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The proposed 2005 edition of the National Building Code of Canada specifies dynamic analysis as the preferred method for computing seismic design forces and deflections, while maintaining the equivalent static force method for areas of low seismicity and for buildings with certain height limitations. Dynamic analysis procedures are categorized as either linear (elastic) dynamic analysis, consisting of the elastic modal response spectrum method or the numerical integration linear time history method, or nonlinear (inelastic) response history analysis. While both linear and nonlinear analyses require careful analytical modelling, the latter requires additional considerations for proper simulation of hysteretic response and necessitates a special study that involves detailed review of design and supporting analyses by an independent team of engineers. The paper provides an overview of dynamic analysis procedures for use in seismic design, with discussions on mathematical modelling of structures, structural elements, and hysteretic response. A discussion of the determination of structural period to be used in association with the equivalent static force method is presented.Key words: dynamic analysis, earthquake engineering, elastic analysis, fundamental period, hysteretic modelling, inelastic analysis, National Building Code of Canada, seismic design, structural analysis, structural design.
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A devastating earthquake and the resulting tsunami hit coastal areas of Indian Ocean on December 26, 2004. A team of Canadian engineers conducted a reconnaissance in Thailand and Indonesia. Their findings are presented in the paper in terms of performance of buildings, bridges, coastal structures and other physical infrastructure. It was observed that non-engineered reinforced concrete structures, low-rise timber frames and unreinforced masonry buildings suffered extensive damage due to hydrodynamic pressures generated by tsunami and impact forces induced by floating debris. Banda Aceh, Indonesia suffered extensive damage due to seismic excitations. A large number of non-engineered and engineered reinforced concrete frame buildings experienced partial or total collapse. A number of 3 to 5 story engineered reinforced concrete government buildings and shopping centers were damaged due to lack of proper seismic design practices. The engineering significance of disaster is presented in the paper with observations made during the reconnaissance visit.
The use of high-strength concrete (HSC) in seismically active regions poses a major concern because of the brittle nature of the material. The confinement requirements for HSC columns may be prohibitively stringent since they require proportionately greater confinement than columns of normal-strength concrete. An alternative to conventional confinement reinforcement is the use of fiber reinforced polymer (FRP) casings, in the form of a stay-in-place formwork. This paper investigates the use of stay-in-place FRP formwork as concrete confinement reinforcement for HSC columns with square cross sections. Large scale HSC building columns, encased in FRP casings, were tested under simulated seismic loading. The columns had 270mm square sections and concrete strengths up to 90MPa. The casings were manufactured from carbon FRP and epoxy resin. The unique aspects of the test program were the introduction of the corner radius as a test parameter, and the presence of internally placed FRP crossties, integrally built with column casings, to improve the effectiveness of concrete confinement. Results indicate that the deformation capacity of HSC columns can be improved significantly by using FRP casings. The results further indicate that the confinement effectiveness of columns is significantly affected by the corner radius of casings. Additionally, the confinement efficiency can be improved with the use of FRP crossties. The columns developed inelastic drift capacities of up to 11%, demonstrating the usefulness of FRP stay-in-place formwork in improving deformability of HSC columns.
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Reinforced concrete (RC) structures deteriorate and as a result crack due to extreme loading and (or) environmental conditions. Damage accumulation as such adversely affects the structure’s durability properties, impairing its service life. The intensity of cracking in an RC structure is usually regarded as the key criterion toward damage assessment and repair intervention. This paper presents the results of an experimental program in which the concrete strains of a small-scale RC slab sustaining in-service loads were monitored by traditional electrical strain gauges and distributed Brillouin fibre optic sensors in an attempt to detect damage due to crack formation. A comparison of these measurements with classical bending theory is also presented. The results show that distributed Brillouin fibre optic sensors can capture both tensile and compressive strains in concrete; however, the accuracy of their measurements is dependent on the proper installation of the sensors and the fibre length over which the strains are to be measured.
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An analytical model is proposed to construct a stress‐strain relationship for confined concrete. The model consists of a parabolic ascending branch, followed by a linear descending segment. It is based on calculation of lateral confinement pressure generated by circular and rectilinear reinforcement, and the resulting improvements in strength and ductility of confined concrete. A large volume of test data, including poorly confined and well‐confined concrete was evaluated to establish the parameters of the analytical model. Confined concrete strength and corresponding strain are expressed in terms of equivalent uniform confinement pressure provided by the reinforcement cage. The equivalent uniform pressure is obtained from average lateral pressure computed from sectional and material properties. Confinement by a combination of different types of lateral reinforcement is evaluated through superposition of individual confinement effects. The descending branch is constructed by defining the strain corresponding to 85% of the peak stress. This strain level is expressed in terms of confinement parameters. A constant residual strength is assumed beyond the descending branch, at 20% strength level. The model is compared against a large number of column tests. Circular, square, and rectangular columns, with spiral and rectilinear reinforcements, as well as welded wire fabric, are used for comparison. Comparisons include concentric and eccentric loadings, as well as slow and fast strain rates. The results indicate good agreement.
This is the second of two companion papers on improved intensity measures of strong seismic ground motions for use in probabilistic seismic demand analysis of reinforced concrete frame buildings. The first paper discusses the development of improved intensity measures. This paper describes the application of the developed intensity measures in probabilistic seismic demand analysis. The application is illustrated on the three reinforced concrete frame buildings (4, 10, and 16-storey high) that were used in the first paper. This involved computations of the seismic responses of the structures and the seismic hazard using the improved intensity measures. The response and the hazard results were then combined by means of probabilistic seismic demand analysis to determine the mean annual frequencies of exceeding specified response levels due to future earthquakes (i.e., the probabilistic seismic demands). For the purpose of comparison, probabilistic seismic demand analyses were also conducted by employing the spectral acceleration at the fundamental structural periods (Sa(T 1 )) as an intensity measure, which is currently the most used in practice. It was found that the use of the improved intensity measures results in significantly lower seismic demands relative to those corresponding to the intensity measure represented by Sa(T 1 ), especially for long period structures.
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