Análise dinâmica de passarela metálica submetida a carregamento decorrente da ação humana

Estudos indicam que estruturas chegam a sofrer colapso a partir da ação de vandalismo por parte de pedestres. Neste contexto, este trabalho objetivou analisar o comportamento da passarela metálica devido às ações provocadas por humanos e, adicionamente, verificar se a estrutura foi dimensionada corretamente e se é capaz de suportar uma travessia segura e confortável para os pedestres. Foram calculadas as matrizes de massa, rigidez e amortecimento, bem como as frequências naturais pelo software Matlab. Após, foi definido o carregamento de um pedestre pulando no centro da estrutura. Com o problema e suas condições de contorno elaboradas, o método de integração numérica de Newmark foi utilizado para determinar a resposta dinâmica das passarelas em termos de deslocamento, velocidade e aceleração em cada nó. Os resultados demonstraram que a passarela estudada é facilmente excitada pela ação de pedestres, encontrando-se acelerações que extrapolam os limites de estudos e normas. Diante destes resultados, pode-se perceber que a estrutura situou-se fora da faixa de segurança e conforto, assim, ficando evidente a necessidade de um sistema de controle de vibrações.Studies show that the structure suffers degradation by the action of pedestrians. In this context, the objective was to analyze the behavior of the metallic footbridge due to the actions caused by humans, verifying if the structure was correctly dimensioned and if it is capable of supporting a safe and comfortable crossing for pedestrians. The mass, stiffness and damping matrices were calculated, as well as the natural frequencies by the Matlab software. Afterwards, the loading of a pedestrian jumping in the center of the structure was defined. With the problem and its boundary conditions elaborated, the Newmark numerical integration method was used to determine the dynamic response of the footbridge in terms of displacement, velocity and acceleration at each node. The results showed that the studied footbridge is easily deformed by the action of pedestrians, accelerations were found that go beyond the limits of studies and standards, soon, the structure is outside the safety and comfort range, thus the need for a vibration control system is evident

Rehearsing in the margins: mathematical print and mathematical learning in the early modern period

Early modern mathematical culture used the written word in highly distinctive ways. The various kinds of mathematical activity were all experienced in the early modern period as special kinds of performance: arithmetical calculation, proportional reasoning, algebraic manipulation and geometrical proving. The normal way they were transmitted—taught and learned—involved demonstration by a teacher, private rehearsal and finally specimen performance by the student. Slates, waste paper, and the margins of printed texts all bear the traces of learners’ rehearsals. This chapter examines the evidence for this mathematical culture and the influences on it of ancient and early modern examples

The shaping of deduction in Greek mathematics: a study in cognitive history

An examination of the emergence of the phenomenon of deductive argument in classical Greek mathematics

The works of archimedes: translation and commentary

Volume I of the first authoritative translation of Archimedes'' works into English