Different structures respond differently to the earthquake in a dynamic phenomenon that depends on the intensity, dynamics of structural properties, frequency and duration of the earthquake. Earthquakes one of the most dangerous natural disaster that leads to devastating effect in buildings and structures. The magnitude of the effects on structures are related to either shoddy construction procedures and deliberately ignoring the possibility of an earthquake on structures during construction. Aa a precautionary measure, it is of importance to analyze and understand the possible seismic effects buildings and structures thus enabling architects and designers to develop structural plans that have detailed consideration to seismic forces on buildings, therefore, enabling prevention mechanisms in case of an earthquake or earth tremor.

When an earthquake occurs, seismic force hit structures; it generates inertia forces that lead to deformation and vertical and horizontal shaking off the building weakening the pillar joints within the government. The study aims to present the static and dynamic analysis of the steel structures in buildings concerning their behavior and strength when subjected to seismic forces. The mode and scope of analysis involve the incremental dynamic analysis and pushover analysis on the resisting steel frames. When steel frames are exposed to inelastic nonlinear time history assessment in different scaled ground motion both in the far-field and near fields. Earthquake actions are dynamic in nature and occurrence there are set building codes and standards that are recommended for use in establishing static loads that offer an earthquake –resistance buildings.

The earthquake-resistance building designs are developed with a focus on the predominant response mode thus facilitating the development of the equivalent static force that produces an equivalent corresponding mode shape with same empirical adjustments on the higher mode effects. Static load analysis in determining seismic effects on the seismic designs is justified due to difficulties and complexities in the modes of dynamic analysis of steel structures. In the case when non-linearity in geometry and material is considered in the design of systems, the dynamic analysis of such structures becomes more complex and demanding. Nonlinearity in geometry and materials structures is essential in the design of structural elements; therefore more advanced analytical tools have been developed in the past few years with intention of simplifying the static and dynamic analysis of the steel structures in buildings.

1.1.1 Steels in multistory buildings

The use of steel frames in multistory buildings has been the trend in the construction of high rise structures. In the last few years, the use steel in building construction has had an increasing application in building and construction industry, this has been due to its numerous advantages such as compatibility and flexibility with different structural designs, safe solutions in constructions using steels and the fact that steel are4 relatively cheap as compared to other alternative metals hence more economical. Generally, steel structures are quick to assemble, slim and efficient in construction processes. Safety is very essential in high rise buildings therefore detailed structural analysis and of slim steel structures are so fundamental since it enables adequate safety analysis of structures and efficient buildings. In some cases, structural steel frames are subjected to dynamic loads of higher magnitude that often causes deformations and permanent damage on the on these steel structure resulting in either partial or permanent damage. However, there have been some elastic mechanisms used in correcting these defects that have been so uneconomical since they consume a lot of funds and time to correct such defects. Due to high-cost expense in correcting defects, the construction standards and codes allow damage to a certain amount as long as the structural safety is not compromised.

The random baes motion occurs whenever the building is subjected to seismic forces caused by earthquake occurrence; the seismic forces are always accompanied by dynamic actions thus affecting the structural strength. Therefore, the structural response of buildings to earthquakes is a transient phenomenon. Although there is low seismicity in other countries, this action cannot always be ignored, even for small buildings. In the events of extreme loading, building structures exhibits nonlinearity in their behaviours due to the start of charging. An analysis of steel structures used in multistory buildings, second-order effects of nonlinearity in geometry, the flexibility of the joints and connection and most importantly the material nonlinearity in inelastic behavior. Ductility nature of steel metal is the main reason being that steel can absorb a considerable amount of energy and withstand a considerable large amount of deformation stresses before failure or rapture.

Ductility always contributes to the capability of absorbing more energy and allowing force redistribution from structures that have reached the ultimate limit to other adjacent structures. This capability of steel becomes more vital in the event of seismic loadings due to earthquake. The plastic analysis of steel frame structures enhances several benefits in terms of strength assessment compared to elastic analysis since plasticity considers the steals ductility in a substantive range. Many pieces of research have been conducted in relation to inelastic nonlinear analysis of frames with rigid and semi-rigid connections for space and plane frames. Though few structural works are found in these kinds analysis is directly related to a dynamic analysis of steel under earthquake conditions. The inelasticity assessment of frame structures, the methodology of evaluating the plastification is conducted by two robust approaches that are the plastic zone with its variations approach known as distributed plasticity approach and the plastic hinge with its variations approach referred to as concentrated plasticity approach. The only disparity in the two inelasticity approaches lies on the level of refinement applied to represent the plastification of each structural member.

There other second-order models that are more precise and accurate since they consider distributed explicitly and plasticity of the effects and residual stresses thus enable extraction of solutions that almost same the actual value. However, the limitation of the distributed plasticity analysis requires additional supplementary systems that involve higher computational efforts. The distributed plasticity is often used in small structures for validation and calibration of numerical computations and other logistics.

1.1.2 The period determination

Period of the time interval is a crucial parameter of design processes that playa an important role in the design computations of the design shears. The estimation of the period are outlined in the structural and construction codes and standards and the codes provide more accurate methods of mechanics are also elaborated in the structural building standards. The rule of permitted mechanics as a mode of estimating time interval should not be more than 1.5 times more than the empirical value. The limit is justifiable by the point of empirical estimations, such as the existence of uncertainties involved in the application of nonstructural elements whose impacts may not have been considered during the period computations and determination of seismic response, possibilities of inaccuracies from model analysis while applying more complex modelling technics such as methods of mechanics and lastly the possibility of potential disparity between as-built and design condition, more especially on terms of stiffness and mass.

1.1.3 Effects of earthquake on structures

Earthquake causes seismic forces to alter the structural strength through various effects. The following are the summarized effects of the earthquake on building structures.

1.1.4 Induction of inertia forces in structures

The generation of inertia forces in a structure is one of the seismic influences that detrimentally affect the structure. When an earthquake causes ground shaking, the base of the building would move but the roof would be at rest. However, since the walls and columns are attached to it, the roof is dragged with the base of the building. It is the induced inertia that keeps the roof of structures to resist motion and tends to remain in their static positions thus causing shearing of the structural elements which eventually translate the accumulated stresses to the weak joint or walls thus resulting to failure and even worse causing the collapse of the structure depending on the magnitude of the seismic forces released by an earthquake.

The direction of induced inertia force on structures

The induced inertia in buildings depends on the weight and mass of structures and frames used in the construction of buildings, induced inertia is proportional to the overall weight of the building. Thus the heavier or larger the structure the more it is vulnerable to seismic forces. For this reason, is why small and lighter buildings often sustain ground shakings caused by earthquake better than huge buildings. Therefore it is of the essence to have a construction with materials with higher seismic resistance.

Inertial force development in a multistory building

1.2 Deformation effect of structures

In the event of an earthquake, the ground shaking also occurs at the same frequency of the seismic waves, making the foundation base of the structure to shake as well, when this occurs to the structure, it creates a difference in motion or stability of the structure since the uppermost parts of the structure might not experience the same motion of the seismic frequency. The difference in the base movement with the top of the structure causes the development if internal resistance forces that tend to force columns to their initial positions. The prolonged disparity in movement dynamics develops to stiffness forces. The stiffness forces would be higher as the size of columns gets higher. The stiffness force in a column is the column stiffness times the relative displacement between its ends.

Lateral forces resisting structural systems

1.3 Vertical and horizontal shakings

Earthquake forces the ground to shake in all directions, that is in all three directions and the ground continuously shake randomly back and forth along each of the directions. Most structures are designed to withstand only vertical loads resulting from substructures therefor ground shaking in a vertical direction either subtracts or adds to the vertical load, these are q=adequately tackled by the structurally designed safety factor for support vertical loads. However, this is quite different with the horizontal ground shaking along Y and X-direction which crucial for the performance of the structure since it gives rise to lateral displacement and inertia forces hence provision of the substantive load transfer path is established to prevent any form of adverse influence on the structures. The inertia transfer path is developed through the adequate design of walls, floor slab, and columns and the beam connection between structural elements. It is worth noting that columns and walls are essential structures in transferring inertia forces from one structural member to another. It is possible to have a fraction of the elastic level of seismic force as possible and when the building can stably sustain a large amount of displacement demand through structural deformation without collapse or undue loss of strength. Through advanced technologies, it is quite possible to design structures that possess both initial stiffness and lateral strength. This is possible through proportionately in the size and material of the members. Achieving effective ductility is more detailed and involves extensive tests and analysis on full-scale fabrics to determine the most preferable detailing approach.

1.4 Engineer and the architect

In most countries like the United Kingdom, United States, India, and Australia among others, the design of new steel structures structural engineer is the team leader and the architect is a team member. And in the design of retrofits of already existing structures, the architect becomes the team leader and the structural engineer becomes a team member. The purpose of this organization s to ensure that the designer that is architect works in close consultation with engineer counterpart to ensure that the developed building is up to design standards. In the construction industry, it is very crucial for architect and engineers to work together in order to create perfect designs with perfect interaction at all stages. The collaboration in work demands that the design architect recommends the structural aspects such as aesthetic, form functionality and contents while structural engineer contributes to measures to attain the desired earthquake-resistant building and the safety factor of the structure in the event of an earthquake. Reinforcement of strong and durable structural steel frames in buildings requires a good merge of thoughts and ideas from both the architect and the engineer, therefore too great extent collaboration between engineers and architects contribute to improved structural resistance to seismic forces induced by the earthquake. Since it’s the architect who best understands the design and plan dynamics and it’s the engineer who understand best the parameters of earthquake performance and safety factor thus working in unison results to structures with good earthquake resistance both in its plan and design and its directional orientation.

1.5 Problem statement

Earthquake is a natural disaster that no man has control over or could dictate when and how it occurs. But upon its occurrence, its impacts are devastating as it comes along with numerous negativities such as loss of lives, destructions of properties, disconnection on communication networks, and mostly it results in other calamities such a fire outbreaks in the surrounding, causing the double tragedy. More often, large magnitude earthquakes cause a fire on buildings within metropolitan areas due to interference on electric cables. The fire escalates depending on the materials used in the construction of the building. Research has revealed that the effects of fire on structures can be significantly controlled by using fire-resistance materials such as steel in construction.

Most importantly is to ensure that any construction project within regions considered as earthquake-prone areas need to be carried out using earthquake resistance materials and techniques to avoid all these effects caused by earthquake such as the collapse of the structure. Since steel structures have gained favour in such construction activities, there is dire need to comprehensively understand the dynamics of structural steel members and their behaviour when subjected to seismic forces.

1.6 Research objective

This research study aims to evaluate the performance of steel structural members and systems of buildings under the cascading hazard of seismic forces and earthquake using both probabilistic and deterministic approaches. The major focus of the study is to evaluate the stability of steel structures and columns when subjected to lateral sway as a result of earthquake effects in a probabilistic and deterministic manner.

This research analysis also aims at providing the most suitable recommendation on the most appropriate structural strength of materials that should be incorporated in civil constructions on areas that are prone to earthquake and frequent ground shaking

1.7 Research justification

Due to the rapid increase in infrastructural developments all over the world, the construction of these infrastructures needs to be established with all the relevant safety measures against any kind of natural disaster. The earthquake has caused havoc and fear among many as it is associated with dreadful outcomes upon its occurrence. For decades now, the construction industry has been on the look to find ways and measures that would ensure that buildings in earthquake-prone areas have improved resilience for earthquakes and other natural calamities. Thanks to the introduction of metals, most specifical steel in construction processes. Steel in the last 20 years has gained favour in structural construction in high rise constructions due to its relatively reduced cost and most importantly its improved strength and cushion against seismic forces caused by earthquakes.

Steel as a metal has various properties that make it the darling of most recent constructions; however, these properties are dictated by various underlying factors. Therefore there is a need to have an exclusive and intensive dynamic analysis of these steel buildings when subjected to different earthquake loadings to establish the most suitable properties of steel for application on a varied range of earthquake magnitudes.

chapter two

LITERATURE REVIEW

2.1 Overview

This chapter presents and explains an elaborated research review on the development of steel structures in the field of civil industry. It shows findings obtained by different assessments done by researchers. It also outlines some of the reasons why steel structures are fast encroaching and taking over construction and replacing other construction modes such as timber and concrete construction modes. Due to the rapid increase in population that resulted to an equivalent rise in demand for structures, steel building construction emerges to as a supplement to the then-dominant concrete construction, at this time it was not utilized in bulk since concrete and time frames were still stuffiest to cater for the much-needed structures. With the evolution in construction technology, man discovered the need to conserve and make good use of the scares available land to settle its fast-rising population and therefore the construction of multistory buildings became the order of the day. But still, the strength in these multistory structures became a challenge for a long period of time until steels were incorporated in the construction of more stringer high rise multistory buildings.

2.2 Use of steel in construction

Expansion of settlement as a result of rapidly growing human population pushed people to settle even to areas and regions that were kept off due to the fact to that they were prone to seismic effects, earthquake and sliding of the plate tectonics within the earth’s crust. Structures in these red zone areas were constantly faced with damages or collapse of the entire building even when they subecte4d to low-intensity earthquake or ground shaking. For this reason, various techniques and methods were devised to help overcome the challenge of structural deformation when subjected to seismic or tectonic forces. Steel buildings became handy in these regions as it provided the much needed structural strength both lateral stiffness and vertical strength of the buildings erected in seismic zones. Steel structure becomes the darling in a construction project in areas that were considered earthquake-prone areas since it provided higher strength than concrete structures, it had improved safety factor that any other construction mode, improved strength boosted the durability and service life of steel buildings and most importantly was on its economy and sustainability. Steel buildings are considerably less expensive to erect as compared to the masonry of concrete structures.

Apart from favourable earthquake-resistant properties of steel structures, a steel building is preferred for their good wind resistance properties that make its use more rampant in the construction of superstructures and skyscrapers in towns and urban centres. The dynamics of wind movement is that the velocity of wind increases with height therefor at higher heights the velocity of wind blowing is huge to the extent of demolishing structures. When the disparity in wind speed not properly factored in the structural design might lead to devastating effects such collapse of the structure. For this reason, high rise buildings are made using steel since it has high lateral stiffness and improved ductility that can withstand up to huge values of wind velocity hence improved safety factor of such buildings. To other reasons, steel structures were fully embraced in the construction industry since it was in line with the sustainable goals in the construction industry. It provided an alternative solution for structural concretes that were considered as the contributors to the greenhouse emission through Portland cement used in concrete preparation.

Therefore this chapter elaborates the chronological development in the application of steels in the construction industry, with its numerous advantages in earthquake-resistant buildings and wind-resistant structures. It outlines the progress in the dynamic assessment of these steel structures in the development of improved earthquake resistant structures around the globe. This chapter draws information from already published articles, journals, and book reviews relating to seismic effects on structures, structural resilience in the event of an earthquake and the dynamic analysis of these structures in relation to earthquake resistance properties. The chapter is segmented into subsections relevant to the subject of the research study.

2.3 Basic concept of structural seismic design

The design of steel structures with seismic controllable measures in designing additional to the building stiffness, since earthquake induces inertia forces that are proportional to the building weight and masses. Designers are thriving to develop designs that with plasticity and behave elastically during earthquakes without damage may render the project economically unavailable. As a result, it may be appropriate for the structures to undergo damage and thereby dissipate the energy input during a normal earthquake. Hence the convectional earthquake-resistant building design philosophies need to upgrade to consider resisting the seismic effects up to earthquake of greater magnitude. Traditionally buildings are designed to resist disturbance only to a fraction ranging between 8% to 14% of the maximum force that the building could sustain. The safety factor provides protection to the structure from damages that would be caused by ground shaking. The structures need to have sufficient stiffness to avoid structural form collapsing due to minor ground shaking. Hence seismic design factor reduces and balances the cost and acceptable damage level that can be sustained by the structure. Acceptable balance is attained through extensive research with proper post-earthquake assessment analysis. The results and the wealth of these studies are then translated in into more precise seismic design provisions. There is a clear cut between earthquake-proof design, that entails design against wind damage and earthquake resistance design that entails design against the effects of seismic forces.

The strategy of earthquake design

The ductility of the structure is the most essential factor desired in the buildings since it enables structures to withstand the e4ffects of ground shaking that would cause damage in buildings. It might seem simple to design buildings and structures that have sustainable inertia and stiffness but it’s a tall order to attain sustainable ductility on the structural designs.

Loading imposed on structures are ground shaking caused by an earthquake is of structural displacement while the effects of wind impact on structures are of force type effects. For wind and related hazards, the building is required to adequately resist and sustain forces subjected to the building to a certain required level. Whereas earthquake resistance requires that buildings develop a resisting mechanism to avoid and resist shift or movement on the building’s foundation that would cause a collapse of the building. The maximum displacement that the building can withstand is quite a challenge in estimating unlike as it is to estimate the maximum force that the building can withstand and sustain thus earthquake effects on structures is more complex as compared to force analysis of the structure. In wind safety factor design it only requires the analysis of elastic behavior of the structure in the entire range of the structure while for seismic safety factor design, there are two options, that is to design the structure in an inelastic behavior or consider the elastic structural behavior. With the latter implemented in special buildings and the former mostly in normal buildings.

2.4 The virtues of earthquake resistance buildings

2.4.1 Characteristics of structures

The success or capability of the building to adequately resist and sustain the effects of the earthquake, it must consider the discussed aspects of earthquake-resistant buildings as outlined in the previous section of the study. This section gives a description of the four fundamental virtues of structures that design engineers and architects apply to develop a steel structural earthquake resistance building. These fort aspects of designs include; lateral stiffness, ductility, seismic structural configuration and lateral strength. To other supplementary aspects of earthquake resistance steel structures, the following are used, they include functionality, aesthetic, and comfortability of the structures. Lateral strength, lateral stiffness and ductility of steel structures can be estimated and figured by following the relevant seismic codes. However perfect seismic steel structural configuration can easily be attained through upholding to the coherent architectural properties that provide a good structural behavior.

2.4.2 Seismic structural steel configuration

The steel structural configuration consists of three major aspects, namely; size and location of steel structural element, shape, geometry and size of the steel structure and size and location of crucial non-structural elements. The geometry influence of buildings on its earthquake resistance is best determined through understanding the simple geometric concept of concave and convex lenses. Influence of the geometry of a building on its earthquake performance is best understood from the basic geometries of convex and concave lenses from school-day physics class. This methodology implies that any two lines joining any two points within the convex lens. Concave geometry is most preferred that convex geometry since concave geometries show improved earthquake performance compared to the performance of the convex. When this analogy is transferred into the building context, convex shaped structures have direct load path for transferring an transforming the earthquake shaking induced forces to the base of building in any direction whereas concave-shaped structures only necessitate the bending of the load path for shaking of the building base and the ground along a specific direction thus resulting to stress concentration at all direction and points of the load path bends.

Basing on the above descriptions, it is therefore evident the steel structures can be placed in two broad categories, that is simple and complex steel structures. Steel structures with straight elevation and rectangular plans stand higher chances for better earthquake resistance since the inertia forces are directly transferred without having any bend due to structural geometry. While structures of central openings and setbacks provide geometric constrain to the free flow of the induced inertia forces, due to restriction in movement of inertia, it forces their own path, therefore, bending effect as they reach the ground.

2.4.3 Ductility, strength and structural stiffness

Steels lateral stiffness refers to the structural initial stiffness, however, the structural stiffness declines with increasing damage while structural lateral strength is the optimum resistance that the structure can produce in are the entire history of resistance to deformation caused by either inertia forces or ground shaking from an earthquake. Then structural ductility is the most important structural property that makes steel most preferable element in the construction of earthquake resistance structures, in simplicity, ductility refers to the ratio of maximum deformation that the structure can sustain when subjected to deformation load. If the load curve does not drop and the structures retain more than 85% of its initial strength limits or lateral strength is reached thus the load-deformation curve does not drop after attaining peak strength.

2.5 The four steel virtues

The design and construction of almost all structures are in the form of a vertical cantilever that projects outwards from the earth’s surface. This projection, when ground shaking occurs, the cantilever structures experiences whiplash effects most so when the ground shaking is of high magnitude. Therefore there is a need to establish special care to these structures to avoid the adversity of these jerky movements that may result in structural deformation of even total collapse. Buildings intended to be earthquake-resistant have competing demands. Firstly, buildings become expensive, is designed not to sustain any damage during strong earthquake shaking. Secondly, they should be strong enough to not sustain any damage during weak earthquake shaking. Thirdly, they should be stiff enough to not swing too much, even during weak earthquakes. And, fourthly, they should not collapse during the expected strong earthquake shaking to be sustained by them even with significant structural damage. The four desirable characteristics of structures to effectively resist earthquake are referred to as the virtues of earthquake-resistant buildings. These desired features include

Excellent seismic configuration, this implies to structures with no exception on architectural design or form of structure that are detrimental to good earthquake performance and there no introduction of new complexity in structural behavior than the damage already induced y the ground shaking.
The structures with the minimum lateral stiffness in either of its plan directions and have its lateral stiffness evenly distributed in all its plan directions such that there are no cases of discomfort to occupants in the building and no building content damages in the event of ground shaking.
The structures with at least a minimum lateral strength in all its lateral plan directions and are evenly distributed in all plan directions of buildings such that the building can adequately resist low intensity or magnitude earthquake without any damage to the structure and not too strong to maintain the expense of construction in check along with the least minimum vertical strength of the building to enable it to continue to provide support the structural load due to gravity there4fore resist and prevent the structural collapse when subjected to strong earthquake shaking.
Then the most crucial aspect of structural ductility, the overall structural ductility that can comfortably accommodate all the imposed lateral deformations between the building’s roof and base along with the desired behavior mechanism at an ultimate stage. Behavior of the buildings during an earthquake depends critically on these features.

2.6 Resilient structures

The earthquake has caused havoc and damages to properties mostly structural assets. Since time immemorial, it has been the responsibility of the government, semi-government and non-government agencies to organize and deal with the management of the earthquake aftermath. These undertakings relegated engineers responsibility to retrofitting of structural elements strengthening of the weaken structural elements by ground shaking. The rate of earthquake disaster has been in continuous rise for decades now with areas that were initially considered as stable grounds now experiencing landslides. The research conducted in the 1980s showed that these regions traditionally marked as disaster zones areas are ever-expanding into a new domain. These trends led to the institution of international codes and standards that guide and control building construction in these areas regarded as the earthquake zones as a measure of reducing on the very many cases of deaths and lost properties as a result of the earthquake. The increased cases of damages registered annually caused by the earth-shaking prompte4d the call to architects and engineers together with non-engineer residents to help in an online and physical campaign to create awareness and collectively work with one another to find an alternative prevention and mitigation effects. Available publications give various aspects of individual analysis methods of earthquake disaster on structures as a whole. Through the study of international publications on the prevention and mitigation techniques for natural disasters such as earthquake, they give set methodologies that are for use on structural design and structural analysis for earthquake resistance on buildings. However, there are no common or universal methodologies or standardized procedures for other standardized protocol for disaster control and management. Therefore in the past, before the advanced innovation on technology methods and tools of analysis, the process of assessing complex dynamics and real-time forces of the earthquake on structures was quite challenging. Then with the introduction of assessment software, there was an improvement of structural assessment techniques, though software analysis gave little scope of flexibility on the specific structural needs and special aspects that would be disastrous to the structure. In the plight of software development, there came the development of more advanced modelling software that would analysis the seismic effects on the structure before it is even constructed, allowing both static and dynamic analysis of structural elements such as steel used in frames, column and beans of the building. This modelling software improved the efforts and assurance of a robust model that depict the real situation upon the occurrence of any given natural disaster such as an earthquake.

Therefore through literature and developed software-enabled engineers and architects to develop a mechanism of finding solutions to the problems that have not incurred yet through the use of past information extracted from literature, previous findings and recommendation in the line of good governance. Both works of literature covered and technological methods through software have necessitated engineers work towards finding the most appropriate mechanism of finding solutions that are capable of customizing the behavior of buildings when exposed to seismic forces thus allowing the presentation of obtained data in 2D and 3D dimensional graphical outputs.

Considering the studies and research conducte4d in the past that were focused on the analysis of structural behavior subjected to various aspects of natural disasters. The review of some of the publications is presented here in sections as follows.

Pushover technique bases on performance assessment of buildings
Retrofit options and damages due to seismic forces
Virtual reality analysis in structural steel engineering
Cyclonic wind mitigation on structural buildings
Fire loads on steel structures
Flood effects mitigation of flood effects
Damage and repair tsunami and blast

2.6.1 Pushover analysis

Structural designs have set codes and standards outlining basic procedures and guidelines for dynamic and static analysis of structures when exposed to seismic forces. Though in other engineering disciplines, performance analysis has been preferred for giving detailed design analysis of system structures. Following the continuous occurrence of earthquake leads to an increased need for structural seismic analysis, hence pushover analysis tool emerged as a technique for seismic analysis of non-linear static performance based on methods of examining the response any given structure when exposed to seismic forces.

Pyle and Habibullah in their 1998 research established a simple procedural step for performing pushover analysis using simple software known as SAP2000. The software basically could do static pushover analysis with the integration of the findings into p-program that allows easy and quick interpretation and implementation of the pushover analysis procedures as outlined in the FEMA-273 and ATC-40 standards for both 2D and 3D structural analysis.

In 2000 Tso and Moghadam, improved the pushover analysis to widen the scope of methodology to cover eccentric buildings and accommodate the three-dimensional torsional effects on structures. Tso and Moghadam argued that due to floor displacement and torsional deformation, and then the structure or building obviously will consist of both rotational and torsional components. Therefore they added that torsional effects could be damaging factors to members located at or near the flexible edges of buildings where the rotational and torsional elements of the floor displacement are additive. Moghadam and Tso based their findings on the observations made on the damages on many eccentric structures from the pat ground shaking and seismic effects from the earthquake.

Chopra in 2001 made a publication of PEER report, where he mentioned the of the standard response spectrum (RSA) analysis for elastic buildings through the formulation of modal pushover analysis (MPA). In her study, she mentioned that the peak response of elastic buildings are due to their nth vibration mode and the mode of structural vibration could be determined by pushover analysis on the building subjected to lateral forces distribute over the building’s height according to expression S_n = mœ_n.Where œ_n.Is the nth mode and m is the mass matrix. Combining these peak modal responses by modal combination rule leads to the MPA procedure. Thus the trend of comparing computed hinge plastic rotations against rotation limits established in FEMA-273 to judge structural performance should be replaced and Performance evaluation should be based on story drifts known to be closely related to damage and can be estimated to a higher degree of accuracy by pushover analyses. Another PEER report in 2001 given by the same team investigates the basic premise that the roof displacement of a multistory building can be determined from the deformation of an SDF system. The data for generic frames indicate that the first- mode SDF system overestimates the median roof displacement for systems subjected to large ductility demand, but underestimates for small. The SDF estimate of roof displacement due to individual ground motions can be alarmingly small (as low as 0.312 to 0.817 of the value for the six SAC buildings) or surprisingly large (as large as 1.45 to 2.15 of the value for Seattle and Los Angeles buildings) when P-delta effects were included. The situation was worse than indicated by these data because they do not include several cases where the first mode SDF system collapsed but the building as a whole did not. Owing to the simplicity of inelastic static pushover analysis compared to inelastic dynamic analysis, the validity and the applicability of this technique were assessed by Mwafy in 2001. Comparison with ‘dynamic pushover’ idealized envelopes was obtained from incremental dynamic collapse analysis. This involved successive scaling and application of each accelerogram from 12 experiment buildings, followed by an assessment of the maximum response, up to the achievement of the structural collapse. The results of over one hundred inelastic dynamic analyses using a detailed 2D modelling approach for each of the twelve RC buildings were utilized to develop the dynamic pushover envelopes and compare these with the static pushover results. Good correlation was obtained between the calculated idealized envelopes of the dynamic analyses and static pushover results for a defined class of structure. FEMA-368 (2001) defines criteria for the design and construction of new buildings, additions and alterations to existing buildings to enable them to resist the effects of earthquake ground motions. These provisions provide minimum seismic design criteria of safety for structures by minimizing the earthquake-related risk to life and improve the capability of existing structures to function during and after design earthquakes. Whereas, FEMA-369 (2001) provides general requirements, background information, and explanations for applying the analysis and design criteria in the Provisions of FEMA-368. Hasan R. in 2002 presented a simple computer-based push-over analysis technique for performance-based design of building frameworks subject to earthquake loading. The technique was based on the conventional displacement method of elastic analysis. Through the use of a plasticity-factor that measured the degree of plastification, the standard elastic and geometric stiffness matrices for frame elements (beams, columns, etc.) were progressively modified to account for nonlinear elastic-plastic behavior under constant gravity loads and incrementally increasing lateral loads. The method accounted for first-order elastic and second-order geometric stiffness properties, and the influence that combined stresses have on plastic behavior. After designing and detailing the reinforced concrete frame structures, Korkmaz in 2002 carried out a nonlinear pushover analysis and nonlinear dynamic time history analysis for evaluating the structural seismic response for the acceptance of load distribution for inelastic behavior. It was assumed for pushover analysis that seismic demands at the target displacement are approximately maximum seismic demands during the earthquake. First yielding and shear failure of the columns was experienced at the larger story displacements and rectangular distribution always give the higher base shear weight ratio compared to other load distributions for the corresponding story displacement. The pushover analyses results for rectangular load distribution estimated maximum seismic demands during the given earthquakes were more reasonable than the other load distributions. A trial application of the SAC-FEMA method was presented by Lupoi in 2002. Existing RC buildings not designed for earthquake loads may fail due to several possible weak mechanisms, whose relevance was unpredictable before an accurate analysis was carried out. Concepts and procedures of the SACFEMA method were proven to apply to such complicated cases as well. In particular, the stability of the final outcome of the analysis, the total annual risk, record-to record variability, the randomness of the material properties and inadequate knowledge on the capacity side, was fully confirmed. This fundamental feature, together with the relative simplicity of the approach, made it all the more desirable for it to be gradually adopted as a design method for new, well-conceived and detailed, earthquake-resistant constructions Minibar and Pinto in 2003 extended the pushover method to assess the performance of 3D irregular RC structures. The issues of diaphragm effects, loading profiles and incremental dynamic analysis were studied. The modelling based on Displacement Based and Force Based Pushover was compared. Conventional versus Adaptive Pushover results have been compared and were found to be close. Jan in 2004 stated that when evaluating the seismic demands of tall buildings, engineers were more likely to adopt simplified non-linear static analytical procedures, or pushover analyses, instead of the more complicated non-linear response history analysis. Since the conventional procedure has some drawbacks in predicting the inelastic seismic demands of high-rise buildings, in this paper, a new simplified pushover analysis procedure, considering higher mode effects, was proposed. The basic features of the proposed procedure were the response spectrum-based higher mode displacement contribution ratios, a new formula for determining the lateral load pattern and the upper-bound (absolute sum) modal combination rule for determining the target roof displacement

chapter three

Methodology

Dynamic analysis of structural members is specified under the NBCC 2005 as one of the fundamental methods of analysis that aid the design and computation of earthquake and seismic actions on buildings. Among methods used to collect and consolidate information and data used in the dynamic analysis included, extensive and critical literature review of the published scientific journals books. Through this method, background information on the seismic analysis of buildings made from different materials was obtained and it facilitated the essential aspect of comparison analysis between concrete structures and steel structures under seismic force effects. Mathematical models were also incorporated in the analysis of steel buildings response to earthquake loadings.

Through dynamic analysis of structures designers, can conveniently give the recommendation on the minimum and the maximum threshold for the seismic resilience factor with equivalent static forces of action permitted for structures on different regions such as construction on regions of low seismic forces, short buildings with irregularities and buildings below given height level. Building with these conditions might be exempted from dynamic analysis due to the simplicity of construction processes and the fact that there are no much risks and safety hazards posed to them in the event of an earthquake with moderate magnitude. For example, short buildings are more stable since there their centre of gravity mostly lies within the centre of the structure or building, unlike tall building whose centre of gravity often lie without the building thus reduced natural stability.

3.2 Standards and Codes

In NBCC 2005, dynamic analysis is mandatory for buildings and structures with the following specifications, regular buildings and structures that have a fundamental frequency or period higher than 2.0 seconds, buildings that are more than 65 metres tall or buildings on regions with seismicity greater than or equal to 0.36. Dynamic analysis is also fundamental to irregular buildings of height more than 20 meters and having a period of more than or equal to 0.5 seconds and are located in the regions of high seismicity greater than or equal to 0.36. And it is an essential analysis of all structures with the rigid diaphragm and is torsionally sensitive.

The research involved various methodologies of dynamic analysis of steel structures to establish the linear response (elastic) and nonlinear response (inelastic). For linear dynamic analysis, empirical assessment of inelastic response is made since the structural design is philosophy is based on nonlinear structural behavior when exposed to high or large magnitude earthquake. This is a crucial parameter considered by design engineers in determining elastic dynamic analysis because of the simplicity of the process and direct correspondence to design spectra outlined in the NBCC 22005 building codes and standards.

The first step of action in steel structures dynamic analysis was devising an appropriate mathematical model of the structures. The model is quite essential in estimating and evaluating the structural stiffness, strength, mass and other inelastic member properties where applicable.

3.3 Mathematical model

Dynamic linear analysis for the structural steel buildings was facilitated by mathematical modelling of steel buildings. Mathematical models were achieved in various ways depending on the parameter analyzed. Dynamic analysis of steel structures involved the representation of the building and structural members to which material and physical properties are designated and the desired loading conditions are applied to the members. These members exhibit different degrees of discretization of the structural members under loading. The outcomes of mathematical modelling are therefore enhanced through the application of finite element analysis and line element analysis techniques. For inelastic response analysis, it is more convenient and reliable to give a representation of structural behavior of the entire building under assessment of earthquake loading. The obtained results from the mathematical models were transferred and tabulated for discussion and conclusion. Therefore mathematical models through finite and line element analysis was used to illustrate the crucial aspect of modelling for dynamic analysis while also highlighting some of the pitfalls that should be avoided to improve the accuracy of results.

3.4 Structural modelling

The start of analysis began with mathematical modelling that gave the full representation of the entire building and its structures to which various material and physical properties were designated or assessment. In frame wall and frame interactive systems and the vertical finite element and horizontal elements such as slab diaphragms and beams are generally presented in horizontal line elements and the shear panels, bracings and infill walls are modelled by diagonal struts and ties. An important aspect of structural modelling involves the selection of the right boundary conditions representing the desired connections and supports with the most relevant and appropriate end result. Another important aspect is the consideration of finite widths of members and corresponding stiffness variations. This becomes especially important in modelling wide columns and structural walls for which the segments of elements that are integral with the adjoining members can be represented with infinite stiffness. The analysis entailing finite widths were conducted with a lot of precautions and in accordance with the standard procedures. The models were developed in the form of member-end-eccentricities through graphic software.

Seismic analysis of steel structures was conducted in two orthogonal aspects, independently and separately. Steel structures with rigid diaphragms and torsionally irregular, a 3D analysis was carried out to determine the behavior when members are subjected to various earthquake loadings. In some conditions, buildings may not show torsional irregularities, it is recommended to still have a 3D analysis of the members since it might be subjected to accidental torsional eccentricity thus affecting structural response to seismic forces.

3.5 Time history analysis method

In the analysis and assessing the dynamic structural response at every time increment, when the foundation and base of steel structures are subjected to specific ground movement in time history, this is the most basic analysis method though so crucial in regional analysis. Through the study of the patterns of historical ground movement and earthquake occurrence facilitates the process of linear and nonlinear dynamic analysis of buildings erected in such regions. Kept inventories and past recorded ground motions give reliable information for designers and architects in having an explicit background on the seismological condition of the site before proceeding to structural design and dynamic analysis of its structural members. For this project, recorded ground reports were randomly selected from analogous, sol, magnitude, and magnitude and sol category conditions. On the selected history records on ground movement, a response spectrum analysis is conducted around a crucial period of the structure to establish seismic hazards associated with the given ground condition.

3.6 Response spectrum method

The response spectrum method of analysis was used in the dynamic analysis of steel structure of the case multi-storey building to obtain a representation of the idealized maximum response in single degree systems with specified dumping and period, in the event of an earthquake and any form of ground movement. The obtained maximum response was plotted against the values of un-dumped natural periods with different dumping values expressed in terms of maximum relative velocity, maximum absolute acceleration of relative displacement. For this method analysis, the steel structures involved were analyzed and assessed in relation to the standards outlined in the IS1893.

3.7 Member modelling

Determination of characteristics and features of individual members of structures is quite crucial in dynamic structural analysis, and these properties are best assessed through member models. For linear dynamic analysis of structural members were modelled by elastic line elements while nonlinear dynamic analysis of structural members followed finite element methods of modelling, each member analysis considered the most convenient analysis technique. The single-component models, the inelastic member-end force at the same end thus making it convenient structural analysis model. Inelasticity along the member is lumped at the springs whose characteristics are determined by assuming deformed shapes for members. Beams and columns having fixed contra flexure are assessed by assuming the double curvature in the structure.

CHAPTER FIVE

Results and discussion

This chapter presents the outcome of the analysis study on different aspects of the dynamic analysis of steel structures under different seismic conditions. Quite a number of methods were used in the study analysis and the results are discussed as follows.

From response spectrum analysis, the findings showed that in steel buildings and infrastructures such as bridges, the peak of ground acceleration caused by ground movement as a result of the earthquake is much less than the standard spectrum. Therefore the steel structures prove to have slightly improved earthquake resilience making them applicable in time history analysis of buildings. The figure below shows the spectral response for standard models used in the analysis

Spectrum response for standard models

Electro response spectrum analysis

The study established that the response spectrum of steel structures is an essential tool for structural strength analysis used by designers and architects to establish the correct size and shape specifications for steel construction under deferent ground conditions. From the graph of spectrum response comparison between Taiwan region and the standard electro model, it is quite evident that the response differs even though the structures are of the same material thus proving the essence of dyanmi9c analysis on structures based on the region’s susceptibility to earthquakes. Through time history analysis and literature review, Taiwan is one of the most affected cities of the middle east that are prone to seismic movement and earthquake, the civil and construction authorities formulated codes and standards that guide structural constructions n the region to ensure that, any structure erected in the region has excellent earthquake resistance factor. This was aimed to reduce the overstating effects of earthquakes such as building collapse. Steel structures are the major constructions in Taiwan since it provides strength and durability and through dynamic analysis, they can sustain up to large magnitude earthquakes.

5.2 The effects of plan shape on structural dynamic features

Construction plans and designs are formulated by architects and structural designers and they entail a lot in terms of structural dynamic behaviours. The structural stability is dictated by its overall mass and weight of the both live and dead load. There are regular shape structures irregular shape structures. From the considered case studies on steel structures of different shapes, it was established that regular structures are staler and can sustain earthquake effects better compared to irregular structures. This is informed by the fact that the regular structures, mostly their centre of gravity lies within the building envelope and thus in the event of an earthquake they swing uniformly to and forth and then back to their original position after the effect disappears. Irregular shape structures are at higher risk of collapsing in the event of ground shaking since mostly the centre of gravity lies outside structural envelope this poses potential hazards even to low magnitude earthquake.

5.3 Structural wall frame systems

From structural modelling, member modelling and mathematical modelling, the study established that it is essential to have effective nonlinear dynamic analysis and linear analysis on steel buildings to establish the member’s behavior when exposed to earthquake loading. For earthquake-resistant buildings, they should have at least a minimum lateral stiffness to regulate the swinging frequency during ground shaking. Therefore sheer walls made of steel structures are needed to enhance the dissipation of the lateral effects caused by swinging of the building members and reduce overall displacement in the building, steel shear walls are best appropriate since they have extended vertical like structures with boosted strength and stiffness in-plane properties.

5.4 Capacity of design buildings

After analyzing different strength-based design techniques, an important design strategy needs to be incorporated in the design of the earthquake resilient structures. The study uploaded the adoption of the capacity design concept. The linear and nonlinear dynamic analysis on steel structures involved hierarchical phases of analysis and it aims to ensure elastic and inelasticity to confine to predetermined and preferred structural components.

In the design for earthquake impacts on essentially involves controlling mobilizations of the forces from within in structural members due to imposed deformation in buildings. When an earthquake occurs; buildings are often subjected to continuous random motion at the same frequency of the ground motion. The ground movement the n induces unbalance stiffness forces in members. Steel structures use force as an aspect of design parameter in beams, hence each member of the structure. When structural beams are subjected to relative transverse displacement at its ends during an earthquake, the bending moment and shear forces at each end are interdependent. For beams and columns made of steel, the maximum magnitudes of bending moment and shear force mobilized depend on the limiting resistance of the cross-section of the beam since steel has relatively higher shear and tensile strength. This aspect if well elaborated by the ductility chain analogy, where chain made of brittle links with exception to the middle joint made of ductile materials. A chain like analogy is essential in dynamic analysis of structural designs as week-links within structure members are connected with the strong links to enable the transfer of strength even to the week links thus improving the overall structural strength and resistance to earthquake.

Conclusion

Dynamic actions in buildings are caused by either earthquake or wind. Both earthquake and strong blowing wind almost have the same effects on the structures or buildings, that is upon their occurrence they are accompanied with overstating effects of the destruction of properties and the magnitude of damage depends on the strength and velocity of wind or the magnitude of the earthquake. Though the two are classified under natural calamities, cyclones and earthquake for years have been a challenge to the civil and construction engineering. Through century to century, engineers and architects have been on research t establish techniques and ways of obtaining a perfect resilient structure most so to earthquake loadings.

Most structural designs are based on the intuitive philosophy, that is, they are designed using force and weight evaluation technique that can only sustain wind effects on relatively short structures (four-storey building) but is overwhelmed by seismic actions on the base of buildings. During an earthquake, structures are subjected to the continuous random motion on the ground and thus transfer these random motions to the building. Thus causing the instability in the structures due to the induced inertia forces that in turn causes stress and displacement type loading on structural members. In the last decade, architects and engineers through collaboration have developed structures with improved earthquake resilience by incorporating high strength and ductile material like steel metal in construction processes. Steel is metal has favourable properties that are essential in designing and construction of more earthquake resistance buildings.

The project was based on the dynamic analysis of steel structures when exposed to earthquake loading and from the case studies and simulation analysis considered in this study shows that steel despite having favourable properties and strengths they cannot just be used in any construction. The importance of dynamic analysis is that it gives the best and most appropriate design specifications of structural designs to attain the required strength to sustain a specific range of earthquake magnitude depending on the region. Seismic design conditions of structures are defined by the mass of steel structures involved in the construction in addition to stiffness because earthquake induces seismic and inertia forces that are proportional to the mass of the building. Therefore perfect earthquake-resilient steel structures require that the building should adequately resist minor and frequent ground shakings with no damage to non-structural and structural elements, moderate ground shaking with minor damages to structural elements and upon server or higher magnitude earthquake, the structure need not collapse.

Dynamic Analysis of Steel buildings under earthquake loading

chapter one

Introduction

1.1 Background