probabilistic calibration and experimental validation of...

Journal of Earthquake Engineering, 13:426–462, 2009

Copyright � A.S. Elnashai & N.N. Ambraseys

ISSN: 1363-2469 print / 1559-808X online

DOI: 10.1080/13632460802598610

Probabilistic Calibration and ExperimentalValidation of the Seismic Design Criteria

for One-Story Concrete Frames

FABIO BIONDINI and GIANDOMENICO TONIOLO

Department of Structural Engineering, Politecnico di Milano, Milan, Italy

This article investigates the seismic performance of one-story reinforced concrete structures for indus-trial buildings. To this aim, the seismic response of two structural prototypes, a cast-in-situ monolithicframe and a precast hinged frame, is compared for four different levels of translatory stiffness andseismic capacity. For these structures an incremental nonlinear dynamic analysis is performed within aMonte Carlo probabilistic simulation. The results obtained from the probabilistic analysis prove thatprecast structures have the same seismic capacity of the corresponding cast-in-situ structures andconfirm the overall goodness of the design criteria proposed by Eurocode 8, even if a noteworthydependency of the actual structural behavior from the prescribed response spectrum is pointed out.

The experimental verification of these theoretical results is searched for by means of pseudo-dynamic tests on full-scale structures. The results of these tests confirm the overall equivalence ofthe seismic behavior of precast and cast-in-situ structures. Moreover, two additional prototypeshave been designed to investigate the seismic behavior of precast structures with roof elementsplaced side by side. The results of these further tests show that an effective horizontal diaphragmaction can be activated even if the roof elements are not connected among them, and confirm theexpected good seismic performance of these precast systems. Finally, the results of the experimentaltests are compared with those obtained from nonlinear structural analyses. The good agreementbetween numerical and experimental results confirms the accuracy of the theoretical model and,with it, the results of the probabilistic investigation.

Keywords Concrete Structures; Seismic Design; Behavior Factor; Probabilistic Analysis;Eurocodes; Pseudodynamic Tests

1. Introduction

Seismic design of structures is usually based on the results of elastic analyses under static

forces corresponding to the peak acceleration of the system subjected to the ground

motion and properly reduced to take into account the structural resources able to attenuate

the seismic effects (i.e., ductility, overstrength, damping, redundancy). According to

Eurocode 8 (EC8) [CEN-EN 1998-1, 2004], the static force F equivalent to seismic

action can be evaluated as follows:

F ¼ 2:5�g

qS�ðTÞW ; (1)

where W is the weight of the vibrating mass, ag = ag/g is the peak ground acceleration

(PGA) normalized with respect to the gravity constant g, S is the soil factor, Z(T) � 1 is

Received 22 October 2007; accepted 18 September 2008.

Address correspondence to Fabio Biondini, Department of Structural Engineering, Politecnico di Milano,

Piazza L. Da Vinci 32, 20133 Milan, Italy; E-mail: [email protected]

426

the decreasing function of the elastic response spectrum computed for the natural vibra-

tion period T of the structure, and q is a proper reducing behavior factor. This factor

simulates, in an overall way, the effects of plastic hysteretical dissipation of energy and

other nonlinearities of the structure under seismic events.

EC8 gives a set of q-factors related to the different types of structures, with their

potential capacity of energy dissipation conventionally evaluated on the base of the

ultimate failure mechanism. At present such q-values are defined more or less on the

basis of empirical choices, not supported by a rigorous investigation of sufficient relia-

bility, and are assumed to be independent from the type of ground motion as represented

by the specific response spectrum. This empirical procedure may obviously lead to

unjustified inequalities between different materials and structures. Therefore, there is a

need of a more accurate calibration of the behavior factors by also taking into account the

random nature of the seismic event.

In the old ENV version of EC8 (ENV 1998-1:1994) precast frames were penalized

by a lower q-factor with respect to cast-in-situ frames. This inequality resulted from a

wrong statement of the fundamental requirement for the structural ductility necessary for

energy dissipation: ‘‘An overall ductile behaviour is ensured if the ductility demand is

spread over a large number of elements and locations in the structure.’’ According to this

statement, the cast-in-situ monolithic frame shown in Fig. 1a should be characterized by

better seismic performance than the precast hinged frame shown in Fig. 1b, since the

critical zones where the energy dissipation takes place are four in the monolithic case and

only two in the hinged case. Contrary to this assumption, the actual behavior is that, under

the same seismic force, the monolithic arrangement of Fig. 1a, with four critical sections

dimensioned for a moment m @ Fh/2, may dissipate the same amount of energy which the

hinged arrangement of Fig. 1b dissipates in its two critical sections, dimensioned as they

are for a doubled moment M = Fh @ 2m (4u = 2U) [Biondini and Toniolo, 2000]. This

point of view is also reflected by the new statement included in the last version of EC8

[2004]: ‘‘An overall ductile behaviour is ensured if ductility demand involves globally a

large volume of the structure spread to different elements and location of all its storeys.’’

In fact, it is the global volume involved in dissipation, and not the number of plastic

hinges, that gives the total amount of energy dissipated by the structure.

In order to verify the accuracy of the design criteria proposed by EC8 for reinforced

concrete frame systems, this article presents a fully probabilistic approach for the

calibration of the behavior factors made through the comparison between the results of

the simplified design in which they are used, and the results of nonlinear dynamic

h

u

u

u

u

m m

m m

FF

UU

M M

F F

h

)b()a(

FIGURE 1 Energy dissipation in one-story frames: (a) monolithic and cast-in-situ;

(b) hinged and precast.

Seismic Design of Concrete Frames 427

analyses which should simulate the actual seismic behavior of the structure [Biondini and

Toniolo, 2002]. In particular, the attention is focused on the seismic performance of one-

story frames for industrial buildings, either cast-in-situ or precast. The seismic response

of two structural prototypes, a cast-in-situ monolithic frame and a precast hinged frame, is

compared for four levels translatory stiffness and seismic capacity. For these structures,

an incremental nonlinear dynamic analysis is performed within a Monte Carlo probabil-

istic simulation by taking the randomness of both the ground motion and the material

properties into account. The use of recorded accelerograms provided by strong motion

collections, as well as of artificial accelerograms properly generated to comply with

prescribed design response spectra, is also discussed [Biondini et al., 2001; Biondini and

Toniolo, 2003]. The whole process is repeated for the different types of response spectra

and, with each spectrum, for a set of different natural vibration periods, so to investigate a

wide range of structural solutions [Biondini and Toniolo, 2006].

The results of the probabilistic analysis are described in terms of ‘‘overstrength’’

ratio between the computed ultimate resistance and the seismic capacity deduced from

the EC8 design rules. The distributions of the overstrength show that precast structures

have the same seismic capacity of the corresponding cast-in-situ structures and highlight

a good accuracy of the design rules of EC8, even if some unreliable values of over-

strength are obtained for the higher vibration period and a noteworthy dependency of the

behavior factor from the prescribed response spectrum is pointed out.

The experimental verification of these theoretical results is searched for by means of

pseudodynamic tests on full-scale structures carried out at ELSA Laboratory of the Joint

Research Center of the European Commission at Ispra (Italy) within the scope of the

European research project ECOLEADER (2001–2003). Two structural prototypes con-

sisting of six-columns with two lines of beams and an interposed continuous slab have

been designed [Biondini et al., 2004]. The prototypes differ for the beam-column con-

nections only, made with monolithic joints for the cast-in-situ solution and with hinged

joints for the precast solution. The results of these tests confirm the overall equivalence of

the seismic behavior of precast and cast-in-situ structures.

The seismic behavior of precast structures with roof elements placed side by side and

lateral wall panel claddings is also investigated. To this purpose, two additional prototypes

have been designed and tested at ELSA Laboratory within the scope of the European

research project GROWTH (2002–2006). These prototypes are similar to the previous ones

and differ only for the orientation of the roof elements with respect to the direction of

the seismic action [Biondini and Toniolo, 2007; Ferrara et al., 2006; Kramar et al., 2006].

The results of these additional tests show that an effective horizontal diaphragm action can

be activated even if the roof elements are not connected among them. Moreover, they

confirm the expected good seismic performance of this type of precast systems.

2. Short Survey of European Codes

An overview of the seismic design criteria adopted for the type of buildings investigated

in this study is given with reference to the code provisions adopted by Eurocodes and

national codes of European countries particularly subjected to seismic risk.

As already pointed out, the new version of EC8 – Part 1 [EN1998-1:2004, 2004] in

Clause 5.11.1.4 gives to precast structures the same q-factors of cast-in-situ structures,

provided they have what in this survey we call ‘‘seismic connections’’ for the sake of

brevity. These connections, as regulated in Clause 5.11.2.1, are those ‘‘located away

from critical regions,’’ or ‘‘overdesigned’’ with respect to the critical regions, or with

‘‘energy dissipation’’ capacity. In particular, for ‘‘precast frame systems with hinged

428 F. Biondini and G. Toniolo

column-to-beam connections’’ a special requirement for the base supports is added in

Clause 5.11.3.2 (overdesigned pocket foundations).

In Portugal, precast integrated systems shall be certified by the National Laboratory

of Civil Engineering (LNEC). Precast structures designed by order do not need this

certification and are designed with the same rules of cast-in-situ structures. For both

precast and cast-in-situ structures, the q-factors are lower than those given in EC8.

However, within 2008 the EC8 should be adopted and the draft of the National Annex

equalises precast structures with ‘‘seismic connections’’ to cast-in-situ structures.

In Italy, a new code has been issued in 2008 (Technical rules for contructions – DM

14.01.2008). The seismic design rules of this code are very similar to those of EC8. Precast

structures are equalized to the cast-in-situ ones, with the addition of a specific type of ‘‘isostatic

frames’’ (frames with sliding column-to-beam bearings) which is penalized with a lower

q-factor. The other type of structures, including the hinged frames, have the same q-factors as

given by the EC8. The previous code (DM 16.01.1996) had no disequalities between precast

and cast-in-situ structures. For a short period (2003–2008), a provisional code for seismic

design (Ordinance PCM 3274) was in force, with rules that were very similar to those of EC8.

Slovenia has adopted Eurocodes as the only applicable codes since the beginning of

2008, and this includes the equalization between precast and cast-in-situ structures. For

one-story precast frames, design in high ductility class DCH is allowed only if the

‘‘column tops are connected along both the main directions.’’ In the other cases, special

tests are required, or the design shall be made in medium ductility class DCM. Before

2008, the Yugoslavian seismic design code YU1981 was used. In terms of seismic

equivalent forces, this code did not make differences between precast and cast-in-situ

structures. Tests were obligatory for ‘‘industrially produced prefabricated buildings,’’ or

precast integrated systems ‘‘produced in large series.’’

Since 2000, Greece has in force two codes—the seismic code EAK and the code for

reinforced concrete EKOS—which are very similar to the final version of EC8 and EC2,

respectively. For seismic design there are no disequalities between cast-in-situ and precast

structures with seismic connections. For both these types of structures the q-factors are lower

than those given by EC8. Since 1999, there is a special code for precast structures based on

the previous ENV version of the Eurocodes. For seismic design of hinged frames this code

gives a penalization of 2/3 in terms of q-factor. However, even though it is at present still

applied, this special code will be withdrawn when only the Eurocodes will be in force.

3. Measure of the Seismic Performance of Concrete Frames

3.1. Cast-In-Situ and Precast Structural Prototypes

The prototypes shown in Fig. 2 are considered, where (a) represents the typical arrangement

of a cast-in-situ monolithic frame, and (b) represents the typical arrangement of a precast

hinged frame. A span length of the beam l = 12.0 m is chosen for both the arrangements,

while two different cases are considered for the heights h of the columns. For the cast-in-situ

arrangement, a taller solution with h = 6.0 m and a lower solution with h = 5.0 m are firstly

selected. The heights h for the precast arrangement are then correspondingly chosen to

achieve the same vibration periods T of the cast-in-situ structures. The size and the

reinforcement of the columns vary for each type of frame over two levels of strengths as

indicated in Fig. 3, where the details of the cross sections are shown. Such cross sections are

proportioned in such a way that the two type of frames have approximately the same design

seismic capacity in terms of base shear strength. In addition, a minimum stirrups spacing of

3.5� is assumed and the shear reinforcement is chosen to achieve the same mechanical ratio


ow. Combined with the two heights, the four types of frames listed in Table 1 are selected for

each arrangement, which correspond to as many levels of translatory stiffness and seismic

capacity.

The beams are proportioned for the non seismic load conditions. In the cast-in-situ

arrangement the beam has flexural stiffness much larger than the columns and its resistant

moment at the ends remains larger than the ones at the connected columns. In this way,

with negligible rotations of the joints the structural systems are reduced to a single degree

of freedom model associated with the story drift d and controlled by the behavior of the

critical sections of the columns. By assuming a total weight 2W = 2 · 180 kN acting on the

frame, the axial force on each column is Nad = W = 180 kN. This may correspond to an in

plan mesh of 12 · 15 m covered by ordinary precast roof elements with 1.7 kN/m2 of dead

loads, or to an in plan mesh of 12 · 6 m covered by a cast-in-situ floor with 4.0 kN/m2 of

dead loads. The snow live load is not considered in the seismic combination of actions.

TABLE 1 Design data of the prototypes

Type

h

[m]

Mrd

[kNm] nd nEdy

[mm]

Frd

[kN]

k’[kNm2]

kd[kN/m]

T

[sec]

1a/tall 6.00 87.3 0.06 0.11 78.0 29.1 5739 289 1.58

1a/low 5.00 87.3 0.06 0.08 54.2 34.9 5739 515 1.19

2a/tall 6.00 171.2 0.04 0.04 47.5 57.1 18418 993 0.85

2a/low 5.00 171.2 0.04 0.02 33.0 68.5 18418 1732 0.65

1b/tall 5.56 171.2 0.04 0.12 81.7 30.8 18418 289 1.58

1b/low 4.64 171.2 0.04 0.08 56.8 36.9 18418 515 1.19

2b/tall 5.25 339.8 0.03 0.04 53.4 64.7 49511 993 0.85

2b/low 4.38 339.8 0.03 0.03 37.1 77.7 49511 1732 0.65

l

h h

l

(b)(a)

FIGURE 2 Prototypes of one-story frames: (a) monolithic and cast-in-situ; (b) hinged

and precast.

300 mm

300 8φ14

450 mm

300 8φ16

TYPE 1a TYPE 1b TYPE 2a

300

600 mm

8φ20

TYPE 2b3 0

0

450 mm

8φ161st.φ8/55 1st.φ8/45 1st.φ8/45 1st.φ10/65

FIGURE 3 Cross-section details of the columns (concrete cover 25 mm + �/2).


The principal structural and vibratory parameters are summarized in Table 1, where

[Biondini and Toniolo, 2000]:

� Mrd = Mrd(Nad) is the resistant moment of the section corresponding to the design

values of the material strengths fcd = fck / gc = 40/1.5 = 26.7 N/mm2 and fsd = fyk / gs

= 500/1.15 = 437 N/mm2;

� Frd = cMrd/h is the first order contribution of the shear force at the column base,

with c = 2 for the cast-in-situ frame and c = 1 for the precast frame (Fig. 4);

� nd = Nad/Nrd is the specific value of the design axial force Nad with respect to the

ultimate strength Nrd = Acfcd+Asfsd;

� nE = Nad/NE is the specific value of the axial action with respect to the critical load

NE @ 10k’(c/2h)2;

� dy = wyh2/3c is the first yield displacement, where the curvature wy is computed on

the cracked section with N = Nad and M = 0.75 Mrd;

� k’ is the flexural stiffness of the cracked cross-section;

� kd = 3c2 k’ / h3 - Nad / h is the traslatory stiffness of the column, inclusive of the

second order effects associated with the axial load Nad;

� T ¼ 2�ffiffiffiffiffiffiffiffiffiffim=k�

pis the first natural vibration period associated with the vibrating

mass m = W/g.

3.2. Modeling of Cyclic Behavior

The modeling techniques for nonlinear analysis of concrete structures are usually developed

in the context of finite element analysis and may refer to different levels of description

[CEB, 1996]. The more accurate modeling is developed at the material level. The structure

is subdivided in a proper number of finite elements whose characteristics are mainly

derived on the basis of the cyclic constitutive laws of the materials, concrete and steel. In

general, these models allow to accurately reproduce many aspects of experimental results,

and their use in seismic design can be very effective [Biondini, 2004]. However, due to the

high computational effort, the use of these models is not suitable when a large number of

analyses is involved, as it is usually required in probabilistic investigations aimed to

calibrate probability based design rules [Biondini and Toniolo, 2002, 2003, 2006]. In

such cases, more simplified models, characterized by a limited number of degree of

freedoms and able to catch the overall structural behavior, should be chosen.

Based on such considerations, a single degree of freedom model is adopted to

describe the behavior of the structural prototypes considered in the present investigation.

h

MV

Nadd

MV

(a)V

h

M(b)

Nd

V

ad

FIGURE 4 Traslatory behavior of (a) cast-in-situ and (b) precast columns.


With reference to the schemes shown in Fig. 4, this model relates the story drift d to the

first order contribution F of the shear force V at the base of the columns:

V ¼ F � Nad

hd; (2)

where F = cM/h is the force evaluated on the basis of the bending momentM of the critical

sections, with c = 2 for the monolithic arrangement of Fig. 4a, and c = 1 for the hinged

arrangement of Fig. 4b, and the negative term represents the second order effect associated

with the acting axial load Nad.

The cyclic model F = F(d) is based on the model proposed by Takeda et al. [1970],

completed with a final decreasing branch as suggested by Priestley et al. [1994] for wall

elements, and applied by Biondini and Toniolo [2000], to columns in flexure. The envelope

curve of the hysteretic cycles is shown in Fig. 5. The limit points of this curve correspond

respectively to the first cracking of the critical section, to the full yielding of the reinforce-

ment, to the spalling of the concrete cover, and to the failure of the concrete confined core.

The co-ordinates (Fi, di) of the limit points i = 1, . . ., 4 are computed as described in

Biondini and Toniolo [2000, 2006].

The slope of the descending end branch after point 4 has been empirically defined as

ku = – F2 / d2 and verified a posteriori by comparing the outcome of the analysis with the

results of experimental tests. This branch represents the failure process which leads to the

collapse of the structure, due to the fall of local flexural stiffness combined with the

increasing second order effects of the vertical load.

3.3. Incremental Non-Linear Dynamic Analysis

For the types of one-story frames considered in the present study, the nonlinear dynamic

analysis refers to a single degree of freedom model based of the following motion equation:

m€dðtÞ þ c _dðtÞ þ kðdÞdðtÞ ¼ �maðtÞ; (3)

where m is the vibrating mass, c is the viscous damping coefficient (assumed equal to the

5% of the critical one), k(d) is the degrading elastoplastic stiffness, and a(t) is the ground

acceleration. The static term is given by:

1

F

d1'

4

4'

2 3

2'3'

FIGURE 5 Cyclic model.


kðdÞdðtÞ ¼ VðdÞ ¼ FðdÞ � Nad

hdðtÞ; (4)

with F = F(d) deduced from the hysteretic model shown in Fig. 5.

The dynamic variation of the vertical loads during the earthquake is neglected. The

axial compression forces on the columns is consequently assumed equal to the static value

Nad. Moreover, since the analytical model considers only the flexural mode of failure of the

critical zones of the columns, it is assumed that shear failures and other types of failures,

such as those of joint connections, are avoided by proper capacity design.

A tangent representation of the static term V(d) = k(d)d(t) is adopted. The numerical

integration of the motion equation is performed by using the Newmark method

[Newmark, 1959] with b = 0.25 and g = 0.50 (mean acceleration method).

The incremental procedure, assumed for the definition of the ultimate capacity of the

structure, consists of the repetition, under a prescribed accelerogram a = a(t), of the

integration mentioned above, with intensities ag = ag/g increasing up to failure. Starting

from a basic value ag0, corresponding to the serviceability level of the structure, the

intensity ag is increased with small increments Dag so to catch, with adequate accuracy,

the ultimate capacity agmax of the structure, that is the ultimate response of stable vibratoryequilibrium before collapse. In the numerical analysis the collapse is pointed out by the loss

of vibratory equilibrium, with unlimited amplification of the displacements due to the

effects of the second order moments on the decreasing stiffness of the structure.

3.4. Overstrength Ratio

For a reliable calibration of the behavior factor q, a comparison shall be made between the

ultimate capacity calculated with the seismic design rules and the ultimate capacity tested on

the structure under the same seismic action. The tested capacity of the structure is assumed

to be the seismic intensity agmax at collapse obtained from the incremental dynamic analysis

procedure. The corresponding design seismic capacity agd is computed as follows:

�gd ¼ agd

g¼ qFrd

2:5S�W(5)

with:

Frd ¼ cMrd

h(6)

and where S is the soil factor and Z = Z(T) is the reduction function of the design responsespectrum:

�ðTÞ ¼ 1 for TB � T � TC

�ðTÞ ¼ TCT� 0:08q for TC � T � TD

�ðTÞ ¼ TCTDT2 � 0:08q for TD < T

: (7)

Table 2 gives the values of SZ associated to the four couple of prototypes for the soil

classes proposed by EC8. The corresponding values of the design capacity agd computedwith a behavior factor q = 4.5 are listed in Table 3.

It is worth noting the very high intrinsic design seismic capacity agd of the structureshere examined. This is due to the relevant attenuation of the vibratory response of the


more flexible proportioning and to the large overstrength of the stiffened proportioning.

In fact, the sizes and reinforcement deduced for the columns from the non-seismic

loading conditions (wind pressure or crane actions) are normally sufficient also for the

no-collapse verification under seismic conditions. Therefore, the threshold values given

to the story drift for the serviceability limit states, under the reduced action of the more

frequent earthquakes, usually govern the design of this type of structures.

The comparison between the results agmax of the numerical analyses and the com-

puted design capacity agd is made with reference to their ratio:

� ¼ �gmax

�gd

(8)

which will be called overstength ratio. A value k =1.0 would mean coincidence of EC8

design capacity and actual tested capacity, and values k � 1.0 are expected to verify the

reliability of the design rules.

4. Modeling of Uncertainty

For the evaluation of the seismic capacity a full probabilistic procedure based on the Monte

Carlo method is applied. To this aim, the randomness of both the seismic action and the

material properties are considered, since they are the parameters which lead to the larger

variability of the response. Smaller effects come from the variability of the geometric

dimensions of the structure which are taken here as deterministic, corresponding to the

design values used in calculation. Also the mass involved in the vibratory response is taken

as deterministic. Actually, the random variability of the mass could lead to significant

effects on the response, but in the present work it has not been investigated. Statistical

independence among the random variables is also assumed.

TABLE 2 Values of the coefficient SZ of the design response spectra Type 1 of EC8

Prototype A (S = 1.00) B (S = 1.20) C (S = 1.15) D (S = 1.35) E (S = 1.40)

1/tall 0.360 0.379 0.436 0.682 0.442

1/low 0.360 0.506 0.582 0.910 0.590

2/tall 0.468 0.702 0.808 1.264 0.820

2/low 0.618 0.928 1.067 1.350 1.082

TABLE 3 EC8 design seismic capacity agd of the prototypes

Prototype A B C D E

1a/tall 0.808 0.768 0.668 0.427 0.658

1a/low 0.970 0.690 0.600 0.384 0.592

2a/tall 1.219 0.812 0.706 0.451 0.696

2a/low 1.107 0.738 0.642 0.507 0.633

1b/tall 0.855 0.813 0.707 0.451 0.696

1b/low 1.025 0.730 0.635 0.405 0.626

2b/tall 1.383 0.922 0.802 0.512 0.790

2b/low 1.256 0.837 0.728 0.575 0.718


4.1. Randomness of the Material Properties

For concrete the randomness of the compression strength fc is modeled by a lognormal

distribution with characteristic value fck = 40 MPa (5% fractile) and standard deviation

s = 5 MPa.

For any random value fc, the limit strains, the tensile strengths, and the elastic

modulus are computed with:

fct ¼ 0:25f 2=3c (9)

fctf ¼ 1:3fct (10)

Ec ¼ 22000ðfc=10Þ0:3 (11)

"ctu ¼ fctf =Ec (12)

"c1 ¼ 0:20% (13)

"cu ¼ 0:35%: (14)

The concrete constitutive laws shown in Fig. 6a are assumed for sectional analysis at the

full yielding limit and ultimate collapse limit. The cyclic strength decay of the section at

the ultimate collapse limit is simulated by assuming the reduced strength f’c = fc/gc, with

c

f

f 'c

c

cεcuεε ε cuε∗ ∗c1 c1

cuε =ε ε /ε c1∗c1

∗cu

(a)

f

ε

s

s

y

yf '

ε = / Ey sy f

E =206000 MPas

(b)

FIGURE 6 Constitutive laws of the materials: (a) concrete and (b) steel.


gc = 1.5. Due to the low axial load acting on the columns, the effect of confinement on the

concrete strength is not considered. The ultimate strain "�cu of the confined concrete is

computed as a function of the stirrup mechanical ratio as follows [CEB, 1985]:

"�cu ffi "cu þ 0:05!w (15)

For reinforcing steel the randomness of the yielding strength fy is modeled by a

lognormal distribution with characteristic value fyk = 500 MPa (5% fractile) and standard

deviation s = 30 MPa.

For any random value fy, the constitutive laws described in Fig. 6b are assumed for

sectional analysis at the full yielding limit and the ultimate collapse limit. The cyclic strength

decay of the section at the ultimate collapse limit is simulated by asuming the reduced strength

f’y = fy/gs, with gs = 1.15.The material properties described above, with the related constitutive laws, are used

to define the limit points of the envelope curve of Fig. 5. The random variation of the

degrading stiffness model, consequent to the material variability, is shown in Fig. 7,

where the envelope curves for a sample of 100 couples of random values fc, fy, are drawn

for the frame type 2a/tall previously described.

4.2. Randomness of the Ground Motion

The choice of the input action for the dynamic analysis may be oriented to real accel-

erograms recorded during the earthquakes, or to artificial analytical simulations of the

ground motion. The use of these accelerograms in the present probabilistic investigation

is aimed at comparing the actual seismic capacity of the prototypes with the correspond-

ing value computed following EC8 design rules. To make this comparison possible, the

features of the input action should be consistent with the corresponding design models

assumed in the code.

Recorded accelerograms are available in large number in the database of specia-

lized institutions (see for example the European Strong Motion data base [2000] and

Strong Motion Collection [2000]). Figure 8 shows three of these accelerograms,

–100

–75

–50

–25

0

25

50

75

100

–1000 –750 –500 –250 0 250 500 750 1000Displacement d [mm]

For

ce F

[kN

]

FIGURE 7 Sample of 100 envelope curves of the cyclic model (prototype 2a/tall).


together with the corresponding elastic response spectra superimposed to EC8 spec-

trum for ground type A. Despite that these accelerograms have been chosen to comply

as best as possible with the target spectrum, their compliance is not sufficiently

accurate. In addition, from the whole database in Strong Motion Collection [2000],

only 65 accelerograms could be found with a reasonable minimum compliance. A

probabilistic analysis using this set of accelerograms has been attempted in Biondini

et al. [2001], but, as expected, the results showed a large scatter due to the limited

compatibility of the recorded ground motions with the response model assumed in

EC8, and the sample size was too small to allow a reliable statistical interpretation of

the results.

0.00–0.15

–0.10

–0.05

0.00

0.05

0.10

0.15

0.20

–0.15

–0.10

–0.05

0.00

0.05

0.10

0.15

0.20

10.00 20.00 30.00 40.00 50.00 60.

0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.

0.00 0.40 0.80 1.20 1.60 2.00 2.40 2.80 3.20 3.60 4.0

Time (sec)

Time (sec)

Time (sec)

0.00

0.30

0.60

0.90

1.20

1.50

1.80

2.10

2.40

2.70

3.00

0.00

0.30

0.60

0.90

1.20

1.50

1.80

2.10

2.40

2.70

3.00

0.00

0.30

0.60

0.90

1.20

1.50

1.80

2.10

2.40

2.70

3.00

0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 4.0

0.00 0.40 0.80 1.20 1.60 2.00 2.40 2.80 3.20 3.60 4.0

0.00 0.40 0.80 1.20 1.60 2.00 2.40 2.80 3.20 3.60 4.0

T(s)

T(s)

T(s)

0.25

0.20

0.15

0.10

0.05

0.00

–0.05

–0.10

–0.15

–0.20

–0.25

FIGURE 8 Sample of three recorded accelerograms a(t)/g and their elastic response

spectra Se(T)/ag [Strong Motion Collection, 2000].


Therefore, recorded accelerograms have the following main drawbacks:

� They are in general poor of frequency content and may lead, for the same value of

the peak acceleration, to much different responses of the structure.

� They have a rough compatibility with the response spectra of the code, and lead to

additional uncertainty in the comparison with the design rule.

� They form non homogeneous sets which are not suitable for a statistical elabora-

tion of the results.

� They are of insufficient numerousness for the computation of stabilized statistical

parameters of the structural response.

On the other hand, they properly reproduce the nature of the real earthquakes.

In order to overcome the drawbacks related to the use of recorded accelerograms,

artificial accelerograms can be generated so to match with good compatibility the

response spectrum of the code [SIMQKE, 1976]. The amplitude of the generated ground

motion follows an envelope curve with random duration of its phases (initial, stationary,

and descending), as shown in Fig. 9. The present application assumes a random duration

of the strong stationary phase uniformly varying in the range 1–20 s. The signal is a

composition of many sinusoidal harmonics where any single amplitude is chosen so to

match the prescribed response spectrum along the whole range of frequencies, while the

phase is a random variable. Figure 10 shows three of these accelerograms, generated

according with the EC8 spectrum for ground type A, together with the corresponding

elastic response spectra. The compliance of these accelerograms with the target design

model is, as expected, very good.

Therefore, the main features of artificial accelerograms can be summarised as

follows:

� They are rich of frequency content with a more defined response of the structure

for a given value of the peak ground acceleration.

� They can be generated so to match with good accuracy the response spectra of the

code and allow a reliable comparative verification of its design rules.

� They may have homogeneous features, through a wide random variation of the

shape parameters, so as to allow a proper statistical elaboration of the results.

� They may give sets of numerousness large at will following the requirements of

the statistical process.

For these reasons, despite that they are not fully realistic with respect to the nature of

actual earthquakes, artificial accelerograms are used in the present investigation.

I(t)

tttt0.05

321

1.0

s30 to5s20 to1s10 to2

23

12

1

===

−−

tttt

t

FIGURE 9 Envelope shape curve of ground motion.


5. Probabilistic Analysis

The probabilistic model is based on the material strengths with lognormal distribution and

the random sets of artificial accelerograms. A Monte Carlo simulation based on a sample

of 1,000 nonlinear analyses is carried out for each one of the five considered ground

types. The target of this analysis is to quantify the seismic capacity in terms of the

characteristic value of the peak ground acceleration of the ground motion which takes the

structure to the no-collapse limit state. The diagrams of Figs. 11–15 show the results of

these analyses in terms of overstrength ratio k as a function of the first natural vibration

period T of the structure. The five lines of each diagram refer the mean values m, to theboundaries m ± s of the standard deviation s, and to the extreme minimum and maximum

values found in the simulation process. Diagrams (a) refer to cast-in-situ monolithic

frame; diagrams (b) refer to precast hinged frames.

Moreover, as an example of the distribution features of these simulation results, Fig. 16

shows the density distributions of the overstrength ratio k for the prototype 1a/tall with

(a) ground type A and (b) ground type E. A lognormal model starting from a minimum

value kmin = m �3s represents with good accuracy these distributions and leads to the

following 5% and 10% fractiles: k0.05 = 1.13 and k0.10 = 1.18 for ground type A; k0.05 =0.79 and k0.10 = 0.85 for ground type E. Table 4 gives the maps of the corresponding

fractile values of the behavior factors q = 4.5k for all the examined cases. Finally, the

–1.0–0.8–0.6–0.4–0.20.00.20.40.60.81.0

0 5 10 15 20 25 30 35 40 45 500.0

0.5

1.0

1.5

2.0

2.5

3.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

–1.0–0.8–0.6–0.4–0.20.0

0.20.40.60.81.0

0 5 10 15 20 25 30 35 40 45 500.0

0.5

1.0

1.5

2.0

2.5

3.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

–1.0–0.8–0.6–0.4–0.20.0

0.20.40.60.81.0

0 5 10 15 20 25 30 35 40 45 500.0

0.5

1.0

1.5

2.0

2.5

3.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

a(t)

/ag

S e(T

)/a g

a(t)

/ag

S e(T

)/a g

a(t)

/ag

S e(T

)/a g

Time t T [sec]

FIGURE 10 Sample of three artificial accelerograms and their elastic response spectra.


validity of the simulation results with respect to the sample size is highlighted by the

diagrams of Fig. 17, which allow to verify the expected convergence towards stable values

of both the mean and standard deviation of the two distributions shown in Fig. 16.

The direct comparison of the results obtained from the probabilistic analysis proves

that precast structures have the same seismic capacity of the corresponding cast-in-situ

structures, with a very high correlation varying between 93% and 99%. The results also

confirm the overall goodness of the design criteria proposed by EC8, even if a noteworthy

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

5.00

0.60 0.80 1.00 1.20 1.40 1.60Period T [s]

Ove

rrst

reng

th κ

Ove

rrst

reng

th κ

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

5.00

0.60 0.80 1.00 1.20 1.40 1.60Period T [s]

µµ ± σmin/max

µµ ± σmin/max

(a) (b)

FIGURE 11 Statistical parameters of the overstrength ratio k for a ground type A

(response spectrum type 1): (a) monolithic prototype; (b) hinged prototype.

µµ ± σmin/max

µµ ± σmin/max

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

5.00

0.60 0.80 1.00 1.20 1.40 1.60Period T [s]

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

5.00

0.60 0.80 1.00 1.20 1.40 1.60Period T [s]

(a) (b)

Ove

rrst

reng

th κ

Ove

rrst

reng

th κ

FIGURE 12 Statistical parameters of the overstrength ratio k for a ground type B



dependency from the prescribed response spectrum is found. In addition, the analysis of

the results shows that for all ground types the overstrength systematically decreases with

the increasing of the vibration periods, down to values which are in some cases lower

than 1.0. This means that the design methods based on lump factors of force reduction are

not always reliable. They are not able to capture the dependence of plastic hysteretical

dissipation from the specific pattern of the response spectrum. Also, the correlation

µµ ± σmin/max

µµ ± σmin/max

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

5.00

0.60 0.80 1.00 1.20 1.40 1.60Period T [s]

(a) (b)

Ove

rrst

reng

th κ

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

5.00

0.60 0.80 1.00 1.20 1.40 1.60Period T [s]

Ove

rrst

reng

th κ

FIGURE 13 Statistical parameters of the overstrength ratio k for a ground type C


µµ ± σmin/max

µµ ± σmin/max

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

5.00

0.60 0.80 1.00 1.20 1.40 1.60Period T [s]

(a)

Ove

rrst

reng

th κ

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

5.00

0.60 0.80 1.00 1.20 1.40 1.60Period T [s]

(b)

Ove

rrst

reng

th κ

FIGURE 14 Statistical parameters of the overstrength ratio k for a ground type D



µµ ± σmin/max

µµ ± σmin/max

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

5.00

0.60 0.80 1.00 1.20 1.40 1.60Period T [s]

(a)

Ove

rrst

reng

th κ

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

5.00

0.60 0.80 1.00 1.20 1.40 1.60Period T [s]

(b)

Ove

rrst

reng

th κ

FIGURE 15 Statistical parameters of the overstrength ratio k for a ground type E


0.00

0.50

1.00

1.50

2.00

Overstrength κ0.00 0.80 1.60 2.40 3.20 4.00

Prob

abili

ty D

ensi

ty f

(κ)

(a)

0.00

0.50

1.00

1.50

2.00

Overstrength κ0.00 0.80 1.60 2.40 3.20 4.00

Prob

abili

ty D

ensi

ty f

(κ)

(b)

FIGURE 16 Example of density distributions of the overstrength ratio k (prototype 1a/tall):(a) ground type A; (b) ground type E.

TABLE 4 Fractile values of the behavior factors q = 4.5k

A B C D E

Prototype q0.05 q0.10 q0.05 q0.10 q0.05 q0.10 q0.05 q0.10 q0.05 q0.10

1a/tall 5.09 5.31 3.38 3.60 3.78 4.05 4.23 4.46 3.56 3.83

1a/low 4.28 4.50 4.01 4.28 4.37 4.64 4.82 5.09 4.32 4.59

2a/tall 5.45 5.76 5.54 5.90 5.99 6.39 6.66 7.02 5.94 6.35

2a/low 6.62 6.98 6.93 7.29 7.16 7.56 6.30 6.66 7.34 7.79

1b/tall 4.91 5.13 3.24 3.47 3.60 3.87 4.05 4.32 3.47 3.69

1b/low 4.14 4.37 3.83 4.10 4.14 4.41 4.64 4.91 4.14 4.41

2b/tall 5.00 5.31 5.00 5.36 5.45 5.81 5.99 6.35 5.36 5.76

2b/low 5.99 6.30 6.26 6.57 6.44 6.80 5.67 5.99 6.62 7.02


between the ductility factor and the behavior factor, based on the equal displacement

criterion, seems to be not fully verified.

However, with regard to these comments it is reminded that, to allow a proper

comparison of the results, the analyses for the different values of the vibratory stiffness

of the frames have been performed with the same mechanical ratio of transverse reinfor-

cement so to have the same degree of confinement of the concrete core. Starting from the

smaller section type 1a, a minimum diameter of stirrups of � = 8 mm has been taken

which leads, together with a spacing of 3.5�, to a high value ow @ 0.40 of the mechanicalratio, value which has been kept the same also for the other sections. For the larger

sections, this value is clearly not consistent with the detailing adopted in current practice

for this type of structures. Moreover, the specific values of axial force for larger sections

of the columns are rather low and not consistent with the ordinary situations. Without any

loss of validity of the results previously obtained, it is outlined that a further wider

investigation needs to be performed to cover all the field of practical applications.

6. Experimental Investigation

The experimental verification of the previous theoretical results is searched for by means

of pseudodynamic tests on full-scale structures. The pseudodynamic tests described in the

following have been performed at ELSA European Laboratory for Structural Assessment

of the Joint Research Center of the European Commission at Ispra (Italy).

6.1. Pseudodynamic Tests on Cast-In-Situ and Precast Frames

This experimental activity has been performed within the scope of the European research

project ECOLEADER (2001–2003). Two structural prototypes have been designed, both

consisting of six columns with height equal to 5.00 m, connected by two lines of beams

with span equal to 4.00 m, and an interposed slab with span equal to 3.00 m (Figs. 18 and

19). The overall size has been proportioned to the limits of the testing plant, reducing the

dimensions which do not have a relevant effect on the dynamic response (roof span and

beam length). The connections between columns and beams are made with monolithic

joints for the cast-in-situ prototype, shown in Fig. 18, and with hinged joints for the

precast prototype, shown in Fig. 19. Figure 20 shows some details of the testing plant.

The cross-sections of the columns and the joints details are shown in Figs. 21 and 22,

(a) (b)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 100 200 300 400 500 600 700 800 900 1000

Sample Size

Stat

istic

al P

aram

eter

s

Mean

Standard Deviation

Mean

Standard Deviation

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 100 200 300 400 500 600 700 800 900 1000

Sample Size

Stat

istic

al P

aram

eter

s

FIGURE 17 Evolution of the statistical parameters during the simulation process

(prototype 1a/tall): (a) ground type A; (b) ground type E.


FIGURE 18 Main dimensions of the cast-in-situ prototype with monolithic beam-column

connections.


FIGURE 19 Main dimensions of the precast prototype with hinged beam-column

connections.


(a)

(b) (c)

FIGURE 20 (a) Testing plant and location of the actuators. (b)-(c) Details of the

instrumentation at the base of the columns.


respectively. Steel class B500 and concrete strength class C40/50 have been used. The total

virtual weight of the deck is W = 720 kN. Such realistic weight is actually distributed as

axial actions on the columns by means of vertical jacks. The corresponding vibration period

of the frames is T = 1.02 s for the cast-in-situ arrangement, and T = 1.15 s for the precast

arrangement. The inertia forces are numerically simulated within the model governing the

pseudodynamic procedure, together with the related second order effects. More detailed

information about the testing set up can be found in Biondini et al. [2004].

The pseudodynamic test has been performed using an artificial accelerogram com-

patible with the EC8 response spectrum for ground type B (Fig. 23). Taking into account

the expected collapse limit agu, as computed by EC8 design rules, the following

three load steps have been scheduled: ag = 0.32 (0.33agu), ag = 0.64 (0.67agu), and

FIGURE 22 Joint detail for the precast prototype.

300 mm

300

8φ14

450 mm

300

8φ16

)b()a(

FIGURE 21 Cross-section of the columns for (a) cast-in-situ and (b) precast prototypes.


ag = 0.80 (0.83agu) for the cast-in-situ frame; ag = 0.36 (0.33agu), ag = 0.72 (0.67agu), andag = 1.08 (1.00agu) for the precast frame. Figure 24 shows a view of the prototypes during

the pseudodynamic tests.

From the large set of data recorded during the test, this article reproduces only the

force-displacement diagrams referred to the horizontal displacement of the upper deck

and the total force recorded by the actuators. Such diagrams are shown in Fig. 25 for the

three levels of seismic action.

The direct comparison of the cycles shown in Fig. 25 highlights the expected large

strength resources of this type of structures against seismic collapse and confirms the

overall equivalence of the seismic behavior of precast and cast-in-situ structures. It is

worth noting that at the third level for the precast prototype (ag = 1.08), the amplitude of

the motion took the jacks to the end of stroke and the test had to be stopped. However, the

maximum displacement of 400 mm was reached without any incipient decay of the

reaction force and the cover of the critical zones of the columns was still intact. The

structural collapse was still far.

6.2. Pseudodynamic Tests on Precast Frames with Side by Side Roof Elements

This experimental activity has been performed within the scope of the European research

project GROWTH (2002–2006). Two prototypes have been designed to investigate the

seismic behavior of precast structures with roof elements placed side by side. These

prototypes are shown in Figs. 26–29. They are similar to the precast prototypes previously

investigated, and differ only for the orientation of the roof elements with respect to the

seismic action. The axis of the roof elements and the direction of the seismic action are

parallel in the first prototype (Figs. 26 and 27), and orthogonal in the second one (Figs. 28

and 29). In the following, for the sake of synthesis these structures are referred as prototype 1

and prototype 2, respectively.

The typical connections adopted for precast one-story frames are reproduced. The

beam-column joint connections allow the relative rotation in the plane of the beam only.

Moreover, the beam-roof joint connections allow, in each one of the four supports of the roof

elements, the relative rotation in the vertical plane parallel to the axis of the roof elements.

The dead loads are the weight of roof elements (2.94 kN/m2), beams (6.95 kN/m),

columns (4 kN/m), and test devices (8.5 kN). The corresponding axial load at the base

of the columns is: N = 178.2 kN for central columns, and N = 99.1 kN for lateral

columns of prototype 1; N = 152.1 kN for central columns, and N = 100.6 kN for lateral

columns of prototype 2.

Time t [sec] Period T [sec]

a(t)

/ag

S e(T

)/a g

–1.00

–0.75

–0.50

–0.25

0.00

0.25

0.50

0.75

1.00

0.0 5.0 10.0 15.0 20.0 25.0 30.00.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0

FIGURE 23 Time-history and response spectrum of the artificial accelerogram used in

the pseudodynamic tests.


Figure 30 shows the geometry and the reinforcement layout of the column cross-

sections. Steel class B500 and concrete strength class C40/50 have been used.

Experimental tests carried out on specimens made with the adopted materials highlighted

for concrete a cubic compressive strength varying in the range 55–56.5 MPa, with mean

value of the cylindrical strength fc = 46 MPa, and for steel a yielding strength varying in

the range 532–576 MPa, with mean value fy = 555 MPa.

(a)

(b)

FIGURE 24 A view of the prototypes during the pseudodynamic tests: (a) cast-in-situ

frame; (b) precast frame.


The control of the pseudodynamic test is based on the two degree of freedoms

associated with the top horizontal displacements of the lateral frames, assumed to have

symmetric behavior, and of the central frame, respectively. Based on this assumption, for

prototype 1 a set of four actuators connected by spherical joints to the first and the last

roof element of each span has been used. Actuators in symmetric locations are enforced

to have the same displacements. For prototype 2, a set of two actuators, connected each

one at the midspan of the roof elements, has been used. Figure 31 shows a global view of

the two prototypes and of the corresponding testing plants. Further details on the testing

set up can be found in Ferrara et al. [2006].

The pseudodynamic tests are aimed to investigate the effectiveness of the horizontal

diaphragm action in both the configurations of the roof elements. A preliminary experi-

mental test aimed to investigate the role of lateral panels on the seismic response of

prototype 2 (Figs. 28 and 29), is performed. Actually, the two lateral supports provided by

the cladding panels, which are much stiffer than the central frame, take over most of the

horizontal force through a strong diaprhagm action which releases the central frame. The

Displacement [mm] Displacement [mm]

(a) (b)

-400

-300

-200

-100

0

100

200

300

400

-400 -300 -200 -100 0 100 200 300 400

Fo

rce

[kN

]

-400

-300

-200

-100

0

100

200

300

400

-400 -300 -200 -100 0 100 200 300 400

Fo

rce

[kN

]

-400

-300

-200

-100

0

100

200

300

400

-400 -300 -200 -100 0 100 200 300 400

Fo

rce

[kN

]

-400

-300

-200

-100

0

100

200

300

400

-400 -300 -200 -100 0 100 200 300 400

Fo

rce

[kN

]

-400

-300

-200

-100

0

100

200

300

400

-400 -300 -200 -100 0 100 200 300 400

Fo

rce

[kN

]

-400

-300

-200

-100

0

100

200

300

400

-400 -300 -200 -100 0 100 200 300 400

Fo

rce

[kN

]

ag = 0.32g ag = 0.36g

ag = 0.72gag = 0.64g

ag = 0.80g ag = 1.08g

FIGURE 25 Force-displacement diagrams of the pseudodynamic tests: (a) cast-in situ

frame; (b) precast frames.


(a)

(b)

FIGURE 26 Prototype with roof elements parallel to the direction of the seismic action

(prototype 1): (a) foundation plant; (b) roof plant.


results of this test, that for the sake of synthesis are not shown here, highlighted a very

high cooperation between frame and panels, with very limited cracking of the columns.

After the preliminary tests, a set of three pseudodynamic tests have been carried out

under the artificial accelerogram shown in Fig. 23 with increasing values of seismic

intensity ag = 0.14, 0.35, and 0.525. These values have been defined on the basis of the

EC8 design seismic capacity of the prototypes, computed as agu = 0.86 for prototype 1,

and agu = 0.93 for prototype 2. At the end of the pseudodynamic tests, both prototypes

have been subjected to a cyclic test under imposed displacements. The semi-amplitude of

the symmetric cycles started from the displacement limit associated with the first yielding

(a)

(b)

FIGURE 27 Prototype with roof elements parallel to the direction of the seismic action

(prototype 1): (a) frontal view; (b) lateral view.


(a)

(b)

FIGURE 28 Prototype with roof elements orthogonal to the direction of the seismic

action (prototype 2): (a) foundation plant; (b) roof plant.


(a)

(b)

FIGURE 29 Prototype with roof elements orthogonal to the direction of the seismic

action (prototype 2): (a) frontal view; (b) lateral view.

400 mm

400

8φ1640

φ8/75φ8/75

FIGURE 30 Geometry and reinforcement layout of the cross section of the columns.


(a)

(b)

FIGURE 31 Global view of the prototypes and of the testing plants. Roof elements with

axis (a) parallel and (b) orthogonal to the direction of the seismic action.


of reinforcement, approximately evaluated at the design stage as dy � 80 mm, and has

been increased by 40 mm after each sequence of three subsequent cycles up to collapse.

The measured top displacements of lateral and central columns resulted practically

coincident. Significant differences have been found only during the pseudodynamic tests

with ag = 0.525. This result confirms that double connections between beams and roof

elements (see Fig. 32) gives a rotational restraint which enables the activation of an

effective diaphragm action, even if the roof elements are not connected among them (see

Ferrara and Toniolo [2008]).

From the large set of recorded data, this article reproduces only the force-

displacement diagrams shown in Fig. 33. These diagrams refer to the total force recorded

in the actuators, and to the mean value of the displacements measured at the top of the

columns. It is worth noting that these displacements are sensibly smaller than the

corresponding displacements imposed by the actuators at the top of the roof.

The direct comparison of the cycles shown in Fig. 33 highlights the overall good

seismic behavior of both prototypes, with moderate damage and small residual deforma-

tions, at least for the first two levels of pseudodynamic tests. For the higher level, the

spalling of concrete cover with incipient buckling of the longitudinal bars placed on the

same side at the base of one central column occurred for prototype 1. This local damage

had a consequence on the global seismic behavior of the prototype during the subsequent

cyclic test. In fact, the results of this test show a non symmetric strength decay associated

with positive and negative displacements (Fig. 33.a). With this regards, as already pointed

out, it should be noted that a stirrup spacing equal 5�, as adopted for prototype 1 in thecritical zones at the base of the columns, is not sufficient to prevent the early rupture of

FIGURE 32 Detail of the double joint roof-to-beam connection.


the buckled bars during their reloading in tension. This experimental evidence was

already noted during some cyclic tests carried out on single columns [Saisi and

Toniolo, 1998], for which the obtained results indicated a limit spacing of stirrups

equal 3.5� in order to obtain a displacement ductility of 4.5 with a stable force response.

0 0

–120

–90

–60

–30

30

60

90

120

–60 –45 –30 –15 0 15 30 45 60

–100 –75 –550 –25 0 25 50 75 100

–160 –120 –80 –40 0 40 80 120 160

–400 –300 –200 –100 0 100 200 300 400

Forc

e [k

N]

–120

–90

–60

–30

30

60

90

120

–60 –45 –30 –15 0 15 30 45 60

Forc

e [k

N]

–180

–135

–90

–45

0

45

90

135

180

Forc

e [k

N]

–100 –75 –550 –25 0 25 50 75 100–180

–135

–90

–45

0

45

90

135

180

Forc

e [k

N]

–200

–150

–100

–50

0

50

100

150

200

Forc

e [k

N]

–160 –120 –80 –40 0 40 80 120 160–200

–150

–100

–50

0

50

100

150

200

Forc

e [k

N]

–220

–165

–110

–55

0

55

110

165

220

Displacement [mm]

Forc

e [k

N]

–400 –300 –200 –100 0 100 200 300 400–220

–165

–110

–55

0

55

110

165

220

Forc

e [k

N]

Displacement [mm]

(a) (b)

ag = 0.14 g ag = 0.14 g

ag = 0.525 g ag = 0.525 g

ag = 0.35 g ag = 0.35 g

FIGURE 33 Force-displacement diagrams of the pseudodynamic tests (ag = 0.14, 0.35,

and 0.525), and of the cyclic test. Roof elements with axis (a) parallel and (b) orthogonal

to the direction of the seismic action.


Based on these considerations, the stirrup spacing in the critical zones has been

reduced to 3.5� for prototype 2. This allowed to avoid the early failure of the compressed

bars during the pseudodynamic test with ag = 0.525, and allowed to obtain a subsequent

cyclic response more stable and characterized by higher dissipative resources (Fig. 33b).

For both prototypes a ultimate displacement du � 360 mm has been reached. With

reference to a yielding displacement dy � 80 mm, a global displacement ductility equal

4.5 is deduced, as assumed by EC8 for the behavior factor of frame systems.

6.3. Calibration of the Numerical Model

The results of the pseudodynamic tests have been used also to assess the accuracy of the

numerical model used in the dynamic analyses required by the probabilistic investigation.

A first calibration of this model has been performed with reference to the pseudodynamic

tests carried out on the first two prototypes, the cast-in-situ frame and the precast frame.

The results of this preliminary calibration showed a good accuracy of the numerical

model. Details on this calibration process can be found in Biondini and Toniolo [2003]. In

the following, the results obtained from the numerical simulation of the pseudodynamic

tests on the GROWTH precast prototypes with roof elements placed side by side are

presented [Biondini and Toniolo, 2007].

In the numerical model, the strength parameters have been introduced with their

actual mean values as tested in samples of the materials. The vibrating mass is m = 57912 kg.

Consistently with the physical behavior of the prototypes under the pseudodynamic tests

and with the control algorithm, a value c = 0 of the viscous damping has been assumed.

The limit points of the envelope curve of the hysteretic model used to evaluate the

degrading stiffness k = k(d) are defined with the previously introduced criteria. It is worth

noting that the co-ordinates of the first point, of great importance to achieve a proper

calibration of the model, have been defined by using a value of the secant elastic modulus

Ec* directly assessed on the experimental curves. By denoting Ec* = aEc, with Ec tangent

modulus evaluated as proposed by EC2, for the first two levels of the pseudodynamic

tests the values aI = 0.65 and aII = 0.40 for prototype 1, and aI = aII = 0.55 for prototype 2,have been adopted. For the third level, this point has been omitted since the critical

sections were already fully cracked. In addition, a posteriori calibration of the model

required to slightly modify the co-ordinate of the second point associated with the full

yielding force that, for all test levels, has been assumed equal to 90% and 80% of the

theoretical values for prototypes 1 and 2, respectively.

The good agreement between numerical and experimental results are shown in

Figs. 34 and 35, which give the vibration curves obtained for the three levels of

pseudodynamic tests in terms of displacements d = d(t) measured at the top of the

columns and total force F = F(t) recorded by the actuators. This comparison highlights

the effectiveness of the proposed global hysteretic model to reproduce with good

accuracy the overall structural behavior, particularly for the third level of the pseudo-

dynamic tests, which results are not affected by the large uncertainty associated with

the definition of the cracking limit point. This confirms the accuracy of the theoretical

model to evaluate the seismic capacity of the structure and, with it, the results of the

probabilistic investigation.

7. Conclusions

The seismic performance of one-story reinforced concrete structures for industrial build-

ings has been investigated. In the first part of the article it has been shown by a


probabilistic approach that precast structures have the same seismic capacity of the

corresponding cast-in-situ structures, with a very high correlation varying between 93%

and 99%. Moreover, the value 4.5 given by EC8 to behavior factor of frame systems has

been proven to be generally appropriate, even if a noteworthy dependency from the

specific response spectrum is found. For all ground types, its value systematically

–60

–45

–30

–15

0

15

30

45

60

0 5 10 15 20 25 30 35

0 5 10 15 20 25 30 35

0 5 10 15 20 25 30 35

Dis

plac

emen

t [m

m]

–60

–45

–30

–15

15

30

45

60

0 5 10 15 20 25 30 35

Dis

plac

emen

t [m

m]

ExperimentalNumerical

0


–140

–105

–70

–35

0

35

70

105

140

Dis

plac

emen

t [m

m]

0 5 10 15 20 25 30 35

0 5 10 15 20 25 30 35

–140

–105

–70

–35

0

35

70

105

140

Dis

plac

emen

t [m

m]



–200

–150

–100

–50

0

50

100

150

200

Time [sec]

Dis

plac

emen

t [m

m]


–200

–150

–100

–50

0

50

100

150

200

Time [sec]

Dis

plac

emen

t [m

m]


(a) (b)

ag = 0.14 g

ag = 0.525 g

ag = 0.35 g

ag = 0.14 g

ag = 0.525 g

ag = 0.35 g

FIGURE 34 Displacement time-histories d = d(t) for the thee levels of pseudodynamic

tests. Roof elements with axis (a) parallel and (b) orthogonal to the direction of the

seismic action.


decreases with the increasing of the vibration period, down to values which are in some

cases lower than 4.5. This means that the design methods based on lump factors of force

reduction are not generally reliable. They are not able to capture the dependence of

plastic hysteretical dissipation from the specific pattern of the response spectrum.

However, with this regards it is reminded that, to allow a proper comparison of the

–100

–75

–50

–25

0

25

50

75

100Fo

rce

[kN

]



–200

–150

–100

–50

0

50

100

150

200

Forc

e [k

N]



–200

–150

–100

–50

0

50

100

150

200

Time [sec]

Forc

e [k

N]


Time [sec]


(a) (b)

ag = 0.14 g

ag = 0.525 g

ag = 0.35 g

ag = 0.14 g

ag = 0.525 g

ag = 0.35 g

0 5 10 15 20 25 30 35

0 5 10 15 20 25 30 35

0 5 10 15 20 25 30 35–200

–150

–100

–50

0

50

100

150

200

Forc

e [k

N]

0 5 10 15 20 25 30 35

–200

–150

–100

–50

0

50

100

150

200

Forc

e [k

N]

0 5 10 15 20 25 30 35

–100

–75

–50

–25

0

25

50

75

100

Forc

e [k

N]

0 5 10 15 20 25 30 35

FIGURE 35 Force time-histories F = F(t) for the thee levels of pseudodynamic tests. Roof

elements with axis (a) parallel and (b) orthogonal to the direction of the seismic action.


results, the analyses for the different values of the vibratory stiffness of the studied frames

have been performed with the same mechanical ratio of transverse reinforcement so to

have the same degree of confinement of the concrete core. Moreover, for the larger

sections rather low values of axial force in the columns have been considered. Therefore,

without any loss of validity of the obtained results, a further wider investigation needs to

be performed to cover all the field of practical applications.

The second part of the article has been devoted to find an experimental verification

of these theoretical results by means of pseudodynamic tests on full-scale structures. The

results of these tests confirmed the overall equivalence of the seismic behavior of precast

and cast-in-situ structures. They also highlighted the good seismic performance of precast

structures with roof elements placed side by side, for which an effective horizontal

diaphragm action can be activated even if the roof elements are not connected among

them. Finally, the results of the pseudodynamic tests have been compared with those

obtained from dynamic nonlinear structural analyses, by obtaining a very good agreement

between numerical and experimental results. This successful comparison confirmed the

accuracy of the numerical model and, with it, the results of the probabilistic investigation

carried out for the calibration of the behavior factor.

In this article only the seismic capacity in terms of strength and ductility at the no-

collapse ultimate limit state (ULS) has been investigated and, to this requirement, the

behavior q-factor has been calibrated. However, it is worth noting that for the type of

structures of concern, as for other types of structures, in some conditions the damage limit

state (DLS) related to deformations might govern the structural proportioning. In such

cases, since the requirements related to both ULS and DLS have to be fulfilled with

proper separate verifications, an excess of structural strength can be achieved.

Acknowledgments

The present research has been performed within the scope of the European projects

ECOLEADER (contract No. HPRI-CT-1999-00059) and GROWTH (contract No.

G6RD-CT-2002-70002). The experimental pseudodynamic tests have been performed

at the ELSA Laboratory of the Joint Research Center of the European Commission at

Ispra (Italy) under the supervision of Dr. Paolo Negro, Dr. Georges Magonette, and Dr.

Javier Molina.

References

Biondini, F. and Toniolo, G. [2000] ‘‘Comparative analysis of the seismic response of precast and

cast-in-situ frames,’’ Studies and Researches, Graduate School for Concrete Structures,

Politecnico di Milano, 21, 1–17.

Biondini, F., Toniolo, G., and Tsionis, G. [2001] ‘‘Design reliability of cast-in-situ and precast

concrete frames under recorded earthquakes,’’ Studies and Researches, Graduate School for

Concrete Structures, Politecnico di Milano, 22.

Biondini, F. and Toniolo, G. [2002] ‘‘Probabilistic parameters of the seismic performance of

reinforced concrete frames,’’ 1st fib Congress, Paper E-228, Osaka, Japan, October 13–19.

Biondini, F. and Toniolo, G. [2003] ‘‘Seismic behaviour of concrete frames: experimental and

analytical verification of Eurocode 8 design rules,’’ fib Symposium on Concrete Structures in

Seismic Regions, Athens, Greece, May 6–9.

Biondini, F., Ferrara, L., Negro, P., and Toniolo, G. [2004] ‘‘Results of pseudodynamic test on a

prototype of precast R.C. frame,’’ International Conference on Advances in Concrete and

Structures (ICACS), Beijing-Xuzhou-Shangai, China, May 25–27.


Biondini, F. [2004] ‘‘A three-dimensional finite beam element for multiscale damage measure and

seismic analysis of concrete structures,’’ 13th World Conference on Earthquake Engineering,

Paper No. 2963, Vancouver, B.C., Canada, August 1–6.

Biondini, F. and Toniolo, G. [2006] ‘‘Probabilistic calibration of behaviour factor for concrete

frames,’’ 2nd fib Congress, Naples, June 5–8.

Biondini, F. and Toniolo, G. [2007] ‘‘Analisi teorico-sperimentale del comportamento sismico di

strutture prefabbricate,’’ XII Convegno Nazionale L’Ingegneria Sismica in Italia (ANIDIS

2007), Pisa, June 10–14 (in Italian).

CEB. [1985] Model Code for seismic design of concrete structures. Bulletin 165.

CEB. [1996] Reinforced concrete elements under cyclic loading. State-of-the-art report. Bulletin 230.

CEN-EN 1998-1: 2004 [2004] Eurocode 8: Design of Structures for Earthquake Resistance. Part 1:

General Rules, Seismic Actions and Rules for Buildings, European Committee for

Standardization, Brussels.

European Strong Motion database. [2000] Imperial College of London-UK, SOGIN and Servizio

Sismico Nazionale-I, ENEA-I, IPSN-F.

Fajfar, P., Banovec, J., and Saje, F. [1978] ‘‘Behaviour of a prefabricated industrial building in

Breginj during the Friuli earthquake,’’ 6th European Conference on Earthquake Engineering

(ECEE) 2, 493–500, Dubrovnik, September.

Fardis, M. N. [1994] ‘‘SOA lecture: Lessons learnt in past earthquakes,’’ 10th European Conference

on Earthquake Engineering (ECEE), 1, 779–788, Vienna, Austria, August 28-September 2.

Ferrara, L., Mola, E., and Negro, P. [2006] ‘‘Cyclic test on a full scale prototype of r/c one storey

industrial building,’’ 2nd fib Congress, Naples, June 5–8.

Ferrara, L. and Toniolo, G. [2008] ‘‘Design approach for diaphragm action of roof decks in precast

concrete buildings under earthquake,’’ fib Symposium ‘‘Tailor Made Concrete Structures: New

Solutions for Our Society,’’ Amsterdam, The Netherlands, May 19–22.

Kramar, M., Fishinger, M., and Isakovic, T. [2006] ‘‘Seismic vulnerability of the EC8 designed

columns in industrial buildings,’’ 2nd fib Congress, Naples, June 5–8.

Newmark, N. M. [1959] ‘‘A method of computation for structural dynamics,’’ ASCE Journal of the

Engineering Mechanics Division 85(3), 67–94.

Park, R. and Paulay, T. [1975] Reinforced Concrete Structures, John Wiley & Sons, New York.

Priestley, M. J. N., Verma, R., and Xiao, Y. [1994] ‘‘Seismic shear strength of R.C. columns,’’

ASCE Journal of Structural Engineering 120(8), 2310–2329.

Psycaris, I. N., Mouzakis, H. P., and Carydis, P. G. [2006] ‘‘Experimental investigation of seismic

behaviour of prefabricated rc structures,’’ 2nd fib Congress, Naples, June 5–8.

Saisi, A. and Toniolo, G. [1998] ‘‘Precast r.c. columns under cyclic loading: an experimental

program oriented to EC8,’’ Studi e Ricerche, School for Concrete Structures ‘‘F.lli Pesenti,’’

Politecnico di Milano, 19, 373–414.

SIMQKE, [1976] A Program for Artificial Ground Motion Generation. User’s Manual and

Documentation, NISEE, Department of Civil Eng., Massachusetts Institute of Technology.

Strong Motion Collection [2000] National Geophysical Data Center, Boulder, Colorado.

Takeda, T., Sozen, M. A., and Nielsen, N. N. [1970] ‘‘Reinforced concrete response to simulated

earthquakes,’’ ASCE Journal of the Structural Division 96(12), 2557–2573.


probabilistic calibration and experimental validation of...

Documents