Model of human rhythmic activities on structures

Crowd induced dynamic loading in large structures, such as gymnasiums or stadiums, is usually modelled as a series of harmonic loads which are defined in terms of their Fourier coefficients. Different values of these Fourier coefficients that were obtained from full scale measurements can be found in codes. Recently, an alternative has been proposed, based on random generation of load time histories that take into account phase lags among individuals inside the crowd. Generally the testing is performed on platforms or structures that can be considered rigid because their natural frequencies are higher than the excitation frequencies associated with crowd loading. In this paper we shall present the testing done on a structure designed to be a gymnasium, which has natural frequencies within that range. In this test the gym slab was instrumented with acceleration sensors and different people jumped on a force plate installed on the floor. Test results have been compared with predictions based on the two abovementioned load modelling alternatives and a new methodology for modelling jumping loads has been proposed in order to reduce the difference between experimental and numerical results at high frequency range.

Structures subjected to Human Actions

In this paper we present the tests on a structure designed to be a gymnasium, which has natural frequencies within that range. In these tests the gym slab was instrumented with acceleration sensors and different people jumped on a force plate installed on the floor. The test results have been compared with predictions based on the two existing load modelling alternatives (Sim and SCI Guide) and two new methodologies for modelling jumping loads has been proposed. The results of the force plate trials were analysed in an attempt to better characterize the profile of the jump force and determine how best to approximate it. In the first proposed methodology the study is carried out in the frequency domain using an average power spectral density of the jumps. In the second proposed methodology, the jump force is decomposed into the summation of one peak with a large period and a number of peaks with smaller periods. Utilizing a similar model to that of the Sim model, the approximation will still be comprised of the summation of two quadratic cosine functions.

Acciones humanas sobre estructuras

En esta tesis se propone un nuevo modelo de carga para caracterizar los saltos de personas sobre estructuras y se estudia la influencia de las personas en las propiedades dinámicas de la estructura. En el estudio del comportamiento estructural de construcciones como gimnasios, salas de baile, estadios, auditorios o pasarelas peatonales sometidas a cargas producidas por un gran número de personas, se deben tener en cuenta las fuerzas dinámicas, lo cual implica el uso de modelos de cálculo más complejos y criterios de dimensionamiento con nuevos parámetros. Por ello, es necesario determinar a qué cargas van a estar sometidas este tipo de estructuras y cómo van a cambiar cuando se encuentren ocupadas por personas. En la primera parte del trabajo se presenta el problema de considerar las fuerzas dinámicas en el análisis de estructuras. Se indican los factores que influyeron en el interés por este tipo de estudios. Se exponen los objetivos de la tesis y se propone la metodología para conseguirlos. También en esta primera parte se describe el estado del arte. Se explican los modelos existentes de carga generada por saltos de personas y se hace un repaso de los principales autores y estudios sobre este tema. Por último se exponen algunas ideas sobre las modificaciones dinámicas que provoca la presencia de las personas en las estructuras. En la segunda parte de la tesis se explica el modelo de carga de saltos propuesta en este trabajo, donde se incluye una campaña de ensayos con saltos sobre una placa de carga. Se describen las estructuras de ensayo, un gimnasio y una losa que cubre un aljibe. Se detalla la identificación de las propiedades dinámicas de las estructuras, describiendo los ensayos correspondientes y los resultados de un Análisis Operacional Modal. Por último se presenta el modelo de elementos finitos de la estructura elegida para los ensayos. En la tercera y última parte del trabajo se comprueba la validez de los modelos de carga estudiados mediante la realización de ensayos dinámicos con personas saltando y la posterior comparación de los resultados experimentales con las simulaciones numéricas. Como último resultado se estudia la influencia de las personas en las propiedades dinámicas de la estructura. Para ello se utilizan los datos obtenidos mediante un ensayo con personas pasivas. ABSTRACT In this thesis, a new load model is proposed to characterize people jumping on structures and the influence of people in the dynamic properties of the structure is studied. In the study of the structural behavior of buildings such as gymnasiums, dance halls, stadiums, auditoriums or footbridges subjected to loads generated by crowd, dynamic forces must take into account, which involves the use of more complex calculation models and dimensioning criteria with new parameters. Therefore, it is necessary to determine these dynamic loads and how structures will change when they are occupied by people. In the first part of the work the problem of considering the dynamic forces in the analysis of structures is presented. The factors that influence on the interest in this type of study are indicated. The objectives of the thesis are presented and also the proposed methodology in order to achieve them. In this first part the state of the art is described. Existing jumping load models are explained and a review of the main authors and studies on this subject is done. Finally some ideas about the dynamic changes caused by the presence of people in the structures are exposed. In the second part of the thesis the proposed jumping load model is explained, including jump tests on a force plate. Test structures, a gym and a concrete slab are described. Dynamic properties identification of the test structures is detailed with the corresponding tests and Operational Modal Analysis results. Finally, a finite element model of the structure chosen for the tests is presented. In the third part of the work, the studied jump load models are validated by performing dynamic testing with people jumping and the subsequent comparison of experimental results with numerical simulations. As a last result, the influence of people on the dynamic properties of the structure is checked. For this purpose, obtained data from a test with passive people are used.

Wedges and plate-bandes: mechanical theories after De la Hire

Plate-bandes are straight masonry arches (they are called, also, flat arches or lintel arches). Ideally they have the surfaces of extrados and intrados plane and horizontal. The stones or bricks have radial joints converging usually in one centre. The voussoirs have the form of wedges and in French they are called "claveaux". A plate-bande is, in fact, a lintel made of several stones and the proportions of lintels and plate-bandes are similar. Proportions of plate-bandes, that is the relationship between the thickness t and the span s (t/s)varies, typically between 1/4–1/3 in thick plate-bandes, and is less than 1/20 in the most slender ones. A ratio of circa 1/8 was usual in the 18th Century and follows a simple geometrical rule: the centre form with the intrados an equilateral triangle and the plate-bande should contain an arc of circle. The joints are usually plane, but in some cases present a «rebated» or «stepped» form. Plate-bandes exert an inclined thrust as any masonry arch. This thrust is usually very high and it requires either massive buttresses, or to be built in the middle of thick walls. Master builders and architects have tried since antiquity to calculate the abutment necessary for any arch. A modern architect or engineer will measure the arch thrust in units of force, kN or tons. Traditionally, the thrust has been measured as the size of the buttresses to resist it safely. Old structural rules, then, addressed the design problem establishing a relationship between the span and the depth of the buttress. These were empirical rules, particular for every type of arch or structure in every epoch. Thus, the typical gothic buttress is 1/4 of the vault span, but a Renaissance or baroque barrel vault will need more than 1/3 of the span. A plate-bande would require more than one half of the span; this is precisely the rule cited by the French engineer Gautier, who tried unsuccessfully to justify it by static reasons. They were used, typically, to form the lintels of windows or doors (1-2 m, typically); in Antiquity they were used, also, though rarely, at the gates of city walls or in niches (ca. 2 m, reaching 5.2 m). Plate-bandes may show particular problems: it is not unusual that some sliding of the voussoirs can be observed, particularly in thick plate-bandes. The stepped joints on Fig. 1, left, were used to avoid this problem. There are other «hidden» methods, like iron cramps or the use of stone wedges, etc. In seismic zones these devices were usual. Another problem relates to the deformation; a slight yielding of the abutments, or even the compression of the mortar joints, may lead to some cracking and the descent of the central keystone. Even a tiny descent will convert the original straight line of the intrados in a broken line with a visible «kink» or angle in the middle. Of course, both problems should be avoided. Finally, the wedge form of the voussoirs lead to acute angles in the stones and this can produce partial fractures; this occurs usually at the inferior border of the springers at the abutments. It follows, that to build a successful plate-bande is not an easy matter. Also, the structural study of plate-bandes is far from simple, and mechanics and geometry are related in a particular way. In the present paper we will concentrate on the structural aspects and their constructive consequences, with a historical approach. We will outline the development of structural analysis of plate-bandes from ca. 1700 until today. This brief history has a more than purely academic interest. Different approaches and theories pointed to particular problem, and though the solution given may have been incorrect, the question posed was often pertinent. The paper ends with the application of modern Limit Analysis of Masonry Structures, developed mainly by professor Heyman in the last fifty years. The work aims, also, to give some clues for the actual architect and engineer involved in the analysis or restoration of masonry buildings.