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Institute for the Protection and Security of the Citizen
European Laboratory for Structural Assessment (ELSA)
I-21020 Ispra (VA), Italy
Seismic Assessment of a
Reinforced Concrete Block Masonry House
PROARES Project in El Salvador
Armelle Anthoine, Fabio Taucer
2006
EUR22324 EN
Institute for the Protection and Security of the Citizen
European Laboratory for Structural Assessment (ELSA)
I-21020 Ispra (VA), Italy
Seismic Assessment of a
Reinforced Concrete Block Masonry House
PROARES Project in El Salvador
Armelle Anthoine, Fabio Taucer
2006
EUR22324 EN
LEGAL NOTICE
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acting on behalf of the Commission is responsible for the
use which might be made of the following information.
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It can be accessed through the Europa server
(http://europa.eu.int)
EUR22324 EN
ISSN 1018-5593
© European Communities, 2006
Reproduction is authorised provided the source is acknowledged
Printed in Italy
Abstract
The report deals with the evaluation and assessment of the seismic performance of the
reinforced masonry house proposed by PROARES (Programa de Apoyo a la Reconstruccion
de El Salvador) for the construction of new houses in the areas that were mostly affected by
the earthquakes of 2001 in El Salvador. The study relies on nonlinear dynamic finite element
numerical analyses. On the basis of the drawings and data provided by FONAVIPO (Fondo
Nacional de la Vivienda Popular), a finite element model of the house has been generated
and submitted to a set of artificial acceleration time histories compatible with the response
spectrum specified by the Norma Técnica para Diseño por Sismo isued by the Ministry of
Public Works of the Republic of El Salvador. The numerical results show that the seismic
behaviour of the house is adequate provided that the anchorage of the metallic supports
normal to the plane of the masonry walls is improved. Additional recommendations aiming at
improving the construction quality are also addressed.
Acknowledgements
The authors wish to acknowledge their gratitude towards the personnel of FISDL and
FONAVIPO for their availability in providing all the necessary information for the preparation
of the present report, as well as for their assistance during the field visits to El Salvador.
The support of the European Technical Assistant for PROARES, Hossein Asgarián, is also
greatly appreciated, especially for providing to the JRC all the necessary material for
completing this report and for acting as liaison with the Governmental Institutions of El
Salvador.
Table of Contents
1
Introduction..........................................................................................................1
2
Description of the Structure ...............................................................................3
2.1
Geometry ........................................................................................................3
2.2
Detailing ..........................................................................................................8
2.3
Material Properties ........................................................................................16
2.3.1
Concrete Hollow Masonry Units .............................................................17
2.3.2
Mortar .....................................................................................................18
2.3.3
Masonry..................................................................................................18
2.3.4
Concrete .................................................................................................19
2.3.5
Grout.......................................................................................................19
2.3.6
Steel Reinforcement ...............................................................................19
2.3.7
Cold-Formed Members...........................................................................20
2.3.8
Anchorage of Single Channel Sections P1.............................................21
2.3.9
Anchorage of Double Channel Sections P2 ...........................................22
2.3.10
3
Loads ..................................................................................................................25
3.1
Dead Loads...................................................................................................25
3.2
Earthquake Loads .........................................................................................25
3.2.1
Response Spectrum ...............................................................................25
3.2.2
Acceleration Time Histories....................................................................26
3.3
4
Zinc-Aluminium Corrugated Roof ........................................................23
Load Combinations .......................................................................................28
Numerical Model of the Structure ....................................................................29
4.1
Mesh .............................................................................................................29
4.1.1
Masonry Walls ........................................................................................29
4.1.2
Reinforced Concrete Elements (SF-1, T1, C1, SC)................................29
4.1.3
Reinforced Masonry Elements (SU) .......................................................30
4.1.4
Distributed Vertical Steel Reinforcement................................................30
4.1.5
Distributed Horizontal Steel Reinforcement............................................31
4.1.6
Channel Sections (polines) P1 and P2...................................................31
4.1.7
Steel Tensors (templetes) ......................................................................32
4.1.8
Roof ........................................................................................................32
4.2
4.2.1
Masonry..................................................................................................34
4.2.2
Concrete and Grout (in SF-1, T1, C1, SC and SU) ................................35
4.2.3
Steel Reinforcement (for concrete and masonry)...................................36
4.2.4
Channel Sections and Tensors ..............................................................36
4.2.5
Roof ........................................................................................................36
4.3
5
Boundary Conditions.....................................................................................37
Modal and Nonlinear Time History Analyses..................................................39
5.1
Original structure...........................................................................................39
5.1.1
Modal Analysis .......................................................................................39
5.1.2
Gravity Loads .........................................................................................40
5.1.3
Seismic Loads ........................................................................................41
5.2
6
Models and Materials ....................................................................................34
Structure without the P2 Anchorage .............................................................45
5.2.1
Modal Analysis .......................................................................................45
5.2.2
Gravity Loads .........................................................................................46
5.2.3
Seismic Loads ........................................................................................46
5.2.4
Ultimate Load .........................................................................................49
Conclusions and Recommendations ..............................................................51
6.1
Anchorage of the P2 Double Channel Sections............................................51
7
6.2
Vertical Reinforcement..................................................................................51
6.3
Realization of the Joints between Structural Elements .................................51
6.4
Alternative Anchorage of the Roof Support...................................................51
6.5
Anchorage of the Vertical Reinforcement at the Top Beams ........................52
6.6
Realization of the Corners ............................................................................52
References .........................................................................................................57
1
1 Introduction
The European Union (EU) is one of the major actors in International co-operation and
development assistance, providing along with Member States 55% of total International
Official Development Assistance (ODA) and more than two thirds of grant aid. In this context,
the European Commission (EC), through the Europe-Aid Cooperation Office (AIDCO)
established a Co-operation Project in 2002 with a contribution of 25 million euro to the
Government of El Salvador for the construction of approximately 6000 new houses for the
recovery of the population affected by the January and February earthquakes of 2001.
The Co-operation project involves the participation of Institutions form El Salvador
Government, namely the El Salvador Social Investment Fund (FISDL) and the Popular
Housing National Fund (FONAVIPO), who are responsible for the implementation and
execution of the project. The progress and fulfilment of the project is monitored by the EC
Delegation in Managua, who is interested in maintaining a high standard of the quality of the
project.
In this framework the Joint Research Centre (JRC) of the EC offered Scientific and Technical
(S&T) support to the EC Delegation to assess the seismic performance of the new houses
constructed under the co-operation project.
The designs proposed for the project consisted of two building types, a reinforced concrete
block masonry (RCBM) house (Fig. 1-1), and a reinforced concrete (RC) prefabricated house,
with an area of approximately 36 m2 for a family of four to be constructed in rural and semirural areas. The designs were produced at a preliminary stage by FONAVIPO and their
construction was contracted to NGOs and other contractors from El Salvador, who are
responsible for the production of executive drawings that included construction details and
eventual variations from the preliminary design.
Fig. 1-1 Reinforced concrete block masonry house
The S&T support given by the JRC consisted in assessing the seismic performance of the two
building types, in order to determine the level of damage sustained at earthquakes of
increasing intensity, and propose eventual modifications and/or additions to improve
performance, especially for those houses presently under construction.
The intervention of the JRC is considered of outmost importance, as many of the details and
modifications proposed by the contractors are not always reviewed by the Governmental
institutions, and construction details are not always executed as indicated in plans.
In the following paragraphs, an overview of the contents of the different chapters comprising
the present report is given.
2
Chapter 2 deals with the description of the structure. This includes the design plans and
elevations of the house, the detailing of the members sections and connections as well as the
material characteristics of the materials and components. Most of these data have been
provided by the designer. However some missing material/component properties have been
derived according to the Uniform Building Code - UBC [1].
Chapter 3 describes the loads against which the structure will be assessed: gravity loads and
earthquake loads. The latter have been generated according to the El Salvador design norm
[2] , while their combination conforms to the UBC.
The numerical
meshes of the
the associated
At each step,
justified.
model of the structure is described in Chapter 4. First, the finite element
sub-structures are built and assembled. Then the finite element models and
material parameters are given. Finally the boundary conditions are specified.
the chosen hypotheses (type of finite element, material models, etc.) are
The results of the numerical analyses are presented in Chapter 5. After a preliminary modal
analysis, aiming at determining the fundamental modes and frequencies of the structure, the
full nonlinear dynamic response of the structure to the design earthquake is computed and
examined. Such analyses are carried out twice, with and without bonding between the double
channel sections (polines) and the top beams, because this connection plays a key role but is
not designed adequately.
Conclusions are drawn in Chapter 6 and several recommendations/suggestions concerning
the design and the construction of the structure are provided.
3
2 Description of the Structure
2.1
Geometry
The structure of the house has a square base, with sides of 5.85 m measured from centre to
centre of the exterior walls. For reference, axes 1, 2, 3 and A, B, C are defined along the two
orthogonal directions of the structure, creating four areas within the plan of the house with
dimensions of 2.80 m x 2.80 m, 2.80 m x 3.05 m and 3.05 m x 3.05 m, as shown in Fig. 2-1.
The external walls run along all the sides of the square plan of the structure, other than along
axis A, between axes 1 and 2, and along axis 1, between axes A and B, thus leaving an open
space for a veranda framed by reinforced concrete members. The veranda is flanked at the
interior side by masonry walls running along axis 2 and axis B, with an entrance door at the
intersection of the two axes. Window openings of 0.80 m x 1.00 m are provided along the
walls of axes 1, 3, A and C, with the main entrance door of dimensions of 0.80 m x 2.00 m
located at the wall along axis C. The geometry of the masonry walls along axes 1, 2, 3, and A,
B, C and 2-B is shown in elevation in Fig. 2-2, Fig. 2-3, Fig. 2-4, Fig. 2-5, Fig. 2-6, Fig. 2-7
and Fig. 2-8.
To prevent excessive out-of-plane displacements of the long walls (along axis C and 3), a
steel box section (built-up from two welded steel channel sections), denominated in the
drawings as Polín P2, connects the top centre of each long wall to the top corner of the
perpendicular wall standing in front (resp. of axis 2 and B). The two double channel sections
follow the roof surface (horizontal along axes 2, sloping up and down along axis B) and thus
cross in the middle of the house (the channel section along axis B is cut and welded on the
channel section along axis 2).
The design plan of the roof structure is shown in Fig. 2-9. The roof cover is made of a
lightweight zinc-aluminium corrugated plate, with channels sloping down orthogonal and away
from the centreline defined by axis 2 (called cumbrera). The roof cover is supported onto eight
channel section steel members (called polín P1) running parallel to axis 2 and supported onto
the walls of axis A, B and C, on the reinforced concrete beam of the veranda along axis A and
on the double channel section along axis B. The polines P1 are spaced at 0.87 m between
axes 1 and 2, and at 0.98 m between axes 2 and 3. They are stiffened by two lines of tensors
running parallel to and in-between axes A & B and B & C respectively. Along axis B, the
polines P1 are imbedded in the masonry wall or welded to the polín P2, making superfluous
the addition of tensors along this axis.
The masonry walls have a nominal width of 15 cm, with bond beams (denominated in the
drawings as SU) running horizontally below and above the window openings, next to the
base, at the top of walls and along the eaves of the sloping roof. The reinforced concrete
beam and column members that frame the veranda, denominated in the drawings as SC and
C-1, have cross sections of 15 cm x 20 (height) cm and 20 cm x 20 cm respectively.
The masonry walls of the structure rest on a continuous reinforced concrete strip footing
beam with a base of 30 cm and a height of 25 cm (SF-1 in the drawings). The reinforced
concrete column C-1 is supported by a 20 cm deep, 80 cm x 80 cm, reinforced concrete
footing, at 0.35 m below the bottom surface of the foundation beam. The foundation beams
are connected to the column by a 20 cm x 25 cm (height) reinforced concrete tensor T-1. The
bottom of the footing rests at 0.90 m below ground level, while the surface of the interior of
the house is filled to a level of 0.10 m above the ground.
The height of the structure varies according to the axis of reference as a function of the
sloping of the roof, from a minimum of 2.80 m (axes 1 and 3), to a maximum of 3.63 m (axis
2), measured from the top of the foundation beam.
4
Fig. 2-1 Structure Plan
Fig. 2-2 Elevation along axis 1
5
6
Fig. 2-5 Elevation along axis A
Fig. 2-6 Elevation along axis B
7
Fig. 2-7 Elevation along axis C
Fig. 2-8 Elevation along axis 2-B
8
Fig. 2-9 Plan of the roof structure
2.2
Detailing
The details related to the distribution of steel reinforcement and the connections of the various
elements are contained in a set of AUTOCAD files prepared by the Designer. These details
are organised as follows:
Foundations:
Fig. 2-10, Fig. 2-11, Fig. 2-12, and Fig. 2-13
Reinforced concrete members:
Fig. 2-14
Wall elements and connections:
Fig. 2-15, Fig. 2-16, Fig. 2-17, Fig. 2-18, Fig. 2-19,
and Fig. 2-20
Roof:
Fig. 2-21, Fig. 2-22, Fig. 2-23, Fig. 2-24, Fig. 2-25,
Fig. 2-26, Fig. 2-27, Fig. 2-28, Fig. 2-29, and Fig.
2-30
Other details related to the distribution of the vertical reinforcement are found in Fig. 2-2, Fig.
2-3, Fig. 2-4, Fig. 2-5, Fig. 2-6, Fig. 2-7, and Fig. 2-8.
The footing and the strip footing beam rest over a soil mixed with 3 % cement and compacted
to a 95% Modified Proctor Density as per ASTM D 558 (or AASHTO T190) (Type A fill).
The soil over the bottom of the footing and along the sides of the foundation beam (Type B
fill) is compacted to a 95% Modified Proctor Density as per ASTM D 558 (or AASHTO T190),
using suitable or improved soils (Fig. 2-10).
The pavement of the house consists of 4 cm of unreinforced concrete (with a strength of
approximately 14 MP) poured over a soil fill of 40 cm, with the upper 20 cm compacted to a
9
90% Modified Proctor Density, as per ASTM D 1557 (or AASHTO T180), with selected soil or
with a mixture of one part of cement to forty parts of soil from the site (Fig. 2-2).
Two horizontal steel bars of 4.5 mm in diameter are placed at the exterior and interior faces at
every other bed joint between the concrete masonry blocks, namely, at heights of +0.40 m,
+1.50 m and +1.80 m with respect to the top of the bond beam at the base (Fig. 2-17).
The steel tensors (templete) are welded to the web of the single channel sections (polines P1)
(Fig. 2-21). The single channel sections are connected to the zinc-aluminium roof by means
of 5/16” x 1” (8 mm x 25.4 mm) screws. Each 1.05 m portion of the roof is connected to each
channel section (polín P1) by means of 3 screws (spaced at 0.35 m). Portions of the roof are
connected to each other by means of 5/16” x 3/4” (8 mm x 19 mm) screws spaced at 0.50 m.
The top of the roof (cumbrera) is linked to the corrugated roof by means of 5/16” x 3/4” (8 mm
x 19 mm) screws spaced at 0.30 m (Fig. 2-25). A neoprene washer is used between the head
of the screws and the surface of the corrugated in roof, in order to prevent rain from entering
the house.
The concrete cover is also specified in the design drawings as follows:
For foundation members in contact with soil
7.5 cm
For other members in contact with soil
5.0 cm
For reinforced concrete columns and beams
2.0 cm
The anchorage and splicing lengths for the various diameters of steel reinforcement are:
Table 2-1 Anchorage and splicing lengths as per design specifications
Designation
Diameter
anchorage length
mm
inches
cm
#2
6.35
1/4"
30
#3
9.53
3/8"
40
#4
12.7
1/3"
50
The development lengths of 90º and 135º hooks are show in Fig. 2-31.
Fig. 2-10 Footing Z1 geometry and detailing
10
Fig. 2-11 Tensor T1 cross section
Fig. 2-12 Tensor T1 to column C1 joint detail
Fig. 2-13 Tensor T1 to strip footing beam SF joint detail
11
(b)
(a)
Fig. 2-14 (a) Column C1 cross section; (b) Beam SC to Column C1 joint detail
Fig. 2-15 Beam SC to bond beam SU joint detail
(a)
(c)
(b)
Fig. 2-16 (a) Beam SC cross section; (b) Bond beam SU cross section; (c) N1 Detail
12
Fig. 2-17 Typical Elevation of masonry wall cross section
Fig. 2-18 Joint detail between vertical reinforcement and top bond beam
Fig. 2-19 Bond beam end detail
13
Fig. 2-20 Bond Beam “L” joint detail
Fig. 2-21 Lateral supports of channel sections (polines P1)
Fig. 2-22 Polín P1 to bond beam SU (or beam SU) joint detail
Fig. 2-23 Lateral view of polín P1 to beam SC connection
14
Fig. 2-24 Lateral view of polín P1 to bond beam SU joint
Fig. 2-25 Roof top detail with cumbrera
Fig. 2-26 Polín P2 cross section
Fig. 2-27 Polín P2 to bond beam SU (along axis 3) joint detail
15
Fig. 2-28 Polín P2 to bond beam SU (along axis 2) joint detail
Fig. 2-29 Plan view: Polín P2 connections to bond beams
Fig. 2-30 Elevation: Polín P2 connections to bond beams
16
Fig. 2-31 Detail specifications for 90º and 135º hooks
The construction procedure to be followed during construction of the masonry walls is given in
the design drawings. An English translation of these procedures is given hereafter:
o
All the masonry units must be placed in such a way to guarantee the vertical
continuity of the cells and allow for 100 % of grout filling.
o
All the webs of the masonry units must be completely covered by mortar.
o
All the cells of the masonry units must be vertically aligned and free of any
obstructions, such that the upper cell has a cross section no smaller than 50 mm x 75
mm.
o
Prior to grouting, the total height of grout space should not exceed 1.40 m and
cleanouts should be provided at the bottom of the wall; if this height is exceeded, a
cleanout must be provided at mid-height.
o
A sufficient length of steel reinforcement must be provided at the base of walls in
order to allow for adequate splicing of the vertical reinforcement.
o
The longitudinal reinforcement must not interfere with the grouting of the masonry
units. If a grout pour is stopped for more than an hour, key joints must be provided in
the grout space, with a minimum dimension of 15 mm.
o
The masonry units of the intermediate bond beams must have holes at their bases,
with the same dimensions as the grout space to be filled, in order to allow the
penetration of the grout pour.
o
When the masonry walls support a flexible roof, or their height exceeds 2.40 m,
supports normal to the plane of the wall must be provided, in the form of metallic or
concrete elements, spaced at a distance no larger than 4 m in the longitudinal
direction of the wall.
Internal partition walls are constructed along axes 2 (from axis B to C) and B (from axis 2 to
3), with a height of 2.2 m and made of fibre-cement with a cross section of 8 mm. The
partition walls are anchored to the base floor and are structurally independent from the rest of
the house. The partition walls are not considered in the present analysis.
2.3
Material Properties
The materials used in the structure that contribute to resist both lateral and gravity loads, as
well as making up connections and attachments are the following:
Concrete hollow masonry units
Mortar
17
Concrete
Grout
Reinforcing steel
Structural steel
Zinc-aluminium corrugated roof
The material properties consist of physical and mechanical properties. The physical
properties consist of geometry and mass density, while the mechanical properties are
described by the modulus of elasticity, the Poisson’s ratio and, depending on the material, the
yield and/or ultimate strengths in tension and/or compression.
From the properties of the concrete unit and of the mortar are derived the properties of the
masonry.
2.3.1 Concrete Hollow Masonry Units
The concrete hollow masonry units have a length of 39.5 cm, a height of 19.5 cm and a width
of 14.5 cm, with face-shells and webs of 2.5 cm thickness, as shown in Fig. 2-32. The net
area of the block is 47% of the gross area.
Fig. 2-32 Geometry of a standard masonry unit
The physical and mechanical properties of the unit material are:
Mass density
2100 kg/m3
Modulus of elasticity
9000 MPa
Compressive strength
9000 kPa
Tensile strength
1350 kPa
Shear strength
2700 kPa
The total weight of each block is computed by taking into account 1.9 cm (3/4”) deep
channels at each side of the block; the added mass contribution of mortar is accounted for by
increasing 0.5 cm the total length and height of the block:
Mass of one standard unit
11.4 kg (including mortar)
There is no information from the designer on the type of moist control of the masonry units,
however, this should not influence the data required for computing the mechanical properties
of masonry.
18
Apart from the standard unit shown in Fig. 2-32, a bond beam unit (solera) is also used in the
construction, with the same physical and mechanical properties outlined above. The geometry
of the bond beam unit is shown in Fig. 2-16 (b). The thickness of the bottom shell is equal to
2.5 cm. Although not visible in the figure, the bottom shell contains two holes, in
correspondence to the holes of the standard unit.
Fig. 2-33 Geometry of the bond beam unit
Since the bond beam is always filled with grout, only the total weight of the bond beam is
computed, considering the density of concrete and the increase of 0.5 cm in length and height
of the beam to include the weight of mortar.
Mass of 1 bond beam unit
26.3 kg (including mortar and concrete)
2.3.2 Mortar
The properties of mortar are given by the designer and are the following:
Mass density
2100 kg/m3
10000 kPa
2.3.3 Masonry
The compressive strength of masonry f’m is obtained from Table 21-D of UBC, based on a
compressive strength of the unit equal to 9000 kPa (Section 2.3.1) and a Type S mortar:
f’m = 7189 kPa
The tensile stress of masonry is equal to the modulus of rupture fr specified by UBC on article
2108.2.4.6 for partially grouted hollow-unit masonry:
fr = 0.21 fm'
Units in MPa
(2-1)
According to this formula:
fr =
563 kPa
The modulus of elasticity for masonry is estimated from (2-2) based on the value of f’m as
specified in article 2106.2.12.1 of UBC:
Em = 750 fm'
(2-2)
19
so that
Em = 5392 MPa
The shear modulus of masonry is computed based on a Poisson coefficient of 0.25:
G = 0.4 Em
(2-3)
which amounts to:
G=
2157 MPa
2.3.4 Concrete
The concrete specified for the project has the following properties:
Mass density
2400 kg/m3
Compressive strength f’c
20600 kPa
(210 kg/cm2)
The modulus of elasticity is computed from article 1908.5.1 of UBC using the following
expression:
Ec = 4730 fc'
with fc' in MPa
(2-4)
which gives
Ec = 21468 MPa
2.3.5 Grout
It is assumed that the physical properties of the grout correspond to those of the concrete as
called for in the design drawings:
Mass density
2400 kg/m3
Modulus of elasticity, Ec
21468 MPa
(see Section 2.3.4)
20600 kPa
(210 kg/cm2)
The mass of grout is computed for each of the voids filled in one block (20 cm x 14.1 cm x 9.5
cm):
Mass of one filled void
6.43 kg/unit
2.3.6 Steel Reinforcement
The steel reinforcement specified for the project corresponds to deformed bars of Grade 40
ASTM-615 steel (and ASTM A-160), with the exception of the #2 (6.35 mm diameter) bars
that may have a smooth surface.
The properties Grade 40 ASTM-615 steel are:
Mass density
7850 kg/m3
Modulus of Elasticity, Es
200000 MPa
Yield strength, fy
300 MPa
Ultimate strength, fu
525 MPa
Elongation
12 %
(1.75 fy)
The values given above were extracted from data given by different US steel producers.
The diameters, weights and cross sectional areas are summarized in the following table:
20
Table 2-2 Diameter, cross section area and mass of steel reinforcement
Diameter
Designation
Area
Mass / unit length
2
kg/m
mm
inches
#2
6.35
1/4"
31.7
0.249
#3
9.53
3/8"
71.3
0.560
#4
12.7
1/3"
126.7
0.994
mm
2.3.7 Cold-Formed Members
The structural steel used in the construction of the house corresponds to channel sections
and tensors used to support the roof structure. The only reference made by the designer to
the type of material used concerns the yield strength, however, no data is given on the tensile
strength or on the type of steel used. It is assumed that the steel type corresponds to A36
structural steel, with the following properties:
Mass density
7850 kg/m3
200000 MPa
Yield strength, fy
245 MPa
Tensile strength, fu
430 MPa
(1.75 fy)
can vary between 400 and 500 MPa [Table 22-1-A].
The channel section is a Calibre 16 (as shown in Fig. 2-34) cold-formed “C” section 1.6 mm
(1/16”) thick with a 102 mm (4”) deep web and flanges of 51 mm (2”) with 19 mm (3/4”)
closing ends. The channel sections are used to support the roof structure and are
denominated in the drawings as polines.
There are two types of polines, when these are made of single channel sections they are
designated as polín P1, while when they are built up from two welded channel sections
forming a 102 mm x 102 mm box section, they are designated as polín P2.
Fig. 2-34 Channel cross section
The physical and mechanical properties of the polín P1 are:
Cross Sectional Area
373 mm2
Major moment of inertia
6.218·105 mm4
Minor moment of inertia
8.887·104 mm4
Mass per unit length
2.93 kg/m
Center of Mass
18 mm (from centre of web)
The physical and mechanical properties of the Polín P2 are:
746 mm2
1.244·106 mm4
21
Minor moment of inertia
1.009·106 mm4
5.86 kg/m
The tensor elements are made up of #3 steel bars (diameter of 9.53 mm), and have the
following properties:
71.3 mm2
404 mm4
0.560 kg/m
The strength of cold-formed members may be computed according to the provisions of the
Specifications for the Design of Cold-Formed Steel Structural Members from the American
Iron and Steel Institute (AISI) as found in [3]; In particular, the computation of the compressive
capacity follows the expressions given in [5] that account for local buckling. The capacities
(compression, shear, torsion and bending) of the channel sections are summarised in Table
2-3. The tensile strength is approximately twice as large as the capacity in compression
(91381 N and 182762 N for P1 and P2, respectively).
Table 2-3 Strength of the channel sections
Section
V3
V2
P
T
N
M2
M3
N-m
Polin P1
51701
23896
23896
30
886
2999
Polin P2
99035
47793
47793
4856
3205
5997
2.3.8 Anchorage of Single Channel Sections P1
The eight single channel sections P1 are all parallel to axis 1 and are supported in three
points: at both extremities, they go through the top beams (SU or SC of axes A and C),
whereas in the middle, three sections go through the top beam SU of axis B; the other five are
cut and welded to the double channel section P2 of the same axis B.
The strength of the grouted connection between the channel section and the bond beam (SU
or SC) may be computed on the basis of the bond strength given by Eurocode 2 for plain
reinforcing bars:
fbd =
( 0.36 f
1/ 2
ck
)
γc
for plain bars
(2-5)
Where fck is the characteristic strength of concrete/grout and γc a reduction factor equal to 1.5.
To convert the characteristic value used in UBC (f’c) to that used in Eurocode 2 (fck), the
following expression is used, as suggested by [3] :
fck = 1.3 fc'
(2-6)
The value given in equation (2-5) is reduced by a factor of 0.7 for poor bond conditions.
For a value of fck equal to 26.8 MPa (from f’c = 20.6 MPa) the following bond strength is
obtained:
fbd = 0.87 MPa
for plain bars
The strength of the connection is then computed as the product of the bond strength and the
contact area Asurface between the channel and the grout:
P = Asurface fbd
(2-7)
22
The surface of the channel section in contact with the grout of the bond beam is equal to the
height of the channel (10.2 cm) multiplied by the depth of the grouted connection, equal to 10
cm. The web of the channel is in contact with both the inner and the outer side so that the
total surface area of contact is equal to 204 cm2. The strength of the connection for axial
forces is thus equal to:
P = 17748 N.
In case of the top beam SU, this capacity is limited by the capacity in shear of the wall to
transfer the normal force from the channel section. The shear capacity is computed using the
expression from article 2108.2.3.6.2 of UBC:
Vm = 0.083 Cd Ae fm'
fm' in MPa
(2-8)
The value of Cd varies between 1.2 and 2.4 for sections subjected to high and low bending
moments; Ae is the effective area of the masonry section.
The effective area is computed as the surface of the masonry block where the channel
section is anchored to in contact with the rest of the wall. Since the masonry block is part of
the bond beam located at the top of the wall, the surface is equal to the sum of the two lateral
faces and the bottom face; the two lateral faces include the area of the grout:
Alateral
= 2 x10 cm x 15 cm
Abottom
= 0.47 x 40 cm x 15 cm (0.47 is the ratio of gross to net area)
Ae
= 582 cm2
Assuming a value of Cd equal to 2.4 (the section at the top should not be subjected to high
moments), the reduced shear strength (with a reduction factor φ of 0.6 for shear) is equal to:
φVm = 18651 N
The capacity of the connection is then equal to 17748 N. It is important to note that if no
special inspection is enforced, UBC recommends that f’m values be reduced by half, thus
reducing the capacity by a factor of square root of 2. Therefore, the axial capacity of the
connection may be as low as 12550 N.
2.3.9 Anchorage of Double Channel Sections P2
The anchorage of the double channel sections P2 depends on the relative orientation of the
section with respect to the supporting beam SU. The double channel section P2 is
perpendicular to the top beam SU of axes 3 and C but parallel to those of axes 2 and B.
Theoretically, the strength of the grouted connection between the double channel sections
and the bond/top beams is the same as for the single channel sections because the contact
area between the channel and the grout is the same. However, in practice, the anchorage of
the P2 sections is quite different from the anchorage of the P1 sections. In particular:
o
When orthogonal (walls 3 and C), the sections P2 do not go through the top beams.
o
On wall 3, the P2 section is not horizontal and thus is not completely embedded into
the beam (Fig. 2-30).
o
On wall C, the P2 section is anchored at the junction between the two inclined SU
beams (no detailed design of this particular connection is provided).
o
On walls 2 and B, the P2 sections are embedded into concrete but the cover is
particularly weak at least on one side.
For all these reasons, it is likely that the strength of these connections will be weaker that in
the case of the P1 sections, especially in the presence of bending moments.
23
2.3.10 Zinc-Aluminium Corrugated Roof
The roof of the structure is made of cold-formed E-25 Grade 80 1.05 m wide steel corrugated
sections, with a depth of 2.5 cm, horizontal sections of 5 cm and inclined sections of 2 cm by
2.5 cm. The physical and mechanical properties of the roof are:
Yield strength
550 MPa
Thickness
0.45 mm
Mass per unit area
4.40 kg/m2
The cross section of the roof is shown in Fig. 2-35. The channels of the roof run in the
direction of axis 1, 2 and 3 of the structure.
Fig. 2-35 Corrugated roof cross section
In the direction of axes A, B and C, the compression capacity of the corrugated roof is
reduced to account for local buckling. Considering a buckling length of 1.02 m (spacing of
joist truss or channels along the span of 3.05 m), the critical stress is, according to [5]:
fcr = 114 MPa
24
25
3 Loads
3.1
Dead Loads
Dead loads consist of the weight of all materials incorporated into the building structure. The
materials that make up the dead load of the structure are:
Reinforced Concrete hollow masonry units
Grout
Reinforced Concrete
Steel members (polines and tensors)
Zinc-aluminium corrugated roof
The total load contribution of each of these materials is computed from the material properties
given in Section 2.2 and from the geometry of the structure presented in Section 2.1.
3.2
Earthquake Loads
The earthquake loads are specified as a set of artificial acceleration time histories compatible
with the response spectrum specified by the Norma Técnica para Diseño por Sismo issued by
the Ministry of Public Works of El Salvador.
3.2.1 Response Spectrum
The response spectrum is elastic and corresponds to a ground motion having a 10-percent
probability of being exceeded in 50 years, with characteristics consistent with the specific site
and developed with a damping ratio of 5 percent, as described by the following expressions
taken from Chapter 5.2 of [2]:
If Tm <
If
T0
3
⎡ 3 (C0 − 1)Tm ⎤
Sa = I A ⎢1 +
⎥
T0
⎣
⎦
T0
≤ Tm ≤ T0
3
If T0 ≤ Tm ≤ 4 sec
If Tm > 4 sec
Sa = I AC0
⎡T ⎤
Sa = I AC0 ⎢ 0 ⎥
⎣Tm ⎦
Sa =
2.5I AC0T0 2 / 3
Tm 4 / 3
(3-1)
(3-2)
2/3
(3-3)
(3-4)
26
I
importance factor
A
seismic zone factor
Sa
spectral acceleration (multiple of g)
Tm
modal period of the structure.
C0
coefficient specific to the site where the structure is located
T0
coefficient specific to the site where the structure is located
The site characteristics are chosen following the recommendations given in Table 5 of [2],
that state that when soil properties are not known, an S3 soil type must be selected,
corresponding to a 3 to 12 m deep layer of soft cohesive soil. For an S3 type soil, C0 and T0
take the values of 3 and 0.6, respectively.
The shape of the response spectrum is shown in Fig. 3-1 for an S3 soil type, an importance
factor of 1.0 (for standard occupancy structures) and a value of A equal to 0.4, corresponding
to Seismic Zone I, located South of the seismic dividing line and covering the entire coastline
and most of the urbanised areas of El Salvador.
1.4
Spectral Acceleration (g)
1.2
1.0
0.8
0.6
0.4
0.2
0.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Period (s)
Fig. 3-1 Elastic response spectrum
3.2.2 Acceleration Time Histories
Three artificially acceleration time histories were generated to conform to the response
spectrum of Fig. 3-1, as shown in Fig. 3-2, Fig. 3-3 and Fig. 3-4, for signals 1, 2 and 3,
respectively. The time histories have a total duration of 10.22 seconds each, with a time step
of 0.02 seconds.
The comparison between the response spectra of the artificially generated acceleration time
histories and the target spectrum is shown in Fig. 3-5, indicating good agreement between the
two.
27
0.8
0.6
0.2
0.0
-0.2
-0.4
-0.6
-0.8
0
1
2
3
4
5
6
7
8
Time (s)
Fig. 3-2 Acceleration time history of Signal 1
0.8
0.6
Acceleration (g)
0.4
0.2
0.0
-0.2
-0.4
-0.6
-0.8
0
1
2
3
4
5
6
7
8
Time (s)
0.8
0.6
0.4
Acceleration (g)
Acceleration (g)
0.4
0.2
0.0
-0.2
-0.4
-0.6
-0.8
0
1
2
3
4
5
6
Time (s)
7
8
28
1.4
1.2
Signal 1
Signal 2
Spectral acceleration (g)
Signal 3
1.0
Target Spectra
0.8
0.6
0.4
0.2
0.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Period (s)
Fig. 3-5 Response spectrum of acceleration time histories and comparison with target spectra
3.3
Load Combinations
The UBC, in article 1631.2, states that each pair of horizontal time-histories shall be applied
simultaneously to the model considering torsional effects, with the vertical component of
ground motion defined by scaling the corresponding horizontal accelerations by a factor of
two thirds.
The horizontal acceleration time histories are applied simultaneously along the two orthogonal
directions of the structure for each acceleration time history signal, as recommended by the
UBC in article 1631.6.1, that states that each pair of horizontal ground motion components
should be scaled such that the square root of the sum of the squares (SRSS) of the 5
percent-damped site-specific spectrum of the scaled horizontal components does not fall
below 1.4 times the 5 percent-damped spectrum of the design-basis earthquake for periods
from 0.2T to 1.5T seconds, where T is the period of the structure. In this case, the horizontal
component of the resulting base acceleration always results diagonal with respect to the
orthogonal directions of the structure.
The response of the structure is computed by taking the maximum response obtained from
the three time history simulations using the three artificial signals, as recommended by the
UBC in article 1631.6.1.
29
4 Numerical Model of the Structure
The finite element code used for this study is CAST3M, a code co-developed by CEA and
JRC [6].
4.1
Mesh
The mesh of the different structural components of the house is hereafter described. The type
of finite element (bar, beam or plate) has been chosen so as to best represent the relevant
contribution of each structural component while keeping a reasonable total number of
degrees of freedom.
4.1.1 Masonry Walls
Masonry walls are modelled as a double homogeneous plate composed of 3-node triangular
elements and representing the face-shells of the concrete blocks. In particular, the mortar
joints are not represented separately. Furthermore, the internal webs of the blocks are
neglected in the model, although their mass is taken into account through an appropriate
increase of the volumetric mass of the plate. The masonry elements were generated so as to
facilitate their connection with the reinforcing elements (bars and beams). For example, the
boundaries of the masonry elements include the vertical and horizontal reinforcements, the
mean fibre of the reinforced masonry elements, the point of anchorage of the channel
sections, etc. The masonry wall mesh is shown in Fig. 4-1.
Fig. 4-1 Mesh of the masonry walls
4.1.2 Reinforced Concrete Elements (SF-1, T1, C1, SC)
The reinforced concrete foundation SF-1, tensors T1, column C1 and beams SC are
considered as 2-nodes linear elements supporting a fibre Timoshenko beam. This type of
modelling requires the description of the section through a two-dimensional local mesh. The
four existing sections and the global mesh are shown in Fig. 4-2.
30
SF-1
T1
C1
SC
Fig. 4-2 Section meshes (left) and global (right in red) mesh of the reinforced concrete
foundation SF-1, tensors T1, column C1 and beams SC
4.1.3 Reinforced Masonry Elements (SU)
The reinforced masonry beams are modelled by fibre Timoshenko beam elements (as the
reinforced concrete) with a section mesh excluding the face-shells of the blocks, which are
already taken into account in the masonry walls. The section and global meshes are
presented in Fig. 4-3.
Fig. 4-3 Section mesh (left) and global mesh (right in pink) of reinforced masonry beams SU
4.1.4 Distributed Vertical Steel Reinforcement
The vertical steel reinforcement is modelled by bar elements perfectly connected to the
masonry. The grout around the vertical steel bars is not represented but its mass is taken into
31
account through an appropriate increase of the volumetric mass of the bar. The global mesh
is presented in Fig. 4-4.
Fig. 4-4 Mesh of vertical steel reinforcement (#4 in deep blue, #3 in light blue)
4.1.5 Distributed Horizontal Steel Reinforcement
The horizontal steel reinforcement is modelled by a couple of eccentric bars perfectly
connected to the masonry. In practice, each couple of bars is represented by fibre
Timoshenko beam elements having a section composed of two points 12 cm away from each
other. The section and global meshes are presented in Fig. 4-5.
Fig. 4-5 Section mesh (left) and global mesh (right in green) of horizontal steel reinforcement
4.1.6 Channel Sections (polines) P1 and P2
The channel sections are modelled by fibre Timoshenko beam elements with a section mesh
composed of quadrangular elements. Whenever a channel beam intersects a reinforced
concrete/masonry beam (P1-SC, P1-SU or P2-SU) or another channel beam (P1-P2 or P2P2), a clamping condition is assumed (continuity of displacements and rotations). The section
and global meshes are presented in Fig. 4-6.
32
Fig. 4-6 Section (left) and global (right) meshes of channel sections P1 (blue) and P2 (red)
4.1.7 Steel Tensors (templetes)
Each steel tensor is modelled by a 2-node bar element and is anchored to the neighbouring
channel sections. The three steel tensors initially foreseen along axis B were removed
because of the addition of the P2 channel section. The global mesh is presented in Fig. 4-7.
Fig. 4-7 Mesh of the steel tensors (in blue)
4.1.8 Roof
The roof is modelled by large plate triangular elements, covering the spaces defined by the
net of channel sections and steel tensors (Fig. 4-8). The roof plate elements are considered
33
clamped on the channel section beam elements (continuity of displacements and rotations)
but no connection is assumed along the top line between the two half-planes.
Fig. 4-8 Mesh of the roof
The total mesh is shown in Fig. 4-9 and also with shrunk elements in Fig. 4-10 so as evidence
the bar and beam segments.
Fig. 4-9 Total mesh of the house
34
Fig. 4-10 Total mesh of the house after shrinkage of the elements
4.2
Models and Materials
4.2.1 Masonry
The geometrical properties of the double thin plate representing the masonry are:
Thickness of each plate = thickness of the face-shells = 2.5 cm
Distance between the two mean surfaces = 14.5 - 2.5 = 12 cm
The mechanical characteristics result from an average between the properties of the blocks
and the mortar (see section 2.3.3):
Young modulus Em
5392. MPa
Poisson ratio νm
0.25
Compression strength fc
7.189 MPa
Tension strength ft
0.563 MPa
The nonlinear behaviour of masonry is represented by the Ottosen smeared crack model [8],
which allows cracking in tension but remains elastic in compression. The possible reaching of
the compressive strength will nevertheless be checked a posteriori (Rankine criterion). In the
Ottosen model, the degree of tension damage at any material point is characterized by the
opening of the cracks which is zero until the tension strength is reached for the first time in a
given direction. Once a crack is formed, the stress-strain relationship is modified according to
the opening of the crack. In particular, the stress normal to the crack decreases linearly until
zero with a more or less steep slope depending on the fracture energy of the material. At the
same time, the behaviour tangentially to the crack is also modified through the so-called slip
35
modulus. In case of unloading (closing of a crack), a fraction of the developed crack is
assumed to remain when the normal stress has dropped to zero, while the stress-strain is a
straight line directed towards that point. Finally, in case of reloading, the unloading path is
followed until the maximum crack width is regained. After that, the original constitutive
behaviour is used again.
Fracture energy, Gf
5392 MN/m
Slip modulus, Gs
0.48528 MPa
Residual opening fraction, β
0.2
From these mechanical characteristics, it can be deduced that the width of the fully opened
crack (zero tension strength) is:
w0 =
2Gf
ft
(4-1)
that is,
w0 = 0.039 mm.
An index of damage is thus given by the ratio D = w/w0 where w is the maximum crack
opening ever reached in each point: when D = 0, no cracking has occurred yet; when 0<D<1,
partial cracking has occurred and the residual tension strength is (1-D)ft; when D ≥ 1, cracking
has fully developed and no residual tension strength is available any more.
The relation between the crack opening and the corresponding strain is made objective
through the definition and use of the equivalent lengths. These are purely geometrical
quantities determined by the size and shape of the finite element region around the gauss
point of interest. The values of the equivalent lengths are subject to a general restriction: the
slope of the stress-strain curve in the post-peak region should always be negative. In other
words, the fracture energy, which is proportional to the length (surface in 3D) of the region in
the direction of the crack, cannot be less than the stored elastic energy, which is proportional
to the surface (volume in 3D) of the region. This leads to a maximum allowable size of the
region around the gauss point, namely:
Lmax =
2Gf Em
ft (1 + ν m )
2
(4-2)
that is,
Lmax = 0.311 m
whereas the finite element mesh of the masonry part is made of triangular elements having a
maximum dimension of 0.283m.
4.2.2 Concrete and Grout (in SF-1, T1, C1, SC and SU)
The concrete material is used in the fibre models used for the foundation beam SF-1, the
tensor T1, the column C1 and the beams SC, whereas the grout material is used in the fibre
model of the beams SU. Concrete and grout materials are assumed to have the same
characteristics. The uniaxial model used is of the Hognestad type [7], the material
characteristics are the following:
Mass density
2400 kg/m3
Modulus of elasticity
21468 MPa
Poisson ratio
0.2
20.6 MPa
Tension strength
1.5 MPa
36
4.2.3 Steel Reinforcement (for concrete and masonry)
The reinforcing steel material is used in the fibre models for the foundation beam SF-1, the
tensor T1, the column C1, the beams SC, the beams SU and also in the bar models figuring
the representing vertical and horizontal reinforcement of the masonry. The characteristics of
the reinforcing steel correspond to Grade 40 ASTM-615:
Mass density
7850 kg/m3
200000 MPa
Yield strength, fy
300 MPa
Ultimate strength, fu
525 MPa
Ultimate elongation
12 %
(1.75 fy)
The uniaxial model is a simply elasto-plastic with linear kinematic hardening, the possible
occurrence of failure and buckling being checked a posteriori.
4.2.4 Channel Sections and Tensors
The constitutive material of the channel sections and templetes is assumed to be the same,
(A36 steel) with the following properties:
Mass density
7850 kg/m3
200000 MPa
Yield strength, fy
245 MPa
Tensile strength, fu
430 MPa
(1.75 fy)
For the analysis, the material will be considered elastic-plastic with linear kinematical
hardening. Again, the possible occurrence of failure, buckling and/or pulling out at the
anchorage points will be checked a posteriori.
4.2.5 Roof
Due to its corrugated cross section, the roof behaves like an orthotropic plate. The roof is
indeed much stiffer and stronger in the direction parallel to the channels than in the direction
perpendicular to them. The homogenisation theory allows the derivation of the in-plane and
out-of-plane elastic characteristics of an equivalent homogeneous plate of arbitrary thickness
w (inertia J = w3 /12). Assuming that the Young modulus and the Poisson ratio of the material
are 200000 Mpa and 0.3 respectively, the in-plane (membrane) elastic characteristics are:
Young modulus parallel to the channels E1i = 105 / w MPa
Young modulus perpendicular to the channels E2i = 0.0128 / w MPa
i
i
= 0.0000366 )
= 0.3 ( ν 21
Poisson ratio ν 12
i
Shear modulus G12
= 29.7 / w MPa
The out-of-plane (bending) elastic characteristics are:
Young modulus parallel to the channels E1o = 0.141/ J MPa
Young modulus perpendicular to the channels E2o = 0.0000172 / J MPa
o
o
Poisson ratio ν 12
= 0.3 ( ν 21
= 0.0000366 )
i
= 0.00000818 / J MPa
Shear modulus G12
37
Since the in-plane behaviour of the roof is expected to be more relevant in the case of seismic
loading (diaphragm effect), the parameters (w, E1, E2, ν12 and G12) of the equivalent plate are
chosen so as to fit the membrane characteristics. However, since the in-plane and out-ofplane Young moduli are proportional and the Poisson ratios are the same, it is possible to
choose a set of parameters such that most of the out-of-plane elastic characteristics of the
roof are also reproduced:
Thickness w = 0.0366 m
Young modulus parallel to the channels E1 = 2870. MPa
Young modulus perpendicular to the channels E2 = 0.350 MPa
Poisson ratio ν 12 = 0.3 ( ν 21 = 0.0000366 )
Shear modulus G12 = 811. MPa
Indeed, with these parameters, all the in-plane and out-of-plane characteristics of the roof are
reproduced except the bending shear modulus, which remains largely overestimated (it
should be only 0.167 MPa). The choice of a fictitious thickness w of 3.66 mm much larger
that the physical one (0.45mm) allows to take into account the corrugated cross section and
explains why the Young and shear moduli of the equivalent material are so small. Similarly,
the fictitious volumetric mass ρ should be such that the mass per unit area (4.40 kg/m2) is
respected, i.e
ρ = 4.40 / w = 0.0465 kg/m3
The roof plate will be assumed to remain elastic since yielding is unlikely to occur. In any
case, the stresses induced in the roof can be checked a posteriori against plasticity/bucking
(yield strength = 550 MPa).
4.3
Boundary Conditions
At the base of the column C1 (level –0.8m), all displacements and rotations are blocked to
account for the footing plate, which is not represented in the numerical model.
On the reinforced concrete tensors T1 and foundation SF-1 (level –0.4m), the displacements
are fixed. Such a boundary condition greatly reduces the utility of a detailed model for tensors
T1 and foundation SF-1. However, to keep the possibility of assessing the effect of relaxing
the boundary condition at the base, the detailed fibre Timoshenko models for T1 and SF-1
have been maintained.
It has been decided to disregard the soil fill and the pavement above the foundation so that
the masonry walls and reinforced concrete column are considered free also along the 40 cm
below the level of the surrounding soil. This assumption takes into account possible
imperfections of the soil fill and pavement (e.g. limited stiffness, gap) and, in any case, is on
the safety side.
38
39
5 Modal and Nonlinear Time History Analyses
The fundamental frequencies and associated modes of the structure are determined from
modal analysis in view of imposing a Rayleigh damping of 2% on the two first modes for the
nonlinear dynamic analyses. The results of modal analysis give also a rough estimation of the
kind of response to be expected in relation with the response spectrum of the site.
The nonlinear dynamic response of the structure is computed for different imposed
accelerograms, as stated in Section 3.3, and the damage suffered by the structure is
evaluated: this includes mainly cracking of masonry (opening of cracks), yielding of
reinforcement and, more generally, any nonlinearity of the fibre models representing the
beams, the columns and the polines.
The potential failures not accounted for in the modelling are checked a posteriori. In
particular, the compression failure of masonry, omitted in the Ottosen model, may be
characterised by the ratio:
Ic = −
σ III
fm'
(5-1)
where f’m is the compression strength of masonry (7.189 MPa) and σIII the lowest principal
value of the stress tensor. The ratio Ic is computed at the mid-surface of each plate
representing the face-shells of the concrete blocks; at each location, only the higher value at
each of the face cells is kept. At the end of any analysis, the maximum value reached by this
ratio is plotted for the masonry walls as a function of time.
The results from nonlinear analysis are valid only if the ratio Ic remains lower than unity;
higher values of Ic indicate compression failure by crushing of at least one of the face shells,
which cannot be taken into account by the Ottosen model.
In addition, the maximum reaction forces at each connection are evaluated: if the
corresponding strength is exceeded, the computation is repeated without that connection.
5.1
Original structure
5.1.1 Modal Analysis
The first four fundamental frequencies of the original structure are shown in Fig. 5-1 together
with the associated modes: these frequencies are relatively high, and are mainly due to the
size (one-storey) and structure (load-bearing shear walls on all sides) of the house. However,
these numerical values should be taken as upper bound estimates, because the modal
analysis is based on a perfect and purely elastic model, while:
o
The elastic domain for masonry, concrete, mortar and grout material is particularly
limited in tension, so that cracks are likely to appear at very low vibration amplitudes.
o
The interfaces between different materials (steel-concrete, steel-grout, grout-unit,
unit-mortar, polines-beams, etc.) may be defective from the beginning (incomplete
grouting, partial contact, gaps, etc.) and are often subject to rapid deterioration under
tension (cracking).
o
The boundary conditions at the base have been idealized (perfect contact with a
perfectly rigid sub-soil) but this is somehow counteracted by the non representation of
the soil fill and the pavement.
If taken into account separately, any of these factors will lead to a more or less significant
decrease of the fundamental frequencies. For example, assuming concrete, grout and
40
masonry as no-tension materials, the bending stiffness of reinforced concrete beams and
masonry walls is reduced up to one-half, due to the presence of steel reinforcement and to
the beneficial effect of the compressive normal/membrane forces. As a consequence, the
fundamental frequencies are reduced by a factor on the order of √2. The weakness of some
particular interfaces may also lead to a more or less pronounced reduction of the first
fundamental frequencies as it will be shown later.
Mode 1: 14.7 Hz
Mode 3: 21.2 Hz
Mode 2: 17.5 Hz
Mode 4: 21.8 Hz
Fig. 5-1 First four fundamental modes of the original house
5.1.2 Gravity Loads
The gravity loads result from the multiplication of the mass distributed in the structure by a
uniform gravity acceleration field of 9.81m/s2. In the present analysis, there are no dead loads
other than the weight of all materials incorporated into the building structure. The gravity load
analysis is performed statically and the result is the starting point for the nonlinear dynamic
seismic analyses.
The house remains almost elastic under the gravity loads, and very limited tension cracking
occurs in the reinforced concrete beams SC (fibre model) above the veranda. The
compression failure criterion of the masonry walls is far from being reached: in Fig. 5-2, the
ratio Ic is lower that 0.04. The biggest displacement is 0.3 mm and occurs at the roof in the
vertical direction. The total vertical reaction at the base is 233 kN (i.e., the weight of the
house).
41
Fig. 5-2 Gravity loads – Masonry failure criterion in compression (scale up to 0.1)
5.1.3 Seismic Loads
As stated in Section 3.3, each of the three acceleration time histories is applied
simultaneously along the two orthogonal directions of the structure and along the vertical
direction with a reduction factor of 2/3. In the reference frame formed by an x axis coinciding
with wall B and directed towards wall 3, a y axis coinciding with wall 2 and directed towards
wall A and a z axis directed upwards, the resulting vector is a unidirectional acceleration
scaled by a factor of √22/3≅1.56 along one of the eight directions in space (±1, ±1, ±2/3).
Since the structure does not exhibit any symmetry, the response depends on the chosen
direction. This means that, theoretically, 3x8=24 computations are necessary in order to find
the most severe case. In practice, it was observed that the response of the house is not much
influenced by the direction of application of the time history.
In all cases, the response of the structure is slightly nonlinear: all elements remain in the
elastic range, except the reinforced concrete beams and part of the masonry elements, which
undergo some cracking. If the severity of the earthquake is measured by the total damage
observed in the masonry (integral over the structure of the maximum opening of the cracks in
the Ottosen model), the most severe result was obtained with the 3rd time history when
applied along direction (-1, +1, +2/3). In Fig. 5-3 the location and intensity of cracking is
shown: the highest value of the scale refers to the fully developed crack (w0 = 0.039mm) as
defined in equation (4-1). Cracking takes place near most structural singularities (corners of
the openings, bottom/top junctions between orthogonal walls, anchorage of section P2 on wall
3). In addition, wall C is also cracked between the two openings. With the 1st time history
along direction (-1, +1, +2/3), the observed damage is lower, but distributed differently, since
cracking takes place between the openings of wall 3 (Fig. 5-4). In both cases, cracking is due
to out-of-plane bending of the affected wall: cracks appear both in the inner and outer flanges
of the masonry wall, opening and closing alternatively. Although this cracking is unavoidable,
given the low tension strength of masonry, the stability of the structure is not jeopardised,
because the compressive strength is never reached in the compressed flange. In the worst
case (Fig. 5-5) the masonry failure criterion does not exceed 0.25.
42
Fig. 5-3 Third time history along direction (-1, +1, +2/3) – Masonry cracking
Fig. 5-4 First time history along direction (-1, +1, +2/3) – Masonry cracking
43
Fig. 5-5 Third time history along direction (-1, +1, -2/3) – Masonry failure criterion in
compression (scale up to 1)
It is interesting to check how cracking lowers the first frequency of the house. For example,
the spectrum of the normal force along the double channel section at the anchorage point on
wall 3 (Fig. 5-6) clearly exhibits a peak at 13.4 Hz, which is slightly lower than the original first
fundamental frequency (14.7 Hz).
Frequency [Hz]
0
5
10
15
20
25
Fig. 5-6 Normal force spectrum along P2 at the anchorage point on wall 3
An important point to be checked is the reaction force and moment at the anchorage of the
single and double sections, having in mind that the strength of the latter might be lower that
the one calculated for the former, as mentioned in Section 2.3.9.
44
The reaction forces are not collinear to the channel section and often exhibit a substantial
vertical and/or horizontal component due to the transmission of the inertial forces from the
roof. In order to take into account the possible negative effect of this component when
oriented upwards, the norm is compared to the theoretical strength of the connection. The
reaction moment has also three components and, considering that all are equally damaging
for the anchorage, the norm is again considered.
For the P2 double section, the biggest reaction force is always observed at the anchorage
point on wall 3. This was foreseeable, because only one P2 section is mitigating the out-ofplane displacement of this long wall, whereas, on wall C, the P2 double section is “helped” by
8 single P1 sections. The worst case (Fig. 5-7) was obtained for the 1st time history along
direction (+1, -1, +2/3).
The maximum reaction force reached on wall 3 is 12.4 kN, which is slightly below the strength
calculated in Section 2.3.8 (12.6 kN). The maximum force at the three other anchorage points
is much lower (around 5.3 kN on wall 2 and less than 2.5 kN on walls B and C).
14
Force [kN]
12
10
8
6
4
2
Time [s]
0
1
2
3
4
5
6
7
8
9
10
Fig. 5-7 Norm (kN) of the reaction force at the anchorage points of P2 on wall 3 (red), wall 2
(turquoise), wall B (pink) and wall C (blue)
Similarly, the biggest reaction moment is always observed on wall 3 (Fig. 5-8) and the highest
value (0.56 kNm) was obtained for the 1st time history along direction (+1, +1, +2/3). Again, on
the other walls, the values reached are much lower (0.31 kNm on wall 2, 0.19 kNm on wall B
and 0.17 kNm on wall C).
The reaction force at the anchorage points of the P1 single sections never exceeds 2 kN and
the resultant moment remains under 0.1 kNm.
The anchorage of the P2 double channel section is therefore likely to fail on wall 3, whereas it
should resist on the three other walls. The anchorage of the P1 single sections is far from
being at risk. However, the demands on the remaining connections and on the whole
structure will change drastically after the failure of the connection on wall 3. It is therefore
necessary to repeat the nonlinear dynamic analyses on the structure without the connection
on wall 3. To remain on the safe side, all four connections are removed, while the single
channel section remains perfectly anchored.
45
0.6
Moment [kNm]
0.5
0.4
0.3
0.2
0.1
Time [s]
0
1
2
3
4
5
6
7
8
9
10
Fig. 5-8 Norm (Nm) of the reaction moment at the anchorage point of P2 on wall 3 (red), wall
2 (turquoise), wall B (pink) and wall C (blue)
5.2
Structure without the P2 Anchorage
For the numerical simulations, the double channel sections (P2) are not removed from the
mesh, but only disconnected from the masonry walls.
5.2.1 Modal Analysis
The results of modal analysis without the P2 anchorage are displayed in Fig. 5-9. Three
additional modes involving the double channel section and/or the roof are not displayed.
Mode 1: 8.56 Hz
Mode 3: 19.9 Hz
Mode 2: 14.7 Hz
Mode 4: 20.7 Hz
Fig. 5-9 First four fundamental modes of the modified structure
46
The main effect of the absence of the connection between the double channel sections P2
and the beams SU is the appearance of a new fundamental mode at a much lower frequency
(mode 1 in Fig. 5-9). This new mode involves mainly the out-of-plane bending of the wall on
axis 3 and replaces the old mode number 2. The three other modes are similar (in shape and
frequency) although the participation of the roof is sometimes more pronounced (e.g., mode 2
of Fig. 5-9 compared with mode 1 of Fig. 5-1). This first numerical analysis highlights the
consequence of a weak anchorage of the double channel sections, especially along axis B.
Along axis 2, the absence of the anchorage has little effect, due to the existence of the P1
single channel sections supporting the roof. Again, this supposes that the anchorage of the
P1 elements on the beams SU and SC is indeed strong enough.
5.2.2 Gravity Loads
The response of the house under the gravity loads is nearly elastic, despite the absence of
the anchorage between the P2 sections and the walls. In particular, the compression failure
criterion is hardly affected: in Fig. 5-10 the ratio Ic is still lower than 0.04 and no concentration
of compressive stresses emerge at the top middle of wall 3. The main difference lies in the
deflection of the roof between axes 2 and 3: the maximum vertical displacement is 3.8 mm,
owing to the absence of support along axis B.
Fig. 5-10 Gravity loads – Masonry failure criterion in compression (scale up to 0.1)
5.2.3 Seismic Loads
In all cases, the response of the structure is highly nonlinear, due to extended cracking in wall
3. The most severe results were obtained with the 1st time history along direction (-1, -1, -2/3).
In Fig. 5-11, the location and intensity of cracking is displayed according to the same scale
used in the previous graphs. In wall 3, cracking fully develops in the central part of the base
and is considerable around the windows and at the junctions with the orthogonal walls, while
the other walls are only marginally damaged. However, the masonry compression failure
criterion is still far from being reached (ratio Ic lower than 0.35 in Fig. 5-12).
47
Fig. 5-11 First time history along direction (-1, -1, -2/3) – Masonry cracking
Fig. 5-12 First time history along direction (-1, -1, -2/3) – Masonry failure criterion in
compression
48
The results from the second modal analysis (Section 5.1.1) show that wall 3 undergoes a
pronounced out-of-plane bending due to the absence of support at its top centre. In Fig. 5-13,
the transverse displacement at the top middle of wall 3 is plotted together with the transverse
displacements at the top middle of wall C. When the anchorage of the double section is
operational, the maximum out-of-plane displacement on wall 3 is only 0.7 mm, while after the
loss of the anchorage, the out-of plane displacement on wall 3 increases up to 9.4 mm,
remaining under 0.3 mm on wall C. Nevertheless, the out-of-plane failure mechanism of wall 3
is not complete, because the hinge that fully develops at the bottom does not extend to the
hinges that partially develop at the top. Furthermore, compression failure of the wall is not
reached. Wall C is not affected by the absence of the anchorage of the double section
because it is still supported by the single sections; the remaining walls are not long enough to
undergo significant out-of-plane displacements.
10
Displacement [mm]
8
6
4
2
0
-2
-4
-6
-8
Time [s]
-10
0
1
2
3
4
5
6
7
8
9
10
Fig. 5-13 Transverse displacement at the top middle of wall 3 (red) and C (blue)
Again, it is possible to check how cracking lowers the first frequency of the house. The
spectrum of the transverse displacement at the top centre of wall 3 (Fig. 5-14) clearly exhibits
a peak at 7.6 Hz, which is again slightly lower than the original frequency (8.56 Hz).
Frequency [Hz]
0
5
10
15
20
25
Fig. 5-14 Spectrum of the transversal displacement at the top centre of wall 3
It is worth noting that these results are consistent with the design rules regarding the provision
of lateral support to masonry walls: “When the masonry walls support a flexible roof, or their
height exceeds 2.40 m, supports normal to the plane of the wall must be provided, in the form
49
of metallic or concrete elements, spaced at a distance no larger than 4 m in the longitudinal
direction of the wall”. As a matter of fact, if not supported laterally, wall 3 can suffer
substantial damage.
5.2.4 Ultimate Load
In order to assess the ultimate resistance of the house, the most severe acceleration time
history identified in the previous Section is imposed with a progressively increasing intensity
factor until a failure is reached. In practice, the acceleration values of the design
accelerogram are multiplied by 1.2, 1.4, 1.6, etc. Each computation is carried out on the
original undamaged house, so that the damage is not cumulated from one run to the next.
The damage observed at the end of each computation is shown in Fig. 5-15. The out-of-plane
failure mechanism of wall 3 that initiates at the reference input (intensity factor = 1) clearly
develops further as the intensity increases. The hinges are fully formed for an intensity factor
of 2, with the maximum displacement at the top of wall 3 reaching nearly 2 cm. At this stage,
substantial damage associated to another out-of-plane failure mechanism occurs in wall C
(between the windows and at the base). In walls 2 and B shear failure characterised by
diagonal cracking appears around the door, while walls 1 and A remain practically
undamaged. Yet, the stress in the compressed flange remains under the compression limit (Ic
< 0.72), while the vertical and horizontal steel reinforcement prevent the out-of-plane failure of
walls 3 and C.
The results suggest that the house is able to sustain even higher intensity factors, despite
extended damage. However, the numerical model assumes that perfect bond between the
reinforcement and the masonry is maintained, therefore cracking of masonry associated to
the degradation of bond between the reinforcement, the grout and the block unit, is not
accounted for. Consequently, the contribution of the reinforcement is probably overestimated
in the numerical simulations, so that the out-of-plane stability of wall 3 becomes questionable
for an intensity factors equal or larger than 1.8. Moreover, the numerical model does not take
into account any possible defects of the structure, such as poor grouting, badly executed
corners, and other problems that may arise during the construction phase. However, in the
absence of any major defects, the analysis indicates that the house is be able to withstand an
earthquake 50% higher than the design one, at the expense of extensive damage of the two
major walls.
50
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
Fig. 5-15 Masonry cracking for increasing intensity factors
51
6 Conclusions and Recommendations
The seismic behaviour of the house appears to be satisfactory for the design earthquake,
provided that it is built in conformity with the design plans and that the construction quality is
good. The only detail that needs to be reviewed is the anchorage of the double channel
sections at the top beams SU. This point, as well as other details susceptible to be improved,
is addressed hereafter.
6.1
Anchorage of the P2 Double Channel Sections
This anchorage should be improved, especially in the middle of the wall along axis 3.
According to the calculation, the tension capacity of this connection should be higher than
12.5 kN, in combination with moments up to 0.6 kNm otherwise the wall along axis 3 may
suffer extensive damage, even if complete out-of-plane failure is improbable.
The proposed connection (Fig. 2-27, Fig. 2-29 and Fig. 2-30) does not appear strong enough
as it relies exclusively on the resistance of the channel-grout interface. To reach a larger
capacity, the double channel section can be attached to the vertical and horizontal
reinforcement existing in the wall (horizontal reinforcement #4 in the beam SU and vertical
reinforcement #3). Alternatively, two steel vertical pins could be welded to the extremities of
the channel sections and embedded in the grout. The axial and flexural strength required in
the other connections is not as high (5 kN and 0.4 kNm on wall 2; 2 kN and 0.2 kNm on walls
B and C) but it is nevertheless recommended to improve the corresponding anchorage,
especially on wall 2 because it is at the opposite end of the P2 section supporting wall 3.
6.2
Vertical Reinforcement
The amount and position of vertical reinforcement #3 should be clearly set: currently, there
are inconsistencies between the plan view (Fig. 2-1) and the elevations (Fig. 2-2, Fig. 2-3,
Fig. 2-6). For example, in wall A, the third vertical reinforcement starting from the right is
superfluous.
6.3
Realization of the Joints between Structural Elements
It would be useful to specify the in the drawing plans in which order the different structural
parts are built, especially when they are connected to each other through special joints. This
is particularly true for the joints between the reinforced concrete beams CS and the bond
beams SU (Fig. 2-15), the polines P1 and the beams SU (Fig. 2-22, Fig. 2-24) or the beams
SC (Fig. 2-23), and between the polines P2 and the beams SU (Fig. 2-27, Fig. 2-28, Fig.
2-29, Fig. 2-30). For example, it should be stressed that the units of the top bond beam, the
top reinforced concrete beam frameworks and reinforcement, as well as all the P1 and P2
channel sections, should be positioned in their final place before pouring the concrete and the
grout.
6.4
Alternative Anchorage of the Roof Support
Besides being difficult to realize, the proposed scheme for anchoring the channels sections
P1 and P2 onto the top beams SC and SU requires a lot of additional tasks (breaking of the
units, welding of steel pieces, cutting of the channel sections). An alternative scheme could
52
be to embed in the top beams steel anchors on which the channel sections P1 could be fixed
afterwards, as shown in Fig. 6-1. In this case, a 10 cm space remains between the top beams
and the roof and the channel sections can be easily and safely fixed after the completion of
the top beams. For fixing the double channel section P2, stronger anchors will be necessary.
Fig. 6-1 Embedded anchors for fixing the channel sections P1 on the SU and SC beams
6.5 Anchorage of the Vertical Reinforcement at the Top
Beams
According to the typical elevation Fig. 2-17 and the detail of Fig. 2-18, the vertical
reinforcement (#3 or #4) should be anchored in the foundation beam SF-1, and also in the top
beam SU (or SC in some cases). This requires the use of hollow units not only in the
intermediate bond beams SU, but also in the top ones. However, when the top bond beam
SU does not run horizontally (axis A, B, C and 2B), the holes of the top bond beam units do
not generally match with the holes of the standard units below. It is therefore recommended to
pour the grout filling before placing the top bond beam units. In some cases, the passing of
the vertical reinforcement will also require to break the bottom shell of the unit.
6.6
Realization of the Corners
Particular attention should be paid to the corners where the masonry units should be
alternated in order to avoid continuous vertical joints. This implicitly appears in the elevations
(Fig. 2-2, Fig. 2-3, Fig. 2-4, Fig. 2-5, Fig. 2-6 and Fig. 2-7) but is rather difficult to realize in
practice because the plane dimensions of the units (40 cm x 15 cm) are not in a 2:1
proportion. Even if all walls have a length multiple of 20 cm and, in principle, can be built with
full and half units only, it will be necessary to use also units of different length (35, 25, 15
and/or even 5 cm) near the corners and/or near the openings. Also, the vertical continuity of
the holes should be ensured. Hereafter, four possible solutions are examined:
o
In the first solution (Fig. 6-2), the bricks are alternated without ensuring the exact
vertical alignment of the holes. This solution requires a 5 cm horizontal shifting of
every other masonry course, so that a 1/3 running bond pattern is obtained. This has
major drawbacks: the vertical misalignment of the holes leads to a substantial
53
reduction of every other hollow, and the transverse webs of two superimposed units
do not coincide and thus cannot be mortared. This scheme is incompatible with the
plan dimensions and position of the walls and openings (not only half units, but also
units of 25 cm and 5 cm length will be required every other course to match the plan
dimensions), and it is difficult to achieve a regular 1/3 running bond pattern (lack of
points of reference).
Fig. 6-2 Corner without vertical alignment
o
The second solution (Fig. 6-3) preserves the original running bond pattern and thus
achieves a perfect vertical alignment of the holes. However, it requires the
preparation of units 35 cm in length. Furthermore, it is still incompatible with the plan
dimensions and position of the walls and openings (not only units of 35 cm in length,
but also units with lengths of 25 cm, 15 cm and 5 cm will be required to match the
plan dimensions). This last drawback can however be easily eliminated by modifying
slightly the plan of the house (5 cm reduction in both directions at each corner of the
house, keeping the same absolute positions of the openings).
54
Fig. 6-3 Corner with vertical alignment but incompatible with the original plan
o
The third solution (Fig. 6-4) again preserves the original running bond pattern and
thus achieves a perfect vertical alignment of the holes. It is perfectly compatible with
the original plan. However, it requires the preparation of units of length 25 cm,
besides the half bricks already needed around the openings. Furthermore, the
misalignment of the vertical joints near the corner is limited (only 5 cm).
Fig. 6-4 Corner with vertical alignment and compatible with the original plan
55
o
The fourth solution (Fig. 6-5) preserves the original running bond pattern and thus
achieves a perfect vertical alignment of the holes, is perfectly compatible with the
original plan and does not require the preparation of any special bricks. The
mismatch between the length and the width of the units is simply compensated by
one 5 cm thick vertical mortar joint at each course, but on alternate sides of the
corner. Only the first course will required some care as no reference will be available
(underlining unit).
Fig. 6-5 Corner not requiring brick cutting
Among the four possible solutions, only the second (provided that the plan of the house is
modified accordingly) and the fourth ones are recommended.
At the corner of the bond beams SU, the units should be broken so as to allow the horizontal
reinforcement #4 to run continuously or to have a sufficient splicing length (50 cm) as show in
Fig. 2-20.
56
57
7 References
[1]
Uniform Building Code 1997: Volume 2, International Building Code Council.
[2]
Ministerio de Obras Públicas República de El Salvador, “Norma Técnica para Diseño por
Sismo”, Reglamento para la Seguridad Estructural de las Construcciones. El Salvador,
1994.
[3]
Priestley, M. J. N., Seible, F. and Calvi, G. M., Seismic Design and Retrofit of Bridges,
John Wiley and Sons, 1996.
[4]
Salmon, C. G. and Johnson, J., Steel Structures: Design and Behaviour, Harper Collins,
1996.
[5]
Bambach, M. R. and Rasmussen, K. J. R., “Elastic and plastic effective width equations
for unstiffened elements”, Department of Civil Engineering, Centre for Advanced
Structural Engineering, The University of Sydney, 2002.
[6]
CAST3M
[7]
Hognestad, E., “A Study of Combined Bending and Axial Load in Reinforced Concrete”,
Bulletin Series 339, Univ. of Illinois Exp. Sta., November 1951,
[8]
Dahlblom O., Ottosen N.S., “Smeared Crack Analysis Using Generalized Fictitious Crack
Model”, J. Engrg. Mech. 116(1), pp55-76, 1990.
European Commission
EUR 22324 EN – DG Joint Research Centre, Institute for the Protection and Security of the Citizen
Armelle, Anthoine - Taucer, Fabio
Seismic Assessment of a Reinforced Concrete Block Masonry House - PROARES Project in El Salvador
Luxembourg: Office for Official Publications of the European Communities
2006 – 72 pp. –
21 x 29.7
cm
EUR - Scientific and Technical Research series; ISSN 1018-5593
Mission of the JRC
The mission of the JRC is to provide customer-driven scientific and technical support for the
development, implementation and monitoring of EU policies. As a service of the European
Commission, the JRC functions as a reference centre and technology for the Union. Close to
the policy-making process, it serves the common interest of the Member States, while
independent of special interests, whether private or national.

full text - European Laboratory for Structural Assessment

Transcription

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