 7

0 85 9

).

..

=

= =

in.

in.ca

φθ θ

ε φ

pp y

p

c pc

=−

= =

= =

�0 0392

7 50 0052

0

.

.. .rad./in

.. ( ) .

( ) . ( .

0052 6 0 031

0 0052 12

=

= − =

in./in.

ε φs p d c 225 0 064) . .= in./in

M T d d Th a

T T da

pr ns ps s ns= − ′( )+ −

+ −( ) −2 2 2

= + − + −52 8 16 5 286 10 2 35 35 18 25 2 35. ( . ) ( . ) ( . . )) = + + =871 2188 373 3432 in.-kips

V Mh

c pr prc

, =

=

��

13432

72

62

1

1117 534 7

..

= kips

V T T Vjh prob o nps o s c, = + −λ λ2



And the shear stress imposed on the joint (υjh,prob) is:

where Aj is the gross area of the column. The allowable joint shear stress (υjh,allow) is:

34.3.3.2 Bolted Assemblies (DDC®)

Joint shear stress analysis follows those procedures adopted for cast-in-place concrete (Figure 34.20). Thediscontinuity between ductile rods may be handled in a variety of ways, as it increases the ability of thejoint to transfer loads (Englekirk, 2003). The test specimen followed the load flow described in Figure 34.20where the tension rod (DR1) activates the proximate tie sets, which then deliver it to the compression node.Alternatively, an interior node may be presumed at the rod heads. Given this alternative, an �c secondarystrut and tie transfer will be developed, and this undoubtedly accounts for the superior performance of theDDC® beam–column joint (to drift ratios of 6%). Joint shear stress analysis procedures are conservativelydeveloped, as they are for conventionally reinforced cast-in-place concrete beam–column joints.

34.4 The Conceptual Design Process

The process described herein is intended to provide the development team with enough data to make aninformed decision regarding the appropriateness of alternative systems. The design process, in conjunctionwith the constructor, must create alternative solutions using these generic approaches as points of departure.

34.4.1 Bolted SystemsThe approach described specifically utilizes the Dywidag Ductile Connector (DDC®) system, which iscontrolled by patents. This control of product is important because many subtle quality-control designissues are dealt with in the product provided; these include a fail-proof bolt setting length as well assystem tolerances and ductility. The design process begins with development of the seismic-induced shearloads that the bracing system must sustain. The major system constraint lies in the fact that one assembly(two ductile rods) has a relatively high yield strength, and this strength cannot be fine tuned. This

FIGURE 34.19 Forces acting on a hybrid beam–column joint. (From Englekirk, R.E., Reinforced and Precast ConcreteBuildings, John Wiley & Sons, New York, 2003. Reprinted with permission of John Wiley & Sons, Inc.)

Ts, max+ Tps, max

Ts, max+ Tps, maxTs, max

Vc , max

Vc , max

Tps, max

Ts, max

Tp s , max

υ jh probjh prob

j

V

A,

,=

υ φjh allow cf, = ′15



constraint must be considered very early in the design process and the bracing program modified toaccommodate system and functional objectives. The assembly described in Figure 34.9 contains twoductile rods, which establish its yield strength at about 300 kips (Tn), and this sets the strength increments.

The basic geometry of the building bracing program has been established: column spacing and storyheight; thus, given a story shear, the first question to be addressed is the number of frame bays required.The process must be reduced to its simplest form, and this means discounting compensating factors; forexample, building torsion will increase the demand on some components, while using center-line dimen-sions will understate the capacity of a subassembly (they usually counterbalance each other). Hence,

(34.15)

where V is the objective base shear for the building (kips); n is the number of frame bays; Mu is thefactored moment capacity of the frame beam (ft-kips); and hx is the story height (ft).

• Step 1: Determine the number of frames required.

Conclusions: 24 assemblies of the type described in Figure 34.9 are required. Two assemblies per beamseems most logical. System proposed should be 12 frame bays in each direction, two DDC®s per beam.

Comment: The number of required frame bays may be significantly reduced by combining the boltedand hybrid systems.

FIGURE 34.20 Load flow within a DDC® beam–column joint. (From Englekirk, R.E., Reinforced and Precast ConcreteBuildings, John Wiley & Sons, New York, 2003. Reprinted with permission of John Wiley & Sons, Inc.)

Compression

node

Tension rodDR1Vc

λo N1 Ty

λo N1 Ty

λo N2 Ty

Compression

Strut

VnM

hu

x

= 2

V

h

M d d

x

u

=

=

= − − ′ =

2000

11

900 1

kips

ft

ft-kips DDC; 33 33

2000 11

90024

.

( )

ft( )= =n



• Step 2: Size and detail the beam.

b = 30 in., h = 46 in., 2 DDC® assemblies per beam (see Figure 34.9)

• Step 3: Check beam–column joint shear.

Use procedures adopted by ACI, replacing λofyAs and λofyAs′ with λonTy, where n is the number of DDC®assemblies, and Ty is the yield strength of one assembly (two rods ≅ 300 kips).

• Step 4: Proceed to develop the system load path as appropriate for a cast-in-place system using a capacity-based design approach.

34.4.2 Post-Tensioned SystemsGiven that the capacity of a hybrid system can be changed quite readily, the number of frames required isusually more closely related to building geometry, constructability, and function. The size of the beamsand their grouping will tend to control the design process. When the objective beam size has been estab-lished, the developable strength is established and from this the bracing program for the building created.

• Step 1: Determine a trial reinforcing program.

It is advisable to maintain a reasonable level of restoring force, for this is clearly a very positive attributeof post-tensioning. Accordingly, a design objective should be to provide at least 50% of the momentcapacity with the post-tensioning. Begin by selecting the appropriate level of mild steel reinforcing:

Then determine the amount of post-tensioning steel required to satisfy the strength objectives:

(34.16)

(34.17)

where fps may be conservatively assumed to be the effective level of prestress, usually 162 ksi.

Comment: A nominal strength projection based on an effective prestress of 162 ksi will result in a strengthequivalent to about 95% of its nominal strength, but this seems reasonable given the softness of thesystem (Figure 34.17).

• Step 2: Determine the minimum size of the beam–column joint.

The analysis procedure for the hybrid beam system is developed in Section 34.3.3. An approximaterelationship between the area of the beam–column joint and the amount of beam reinforcing is developedin Englekirk (2003):

(34.18)

• Step 3: Check the feasibility of placing the reinforcement suggested by the trial design.

• Step 4: Check to ensure that the provided level of post-tensioning is reasonable, on the order of 1000 psi.

Comment: The hybrid beam will become an integral part of the floor system. Large stress differentialsmay cause undesirable cracking in unstressed floors. Accordingly, it is best to use 1000 psi as an objectiveprestress limit.

M M

AM

f d d

us u

su

y

≅

=− ′( )

0 4

0 4

.

.

φ

M M f d d Aups u y s= − − ′( )0 9.

AM

fh a

psups

ps

=−

φ2 2

A A A Aj s s ps= + ′( )+62 210



• Step 5: Check the shear capacity/demand ratio to ensure that objective shear stress limit states have notbeen exceeded:

(34.19)

where VD and VL are the dead and live load shears, respectively, and �c is the clear span of the beam.

Comment: Sufficient accuracy for design purposes may be attained through the use of an overstrengthfactor (λo) of 1.25:

Remember that, in this case, because the adopted limit state ( ) is less than that proposed in mostcodes, VD and VL should be realistically selected, not the factored loads used in a code-compliance analysis.This limit state is perhaps somewhat conservatively applied to the hybrid system because the hingedeformation tends to accumulate at the joining of the beam and the column (see Figure 34.6) and theplastic hinge region is prestressed.

• Step 6: Check column shear if the beam is deep and the column short.For an exterior subassembly (Figure 34.15) this is:

Design Example

Design a 20 × 32-in. hybrid interior beam for the described subassembly:

• Step 1: Select a trial beam reinforcement program.

For an interior column and an objective column shear of 200 kips,

Select a mild steel reinforcing program:

VM M

V Vbo ns nps

cD L=

+( )+ +

2λ�

bdV

fb

c

≥′5

5 ′fc

b hM M

f h

M M

hc c

o ns nps

c x

ns nps

x

≥+( )′

≥+( )λ

5

3 6.

Vcu

c

=

= =

200

24 211 1

kips (column shear)

ft ft� �

�

;

22 216 13

9

= =

=

ft ft

ft

;�c

xh

V h Mc x buc c

= +

��

��

1

1

2

2

MV h

buc x

c c

=+

=+

=��

��

1

1

2

2

200 9

1 14 1 237

( )

. .660 ft-kips

M M

AM

f d d

us bu

sus

y

= = =

=− ′

0 4 0 4 760 304. . ( ) ft-kips

φ (( ) =−

=304 12

0 9 60 29 32 6 3( )

. ( )( ). in.



Try three #9 bars. Select the post-tensioning reinforcement:

Accordingly, the flexural strength provided by the post-tensioning exceeds that provided by the mildsteel, and this was identified as a design objective. For design purposes the nominal strength of unbondedstrands (fpn) is assumed to be its effective strength:

Comment: The development of fpn in ACI 318-05 (fps, Equation 18-5) is based on a correlation betweentest data and analysis. Observe that a similar relationship (fpse + 10,000) between effective and nominalstrength is not appropriate for the hybrid system. The tensile force in the tendon corresponding to astrand stress of 162 ksi in the test described in Figure 34.18 would be 223 kips, and this force is notdeveloped until the drift reaches 1.5%. Accordingly, the use of fpse to define the nominal strength of ahybrid beam is viewed as being appropriate:

where the depth of the compressive stress block (a) is presumed to be about 6 in.

Aps = 2.59 in.2

Use 0.6-in. ø strands (A = 0.217 in.2).

Comment: 0.6-in. ø strand hardware is most common in the United States but local availability shouldbe confirmed.

Number of strands required = 2.59/0.217 = 11.9

Check the level of prestress provided by 12 strands:

Conclusion: The trial reinforcing program will consist of 12 0.6-in.-diameter strands and 3 #9 (GR 60)reinforcing bars, top and bottom. The nominal strength of this beam is:

M A f d dus s y= − ′( ) = − =φ 3 0 0 9 60 29 3 4212. ( . )( )( ) in.-kkips in.-kipsM

M M M

ns

nps bu us

=( )= − =

4680

760 12φ ( ))− = >4212 4908 4212in.-kips in.-kips (OK)

f fpn pse=

AM

fh a

psnps

pse

=−

=−

φ

φ2 2

4908

0 9 162 16 3. ( )( ))

fc = =12 0 217 162

20 320 660

( . )( )

( ). ksi (OK)

M M M

aT

f b

n nps ns

ps

c

= +

=′

=0 85

12 0 217

0 85 5 2.

( . )

. ( )( 005

2 2422 16 2 5 56

)

( . )

=

= −

= − =

in.

M Th a

nps nps 997

9340 9310

in.-kips

in.-kips in.-kips (OKφMn = > ))



• Step 2: Determine minimum size of the beam–column joint.

Conclusion: Column size should be at least 30 × 32 in.

• Step 3: Develop the beam and column reinforcing program.The mild steel must be placed in ducts and grouted. The post-tensioning strands will also be placedin a duct and stressed using a multistrand jack. Mild steel tubes should have a diameter of at least 2db.The post-tensioning duct will be of the size suggested by the supplier. Column bars will have to beplaced in this central region, and they must pass the post-tensioning duct and yet be inside the outermild steel duct (see Figure 34.21). Beam bars cast in the corners of the precast beam are also requiredif for no other reason than to reinforce an otherwise unreinforced region. Minimum flexural reinforcingrequirements are usually satisfied by the post-tensioning, so the basis for the sizing of these barsdepends on the designer’s convictions relative to splicing concerns. ACI 318-05, Section 18.9, requiresa minimum amount of bonded reinforcement in all flexural members with unbonded prestressingtendons:

As,min = 0.004Act

where Act is the area between the tension face and the center of gravity of the gross section. The beam-sizing process must then allow for the flexural reinforcing provided in the precast beam as well as thespace that may be required to pass the column bars (see Figure 34.21). The minimum beam widthbecomes:

Conclusion: The minimum beam width should be 20 in.

FIGURE 34.21 Hybrid beam reinforcement program. (From Englekirk, R.E., Reinforced and Precast Concrete Build-ings, John Wiley & Sons, New York, 2003. Reprinted with permission of John Wiley & Sons, Inc.)

One post-tensioning duct 3.50 in.Two #11 column bars 2.75 in.Two mild steel ducts 4.50 in.Two corner bar diameters 2.00 in.Two corner bars 2.00 in.#5 hoop ties 1.25 in.Fire cover 3.00 in.Total 19.00 in.

Mild steel duct 2-1/4" dia.Room for column

bars (1-1/2" min.)

Symmetrical

db

Precast beam

Post-tensioningstrand duct (3-1/2"ø)

Mild steel duct

Mid-heightof beam

ine beam

A A A Aj s s ps= + ′( )+ = + =62 210 62 6 210 12 0 217 9( ) ( )( . ) 119 in2



The minimum bonded reinforcement (ACI 318-05, Equation 18-6) is:

Conclusion: The beam should be 20 in. wide. At least one #8 bar should be provided in each corner.

Comment: This mild steel may have to be increased to reduce concrete cracking during transportation,but this will be the concern of the fabricator.

34.5 Concluding Remarks

The design of precast systems does not require special knowledge, for it follows principles used bystructural engineers to design ductile moment resisting frame systems. A more detailed development ofboth cast-in-place and precast systems is contained in Seismic Design of Reinforced and Precast ConcreteBuildings (Englekirk, 2003). The designer of precast frame systems is encouraged to be creative in thedevelopment of systems. The combining of the DDC® system with the hybrid system is but one example.The design–build delivery system lends itself to creative solutions, but both the hybrid and DDC systemshave been constructed using the traditional design–bid–build delivery system.

References

ACI Committee 318. 2005. Building Code Requirements for Structural Concrete and Commentary, ACI318-05/318R-05. American Concrete Institute, Farmington Hills, MI.

Cheok, G.S. and Lew, H.S. 1993. Model precast concrete beam-to-column connections subject to cyclicloading. PCI J., 38(4), 80–92.

Englekirk, R.E. 2003. Seismic Design of Reinforced and Precast Concrete Buildings. John Wiley & Sons,New York.

Ghosh, S.K. and Hawkins, N.M. 2001. Seismic design provisions for precast concrete structures in ACI318. PCI J., 46(1), 28–32.

Priestley, M.J.N. 1991. Overview of PRESSS research program, PCI J., 36(1), 50–57.

A bh

s ,min . . ( ) .= = =0 0042

0 004 20 16 1 28 2in.


Flexural cracking at ultimate load of post-tensioned prestressed beams. (Photograph courtesy of Edward G. Nawy.)


Design of Precast Concrete Seismic Bracing Systems · PDF fileResisting Ductile Frame Systems...

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