Vulnerability assessment and seismic retrofit of an industrial steel structure

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Università di Pisa

Scuola di Ingegneria

Corso di Laurea Magistrale in Ingegneria Edile e delle Costruzioni Civili

Tesi di Laurea

VULNERABILITY ASSESSMENT AND SEISMIC

RETROFIT OF AN INDUSTRIAL STEEL STRUCTURE

Relatori: Candidato: Prof. Ing. Walter Salvatore Laura Proserpio Prof. Dr.-Ing. Benno Hoffmeister

Correlatori:

Ing. Francesco Morelli Ing. Nicola Mussini

Dipl.-Ing. Marius Pinkawa

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TABLE OF CONTENTS

1 Introduction

Industrial plants are complex systems and it is such a complexity, due to numerous connections, equipment and components, together with the complexity of their operations that makes them particularly vulnerable (local vulnerability) to earthquakes.

Activities carried out in process plants can also be arranged in series, which means that process activities are realized with specific sequence and boundary conditions.

Consequently, the “failure” of a single element can get out of order the entire system. This is of fundamental importance for the seismic vulnerability of a plant (general vulnerability). Seismic action can cause serious accidents to industrial plants as shown in several occasions. The actual worldwide situation of major-hazard plants against earthquakes should be considered as critical. For instance, in Italy about 30% of industrial plants with major accident hazards are located in areas with a high seismic risk. In addition, in case of a seismic event, the earthquake can induce the simultaneous damage of different apparatus, whose effects can be amplified because of the failure of safety systems or the simultaneous generation of multiple accidental chains. (1)

The overall objective of the investigations presented in this thesis is to analyse the seismic vulnerability of an industrial building with steel structure, in particular the case study of Silos. Then there is the study of seismic retrofitting obtained to insert some dampers in the braces. The industrial building element studied is the support steel structure of a Silos ILVA Taranto plant. The Silos is tall, slender and contains a hydrated lime. The structure is a part of a wider industrial system that is formed also by supporting works for filters, a pipeline and a chimney. The seismic retrofitting is based on the use of dissipative braces that have been arranged and dimensioned so as to obtain an improvement in the seismic response.

The thesis work is part of a wider research project, funded by the European Commission, called PROINDUSTRY (Seismic PROtection of Industrial Plants enhanced by steel based Systems) coordinated by the Department of Civil and Industrial Engineering at the University of Pisa, which involves European universities (including the RWTH Aachen University, where this work has been carried out during a period abroad of 6 months) as well as big

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INTRODUCTION

2 companies, including ILVA SpA. The purpose of the research is to study and develop innovative seismic protection systems for existing industrial buildings and newly designed.

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SEISMIC RISK OF INDUSTRIAL STRUCTURES

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2 Seismic risk of industrial structures

2.1 Seismic risk (hazard, vulnerability, exposure)

The seismic, a physic characteristic of the territory, means the frequency and the force of the earthquakes.

The seismic risk is the measure of damages during a determinate period based on the kind of the seismic, the buildings’ resistance and the anthropization. Moreover it is determined by the combination of hazard, vulnerability and exposition.

The seismic hazard is the odds that in an area and in a period would be an earthquake that overtakes the intensity’s limit, the magnitude or the peak ground acceleration (PGA) of our interest. The seismic hazard is studied during the last period with regional and territorial researches to create a seismic classification of each local area (see Figure 1).

Figure 1 – Map of seismic hazard (Italy)

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4 There are two types of approach to study this problem: the first one is deterministic approach, while the second one is probabilistic. The probabilistic approach is better because the seismic hazard is declared by the probability that, during a time period, would happen an event with the assigned features.

The seismic vulnerability, during a high seismic event, is the bent of a structure to endure a damage of determinate level. The damage’s type depends on: building structure, age, materials, location, non-structural elements, proximity with other constructions and duration and intensity of the earthquake. To evaluate the buildings’ vulnerability it is necessary to measure the cause damages and their shake intensity.

For this purpose there are two methods: statistic and mechanistic. The statistic method is based on the past data about previous earthquakes, while the mechanistic method uses theoretical models that reproduce the major characteristic about evaluated buildings.

Finally, exposure means safety of human life. Generally, it is possible to estimate a number of the people involved during an earthquake, through calculations that based on number of collapsed or damaged buildings. (2)

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2.2 Seismic risk associated to industrial plants

From the recent earthquakes it is noted that the industrial plants have an high vulnerability. The industrial damages, that are caused by natural events, are defined Na-Tech risk and they can be sometimes really dangerous, both from structural view and environmental. It is necessary to prevent these disasters, to study from past events.

Some research are made by a team of engineers of University of Udine, associated with Italian National Fire Department. The aim is to find some solutions to increase the safety level in the industrial plants. In particular, L’Aquila (2009) and Emilia (2012) earthquakes are studied.

Even if the 6.3 magnitude L’Aquila earthquake is classifiable as moderate, there were significant damages to industrial facilities and life-lines present in that area. The PGA (peak ground acceleration) was higher than 0.6g. (3)

Three industrial zones were inspected, in particular high-tech, pharmaceutical, construction, mechanical and manufacturing industries. The most diffuse typology of building is represented by precast concrete structures and steel frames with precast panel walls.

The main damages were in non-structural elements, but the criticism were related to the connection between the secondary elements and the structures. Other minor damages were in beams and columns and the criticisms were in the weakness of the joints and the unseating effects, in particular the “soft-storey” behaviour.

A particular case is the collapse of three tall steel Silos storing polypropylene beads. This event is caused by the inadequacy of braces to avoid relative movement during the earthquake (Figure 2).

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Figure 2 - L’Aquila earthquake: damage to, and caused by, silos at VIBAC facility in the Bazzano industrial area, 7 km south far from L’Aquila town

(taken from S. Grimaz, Bollettino di Geofisica Teorica e Applicata, 10: 227-237, 2014)

Another important aspect is the restriction of rescue after an earthquake. In fact, during L’Aquila event, a lot of gas pipelines, pipe-break, phone services and transport infrastructures were damaged. These interruptions caused some difficult transit for the emergency rescue services.

The lesson, learnt from L’Aquila earthquake, is that the industrial buildings has shown significant seismic vulnerabilities both in the structure and the equipment. So, this means that it is necessary to introduce specific precaution measures. The Italian National Fire Department set up a specific working group with the aim of defining technical guidelines for reducing seismic vulnerability. (4)

On other important example in Italy is Emilia earthquake in 2012 (Figure 3). The Emilia seismic sequence has been characterized by the occurrence, in 13 days, of seven Mw>5 main

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Figure 3 - Geographic representation of the area interested by the Emilia sequence. The figure shows the epicenters and magnitudes of the seven major events analyzed in this study (black stars). Gray stars represent the aftershocks of the whole sequence, whereas the black triangles identify the stations used

to compute the response spectra

(taken from A. Tramelli et al., Seismological Research Letters, 10:970-976, 2014)

Epicenters were located in an area of about 50km along west-east direction, but they were concentrated mainly in the depth range 0-15 km, and a limited number of earthquakes occurred between 15 and 30 km of depth.

Several industrial plants, mainly of precast concrete, are present in the area, as well as several masonry rural buildings. These type of buildings have natural period greater than that of ordinary buildings, suggesting low frequency components in the ground motion.

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8 A specific example is the Sant’Agostino (industrial area), where the building was used for the storage of pottery produced in a near factory (see Figure 4). The building is composed by steel truss stand connected to each other only at roof level, in the longitudinal direction there are not any braces. The industrial structure is collapsed because it is very flexible and there is a considerable masses. Moreover, the second order P- effect due to horizontal deformations, so there is a loss of the stability and the consequent collapse of a part of the building.

Figure 4 – Sant’Agostino, pottery warehouse

(taken from http://www.eqclearinghouse.org/2012-05-20-italy)

In order to assess and reduce possible Na-Tech risk, observed after the L’Aquila and Emilia earthquakes, suggests a better integration of seismic aspects in the law and codes for industrial plants design and reinforcement. It is necessary to highlight the criticisms related to steel construction and to non-structural element and equipment. This requires to take into account the interdependence between natural and technological hazards in the policies of risk reduction. (5)

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ASSESSMENT AND MITIGATION OF THE SEISMIC RISK

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3 Assessment and mitigation of the seismic risk

3.1 Methods for the seismic risk assessment

It is necessary to make seismic analysis’, to value the structure’s vulnerability and to propose an adaptation. The legislations, EC8 and NCT2008, permit to use four analysis methods:

1) Static linear analysis; 2) Dynamic linear analysis;

3) Static non-linear analysis (pushover); 4) Dynamic non-linear analysis.

The static linear analysis procedure consists of first calculating a base shear corresponding to the lateral load-carrying capacity if the structure were to remain elastic. This elastic base shear is then divided by force reduction factor to reflect the ductility capacity of the lateral load-resisting system selected the design.

For tall and/or irregular structures for which higher modes and torsional effects are important, the forced-based seismic design procedure is applied through the so-called Linear Dynamic

Analysis Method. This method is based on a dynamic analysis procedure using linear modal

superposition and design absolute acceleration response spectra to define the ground excitation. The peak transient linear response in each mode of vibration of the structure is first computed. These peak modal responses are then combined statistically to obtain an estimate of the multi-modal peak transient response of the structure. The main purpose of the Linear Dynamic Analysis Method is to obtain an improved distribution of the design lateral forces on the structure that includes the effect of higher modes and/or torsional effects.

The nonlinear static analysis method consists of first developing a nonlinear model able to capture all local nonlinearity effects of importance to the global response of the structure, and subjecting this model to increasing levels of lateral loads. The lateral loads are increased until a target displacement is reached or until it reaches collapse under combined lateral loads and P-Δ effects. Figure 5 shows a typical pushover curve for multi-degree-of-freedom structure. As the lateral load is increased, additional elements yield progressively until a full mechanism is formed. Once the mechanism is fully formed, the structure undergoes inelastic

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10 deformations until elements progressively fail. The pushover curve terminates when the complete collapse of the structure is reached.

Figure 5 – Typical Pushover Curve for a Framed Structure

(taken from C. Christopoulos et al. Principles of passive supllemental dampign and seismic isolation, 2006)

The pushover analysis procedure does not capture the cyclic behaviour that is expected under seismic loading but relies on an estimate based on the strength envelope of the system. Considering that numerical models capable of adequately reproducing the nonlinear behaviour of the structure under monotonically increasing loads can usually be extended with little additional effort to capture the cyclic response of the structure, valuable information can be obtained by applying cyclic loading to the structure (see Figure 6). Information on stiffness degradation as well as energy dissipation, both key parameters in the nonlinear seismic response of structure, can be derived by simply reversing the loading once the target displacement has been reached, and by repeating the pushover analysis in the opposite direction. This can also be done for different values of positive and negative peak displacement, thus yielding a complete relationship between maximum displacement and energy dissipation characteristics. This information is especially useful for the derivation of ductility-damping curves for a direct displacement-based seismic design.

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Figure 6 – Cyclic Pushover curve for a Frame Building

(taken from C. Christopoulos et al. Principles of passive supllemental dampign and seismic isolation, 2006)

For very tall and/or highly irregular important structures, nonlinear time-history dynamic

analyses can be performed. For this purpose, the ground motion input must be represented by

an ensemble of acceleration time-histories that are compatible with the seismic hazard level at the construction site, including the possibility of multiple sources capable of producing significant ground shaking at the considered site. Scaled historical ground acceleration time-histories, recorded in the same region or other regions, exhibiting similar seismo-tectonic mechanisms as that of the construction site must be selected. As an alternative, synthetic records that are compatible with the design response spectrum for the site can be generated. A nonlinear model of the structure needs also to be generated. This model needs to contain sufficient degrees-of-freedom to represent adequately the spatial distribution of the mass and stiffness of the structure in order to capture its dynamic behaviour. Furthermore, the cyclic behaviour of the structural elements that are deemed to respond in the inelastic range of the material needs to be included, with realistic representation of limit states. Typically, this nonlinear behaviour is taken into account by lumped hysteretic plasticity rules. Finally, nonlinear geometric effects may also need to be included. (6)

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3.2 Concept of seismic risk mitigation

3.2.1 Methods for seismic risk mitigation

The Italian legislation (NTC 2008) defines various category of intervention for existing structures.

These interventions are possible to divide into:

 seismic adaptation: to obtain a safety level, that is obligated to legislation.

 seismic improvement: to increase the safety of existing building, but it is not request of legislation.

The seismic adaptation is compulsory for everyone who wants:

 to raise a building;

 to build up a building with some structure connected to the main one;

 to make some improvement that produces a variation of use destination;

 to totally change the employment of a structure.

The capacity of resistance of existing structures increases, during the seismic improvement. It is possible to make these interventions when the seismic adaptation is not requested.

In the NTC 2016 there are some new insertions. In fact, for the seismic adaptation, there is the ζE coefficient that depends on the type of interventions.

While, for the seismic improvement, there is the ξE coefficient that depends on the classes of

used:

 I class: constructions where sometimes there are people, rural building;

 II class: constructions where there are a standard crowd;

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3.2.2 Retrofitting

Life-cycle had an important development during the last twenty years. This concept means, not only how much cost to build a structure, but also to make a valuation of the total price for a building’s conservation.

At the beginning, the earthquake’s damages were not considered into the total amount, but, then, it will be necessary to consider them because the problem is been more important.

Figure 7 – Life-Cycle Cost Framework

(adapted from S. E. Chang et al., Journal of infrastructure systems 2:118-126, 1996)

Theoretically, the life-cycle is based on four factors: Where:

 C1: total amount

 C2: planned costs

 C3: costs link with C1

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14 C3 is the member where there are considered damages from earthquake. It is quite

complicated to understand the influence of a natural disaster, but, for example, for an earthquake can be contemplated the local hazard curve and so to empirically estimate it. In general, the sensitivity of these analysis depends on three factors:

 the prevalent parameter has the major effect;

 it is necessary to have a significant range of data, based on past experiences;

 to make a combination with hazard, retrofit cost and damage

So, the calculation of life-cycle is going to have a bigger importance into the development of civil infrastructures. Moreover, the environmental disasters, especially the earthquake’s damages, have a major consideration. (7)

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3.2.3 Systems for seismic energy dissipation

Supplemental damping systems are intended to consume a portion of the seismic energy input into a structure. These devices are called as “mechanical dampers” and their energy dissipation reduces the energy dissipation demand on the structural system, so it is possible to reduce the dynamic response during a major earthquake.

Supplemental damping system can be divided in three wide categories:

 Active systems: are projected to monitor the structure during the time, to elaborate the information and to apply, in real time, a set of internal forces due to calibrate the dynamic statement of the structure;

 Semi-active systems: need a small supply external power, but they don’t need a global system of monitoring. The control is limited to a local proprieties of the damper.

 Passive systems: don’t need energy, computer or any other actuators; they endure passively the dynamic action of the earthquake and they deform elastically or not elastically.

The principal components of active systems are:

 Monitoring system: able to understand the state of the structure;

 Controlling system: receives data and decides which countermeasure to use

 Actualization system of the commands: that applies physically the countermeasure to the structure.

The advantages and disadvantages of dissipation systems are summarized in the table below (Table 1):

Table 1 – Advantages and disadvantages

ADVANTAGES DISADVANTAGES

A big capacity control of the dynamic

response Design extremely difficult

There is the possibility to optimize the response of the excitation from wind and

earthquake

Systems very expensive

It is necessary to generate external power, especially during the seismic event

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16 Semi-active systems are in the same category of active systems but they require a small amount of external energy without to need a global monitoring system. The control is limited to modifying the local proprieties of the dampers, so the aim is to eliminate the possibility of instability.

The principal function of a passive energy dissipation system is to reduce the inelastic energy dissipation demand on the framing system of a structure. There are several passive energy dissipation devices (see Figure 8):

Figure 8 - Summary of construction, hysteretic behavior, physical models, advantages, and disadvantages of passive energy dissipation devices for seismic protection applications

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 Viscous fluid dampers

Such dampers consist of a hollow cylinder filled with fluid, the fluid typically being silicone based (Figure 9). As the damper piston rod and piston head are stroked, fluid is forced to flow through orifices either around or through the piston head can produce very large forces that resist the relative motion of the damper. The friction forces give rise to energy dissipation in the form of heat.

The term viscous fluid damper is associated with the macroscopic behaviour of the damper which is essentially the same as that of an ideal linear or nonlinear viscous dashpot.

Figure 9 – Viscous fluid dampers

(taken from http://taylordevices.com/papers/history/design.htm)

An alternative to viscous fluid dampers, viscoelastic fluid dampers, which are intentionally designed to provide stiffness in addition to damping, have recently become available for structural application. These dampers provide damping forces via fluid orificing and restoring forces via compression of an elastomeric. Thus, more accurately, the dampers may be referred to as viscoelastic fluid/solid dampers.

 Viscoelastic solid dampers

Viscoelastic solid dampers consist of solid elastomeric pads bonded to steel plates (Figure 10). The steel plates are attached to the structure which chevron or diagonal braces. These devices, by their very nature, exhibit both elasticity and viscosity.

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Figure 10 – Viscoelastic solid damper

(taken from http://www.conservationtech.com/RL%27s%20resume&%20pub%27s/RL-publications/Eq-pubs/1991-Woodrow/1991-Woodrow.htm)

The mechanical behaviour is presented in terms of shear stresses and strains rather than forces and displacement. So, the mechanical proprieties become the storage and loss moduli that define the proprieties of the viscoelastic material rather than proprieties of the dampers. In general, the storage and loss moduli are depend on frequency of motion, strain amplitude and temperature.

 Metallic dampers

There are two types of metallic dampers: buckling-restrained brace (BRB) damping and added damping and stiffness dampers (ADAS).

A BRB (see Figure 11) consists of a steel brace with a cruciform cross section that is surrounded by stiff steel tube. The most of the times, they are installed within a chevron bracing arrangement, so, under the lateral load, one damper is in compression and the other is in tension.

Figure 11 – BRB Materials and parts

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19 During the initial elastic response of the BRB damper, the device provides only stiffness. As the BRB damper yields, the stiffness reduces and energy dissipation occurs due to inelastic hysteretic response.

ADAS damper consists of a series of steel plates wherein the bottom of the plates are attached to the top of a chevron bracing arrangement and the top of the plates are attached to the floor level above the bracing.

The geometrical configuration of the plates in such that the bending moments produce an uniform flexural tress distribution over the height of the plates. Thus, the inelastic action occurs uniformly over the full height of the plates.

 Friction dampers

Friction dampers dissipate energy via sliding friction across the interface between two solid bodies (Figure 12). Examples of such dampers include slotted-bolted dampers wherein a series of steel plates are bolted together with a specified clamping force. The clamping force is such that slip occurs at a prespecified friction force.

Figure 12 – Friction damper

( taken from https://www.researchgate.net/figure/

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20 An alternative configuration consists of cross-bracing that connects in the centre to the rectangular damper. This force system causes the rectangular damper to deform into parallelogram, dissipating energy at the bolted joints through sliding friction.

Other configuration include a cylindrical friction damper in which the damper dissipates energy via sliding friction between copper friction pads and a steel cylinder. The copper pads are impregnated with graphite to lubricate the sliding surface and ensure a stable coefficient of friction. (8)

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3.2.4 Systems for seismic isolation

Seismic isolation is a technique used to reduce the effects of earthquake ground shaking on structure.

A system for seismic isolation should have these features:

 Capacity to support a gravity loads in repose conditions and seismic conditions;

 High deformability in horizontal direction under seismic actions;

 Good dissipative capacity;

 Adeguate resistance of non-seismic actions (wind, traffic, …).

The damping by energy dissipation influences the displacement and the acceleration response as at shown in Figure 13:

Figure 13 - Effects of base isolation: a) on spectral acceleration, b) on lateral displacement, c) for different soil conditions

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22 The local soil conditions have a great impact on the reliability of the base isolation. In stiff soil conditions a significant reduction in spectral acceleration is attained while in soft soil the adverse occurs.

There are two types of base isolator devices:

 Elastomeric bearing

 Sliding bearing

The first one is divided in these typologies:

 Low-damping natural or synthetic rubber bearing

 High-damping natural rubber bearing

 Lead-rubber bearing

While in the second one it is possible to find:

 Flat sliding bearing

 Spherical sliding bearing

Natural and synthetic rubber bearing (NRB)

As it can be seen in Figure 14 are made of alternating elastomeric layers that are made of natural rubber or neroprene and steel shims vulcanized or glued together. The elastomeric layers provide lateral flexibility and elastic restoring force. The steel plates reinforce the bearing by providing vertical load capacity and preventing lateral bulge.

Figure 14 – Natural rubber bearing

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23 NRB are available as either low damping or high damping, depending on the elastomeric compounds used.

The low damping bearings are used in conjuction with supplementary damping devices. They have a linear behaviour in shear for shear strains up to and exceeding 100%. The damping ratio is about 2-3%.

The advantages and disadvantages of NRB system are summarized in the table below (Table 2):

Table 2 – Advantages and disadvantages

ADVANTAGES DISADVANTAGES

Simple to manufacture

Need supplemental damping system Easy to model

Response not strongly sensitive to rate of loading, history of loading, temperature and

aging.

The high damping ones are able to provide sufficient inherent damping and eliminate the need of other tools. Damping is increased by adding extrafine carbon black, oils or resins, and other proprietary fillers. Damping ratio is about 10-20% at shear strains of 100%. The effective stiffness and damping depend on: elastomeric and fillers, contact pressure, velocity of loading, load history and temperature.

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24 Lead rubber bearings (LRB)

They are similar to the NRB, but contain a lead core Figure 15, that is press–fitted into central hole of elastomeric bearing.

Figure 15 – Lead rubber bearing

(taken from http://www.bridgestone.com/products/diversified/antiseismic_rubber/product.html)

The lead plug is introduced to increase the damping by hysteretic shear deformations of the lead. The main reason why lead is chosen as the material for the central plug is that, at room temperature, lead behaves approximately as an elastic-plastic solid and yields in shear at relatively low stress of about 10 MPa. Also, lead is hot-worked at room temperature. This means that lead’s proprieties are continuously restored when cycled in the inelastic range. Therefore, lead has very good fatigue resistance proprieties. Finally, another advantage of lead is that it is commonly available since it is used in batteries at a purity level of more than 99.9%.

Sliding bearings

Sliding bearings can be uni-directional and multi-directional and they permit displacements in one direction or in all directions of the horizontal plane. In the buildings is preferred to have an isotropic behaviour of isolation system in its complex and so the multi-directional isolators are preferred. These last systems are composed by two or more discs of different diameter that they slid one on the other, the surfaces are realized by particular materials that have a low resistance of contact friction. The major sliding surfaces used are in inoxidizable polished steel and PTFE (Teflon). The dynamic friction coefficient is about 6-18% in PTFE, reducing at 1-3% in case of lubrication of the surfaces.

The PTFE are not used as an only component of the isolation system, unless they have some elements that increase the initial stiffness and the dissipative capacity. In practice, the friction

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25 energy of dissipation is renounced by to take advantage of the sliding supports in PTFE, due to excessive variability of friction coefficient during the time and to different environmental conditions (temperature, humidity). So, some lubricate isolators are used with the only function to support the vertical loads, while the horizontal loads are free. In this case it is necessary to use the PTFE system with some auxiliary devices with the dissipative function. These devices are the elastomeric bearing, explained in the paragraph below. So it is possible to create an hybrid isolation system, where sliding and elastomeric bearing coexist.

This configuration has some technical and economic benefits. It is possible to obtain a low stiffness systems (long period), with a lot of breakdowns of seismic effects, also when the structural mass of each isolator is limited, and good re-entrant capacity. The principal disadvantage is about vertical deformability that could give some differential vertical displacements where there is the isolator system.

The friction pendulum system (Figure 16) is the only sliding bearing isolator that has both re-entrant and dissipative functions because it is composed by curve sliding surface that is not lubricate, so it could dissipate energy.

Figure 16 - Friction pendulum system

(taken from L. Petti et al., Open Journal of Civil Engineering 10:86-93, 2013)

The equivalent stiffness of the device depends on radius of curvature of curve surface. These isolators permit to realize some isolation systems with independent oscillation period of considered building’s mass. Moreover, the stiffness is proportional to a lead weight, so the centre of stiffness of the isolation system coincide with the projection of mass centre, reducing any rotational possibilities of the system respect to the vertical axis. (9) (10)

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3.2.5 Multi-directional Torsional Hysteretic Damper (MRSD)

As it is explained in §3.2.3 and §3.2.4, isolators reduce the force demand on superstructure by increasing the effective period and bringing the structure to low-energy region of the design spectrum, while the energy dissipaters absorb and dissipate part of the energy that has already swept into the structure and reduce the displacement an ductility demand on structural components.

Plastic deformation of steel is one of the most effective mechanisms available for the dissipation of energy, from both economic and technical point of view. The idea of utilizing Steel Hysteretic Dampers (SHDs) within a structure to absorb large portions of seismic energy began with the conceptual and experimental work in 1970s.

Steel dampers have strong points:

 Good reliability;

 Constant performance independent from temperature and impressed velocity;

 High resistance to ageing;

 No need for maintenance;

 Limited cost.

The only point is that they have a limited capacity of accommodating large displacements, as required in structure in high seismic area.

In response to this concern, MAURER, a structural company specialized in seismic hardware, has developed and experimentally investigate two types of SHDs, in which energy dissipation is achieved by subjecting the hysteretic elements to two distinct impressed movements, namely axially and in torsion respectively.

I. A compact steel damper (MCSD) operating in one direction (tension and compression) with moderate re-centring capability

The BRB system, descripted in §3.2.3, has already used as diagonal brace in building and also in long-span bridges, but the only drawback is in its excessive length because there are some problems with the installation.

The patented MCSD device solves this problem by reducing by a factor of 3 the axial overall dimension. Thus, according to Euler’s theory, the buckling load increases by a

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27 factor of 9 compared with an existing BRB, the reaction force and displacement capacity being equal (Figure 17 and Figure 18).

Figure 17 – Compression and tension behaviour of MCSD

(taken from www.maurer.eu .pdf file: MAURER Earthquake Protection Systems)

Figure 18 – MCSD geometrical characteristics

(taken from www.maurer.eu .pdf file: MAURER Earthquake Protection Systems)

II. Re-centring steel damper (MRSD) horizontally operating in two directions and providing excellent re-centring

MRSD is designed to dissipate energy by torsionally-yielding cylindrical energy dissipaters, named yielding cores.

It works equally in any horizontal direction, using eight identical yielding cores. To convert translational motion of the structure to twisting in the cylindrical cores, each arm is coupled with guiding rail which through a low-friction slider block guides

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28 the motion of the arm. The yielding cores are configured in an upright position around a central column to which they are attached through a thick plate (see Figure 19).

Figure 19 - MRSD: (a) Isometric view showing the rail system and base device underneath; (b) side view; (c) energy dissipation unit of MRSD: A yielding core, as attached to other components

of the device

(taken from M. Dicleli et al., International Journal of Civil, Environmental, Structural, Construction and Architectural

Engineering, vol.9, 2015)

The plate functions as a diaphragm in transmitting the shear and bending forces imposed by the arms to the top part of the corresponding yielding cores, into the central column, base plate and base anchorage. The uniform part of the yielding cores is where energy dissipation due to torsional yielding occurs.

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29 It can be apply to the structure a great force (2000kN and more) with a big high displacement of up to +/-1,5m. In the view of the changing rigidity as a function of the displacement amplitude and powerful force increase at the end of the movement displacement capacity, the structural displacements are reduced by up to 30% compared to the conventional hysteretic dampers. The dampers are therefore ideal as for structural re-centring dissipators in addition to seismic isolators within buildings and bridges. They can also be inserted into diagonal struts of any steel structures. The concept behind MRSD has been applied recently in development of an isolator/dissipater unit named MARTI (see Figure 20), that is an integrated bearing-damper system, composed of a flat slider and four torsional energy dissipation units, similar to those of MRSD.

Figure 20 - MARTI, an integrated bearing-damper isolation system

(taken from M. Dicleli et al., International Journal of Civil, Environmental, Structural, Construction and Architectural

Engineering, vol.9, 2015)

The isolator part of the device will provide vertical load transmission, lateral flexibility and a small amount of damping by friction, complemented by the hysteretic damper part through further damping and re-centring. The damper part is identical to the MRSD, which is device for its own and the MARTI is a combined device. (11) (12)

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3.2.6 Torsional Bracing System

The Torsional Bracing System is an improvement of the MARTI system: it is based on the same fundamentals, but it is placed into the braces.

This new system is composed by two elements with the extremities hinged to the arms of an X-bracing structure, as shown in Figure 21. A steel cylinder (denoted as control element) connects these two hinged elements.

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31 The displacement of hinged elements induces a twisting moment on the control element. When the steel cylinder reaches the yield strength, there is an onset of plastic deformation and a concomitant overheating of this element that dissipates energy (see Figure 22).

Figure 22 – Steel Cylinder element

The Torsional Bracing System displays the cinematic behaviour shown in Figure 23, where the angle inside the dissipator (α) is equal to 90° in the initial “unperturbed” configuration (Fig. 23a). The application of a horizontal displacement δ through an external piston results in α > 90° and induces a twisting moment on the steel cylinder which starts to dissipate heat energy (Fig. 23b).

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Figure 23– Bracing Torsional System: (a) Initial configuration; (b) System perturbed with displacement (δ) originating a twisting moment

In general, this Torsional Bracing System shows a better behaviour with respect to a tension o compression one, as confirmed by cyclic analyses performed at the laboratory of RTWH Aachen University (experiments are described in detail in chapter §8).

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OBJECTIVE AND METHODOLOGY

33

4 Objective and methodology

The aim of this thesis is to evaluate the seismic vulnerability of a silo structure belonging to the ILVA steel industrial plant in Taranto (Italy) and to study an eventual operation of seismic retrofit.

The case study is composed of two identical Silos and, considering the low stiffness of the connecting elements, only one has been studied in this thesis. The Silos is used for storing hydrated lime, that is produced in particular furnaces and then is distributed and utilized for two main purposes: (1) to remove the phosphor from “pig iron” in blast furnaces, and (2) to remove the sulphur from liquid steel in a steel plant.

In order to reach the aforementioned objective, the work was organized in the following steps:

 analysis of the available information on the silo, such as technical drawings:

during this step, it is important to check and review any structure information and documentation available (provided by PROINDUSTRY), examining the technical drawings and the previous reports to understand how it was designed and the eventual structural changes it underwent during its lifetime (see §5);

 3-dimension model creation:

during this step it is necessary to spend a little time to learn OpenSees, an open-source software based on a C++ language, to have a good knowledge of this software. Then it is possible to think how to sketch the structure statically and to create the total silo in 3-dimensions in OpenSees (description in §6);

 linear modal analysis of the silo:

the aim of this step is to obtain a simplified yet realistic representation of the actual structure allowing computational analyses to be performed. The latter should help us in finding the eventual criticalities of the structure and understanding how to improve its behaviour, with particular regards to the resistance against seismic actions (see §6);

 non-linear static analysis (N2 method - theoretical description in §3.1):

(1) identification of the critical elements: specific study for buckling into the braces and for a tension behaviour of the braces in a simplified model (see §7.2);

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OBJECTIVE AND METHODOLOGY

34 (2) simplified model without imperfection in the braces: to learn the shear

behaviour of the column (capacity curve – see §7.3);

(3) model with imperfection in the braces: to compare the capacity curve with the simplified model and to find the differences and the reasons (see §7.4);

 dissipator integration into the braces:

to make a study of 2D nonlinear modelling of a portion of the supporting structure to improve the behaviour under seismic effects. In particular, in this case, it is used Torsional Bracing System, a new type of torsional steel hysteretic damper (see §3.2.6). Then the system dissipator is simplified to insert it into the 3D model of the total structure. Finally, there is a compare between the original system and the new model (see §8).

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STATE-OF-THE-ART

35

5 State-of-the-Art

5.1 The plant ILVA of Taranto

The plant ILVA is located to the north - west to the city of Taranto (Italy). It occupies an area of about 15 million square meters of which 1.7 are covered.

The plant is aimed at the production of steel (plates, coils, tubes, etc.) through various processes of transformation of raw materials (mineral and fossil). During the manufacturing cycle, some by-products are produced and they could create some hazard for considerable incident, due to the amount and intrinsic features of the materials.

Within the perimeter of the ILVA plant in Taranto it is also the powerhouse Edison S.p.A. The activities into the plant are:

 Coke oven plant

 Gas distribution network

 Air separation plant

These activities, due to materials or formulation used or products, put the plant into the category of risk.

The main elements in the plant are: 2 thermal power plants, 5 blast furnaces, 2 steel plant, 2 conveyor belts for coke production, 2 rolling mills, 2 steel galvanisation plants, 2 silos and 2 pipe mills.

The annual production amounted to 8.2 million of steel ton in 2012.

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STATE-OF-THE-ART

36

5.2 The case study: Silos FOC

The Silos FOC case study was built in 2001 and is an elevated silo structure. The structure is used for storing hydrated lime, that is produced in particular furnaces and then is distributed and utilized for two main purposes: (1) to remove the phosphor from “pig iron” in blast furnaces and (2) to remove the sulphur from liquid steel in a steel plant. Figure 24 gives a general view on the structure which is assembled by four main parts:

 two identical silos connected to each other by two catwalks,

 supporting structure for each Silos made by braced frames also supporting an intermediate floor,

 bucket elevator,

 stairs.

Figure 24 - Pictures of Silos FOC case study showing two elevated silos, braced supporting structure, stairs with bucket elevator and connecting catwalks

(taken from PROINDUSTRY, Silo FOC description - review -)

The following figures give a more detailed view on the structure. The columns of the main supporting structure are lying within a hexagon (see Figure 25). These six HEA 340 columns are linked by X-bracings (see Figure 27 and Figure 28). The support boundary conditions are assumed to be fixed rather than hinged, since the structural steelwork is constructed to

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STATE-OF-THE-ART

37 transmit bending moments, as can be seen in Figure 26. Two horizontal bracings divide the main supporting system at 5.27 m and 9.13 m height level (Figure 27). The columns also support a floor which is used to verify the pneumatic driven valve underneath the outlet of the hopper (see Figure 29). Used cross section for the supporting structure are shown in Figure 30 and the bracings with their connection details in Figure 31.

Figure 25 - Section view at the first level

(taken form project board)

Figure 26 – Column support

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STATE-OF-THE-ART

38

Figure 27 – Elevated view of whole structure

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STATE-OF-THE-ART

39

Figure 28 - Main supporting structure: six columns HEA 340, horizontal and vertical bracings

(taken form project board)

Figure 29 - Arrangement of beams on the first storey

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STATE-OF-THE-ART

40

Figure 30 - Elevated silos with detail of supporting structure

Figure 31 - Horizontal bracing and X-bracing hinged connections to the columns (right) and connection detail at mid of X-bracing (left)

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STATE-OF-THE-ART

41 Silo structure

The support detail of the stiffened silo shell structure can be seen in Figure 32. It is assembled by a reinforced ring beam connected to the thin-walled cylindrical part. The ring channel beam has the function of connecting the silo shell with the columns and the inverted V-braces. Each silo shell is divided by vertical and circumferential stiffeners. The horizontal stiffeners divide the silo into seven segments of varying wall thickness and the vertical stiffeners are evenly distributed around the circumference of the silo body. The thickness ratio varies from 4 mm to 6 mm, as shown in Figure 27. The flanges of the circular sheets are spliced together by bolts as can be seen in Figure 32. Shear is transferred by 20 M14 grade 8.8 bolts placed on each segment of the silo shell. The same connection is realized in the hopper of the silo, where the shear is transferred by 18 M16 grade 8.8 bolts.

Figure 32 - Detail of connection between circular sheets of the silo

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STATE-OF-THE-ART

42 Catwalks

Two catwalks link the two silos to each other. The connection at the first floor is bolted (see

Figure 33) while at the top floor it is welded. The connection at the top is performed by four

supports with CNP 140 cross sections welded on the floor as shown in Figure 34.

Figure 33 - Detail of bolted connection at the 1st floor

Figure 34 - Detail of welded connection at the top floor

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STATE-OF-THE-ART

43 Bucket elevator

Beams welded on the silo walls connect the bucket elevator to the silo as shown in Figure 35. The stored material is lifted above the two silos through the bucket elevator, which is self-supported. The bucket elevator consists of 135 buckets attached to a chain with a pulley at the top of the unit. Bulk material is loaded into each bucket moving past an inlet point. Each bucket contains 567 kg of lime hydrate. The top pulley is powered by an electric motor. The bucket elevator height is 29.7 m with hollow rectangular cross section of 1.4x0.51 m and 30 mm thickness. The elevator casing is stiffened by vertical and horizontal bracings.

Figure 35 - Front and lateral elevation of bucket elevator

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STATE-OF-THE-ART

44 Staircase

In order to check equipment that is installed on the roof of the silos, a staircase is linked to the silo in six points (see Figure 36). The main stairs frame, made in steel S275, consists of two HEA 200 cross section columns, connected to each other at each landing through IPE 160 beams. The structure is reinforced by -braces along all the height.

Figure 36 - Front and lateral elevation of staircase

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STATE-OF-THE-ART

45 Foundation

The two silos are supported on a mat foundation, that encompasses the entire footprint of the structure. Four micro pales with 200mm diameter and 60cm length of dimension, that are integrated by means of a square pile cap of 90x90cm, support each single column.

Figure 37 -Front and lateral elevation of foundation

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STATE-OF-THE-ART

46 Material handling system and sequence

As shown in Figure 38, the material handling system consists of two one-way screw feeders as well as a bucket elevator. The hydrated lime is coming from a screw feeder (1), located downstream the crushing and screening plant, and is discharged into the bucket elevator (2). The stored material is then lifted (3) above the two silos into a screw feeder (4) which delivers the material into the circular silos. To discharge the circular silos, the pneumatic driven valve underneath the outlet is opened (5) and the silo is emptied. A pipe system and compressors allow to keep a constant depression in the entire system, manage dosing operations and avoid the distribution of lime.

Figure 38 - Filling and discharge sequence

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STATE-OF-THE-ART

47 Bulk material

The stored bulk material inside the silo is hydrated lime. Table 3summarizes relevant values taken from Eurocode 1-4 Annex E.

Table 3 - Hydrated lime properties according to EC 1-4.

The storage capacity of each silo is in total 667.5 m³. This results in a stored material mass of 534 t for the full silo if the upper value of the unit weight is used, and to 400 t and 467 t if lower or mean values respectively are used.

Steel grade

Two different steel grades are used for the structure: Fe360B and Fe430B. According to Table 4 they correspond to European current steel grade labels S235 JR and S275 JR. The lower steel grade is used for the shell elements whereby the higher grade is used for the beam cross sections. (13)

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MODELLING APPROACH

48

6 Modelling approach

6.1 OpenSees

The Open System for Earthquake Engineering Simulation, OpenSees, is a software framework for developing sequential, parallel and grid-enabled finite element applications in earthquake engineering. It is written primarily in the object-oriented programming language C++.

OpenSees is comprised of a set of modules to perform creation of the finite element model, specification of an analysis procedure, selection of quantities to be monitored during the analysis, and the output of results. In each finite element analysis, an analysis is used to construct four main types of objects, as shown:

 Domain: holds the state of the model at time ti and (ti+dt) and is responsible for storing

the objects created by the ModelBuilder object and for proving the Analysis and Recorder objects access to these objects;

 ModelBuilder: constructs the objects in the model and adds them to the domain;

 Analysis: moves the model from state at time ti to state at time and (ti+dt);

 Recorder: monitors user-defined parameters in the model during the analysis (14). Modal and push-over analyses are made with this software framework. The major point is to build the structure, in this case the Silos that is described in §5.2.

So, in the paragraphs below there is the explanation about each step for creating the structure and, at the end, the results of the analyses.

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MODELLING APPROACH

49

6.1.1 OpenSees Model

Coordinates of the points

First at all it is necessary to define the ModelBuilder, to indicate the dimension of the problem (ndm) and the number of degrees of freedom at node (ndf). In this case we are in 3-dimesions system.

Figure 39 – Model builder definition

So it is possible to define the coordinates of the points of the model. A reference system is chosen and then, for each point, the coordinates are extracted. Figure 40 shows the reference system, while Figure 41 shows the two principal views of the structures.

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MODELLING APPROACH

50

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51 For each point there are 3 coordinates because the system is draw in 3-dimensions:

node $nodeTag (ndm $coords)

Figure 42 – Coordinates of node definition

Then it is necessary to define which points are constraints and the type. Each column on the basement is fix, as it is possible to see in Figure 43 and Figure 44.

fix $nodeTag (ndf $constrValues)

Figure 43 – Fix definition

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MODELLING APPROACH

52 Material definition

All the elements of the system have the same steel: S275. To define this material is used the Steel01 command. This command is used to construct a uniaxial bilinear steel material object with kinematic hardening and optional isotropic hardening described by a non-linear evolution equation, but in this case the last option is not used.

Figure 45 – Steel01, material parameters of monotonic envelope

(taken from S.Mazzoni et al.,OpenSees Command Language Manual, 2007)

Figure 46 – Material Steel01 definition

Then there is the definition of two other materials that are used to model the hinge, one is rigid with young modulus of 1013 N/mm2 and the other one is soft with 100.0 N/mm2 of young modulus. These materials are elastic, as Figure 47 shows:

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MODELLING APPROACH

53

Figure 47 – Elastic material

(taken from S.Mazzoni et al.,OpenSees Command Language Manual, 2007)

Section definition

Each element is defined by a fiber section (see Table 5). A fiber section has a general geometric configuration formed by subregions of simpler, regular shapes (e.g. quadrilateral, circular and triangular regions) called patches. In addition, the material is indicated. Figure 48 shows the definition for HEA340 section.

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MODELLING APPROACH

54 In Figure 40 and Figure 41 is clear the collocation in the structure for each element.

Table 5 – Section element

ELEMENT FIBER SECTION

column HEA340

beam IPE200/UPN140

brace 2L80x80x8

Elements definition

In OpenSees there are different types of element, in this case the Table 6 shows the codification used in this thesis:

Table 6 – Codification elements

ELEMENT CODIFICATION

column forceBeamColumn

beam forceBeamColumn

brace truss element / nonlinearBeamColumn

The forceBeamColumn element is based on the iterative force-based formulation, in this case Gauss-Lobatto integration is used.

element forceBeamColumn $eleTag $iNode $jNode $numIntgrPts $secTag $transfTag

For brace element is defined two types of elements: 1. truss element with a specific section:

element truss $eleTag $iNode $jNode $secTag

2. nonlinearBeamColumn element is based on the non-iterative (or iterative) force formulation, and considers the spread of plasticity along the element:

element nonlinearBeamColumn $eleTag $iNode $jNode $numIntgrPts $secTag $transfTag

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MODELLING APPROACH

55 For each element is necessary to define the start point and the end point, then the number of points of integration, the section type and the geometric transformation.

The geometric-transformation command (geomTransf) is used to construct a coordinate-transformation (CrdTransf) object, which transforms beam element stiffness and resisting force from the basic system to the global-coordinate system. The command has at least one argument, the transformation type:

 Linear transformation is used to construct a linear coordinate transformation

(LinearCrdTransf) object, which performs a linear geometric transformation of beam stiffness and resisting force from the basic system to the global-coordinate system;

 P-Delta transformation is used to construct the P-Delta Coordinate Transformation

(PDeltaCrdTransf) object, which performs a linear geometric transformation of beam stiffness and resisting force from the basic system to the global coordinate system, considering second-order P-Delta effects;

 Corotational transformation is used to construct the Corotational Coordinate

Transformation (CorotCrdTransf) object, which performs an exact geometric transformation of beam stiffness and resisting force from the basic system to the global coordinate system.

Table 7 – Geometric transformation

ELEMENT GEOMETRIC TRANSFORMATION

column P-Delta

beam Linear

brace Corotational

Finally the last type of element is the zeroLength element that is used to create hinges. This command is used to construct a zeroLength element object, which is defined by two nodes at the same location. The nodes are connected by multiple UniaxialMaterial (see paragraph before) objects to represent the force-deformation relationship for the element.

element zeroLength $eleTag $iNode $jNode -mat $matTag1 $matTag2 ... –dir $dir1 $dir2 ... <-orient $x1 $x2 $x3 $yp1 $yp2 $yp3>

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MODELLING APPROACH

56 In Appendix F – Orientation for zeroLength element, there is a complete description about the orientation for zeroLength element.

Mass definition

The major mass is about the material into the Silos and the weight of the structure. It is put on the top of the Silos, as Figure 41 shows, with some rigid elements connect with the total structure.

Considering the capacity of the Silos is 740 m3 and the density material is 8 kN/m3 the total mass is (see Table 8):

Table 8 – Mass definition

Planking level+ Cleaner weight+ Fan on the

roof+ Cochlea on the roof 19 ton

Silos self-weight 24 ton

Stored material 534 ton

TOTAL 577 ton

Geometric imperfection

In Eurocode 3 §5.3.3 there are some advices about the use of equivalent geometric imperfections.

The imperfections can be:

1. Local: for single structural element

2. Global: for frame portal and braces system

In this case, there is an evaluation about the single brace element that can be in tension or compression. So, there is a local imperfection and a check of the stability of the element. The global imperfection is considered when it is inserted the imperfection (e0) into the brace

system.

The first imperfections are inserted with an initial bending of the frame that has a flexional instability of e0/l where l is the element length.

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MODELLING APPROACH

57 In this case the value that is used for plastic analyses is:

 Instability curve “b”:

The imperfection is introduced in the weak axis of the element because it is more probable that is strayed in this direction.

Figure 49 shows the final model with the number of principal points:

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MODELLING APPROACH

58

6.1.2 RSTAB model

RSTAB is a structural analysis program which is possible to project several types of structures with different materials (steel, concrete, wood, etc…).

This software was invented since 1987 by DLUBAL ENGINEERING SOFTWARE and it is developed to be user-friendly and powerful for structural and dynamic analysis.

It is easy to define a structural model and to calculate the internal forces, displacements and fix actions. The program combines automatically the actions following Eurocode.

The modelling for simple and complex structures is very intuitive thank to a simple input of data and practical constants. It is very important, for this point, the graphic interface such as CAD.

In this case, it is used to compare the results from modal analysis in OpenSees that is explained in the §6.2 below.

Figure 50 shows the Silos model in RSTAB:

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MODELLING APPROACH

59

6.2 Modal analysis

Modal analysis is made with the model descripted in §6.1.1 using this OpenSees script (Figure 51):

Figure 51 – Modal analysis in OpenSees

It is obtained the period for each mode of deformation shape of the structure.

The results are compared with the results in RSTAB. The values, obtained in OpenSess, are pushed away not many from RSTAB values and represent a good parameter of validation of the analysis (Table 9).

Table 9 – Modal analysis results

OpenSees RSTAB

T f  T f 

1st mode 1.732 0.577 3.626 1.619 0.6 3.878

2nd mode 1.054 0.948 5.956 1.101 0.907 5.703

3rd mode 0.121 8.226 51.689 0.298 3.352 21.061

At the end, using some scripts of OpenSees Navigator in MATLAB, it is been possible to have a graphic visualisation about each mode of shape. In Figure 52 and Figure 53 is possible to see the first and the second period, about x-axis and y-axis translation respectively.

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MODELLING APPROACH

60

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61

Figure 53 – Deformation about 2nd period

For pushover analysis, it will be considered the second mode of deformation shape (Y-direction) because it has a major sense for the evaluation of braces instability.

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VULNERABILITY ASSESSMENT

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7 Vulnerability assessment

7.1 Objective and pushover N2-method analysis

During this phase there is, firstly, a research of a critical elements of the silo, secondly, a study of the total structure, made in different ways. Two models of the structure are built, one simplified where the braces have not the imperfection, while the second with the realistic structure. The aim is to study the capacity curve of both and compare the results.

The capacity curve is obtained with the N2-method of a pushover analysis. A general description about static non-linear analysis is in §3.1, while, in this paragraph, there is a specific explanation of N2-method.

The aim of N2-method is to combine a non-linear analysis of m-DoF system with a spectrum analysis. The methodology is based on a correlation between the answer of m-DoF system and the response of an equivalent system with 1-DoF with an appropriate hysteretic characteristic. Below there are the steps:

1. Calculation of capacity curve of m-DoF system

The horizontal displacement of a control point is grown monotonically by the horizontal forces shift along the high of the structure. The result is the non-linear curve of the shear on the basement and the displacement of the control point that represents the capacity curve of the structure.

2. Determination of an equivalent 1-DoF system with bi-linear behaviour T*

The participation coefficient of the first shape is calculated:

where 1 is the vector of the first deformation shape.

Then the characteristic curve force-displacement is approached by a bi-linear curve defined with the equal area criteria.

The elastic period of the 1-DoF system is:

√ where m* is:

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VULNERABILITY ASSESSMENT

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∑

3. Calculation of seismic domain

Calculated the spectrum response of the area, it is necessary to pass from Sa[m/s2]-T[s]

system to a Sd[m]-T[s] system.

The formula for this process is:

( ) ( )

4. Transformation to effective domain of the m-DoF system

Known d*max it is possible to calculate the effective displacement of the control point

of the the m-GoF:

Vulnerability assessment and seismic retrofit of an industrial steel structure

Università di Pisa

Scuola di Ingegneria

Corso di Laurea Magistrale in Ingegneria Edile e delle Costruzioni Civili

Tesi di Laurea

VULNERABILITY ASSESSMENT AND SEISMIC

RETROFIT OF AN INDUSTRIAL STEEL STRUCTURE

Table of contents

1 Introduction

2 Seismic risk of industrial structures

2.1

Seismic risk (hazard, vulnerability, exposure)

2.2

Seismic risk associated to industrial plants

3 Assessment and mitigation of the seismic risk

3.1

Methods for the seismic risk assessment

3.2

Concept of seismic risk mitigation

3.2.1 Methods for seismic risk mitigation

3.2.2 Retrofitting

3.2.3 Systems for seismic energy dissipation

3.2.4 Systems for seismic isolation

3.2.5 Multi-directional Torsional Hysteretic Damper (MRSD)

3.2.6 Torsional Bracing System

4 Objective and methodology

5 State-of-the-Art

5.1

The plant ILVA of Taranto

5.2

The case study: Silos FOC

6 Modelling approach

6.1

OpenSees

6.1.1 OpenSees Model

6.1.2 RSTAB model

6.2

Modal analysis

7 Vulnerability assessment

7.1

Objective and pushover N2-method analysis