CHAPTER 1 INTRODUCTION

CHAPTER 1

INTRODUCTION

The basic principle of conventional earthquake-resistant design that has been applied for the last 75 years is intended to ensure an acceptable safety level while avoiding catastrophic failures and loss of life. A structure is considered that it has fulfilled its functions when it does not collapse when subjected to a design-level seismic ground motion, and the occupants can evacuate it safety, even thought it may never be functional again. The aim of the earthquake engineering community was mainly to achieve this life safety performance objective under a rare level of ground shaking intensity. The performance levels of important structures such as hospitals, police stations, communication centres and major highway bridges must be higher and they have been designed to achieve a severe earthquake shaking because of their importance in the immediate emergency response and recovery activities following a catastrophic event. Furthermore, building owners are increasing considering the impact of a major earthquake on their structures as an economic decision variable. The cost of a new structure designed to meet higher performance levels or the cost of an upgrade to an existing structure are weighed against the estimated losses associated with damage, loss of property and downtime in the event of a major earthquake. This is reflected in the recently published European Code (EC 2005) which favours performance-based assessment approaches, and leads to the seismic design of structures to meet several specific performance levels under increasing levels of seismic intensity. For structure of common importance, the basic safety objective translates into a life safety performance level under the design-level earthquake and to collapse prevention performance level under the maximum credible earthquake.

Over the last half century, a large amount of research has been conducted into developing innovative earthquake-resistant system in order to raise seismic performance level while keeping construction costs reasonable. Most of these systems are designed to dissipate the seismic energy introduced into a structure by supplemental dumping mechanism and/or designed to limit the transmission of seismic energy to the main structure by isolation of the main structural elements. Ever since their appearance in late sixties and early seventies hysteretic dampers have come under increasing attention as an effective means for response control, including retrofit purposes, and numerous types of hysteretic (yielding-type)

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dampers for use in structures are developed. This research is devoted to development of a new hysteretic damper. A review of energy concepts in earthquake engineering, referring to the book “Principles of passive supplemental damping and seismic isolation” C. Christopoulos, A. Filiatrault. IUSS Press Pavia, and literature related to development of different hysteretic dampers over the last forty years are given in this Chapter.

1.1 THE RAINFLOW ANALOGY FOR THE DISSIPATIVE STRUCTURES UNDRE SEISMIC ACTION

Special seismic protection, usually in form of a combination of isolation/dissipation devices integrated into an isolation system is often required for seismic protection of important structures, to satisfy design objectives of controlled displacement and limited or no damage. While isolators reduce the force demand on superstructure by increasing the effective period and bringing the structure to low-energy region of the design spectrum, energy dissipaters (dampers) absorb and dissipate part of the energy that has already swept into the structure and reduce the displacement and ductility demand on structural components.

Since the main purpose of using supplemental dumping and seismic isolation system is to dissipate a significant portion of the seismic input energy and/or to isolate the structure from receiving this energy, it is natural to formulate the seismic problem within an energy framework. The main advantage of the energy formulation is the replacement of vector quantities, such as displacement, velocities and acceleration, by scalar energy quantities. With this approach, the flow of these energy quantities can be tracked during the seismic response of the structure and it is presented in this paragraph form discussion and analytical point of view.

The rain flow analogy can describe easily the mitigation of energy quantities in a structure during an earthquake and it is shown in Fig. 1.1. In the first one figure (Fig. 1.1-a) a fictitious hangar with a retractable roof subjected to a rainstorm is illustrated. The rainstorm symbolizes the earthquake input into the structure and the total seismic energy is represented by the amount of entering the system. The extend of the roof opening is related with the amount of the rainwater and it is the symbol of the dependence of the input energy on the structural proprieties during an earthquake. All the energy input generated at the site by an earthquake is absorbed if the roof is completely open and it is the symbol of the case of quasi-resonance between the ground motion and the dynamic response of the structure. If the roof is completely closed the structure does not receive seismic input energy and it is the symbol of a perfectly isolated structure. The kinetic energy generated by the masses of the structure as their inertia reacts to the seismic input energy is the amount of the rainwater collected by the pail.

Not all the seismic input energy generated at the site is absorbed by the structure and it is symbolized by the rainwater that slides down on each side of the closed portion of the roof.

_{The Fig. 1.1-a illustrates a two way oscillating pump connecting the bottom of} the kinetic energy pail to the top of the strain energy pail and the bottom of the strain energy pail to the top of the kinetic energy pail and all this illustration describes when a mass vibrates the structural elements deform and absorb strain energy and when it stops moving at the end of the cycle of vibration, the kinetic energy is transferred into strain energy. The vibration of the structure can therefore be visualized as a constant transfer of kinetic energy into strain energy and vice-versa. The equivalent viscous damping of the structural system is symbolized by a flow loss in the two-way oscillating pump between the kinetic energy pail and the strain energy pail. This flow loss is proportional to the flow rates transiting thought the pump and the amount of lost rainwater is collected permanently by a viscous damping pail symbolizing the amount of energy absorbed by equivalent viscous damping.

When the level of rainwater in the strain energy pail reaches a critical level, some of the water is drained into a hysteretic energy pail. This representation symbolizes the amount of strain energy that is absorbed by the structure before it starts deforming in the inelastic range and the manometer indicates the maximum total strain energy absorbed by the structural element during the earthquake. This reading is directly related to the peak transient response of the structure.

Figure 1.1. Rain flow analogy: a) during the seismic shaking, b) at the end of the seismic shaking.

(“Principles of passive supplemental damping and seismic isolation” C. Christopoulos, A. Filiatrault. IUSS Press Pavia).

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In Fig. 1.1-b the energy state of the structure at the end of the shaking is illustrated where the kinetic and recoverable strain energy are empty after the seismic event. All the input energy ends up in the equivalent viscous damping pail if the structure, during the earthquake, remains in elastic range otherwise a portion of the seismic input energy is also collected by the hysteretic energy pail if the structural elements shows inelastic deformation. Therefore the sum of the volumes of rainwater collected by the equivalent viscous damping pail

Vd

V

V

𝑉_!"= 𝑉_!+ 𝑉_! (1.1) From this analogy discussed above, two possible intervention strategies are possible. The first one consists to minimizing the amount of rainwater collected by the hysteretic energy pail that is linked to damage and it can be reached by introduction of supplemental damping mechanism. The second strategy consists of reducing the size of the roof opening in order to minimize the amount of rain flow collected by the seismic input energy pail and it symbolizes the function of a seismic isolation system.

If it is analysed from analytical point of view, the differential equation for a general nonlinear MDOF system excited at the base by a horizontal translation from an earthquake ground motion are given in matrix form by:

𝑀 𝑋 𝑡 + 𝐶 𝑋 𝑡 + 𝐹! 𝑡 = − 𝑀 𝑟 𝑋! 𝑡 + 𝐹! (1.2)

This formulation is derived for equal excitation at all support points of the structure and the energy formulation is obtained by integrating the work done by each element over an increment of global displacements

{dx}

𝑑𝑥 ! _{𝑀 𝑋 𝑡 + 𝑑𝑥} ! _{𝐶 𝑋 𝑡 + 𝑑𝑥} ! _𝐹 ! 𝑡

= − 𝑑𝑥 ! _{𝑀 𝑟 𝑋}

! 𝑡 + 𝑑𝑥 ! 𝐹! (1.3)

Recalling the differential relationships:

𝑑𝑥 𝑡 = 𝑋 𝑡 𝑑𝑡 (1.4) 𝑑𝑥 𝑡 = 𝑋 𝑡 𝑑𝑡 (1.5) The energy formulation is finally written as:

𝑋 𝑡 ! 𝑀 𝑑𝑥 𝑡 + 𝑋 𝑡 ! 𝐶 𝑑𝑥 𝑡 + 𝑑𝑥 ! _𝐹

! 𝑡

= − 𝑑𝑥 ! _{𝑀 𝑟 𝑋}

_{Based on Equation (1.6) the energy balance equation is defined as:} 𝐸_!! _{𝑡 + 𝐸}

!" 𝑡 + 𝐸! 𝑡 = 𝐸!"#! 𝑡 + 𝐸!" 𝑡 (1.7)

where:

• 𝐸!! 𝑡 is the relative kinetic energy at time t:

𝐸_!! _{𝑡 =} ! ! 𝑋 𝑡

!

𝑀 𝑋 𝑡 (1.8) • 𝐸!" 𝑡 is the energy dissipated by viscous damping during the time t:

𝐸_!" 𝑡 = 𝑋 𝑡 ! 𝐶 𝑑𝑥 𝑡 (1.9) • 𝐸! 𝑡 is the absorbed energy during the time t:

𝐸! 𝑡 = 𝑑𝑥 ! 𝐹! 𝑡 (1.10)

• 𝐸!"#! 𝑡 is the relative input energy during the time t:

𝐸_!"#! _{𝑡 = − 𝑑𝑥} ! _{𝑀 𝑟 𝑋}

! 𝑡 (1.11)

• 𝐸!" 𝑡 is the work done by static loads applied before and maintained

during the seismic excitation from the moment of application of the forces up to time t:

𝐸_!" 𝑡 = 𝑑𝑥 ! _𝐹

! (1.12)

The absorbed energy term 𝐸_! 𝑡 represents the total amount of energy that the structure has absorbed either through elastic straining or unrecoverable inelastic deformations of its elements. The peak absorbed energy during an earthquake represents the largest demand on structural members and is expressed ad the sum of two components:

𝐸! 𝑡 = 𝐸! 𝑡 + 𝐸!" 𝑡 (1.13)

where 𝐸_!" 𝑡 is the recoverable elastic strain energy at time t and 𝐸_! 𝑡 is the energy dissipated through hysteretic damping of the structural elements up to time t, and depends on the hysteretic relation of each structural member.

It can be seen in Eq. (1.9) that the damping energy monotonically increases throughout the time-history, whereas the absorbed energy in Eq. (1.10) fluctuates while generally increasing. Referring to Eq. (1.13) the fluctuations in the absorbed energy are caused by the elastic strain energy that is absorbed and then restored.

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1.2 STEEL HYSTERETIC DAMPERS

In this paragraph the topic about steel dampers is introduced, explaining the difference between the hysteretic and viscous behaviour and the various loading process. An historical report and a features description are presented. Starting from the case for energy dissipaters which is thus in designing to direct the damage to certain secondary elements and thus reducing or eliminating damage on primary structural members or weaker structural members (as in the case of retrofit); alternatively, from an energy standpoint, increasing energy dissipation capacity through implementation of these secondary elements. The names “structural fuse” or “sacrificial element” and “damper” emerge from the former and the latter descriptions, respectively.

Energy dissipation can be achieved by exploiting well known physics phenomena as it is explained in the previous paragraph. Many of the latter have been explored and numerous devices have already been developed with success within the last three decades. Said solutions, notwithstanding their large variety, can be roughly grouped into two main categories, and precisely those whose reaction force depend on the amount of the imposed displacement and on the rate at which the displacement is inputted (i.e. the velocity). To the above categories correspond two distinct families of devices, namely: the hysteretic dampers and the viscous dampers. The hysteretic dampers exploit different kind of phenomena as friction, extrusion and yield. Friction has been widely used. However, hysteretic devices based on friction show poor reliability and reproducibility due to the uncertainty and instability of the coefficient of friction. The latter undergoes to important changes induced by aging, environmental attack, temperature variations, wear during use, etc. A further problem is the “stick-slip”, where after some time the device requires a very large force to initiate sliding. Extrusion in practice utilizes only lead and has been seldom used, without great success, due to the high cost of the devices. Yield (i.e. deformation beyond the elastic limits) can be obtained through: uniaxial tension (or compression), shear, torsion and bending. All the types of stressing mechanisms have been practically used. Tension-compression has been seldom used, due to the limited amount of obtainable displacements and the risk of buckling as in the case of BRBs. In practice they only find application in bracings to control the inter-story drift of flexible edifices. The problem of buckling is solved by encasing the steel beam into a pipe filled with concrete. Shear is commonly and extensively employed in lead cores of LRBs. The reasons for choosing lead for this type of isolators are multiple, the most important being the good fatigue properties during cycling at plastic strains, due to the simultaneous interrelated processes of recovery, re-crystallisation and grain growth. Torsion has found limited application because of the difficulties related to the transformation of linear movements into rotational ones. The major advantage of torsion resides in the fact that this kind of stressing allows an elevated number of cycles (over 200). Bending is the most commonly used way to stress the dissipating elements in Steel Hysteretic Dampers.

_{However, it should be warned that in principle they do not possess adequate} re-centring capability when used in an isolation system. Therefore they require the installation of a spring-like device acting in parallel.

1.2.1 History of steel hysteretic dampers

By the late 1960s a number of damping mechanisms and devices were being used to increase the seismic resistance of a range of structures. At that time the logical approach to developing high-capacity dampers for structures was to utilise the plastic deformation of steel beams. During that decade the plastic deformation of steel structural beams had been increasingly used to provide damping and flexibility for anti-seismic steel beam-and-column (frame) buildings. The cyclic ductile capacity of structural members was limited by material properties, local buckling and the effects of welding.

Early steel-beam dampers developed in the both New Zealand (mid ‘70s) and Italy (early ‘80s) were given a much greater fatigue resistance than typical steel structural members by adopting suitable steels and beam shapes, and attachments with welds remote from regions of plastic deformation. An early New Zealand application of steel-beam dampers was in the stepping seismic isolation system for the tall piers of the South Rangitikei Viaduct. Construction of the viaduct commenced in 1974 and it was opened in 1981. In 1979 uniform-moment steel dampers were used in the superstructure isolation system for the Cromwell Bridge (NZ). In 1981 conically tapered steel dampers (pins) were inserted in Italy in laminated rubber bearings to provide energy dissipation; in practice these elements replaced the lead core (at that time there was a patent pending on LRBs). In 1983 the isolation systems of a stepping chimney in Christchurch and the Union House in Auckland included triangular plate dampers. Also in Japan steel dampers have been used in the seismic isolation systems of a range of structures.

During the ’80s steel hysteretic dissipaters became very popular in Italy and numerous types of the most diverse geometric shapes were developed and patented, and at least a dozen different models have found practical application. To create seismic isolators, several combinations of sliding bearings and steel hysteretic dissipaters are possible, and the choice of an optimal combination depends either on the basis of requirements to be fulfilled or considerations of a practical nature such as overall dimensions, ease of installation, maintenance, etc. An inquiry in 1992 demonstrated that, in Italy, the sliders with steel hysteretic dissipaters have been utilized in over 80% of bridge seismic retrofit projects. In mid ’90 these type of isolators were also exported (e.g. Turkey, Azerbaijan, USA, Venezuela etc.). In the recent years their good fortune began to wane, mainly because of the discovery of lack of restoring force.

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1.2.2 Features of steel hysteretic dampers

Steel was initially chosen as the damper material since it is commonly used in structures and should therefore pose no very unusual design, construction or main-tenance problems, apart from possible fatigue failure at welds and stress concentra-tions. Moreover, it was hoped that the development of these dampers would throw additional light on the performance of steel in ductile anti-seismic structures. The performance of steel-beam hysteretic dampers during earthquakes is closely related to the performance of high-ductility steel-frame structures. However, the dampers are designed to have a much higher fatigue resistance and to operate at higher levels of plastic strain. This is achieved by using high-ductility mild steels, damper forms with nominally equal strain ranges over each plastic-beam cross-section, plastic beams of compact section, and detailing the connections between the plastic beams and the loading members so as to limit stress concentrations, particularly at welds.

Hereinafter the results of many years of experience with different shapes and designs of steel damper are summarised in terms of a “scaling” procedure, which generalises many different findings and also makes it possible to arrive at initial parameters for the design of steel-beam dampers with the desired properties. Other steels and heat treatments are expected to give similar, but not necessarily identical, results, particularly for the life of the damper. For a given strain range, the load-displacement loop changes only moderately with repeated cycling, with a moderate reduction in damping capacity, until the yielding elements are near the end of their low-cycle fatigue life. The damper loop parameters and their fatigue life can be estimated adequately, on the basis of cyclic tests on damper prototypes or on small-scale models. Since steel-beam dampers have a strictly limited low-cycle fatigue life, controlled by fatigue-life curves of the type, it is necessary to design the dampers so as to limit the cyclic strain ranges during earthquakes, and to ensure that there exists a capacity to resist several design-level earthquakes as well as at least one extreme-level earthquake. For a typical well designed isolator and for El Centro-type earthquake, this might call for a nominal maximum strain range of ±3% during design earthquakes and ±5% during extreme earthquakes. Again, to avoid premature failure the isolator installation should ensure that wind leads do not impose more than a few tens of cycles of plastic deformation on damper beams during the design life of the isolated structure.

1.2.3 Types of steel hysteretic dampers

As already stated, over the years many numerous types of Steel Hysteretic Devices (hereinafter referred to as SHD). The most commonly used are listed in this section. For sake of simplicity they are identified with two capital letters. The first letter represents the type of damper, while the second denotes the form of the bent element cross section, which can be circular (C), square (S) or rectangular (R).

_{and early 70s came about as the outcome of a study in the Engineering Seismology} Section of the Physics and Engineering Laboratory (DSIR) (Kelly et al. 1972; Skinner et al. 1975). The first type discussed is the so called “uniform”-moment bending-beam damper with transverse loading arms, sloped at an angle as shown in Fig. 1.2. This will be indicated as “Type U” damper. The second type discussed is the plate damper shown in Fig. 1.3. This type of steel dampers have also been developed for use in braced frames, the most well-known is the added damping and stiffness (ADAS) elements (Whittaker et al. 1991), shown in Fig. 1.3-a. ADAS is composed of a series of X-shaped plates clamped and fixed at top and bottom through a bolted connection. Full- scale tests have shown advantages of incorporation of ADAS dampers in terms of reduction of damage in primary structural members, reduction of inter-story deformations at minor and moderate level earthquakes and stable hysteretic behaviour of the bracing system. Triangular-plate added damping and stiffness (TADAS) devices, developed by Tsai et al. (1992, 1993), is a variation of the ADAS elements. This will be indicated as “Type T” damper. TADAS elements are similar in shape to the earlier tapered cantilever dampers (Tyler 1978, Kelly 1980). As shown in Fig. 1.3-b and 1.3-c, in TADAS, triangular plates are fixed at one end to a plate through welding and hinged at top using pins and slotted plate connection. Tapered plates of this shape had been used for base isolation (Kelly et al. 1972, Boardman et al. 1983) before their application to building frames. TADAS dampers also exhibit stable hysteretic behaviour under cyclic loading without stiffness or strength reduction. Performance of TADAS dampers in braced frames is also verified through full-scale tests (Tsai et al. 1993).

Compared to building frames, deployment of hysteretic dampers in bridges encounters the additional difficulty of multi-directional displacements. Multi-directionality of displacements demands that the device be both mechanically capable of displacement at all planar directions and also providing a uniform response irrespective of displacement direction. Consequently, bridge hysteretic dampers are not as diverse as the building ones.

Hysteretic dampers which have multi-directional action are so called “tapered” cantilevered beam shown in Fig. 1.5. It should be noted that this type of element is sometimes described as “conical”, something that is erroneous, since the radius of the cross section at a distance x from the loading point is given by an equation, where x is third degrees rise multiplied with an appropriate constant. For the above reason, the apex of the approximated cone is substantially above the loading level. Due to the circular-section of the cantilevered beam, this damper may be loaded in any direction perpendicular to the beam axis. This represent the major advantage of this type of damper, which is commonly named “pin” and thus it will be indicated as “Type P” damper.

The fourth type is the “crescent moon” dissipater (Ciampi at al. 1993). In principle this element is capable of reacting in one direction only. Nonetheless, dampers active in all directions may be fabricated by means of a radial arrangement shown in Fig. 1.6. The fifth type is the E-shaped hysteretic element and it is depicted in Fig. 1.7. Similarly to the case of the “crescent moon”, also this element

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is unidirectional, but multi-directionality can be achieved by combining elements in two orthogonal directions.

It is also important to introduce hysteretic dampers which have mono-directional action especially because that are the starting point of this research. Buckling Restrained Brace (BRB) is the well known type of hysteretic element which acts under axial load and its response develops only longitudinal displacement (Fig. 1.8). It consists of a slender steel core, a concrete casing

designed to continuously support the core and prevent buckling under

axial compression, and an interface region that prevents undesired interactions between the two. Three major components of a BRB can be distinguished are its steel core, its bond-preventing layer, and its casing. The steel core is designed to resist the full axial force developed in the bracing. Its cross-sectional area can be significantly lower than that of regular braces, since its performance is not limited by buckling. The core consists of a middle length that is designed to yield inelastically in the event of a design-level earthquake; and rigid, non-yielding lengths on both ends. Increased cross-sectional area of the non-yielding section ensures that it remains elastic, and thus plasticity is concentrated in the middle part of the steel core. Such configuration provides high confidence in prediction of the element behaviour and failure. The bond-preventing layer decouples the casing from the core. This allows the steel core to resist the full axial force developed in the bracing, as designed. The casing – through its flexural rigidity – provides the lateral support against flexural buckling of the core. It is typically made of concrete-filled steel tubes. The design criterion for the casing is to provide adequate lateral restraint (i.e. rigidity) against the steel core buckling. Because BRBs achieve a high level of ductility and stable, repeatable hysteresis loops, BRBs can absorb significant amount of energy during cyclic loadings, such as an earthquake event. Preventing buckling leads to similar strength and ductile behaviour in compression and tension, illustrating the envelope of the hysteresis curves, also referred as a backbone curve. This curve is considered as an important basis of practical design. The beneficial cyclic behaviour of the steel material can therefore be extrapolated to an element level and thus to the overall structural level; an extremely dissipative structure can be designed using BRBs.

Comparative studies, as well as completed construction projects, confirm the advantages of buckling-restrained braced frame (BRBF) systems but to reach a large displacement they need a high length of the elements in according to the axial stiffness. To overtake this limitation in this research the invention of an innovative protection system is investigated whit the characteristic to be compact and keeping the costs of production reasonable. To better understand this assumption chapter 2 is referred.

Figure 1.2. First generation hysteretic dampers (Kelly at al. 1972 and Skinner at al. 1975): Steel “Type U” bending-beam damper.

Figure 1.3. Steel plate hysteretic damper: (a) ADAS elements; (b) TADAS elements or Triangular Plate Damper; (c) Load application on TADAS.

b)

c)

F

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Figure 1.4. Typical hysteretic loop of TADAS

Figure 1.5. Pin hysteretic damper

Figure 1.7. Sliding guided pot bearing combined with E-shaped hysteretic elements

Figure 1.8. Picture of Buckling Restrained Brace (BRB)

1.3 VISCOUS FLUID DAMPERS

The working principle for viscous fluid dampers is based on pressuring a viscous fluid through an orifice, as in a dashpot. The energy dissipation is due to the transformation in heat by the interaction between the fluid and the surface of the orifice. The reaction force in such a mechanism, F, will be proportional to velocity,

v

𝐹 = 𝐶𝑣! _(1.14)

Where C and α are constants, but the value of velocity exponent α depends on mechanical and geometrical properties of the device and can be adjusted. This is a very important value because a lower value of α means lower dependency of reaction force on velocity. Impact of rising temperature on diameter of the orifice or the effect of elastic response of the fluid as a result of its compressibility are secondary factors affecting the overall force-displacement of the damper. Therefore, despite the simple concept behind it, practical issues introduce

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complexities in design. Reliable performance rests on limiting unwanted variations in reaction force due to pressure fluctuations, stable performance of components including fluid and seals at high temperatures and proper sealing against leakage of highly pressurized fluid. Viscous fluid dampers are thus the most technologically advanced product in the family of passive earthquake protection devices. In this paragraph a MAURER SÖHNE hydraulic damper (MHD) is presented. Fig. 1.9 shows a longitudinal section cut of a viscous damper consisting of two fluid chambers and an orifice head on which orifices are made. Relative movement between the two mounting points of the device, forces the fluid from one chamber to the other through the orifices. Highly-pressurized fluid passes through the orifices at high speed as it loses its pressure, creating a turbulent flow in the other chamber followed by head loss (energy dissipation) in this turbulent motion. The MHD is providing substantial amount of damping and energy dissipation respectively at structural location with relative deformations bigger than +/- 10mm. MHDs are devices, which enable displacements (thermal changes, creep, etc.) during service condition without creating significant response forces, but dissipate huge amounts of energy during sudden appearance of vibration. Fig. 1.9 shows that very slow displacements create insignificant response forces FT and the fluid can flow from one piston to the other. When sudden vibrations with relative displacements occur between the linked structural sectors, inducing displacement velocities in the range of 0.1 mm/s to 0.7 mm/s the MHD is responding with a force.

Adoption of viscous fluid dampers to seismic applications is a rather recent trend in the history of these devices. Their first usage, dating back to 1897, was in artillery used by French military (Constantinou 1994, Taylor). More information on this class of dampers can be obtained from the online database of Taylor Devices

Figure 1.9. Longitudinal section view of a viscous fluid damper (MAURER SÖHNE Tuned Mass and Viscous Dampers product Brochure 2011).

Figure 1.10. Force displacement plot of a viscous fluid damper (MAURER SÖHNE Tuned Mass and Viscous Dampers product Brochure 2011)

1.4 OBJECTIVES AND METHODOLOGY

The research was embarked upon with the goal of developing an innovative hysteretic damper. The starting idea belongs to the German company MAURER SÖHNE which patent is secured through the European Patent Organization EPO (Dr. Christian Braun and Dr. Renzo Medeot, 2015). For Anti-seismic energy dissipation devices, plastic deformation of steel is one of the most effective mechanisms available for the dissipation of energy, for both economic and technical point of view. An innovative concept of a steel hysteretic damping device (MAURER Compact Steel Damper - MCSD) by inserting three pipes, which are loaded alternating in tension and compression, leads to a compact device and a reduced risk of buckling failure.

The principal topic concerns the feasibility study of the device linked to the company resources and keeping the cost low thanks using commercial pipes. The aim of this Master Thesis is the engineering and design of a prototype tube-in-tube steel hysteretic damper based on analytical and numerical calculation and the verification by testing.

The investigation is the main scope of this research and it covers all the developmental stages of the device itself and necessary analytical tools essential for its implementation in practice. The analytical tools are supported by numerical calculation with Finite Element program (ANSYS Workbench, 2017). The prototype dimensions are evaluated by material characteristics obtained by tensile test made on probes cut from the commercial pipes. Therefore, the design, the execution and the evaluation of tensile test are used as input for numerical simulations with the real measured stress-strain behaviour to obtain an acceptable curve to compare with the experimental results. The experimental phase, where the single pipes of the prototype designed are tested under various kind of cyclic load, represents the conclusion of this thesis and the comparison with the numerical calculation is one of the goals.

16 1.5 DISSERTATION OUTLINE • Chapter 2:

The concept of the device is described starting from the main idea reported on the patent. It is also described the possible configurations and the favourite one which is used as object of this thesis. The motivations of this choice are explained too as its relation with the company requirement.

• Chapter 3:

In this chapter the analytical calculation is shown. The deformation theory of plasticity is introduced to define the stress-strain and load-displacement relationship related on element under pure axial load. The calculation concerns to two different configurations: one complete cylindrical shell and the same one with two symmetrical longitudinal slots. For both the cinematic behaviour is calculated analytically especially the attention is pointed to the surfaces displacement as function of the load. The following step is to understand the buckling phenomenon as a local event for the complete shell and as a global event for the cut one. The stiffness of the system is evaluated analytically too and it is interesting to note the participation of the increasing of stiffness due by contact between surfaces. In closing the prototype is designed using two different kind of material characteristics reached by tensile tests made with two different load speed application. The results are shown as load-displacement response curve using monotonic and cyclic load.

• Chapter4:

Starting from a literature review of FEM calculation and pointing the attention especially on solution strategies in nonlinear analysis, the modelling of the device is described. It is shown all passages to create the model explaining the geometry of the solid, the mesh generated and the type of contact used. The goal is to repeat all of the calculations described into chapter 3 and to prove numerically thanks to the help of FEM program (ANSYS Workbench). It is possible to note a conformity of the results that proves the correct supposition made.

• Chapter5: