aci structural journal mar.-apr. 2015 v. 112 no. 02

V. 112, NO. 2MARCH-APRIL 2015

ACISTRUCTURAL

J O U R N A L

A J O U R N A L O F T H E A M E R I C A N C O N C R E T E I N S T I T U T E

ACI Structural Journal/March-April 2015 121

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CONTENTSBoard of Direction

PresidentWilliam E. Rushing Jr.

Vice PresidentsSharon L. WoodMichael J. Schneider

DirectorsRoger J. BeckerDean A. BrowningJeffrey W. ColemanAlejandro Durn-HerreraRobert J. FroschAugusto H. HolmbergCary S. KopczynskiSteven H. KosmatkaKevin A. MacDonaldFred MeyerMichael M. SprinkelDavid M. Suchorski

Past President Board MembersAnne M. EllisJames K. WightKenneth C. Hover

Executive Vice PresidentRon Burg

Technical Activities CommitteeRonald Janowiak, ChairDaniel W. Falconer, Staff LiaisonJoAnn P. BrowningCatherine E. FrenchFred R. GoodwinTrey HamiltonNeven Krstulovic-OparaKimberly KurtisKevin A. MacDonaldJan OlekMichael StenkoPericles C. StivarosAndrew W. TaylorEldon G. Tipping

StaffExecutive Vice PresidentRon Burg

EngineeringManaging DirectorDaniel W. FalconerManaging EditorKhaled NahlawiStaff EngineersMatthew R. SenecalGregory M. ZeislerJerzy Z. ZemajtisPublishing ServicesManagerBarry M. BerginEditorsCarl R. BischofTiesha ElamKaitlyn HinmanKelli R. Slayden

Editorial AssistantAngela R. Matthews

ACI StruCturAl JournAl

MArCh-AprIl 2015, V. 112, no. 2a journal of the american concrete institutean international technical society

123 Evaluation of Column Load for Generally Uniform Grid-Reinforced Pile Cap Failing in Punching, by Honglei Guo

135 Design Implications of Large-Scale Shake-Table Test on Four-Story Reinforced Concrete Building, by T. Nagae, W. M. Ghannoum, J. Kwon, K. Tahara, K. Fukuyama, T. Matsumori, H. Shiohara, T. Kabeyasawa, S. Kono, M. Nishiyama, R. Sause, J. W. Wallace, and J. P. Moehle

147 Inverted-T Beams: Experiments and Strut-and-Tie Modeling, by N. L. Varney, E. Fernndez-Gmez, D. B. Garber, W. M. Ghannoum, and O. Bayrak

157 Energy-Based Hysteresis Model for Reinforced Concrete Beam-Column Connections, by Tae-Sung Eom, Hyeon-Jong Hwang, and Hong-Gun Park

167 Ductility Enhancement in Beam-Column Connections Using Hybrid Fiber-Reinforced Concrete, by Dhaval Kheni, Richard H. Scott, S. K. Deb, and Anjan Dutta

179 Behavior and Simplified Modeling of Mechanical Reinforcing Bar Splices, by Zachary B. Haber, M. Saiid Saiidi, and David H. Sanders

189 Bond-Splitting Strength of Reinforced Strain-Hardening Cement Composite Elements with Small Bar Spacing, by Toshiyuki Kanakubo and Hiroshi Hosoya

199 Wide Beam Shear Behavior with Diverse Types of Reinforcement, by S. E. Mohammadyan-Yasouj, A. K. Marsono, R. Abdullah, and M. Moghadasi

209 Effect of Axial Compression on Shear Behavior of High-Strength Reinforced Concrete Columns, by Yu-Chen Ou and Dimas P. Kurniawan

221 Experimental Investigations on Prestressed Concrete Beams with Openings, by Martin Classen and Tobias Dressen

233 Discussion

Bond-Slip-Strain Relationship in Transfer Zone of Pretensioned Concrete Elements. Paper by Ho Park and Jae-Yeol Cho

Contents cont. on next page

122 ACI Structural Journal/March-April 2015

MEETINGS

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THE ACI CONCRETE CONVENTION AND EXPOSITION: FUTURE DATES2015April 12-16, Marriott & Kansas City Convention Center, Kansas City, MO2015November 8-12, Sheraton Denver, Denver, CO2016April 17-21, Hyatt & Wisconsin Center, Milwaukee, WI

For additional information, contact:Event Services, ACI38800 Country Club Drive, Farmington Hills, MI 48331Telephone: +1.248.848.3795e-mail: [email protected]

ON COVER: 112-S12, p. 136, Fig. 2Reinforced concrete (left) and prestressed concrete (right) specimens on the E-Defense shake table.

Fire Protection for Beams with Fiber-Reinforced Polymer Flexural Strength-ening Systems. Paper by Nabil Grace and Mena Bebawy

Analysis and Prediction of Transfer Length in Pretensioned, Prestressed Concrete Members. Paper by Byung Hwan Oh, Si N. Lim, Myung K. Lee, and Sung W. Yoo

Flexural Testing of Reinforced Concrete Beams with Recycled Concrete Aggregates. Paper by Thomas H.-K. Kang, Woosuk Kim, Yoon-Keun Kwak, and Sung-Gul Hong

241 Reviewers in 2014

MARCH/APRIL30-2Concrete Sawing & Drilling Association Convention and Tech Fair, St. Petersburg, FL, www.csda.org/events/event_details.asp?id=444478&group

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13-15BEST Conference Building Enclosure Science & Technology, Kansas City, MO, www.nibs.org/?page=best

26-292015 Post-Tensioning Institute Convention, Houston, TX, www.post-tensioning.org/page/pti-convention

26-3057th Annual IEEE-IAS/PCA Cement Industry Technical Conference, Toronto, ON, Canada, www.cementconference.org

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3-7International Cement Microscopy Association Annual Conference, Seattle, WA, www.cemmicro.org

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14-16The American Institute of Architects Convention, Atlanta, GA, http://convention.aia.org/event/homepage.aspx

14-17The Masonry Society 2015 Spring Meetings, Denver, CO, http://www.masonrysociety.org/index.cfm?showincenter=http%3A//www.masonrysociety.org/html/calendar/index.htm

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JUNE1-37th RILEM Conference on High Performance Fiber Reinforced Cement Composites, Stuttgart, Germany, www.rilem.org/gene/main.php?base=600040#next_614

123ACI Structural Journal/March-April 2015

ACI STRUCTURAL JOURNAL TECHNICAL PAPER

Currently, the punching shear resistance of pile caps is frequently evaluated empirically, and although the strut-and-tie model (STM) may be used to calculate the issue, the two weaknesses of STMconservative nature and difficult configurationhinder its rational solution. To attempt to solve these issues, this paper presents a generalized method of spatial STMs to evaluate punching shear resistance of general pile caps with uniform grid reinforcement (TPM). Based on results of the spatial strut-and-tie bearing mech-anism of pile cap punching failure, three-dimensional (3-D) rather than two-dimensional (2-D) strut strength is derived. During this process, nonlinear finite element analysis in conjunction with the derivation of a gradual least-square method for multiple variables is adopted. TPM is verified by 98 specimens in the literature, whose parameters (reinforcement ratio of tension tie, punching-span ratio, concrete strength, pile number, and pile arrangement) vary, respec-tively; the comparisons with the other four methods are made. It is indicated that TPM is extensively applicable to the evaluation of the punching shear resistance of general pile caps with uniform grid reinforcement.

Keywords: building code; pile cap; punching shear resistance; strut-and-tie model (STM).

INTRODUCTIONA pile cap is the load-transfer story between the super-

structure and pile, while the evaluation of its punching shear resistance is an important basis for determining its thickness and arrangement of reinforcement.

Generally speaking, the evaluation of punching shear resistance of a pile cap can be classified into two types according to the theory of plasticity:

Type 1The collapse mechanism is assumed so that the upper-bound solution to punching shear resistance is obtained using the theory of plasticity, called the upper-bound method for short. This method is adopted in the critical section stress method of the ACI 318-08 code (ACI CSM)1 and the Chinese JGJ94-94 code.2 (Although an empirical method in appearance, ACI CSM is theoretically an upper-bound method in essence).

Of the aforementioned, as shown in the Appendix* of the paper, ACI CSM,1 (also, the details of JGJ94-94, ACI STM, CRSI,3 and TPM at the back being given in the Appendix of the paper) similar to the calculating method used for punching shear resistance of slab in the ACI 318-08 code, is divided into two steps:

1. For simplicity of evaluation, the critical sections perpendicular to the plane of the pile cap are used instead

*The Appendix is available at www.concrete.org/publications in PDF format, appended to the online version of the published paper. It is also available in hard copy from ACI headquarters for a fee equal to the cost of reproduction plus handling at the time of the request.

of the oblique sections of the punching cone, and the perim-eter of the critical sections is kept minimum but no closer to the column edge than d/2 (the definition of d being given in Eq. (1) and Fig. 4); and

2. Take the minimum of the three kinds of punching shear resistance in these sections as the ultimate.

Whereas the method in JGJ94-94 code2 is divided into three steps: 1) take the link line between the column side and the nearest pile side to form the punching cone; 2) modify the inclination of the punching cone to ensure it to vary from 45 to 78.7 degrees; and 3) in the end, use a punching coef-ficient containing the punching-span ratio to correct the punching shear resistance (the definition of being given in Eq. (1)).

Type 2The rational stress field is assumed according to the load-transfer route so that the lower-bound solution to punching shear resistance is obtained, called the lower-bound method for short. As far as the practical evaluation of the reinforced concrete is concerned, it has often been the best choice for this method to have the structure likened to a certain kind of structure or a combination of certain struc-tures whose bearing mechanism is well known.

In technical codes, the text and Appendix A of ACI 318-08,1 the CRSI handbook,3 CAN/CSA A23.3-04,4 BSEN 1992-1-1:2004,5 and AS 3600-20016 either adopt or contain this method.

Of the aforementioned, when the center of any one pile is at or within twice the distance between the top of the pile cap and the top of the pile, Section 15.5 in ACI 318-081 states that punching of the pile cap can be likened to an idealized truss, and Appendix A of ACI 318-081 gives the basic components of the truss: strut, tie, and nodal zone, and there is a series of systematic provisions for the strength and dimensions of these components. In fact, a general strut-and-tie design procedure for all discontinuity (D)-regions was introduced.

As a supplement to the ACI 318-08 code, the CRSI hand-book3 recommends another calculating method, separated by three steps: 1) the applicable condition is the horizontal distance between the column side and the nearest axis of the pile is no larger than d/2; 2) the critical section is taken at the perimeter of the column face; and 3) the additional contri-bution of concrete to the punching strength resulting from the small punching span is considered. This shows that the CRSI handbook method effectively likens the evaluation of

Title No. 112-S11

Evaluation of Column Load for Generally Uniform Grid-Reinforced Pile Cap Failing in Punchingby Honglei Guo

ACI Structural Journal, V. 112, No. 2, March-April 2015.MS No. S-2010-415.R3, doi: 10.14359/51687420, received July 29, 2014, and

reviewed under Institute publication policies. Copyright 2015, American Concrete Institute. All rights reserved, including the making of copies unless permission is obtained from the copyright proprietors. Pertinent discussion including authors closure, if any, will be published ten months from this journals date if the discussion is received within four months of the papers print publication.


the two-way shear of the pile caps to the superposition of the one-way shear of two mutually orthogonal deep beams whose width is equal to the length of the column edges.

In the theoretical study, Wen7 modeled the punching of pile caps as the coupling between two orthogonal deep beams, while Kinnunen and Nylander8 regarded it as a spatial shell.

However, recent studies and practice have proved that it is more rational to liken the bearing mechanism of punching failure of pile caps to a spatial STM (SSTM).9-12

Herein, as the basis for the derivation of the column load of pile cap failing in punching to be conducted later, a brief introduction to the authors research conclusions is given as follows.11,12

Load-transfer mechanism of punching failureAs shown in Fig. 1, the load-transfer system of the punching failure of pile caps is analogous to the SSTM, where the compression struts are used to model the zones of concrete with primarily unidirectional compressive stresses, while the reinforce-ments within the range of primarily unidirectional tensile stresses are approximated by tension ties.11,12

The pile load distribution during the punching failure of pile caps can approximately adopt the value of the pile caps in the elastic stage.11

Damage mechanism of punching failureAs shown in Fig. 2 and 3, the strut is represented as three zones: namely, Zone III, the shear-compression zone intersecting the column

bottom; Zone II, the splitting zone in the midpart of the strut; and Zone I, the shear-compression zone intersecting the pile top. The forming process of the punching cone is as follows: when the principal tensile stress in Zone II reaches the splitting strength, the first crack is generated and, with the column load increased, the oblique crack develops toward the two ends of the strut. Soon after, the strut is split into two (Struts A and B) connected at its two ends (Zones I and III), the column load being jointly borne by Struts A and B. Part of the column load is transferred to the longitudinal reinforcement and the uncracked concrete of Zone I by Strut A, and the other part is transferred to the pile by Strut B. When punching failure occurs, Strut A is punched out rela-tive to Strut B to have the punching cone formed. It can be considered that the column load at this moment is jointly borne by Zones I and III, together with the dowel action of the bottom longitudinal reinforcement. The two parts are correlated, and the loss of the punching shear resistance is a result of the damages in the aforementioned parts occurring one after another so that, with no additional external load, the oblique section suddenly collapses. Therefore, the punching failure of pile caps is either the strut failure, which begins with the splitting in the midpart of the strut (Zone II) and ends with shear-compression failure at the two ends of the strut (Zones I and III) or the yield failure of the tension tie resulting from insufficient tension tie reinforcement amount. But the tension tie failure is also accompanied by the strut failure, so the strut failure is an indication of the loss of the pile cap punching shear resistance.12

The two basic factors influencing the strut strength are the punching-span ratio and concrete strength.12 The strengths at the two ends of the strut are not appreciably different; their average can be taken as the strut strength.12

Fig. 2Damage mechanism of SSTM for punching failure of pile caps.

Fig. 3Failure form of the strut by nonlinear finite element analysis. (Note: Model is one-fourth of four-pile cap of symmetrical and determinant pile arrangement, and crack surfaces are represented by circles.)

Fig. 1Load-transfer mechanism of SSTM for punching failure of pile caps.


Dimensions of SSTMConstruct the true rather than imaginary stress field to achieve the dimensions as follows:

1. During the elastic stage, the cross-sectional area at the strut end for the pile near the column is larger than that far from the column. But when the pile cap fails, because the plastic internal force redistributes, the strut for the pile near the column unloads (except for the strut between the column and the pile beneath the column), and the strut for the pile far from the column increases its load; therefore, at the end, as shown in Fig. 2, all the cross-sectional areas at the strut end basically stabilize at the same value0.6 times that of the pile (except for the strut between the column and the pile beneath the column)whatever the distance of pile to column.12

2. As shown in Fig. 4, the upper node of the SSTM is located at 0.1 times the effective depth vertically downwards from the column center on the top surface of the pile caps.12

3. As shown in Fig. 5, for simplicity, take a two-pile cap as an example to illustrate the location of the SSTM lower node, which is obtained in accordance with the three steps: 1) link upper node A to pile center B to obtain line segment AB; 2) project AB onto the plane where the longitudinal reinforcement centroid is located to obtain line segment CD, while obtaining the projection line L of the pile periphery onto the same plane; 3) intercept CD with L to obtain line segment ED, and the midpoint of ED is just lower node F of the SSTM.12

4. As shown in Fig. 6, the effective range of the tension tie is twice the pile diameter that is concentric with the lower node of the SSTM.11

It should be noted that compared with the currently avail-able extensive literature on the bearing mechanism of the SSTM, investigation on the evaluation of the punching shear resistance of pile caps with uniform grid reinforcement is as of yet inadequate. So, based on the previously mentioned research conclusions about the punching bearing mecha-nism, further studies will be made along these lines.

RESEARCH SIGNIFICANCEMany punching shear resistances of pile caps are eval-

uated by design aids with the rule-of-thumb procedures, which have at least two drawbacks: 1) the theoretical calcu-lation values either far exceed the experimental ones or,

although no larger than the experimental ones, are signifi-cantly variable. Hence, the hidden safety risks; and 2) the theory of STM applied to solve the punching of pile caps is significantly conservative. This paper focuses on the derivation of the three-dimensional (3-D) rather than two- dimensional (2-D) strut strength, from which the calculating method for the punching shear resistance of the pile capsthat is, the column load of pile cap failing in punchingis developed. Careful verification, comparison, and analysis show that the results obtained in this paper should contribute to improving the aforementioned situation, and the informa-tion presented in this paper should prove useful to organiza-tions that publish design aids for pile caps.

OVERALL CONSIDERATIONS FOR DERIVATION OF EVALUATION

First, two variables are defined as follows:1. Punching-span ratio

= w/d (1)

where, as shown in Fig. 4, the effective depth d is the depth to the centroid of the bottom longitudinal reinforcement. As shown in Fig. 6, the punching span w is the distance GB1, where line segment AB1 is obtained by linking column center A to pile center B1, and point G is obtained through the interception of AB1 by the periphery of column. If not a round column, convert its cross section to a circular one of equal perimeter.

Fig. 5Location of SSTM lower node.

Fig. 6Effective range of tension tie, punching-span, and As.

Fig. 4Effective depth and location of SSTM upper node.


2. Reinforcement ratio of tension tie

= AD d

s

p2 (2)

where, as shown in Fig. 6, As is the sum of the cross- sectional areas of the longitudinal reinforcements within the effective range of the tension tie; and Dp is the pile diameter.

As pointed out earlier, the strut failure is an indication of the loss of the pile cap punching shear resistance. So the evaluation of punching shear resistance of pile caps is exactly an evaluation of the strut bearing load, while strut bearing load F is the cross-sectional area at the strut end S strut strength fce. It is known from the earlier statement that S is 0.6 times the cross-sectional area of the pile, and fce is the average of the strengths at the two ends of the strut. So F can be expressed as follows

F S f Rf f

cece ce

= = +

0 62

2 1 2. (3)

where R is the radius of the pile; fce1 is the strength at one end of the strut; and fce2 is that at the other end.

Thus, if only the specific expression of fce is found, F will be obtained. Then, depending on static equilibrium at the upper node of the SSTM, the column load of pile caps failing in punching will be readily solved.

DERIVATION FOR fceDefine = fce/fc, where fc is the cylinder compressive

strength of the strut concrete.

It is known from the foregoing conclusion that the two basic factors influencing the strut strength are the punching- span ratio and concrete strength; thus, = (,fc). To find the specific expression for , the ADINA nonlinear finite element (NFE) program, which has successfully evaluated the punching shear resistance of pier deck13 (pier deck is similar to pile cap), is adopted. Analysis and derivation of the expression for are made by referring to mathematical deduction of the gradual least-square method for multiple variables (GLSMV).

In selecting the model for computerization, as the purpose of computerization is simply to derive the strut strength, there is no need for consideration of the pile number or pile arrangement other than the choice of the strut. Therefore, a quarter of the four-pile cap of symmetrical and determinant pile arrangement is selected, as shown in Fig. 3.

In developing the numerical model, the concrete of pile caps is divided into four layers, the greater part of which are 3-D isoparametric elements with eight nodes and three degrees-of-freedom per node, a few triangular prism-shaped degenerate elements being taken as transition ones. Where the pile cap is near the column and pile, the 3 3 3 inte-gration order is adopted, while the 2 2 2 integration order is used elsewhere. The column and pile are linked to the pile cap also in the form of 3-D isoparametric elements. The concrete material model adopted is a nonlinear one with compression crushing, tensile cutoff with strain soft-ening, and shear stress transferring across the cracks taken into account.13 The reinforcing bars are represented by truss elements with two nodes, the constitutive law for which is an elastic-plastic material model.

As shown in Fig. 3, for the strut between the column bottom and the pile top in question, take and fc as 0.15 to 2.0 and 6.7 to 50 MPa (971.7 to 7252 psi), respectively. Thus, a total of 102 cases of combination is investigated.

In the process of analysis, as of the pile caps with uniform grid reinforcement is in general rather small, no larger than 1.2% at most and has little influence on the strut strength,14,15 it can be maintained at 0.6% throughout.

The relationships between and , fc for 0.95 are shown in Table 1 as an example.

The expressions in Table 1 are summed up as follows:1. = a bfc, for 6.7 MPa (971.5 psi) fc 35 MPa

(5075 psi)2. = c, for 35 MPa (5075 psi) fc 50 MPa (7252 psi)Obviously, a, b, c are the functions of . Use the least-

square method once again to obtain

a = 2.90045 0.0170961 2.05 1.41485

b = 0.30668 0.00183469 0.22 1.394

c = 1.05888 0.00459047 0.75 1.41184

In conclusion, for 0.95:

Table 1Relationship between g and l, fc' for l 0.95

6.7 MPa (971.5 psi) fc

35 MPa (5075 psi)35 MPa (5075 psi) fc

50 MPa (7252 psi)

0.95 = 2.89255 0.31042fc* = 1.059

1.0 = 2.89255 0.31042fc = 1.056

1.2 = 2.8618 0.30712fc = 1.04775

1.4 = 2.8782 0.30888fc = 1.05225

1.6 = 2.8659 0.30756fc = 1.04775

1.8 = 2.8618 0.30712fc = 1.04925

2.0 = 2.88025 0.3091fc = 1.0545*Unit of fc is MPa; is nondimensional. Similarly hereinafter.

Table 2Relationship between g and l, fc' for 0.15 l 0.95

6.7 MPa (971.5 psi) fc

35 MPa (5075 psi)35 MPa (5075 psi) fc

50 MPa (7252 psi)

0.75 0.95

= 2.05 (2.341 0.9751) 0.22 (2.398 1.057)

fc = 0.75 (2.32 0.96)

0.35 0.75

= 2.05 (1.972 0.521) 0.22 (1.9738 0.488)fc

= 0.75 (1.9789 0.493)

0.15 0.35

= 2.05 (2.125 0.973) 0.22 (2.14258 0.945)

fc = 0.75 (2.18292 1.085)


1) = 2.05 1.41485 0.22 1.394fc, for 6.7 MPa (971.5 psi) fc 35 MPa (5075 psi); and

2) = 0.75 1.41184, for 35 MPa (5075 psi) fc 50 MPa (7252 psi).

Similarly, the relationships between and , fc for other ranges of are obtained in Table 2. Observing the situation of in each of its ranges shown in Tables 1 and 2 to know:1. Whatever the range is in, for 6.7 MPa (971.5 psi) fc 35 MPa (5075 psi)

= 2.05f1() 0.22f2()fc (4)

2. Whatever the range is in, for 35 MPa (5075 psi) fc 50 MPa (7252 psi)

= 0.75f3() (5)

3. In the same range of , the expressions for f1(), f2(), and f3() are almost identical, so a unified expression can be taken

( ) = ( ) + ( ) + ( )f f f1 2 33

Take () out of Eq. (4) and (5), then

= (fc) ()

where, for (fc):

1) (fc) = 2.05 0.22fc, for 6.7 MPa (971.5 psi) fc 35 MPa (5075 psi)

(6a)2) (fc) = 0.75, for 35 MPa (5075 psi) fc 50 MPa

(7252 psi)

whereas, for ():

1) () = 1.4, for 0.95

2) () = 2.35 , for 0.75 0.95 (6b) 3) () = 1.975 0.5, for 0.35 0.75

4) () = 2.15 , for 0.15 0.35

Observation of Eq. (6b) shows, for 0.15 0.95, that the slopes of all the fold line segments making up () are almost identical. So the straight line linked by point = 0.15 and point = 0.95 can be used to represent () in this range (0.15 0.95) in a unified manner; that is, ultimately

1) () = 2.1125 0.75, for 0.15 0.95 (6c) 2) () = 1.4, for 0.95

Thus, the ultimate expression of the strut strength fce is

f f f fce c c c= = ( ) ( ) (7)which, substituted back into Eq. (3), gives the ultimate bearing load expression of the strut

F R f R f fce c c= = ( ) ( ) 0 6 1 8852 2. . (8)where (fc) and () are found in Eq. (6a) and (6c), respec-tively. As shown in Eq. (7), fce is a constantly increasing function of fc, whatever the range fc is in; for 0.15 0.95, fce is a decreasing function of , while for 0.95, fce is a constant function of .

RESULTS AND DISCUSSIONTable 3 lists the published test data of 98 specimens on

the punching failure of the pile caps with uniform grid rein-forcement in literature, whose pile number, pile arrange-ment, punching-span ratio, concrete strength, and reinforce-ment ratio of tension tie vary, respectively, while Table 4 gives the Pe/Pp (experimental column load/predicted column load) of five theoretical methods, as compared with: 1) the method proposed in this paper (TPM); 2) the critical section stress method of the ACI 318-08 code (ACI CSM)1; 3) the strut-and-tie model method in Appendix A of the ACI 318-08 code1 (ACI STM); 4) the American CRSI hand-book method3 (CRSI); and 5) the method of the Chinese JGJ94-94 code2 (JGJ94-94). For illustrating the calculating process of the five aforementioned methods, as an example, in the Appendix of the paper, give the detailed calculations of specimen TDS3-1 in Table 3.

It is necessary to point out that: 1) in Table 4, the punching shear resistance is represented by the column load of pile cap failing in punching; 2) the bending failure and the failure of one-way shear are not included in Tables 3 and 4 because their failure types are not consistent with the failure of the two-way shear studied in this paper; and 3) as the bottom reinforcement layout concentrated in the vicinity of the pile top and the diagonal on the plane of the pile caps have a larger punching shear resistance than the uniform grid rein-forcement,9,11,12,16 they will be studied elsewhere.

Table 5 summarizes the statistical appraisal of the Pe/Pp obtained by all the theoretical methods in Table 4.

AccuracyIt is known from Table 5 that, when all the calculable

specimens are taken, or after the asterisked specimens (the asterisk implies that the specimens may fail in bending; more details will be given later) in Table 4 are removed, although TPM has the largest number of specimens, it has the highest accuracy. As for evaluations with the remaining four methods, despite their fewer specimens, they agree well only for certain of them.

It is known from Table 4 after further analysis that, as far as individual Pe/Pp calculated by TPM is concerned, except for the two asterisked specimens, PC454 and T441, which have rather large calculating deviation (Pe/Pp of T441* is the minimum in all 98 specimens, while Pe/Pp of PC454* is the maximum in all 98 specimens), the accuracy of the remaining specimens is basically good, whereas for PC454,


Table 3Summary of pile cap test results

SpecimenColumn size, mm

(diameter or side length) d, mm fc, MPaReinforcement layout,

No. of bar bar diameter, mm Bar yield stress fy, MPaTest column load

at failure, kN

Sabnis and Gogate14 (No. of pile: 4; pile arrangement: determinant; pile diameter, 76.2 mm)

SS01

76.2 round

111.44 31.3 3 5.715 each way 499.4 250.4

SS02 111.62 31.3 3 3.429 + 4 2.68 each way :886.0; :410.1 244.6

SS03 110.87 31.3 7 3.429 each way 886 248.0

SS04 111.62 31.3 3 5.715 + 3 2.68 each way :499.4; :410.1 225.7

SS05 108.59 41.0 7 5.715 + 4 2.032 each way :499.4; :480.2 263.5

SS06 108.59 41.0 11 5.715 each way 499.4 280.2

SG02 117.48 17.9 3 9.525 each way 251.2 173.5

SG03 117.48 17.9 4 9.525 each way 251.2 176.8

Jimenez-Perez et al.15 (No. of pile: 4; pile arrangement: determinant; pile diameter, 76.2 mm)

MS01

76.2 round

114.30 28.7

275.5

MS02 114.30 28.7 275.5

MS03 114.30 28.7 306.6

MS04 120.65 28.7 291.1

MS05 120.65 31.5 231.1

MS06 107.95 28.7 261.1

MS07 107.95 28.7 287.7

MS15 117.48 31.5 300.0

MS16 117.50 31.5 288.9

MS17 114.30 31.5 310.0

MS19 114.30 31.5 320.0

MS20 107.95 31.5 310.0

MS23 107.95 31.5 313.3

MS24 107.95 31.5 331.1

MS28 101.60 28.7 318.9

MS29 101.60 28.7 293.3

MS30 101.60 31.5 313.3

Taylor and Clarke16 (No. of pile: 4; pile arrangement: determinant; pile diameter, 200 mm)

A001200 square 400

20.9 10 10 each way 410 1110

A009 26.8 10 10 each way 410 1450

Adebar et al.9 (No. of pile: 4; pile arrangement: diamond; pile diameter, 200 mm)

A 300 square 445 24.8 9 11.3 one way; 15 11.3 other way 479 1781

Shen17 (No. of pile: 4; pile arrangement: determinant; pile diameter, 50 mm)

T415

60 square

96 16.3 23 2.2 each way 233 73.5

T417 79 16.3 12 2.2 each way 233 67.6

T420 104 8.4 18 1.57 each way 285.5 51.0

T421 102 8.4 23 1.57 each way 285.5 52.5

T422 95 10.7 18 2.2 each way 249.9 50.7

T423 92 8.4 20 2.2 each way 249.9 57.1

T424 93 8.4 23 2.2 each way 249.9 55.9

T425 100 8.4 25 2.2 each way 249.9 61.3

T426 100 10.7 17 2.8 each way 276.9 59.3

T427 95 10.7 18 2.8 each way 276.9 60.5

Notes: is no reinforcement data provided in the literature; 1 mm = 0.0394 in; 1 MPa = 0.145 ksi; 1 kN = 0.225 kip.


Table 3 (cont.)Summary of pile cap test results




at failure, kN

T428

60 square

103 10.7 20 2.8 each way 276.9 66.6

T429 97 10.8 22 2.8 each way 276.9 78.9

T430 97 10.8 24 2.8 each way 276.9 69.1

T432 95 12.5 18 2.2 each way 249.9 65.2

T433 96 12.5 18 2.8 each way 276.9 78.6

T435 93 9.8 18 2.2 each way 249.9 55.9

T436 98 9.8 18 2.8 each way 276.9 52.9

T439 105 9.8 24 1.57 each way 285.5 50.0

T441* 104 10.7 24 2.2 each way 249.9 41.2

T442 92 12.5 24 2.8 each way 276.9 72.8


T452 150 square 225 9.4 11 8 each way 276.5 364.6


T601150 square

225 13.5 12 10+20 6 each way :272.0;:276.3 460.6

T602 225 9.4 12 8+20 8 each way , :276.5 441.0

Zhuang18 (No. of pile: 4; pile arrangement: determinant; pile diameter, 100 mm)

PC453150 square

215 12.2 7 12 each way 280.2 370

PC454* 185 17.2 6 12 each way 283.5 500

Guo et al.11 (No. of pile: 6; pile arrangement: determinant; pile diameter, 180 mm)

S1 220 square 259 15.4 20 12 one way;18 12 other way 318.6 1250

Wu et al.19 (No. of pile: 3; pile arrangement: equilateral triangle; pile diameter, 110 mm)

PC1-1 200 square 400.0 25.4 3 10 each way 304.8 910
















Wu and Fang20 (No. of pile: 4; pile arrangement: determinant; pile side length, 100 mm)

C2-1 150 square 520 7.54 5 8 each way 289.3 559

C2-2 150 square 320 13.4 7 8 each way 289.3 630

Yang21 (No. of pile: 3; pile arrangement: equilateral triangle; pile diameter, 100 mm)

YZ1 100 square 210 13.2 3 12 each way 310 441

Notes: is no reinforcement data provided in the literature; 1 mm = 0.0394 in; 1 MPa = 0.145 ksi; 1 kN = 0.225 kip.


there is a statement in Reference 18 that says, As theres no law about the crack distribution of PC454 in the limit state, its hard to say whether the pile cap failure is caused by bending or punching from the final crack shape. So this calculating deviation is probably due to a bending failure.

With respect to T441, no description of the test phenomenon is provided in literature. But, be it TPM or ACI CSM, CRSI and JGJ94-94, or the evaluation in Reference 31, whose author and test conductor of T441 are in the same project group,31 Pe/Pp values all tend to be small. Furthermore,

Table 3 (cont.)Summary of pile cap test results




at failure, kN

Ma22 (No. of pile: 3; pile arrangement: isosceles triangle; pile diameter, 90 mm)

P5 100(one side) 140(other side) rectangle 180 20.1 4 6 each way 340

222.5

P6 226.4

Suzuki et al.23 (No. of pile: 4; pile arrangement: determinant; pile diameter, 150 mm)

TDS3-1250 square

300 28.0 11 9.53 each way 356 1299

TDM3-1 250 27.0 10 12.72 each way 370 1245

Suzuki et al.24 (No. of pile: 4; pile arrangement: determinant; pile diameter, 150 mm)

BDA-30-20-70-2 200 square 250 24.6 6 9.53 each way

358549

BDA-40-25-70-1 250 square 350 25.9 8 9.53 each way 1019

Suzuki and Otsuki25 (No. of pile: 4; pile arrangement: determinant; pile diameter, 150 mm)

BPB-35-20-1 200 square 290 20.4 9 9.53 each way 353 755

Chan et al.26 (No. of pile: 4; pile arrangement: determinant; pile side length, 150 mm)

C(Chan) 200 square 200 30.74 12 10 each way 480.7 870

Ahmad et al.27 (No. of pile: 4; pile arrangement: determinant; pile diameter, 150 mm)

A(Saeed) 150 round 230 20.68 10 12.8 + 6 6.5 each way, :413

480

F(Saeed) 150 round 230 27.6 12 12.8 + 6 6.5 each way 560

Blvot and Frmy28 (No. of pile: 4; pile arrangement: determinant; pile side length, mm: except that 9A3 is 140, others are 350)

4N1 500 square 670 37.3 8 32 + 7 16 each way :276.2; :279.3 7000

4N1b 500 square 680 40.8 8 25 + 7 12 each way :440.3; :516.7 6700

4N3 500 square 920 34.15 4 32 + 4 25 + 8 12 each way :250.6; :281.2; :293.1 6500

4N3b 500 square 920 49.3 4 25 + 4 20 + 8 10 each way :484.5; :446; :429.5 9000

9A3 150 square 470 34.4 16 12 450.25 1700

Blvot and Frmy28 (No. of pile: 3; pile arrangement: equilateral triangle; pile side length, 350 mm)

3N2 450 square 462.5 37.7 3 32 each way 255 3800

3N2b 450 square 480 43.7 4 25 each way 442 4500

3NH 450 square 715 32.65 3 32 + 1 25 each way :261; :333 5200

3NHb 450 square 730 42.45 4 25 439 7200

Miguel et al.29 (No. of pile: 3; pile arrangement: equilateral triangle; pile diameter, mm: except that B30A4 is 300, others are 200)

B20A1/1 350 square 500 27.4 3 12.5 each way 591 1512

B20A1/2 350 square 500 33.0 3 12.5 each way 591 1648

B20A3 350 square 500 37.9 3 12.5 each way 591 1945



Chao and Bo30 (No. of pile: 9; pile arrangement: determinant; pile diameter, 150 mm)

CTA 300 square 314 24.88 6 16 + 5 14 each way :374; :369 1900

Notes: is no reinforcement data provided in the literature; 1 mm = 0.0394 in.; 1 MPa = 0.145 ksi; 1 kN = 0.225 kip.


Table 4Pe/Pp of five theoretical methods

Specimen TPM ACI CSM ACI STM CRSI JGJ94-94 Specimen TPM ACI CSM ACI STM CRSI JGJ94-94

SS01 1.1205 2.0694 3.1300 1.5493 T439 0.6900 0.2450 2.3697 0.5952 0.8139

SS02 1.0934 2.0049 2.4757 1.5087 T441* 0.5349 0.2013 1.5907 0.4791 0.6873

SS03 1.1094 2.0667 2.5101 1.5471 T442 0.9434 0.5352 2.3560 1.0866 1.5390

SS04 1.0093 1.8500 2.2844 1.3916 T452 1.3847 0.4005 2.7189 0.9421 0.7880

SS05 0.9955 1.9812 2.0332 1.4482 T601 1.0280 0.9343 3.3474 0.9948 0.6984

SS06 1.0580 2.1068 2.1620 1.5431 T602 1.2746 1.0730 2.6018 1.1395 0.8579

SG02 1.0580 1.7350 3.0654 1.2674 PC453 1.2084 0.4344 1.8974 0.9439 1.1550

SG03 1.0580 1.7680 3.1237 1.2929 PC454* 1.5010 0.8463 2.0610 1.3163

MS01 1.1140 2.2769 1.7386 S1 0.9789 1.8629 2.8090 1.6480

MS02 1.1140 2.2769 1.7386 PC1-1 1.2248 2.6157 0.2124 0.9141

MS03 1.2400 2.5339 1.9347 PC1-2 1.0957 2.2526 0.2458 0.7544

MS04 1.1120 2.2053 1.6814 PC1-3 1.0719 2.2443 0.2393 0.7279

MS05 0.8593 1.6746 1.2528 PC1-4 1.0602 1.9336 0.2412 0.7533

MS06 1.1080 2.3736 1.8099 PC2-1 1.0414 1.9593 0.2395 0.8462

MS07 1.2220 2.6155 1.9948 PC2-2 1.0651 2.1635 0.3734 0.8422

MS15 1.1470 2.2727 1.6986 PC2-3 0.9564 1.9501 0.3296 0.7267

MS16 1.1042 2.1722 1.6357 PC2-4 0.8808 1.8705 0.2436 0.7949

MS17 1.2199 2.4409 1.8354 PC3-1 1.0276 1.9911 0.4880 0.9706

MS19 1.2590 2.5197 1.8952 PC3-2 0.9888 0.1786 1.8937 0.5871 0.8863

MS20 1.2807 2.6724 2.0164 PC3-3 0.8475 0.1510 1.9978 0.4964 0.7370

MS23 1.2940 2.7009 2.0385 PC3-4 0.8936 1.7954 0.4062 0.9418

MS24 1.3680 2.8543 2.1543 PC4-1 1.0474 0.5268 2.1388 1.0454 1.2011

MS28 1.4070 3.1890 2.4443 PC4-2 1.0145 0.7891 1.9862 1.2694 1.2316

MS29 1.2940 2.9330 2.2487 PC4-3 0.8659 0.6709 2.2386 1.0785 1.0406

MS30 1.3450 2.9838 2.2544 PC4-4 1.0357 0.4404 2.1085 1.0535 1.3710

A001 0.6257 0.3833 2.5850 0.7613 0.7056 C2-1 1.1768 0.4381 3.8819 0.2455 0.8534

A009 0.7302 0.4421 3.3768 0.8783 0.7809 C2-2 0.9722 0.8005 2.3684 0.3652 1.0096

A 1.0730 0.7713 5.9605 YZ1 1.2250 0.4244 3.9305 1.0023 1.3823

T415 0.7691 0.4047 2.3786 0.8547 0.8762 P5 1.0183 0.7986 2.0488 1.1502

T417 0.8524 0.7042 3.3137 1.099 P6 1.0362 0.8130 2.0847 1.1705

T420 0.7971 0.2818 3.0539 0.6711 0.9508 TDS3-1 1.0384 0.1860 3.5395 0.7466 0.8620

T421 0.8346 0.3165 2.7202 0.7292 1.0100 TDM3-1 1.4596 0.7188 2.5305 1.4426 1.0854

T422 0.7110 0.3587 2.0199 0.7456 0.9741 BDA-30-20-70-2 0.6175 0.3690 1.7825 0.7409 0.6046

T423 0.9918 0.5134 2.9133 1.0382 1.2900 BDA-40-25-70-1 0.7998 2.3643 0.4101 0.6105

T424 0.9612 0.4834 2.8376 0.9982 1.2410 BPB-35-20-1 0.9107 0.4704 2.4754 0.8224

T425 0.9894 0.4012 3.0049 0.9015 1.2140 C(Chan) 1.1545 1.4711 2.5285 1.3894

T426 0.7955 0.3433 2.2548 0.7701 1.052 A(Saeed) 0.9878 2.5236 1.2171 2.8267

T427 0.8484 0.4283 2.2000 0.8897 1.1630 F(Saeed) 1.0145 2.7488 1.6577 2.9343

T428 0.8721 0.3401 2.4667 0.7929 1.1300 4N1 0.9685 0.5856 1.9958 0.7903

T429 1.0787 0.5135 2.8901 1.0958 1.4250 4N1b 0.8333 0.5122 2.2440 0.6955

T430 0.9447 0.4497 2.5311 0.9597 1.2480 4N3 0.7217 0.1617 1.1856 0.4876 0.4911

T432 0.8167 0.4245 2.4791 0.8932 1.3100 4N3b 0.7054 0.1864 1.4860 0.5619 0.5324

T433 0.9760 0.4944 2.4952 1.0480 1.5540 9A3 0.9433 1.1479 0.4301 0.7856

T435 0.8548 0.4477 2.4735 0.9164 1.0990 3N2 0.9521 1.1006 2.3088 \Notes: Pe/Pp is experimental column load/predicted column load; is infinite bearing load because piles are totally within critical section; is evaluation cannot be conducted because no reinforcement data provided; is calculating condition not applicable; is not easy to evaluate; and \ is evaluation cannot be conducted because no free end dimensions of pile cap provided.


although Pe/Pp of T441 calculated by ACI STM has reached 1.5907, it is the relatively small value of all the calculable specimens by ACI STM. Therefore, it can be inferred just as well that the rather large calculating deviation of T441 is also attributable to it being probably a bending failure.

In other words, of the five methods, TPM is always capable of maintaining good accuracy whatever the situation.

VariabilityIt is known from Table 5 that, when all the calculable

specimens are selected, or after the asterisked specimens in Table 4 are removed, the variation coefficient of Pe/Pp with TPM is always smaller than the other four methods. Hence, TPM is best in terms of calculating stability.

After further analysis, it is known from Tables 4 and 5 that: 1) the average of Pe/Pp with TPM is only slightly larger than 1.0. With the theoretical essence of lower-bound solution of the SSTM method taken into account, this value should be rational, while that with the other four methods makes some deviation from 1.0. In addition, the degree of variability of the other four methods is also larger, and there is a tendency that the smaller the punching span is, the larger the column load calculated will be; and 2) when the asterisked speci-mens in Table 4 are removed, the minimum or maximum of Pe/Pp value with TPM is still comparatively rational.

In a word, TPM is safe and reliable, and the potential of bearing load is also appropriate.

ApplicabilityTPM is capable of evaluating all the specimens in Table 3,

so its calculating mode is comparatively unified and not restricted by the number of piles and the form of pile arrange-ment. ACI CSM is incapable of evaluation when all the piles are within the critical section, while ACI STM can not perform evaluation unless it meets certain restrictions on the punching span and all the specimen parameters, including reinforcement, have to be provided at the same time. Like-wise, CRSI is not applicable unless it is confined to a certain small punching-span condition. Constrained by the form of pile arrangement, such as the diamond pile arrangement, as shown in Table 4, it is not easy to perform evaluation using JGJ94-94; furthermore, regarding triangle pile arrangement, JGJ94-94 cannot carry out evaluation unless the free-end dimensions of the pile cap are provided. Thus, the applica-bility of TPM is recommendable.

Further analysis is as follows:1. As mentioned earlier, it has been anticipated during

computerization that the of pile caps with uniform grid reinforcement has little influence on its punching shear resis-tance, which is confirmed by test verification in Tables 3 through 5. It should be noted that none of most of the codes in the world has considered the impact of the longitudinal reinforcement ratio on the punching shear resistance of pile caps with uniform grid reinforcement. For instance, it is not considered in ACI CSM,1 JGJ94-94,2 CRSI3 and the

Table 4 (cont.)Pe/Pp of five theoretical methods

Specimen TPM ACI CSM ACI STM CRSI JGJ94-94 Specimen TPM ACI CSM ACI STM CRSI JGJ94-94

T436 0.7733 0.3483 2.1331 0.7557 0.9592 3N2b 0.9436 1.1437 1.8692 \

3NH 0.9345 0.6902 1.5854 \ B20A3 1.1254 0.4720 2.1248 \

3NHb 1.0314 0.2116 1.9773 \ B20A4 1.4631 0.5947 2.5946 \

B20A1/1 1.0100 0.4315 1.9508 \ B30A4 0.6881 0.1063 2.4941 \

B20A1/2 1.0448 0.4286 1.8004 \ CTA 1.0270 1.3172 1.7544 0.9895

Notes: Pe/Pp is experimental column load/predicted column load; is infinite bearing load because piles are totally within critical section; is evaluation cannot be conducted because no reinforcement data provided; is calculating condition not applicable; is not easy to evaluate; and \ is evaluation cannot be conducted because no free end dimensions of pile cap provided.

Table 5Statistical appraisal of Pe/Pp obtained by all theoretical formulas in Table 4

Predicting method Total number of specimens Average Standard deviation Coefficient of variation Minimum Maximum

TPMAll calculable specimens 98 1.0179 0.1940 0.1906 0.5349 (T441*) 1.501 (PC454*)

Asterisked specimens in Table 3 removed 96 1.0179 0.1832 0.1800 0.6175 1.4631

ACI CSM

All calculable specimens 86 1.1177 0.9079 0.8123 0.1063 3.1890


ACI STM



CRSIAll calculable specimens 51 0.7228 0.3126 0.4325 0.2124 1.4426


JGJ 94-94




critical section stress method of the British code,5 nor is it mentioned in the formulae of punching shear resistance of the German32 and Japanese codes.33 This, of course, may involve considerations of the strength reserve, but there is also a factor that should not be ruled outnamely, the punching shear resistance of pile caps with uniform grid reinforcement is not sensitive to its longitudinal reinforce-ment ratio, as demonstrated in References 14 and 15. The aforementioned discussion shows that if longitudinal rein-forcement is arranged according to a uniform grid, it is not necessary to impose restrictions on the reinforcement ratio of tension tie for TPM.

2. As previously mentioned, during derivation of fce, under the prerequisite for punching failure, the punching-span ratio is given a large range of variationnamely, 0.15 to 2.0and concrete strength fc basically contains the whole range of ordinary concrete strength as wellnamely, 6.7 to 50 MPa (971.5 to 7252 psi). Likewise, a large range of vari-ation of and fc is also embodied in Table 4. But it can be seen that for all ascertained punching failure specimens, their theoretical values calculated by TPM just agree well with the test values. Therefore, it can be asserted that, if only what has happened is a punching failure, on the one hand, there is no need to restrict the punching-span ratio for TPM; on the other hand, TPM is also applicable to all the pile caps with ordinary concrete strength.

3. As previously mentioned, the model in computerization is not exclusively developed for a certain pile number or a certain form of pile arrangement. What it selects is the strut model, so, as a result, the obtained results should be generally applicable to an arbitrary pile number and an arbitrary form of pile arrangement as can be seen from Tables 3 through 5. It is necessary to point out that, for pile caps with the pile beneath the column, as frequently seen in engineering prac-tice, it can be imagined that the bearing mechanism of the SSTM is still tenable. But as the punching failure of the pile caps is a result of extension and development of diagonally splitting crack, it is unlikely for punching failure to occur in the strut located between the column and the pile beneath the column. Consequently, the column load of punching failure of this kind of pile caps should be the sum of the following two parts: the first part, the column load of punching failure with no pile beneath the column; and the second part, the actual load borne by the pile beneath the column. Of the two parts, the evaluation of the first part can be carried out with TPM, while that of the second part, as can be seen from the previously mentioned load-transfer mechanism, can be performed reversely with pile load distribution at the elastic stage, thus bypassing quite a lot of inconvenience in the evaluation of the statically indeterminate spatial truss at the plastic stage. Therefore, TPM has extensive applicability.

CONCLUSIONSIn this paper, through the NFE analysis and the derivation

of GLSMV, a new method, TPM, for evaluating punching shear resistance of pile cap with uniform grid reinforcement is presented. In view of the good agreement between TPM and experimental data, with , , fc, pile number, and pile

arrangement form variable, and the definite advantages in terms of accuracy, variability, and applicability as compared with the other four methods, TPM can be widely applicable to the evaluation of the punching shear resistance of the general pile cap with uniform grid reinforcement.

AUTHOR BIOSHonglei Guo is a Professor in the Department of Civil Engineering at Wuhan Polytechnic University, Wuhan, China. He received his BS and MS from Wuhan University in 1988 and 1993, respectively, and his PhD from Southeast University, Nanjing, China, in 1997. His research interests include shear strength and optimal design of reinforced concrete structures.

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ACI STRUCTURAL JOURNAL TECHNICAL PAPER

A full-scale, four-story, reinforced concrete building designed in accordance with the current Japanese seismic design code was tested under multi-directional shaking on the E-Defense shake table. A two-bay moment frame system was adopted in the longer plan direction and a pair of multi-story walls was incorporated in the exterior frames in the shorter plan direction. Minor adjust-ments to the designs were made to bring the final structure closer to U.S. practice and thereby benefit a broader audience. The resulting details of the test building reflected most current U.S. seismic design provisions. The structure remained stable throughout the series of severe shaking tests, even though lateral story drift ratios exceeded 0.04. The structure did, however, sustain severe damage in the walls and beam-column joints. Beams and columns showed limited damage and maintained core integrity throughout the series of tests. Implications of test results for the seismic design provi-sions of ACI 318-11 are discussed.

Keywords: collapse; damage; design; full-scale; moment frame; multi-story; shake table; shear wall.

INTRODUCTIONCode requirements for reinforced concrete have evolved

significantly around the world in the past decades. In the United States, the 1971 San Fernando, CA, earthquake was a watershed event leading to the introduction of require-ments for ductile reinforced concrete buildings, which have evolved incrementally since that time based on field and laboratory experiences. In Japan, following a history of several damaging earthquakes and many laboratory tests, the Japanese seismic design code was substantially revised in 1981. In the 1995 Hyogoken-Nanbu earthquake, many rein-forced concrete buildings designed before 1981 experienced major failures, especially in the first-story columns and walls. Although newer reinforced concrete buildings designed in accordance with the revised 1981 code showed improved resistance against collapse, several sustained severe damage due to their large deformations. Such damage made it diffi-cult to continue using them after the earthquake and resulted in high repair costs. This experience demonstrates that further improvements in seismic design of concrete build-ings might be desirable for the future.

It was in light of the aforementioned experiences that a large-scale shake-table testing program was conducted in 2010. Within the program, a full-scale, four-story, rein-forced concrete building designed in accordance with the present Japanese seismic design code was tested by using the E-Defense shake table. The main objectives of the study related to the concrete building were: 1) to verify methods for assessing performance such as strength, deformation

capacity, and failure mode; 2) to identify suitable compu-tational methods to reproduce the seismic responses of the building; and 3) to develop a practical method for assessing damage states regarding reparability.

Design and instrumentation of the test structure were performed with input from U.S. co-authors. Wherever possible, minor adjustments to the designs were made to bring the final structure closer to U.S. practice and thereby benefit a broader audience. The resulting details of the test building reflected the most current U.S. seismic design provisions (Nagae et al. 2011b).

Summaries of the global behavior of the test building and key local damage and deformation observations are presented. A comparison between the details of the test structure and U.S. seismic design practices is also provided. Implications of test results for the seismic design provi-sions of ASCE 7-10 (ASCE/SEI Committee 7 2010) and ACI 318-11 (ACI Committee 318 2011) are discussed. In a related publication (Nagae et al. 2011a), the seismic design provisions of the Architectural Institute of Japan (AIJ 1999) were evaluated in light of test results.

RESEARCH SIGNIFICANCECurrent Japanese and U.S. seismic design provisions are

based on pseudo-dynamic component tests, sub-assembly tests, and limited dynamic tests of partial structural systems. The test presented is a first-of-its-kind, multi-directional, dynamic test of a complete, full-scale reinforced concrete building system to near collapse damage states. The test provides unique data on component and system performance that are used to evaluate current seismic design provisions and highlight potential code changes.

SPECIMEN DETAILSFigure 1 shows the plans and framing elevations of the

reinforced concrete test building. Figure 2 shows a photo-graph of the test building on the E-Defense shake table. The height of each story is 3 m (118.1 in.). The building footprint measures 14.4 m (47 ft 3 in.) in the longer (X) direction, and 7.2 m (23 ft 7.5 in.) in the shorter (Y) direction. A two-bay moment frame system was adopted in the longer (X) plan direction and a pair of multi-story walls were incorporated

Title No. 112-S12

Design Implications of Large-Scale Shake-Table Test on Four-Story Reinforced Concrete Buildingby T. Nagae, W. M. Ghannoum, J. Kwon, K. Tahara, K. Fukuyama, T. Matsumori, H. Shiohara, T.Kabeyasawa, S. Kono, M. Nishiyama, R. Sause, J. W. Wallace, and J. P. Moehle

ACI Structural Journal, V. 112, No. 2, March-April 2015.MS No. S-2013-022.R2, doi: 10.14359/51687421, received May 21, 2014, and

reviewed under Institute publication policies. Copyright 2015, American Concrete Institute. All rights reserved, including the making of copies unless permission is obtained from the copyright proprietors. Pertinent discussion including authors closure, if any, will be published ten months from this journals date if the discussion is received within four months of the papers print publication.


in the exterior frames in the shorter (Y) plan direction. The thickness of the top slab was 130 mm (5.1 in.). Rigid steel frames were set within the open stories of the test specimen for collapse prevention and measurement of story defor-mations. Representative building mechanical equipment

was incorporated to assess potential damage during strong seismic motions. Table 1 lists the various weights of the test specimen. The weight was estimated based on the reinforced concrete members, the fixed steel frames, and the equip-ment. Figure 1 shows dimensions and reinforcement details of typical members. The test building was designed in accor-dance with current Japanese seismic design practice.

When constructing the test building, columns, walls, beams, and the floor slab were cast monolithically. The longitudinal reinforcement of columns, beams, and the wall boundaries were connected by gas pressure welding. Lap splices were used for the reinforcement of other parts of the walls and the floor slabs. The frames in the test building were nominally identical in design and detailing. The shear walls at axes A and C contained the same amount of longitu-dinal reinforcement but differed in the spacing of transverse reinforcement (Fig. 1). A complete set of drawings and spec-imen details can be found in Nagae et al. (2011b). Additional test data can be found on the NEEShub website (NEEShub 2011) and in Tuna (2012).

SPECIMEN DESIGNThe extent to which the test structure satisfies the seismic

design provisions of ASCE 7-10 and ACI 318-11 is explored

Fig. 1Framing and reinforcing details. (Note: Dimensions are in mm; 1 mm = 0.039 in.)

Fig. 2Reinforced concrete (left) and prestressed concrete (right) specimens on the E-Defense shake table.


in this section. The building specimen was designed to with-stand the seismic lateral forces presented in Table 1 (MLIT 2007) without members exceeding their elastic limits. These forces, which sum to 20% of the weight of the structure, are higher than those that would be specified by ASCE 7-10 (Section 12.8.1.3), which caps seismic lateral forces for a low-rise building to 1/R times the structure weight for a design basis earthquake, where R is the response modifica-tion coefficient (8 for special reinforced concrete moment frames and 6 for special reinforced concrete shear walls). The vertical distribution of the design forces, given by the parameter Ai in Table 1, is similar to the ASCE 7-10 specifi-cation (approximate inverted triangular distribution).

Results of material tests are given in Tables 2 and 3. In subsequent evaluations, the moment and shear strengths of each member were calculated adopting the compressive strength of concrete and the yield strength of steel reinforce-ment obtained by averaging material test results.

To aid in the design of the test specimen, pushover (nonlinear static) analyses were conducted on line-element models of the structure. Figure 3 presents pushover results for the final test specimen details. The analytical model used for pushover analyses was built following work by Kabeya-sawa et al. (1984). The effective flange width of a top slab was adopted in accordance with the recommendations of the 2007 MLIT Standard. A vertical distribution defined by the parameter Ai (Table 1) was adopted for the lateral force distribution. In the analytical model, inelastic deformations of beam elements were represented by rotational springs at the ends of elements. The first and second break points corresponding to member cracking strength and flexural strength were assigned in the tri-linear moment-rotation

relationship. The secant stiffness corresponding to the flex-ural strength was calculated in accordance with provisions of the MLIT standard (2007). Beyond flexural yielding, the stiffness was reduced to 0.01 times the initial effective stiff-ness. The pushover analysis indicates that the ultimate base-shear strength of the building specimen is approximately 0.42W (1500 kN [337 kip]) in the frame direction and 0.51W (1800 kN [405 kip]) in the wall direction.

Figure 4 shows the column-beam moment strength ratios. Reinforcement of the top slab was reflected in the moment strength of beams in negative bending (top in tension). Effec-tive flange widths of beams were adopted in accordance with the recommendations of the 2007 MLIT Standard or ACI 318-11, which produced roughly similar flange widths. Variations of column axial forces due to lateral forces were estimated from pushover analysis in the Japanese calcu-lations. In the U.S. calculations, a plastic mechanism was assumed in which hinging of the columns occurs at the foun-dation and just below the roof, and beam hinging occurs at column faces at intermediate floors in the frame direction. In the wall direction, the assumed plastic mechanism considered hinging of the columns and walls at the foundation, and beam hinging at column and wall faces. Discrepancies in column-beam moment strength ratios evaluated using ACI and MLIT procedures (Fig. 4) can mostly be attributed to differences in the estimates of axial forces on columns. From the second to fourth floors, the column-beam moment strength ratios were slightly below 1.0 for interior columns, while those of exte-rior columns ranged from approximately 1.0 to 1.87.

Assessment of specimen design in accordance with U.S. seismic design practice

The structure was assessed in both the x- and y-direc-tions using ACI 318-11 and ASCE 7-10 provisions. The

Table 1Weight and design forces

(A) Structural elements, kN RoofFourth floor

Third floor

Second floor

RC

Column 53 106 106 106

Beam 240 240 240 240

Wall 40 79 79 79

Slab 484 428 424 420

Sum 816 853 849 845

(B) Non-structural elements, kN Roof

Fourth floor

Third floor

Second floor

SteelStair and handrail 6 6 6 6

Measurement frame 0 3 17 17

Equipment 112 5 0 0

Sum 118 14 23 23

Total of (A) and (B), kN 934 867 872 867

Fourth story

Third story

Second story

First story

Wi, kN 934 1801 2673 3541

Ci = 0.2 Ai 0.29 0.25 0.22 0.20

Qi, kN 273 450 593 708

Notes: Wi is weight of floor i; Ai is shape factor for vertical distribution of lateral forces for floor i; Ci is lateral force at floor i as a fraction of Wi; and Qi is shear at story i; 1 kN = 0.225 kip.

Table 2Material properties of concrete

Fc, N/mm2

B, N/mm2

Ec, N/mm2

Cast of fourth story and roof floor slab 27 41.0 30.5

Cast of third story and fourth floor slab 27 30.2 30.3

Cast of second story and third floor slab 27 39.2 32.8

Cast of first story and second floor slab 27 39.6 32.9

Notes: Fc is specified concrete compressive strength; B is measured concrete compres-sive strength; and Ec is measured secant modulus of concrete; 1 N/mm2 = 0.145 ksi.

Table 3Material properties of steel

Grade Anominal, mm2 y, N/mm2 t, N/mm2 Es, kN/mm2

D22 SD345 387 370 555 209

D19 SD345 287 380 563 195

D13 SD295 127 372 522 199

D10 SD295 71 388 513 191

D10 SD295 71 448 545 188

D10 KSS785 71 952 1055 203

Notes: Anominal is nominal area of reinforcing bars; y is measured yield strength of steel reinforcement; t is measured ultimate strength of steel reinforcement; and Es is measured elastic modulus of steel reinforcement; 1 mm2 = 0.0016 in.2; 1 N/mm2 = 0.145 ksi.


goal was to determine how well the structure compares with U.S. seismic design practices. Rather than presume that the building was to be constructed at a particular site with corresponding site seismic hazard, the assessments of seismic design requirements are based on a seismic hazard represented by the linear response spectrum for the 100% JMA-Kobe ground motion to which the test structure was subjected.

Shear wall direction (y-direction)The approximate natural period in the shear wall direction is 0.31 seconds based on Eq. 12.8-7 in ASCE 7-10. The spectral acceleration corresponding to this period is approximately 2.5g for the 100% JMA-Kobe ground motion imparted to the structure (Fig. 5, y-direction). Elastic analysis was performed using equivalent (static) lateral forces corresponding to the spec-tral acceleration divided by an R factor of 6, as specified in ASCE 7-10 for a building frame system with special rein-

forced concrete shear walls. Equivalent lateral forces were distributed over the height of the structure in accordance with provisions of ASCE 7-10. An effective moment of inertia equal to 50% of the gross moment of inertia was used over the full wall height: an intermediate value between the effec-tive moments of inertia provided in ACI 318-11 for cracked and uncracked walls. Selected wall effective moments of inertia are also consistent with values recommended by ASCE 41-06 (ASCE/SEI Committee 41 2007a) for cracked walls. An effective moment of inertia equal to 30% of the gross moment of inertia was used for beams and columns as per ASCE 41-06 supplement 1 (ASCE/SEI Committee 41 2007b) provisions for beams and columns with low axial loads. Beams were considered T-beams with an effective flange width evaluated in accordance with provisions of ACI 318-11. Joints were taken as rigid. Elastic analysis of the walls decoupled from frames at Axes A and C indicates

Fig. 3Pushover analysis results. (Note: 1 kN = 0.225 kip.)

Fig. 4Moment strength ratios of columns to beams.


that the walls would develop their design moment strength (0.9 nominal moment strength) at approximately 0.37/R of the JMA-Kobe 100% motion. If wall-frame interaction is taken into account, however, the wall-frame system would develop its design moment strength at approximately 0.55/R of the 100% JMA-Kobe motion. Thus, the building in the wall direction has only 55% of the strength that would be required for the JMA-Kobe motion if that motion is consid-ered as the design earthquake shaking level. In subsequent discussion, wall-frame interaction is taken into account. When applying the equivalent lateral-force distribution in accordance with ASCE 7-10, wall flexural yielding occurs at a lower load than that generating the walls factored shear strength. Distributed vertical and horizontal steel satisfied all shear reinforcement requirements of ACI 318-11.

The wall-foundation interface was not intentionally roughened prior to casting the walls. Given the amount of longitudinal steel crossing the interface, the axial force on the walls, and a friction coefficient of 0.6, nominal shear-friction strength in accordance with ACI 318-11 of both wall bases was approximately 2140 kN (482 kip). That shear-friction strength exceeded estimated shear demands by approximately 55% based on the 100% JMA-Kobe ground motion. Nominal shear-friction strength was, however, only 20% higher than maximum base shear demand estimated from pushover analysis (approximately 1800 kN [405 kip]), which accounts to some extent for member over-strength.

ACI 318-11 allows the use of two methods to determine if boundary elements are required in walls. If the drift-based method is considered (ACI 318-11, Section 21.9.6.2), no boundary elements are required in the walls for the 100% JMA-Kobe motion, whether drift estimates are obtained considering wall-frame interaction or not. If the stress-based method is considered (ACI 318-11, Section 21.9.6.3), however, boundary elements are required in the walls up to a height of 7550 mm (297 in.) from the base of the wall if walls are considered decoupled from the frames, and a height of 5060 mm (199 in.) if wall-frame interaction is accounted. If one considers that boundary elements are not required in the walls, minimum boundary detailing in both walls satis-fies ACI 318-11 provisions. If one considers that boundary elements are required, however, the provided spacing of hoops in the boundary elements of the wall at Axis C (100 mm [3.94 in.]) marginally exceeds the required spacing

(83 mm [3.26 in.]). In the wall at Axis A, hoops were spaced at 80 mm (3.15 in.) in the first story and this spacing satis-fies all ACI 318 hoop spacing requirements for the boundary element. In the upper stories of the wall at Axis A, hoops in the boundary regions were spaced at 100 mm (3.93 in.) and therefore did not satisfy the ACI 318-required spacing of 83 mm (3.26 in.).

If wall-frame interaction was considered, beams spanning between shear walls and corner columns were found to have sufficient moment strength to resist moments from elastic analysis based on the 100% JMA-Kobe motion hazard level. Shear strengths of the beams were sufficient to develop beam probable moment strengths.

Because demands on corner columns in the shear wall direction were significantly lower than demands on the same columns in the frame direction, capacity and detailing of corner columns will be described in the section discussing the frame direction (x-direction).

Frame direction (x-direction)The approximate natural period in the moment frame direction is 0.44 secomds based on ASCE 7-10 Eq. 12.8-7. The spectral acceleration corre-sponding to this period is approximately 1.45g for the 100% JMA-Kobe ground motion imparted to the structure (Fig. 5, x-direction). Elastic analysis was performed using equivalent (static) lateral forces corresponding to the spectral accelera-tion divided by an R factor of 8, as specified in ASCE 7-10 for special reinforced concrete moment frames. Equivalent lateral forces were distributed over the height of the structure in accordance with ASCE 7-10. Elastic analysis of the frames indicates that the first-story corner columns reach design flexural strength at a shaking level corresponding to approx-imately 1.4/R of the JMA-Kobe 100% motion. All frame member strengths therefore exceeded the required design strength corresponding to a 100% JMA-Kobe hazard level.

Factored shear strengths of all beams were not sufficient to develop probable moment strengths due to the require-ment that concrete shear contribution be taken as zero (ACI 318-11, Section 21.5.4.2). Maximum beam shear stresses corresponding to the development of probable moment strengths ranged from 2.0 to 2.7 times the square root of the concrete compressive strength in psi (0.17 to 0.22 MPa). The spacing of beam transverse reinforcement was 200 mm (7.87 in.) in the critical plastic hinge regions, which exceeds the maximum allowable spacing of 120 mm (4.72 in.) as required by ACI 318-11.

Factored shear strengths of the third- and fourth-story columns were not sufficient to develop probable moment strengths. Column shear stresses corresponding to the devel-opment of column probable moment strengths ranged from 1.4 to 3.8 times the square root of the concrete compressive strength in psi (0.114 to 0.315 MPa). Column-end trans-verse reinforcement met spacing and layout requirements of ACI 318-11 in the first two stories but not the top two stories. No columns met the requirement for minimum volumetric reinforcement ratio in the critical end regions; columns had 20 to 50% of the hoop volumes required by ACI 318-11 in the critical end regions. Transverse reinforcement ratios varied substantially between columns in different stories due to differences in numbers of crossties.

Fig. 5Acceleration response spectra of input waves. (Note: Damping ratio = 0.05; 1 m/s2 = 39.37 in./s2.)


Joint shear demands for both interior and exterior joints were calculated considering force equilibrium on a hori-zontal plane at the midheight of the joints, in accordance with ACI 318-11. Joint shear demands calculated including the contribution of slab flexural tension reinforcement within the ACI 318 effective flange width were found to be approx-imately 20 to 40% higher than demands computed ignoring the slab contribution. Note that ACI 318 does not require consideration of the slab reinforcement in calculations of joint shear demand. Regardless of whether slab contribution was taken into account, all joint design shear strengths, based on ACI 318-11, exceeded joint shear demands. Because joints were only confined by hoops without crossties, the maximum center-to-center horizontal spacing between hoop or crosstie legs was larger than the ACI 318-11 limit of 350 mm (14 in.). The provided hoop spacing in the joints of 140 mm (5.5 in.) was larger than the maximum spacing allowed by ACI 318-11 of approximately 25 mm (1 in.) for the provided arrangement of hoops without crossties (limited by minimum volumetric reinforcement ratio requirements). Other joint detailing satisfied ACI 318-11 requirements, including those for longitudinal bar anchorage.

Figure 4 shows column-beam nominal moment strength ratios. Below the roof, all strength ratios for exterior columns

satisfied the 6/5 minimum requirement of ACI 318-11. That requirement was not satisfied at interior joints.

E-DEFENSE SHAKE-TABLE FACILITY AND TESTCONDITIONS

The E-Defense shake-table facility has been operated by the National Research Institute for Earth Science and Disaster Prevention of Japan since 2005. The table is 20 x 15 m (65 ft 7 in. x 49 ft 3 in.) in plan dimension and can produce a velocity of 2.0 m/s (78.7 in./s) and a displace-ment of 1.0 m (39.4 in.) in two horizontal directions simul-taneously. It can accommodate a specimen weighing up to 1200 tonnes (1323 tons). In this series of tests, the consid-ered reinforced concrete building was tested side-by-side with a prestressed concrete building having almost the same configuration and overall dimensions (Fig. 2). More detail about the test structure, including detailed drawings, can be found in Nagae et al. (2011b).

LOADING PROGRAMGround motions designated as JMA-Kobe and JR-Taka-

tori, recorded in the 1995 Hyogoken-Nanbu earthquake, were adopted as the input base motions. The North-South- direction wave, East-West-direction wave, and vertical- direction wave were input to the y-direction, x-direction, and vertical direction of the specimen, respectively. The inten-sity of input motions was gradually increased to observe damage progression. The adopted amplitude scaling factors for JMA-Kobe were 10, 25, 50, and 100%. Following the JMA-Kobe motions, the JR-Takatori motion scaled to 40 and 60% was applied to impart large cyclic deformations. Figure 5 presents the acceleration response spectra for the input motions. JMA-Kobe 100% has a strong intensity in the short-period range corresponding to the natural period of the specimen, as can be seen in Fig. 5. The JR-Takatori 60% has a strong intensity in the longer-period ranges corresponding to estimated damaged specimen periods.

TEST RESULTSMaximum recorded story drift and global behavior

White-noise inputs were applied prior to each main test. From these, the initial natural periods of the test building were found to be 0.43 seconds in the frame direction and 0.31 seconds in the wall direction, which compare favor-ably with periods estimated using ASCE 7-10 Eq. 12.8-7 (0.44 seconds in the frame direction and 0.31 seconds in the

Fig. 6Maximum interstory drift distribution.

Table 4Key response values at roof

Test No. Maximum roof acceleration Maximum roof drift* Residual roof drift

Input wave x-direction, m/s2 y-direction, m/s2 x-direction, mm y-direction, mm x-direction, mm y-direction, mm

1 JMA-Kobe 25% 3.12 6.37 16.9 24.2 0.5 0.4

2 JMA-Kobe 50% 7.03 11.01 122.4 106.9 1.1 5.4

3 JMA-Kobe 100% 9.65 14.01 242.7 323.9 6.2 22.5

4 JR-Takatori 40% 6.46 8.13 240.4 240.8 1.3 7.9

5 JR-Takatori 60% 8.09 9.99 278.1 414.0 8.0 11.6*Maximum roof drifts do not include residual drifts accrued from previous tests.

Notes: 1 m2/s = 39.37 in./s2; 1 mm = 0.039 in.


wall direction). Figure 6 shows the distribution of maximum story drift over the height of the specimen for the shaking tests. In the frame direction, the story drift is larger in the first and second stories than in the third and fourth stories. In the wall direction, the story drifts are relatively uniform, although the drifts become larger in the first story than drifts of other stories in the JMA-Kobe 100% test and JR-Takatori tests. The structure remained stable through all the severe dynamic tests and thus satisfied the minimum collapse- prevention performance objective. Table 4 lists the maximum recorded roof level accelerations, drifts, and residual drifts for all

aci structural journal mar.-apr. 2015 v. 112 no. 02

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