Modeling and seismic analysis of dissipative hybrid steel-concrete structure

1 Table of Contents 1. Introduction ... 4 2. State of art ... 5 2.1 Composite Systems ... 5 2.1.1 Materials ... 12

2.1.2 Composite Floor Systems ... 13

2.1.3 Composite Building Systems ... 14

2.1.4 Composite Columns ... 16

2.1.5 Composite Beams... 22

2.1.6 Shear Connection ... 24

2.1.7 Connections ... 27

2.1.8 Coupling Shear Wall ... 31

2.2 Hybrid Coupled Shear Wall (HCSW) ... 34

3. Purpose of the thesis... 36

4. Case of study ... 37

4.1 Configuration of HCSW system ... 39

4.2 Input values ... 43

5. Analysis ... 45

5.1 Global pushover curve ... 45

5.2 ULS1 – Compressive strain in shear wall ... 49

5.3 Long and short links: rotation limits ... 49

5.4 ULS2-3 – Maximum L.S. and C.P rotation of the steel links ... 52

5.5 Concrete wall base ... 56

5.6 DLS - Displacement of interstorey drifts ... 57

5.7 Performance point for 0.15g, 0.25g, 0,35g... 60

5.8 Method N2 ... 61

5.9 Behavior factor q ... 67

6. Analysis of the results ... 69

7. Conclusion ... 72

Annexes ... 72

2 List of Table

Table 1 Comparison of Column Cost [3] ... 21

Table 2 R.C. wall configuration ... 38

Table 3 Bottom link configuration ... 40

Table 4 Top link configuration ... 41

Table 5 Reinforcement of confined and unconfined area ... 41

Table 6 Material properties ... 44

Table 7 Ground Type C [9] ... 44

Table 8 ULS1- Ground acceleration according to concrete strain limits ... 46

Table 9 Rotation values for LS and CP... 51

Table 10 4F07W – Link beam rotation limits ... 51

Table 11 Ground acceleration according to L.S. link limitation ... 52

Table 12 Ground acceleration according to C.P. link limitation ... 53

Table 13 Comparison between the plastic moment values at the base of R.C. wall ... 56

Table 14 DLS - Ground acceleration according to interstorey drift limitations ... 57

Table 15 Performance point values ... 60

Table 16 Values from method N2 (4F07W case) ... 67

Table 17 Behavior factor (based on ductility) for all cases ... 68

Table 18 Maximum sustainable accelerations from pushover curves and ULS/DLS criteria in [g] ... 69

List of Figure Fig. 1 Spiral shear connector ... 6

Fig. 2 Hooks connectors [1] ... 7

Fig. 3 Steel deck with continue concrete coverage ... 8

Fig. 4 Shear connectors welding through steel deck ... 8

Fig. 5 Cellular steel flooring ... 9

Fig. 6 Planimetrical disposition of shear wall in the Nihon Kogyo Bank building [2] ... 10

Fig. 7 Perimeter column in World Trade Center ... 11

Fig. 8 Section of two Union Square (Seattle) [3] ... 11

Fig. 9 Typical composite beam and steel deck system [3] ... 13

Fig. 10 Composite Floor Systems [4] ... 14

Fig. 11 Concrete shear walls with steel link beams [3] ... 15

Fig. 12 Encased Composite Columns ... 17

Fig. 13 Simple beam-to-column connection (a) – Rigid beam-to-column connection (b) [3] ... 17

Fig. 14 Transition Column [3] ... 18

Fig. 15 Composite section with reinforcements welded on the web [5] ... 19

Fig. 16 Transfer Zone in beam-to-column composite connection [5] ... 19

Fig. 17 Composite Column Section [5] ... 20

Fig. 18 Shear Connectors for composite columns ... 20

Fig. 19 Filled Composite Columns ... 21

Fig. 20 Plastic Resistance of Encased Steel Section [4] ... 22

Fig. 21 Deformed shape in case of no interaction (a), perfect interaction (b), normal interaction (c) ... 23

Fig. 22 Transfering Capacity and Degree of interaction [3] ... 24

Fig. 23 Push-out test specimens [3] ... 24

Fig. 24 Shear-slip curve for stud connectors [3] ... 25

Fig. 25 Types of connectors [5] ... 26

Fig. 26 Column Connection using brackets [5] ... 27

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Fig. 28 Column End Plate Connection [5] ... 28

Fig. 29 Beam-to-beam Connection with direct support from the column [5] ... 29

Fig. 30 Beam-to-beam Connection with direct support of the primary beam [5] ... 29

Fig. 31 Beam-to-beam Connection with web plate [5] ... 30

Fig. 32 Beam-to-beam Connection with bracket [5] ... 30

Fig. 33 Beam-to-beam Connection with steel rib [5] ... 31

Fig. 34 Comparison between (a) isolated and (b) coupled shear walls [6] ... 32

Fig. 35 Reinforced Concrete Coupling Beams typical reinforcements [7] ... 33

Fig. 36 Diagonally reinforced concrete couple beam [8] ... 33

Fig. 37 Hybrid Coupled Shear Wall (HCSW) ... 34

Fig. 38 Innovative Hybrid Coupled Shear Wall system... 35

Fig. 39 Floor geometry of the benchmark structure with position of HCSWs ... 37

Fig. 40 Configuration 1 for the shear link ... 38

Fig. 41 Configuration 2 for the shear link ... 38

Fig. 42 Plane view of the numerical model with HCSWs ... 39

Fig. 43 Confined and Unconfined part in a shear wall [9] ... 39

Fig. 44 Link notation ... 42

Fig. 45 Strain plane beam finite element with three nodes ... 43

Fig. 46 Material laws for FinelG ... 44

Fig. 47 Base shear - displacements for 4F07W case ... 46

Fig. 48 4F07W– Global pushover curve with sequence of yielding for each case ... 48

Fig. 49 4F07W – Storeys P – ∆ relationship ... 49

Fig. 50 4F07W - Shear force - rotation relationship ... 54

Fig. 51 4F07W - Bending moment - rotation relationship ... 55

Fig. 52 Bending moment/Shear force - rotation relationship ... 56

Fig. 53 Interstorey drift ... 58

Fig. 54 Determination of the idealized elasto-perfectly plastic force-displacement relationship [9] ... 62

Fig. 55 Determination of the target displacement for the equivalent SDOF system [9] ... 63

Fig. 56 Capacity curve for MDOF and SDOF system (4F07W-60CR) ... 64

Fig. 57 Determination of idealized force-displacemet relationship (4F07W-60CR) ... 65

Fig. 58 Elastic-acceleration and displacement spectrum (4F07W-60CR) ... 65

Fig. 59 Acceleration-displacement spectrum (AD) format (4F07W-60CR) ... 66

Fig. 60 Demand spectra versus capacity diagram (4F07W-60CR) ... 66

Fig. 61 Graphical conception of behavior factor q based on ductility ... 67

Fig. 62 4 Storeys - global comparison ... 70

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1. Introduction

Steel and composite structure are common for buildings in seismic area, while steel and concrete hybrid solution are less diffused. The main difference between commonly used composite structure and hybrid structure, is that in the former case the deformation demands of concrete and steel elements are in the same range (and so steel and concrete act as one member), instead in the latter case the deformation demands depend on the capacity of each material. So, it’s possible to to define innovative steel and reinforced concrete hybrid systems for the construction of earthquake-proof buildings.

One of the aim of INNO-HYCO Project (INNOvative HYbrid and COmposite steel-concrete structural solutions for building in seismic area) is to study steel-concrete hybrid systems obtained by coupling reinforced concrete shear wall and steel frame. This systems will exploit both the stiffness of reinforced concrete and the ductility of steel elements.

In this thesis, an analysis of composite structure will be presented, with their story and the different structural solution for this structural system; we will study in deep the different solutions for composite beams and columns and we will talk about shear connectors. Then we’ll discuss about coupling shear wall and hybrid systems, in particular the Hybrid Coupled Shear Wall system (HCSW system) will be presented.

In order to know the behavior of this system, we will analyze two main solution: 4-storey case and 8-storey case. For each case, three different configurations of the shear wall by a wall ratio (wall height / wall length) will be presented, and for each one of these configuration different solutions depending on the dimensions of the steel cross section of the link will be analyzed. We will analyze the seismic behavior of these structure with a nonlinear static (pushover) analysis, providing their yielding curve, the rotation of the link and of the concrete wall base and the displacements of the floors.

At the end of the work the behavior factor q (based on ductility of the system) for each analyzed case will be determined.

5 2. State of art

2.1 Composite Systems

The term “composite construction” is generally associated with the technique of coupling steel joists and concrete slabs by means of a different type of connectors. This connectors have the function of transmit shear force between concrete and steel elements. Composite structure were known in Europe and in United States since the beginning of 20th century. At the beginning, the steel was considered the only structural element, while concrete was functional for protection. These structures weren’t built to resist seismic actions, but engineers noticed they behaved better under strong earthquakes than a pure steel structure. On August 8, 1988 the Bank of China was topped out in Hong Kong. This is one of the most spectacular buildings of combined structural steel and concrete, and it was like a tribute to a century of progress in the field of composite construction. In this building, the structural engineers made perfect use of the principal virtues of the component materials: the tensile strength of steel and the compressive strength of concrete.

The combined structural use of steel and concrete, was first encountered almost as soon as the two materials became available to structural engineers. Steel-concrete composite structures, were known in Europe and in the USA since the late 19th century. With the production of Portland and the invention of Bessemer converters1 in 1860s, became possible to supply steel in quantity. From that time output grew rapidly. In 1879, William LeBaron Jenny used steel in the skeleton of the Home Insurance Building in Chicago. Its construction commenced with wrought-iron beams for the first six storey, but was completed with steel beams elements. The first well-documented structural use in United States of rolled beams embedded in concrete, was in the Ward House, a private residence completed in Port Chester in 1877. This building was one of the first to use this new combination, which became more common more or less one decade later. The Methodist Building, built in 1894 in Pittsburgh, was one of the first to use concrete-encased steel floor beams. In 1897 a fire started nearby building, and consumed the contents of the Methodist Building, but the structure remained relatively unaffected. From this moment, were made a lot of studies about the fireproofing of composite structure, and in 1905 the American Society of Civil Engineers (ASCE) stated that reinforced concrete proved satisfactory for fireproofing steel in buildings and also as a protection to the steel work over railroad tracks. In the first years of XX century, started the first systematic tests of composite columns, at Columbia University’s Civil Engineering Laboratory, conducted by W. H- Burr. In 1912 N. Talbot and A. Lord reported on test of 31 columns made at University of Illinois including 21 composite and 10 bare steel columns. The tests indicated that the strength of composite columns may be predicted best by adding the separate strengths of the steel and concrete parts of the column. In 1922 started also in Canada test of two panels, each consisting of a concrete slab and two steel H beams encased in concrete. During these tests, the slabs were thought as a structure where the steel and concrete acted together, so as to form a composite beam.

1 _{Bessemer converters was used in Bessemer process, which was the first inexpensive industrial}

process for the mass-production of steel from molten pig iron prior to the open hearth furnace. The process is named after its inventor, Henry Bessemer, who took out a patent on the process in 1855.

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In the same time, in Europe and also in USA, test of composite beams were carried out, and all of them indicated good interaction between the two materials. In 1924, H. M. MacKay, conduced a new series of tests to obtain additional bond and horizontal shear data. As an innovation from the traditional full encasement, several specimens had only their top flanges embedded in the slab. In 1928, R.R. Zipprodt, structural engineer of the Portland Cement Association, reported that American and Canadian codes made no allowance for the strengthening effect of the concrete encasement; in the same year, there were test on six panel floor (12m x 20m), contained steel beams fully encased in concrete, made with gravel aggregates in four panels and cinder in the other two. The tests demonstrated the strengthening effect of the concrete, and the committee recommended higher allowable steel stresses for encased steel beams.

The solution to the loss of bond was indicated in two patents issued in 1903 and 1926. Both patents proposed to connect the steel beam to the concrete slab by mechanical means. These may have been the first proposals for mechanical connectors, an innovation that gave an important contribution to the evolution of composite construction. Beams of this type were evaluated in the first part of the century. Six of the eight specimens test failed in flexural compression after the yielding of the steel beam or failed in bond, and one test was discontinued before failure. Good interaction at working loads and high overloads capacities were observed. The first systematic studies of composite beams with mechanical shear connectors were made in Switzerland in connection with the development of the alpha system. The system appears to have had its origin in Belgium and some early applications in France. In this method of construction, the transfer of horizontal shear from the concrete slab to the steel beam were assured by round bars formed into helix. The helix, called a spiral shear connector (Fig. 1), was welded to the top flange of the steel section at the points of contact along the length of the beam.

Fig. 1 Spiral shear connector

After the early studies of spiral connectors, the European research community turned its attention to two new types:

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Fig. 2 Hooks connectors [1]

• stiff connectors made from rectangular steel bars or from rolled shapes welded to the steel beam in such manners as to offer most resistance to bending

The two types were often combined, with the stiff connector assigned the function of preventing slip while the hook was to resist upfit. These test conducted in Switzerland and Germany were followed by general acceptance in practical application to highway bridges.

In the second half on 20th century, the stud connectors were introduced through experimental investigations started at Imperial College in London. The studs not only provided a more economical shear connectors, but also made practical the application of composite construction to building floors. In USA the first structure with stud shear connectors were erected in 1956 in New York (IBM’s Engineering Laboratory) and in Philadelphia (tank platform of the American Sugar Refinig Company).In a few years, major building were built with composite floors. Today the stud connector is used throughout the world with the exception of those countries where semiautomatic studs welding is uneconomical. The stud connector soon gained a wide acceptance and, thanks to its economy, replace the older spiral and channel connectors within a few years.

Two other related developments had lasting effect on composite floor construction: formed (corrugated) steel decks and cellular steel flooring. Formed steel decks, were designed to support concrete and carry construction loads. However, it was soon observed that the decks bonded to the concrete and contributed to the structural response of the finished slabs. The steel deck form, served as one way slab reinforcement. When loaded to failure, large slips appears between the decking and concrete, before the ultimate load was reached. The final failure of this structural solution, was usually a combination of shear and bond. Based on tests, the deck manufacturers published load table and installation guidelines for their products. Today, deck reinforced slabs are used universally in steel framed buildings. For composite floor construction, the permanent steel forms resulted in a complete elimination of bond between the concrete slabs and the steel section, except in case that the forms spanned only between the flanges of the supporting beams. This last form of construction, was adopted for bridges and has been used to this day. On the other hand, in building constructions, the economy favored continue coverage over the supporting beams (Fig. 3).

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Fig. 3 Steel deck with continue concrete coverage

Thus, to obtain composite action between the concrete slab and the supporting steel beams also in buildings constructions, engineers founded solution to weld the shear connectors (shear studs usually) through the steel deck (Fig. 4). There were studied solutions to weld manually the connectors through the deck to the supporting steel beams. For early applications of stud connectors, holes were punched in the steel deck, but by the seventies the stud manufacturers developed methods for semiautomatic welding also through galvanized deck.

Fig. 4 Shear connectors welding through steel deck

During the same years, there were a development of this structural solution. The new solution was the cellular steel flooring (Fig. 5), a lightweight floor which could be mass produced, simply shipped to the site, rapidly laid in place, making possible an economical saving in the steel frame of foundations and making also possible to use this cellular floor for electrification to run a building’s power, telephone and other installations. But the growth of this early system was limited because it had to be combined with fireproof ceiling systems, invariably and expansive item. The birth of spray on fireproofing set off a rapid growth of cellular steel floors.

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Sprayed on beams and the underside of steel decking, the new fire protection eliminated the need for costly fireproof ceilings.

Fig. 5 Cellular steel flooring

During the eighties, were made also study about design of composite columns, a structural solution used frequently in buildings during the first half of 20th century. While the primary function of the concrete encasement was fire protection, it was assigned a portion of the total load resisted by the column even in some of the very early applications. However, the introduction of lightweight fireproofing concrete after the Second World War, resulted in an almost complete elimination of composite columns from the new buildings. They returned only in the early 1970s. All over the world were made a lot of studies about the behavior of composite columns, initially in terms of working stresses and later adjusted to the ultimate strength level. An area that was not deeply studied, is that of composite structural joints. To this day, most of the joints for composite members are designed as for steel structures without any regard for concrete. Some early experiments, were carried out on beam-to-column joints at Lehight University. Studies of connection were particularly numerous in Japan and where concerned principally with the resistance of joints to earthquake forces. The elements of composite structure are well tied together. This major characteristic of composite construction is particularly beneficial in areas subject to frequent strong earthquakes. It is this characteristic that made composite design particularly popular in Japan.

An example of this good seismic behavior of composite structures was the Nihon Kogyo Bank building of Tokyo (Fig. 6), designed by engineer Tachu Naito in 1921. He decided to use reinforced concrete walls at the boundary of the building and at the staircase. The aim of Naito was to increase structure stiffness and to guarantee fire protection.

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Fig. 6 Planimetrical disposition of shear wall in the Nihon Kogyo Bank building [2]

The building survived the Great Tokyo Earthquake of 1923, demonstrating that the composite system was earthquake-resistant.

Despite these early experiences with composite buildings, reinforced concrete became the most used anti-seismic structural material due to its low cost and versatility. Only in the last 20 years the engineers started to consider composite structure as alternative to reinforced-concrete structures. Extensive studies of the design of composite buildings have been under way in Europe since about 1980, in connection with their development of structural design codes with multinational applicability, the so called Eurocodes. Provisions for composite construction comprise Eurocode 4, the first part of which is concerned primarily with buildings.

Anyway also in other country except Japan there were a lot of building completed with composite structure. For example, about United States, since 1930 the New York City building code permitted higher allowable stresses for steel beams encased in concrete. Connecting steel beams to concrete floor slabs with shear connectors, became a common practice during the 1960s. The beginning of frequent use of composite columns in tall buildings, dates to about 1980s.

A well known example of composite structure was the pair of World Trade Center towers, also known as “Twin Towers”, in New York City. It was noteworthy in its magnitude and complexity and in its pioneering advances of high-rise building technology. At 417 meters above the street level, the towers accommodated 110 floors, each of 63 m2 . Over 200000 tons of structural steel were required for the project. The wind loads was considered only for the exterior walls. The exterior walls are composed of 240 tubular columns that form a steel plate spandrel composing a Vierendeel truss (spaced 1 meter and 1.3 meter deep) (Fig. 7). The vertical loads are transferred from the 10 cm concrete slabs to the core columns by trusses spanning 18 to 11 meters. The 2 meters space between two adjacent trusses is spanned with corrugated steel decking that tied the two trusses into an unique unit. The web of the trusses extend 8 cm above the upper flange of the beams into the slabs to provide composite floor action. To avoid accelerations during high winds, viscoelastic dampers were installed between the exterior columns and the end of the floor trusses.

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Fig. 7 Perimeter column in World Trade Center

Another important example of composite building structure are the two Union Square in Seattle. Union Square has four composite pipe columns (of 3 meters diameter, as we can see in Fig. 8) at the corners of its core. Fourteen more composite pipe columns do smaller diameter are placed along the periphery of the building to support gravity loads. There are no reinforcing bars in the pipes’ interior surfaces. The core provide about 40% of the gravity load of the building and provides resistance to lateral loads as wind. The space between the core and the periphery columns is column free. This construction was completed in 1990.

12 2.1.1 Materials

Composite construction is characterized by interactive behavior between structural steel and concrete components designed to use the best load-resisting characteristics of each material. The most important characteristics of structural steel are high strength, high modulus of elasticity, and high ductility, which result in small size members, thus a smaller weight. Other major advantages relate to steel’s ease modification and high speed of erection. The role of structural steel in composite construction is oriented in:

• Floor framing where the ability to span long column-free areas is required;

• Gravity columns to reduce the cross sectional area requirement, allowing more column-free floor space;

• Areas of high seismic activity where high ductility and low mass are advantages.

Structural steel sections used in composite construction include the entire catalogue of rolled shapes, structural pipe, square and rectangular tubing etc., but the most used rolled shapes are wide flange sections.

Structural concrete for composite building construction is based primarily on compressive strength and unit weight. Lightweight concrete is often used in floor slab construction to keep down the overall weight of the structure and to reduce shoring requirements. Lightweight concrete is a better insulator than normal concrete and can also provide the required fire separation between floors with thinner slabs. Concrete-filled composite steel pipe columns with compressive strength up to 130 MPa have been used recently. One of the most important aspect of composite structure, is the connection between the two materials concrete and steel. Many types of connectors including steel studs, channels, angles, bars, have been used in the past for this purpose. The headed steel stud welded on the upper flange of the beam is the most common type of shear connector today. Shear studs are easily welded trough the steel deck. Steel deck supports fresh concrete in an integral component in many composite systems. Steel deck can be used as a permanent formwork for a conventionally reinforced concrete slab as the positive bending tension reinforcement. Composite steel deck increases floor load capacity and improves horizontal diaphragm action. Typically the steel deck is of trapezoidal profile with wide and connected to the beam with shear studs (Fig. 9).

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Fig. 9 Typical composite beam and steel deck system [3]

2.1.2 Composite Floor Systems

Composite floor systems, typically involve simply supported structural steel beams, joist, girders or trusses linked by shear connectors with a concrete floor slab, to form a T beam which resists to gravity loads by bending. The versatility of this system, depends on the ability of the concrete to work in compression and on the ability of the steel beams to span long distance. Composite floor systems are also advantageous in reducing material cost and construction time. They also result in simple and repetitive connection details. This structural system is also very important especially in seismic zones because of its low building mass. The composite action of the beam or truss element is guaranteed by direct welding of shear studs through steel deck as flexural reinforcement for the concrete. The slab-and-beam arrangement typical in composite floor systems produces a rigid horizontal diaphragm that provides stability to the overall building system. The main advantages in using composite floor system is that their construction does not require highly skilled labor. As told before, steel deck is a permanent formwork for the concrete, and it can be used to receive the electrification or other type of systems. Concrete slab, thanks to the characteristics of concrete, can also provide corrosion and thermal protection for the steel deck (it’s quite simple provide 2h-fire rating for a composite floor system).

There are different methods in construction of floor slab, the most important are: • Cast in situ reinforced concrete slab (Fig. 10(a));

• Precast concrete planks with cast in situ concrete above (Fig. 10(b)); • Precast concrete slab with in situ concrete at the joints (Fig. 10(c)); • A metal steel deck with concrete composite or not (Fig. 10 (d)).

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Fig. 10 Composite Floor Systems [4]

The composite action between steel deck and concrete, results from the embossments on the steel sheet profile.

2.1.3 Composite Building Systems

The success of combining steel and concrete into composite floor systems, gave rise to development of composite building systems. Economic studies all over the world and in particular in United States, have shown that to reach a given strength and stiffness, a concrete or composite column is more economical than a pure steel column. The advantages of steel, as the strength, speed of construction and light weight, can be combined with the advantages of concrete, as stiffness, fireproofing and economics. Engineers have used these ideas to develop a variety of composite building systems which can be categorized as:

• Exterior composite frame • Supercolumn framing • Interior composite frame

The first group includes composite columns with concrete or steel girders and concrete columns with steel girders or trusses. Composite columns with concrete spandrels were first used bi Kahn in 1967 on the 20 story Control Data building in Houston. The combination of exterior

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composite columns with steel girders has received a great deal of research, primarily in Japan where many structure were built using this system because of its resistance to lateral loads. Supercolumn framing has long been considered the most efficient method to resist lateral loads in tall building. It consists in provide a few large columns, called supercolums, as far apart as possible and connect them with diagonals or Vierendeel frames. This construction method has some advantages, because the steel pipe works as formwork and provides confinement for the concrete; generally are not used longitudinal reinforcement bars, so the construction is simpler; in most case there are no diaphragms into the steel pipe and the flange forces are carried directly by the pipe. Concrete-filled steel tubes with steel girders, were used in Japan and also in Taiwan. In case of large concrete-filled steel tubes or pipes, the area of structural steel could be high and so their costs were high. An alternate is to form the supercolumn as a normal reinforced concrete structure and use a light structural steel section.

The group of Interior composite frame, includes shear walls with steel frames or steel link beams and composite columns with welded steel girders. When a building structure is formed by a shear wall with steel frames, the concrete shear wall are placed in the core of the building. General the steel wall provide the entire lateral stability for the structure. The design of this type of construction is limited by the strength and by lateral and torsional stiffness of the wall for large lateral loads. A variation of shear walls with steel represented by composite shear walls with simple steel frame. In the case of composite shear wall, the steel frame is erected first. The frame includes steel columns to be encased in the shear wall, steel beams and concrete slabs. This system has some advantage, as:

The erection of the steel frame is done in a conventional manner without the obstruction of concrete wall;

The need for the weld plates when the wall is built before the steel frame is eliminated.

Analytical models of concrete shear walls with steel link beams indicate that high shear forces are induced in link beams in coupled shear walls. This can result in shear failure of concrete. One possible way to increase the ductility is to provide structural steel link beams as shown in Fig. 10.

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Coupled shear wall systems are an important part of this thesis work, and will be analyzed more deeply in the next chapters.

2.1.4 Composite Columns

The main function of columns is to transfer the vertical forces to the base of structural frame. The column cross section is traditionally determinate by using the most economical combination of material in order to resist only axial loads. But columns can be more than pure compression members. Columns connected to beams with moment-resisting connections, can improve the stiffness of the structure to lateral deflections. For this reason, their cross section has to be chosen for both axial and flexural demands. In composite columns, as in the other composite elements, steel and concrete work together. Concrete is a material with high compressive strength and low cost, while steel is the most efficient structural material for slender columns. Two type of composite columns are used in building, one with the steel section encased in concrete and other one with the steel section filled with concrete. In composite construction, the bare steel sections support the initial construction loads, including the weight of structure during construction. Concrete is later cast around the steel section, or filled inside the tubular sections. The lighter weight and higher strength of steel permit the use of lighter foundations. The subsequent concrete addition give to the structure bigger lateral stiffness.

Using of composite columns with composite floor systems and composite beams it is possible to erect high rise structures in an efficient way. That’s because it’s possible to carry out numerous working group simultaneously. For example

• One group of workers will be erecting the steel frame for one or two storeys; • Two or three storeys below, another group of workers will be fixing the metal

decking for the floors;

• A few storeys below, another group will be concreting the floors;

• Few storeys below another group will be putting the column reinforcement;

• Another group below them will be fixing the formwork and placing the concrete into the formwork.

The use of composite columns present a lot of advantages, as the increasing of the strength for a given cross sectional dimension and of the stiffness, reducing the slenderness of the column and so its resistance to buckling; in the case of concrete encased columns, composite column provides protection to the corrosion and good fire resistance to the column; significant economic advantages over pure structural steel or reinforced concrete alternatives; formwork is not required for concrete filled tubular sections. Steel profile encased in concrete, are also a very common solution because of aesthetic reasons.

Encased composite columns, consist generally in concrete encased hot-rolled steel section. The concrete requires vertical and horizontal reinforcements to sustain the encasement of the steel core. It’s quite common to use shear connectors to ensure interaction and force transfer between the steel profile and the concrete encasement. The transfer of shear force with connectors is

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guaranteed through attachment by welds to the steel shape and by bearing against the surrounding concrete.

Fig. 12 Encased Composite Columns

In this type of composite columns, steel section is designed to carry the construction weight of the steel frame plus the weight of concrete. The steel core of the column, permits standard shear and moment connection between the column and the steel floor beam. The connection can be simple or rigid (Fig. 13(a) or (b)).

(a) (b)

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Another typical connection in composite column, is represented by composite transition columns, which has the function to transfer axial load from steel columns of upper levels, to reinforced concrete columns below (Fig. 14). This solution is typical in buildings that have a steel frame for the upper part of the building, and reinforced concrete frame in the lower floors (as can happen in steel office building with concrete parking garage). Transition column is used in this case, in order to avoid the use of big connecting steel plate at the base of steel column above the concrete frame. Transition column should be extended one or more floors, depending on how big the axial force is.

Fig. 14 Transition Column [3]

The cruciform section (on the right in Fig. 11), is formed by two steel sections, sometimes identical, one of which is cut into two part. The two part are welded to the web of the other steel girder. In this type of composite column are common I sections, with a depth greater than 400 mm. There are used other types of section that combine two steel members, as composite section with reinforcement welded on the web (Figure 15). The main steel girder is reinforced in the area between the flanges by one or more smaller steel sections. The reinforcement profile are typically H sections, which are welded to the web of the main member. The use of this quantity of steel added to the presence of the concrete, generate a composite column with excellent fire resistance.

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Fig. 15 Composite section with reinforcements welded on the web [5]

Loads are rarely transferred into the column through a plate which distributes them correctly between the steel and concrete components. Normally, the floor beams are attached directly to the steel component of the column, so the load must be transferred to the concrete. This necessitates the position of transfer studs in a transfer zone (Fig. 16). Shear transfer is obtained by mechanical shear connection which prevents any significant slip between the steel and concrete. Partially encased sections, with concrete only present between the steel flanges, must in all cases adopt a certain number of mechanical shear connectors fixed to the web of the steel member. Without such connection the concrete may spall away from the web under the action of thermal stresses during a fire. The mechanical shear connection required could be obtained in different ways, using headed studs welded to the web or welding the stirrups to the web, or using bars passing through holes in the web. Some different ways to create shear connection are presented in Fig. 17.

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Fig. 17 Composite Column Section [5]

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Filled composite columns, may be the most efficient application for column cross section. Their steel section can be a pipe, a tube or a result from the welding of steel plates. In this kind of applications, steel section provides form for the concrete core that increasing the strength and the stiffness of the column. The steel also provides transverse confinement to the contained concrete, making the filled concrete very ductile. The interaction between steel and concrete is assured by the geometrical configuration, with the concrete incased in the steel profile. In some cases, is better to provide additional bearing surface for shear transfer with studs welded inside the shell near the connection between the columns and the floor beams.

Fig. 19 Filled Composite Columns

For multistory building, where the steel column needs to receive fireproof treatment, structural engineer could design a reinforced concrete core in order to support the full axial load without the help of steel section during fire. In high building, is common the use of filled concrete supercolumns with high-strength concrete. This kind of composite columns, were developed later than the first type we have talking about before. Filled concrete steel section, are based on a principle that steel and concrete are most effective in tension and compression respectively. The first studies about this solution were in 1960s, and it was an expansive solution because of the thickness of the steel profile. This was the main cause of the limited initially applications of this solution all over the world. One of the country where this solution has been widely utilized, is Japan. Here, thick steel tubes were necessary to give grater ductility to the section, which is desirable for cyclic loads as earthquakes loads. Recently in Australia, Singapore and other developed nations the use of this solution is increased. The main causes of this interest are linked to the speed of construction that can be obtained with this solution, due to the following factors:

• The steel column act as permanent formwork; • The steel column provides lateral reinforcements;

• The steel column can supports several storey before the concrete filling.

An interesting analysis was made by Webb and Peyton about a comparison between the costs of reinforced concrete columns, pure steel column, encased-concrete steel columns, steel tubes filled with reinforced concrete and steel tubes filled with concrete. It was made a comparison for 10-stroreys building and 30-storeys building. (Table 1).

22

(Source: Webb and Peyton, The Institution of Engineers Australian, Structural Engineering Conference, 1990).

The plastic resistance of an encased steel section or concrete filled rectangular or square section is given by the sum of the resistances of the components of the section as the concrete section, the steel section and the steel reinforcement to the concrete section (Fig. 21). For composite columns using circular tubular sections, there is an increased resistance of concrete due to the confining effect of the circular tubular section. However, this effect on the resistance enhancement of concrete is significant only in stocky columns. For composite columns with a limited slenderness, or where the eccentricity e of the applied load does not exceed the value d/10, (where d is the outer dimension of the circular tubular section) this effect has to be considered with corrective coefficients 10 and 20 ,which values are presented in EC4 in function of .

Fig. 20 Plastic Resistance of Encased Steel Section [4]

2.1.5 Composite Beams

Composite beams are recognized as the best elements for composite floor systems thanks to their ease of construction, strength and fireproof characteristics. Over the years, have been developed three variant of steel composite beam:

• Composite beam with web opening; • Composite trusses;

• Stub girders.

Generally the steel element beam and the concrete slab, are mechanically connected using headed steel studs welded to the top flange of the steel beam. The shear connection can be reached trough in different ways, not just shear studs but also reinforcing bars or plates welded on the top of the steel flange. The simplest configuration of composite beam is the one in Fig. 9, which can be used for spans up to 18 m. Is assumed that composite beams carries all the tension and the concrete slab the compression. Can be considered different mechanism for the transfer of shear force, as adhesion, friction and bearing. Adhesion and friction are generally considered just in case of steel sections fully encased in concrete. According to the connection between the concrete slab and the steel profile, there are different behavior for the composite beam. If there is no connection between concrete slab and steel profile, the answer of the two material depend on their resistance (Fig. 22 (a)). This kind of structural solution is rarely used nowadays. If we assume perfect connection between concrete and steel, the beam and the slab respond as a single unit (Fig. 22 (b)). This connection could be solved with a perfect connector which can transfer infinite shear, bending and axial force. This is an ideal solution, because there is no connector which can guarantee this behavior. The most economical design for this solution is to consider that connectors can transfer as shear force the smaller value between tensile capacity

23

of steel beam and compressive capacity of concrete (0,85Acls fcd). Between the two solution reported below, there is the solution of partial shear connection (Fig. 22 (c)). In this case the connection provide a transfer force less than the smaller between tensile capacity of steel beam and compressive capacity of concrete. The strength provided by this solution can be consider with a linear interpolation between the two ideal solution of no connection and perfect connection (Fig. 23). Composite girder forms allow the passage of services through the web of the steel beam. In composite beam, is necessary to avoid floor vibrations. Generally composite floor systems results in low vibration amplitudes, so rarely this structural solution transmit vibrations to the occupants for span up to 12 m. For long span, bigger than 12 m, particular care is required. Other type of composite beam are castellated beams. This kind of beam is realized from hot rolled beams by cutting along the web. Castellated beams have limited shear capacity and are used as long span secondary beams. Composite trusses is another very used system. It has high cost of fabrication, but this solution can be cost effective for long span beams. A disadvantage of this structural solution is the difficult to provide fire protection for all the elements. The resistance of composite truss is governed by yielding of the bottom flange, crushing of the concrete slab, failure of shear connectors, buckling of the top chord or buckling of the web. The first of these mechanism is the better one, because of its ductility.

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Fig. 22 Transfering Capacity and Degree of interaction [3]

2.1.6 Shear Connection

Shear connection at the interface between concrete element and steel element is the key element to provide composite action to the structural member. As shown in the introduction chapter, in the past were used a lot of typology of shear connectors, but the one which is widely used is the welded shear stud. Shear connectors has to resist to the horizontal shear force at the interface of concrete slab and steel beam flange. The behavior of welded shear studs, are generally studied with the push-out test. This test was developed in 1930s, but nowadays there is no standard procedure for the fabrication of specimens. The consequence of the lack of standard procedure, is the difference between the procedures utilized during the research test. The results of push-out test is a relationship between load and slip of the concrete slab. Generally the configuration for the push-out test is show in Fig. 24.

Fig. 23 Push-out test specimens [3]

A problem associated to this configuration, is that the concrete has to be casted in two different days. The result is a difference of the concrete property of the two sides. Modification to the typical specimen can alleviate this problems. Recently has been introduced an important modification to improve the push out procedure. This modification consist in the placement of a

25

yoke device in order to simulate gravity load and in order to prevent the separation between concrete slab and steel profile. Shear load is applied with the testing machine in incremental loads. The control of the displacements start when the load reach the 80% of the expected capacity. In addition to the shear load, is applied a load normal to the slab surface. The normal load is increased along with the shear load. The typical result of this test is shown in Fig. 25.

Fig. 24 Shear-slip curve for stud connectors [3]

The relationship between strength and slip of the concrete slab, can be expressed in analytical form with the relation

Q=Qu(1-e -As

)B

Where Qu is the ultimate strength, s the slip, A and B are constants. The specimens for the push-out test show in Fig. 24, are used in order to determinate the ultimate strength of studs. The nominal strength Qn is given by the following formula:

= 0.5 ′ ≤

where Asc= cross sectional area of the shear stud; f’c= compressive strength of the concrete; Ec= modulus of elasticity of the concrete;

Fu= minimum specified tensile strength of stud steel.

The shear connection strength increases along with the increase of concrete compressive strength up to a maximum represented to the tensile strength of the shear stud. In push-out test, the failure are controlled by the concrete for low values of concrete compressive strength, and by the steel for high values of concrete compressive strength. The design shear resistance of

26

studs in Eurocode 4, if the welded stud fails by fracture of the weld collar, is given bu the following:

PRd= 0.8 fu ( d 2

/4) Mv PRd= 0.29 d2(fck Ecm) 1/2/ Mv where d= is the diameter of the stud;

fu= the ultimate strength of the stud;

fck= The characteristic cylinder strength of the concrete; Ecm= secant modulus of the concrete;

Ec= modulus of elasticity of the concrete; h= The height of the stud;

Mv = safety factor;

= a factor depending of the ratio between the height of the stud and its diameter.

Several other types of connector exist as an alternative to welded studs, including angles fixed on the upper flange (Fig. 26). Although these offer a reduced resistance, they avoid the need for welding and may therefore be appropriate in some circumstances. When possible, shear studs are welded to the steel beams in the fabrication shop. For the thicknesses of decking generally used it is possible to weld the studs to the beams on site using what is known as “through-deck welding”.

27 2.1.7 Connections

The connections between composite members generally are formed between the steel components, thus they are designed and detailed according to the usual rules for steel construction. The connections, the bolts and the weld, are placed in a protected position in case of fire events. It also necessary to maintain sufficient access for bolting and welding, in order to avoid additional fire protection. For example, it is common use to bury the connection in the concrete slab, in order to protect it without any fire protection.

There are different ways to connect beam-to-column. It is possible to use a bracket (Fig. 26). It can be placed either below or within the depth of the beam. Additional bolts are added within the depth of the concrete slab to aid easier erection. In this way there is no need to protect by the fire the bracket, which is not exposed directly to the fire, but buried in concrete. Alternatively, fire protection can be avoided by adding shear studs to the bracket, and passing these through holes drilled in the column flange so that they can be embedded in the column concrete.

Fig. 26 Column Connection using brackets [5]

Another possibility is to use a web steel plate (Fig. 27). After the positioning, this connection has to be protected by the fire with either protection materials or with concrete covering. Concrete covering can be easier with the cutting of the upper flange of the beam, to allow concrete filling during the casting of the slab.

28

Fig. 27 Column Connection using web plate [5]

Another possibility is to use an and plate with “upper” bolts (Fig. 28). In this connection typology, the bolts are concentrate in the concrete slab. A sufficient number of bolts provide the resistance in fire condition.

29

It is also possible to use a direct support from the column (Fig. 29). This detail is used in large prefabricated columns, which are interrupted at each floor level. In order to transfer the loads trough the connection, it is necessary to use thick plates and other steel elements within the slab. In the case of large prefabricated columns used in foundations, it is possible to made them with a web opening at each floor where is possible to accommodate the floor beams.

Fig. 29 Beam-to-beam Connection with direct support from the column [5]

As for the columns, there are different ways to connect beam-to-beam. One solution can be to use a direct support: the result of this solution, which is simply achievable, is a deep floor (Fig. 30). The two beams are welded together and after erection can be welded a continuity plate on the upper flange of the secondary beams. The primary beam, has to be protected from the fire.

30

It is also possible to use a normal web plate attached to the secondary beams (Fig. 31). The plate pass through the concrete encasement of the primary beam. It does not interfere with the reinforcement of the primary beam, otherwise it is possible to cut the reinforcement. As for beam to column connections of this type, it is necessary to fill-in with concrete, or otherwise protect the region around the bolts after erection.

Fig. 31 Beam-to-beam Connection with web plate [5]

Another possibility is connect the beams with a bracket, as for the column detail (Fig. 32). In the upper part of the connection, there is a bolt in order to provide an easier positioning of the beam.

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Another solution can be also the connection with a thick nib welded on the upper flange (Fig. 33). This detail is very common and allows all the members to be completely filled with concrete.

Fig. 33 Beam-to-beam Connection with steel rib [5]

2.1.8 Coupling Shear Wall

The main characteristic of a reinforced concrete shear wall, is its large lateral stiffness and strength, which provides for good control over horizontal displacements and story drifts. In shear walls, the behavior of the entire wall is dependent on the plastic hinge zone at the wall base, where large rotations and yielding of reinforcement takes place. As consequence, the stiffness, strength, ductility and energy of dissipation depends on the response of this region. Reinforced concrete coupling beams that connect two or more walls in series are used to better distribute load and deformation demands through the shear wall rather concentrate it at the plastic hinge region at the wall base. The coupling beams provide transfer of vertical forces between the shear walls, creating a coupling action that resist to a portion of overturning moment at the base of the wall. The coupling beams, however, must also yield before the wall piers and behave in a ductile manner.

This coupling action (shown in Fig. 34), brings some benefits to the structural behavior of the shear wall:

• It reduce the overturning moment which has to be resisted by the base of the shear wall; • The coupling beams are elements of dissipation of the seismic loads;

• The lateral stiffness of the structure is bigger than the sum of the lateral stiffness of the single shear wall.

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Fig. 34 Comparison between (a) isolated and (b) coupled shear walls [6]

The most important parameter to understand the behavior of coupling beams is the Coupling Ratio. If we consider Fig. 34, we have three isolated walls (a) and a series of three coupling beams (b). We can define LSW (Left Side Wall) the wall on the left, RSW (Right Side Wall) the wall on the right and MSW (Middle Side Wall) the wall in the middle. The behavior between the configuration (a) and (b) it is different. In configuration (a), the overturning moment Vbaseh , is taken by the base of each shear wall. In coupling shear wall, the transfer of shear wall trough the coupling beams, induce a tension T on the LSW and a compression C on the RSW. The forces T and C create a couple moment that resist a portion of the overturning moment. If there is symmetry in configuration (b), T=C. At the base of the MSW there is no vertical force. In configuration (b), for the equilibrium:

Vbaseh = m1+m2+m3+CS

The proportion of system overturning moment resisted by the coupling action is defined as the coupling ratio, CR:

)* = )+

,_-+ ,_/+ ,₀+ )+

Coupling ratio is a key parameter to know the behavior of the configuration. If the CR is too little, the system will have a behavior similar to an uncoupled wall and the benefits due to the coupling system will be minimal. Otherwise, if the CR is too big, the system will be very stiff, and the coupling configuration will perform as a single shear wall. Thus, the optimal value of CR will be between this two extreme situation.

33

The most common configuration for the disposition of reinforcements in coupling beams are shown in Fig. 35. In the use of this structural solution with reinforced concrete beams, there are some drawbacks due to the high amount of reinforcement bars, placed in order to connect the shear walls (Fig. 36). This special reinforcement complicates erection, potentially increasing both construction time and cost. Reinforced concrete coupling beams, have also low shear resistance and the only solution to solve this problem is to provide deep members. For this reason, some engineers have turned to structural steel beams, with their ends embedded in the two adjacent shear walls, as an alternative to reinforced concrete coupling beams. Steel beams has the necessary combination of stiffness, strength, and ductility needed for providing the stable hysteretic response required of coupling beam. The resulting system reinforced concrete walls coupled by steel structural beams forms an hybrid coupled shear wall (HCW) system.

Fig. 35 Reinforced Concrete Coupling Beams typical reinforcements [7]

34 2.2 Hybrid Coupled Shear Wall (HCSW)

The main difference between commonly used composite structure and hybrid structure, is that in the former case the deformation demands of concrete and steel elements are in the same range (and so steel and concrete act as one member), instead in the latter case the deformation demands depend on the capacity of each material. Hybrid systems, may suffer from drawbacks typical of concrete walls and steel frames. The post-yielding behavior of the shear wall is characterized by deformations localized at the base of the wall. To avoid concrete crushing at the base of the wall, is necessary provide expensive details. The high overturning moment at the base of the shear wall it’s also the cause of expansive foundations. An innovative example of hybrid system is the connection between reinforced concrete shear wall and steel links (Fig. 37). The horizontal force due to the earthquake is taken almost totally from the shear wall, while the overturning moment is taken from the compression-tension of the steel columns. In this configuration, the steel links connected to the shear wall with a pinned joint should be the only or, at least, the main dissipative element. In this way, the shear force is transmitted while the columns are in traction/compression, reducing the negative effects of the reinforced concrete wall on the foundations. The structure is simple to repair if the damage is concentrate in the steel link, so it’s important to develop an easy replaceable connection between the shear wall and the steel link, to re-establish the seismic connection after the earthquake. The proposed hybrid composite system will be considered as seismic resistant if will be obtained a large number of yielding of the links.

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System like hybrid coupled shear wall, are considered in Eurocode 8. Anyway in the European normative, but in the whole international normative, only limited information are given for the design of this structure. To overcome this lack of information, there were a lot of studies all over the world. One of them was made by the INNO-HYCO Project (INNovative Hybrid and Composite steel-concrete structural solution for building in seismic area).

The objective of the INNO-HYCO Project, founded by European Commission, is to analyze the seismic behavior of coupled shear wall systems obtained by connecting reinforced concrete shear walls by means of beams placed at the floor levels constitute efficient seismic resistant system characterized by good lateral stiffness and dissipation capacity. In this project, developed by Consorzio Pisa Ricerche, University of Camerino, Universitè de Liège, Shelter S.A., Ocam s.r.l., Dezi Steel Design s.r.l., University of Aachen and University of Thessaly, are studied Innovative hybrid coupled Shear Wall systems (HCSW) and Steel Frame with Reinforced Concrete infill Walls (SRCW).

In INNO-HYCO Project is presented a configuration of HCSW which has the aim of overcoming the typical drawbacks of hybrid systems (Fig. 38).

Fig. 38 Innovative Hybrid Coupled Shear Wall system

The configuration shown in Fig. 38, is constituted by a reinforced concrete wall, steel links and side columns. The reinforced concrete wall, resists almost all the horizontal force. The overturning moment at the base of the wall, is resisted by an interaction between the vertical forces developed by the side columns (as shown in Fig. 34 and 37) and by the flexural action of the wall. This resistant mechanism, gives benefits to the foundations. In this configuration, the reinforced concrete wall should remain in elastic field, while damage should be concentrated at steel links. The steel link should be designed in order to guarantee the dissipative mechanism, without involving of the wall. In this way, after the seismic event, it’s possible to replace the steel links in order to restore the seismic resistant capacity of the structure. The side columns in this configuration, are subjected to axial force (compression or tension) with very limited bending moment, and they are characterized by a small cross section. One of the most important aspects in the design of the members in this configuration, is the choice of the stiffness and strength ratio between the link beams, the column and the reinforced concrete wall. The structural solution shown in Fig. 38, can be an effective solution for mid and high-rise building.

36 3. Purpose of the thesis

In this work, it will be analyzed only the first case studied in INNO-HYCO Project, the Hybrid Coupled Shear Wall system (HCSW). This thesis is based on numerical analysis of the structural solution proposed in INNO-HYCO Project. Numerical analysis was carried out with the aid of structural software.

All the solutions proposed by INNO-HYCO Project will be presented, either their geometrical and structural characteristics, with the aid of tables and pictures. The constitutive laws for each structural material utilized will be also presented. The considerations made before starting numerical analysis will be presented and explained. Starting from input values taken by the normative (for steel-concrete composite structure in seismic zone the normative is the Eurocode 8), both of the proposed configurations for the hybrid coupled shear walls (HCSW) will be analyzed. For each configuration, different design solutions and for each of them will be studied the seismic behavior in terms of deformations, inter-storey drift and stresses will be presented. This thesis will deal with seismic analysis which has been carried out.

As the results of the analysis, yielding curves for each case will be discuss. Yielding curves represent the behavior of the seismic connection proposed. It will be also obtained capacity curves in which will be represented displacements due to the shear loads. Finally, behavior factor q will be evaluated for each presented configuration. These factors will give us some information about the behavior of the analyzed structure, which can be ductile or brittle. In this work, only one configuration with its results will be presented and discuss. The results of all cases, will be presented in the annexes.

37 4. Case of study

In this thesis will be considered two case of study, 4-storey and 8-storey steel frame with the same floor geometry as shown in Fig. 39. The planimetric disposition is the same for both cases. It’s characterized by a square structural disposition of the elements. Each face of the building consists in a series of three hybrid coupled shear wall connected by shear links.

Fig. 39 Floor geometry of the benchmark structure with position of HCSWs

In INNO-HYCO Project has been proposed two different configurations for the embedment of the steel profile in the concrete shear wall and for the replaceable connection of the link to the embedded part:

• Configuration 1 (Fig. 40): the bending moment is transferred by the shear link to the embedded part and so to the shear wall, by shear studs welded on the embedded part of the profile. The beam splice connection, is placed at 100 mm from the face of the concrete shear wall in order to allow an easily bolting of the removable shear link; • Configuration 2 (Fig. 41): the bending moment is transferred from the shear link to the

embedded part and so to the shear wall, by a couple of vertical forces. The connection between the removable shear link and embedded part is placed on the face of the concrete shear wall, using threaded bushings.

38

Fig. 40 Configuration 1 for the shear link

Fig. 41 Configuration 2 for the shear link

For both cases of study (4-storey and 8-storey case), three different shear wall dimension will be proposed according to the ratio between the height of the shear wall (the same of the building) and the wall length, as shown in Table 2 . This ratio is called wall ratio.

define wall

storeys # interstorey height wall ratio wall length wall thick

h (m) H (m) H/lw lw (m) bw (m) 4F10W 4 3.40 13.60 10.00 1.36 0.36 4F07W 4 3.40 13.60 7.50 1.81 0.36 4F12W 4 3.40 13.60 12.50 1.09 0.36 8F10W 8 3.40 27.20 10.00 2.72 0.36 8F07W 8 3.40 27.20 7.50 3.63 0.36 8F12W 8 3.40 27.20 12.50 2.18 0.36

39

For each case above, five configuration according to the coupling ratio CR (60, 70, 80, 85 and 90CR) will be proposed, except for 8F07W and 8F12W cases, for which four configuration (60, 70, 80 and 90CR) will be proposed.

4.1 Configuration of HCSW system

As shown in Table 2, for both cases of study (4-storey and 8-storey case), three different shear wall dimension according to the wall ratio will be proposed. Interstorey height in 4-storey and in 8-storey case is the same (3.40 m). Thus, the total height for the building will be 13.60 m for the 4-storey case and 27.2 m for the 8-storey case (Fig. 42).

Fig. 42 Plane view of the numerical model with HCSWs

Each configuration of the shear wall has its specific geometrical and structural characteristics, as shown in Table 5, where the geometrical characteristics of the confined area of the concrete and the amount of the rebars in confined and unconfined area are defined. They are identified in Fig. 43.

40

As told before, for each analyzed case is defined a different steel cross section for the link. The steel links, can be divided in two main groups:

• Bottom link: are positioned in storeys 1 and 2 for the 4-storey case and in storeys from 1 to 4 for 8-storey case;

• Top link: are positioned in storeys 3 and 4 for the 4-storey case and in storeys from 5 to 8 for 8-storey case.

In following tables are reported geometrical characteristics of the link for each case and for each group.

bottom link (storeys 1-2 for the 4storey case; storeys 1-4 for the 8storey case)

name d b tf tw L,link fy (mm) (mm) (mm) (mm) (mm) (Mpa) 4F10W 60CR IPE330 330 160 11.5 7.5 600 355 70CR IPE400 400 180 13.5 8.6 600 355 80CR IPE550 550 210 17.2 11.1 600 355 85CR IPE750 753 263 17 11.5 600 355 90CR IPE750P 753 263 21.6 13.2 600 355 4F07W 60CR IPE360 360 170 12.7 8 600 355 70CR IPE450 450 190 14.6 9.4 600 355 80CR IPE600 600 220 19 12 600 355 85CR IPE750 753 265 17 13.2 600 355 90CR IPE750P 753 265 21.6 13.2 600 355 4F12W 60CR IPE300 300 150 10.7 7.1 600 355 70CR IPE360 360 170 12.7 8 600 355 80CR IPE500 500 200 16 10.2 600 355 85CR IPE500 500 200 16 10.2 600 355 90CR IPE750P 753 265 21.6 13.2 600 355 8F10W 60CR IPE360 360 170 12.7 8 660 355 70CR IPE450 450 190 14.6 9.4 660 355 80CR IPE600 600 220 19 12 660 355 85CR IPE750P 753 265 21.6 13.2 660 355 90CR IPE750PP 753 268 25.4 15.6 660 355 8F07W 60CR IPE360 360 170 12.7 8 660 355 70CR IPE450 450 190 14.6 9.4 660 355 80CR IPE600 600 220 19 12 660 355 90CR IPE600 600 220 19 12 660 355 60CR IPE300 300 150 10.7 7.1 660 355 8F12W 70CR IPE360 360 170 12.7 8 660 355 80CR IPE500 500 200 16 10.2 660 355 90CR IPE600 600 220 19 12 660 355