Development and Testing of a Ductile Connector for Assembling Precast Concrete Beams and Columns

Robert E. Englekirk Ph.D., S.E. Chief Executive Officer Englekirk & Nakaki, Inc. (ENI) Los Angeles, California

Dr. Englekirk has been a strong advocate of the use of precast concrete structural systems in seismic areas. He cofounded ENI in 1994 in response to a need within the community to develop new building systems. The ductile connector system described in this article has gained ICBO approval and will be used in a project this spring.

36

The precast concrete industry has attempted for many years to develop connectors that will perform well during an earthquake. This article describes the development of an energy absorbing ductile connector that can be used to construct a seismic moment resisting frame of precast concrete components that will outperform comparable cast-in­place and structural steel systems. The system was developed by the author working in conjunction with Dywidag­Systems International. The design philosophy, test program, and adaptability of the connection system to real structures are described in detail. This paper is a companion to the largely non-technical article that was recently published in the September-October 1994 PC/ JOURNAL.

T. he development of the de­

scribed ductile connector (DC) was motivated by a desire to

improve the post-yield behavior of concrete ductile frames. The adapta­tion of the ductile connector concept to precast concrete is logical, because it allows post-yield deformations to be accommodated at member joints. Ac­cordingly, it deviates from the more typical cast-in-place emulation ap­proach to the design of precast con­crete connections.

The desired behavior is accom­plished through a merging of steel technology with the basic objectives of seismic load limiting principles es­sential to the development of ductile

behavior in structural sys tems that must survive earthquakes.

The Achilles heel of a properly con­ceived concrete ductile frame beam has always been the toe (no pun in­tended) of the frame beam where large compressive and shear stresses com­bine (see Fig. 1). This condition of high stress is further aggravated by the tensile overstraining of the flexural re­inforcement in the toe region. During reverse cycles of load, the now perma­nently elongated bar buckles when it is subjected to compressive strains. Crushing in the toe region can occur after relatively few cycles of post­yield rotation. These rotations need not necessarily be at high drift angles

PCI JOURNAL

-crushing can also occur after multi­ple cycles at moderate drift angles.

Ductile concrete frames subjected to earthquakes of moderate intensity nearly always exhibit distress at the beam-to-column interface, because shell concrete tends to spall. Even when this spalling is not a structural problem, the confidence of the occupant of a con­crete building is diminished.

If an analytical description of be­havior within the toe region of a frame beam were available, it is still unlikely that the deterioration could be signifi­cantly mitigated. Accordingly, the log­ical mitigation alternative is to relo­cate the causative actions.

To this end, the ductile connector described in Fig. 2: • Relocates the yielding element • Allows the strain in the toe region of

the beam to be controlled • Transfers shear forces by friction

from steel to steel As a consequence, the frame beam

may be designed to behave elastically because the yielding experienced by the ductile rods will limit the shear and flexural load imposed on the frame beam.

DEVELOPING SYSTEM CAPACITY

System capacity is developed herein directly from accepted (codified) load transfer mechanisms and conditions of equilibrium. The strength reduction factors and overstrength factors identi­fied in this section have been adopted by the International Conference of Building Officials (ICBO Research Report). They are typically consistent with values used in the design of con­crete ductile frames (SMRSF).

The key element in a ductile frame that contains the ductile connector de­scribed in Fig. 2 is a ductile rod (see Fig. 3). This ductile rod is the yielding element. The function of the ductile rod is to accommodate post-yield sys­tem deformations . The prototypical ductile rod (see Fig. 14) was milled from a steel alloy bar (AISI 1045). This alloy was selected because it tends to minimize the strain hardening characteristically produced in steels when subjected to cyclic straining well beyond yield strain. The stress-strain

March-April1995

Fig. 1. View of cast-in-place subassembly at 3.5 percent drift- Cycle 3.

Concrete Column Conuete Column

with Beams

BEAM TRANSFER

BLOCK

HIGH STRENGTH BOLTS

Fig. 2. Isometric view of a ductile connector.

relationship for the prototypical duc­tile rod is described in Fig. 4. The cast ductile rod of Fig. 3 will be of AISI 1022M material and this will further reduce strain hardening effects. Our analytic understanding of system be­havior, then, logically starts from the ductile rod and moves first to the beam and then into the column.

The idealized yield strength, Tyi• of the ductile rod described in Fig. 3 is 120 kips (534 kN). When a moment couple is developed between two sets of "N" rods separated by a distance d' (see Fig. 5), the ideal or nominal mo­ment capacity, Mn , developed is:

(1)

37

c ~ .

.!: If) m N .

15 in

(361 mm)

$ OE .!: E

0.39 in RADIUS {10 mm) J_k

(25 mm)

Fig. 3. Cast ductile rod.

eo

0.002 0.05 STRAIN (ln ./ln.)

Fig . 4. Relationship between stress and strain for the prototypical ductile rod .

The nominal capacity of the set of ductile rods must be developed in the beam. Because the adopted design ob­jective for the rest of the system is elastic behavior, an overstrength fac­tor, 1\.0 , must be introduced.

The first load transfer point pro­ceeding towards the beam is the beam­to-column interface where the appro­priate level of shear and moment must be transferred . High strength (A490SC) bolts are used to accom­plish this transfer. The nominal area (NA 8 ) required of the bolt group is de­veloped from LRFD Specifications: '

T 1\, M" Bn = o---;F (2)

38

(3)

where N = number of bolts

A 8 = nominal area of a single bolt F8 = nominal yield strength of the

bolt Observe that the bolts wi ll not yield

provided 1\,)</J, is appropriately cho­sen. The shear load, V11E, induced by the ductile rod at mechani sm on the beam-to-column interface is:

V - 21\.oMn nE- L

c

(4)

where Lc is the clear span of the beam.

The nominal shear capacity required of the connector as developed from Eq. (4) and the ACI Code2 is:

The shear transfer mechanism is frictio n. The load proceeds from the face of the ductile rod to the beam transfer block (see Fig. 5) through a set of shim plates (see Fig. 6). The normal load that activates this friction load path is the larger of the bolt pre­tension , Ppre' or flexurally induced compression (Mid') .

Steel surface treatments will corre­spond to those described for slip criti­cal connections in the LRFD Specifi­cations.' These treatments are required on the ductile rod face, shim plates, beam transfer block, and plate washer in order to provide a positive slip-free shear transfer.

The ability of the connector de­scribed in Fig. 6 to transfer load will depend on the level of pretensioning, 2NPpre' and applied moment, M. At some point during the cyclic loading sequence, the level of applied mo­ment, M, must be zero. Accordingly:

where f is the friction factor allowed by the LRFD Specifications.'

As moment is applied to the connec­tion, the effective level of pretensioning on the tensile bolt group will be re­lieved. The compressive force applied to the compression bolt group will not increase however. This is because the ability of the compression face group of bolts to transfer shear will remain con­stant for the pretensioning force will be relieved as the flexurally generated compressive force increases.' Conserva­tively, one may entirely neglect the pre­tensioning force applied to the tensile group of bolts and, thereby, reduce the level of shear transfer to NPP,.J.

Once the preload (NPP,.J> has been relieved, the ability of the compres­sion face connector to transfer shear will continue to increase, for the com­pression, C, crossing the surface de­scribed in Fig. 6 will now be entirely a fu nction of the level of moment im­posed on the connection. Hence, C will be the larger of NPpre or Mid'.

PCI JOURNAL

Accordi ng ly, the nominal capacity of the shear transfer mechanism is the larger value generated from Eq. (7):

V,, = (:, or NPpre )t (7)

The shea r transfer co ncepts de­scribed are applicable to connec tors that contain a different number of duc­tile rods on each beam face except that NPpre becomes the compression side preload.

Beam component design should log­ically proceed based on the adoption of a variable overstrength factor, A0 .

The required capacity of each element should be modified (A

0/¢) to appropri ­

ately account for uncertainties associ­ated with each of the considered load transfe r mechani sms. The required area of beam fl exural reinforcement, Asb• is:

The yield strength , FY' of the beam reinfo rcement, because it need not yield, may significantly exceed Grade 60. The selection of the strength re­duction factor ¢b should recognize the alignment imposed by the beam trans­fer block as well as the likelihood for under capacity in beam reinforcement. The yield strength of Threadbars (high strength threaded bars manufac tured by Dywidag) is guaranteed; accord­ingly, A0 1¢b need not be overconserva­tively adopted. Shear reinforcement is deve loped f ro m Eq . (5 ) and hig h strength rei nforcement [Fy = 75 ksi (334 kN)] may also be used here. The ratio, A0 1¢v, fo r shear re inforcement should be more conservati ve than the comparable ratio used in the develop­ment of A sb [see Eq. (8)].

The load path from the ductile rod to the column is by bearing (see Fig. 7). Shear loads are equilibrated by bearing stresses under the rod ends at the face of the column while ax ial fo rces in the rod , both tensil e and compress ive, create bearing stresses on the fl ared ends of the ductile rods. The des ign shear load [see Eq. (5)] must be developed under each set (top and bottom) of ductile rods.

The bearing stress allowed for con­fined concrete may appropriately be

March-April 1995

L. . :::u.; L

" \\

~ SYMM.

I

L

I

I

,<;\

m \\._../

LU \\

I

~LOAD TRANSFER TIES

;.u: _j

DUCTILE ROD_/ \\ I

'o

' · -;::::rn;:

'<A» W"<""~ ' BEAM TRANSFER BLOCK

SHIM PLATES

ERECTION CORBEL

Fig . 5. Frame beam-to-column connection.

used because the shear load is only transferred through the compressed zone of the frame beam, and the shim plates and grout provide a significant normal or confining pressure in this part of the column . A bond breaker between rod and concrete should be used to avoid the deterioration of the concrete through repeated cycles of rod extension and shortening.

The internal bearing at the fl ared rod end when two rods abut is sub­jected to a tensile load from the ductile rod on one side and a co mpressive load from the rod on the opposite side. The tensile load will at some point ex­ceed Ty; and is accordingly factored to account for probable overstrength . The worst case bearing load imposed on th e fl a red end of a du ct il e rod is 2A0 Tyi· Because the concrete is well confined and the supporting surface is wider th an the bearing area on all

\\-L \~ -----= I--JOINT DEVELOPME~

)\\ TIES

\\ "~ ,\\

~ -,

LJ \'\'---... r '=

"' I

~LOAD TRANSFER TIES

I

I ~ j--_ COLU MN

k ~CONFINEMEN

~ TIES T

sides, the design bearing stress may be presumed, very conservatively, to be 0.85¢(2)/; (ACI 10.15.P).

A se t of co mpress ive struts d is­tribute bearing stresses imposed on the rod ends to joint reinforcement located above, below, and alongside the duc­tile rod assembly (see Fig. 8). The in­ternal load transfer mechanism within the joint itself, with the exception of the load transfer ties, is much the same as that which occurs in the panel zone of a concrete ductile frame.

DEFINING STRENGTH LIMIT STATES

The objecti ve of any des ign should be to optimize behavior. When earth­quakes are a concern, optimal behav­ior is associated with the ability of a system to deform in the post-y ield be­havior region. The attainment of this

39

n L

l+-------->.!'<--- -""'tt+J..U.Ir---!.0.;;:;; DEVEUif';·!Ei·;T

::t.oc~:

Ef~ECTir:i·J COf~BEi.

Fig . 6. Shear transfer (friction: steel to steel).

CONFINING PLATE \

. I - ·"'

l ,,, Fig. 7. Shear transfer (concrete bearing: confined region) .

40

:::::;

objective is often in conflict with the satisfaction of strength objectives. Both objectives can be attained if we rationally alter classical design ap­proaches, but this should only be con­sidered if behavior is enhanced in the process. We know that available duc­tility is a function of the amount of re­inforcement provided and decreases with added reinforcement. Reinforce­ment is dictated by strength.

The code now requires that A~ be at least A.l2. If this is the provided bal­ance, then available ductility will be less in one direction of applied defor­mation than the other. Further, the provided strength at system yield can significantly exceed strength objec­tives and this is not desirable because it will impose larger loads on the elas­tic portion of the load path.

The extent to which a reinforcing bar is strained before the yield defor­mation level is reached is of little con­sequence from the perspective of at­tainable ductility; hence, the emphasis should be on maximizing the attain­able level of deformation (ductility). The argument for a balanced rein­forcement program is strong.' A bal­anced reinforcement program is espe­cially desirable in a system containing a ductile connector because the hard­ware configuration will dictate beam width. Consider, then, the alternatives available for satisfying strength objec­tives and how they may be developed to enhance ductility.

Two analytical procedures can be used to quantify system strength. Both should be developed in a manner that will facilitate the attainment of design objectives. One is commonly referred to as a first yield analysis; the other is known as plastic design or a mecha­nism based analysis.

Consider the frame described in Fig . 9(a) and the extracted subassembly in Fig. 9(b). In a first yield analysis, an elastic based procedure is used to de­termine the moments and shears re­sulting from the imposition of dead, live, and seismic loads. We know that the required negative and positive mo­ment capacities will be different. As­sume, for purposes of this develop­ment, that the induced moments in the beam at the face of the column (Mb) that must be considered are:

PCI JOURNAL

Mbo =dead load moment

MbL = live load moment

MbE =earthquake moment The resultant ultimate capacities are

for the top, M"T' and bottom, M,8 ,

connectors:

MuT= 0.75[1.4MbD + 1.7MbL + l.7(1.1MbE)] (9)

MuB = 0.75[1.3(1.1Mb£)- 0.9MbD]

(10)

Paulay and Priestley• suggest that the described capacity imbalance can be mitigated without affecting system behavior. A moment redistribution of 30 percent is recommended. Follow­ing this procedure, the yield strength required of the upper set of ductile rods is:

(11)

and that of the bottom set:

(12)

A lesser redistribution may , of course, be used should it accomplish the desired objective: the attainment of capacity equivalence in the top and bottom connectors.

Alternatively, a portion of the dead load could be applied to the system before continuity is created by first pretensioning the bottom bolts and then removing the erection corbels (see Fig. 5). The beam would, during the application of construction loads (Pc), be modeled with pinned end boundary conditions. The remaining loads would logically be applied to the system described in Fig. 9. How these two distinct models are combined in order to develop a seismic capacity criterion is not clearly defined by the ACI, but MuT would clearly be less than that required by Eq. (9).

A mechanism analysis can be used to quantify system strength. A mecha­nism analysis can be developed from a sequential yield procedure.' An energy­based approach may also be used; this method is used herein because it is more simply explained. Three mecha­nisms need to be considered: vertical loads acting alone [see Fig. lO(a)] ;

March-April 1995

1+----+---~-tl v- .LOAD TRANSFER TIES

" -- .\v-- 2

It--~\ \_t---i 1;::=:=='==f /' J.++.ttt-- COMPRESSION STRUT \\ 1-. PLUS TRUSS \\ ~' MECHANISM

lt-----:1f'~\f';~---=:-..i'!+ll.Ul_:_n_:::;T DEVEUif' H:CHT 1\\ : 1~::;

" I \\ 1/ I '" ~~-

c II/ :n::- .., T

LOAD TRANSFER TIES

Fig. 8. Shear transfer (friction: steel to steel).

a) System

Fig. 9. Frame elevation .

vertical and lateral loads [see Fig. IO(b)] ; and lateral loads acting alone [see Fig. IO(c)]. Note that the use of the term "alone" in the first and third mechanisms reflects the fact that lat­eral and vertical loads produce no ex­ternal work on their respective de­formed subassemblies.

Assume for developmental purposes that the capacity of the section given

b) Subassembly

the sense of anticipated curvature is different. Mnn will be used to define the nomjnal moment capacity of the beam when the convex surface (ten­sion) is on the top side of the beam. M np will be used to define the moment capacity of the beam associated with a tensile straining on the bottom surface of the beam at the face of the column and MP the capacity required of the

41

Mnn

Plastic Hinge

a) Vertical Deformation

Analytic Hinge

I 49~M1 I f./ nn 3 ~- h

I I I :v

..-·~ 2

b) Vertical and Lateral Deformations

c) Lateral Deformation

Fig. 10. Subassembly mechanisms.

beam at some point between the sup­ports. The basis for the energy method is attaining equivalence in work done on the system after a mechanism has formed.3

External Work = Internal Work Vertical mechanism [Fig. 10(a)]:

( 2 P,, ~ + Pu ~) () = 2 e( M P + M nn)

P,,L ~2M P + 2M1111

(13)

Vertical and lateral mechanism [Fig. 10(b)]:

(L L 3L) 4 + 2 + 4 P,,() + VEu h()

= 4

3() ( M p + Mnn) (14)

l.SPuL+ VEuh ~ ~Mp +~Mnn

Lateral mechanism [Fig. 10(c)]:

The lateral mechanism of Fig. 10(c) is our design objective, as are identical connectors at each end and at the top and bottom of the beam. Hence, if M1111

is equivalent to Mnp• the strength of each must be:

42

M > VEuh 1.1- 2 (16)

and the desired (idealized) yield strength of a set of ductile rods, NTyi• is:

NT . = VEuh Y' 21j>d'

(17)

An example that describes the alter­native means of developing the appro­priate level of system capacity fol­lows. For the subassembly described in Fig. 10, assume the following:

h = 12ft (3 .66 m) L =40ft (12.2 m)

P0 = 40 kips (178 kN) PL = 12 kips (53.4 kN) VE = 75 kips (334 kN)

Step 1: Start by comparing a se­lected connector capacity to demand, given the recognized objectives . A standard connector is described in Ref. 5. This connector is shown in Fig. 11. NTy; is, for this pair of ductile rods , 240 kips (1068 kN).

VEu = 0 .75(1.7)(1.1)VE = 0.75(1.7)(1.1)75 = 105 kips ( 467 kN)

NT · = VEuh [see Eq. ( 17)] Y' 21j>d'

- 105(12) - 2(0. 9)(3)

= 233.3 kips< 240 kips (1038 kN < 1068 kN)

Conclusion: One connector of the type described in Fig. 11 may be used

provided d' is at least 3 ft (0.92 m).

Step 2: Insure that the mechanism of Fig. 1 O(b) will not precede the mechanism described in Fig. lO(c).

Mnn = Mnp = 240(3) = 720ft-kips (976 kN-m)

P,. = 0.75(1.4?0 + 1.7PL) = 0.75[1.4(40) + 1.7(12)] = 57.3 kips (255 kN)

l.SPuL+ VEuh ~ 1Mp + 1 Mnn

[see Eq. (14)]

Comment: Observe that the only unknown is the required capacity of the beam at the quarter point, MP.

1. 5(57.3)(40)+105(12)~_± M P+_± (720) 3 3

3438 + 1260-960 ~ _± MP 3

MP ~ 2804 ft-kips (3801 kN-m)

Conclusion: Provided the moment capacity at the quarter points exceeds 2804 ft-kips (3801 kN-m), the desired mechanism of Fig. 10(c) will precede that described in Fig. 10(b) during an earthquake.

Step 3: Insure that the mechanism described in Fig. 10(a) will not form:

PuL ~ 2Mp + 2Mnn 57.3(40)- 2(720) ~ 2MP

MP >426ft-kips (578 kN-m)

Conclusion: The nominal moment capacity at midspan must exceed 426 ft-kips (578 kN-m).

Justify the preceding using a first yield approach.

Step 1: Develop moment diagrams that describe the impact of both lateral and vertical loads. See Figs. 12(a) and 12(b).

Step 2: Develop a strength criterion for both top and bottom connections at girder ends.

M1111 > 0.75[1.4(0.2)PuoL + 1.7(0.2)PuLL + (1.7)(1.1)(V Euh/2)]

> 0.75{0.28(40)(40) + 0.34(12)(40) + 1.7[1.1(37 .5)( 12)]}

> 1090 ft-kips (1478 kN-m)

M,P > 1.3(1.1) V~h -0.9(0.2)P,,0 L

PCI JOURNAL

> 1.43(75)6- 0.18( 40)( 40) > 644-288 >356ft-kips (483 kN-m)

Step 3: Redistribute moments.

M"" = 0.7(1090) =760ft-kips (1030 kN-m)

M"P = 356 + 0.3(1090) = 683 ft-kips (926 kN-m)

Conclusion: A first yield analysis that includes a 30 percent redistribu­tion would require a somewhat larger connector for M1711 •

Comments: Note that if a portion of the dead load is applied to the system before continuity is attained, the de­mand on M 1111 will be decreased. The author' s preference is for the mecha­nism approach because the attainment of design objectives is more reliably accomplished.

TEST SUBASSEMBLY DESIGN

Though the load path described is developed directly from understood principles, the need to test a subassem­bly was clear. A test program was de­veloped with the technical assistance of Profs. Seible and Priestley of the University of California, San Diego (UCSD) and Juergen Plaehn of Dy­widag Systems International (DSI). DSI provided the hardware and SEQAD Consulting Engineering, Inc. performed the test at Powell Labora­tory on the UCSD campus. Funding for the test was provided by the author.

The subassembly size and strength was developed from existing test frame characteristics. The resu lting subassembly (see Fig. 13) represents a 213-scale model of a frame that might be used to brace a building in a region of high seismicity. Connector hard­ware was created from steel stock, the assembly being essentially the same as that described in Fig. 2. The ductile rods desc1ibed in Fig. 3 were replaced by milled rods (see Fig. 14) and an in­ternal bearing block, which are shown assembled in Fig. 15 . Fig . 16 is a photo of the ductile connector compo­nents, while Fig. 17 describes the rein­forcing program.

The force required to yield the sub­assembly described in Fig. 13 is devel-

March-April 1995

DUCTll£ ROO

Fig. 11 (a). Frame beam-to-column connection detail elevation.

It 4"X5"X1 ' -2.s/." (Ala) f'OA EACH 2 -

4----,

ROO CROUP

11/i__ OIA. A490 BOLTS PRETENSION TO IOO"EACH

Fig . 11 (b). Frame beam-to-column connection detail plan .

COLUWN REJNF'. NOT SHOWN FOR ~11Y

,., .•

43

l /4 l /4 I U4 l /4 I I I I I

0.2 Pl I 0.2 Pl I I

I I I a) Moment Diagram --~-------~-------~--Vertical Loads I I I

I I I I I I

0.3 Pl

Vh T

b) Moment Diagram Vh

Lateral Loads T

Fig . 12. Moment diagrams - example system.

oped from the yield strength of the milled ductile rods. These rods had a nominal yield strength of 60 ksi ( 414 MPa). The actual yield strength of the rod material was 62 ksi (427 MPa).

The tensile strength at nominal yield, T yi• of the three 13/s in . (35 .0 mm) diameter ductile rods was:

NTy; = 3(1.48)60 = 266 kips (1183 kN)

(18)

The nominal moment capacity of the connector is:

Mn = 2.25(266) =599ft-kips (812 kN-m)

(see Fig. 16)

ll'-----4•1 Actuator lloUDUDI ---·­LocaUoa

i llul 'lledcnra Pill I

\ Bad TledOWD Plll ··-1"

Boltam Pmtl PlD

Fig. 13. Test specimen dimensions.

44

The horizontal load required to acti­vate this moment (see Fig. 13) is:

H = 599 X 12 (.!_§_) y 84 9 (19)

= 152 kips (676 kN)

where 84 in. (2134 mm) [Lc + 2 in . (51.0 mm)] is the estimated shear span of the beam.

Now proceed to evaluate the level of overstrength provided along the load path. Start with the beam. The com­pression imposed on the bolt group that is being compressed is 266 kips (1183 kN) (NTy;). The beam shear as­sociated with Mn is 85.6 kips (381 kN). The friction coefficient, f, required to effect a shear transfer is:

f = 85.6 = 0.32 266

The LRFD Specifications ' recom­mend a friction coefficient of 33 per­cent for surfaces that are clean and free of mill scale (Class A). Slipping should not be expected,u however, at friction coefficients of up to 0.45 . The plate surfaces provided were inten-

____. Hy

,.

Hy

PCI JOURNAL

14.000 &. ±0.063

0.250

&. 9.500

0.500

Fig . 14. Shop drawing- ductile rod.

tionally roughened with a wire brush. Accordingly, they should have been capable of developing the requisite friction load transfer with an over­strength of at least 25 percent.

The tensile strength of the bolt that connects the ductile rod to the beam transfer block is:

March-April 1995

13/4" - 5UNC

}

CONNECTION TO SHEAR PLATE 83/4" ID x3"

¢1.375" ±0.063

}

CONNECTION TO 11/4" HS 490 BOLT

where A8 and F8 are the nominal area and yield strength of the bolt.

T8 y = 1.23(112.5) = 138 kips (614 kN)

This provides an overstrength of 1.56.

Concrete Column

DUCTILE RODS

Fig. 15. Ductile rod assembly -test program.

Fig. 16. Ductile connector hardware.

Two No. 11 Threadbars were used as flexural reinforcement in the beam. The provided overstrength in the flex­ural reinforcement of the beam, based on a nominal yield strength of 120 ksi (827 MPa), was:

A. = 374 =1. 4 0 266

This exceeds the normal over­strength used in ductile frame design (1.25) but does not include the usually appropriate l/J factor; this is believed to be appropriate because nominal yield

45

2' - 3"

2' 4" PRECAST COLUMN

#4 STIRRUPS r- :6 @ 6" BALANCE

o@ 12"0.C. 1' . IU• I .. I ._l r #6TI ES <o•

·--. . ,,_ J.

=ttJ_L j_ JJL_ ~

- t:r !--#6TI Es ia

-11. 11 ,1L_ ,.,_ (L

' _ll 11 J.- ~ r:: ;.. ,.,___.

_l.L I II /I #5 TIES m

lL ll jL_ - s EE FIG. 17(b)

,., I _i-f - ~r-·4~ ~~~.-

I -I II II I '7l ~- .t· ~·

A490 SOL TS BRUSH ALL J v • coNTACT suRFAcEs (TYPJ .i r~~~wg~~~g~~~~~~~~k§ CLASS 8 FINISH (SLIP COEFF. = 0.5) • , PRELOAD TO 10 kips (SNUG FID , •,," ~ ,, ___ /~ ~ d

PLATE #' ~~g~~~~~~~~~~~~~:i--;;r WASHER AS ,._ ~ REQUIRED (TYP) •

II E INTENTIONALLY l ROUGHEN SURFACE -!!"""t+-+-4

............. ,. II

11---1

!I--ff T II 1 FIBER REINFORCED GROUT ---41'-t-t~

~ ~ J.

E~~-~:~~~~Mi'ilil~lk - _.._ .• ·, ' -- • • . • • . ;• / #6 TIES a ; -;- ~l'//.. ....-.

~--------------~~~~ ~ :=u~ ~~ • l--J II 1--"' .,_ ~ ---~ .u...-. L r~

I ! I I II II

Fig . 17(a) . Elevation of beam-t o-column connection .

2' 4" ~--------_. _______________ ~·

4" --:1:

1

• r-- 6 #9 BARS

3/4"THICKPLATE WASHER ~ I . I

- 13/4" ~ HOLE I 1 1 /4"~ A490 BOLTS \ I

+-j -;- ~r--·- ( \ -~l-~~ ~ II I " -~ - -.- 7 · li -- r-~~aJ .. . ;., 1 ! I I ~- --- ~ . .., I

.. I

t- #6 BARS TOTAL 6 #9 BARS ...,!

; I I

i ·-· ! -!.&, ~ ;!. ,? f-- -·---~ 1:: I I I (- ~

-;-,l ~!! ___ !.. ~ ; h/ -]'tJ.:s=l ~~· I oJ IJ ••• J1 ~ 1~11-.L.J I \,.? : _j

vrb ~ b ~Ar c I \1

L #4 TIESTYP 'i_s EE FIG. 17(a)

1 _ _..

13/a" ¢ DUCTILE RODS •(i;

Fig. 17(b ). Plan of beam-to-column connection .

46 PCI JOURNAL

H/Hy

5

Fig. 18. Hysteretic behavior of test subassembly.

1.50

-.5.0%

-1..50

Drift

Fig. 19. NIST load-displacement history.

1..50

1.00

_.,..,.,. ...

------------

-5.0% -4.0%

-0.50

-1.00

-1..50

Drift

Fig . 20. Behavior comparison at 3.5 percent drift.

March-April 1995

--­.. -

1.0%

.. -

Drift(%} 5

------, ...... -------

2.0% 3.0%

,

.... ---· II ,

" " , I

4.0%

DUCTILE CONNECTOR

S.O%

---- NISTSUBASSEMBLY

47

2000

,..... 1500 t.l :t -c: 1000 ..... lll

'"' .. rn 500

Drift Angle (~) - 4.0 - 3.0 -2.0 - 1.0 0.0 1.0 2.0 3.0 4.0

-5004-~~-r-r~~~-,-,r-r-.-r-.-.-.-.--.-r-r-i -5 - 4 -3 - 2 -1 0 1 2 3 4 5

Displacement (in.)

Fig. 21. Joint hoop strain vs. displacement Gauge 4-1.

Drift Angle (•) -4.0 - 3.0 - 2.0 -1.0 0.0 1.0 2.0 3.{) 4.0

10000

9000 3 3

8000

7000 - 6000 t.l :t - 5000 c: ·;;; 4000 '"' ....

3000 fl! Reinforcement Yield

2000

1000

0 I 0.75 0.75

-1000 -5 - 4 - 3 -2 -1 0 1 2 3 4 5

Displacement (in.)

Fig. 22. Joint hoop strain vs. displacement Gauge 1-1.

Stirrups: for the Threadbar used is guaranteed. Further, the Threadbars and the ductile rods are mechanically aligned (see Fig. 2). Accordingly , adverse varia­tions in strength and construction are minimized.

V5 = 16 X 24 X 0.25 = 96 kips (427 kN)

The nominal shear strength of the frame beam was:

Concrete:

Vc = 16x24 x2.J430Q = 51. 5 kips 1000 (229 kN)

48

Shear strength:

Vc + Vs = 147.5 kips (656 kN)

Provided overstrength:

}., =147.5=1.72 0 85.6

Objective overstrength:

}., = 1.25 = 1.47 0 0.85

The probable bearing stress under the ductile rod ends (see Figs. 7 and 14) at nominal yield [V = 85.6 kips (381 kN)] and based on a bearing area external to the shank of the rod of 15.5 sq in. (0.01 m2), is 5.52 ksi (38.1 MPa) . This is 22 percent more than the compressive strength of the con­crete [4500 psi (31.0 MPa)] .

The internal bearing stress imposed on the anchor block at nominal yield [NTy; = 266 kips (1183 kN)] was:

+ = 2

x 266

= 5 8 ksi (1 3 f.') Jb [8(12)-3(1.48)] . . c

The provided level of overstrength is less than unity.

The design of the load transfer mechanism within the joint assumed that the two tie groups surrounding the anchor block (eight legs of No. 6 bar) and the tie groups located immediately above and below the anchor block (six legs of No. 5 and six legs of No. 6 bar) would deliver the flexurally induced force to the joint much as beam ·rein­forcement delivers this load to the panel zone.

The hypothesized nominal tensile strength mobilized to resist the bearing load is:

Tn = (14 X 0.44 + 6 X 0.31)60 = 481 kips (2140 kN)

The nominal force imposed on the internal bearing block is:

2NTy; = 2(266) = 532 kips (2366 kN) [see Eq. (18)]

This apparent understrength was considered acceptable because a por­tion of the anchor block force would undoubtedly activate the second set of internal joint ties (see Fig. 7). The presumed level of overstrength was then unity .

The shear stress at nominal yield in­duced on the joint was:

Vj = 2(266)- 152 = 380 kips (1512 kN) [see Eqs. (18) and (19)]

vj = ~ = 0.633 ksi (9.4-fJ:) 24 x 25 (4.36 MPa)

The provided overstrength within the joint based on the ACI Specifica­tion2 identified nominal capacity of 15 -[1: (Section 21.6.3.1) was 1.6.

The load path within the test sub-

PCI JOURNAL

assembly induced stress levels that in many cases approached identified limit states. This was intentional be­cause it was felt that the behavior would be acceptable in the absence of what was believed to be an overcon­servative approach.

TEST SUBASSEMBLY BEHAVIOR

The subassembly described in Fig. 13 was subjected to the displacement controlled deformations suggested by PRESSS (Precast Seismic Structural Systems). 6 This loading program re­quires the attainment of repeatable de­formation increments of 0.5 percent story drift.

The cyclic behavior of the test pro­gram is best described by the force­displacement plot of Fig. 18. A quali­tative assessment of the post-yield behavior of the ductile connector is best attained by comparing its behav­ior with a comparably designed and tested conventionally reinforced con­crete ductile frame (SMRSF). A proto­typical SMRSF subassembly was de­veloped and tested by the National Institute of Standards and Technology (NIST) .7.8·9 This subassembly (SMRSF) was intended to serve as a baseline to evaluate the post-yield behavior of subsequent precast concrete subassem­bly test programs.

A true comparison is not possible because the NIST program loading se­quence was less severe than the defor­mation cycles subsequently adopted by PRESSS. Behavior at a drift angle of 3.5 percent, however, is informa­tive. The NIST subassembly was sub­jected to three cycles of deformation at this level of story drift and prece­dent levels of deformation were omit­ted because the objective was to test the limit state in the absence of pro­gressive deteriorative load steps. Ac­cordingly , the hysteretic behavior baseline represents the 5th, 6th , and 7th post-yield cycles (see Fig. 19).

Hysteretic behavior of the two sub­assemblies at a drift angle of 3.5 per­cent is shown on Fig. 20. Distress and strength degradation for the NIST sub­assembly occurs in the toe of the beam (see Fig. 1) while some distress absent strength degradation occurred in the

March-April 1995

Fig. 23. Crack pattern at 3.5 percent drift.

ductile connector subassembly below the bearing end of the ductile rods.

Strain hardening of the ductile rod was significant because the story shear required to attain a story drift angie of 4.5 percent was 210.5 kips (936 kN). This corresponds to an overstrength factor of 1.38. Compare this with the theoretical levels of overstrength pro­vided along the load path. Friction - The activated friction factor

remains unchanged because the shear force and axially induced load

on bearing surface~ increase in di­rect proportion.

Tension in bolt - 1.56 Beam flexu'ral reinforcement - 1.4 Beam shear strength- 1.72 Ductile rod bearing - 1.0 Internal bearing block - 1.0 Tension transfer in the joint - 1.0 Joint shear - 1.6

The critical elements are rod bear­ing and tension transfer within the joint. The rod bearing load transfer mechanism was the weakest link in

49

the load chain and the only one that exhibited a deterioration at high drift angles. Behavior of the ductile con­nector has been enhanced by modify­ing this detail.

Induced strain levels in the hoop re­inforcement within the joint were mon­itored. Strains measured within the panel zone were sub-yield throughout the test program (see Fig. 21) while those surrounding the internal bearing block (see Fig. 5) yielded at drift an­gles of 2.5 percent (see Fig. 22). The suggestion is that external hoop rein­forcement at the ductile rod level is most critical arid clearly required to de­velop the compressive struts described in Fig. 8.

The level of post-yield strain expe­rienced by the ductile rod may be esti­mated from the post-yield drift angle sustained by the subassembly. The post-yield drift angle is about 3.5 per­cent (see Fig . 18). All of this post­yield drift is not attributable to defor­mation in the ductile rod because both the panel zone and the beam con­tributed to the deformation.5 However, were one to attribute OP entirely to the post-yield strain, epR• in the ductile rod , it would be concluded that in­duced strains were well within mate­rial limits.

op = 0.035 radians

1. Manual of Steel Construction, Load and Resistance Factor Design, Ameri­can Institute of Steel Construction, Chicago, IL, 1986.

2. ACI Committee 318, "Building Code Requirements for Reinforced Concrete and Commentary (ACI 318R-89)," American Concrete Institute, Detroit, MI, 1990.

3. Englekirk, R. E., Steel Structures: Controlling Behavior Through Design, John Wiley & Sons, Inc., New York, NY, 1994.

4. Paulay, T. , and Priestley, M. J. N., Seismic Design of Reinforced Con­crete and Masonry Buildings, John Wiley & Sons, New York, NY, 1992.

5. Nakaki , Suzanne Dow, Eng1ekirk, Robert E. , and Plaehn, Juergen L.,

8pR = op( ~') = 0.035(13.5) = 0.47 in. (12 mm)

- DpR epR-L

R

where LR is that portion of the ductile rod subjected to post-yield strains.

CONNECTOR ENHANCEMENTS

Two connection enhancements were suggested by the test. First, the rod bearing transfer mechanism could be improved. This was accomplished by increasing the bearing area (see Fig. 3) and adding a confining plate at the face of the column (see Fig. 7). Sec­ond, the strain hardening characteris­tics of _the material used in the casting are better than those used in the milled rod. AISI 1022M material is to be used. This material has a guaranteed yield of 50 ksi (345 MPa) and, when subjected to strain levels comparable to those of the subassembly test, expe­riences a strength increase on the order of 20 percent.

REFERENCES "Ductile Connectors for a Precast Concrete Frame," PCI JOURNAL, V. 39, No. 5, September-October 1994, pp. 46-59.

6. Priestley, M. J. N. (Editor), "Report on the Third U.S. PRESSS Coordinating Meeting," PRESSS Report No. 92/02, University of California, San Diego, August 6-7, 1992.

7. Cheok, G. S., and Lew, H. S., "Perfor­mance of 1h-Scale Model Precast Con­crete Beam-Column Connections Sub­jected to Cyclic Inelastic Loads," Proceedings of the First Meeting of the Joint Technical Coordinating Commit­tee on Precast Seismic Structural Sys­tems (PRESSS) , San Diego , CA, November 1990, p. 104.

8. Cheok, G. S., and Lew, H. S.,

CONCLUDING REMARKS

The Northridge earthquake10 caused a significant amount of damage in steel frame buildings and subsequent re­search11 suggests that it will be difficult to attain post-yield story drifts of 3 per­cent in steel ductile frames. Story drifts of 3.5 percent in concrete frames pro­duce considerable distress and this is also the case in structural steel sub­assemblies. The ductile connector is not only easily capable of exceeding these levels of story drift but does so without damaging .the system (see Fig; 23).

Further, the developed system clearly indicates the potential of sys­tems that are developed to enhance post-yield behavior. This is particu­larly relevant to the development of precast concrete systems because the unitized character of the assembly pro­cess provides an obvious place to ab­sorb earthquake induced deformations. Hopefully, this will be but one of many breakthrough developments in the field of earthquake engineering.

ACKNOWLEDGMENT The advice, encouragement, and as­

sistal)ce of Professors Nigel Priestley and Frieder Seible as well as that of Juergen Plaehn and many of i:ny asso­ciates is gratefully acknowledged.

"Performance of Precast Concrete Beam-to-Column Connections Sub­ject to Cyclic Loading," PCI JOUR­NAL, V. 36, No. 3, May-June 1991 , pp. 56-67.

9. Cheok, G. S., and Lew, H. S., "Model Precast Concrete Beam-to-Column Connections Subject to Cyclic Load­ing," PCI JOURNAL, V. 38, No. 4, July-August 1993, pp. 80-92.

10. Iverson, James K., and Hawkins, Neil M., "Performance of Precast/Pre­stressed Concrete Building Structures During Northridge Earthquake," PCI JOURNAL, V. 39, No. 2, March-April 1994, pp. 38-55.

11. "Northridge Steel Update 1," Ameri­can Institute of Steel Construction, October 1994.

PC! JOURNAL

A= area

d' = distance between sets of ductile rods

f = friction coefficient

fb = bearing stress

J; = specified compressive strength of concrete

F8 =nominal yield strength of a bolt

Fy = yield strength of reinforcement

h = story height

H = story shear force

j =joint

L =length

LR = length of deformable portion of ductile rod

M = applied moment

N = number of bolts

P =load

March-April 1995

APPENDIX- NOTATION P = applied load

Ppre = pretensioning force applied to a slip critical bolt

T = tension (kips)

T8 n = nominal tensile strength re­quired of a set of bolts

T yi = idealized yield strength of duc­tile rod

V =shear

VnE = earthquake induced shear at nominal flexural limit state

e =strain

epR = post-yield strain in ductile rod

o = elongation of ductile rod

A0 = overstrength factor

() = rotation

8p = post-yield rotation

t/J = strength reduction factor

Typical Subscripts

B = bolt or bottom

b =beam

c = column or clear

D =dead load

E = earthquake load

i = initial

L =live load

n =nominal

nn = support at top of beam

np = support at bottom of beam

p = bottom of beam (interior)

s = reinforcing steel

t =top

u = ultimate or factored nominal capacity

y =yield

'>1