The New Zealand Structural Loading Standard, until its latest revision, was using the structural displacement ductility factor as a measure of the deformation demand of all potential plastic hinges in a structure. In the revised version of New Zealand Structural Loading Standard for Earthquake Actions (NZS 1170.5:2004) the detailing of potential plastic regions is determined according to the local inelastic deformation demand in these regions. The change has been prompted by evidence that the structural ductility factor gives a poor indication of the demand on individual plastic regions. This is a major paradigm shift in international design codes. This new approach has been adopted by the New Zealand Concrete Structures Standard (NZS 3101:2006) which classifies potential plastic regions into three categories (namely ductile, limited ductile and nominally ductile) based upon their inelastic deformation demand which has been specified in terms of material strain limits in the form of curvatures or shear deformations. The values of material strain limits currently used in New Zealand Concrete Standard (NZS 3101:2006) to categorise the plastic regions are based on limited evidence and need a closer revision. This research attempts to obtain more justifiable values of material strain limits through experimental data existing in literature. Moreover, experimental testing is also conducted to compensate for a lack of data in the nominally ductile range of detailing. The experimental work explores the effects of transverse reinforcement arrangement, reinforcing steel grade and plastic hinge type. Together the literature review and experimental work provide a sound basis for re-defining the material strain limits for different plastic regions.

Inelastic behavior in steel special moment frames occurs through the development of plastic hinges at locations near the ends of the beam. The main objective of using a reduced beam connection is to force the formation of plastic hinges to be formed at the reduced beam section rather than at the ends of the beam which otherwise would lead to brittle failure of the beam-column connections. The beam has two reduced beam sections, each located at a certain distance from the face of the column, so that the plastic hinges are formed symmetrically at each of this section. When acted upon by lateral loads, the maximum moments occur at the ends of the beam. Therefore, the plastic hinges form at the reduced beam section. However, when a frame is subjected to a combination of gravity and lateral loads, the plastic hinge formation at one of the reduced beam section is not so clear and further analysis has to be done to study the effect. FEMA 350 indicates that the desired plastic hinge location is only valid for beams with gravity loads representing a small portion of the total flexural demand. If gravity demands significantly exceed 30% of the girder plastic capacity then further plastic analysis of the frame should be performed to determine the appropriate hinge locations. The scope of my thesis is mainly to study the combined effect of gravity and lateral loads on the formation of plastic hinges in steel moment frames with reduced beam section connections.

In the seismic design of reinforced concrete frames, plastic hinges are allocated to beams such that a ductile beam-sway mechanism will form in preference to other less ductile mechanisms in the event of a major earthquake. This is achieved by ensuring that the flexural strength of columns is greater than that corresponding to the maximum likely flexural strength of beam plastic hinges. Recent experimental studies in New Zealand have shown that elongation of ductile beam plastic hinges, and its interaction with nearby floor slab containing precast-prestressed floor units, increases the strength of beams much more than that specified in New Zealand and American Concrete standards. This level of strength enhancement has raised concern on the adequacy of the current design provisions. To further investigate this problem, a research project was initiated to examine the strength of beam plastic hinges in reinforced concrete frames containing precast-prestressed floor units. In this research, the strength of beam plastic hinges was assessed through experimental and analytical studies. A three-dimensional, one-storey, two-bay reinforced concrete moment resisting frame with prestressed floor units and cast-in-situ concrete topping was tested under quasi-static displacement-controlled cyclic loading. The experimental results provided insight into the mechanics associated with frame-floor interaction. Subsequently, improved design specifications were proposed based on the observed behaviour. To analytically predict the beam-floor interaction, a ductile reinforced concrete plastic hinge multi-spring element was developed and validated with experimental results from cantilever beam and frame sub-assembly tests reported in the literature. The comparisons have demonstrated the ability of the proposed plastic hinge element to predict the flexural, shear, axial, and most importantly, elongation response of ductile plastic hinges. The proposed plastic hinge element was implemented into an analytical model to simulate the behaviour of the frame-floor sub-assembly tested in this research. Specially arranged truss-like elements were used to model the linking slab (the region connecting the main beam to the first prestressed floor unit), where significant inelastic behaviour was expected to occur. The analytical model was found to be capable of predicting the non-linear hysteretic response and the main deformation mechanisms in the frame-floor sub-assembly test. The analytical frame-floor model developed in this study was used to examine the effect of different structural arrangements on the cyclic behaviour of frames containing prestressed floor units. These analyses indicated that slab reinforcement content, the number of bays in a frame and the position of frame in a building (i.e., perimeter or internal frame) can have a significant influence on the strength and elongation response of plastic hinges.

The Deck truss portion of the I-35W Highway Bridge in Minneapolis, Minnesota collapsed on August 1, 2007 while roadwork was underway on the bridge. The entire truss was recovered from the river to study the causes of failure. The National Transportation Safety Board attributes the collapse to inadequate load carrying capacity of the steel gusset plates connecting the main truss members at four specific nodes. Permanent deformations of the members in proximity to these nodes were documented and a surveillance video camera recorded the collapse event in a major section of the structure. The inelastic behavior of the deck truss during the collapse event is studied in this research by performing nonlinear structural analysis on a simplified two-dimensional model. Nonlinear behavior is discretized at specific locations starting with buckling of the critical gusset plates and continuing with yielding in members where the internal forces increased at a higher rate during the post-buckling behavior. The analysis results show the sequence of failure events that lead to the formation of a collapse mechanism in the center span of the deck truss, which is the first to fall into the river. Comparison between the available evidence and the analysis results validate the conclusions drawn in this research. / Master of Science

Ações sísmicas ocorrem com pouca freqüência e intensidade no Brasil, porém ocorrem em países da América Latina situados na costa do Pacífico e em Portugal, despertando o interesse da engenharia brasileira nesse assunto. Neste trabalho, apresenta-se um modelo numérico para análise de estruturas metálicas aporticadas planas com comportamento elasto-plástico sob excitação aleatória induzida por sismos. Para simular as vibrações aleatórias, utiliza-se uma simulação tipo Monte Carlo fundamentada no ?Vento Sintético?, proposta pelo Prof. Mário Franco. Nessa simulação, combinações de séries de carregamentos harmônicos são geradas com suas amplitudes extraídas de uma Função de Densidade Espectral de Potência (PSDF) das acelerações do solo e com ângulos de fase obtidos por um algoritmo pseudo-aleatório. A PSDF utilizada é um modelo reduzido do modelo Kanai-Tajimi que determina combinações de séries adimensionais, onde seus resultados para o trecho elástico são calibrados com o espectro de resposta elástica sugerido em norma internacional. A integração numérica passo-a-passo no domínio do tempo é feita para cada função de carregamento adotando-se o método de Newmark. O efeito elastoplástico é modelado pelo conceito de rótulas plásticas, assim, a cada passo é verificada a formação da rótula. Se certa seção atingir o momento fletor de plastificação, o valor do momento permanece constante e introduz-se uma rótula nessa seção com rigidez a flexão nula, permitindo rotações finitas livres. Em caso de reversão da direção do momento fletor, a rigidez elástica é integralmente recuperada com a eliminação da rótula do modelo. Ao final desse processo, obtém-se uma grande quantidade de dados de resposta. Faz-se um tratamento estatístico desses resultados de modo a concluir, do ponto de vista da engenharia, a probabilidade de ocorrência dos eventos. Para validar a metodologia proposta, analisou-se um edifício com cinco pavimentos. Os resultados satisfatórios foram obtidos quando comparados com exemplos da literatura, além de apresentarem-se estável com relação a integração no tempo. / Seismic actions occur with low intensity and often in Brazil, however they occur in Latin-American countries on the Pacific Coast and in Portugal, arousing interest in this subject of the Brazilian engineering. In this work, a numerical model is presented for the analysis on the elastic-plastic behavior of steel planar framed structures under random seismic excitation. For random vibrations, a Monte Carlo type simulation is used. This simulation is based on the ?Synthetic Wind?, proposed by Prof. Mario Franco. In this simulation, combinations of series of harmonic loads are generated with their amplitude given by certain provided Power Spectrum Density Functions (PSDF) of ground acceleration and pseudorandomly set phase angles. The used PSDF is reduced model of the Kanai-Tajimi model that determine combinations of non-dimensional series whose results by the behavior elastic are adjusted by international codes Elastic Response Spectra. The step-by-step time integration is performed for each load function using the Newmark method. In order to model, the elastoplastic effect is used the plastic hinge concept. Therefore, at each step the hinge formation is verified. If a certain section reaches its full plastic bending moment, this value of moment is maintained and a hinge in that section is introduced in the model with null stiffness, allowing for free finite rotations. If the rotation in a certain hinged section is reversed, elastic behavior is restored by elimination of the hinge from the model. At the end of this process, a large quantity of response data is obtained. A statistic treatment of these results is performed, in the way that is possible conclude, from the engineering point of view, the probability of occurrence of these events. A statistic treatment based sound engineering conclusions is done for the happened probable events. In order to validate the proposed methodology, a five stories building is analyzed. Satisfactory agreement is obtained when compared to results from the literature, and the results are very stable with respect to the time integration.

Ações sísmicas ocorrem com pouca freqüência e intensidade no Brasil, porém ocorrem em países da América Latina situados na costa do Pacífico e em Portugal, despertando o interesse da engenharia brasileira nesse assunto. Neste trabalho, apresenta-se um modelo numérico para análise de estruturas metálicas aporticadas planas com comportamento elasto-plástico sob excitação aleatória induzida por sismos. Para simular as vibrações aleatórias, utiliza-se uma simulação tipo Monte Carlo fundamentada no ?Vento Sintético?, proposta pelo Prof. Mário Franco. Nessa simulação, combinações de séries de carregamentos harmônicos são geradas com suas amplitudes extraídas de uma Função de Densidade Espectral de Potência (PSDF) das acelerações do solo e com ângulos de fase obtidos por um algoritmo pseudo-aleatório. A PSDF utilizada é um modelo reduzido do modelo Kanai-Tajimi que determina combinações de séries adimensionais, onde seus resultados para o trecho elástico são calibrados com o espectro de resposta elástica sugerido em norma internacional. A integração numérica passo-a-passo no domínio do tempo é feita para cada função de carregamento adotando-se o método de Newmark. O efeito elastoplástico é modelado pelo conceito de rótulas plásticas, assim, a cada passo é verificada a formação da rótula. Se certa seção atingir o momento fletor de plastificação, o valor do momento permanece constante e introduz-se uma rótula nessa seção com rigidez a flexão nula, permitindo rotações finitas livres. Em caso de reversão da direção do momento fletor, a rigidez elástica é integralmente recuperada com a eliminação da rótula do modelo. Ao final desse processo, obtém-se uma grande quantidade de dados de resposta. Faz-se um tratamento estatístico desses resultados de modo a concluir, do ponto de vista da engenharia, a probabilidade de ocorrência dos eventos. Para validar a metodologia proposta, analisou-se um edifício com cinco pavimentos. Os resultados satisfatórios foram obtidos quando comparados com exemplos da literatura, além de apresentarem-se estável com relação a integração no tempo. / Seismic actions occur with low intensity and often in Brazil, however they occur in Latin-American countries on the Pacific Coast and in Portugal, arousing interest in this subject of the Brazilian engineering. In this work, a numerical model is presented for the analysis on the elastic-plastic behavior of steel planar framed structures under random seismic excitation. For random vibrations, a Monte Carlo type simulation is used. This simulation is based on the ?Synthetic Wind?, proposed by Prof. Mario Franco. In this simulation, combinations of series of harmonic loads are generated with their amplitude given by certain provided Power Spectrum Density Functions (PSDF) of ground acceleration and pseudorandomly set phase angles. The used PSDF is reduced model of the Kanai-Tajimi model that determine combinations of non-dimensional series whose results by the behavior elastic are adjusted by international codes Elastic Response Spectra. The step-by-step time integration is performed for each load function using the Newmark method. In order to model, the elastoplastic effect is used the plastic hinge concept. Therefore, at each step the hinge formation is verified. If a certain section reaches its full plastic bending moment, this value of moment is maintained and a hinge in that section is introduced in the model with null stiffness, allowing for free finite rotations. If the rotation in a certain hinged section is reversed, elastic behavior is restored by elimination of the hinge from the model. At the end of this process, a large quantity of response data is obtained. A statistic treatment of these results is performed, in the way that is possible conclude, from the engineering point of view, the probability of occurrence of these events. A statistic treatment based sound engineering conclusions is done for the happened probable events. In order to validate the proposed methodology, a five stories building is analyzed. Satisfactory agreement is obtained when compared to results from the literature, and the results are very stable with respect to the time integration.