Facolt di Ingegneria
L.M. in Ingegneria Civile per la Protezione dai Rischi Naturali
2 A.A. 2008-09
1.1 AIM OF THE WORK
The main purpose of this thesis is to create a model that could be representative of the
structure that will be tested so to forecast the results of the shaking table tests; at the same
time, because of that building is representative of the typical portuguese (but also italian)
constructions, the model created could also be considered a suitable tool for the structural
design with respect to the European Standards.
To reach this objective different types of model have been set and different types of
analysis have been run, how previously stated, to find a model that could be as reliable as
possible without being too much complex: in this direction, the possibility to use two
planar model because of the plan regularity of the structure is a first good step. Then it s
of main importance to check how much are the benefits of the triple strut model: namely
if the shear contribution that is taken into account is determinant for a shear failure of the
columns and if the global results are so different to justify the use this model.
To carry out both static and dynamic nonlinear analysis have been useful to understand
some remarkable aspects and to analyze the differences: with regarding to the
determination of the target displacement on the capacity curve (proceeding of pushover
analysis), could be interesting compare it with maximum displacement got by time-
history curve; it s also possible to evidence divergences or convergences on results of
interstorey drift calculated in the two analysis; moreover, to study the reliability of the
time-history analysis, different kind of accelerograms set have been used: artificial,
recorded unscaled, recorded scaled. Both in static and dynamic nonlinear analysis some
sensitive analysis have been carried out with the aim to calibrate parameters that are no
explicitly mentioned in the codes and to check the importance of other parameters that
control the accuracy of the results, so to get a good compromise between models
precision and reliability on one side, and models simplicity and computational time on
the other side.
The last goal of this work is to verify the safety assessments required by the Eurocodes,
and so understand if the use of reinforced panels, like the ones of the other two buildings
to be tested, are actually essential to a good structural design of the structures.
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L.M. in Ingegneria Civile per la Protezione dai Rischi Naturali
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1.2 THESIS LAYOUT
This thesis is divided into seven chapters and eight annexes.
Chapter 1 is a general introduction to the themes that will be dealt: the main topic is
described, the purposes of the work are set and a brief summary of the present job is
presented.
Chapter 2 presents the scaled building to be tested on the shaking table, its structural
design and the experimental equipment.
Chapter 3 discusses the features of the models used for pushover and time-history
analysis: after a short description of the finite element code DIANA, the strut models
used in the analysis, the elements properties adopted in the modelling phase, the materials
properties assumed, the vertical and horizontal loads applied to the structures, the
boundary condition imposed in the models and the meshing process are explained.
Chapter 4 deals with eigenvalue analysis: the modal properties are studied to analyze the
shape modes of the structure.
Chapters 5 argues about the results of the pushover analysis expressed in terms of
capacity curves, target displacement, interstorey drift and solicitations on the structural
elements, with comparisons between single and triple strut models; sensitive analysis
carried out to calibrate some parameters of the models are presented so to choose the
features of the models to be used in the furthers analysis.
Chapter 6 talks about the dynamic nonlinear analysis: the results are expressed now in
terms of time-history curves, maximum displacement and interstorey drifts: particular
attention is paid on comparisons between the results got from single and triple strut
models, from artificial and recorded accelerograms, and a general comparison is done
between pushover and time-history analysis.
Chapter 7 presents the conclusions of the thesis and the final considerations achieved,
giving some suggestion for further works on this topic.
Facolt di Ingegneria
L.M. in Ingegneria Civile per la Protezione dai Rischi Naturali
4 A.A. 2008-09
2 PRESENTATION OF THE EXPERIMENTAL TEST
How previously stated, three r.c. structures with masonry infills will be tested on the
L.N.E.C. s shaking table: one with unreinforced masonry infills (designed in according to
the portuguese codes with the purpose to be representative of the ordinary national design
practice in the period subsequent the came into effect of the codes) and the others with
two different kind of reinforced infills (designed in according to the Eurocodes with the
purpose to study new solutions in reducing the damages dued to seismic events): in this
work just the first structure is analyzed.
The buildings to be tested have been scaled 1:1.5 because of the shaking table s limits
(dimension and capacity) and because of the laboratory gates height. More detailed
references on the design phase of the buildings and on the relative pushover analysis
results can be found in Leite J. [2009]; this chapter aims just to resume the main
informations on the structure studied in the present thesis.
2.1 GEOMETRY OF THE STRUCTURE
The structure is a two-storey building, with an interstorey height of 3.00 m; the shorter
frame (5.70 m) has just one span, while the longer (6.45 m) has two spans.
Figure 2-1. Geometry of the structure s prototype (in metres)
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L.M. in Ingegneria Civile per la Protezione dai Rischi Naturali
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The criterion used to scale the building is the Cauchy s similarity law, a simple rule that
allows to scale all the physical parameters just by using a single number λ, the scale
factor of the model, in this case 1.5. In the following table relationship between the
prototype s variables and the scaled model s variables are presented.
Table 2-1. Scale factors of the parameters in according to the Cauchy s similarity law
Once that the similarity relationship have been decide set, the prototype could be scaled
and the dimension of beams, columns, foundations and infills have been fixed: so in the
model the beams have a section of 15 x 30 cm2, the columns of 15 x 15 cm2, the
foundation is an reversed T beam with an height of 30 cm, the slab has an height of 12
cm, and the infills are composed by a double leaf of hollow clay bricks with horizontal
perforations, the inner 7 cm depth and the outer 9 cm depth, with air space between the
two leaves. In the next figures the geometry of the scaled model and of its structural and
non-structural elements is presented.
Parameter Scale Factor
Length (L) LP / LM = λ
Area (A) AP / AM = λ2
Volume (V) VP / VM = λ3
Displacement (d) dP / dM = λ
Velocity (v) vP / vM = 1
Acceleration (a) aP / aM = λ-1
Mass (m) mP / mM = λ3
Weight (w) wP / wM = λ3
Density (ρ) ρP / ρM = 1
Force (F) FP / FM = λ2
Moment (M) MP / MM = λ3
Tension (τ) τP / τM = 1
Deformation (ε) εP / εM = 1
Module of elasticity (E) EP / EM = 1
Time (t) tP / tM = λ
Frequency (f) fP / fM = λ-1
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L.M. in Ingegneria Civile per la Protezione dai Rischi Naturali
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Figure 2-2. Geometry of the structure s scaled model (in metres)
Figure 2-3. Geometry of the infill s panels (in centimetres)
Figure 2-4. Detail of the infill in the column s zone (in centimetres)
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2.2 STRUCTURAL DESIGN
To get the solicitations values to be used in the design phase, a response spectrum
analysis with the software SAP2000 has been carried out a 3D model of the building:
frame elements have been used to represent beams and columns, diagonal frame element
have been also choose to replace the infills, and rigid diaphragms have been set in
correspondence of the slabs to simulate their real behaviour regarding to the
displacements.
The vertical loads have been applied to the beams. Regarding to the spectrum employed
(just the horizontal components have been used [EN 1998-1:2003 4.3.3.5.2]) the
portuguese code, like also EC8 does, defines two kind of spectra to use: a closer and a
farer one; in both cases, the parameters required to characterize the spectra are: the return
period that characterizes the considered limit state (475 years because the L.S. of
Significant Damage is supposed to be the most suitable for the investigated kind of
building [EN 1998-3:2003 2.1]), the zone in which the building is located (Lisbon), the
ground type of that zone (very consistent soil); then spectra s acceleration have been
divided for a behaviour factor that take into account the linearity of the analysis and the
energy dissipation capacity (also EC8 requires that, but sets this parameter is a different
way). Obviously, all the loads have been scaled in according to the Cauchy s similarity
law.
The values of bending moment and shear force obtained from that analysis, and used to
design the reinforcement of the structural elements, are perfectly scaled as shown from a
comparison with the analysis results in SAP2000 of the building s prototype. The
materials used in the design phase are those, within the portuguese code s ones, that are
supposed to be the most representative of the constructions that the building object of this
work aims to represent. In the ANNEX 1 it s possible to look at the detailed structural
design of the building.
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L.M. in Ingegneria Civile per la Protezione dai Rischi Naturali
8 A.A. 2008-09
2.3 TEST EQUIPMENT
The division of L.N.E.C. that deals with experimental researches in the seismic field is
the N.E.S.D.E. (Earthquake Engineering and Structural Dynamic Division). Within that
section a triaxial shaking tables is present. It s one of the most capable existing in a civil
engineering laboratory and it s dated 1995: it s a 4.6 x 5.6 m 2 steel shaking table, with a
392 kN maximum load capacity; the actuators system is hydraulic, while the control s
type is mixed analogue-digital.
Besides the platform s dimensions, the other feature that make this shaking table so
performing is the earthquake motions severity that is capable to apply to the specimens
(maximum nominal acceleration values: aTRASV = 15 m/s2, aLONG = 25 m/s2, aVERT = 7.5 m/s2;
maximum nominal velocity values: vTRASV = 70.1 cm/s, vLONG = 41.9 cm/s, vVERT = 42.4 cm/s).
To access the laboratory there are two gates, whose height is 4.5 m.
The building objective of the present thesis was built outside and later moved by bridge
cranes (maximum load 392 kN, useful height 8.0 m) on the shaking table where it was
fixed by metallic tubes inserted in holes presents on the platform, and hence realized also
on the structure s foundation.
All the references on the datas exposed in this paragraph and on more other datas can be
found in http://www.lnec.pt.
Figure 2-5. Scheme of the shaking table
Facolt di Ingegneria
L.M. in Ingegneria Civile per la Protezione dai Rischi Naturali
A.A. 2008-09 9
3 FEATURES OF THE MODELS
A presentation of the software employed in the analysis it was supposed to be useful to
the reader: so, the first paragraph of the present chapter is dedicated to provide a general
approach of what the finite element code DIANA is, to present its main features, the
fields of application in which is most applied, its basic principles and its scheme of work.
Next, the two types of models used to represent infilled frames (local and global models)
are discussed, arguing on their features and on their suitability in characterizing the main
problems present in the kind of construction objective of this thesis: particular attention is
paid in presenting the two global models adopted (single and triple strut model).
Hence, the geometry of the models is described in detail: the element types chosen, the
cross-section assigned and the integration schemes adopted.
In the following paragraph, the mechanical characteristics of concrete, masonry and steel
are examined, paid particular attention on their nonlinear behaviour.
Then, the vertical and horizontal loads assigned to the models are discussed, explaining
the difference between horizontal loads for pushover and for time-history analysis.
The last two paragraphs briefly summarize the boundary conditions applied to the models
and the meshing procedure.
3.1 DIANA FINITE ELEMENT CODE
DIANA is a multi-purpose finite element code, based on the displacement method. It has
been under development at TNO since 1972. In the beginning of 2003 a new organisation
around DIANA was founded: TNO DIANA bv.
DIANA is a well proven and tested software package with a reputation for handling
difficult technical problems relating to various design and assessment activities: civil,
mechanical, biomechanical, and other engineering problems can be solved with the
DIANA program. Standard application work includes: concrete cracking, excavations,
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L.M. in Ingegneria Civile per la Protezione dai Rischi Naturali
10 A.A. 2008-09
tunnelling, composites, plasticity, creep, cooling of concrete, engineering plastics, various
rubbers, groundwater flow, fluid-structure interactions, temperature-dependent material
behaviour, heat conduction, stability analysis, buckling, phased analysis, etc. The
program s robust functionality includes extensive element, material and procedure
libraries based on advanced database techniques, linear and non-linear capabilities, full
2D and 3D modelling features and tools for CAD interoperability.
Concerning the element types, DIANA offers a great variety of this, such as beams
(straight and curved), solids, membranes, axisymmetric and plane strain elements, plates,
shells, springs, and interface elements (gap). All these elements may be combined in a
particular finite element model.
Relating to the material models, here the most important are presented: elasticity (linear
isotropic and orthotropic elasticity, nonlinear elasticity, hyper-elasticity, visco-elasticity,
regular plasticity, orthotropic plasticity, visco-plasticity); cracking (smeared crack, total
strain fixed and rotating crack); soil mechanics (initial stress ratio, undrained behaviour,
liquefaction); interface nonlinearities (discrete cracking, crack dilatancy, bond-slip,
friction, nonlinear elasticity, and a general user-supplied interface model); user-supplied
(to let the user specifies a general nonlinear material behaviour).
The wide range of analysis modules includes: linear static analysis, nonlinear analysis,
dynamic analysis, Euler stability analysis, potential flow analysis, coupled flow-stress
analysis, phased analysis, parameter estimation and lattice analysis.
Nevertheless, one of the most notable benefits is its power in the field of concrete and soil
where excellent material models are available, developed by researchers in the
Netherlands since the early 1970’s: most notably are the models for smeared and discrete
cracking, and for reduction of prestress due to special effects. For the design and
assessment of concrete and reinforced concrete structures, DIANA offers a wide range of
material models for the analysis of the non-linear behaviour of concrete, which comprises
cracking, crushing and shearing effects in cracks and joints, special techniques for
modelling reinforcement and prestressed cables, determination and integration of creep
and shrinkage and advanced solutions for the analysis of young hardening concrete.
A.A. 2008
Moreover, special elements may be used to model embedded reinforcement in concrete
structures: bars, grids and prestressed
a built
The architecture of the DIANA system, as seen from the user’s point of view consists of a
number of
Each module
module INPUT (
data communication with a central database, the FILOS file. After the analysis DIANA
can produce
To have access to this software architecture, there are t
interface
supplied subroutines
an input data file; furthermore, analysis co
analysis should be performed; DIANA will then load the appropriate modules to perform
the analysis; output can be obtained in tabular form for printing or viewing.
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-in pre-processor in which reinforcement can be defined globally.
modules
fulfils
output of the analysis results.
, an interactive graphical
, indicated with
a clearly defined task in the Finite Element Analysis. For instance,
M1) reads the description of the finite element model. All modules have
. In the batch interface the user defines the finite element model via
L.M. in Ingegneria Civile per la Protezione dai Rischi Naturali
M1
Figure 3-1.
user
cables. To model these reinforcements DIANA has
to Mn in Figure
DIANA program architecture
interface (GUI), and an interface with
mmands must be supplied to indicate how the
3.1.
hree basic user
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-interfaces: a
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batch
user-
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L.M. in Ingegneria Civile per la Protezione dai Rischi Naturali
12 A.A. 2008-09
The interactive graphics interface, called iDIANA, is a fully integrated pre- and post-
processing environment to DIANA: the user has to specify the basic model geometry,
loading, materials and other data interactively; this data is stored in a database for pre-
processing from which iDIANA can automatically generate the finite element model in
the form of the input data file: moreover, the necessary analysis commands may be
generated via user-friendly interactive forms; analysis results are written to a database for
interactive post-processing and may then be presented in various styles like coloured
contour plots, diagrams, tables etc. Finally, DIANA offers a user-supplied subroutine
option to the advanced user, with skill in programming; via this option the code of various
subroutines with pre-defined arguments may be supplied to define special material
models, interface behaviour, etc.
All the references on the informations exposed in this paragraph about DIANA features
can be found in http://www.tnodiana.com and in Manie J., Wolthers A. [2008].
3.2 STRUT MODELS
Many years of researches and experimental tests in the field of infilled frames consent to
asses that the influence of the infills on response of r.c. structures subjected to lateral
loads isn t negligible, on the contrary of what in the common structural design is assumed
up to now.
However, there are some problems to understand the interaction between the infills and
the boundary frame, and this is one of the main reason that led the researchers to propose
several models to try to fit the experimental results; is possible to divide these models into
two big classes: the local models (where the infills are modelled adopting discrete or
continuum models for masonry) and global models (where the infills are replaced by
single or multiple compression strut).
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Figure 3-2. Global models (a) and local models (b) for infilled structures
How previously stated, the main aspect that affects the characterization of the infilled
frames under seismic loads is the interaction between the infills and the boundary frames;
experimental evidences have shown that the phenomena is influenced essentially by the
strength of the two materials, concrete and masonry, and by the level of horizontal load
applied to the structure: so it s possible to analyze the pre-peak phase by dividing it into
three stages. At the beginning, when low forces (and thus low deformations) are applied,
there is no separation between the boundary frames and the wall (if there are no gaps
between the two component), and its contribute in terms of stiffness is very high: this
stage lasts just for very low values of load, and so it s supposed to be no such essential.
Successively, when forces start to increase to consistent values, a separation occurs
between the wall and the frames (both columns and beams), and so the resistant
mechanism of the infills becomes very similar to a compression strut, with compressive
stresses concentrated at the compressed corner and rapidly decaying in the central zone:
in this stage there is a quite small energy dissipation because cracking is still not reached.
Finally, once the crack strength has been reached, two cases are possible: shear collapse
in the concrete element if the infill is very resistant and the frame is very poor detailed, or
diffusion of the cracks in the infill panel with consequent growth of energy dissipation in
hysteretic cycles; three types of crack pattern have been in the most of the experimental
tests: horizontal slip crack (when the mortar is very weak), diagonal cracks (stair-step
configuration when the bricks are very strong or diagonal configuration when also the
mortar is of good quality), corner crushing (when both masonry and frame are strong, and
the strut failure mechanism is so fully developed).
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