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.

The builder's complete assistant, or, A library of arts and sciences, absolutely necessary to be understood by builders and workmen in general : viz. I. Arithmetick, vulgar and decimal, in whole numbers and fractions. II. Geometry, lineal, superficial, and solid. III. Architecture, universal. IV. Mensuration. V. Plain trigonometry. VI. Surveying of land, &c. VII. Mechanick powers. VIII. Hydrostaticks : illustrated by above thirteen hundred examples of lines, superficies, solids, mouldings, pedestals, columns, pilasters, entablatures, pediments, imposts, block cornices, rustick quoins, frontispieces, arcades, porticos, &c. : proportioned by modules and minutes, according to Andrea Palladio, and by equal parts : likewise great varieties of trussed roofs, timber bridges, centerings, arches, groins, twisted rails, compartments, obelisks, vases, pedestals for bustos, sun-dials, fonts, &c. and methods for raising heavy bodies by the force of levers, pulleys, axes in peritrochio, screws, and wedges, as also water, by the common pump, crane, etc. : wherein the properties, and pressure of the air on water, &c. are explained : the whole exemplified by 77 large quarto copper-plates /

All of the numbered plates in the atlas are double plates, and thus are counted twice in the adjusted plate count.

Damping of rectangular plate vibrations

"Materials Laboratory, Contract no. AF 33(616)-5426, Project no. 7360."

Damping energy dissipated by interfaces in beam and plate supports and in sandwich cores.

"Materials Laboratory, Contract no. AF 33(616)-5426, Project no. 7360."

Exact eigenvalue correspondences between laminated plate theories via membrane vibration

Based on Reddy's third-order theory, the first-order theory and the classical theory, exact explicit eigenvalues are found for compression buckling, thermal buckling and vibration of laminated plates via analogy with membrane vibration, These results apply to symmetrically laminated composite plates with transversely isotropic laminae and simply supported polygonal edges, Comprehensive consideration of a Winkler-Pasternak elastic foundation, a hydrostatic inplane force, an initial temperature increment and rotary inertias is incorporated. Bridged by the vibrating membrane, exact correspondences are readily established between any pairs of buckling and vibration eigenvalues associated with different theories. Positive definiteness of the critical hydrostatic pressure at buckling, the thermobukling temperature increment and, in the range of either tension loading or compression loading prior to occurrence of buckling, the natural vibration frequency is proved. (C) 2000 Elsevier Science Ltd. All rights reserved.

AVALIAÇÃO DAS TÁBUAS ÓSSEAS VESTIBULARES E LINGUAIS DOS DENTES ANTERIORES INFERIORES E MOLARES SUPERIORES APÓS O TRATAMENTO COM OS APARELHOS FUNCIONAIS FIXOS FORSUS E TWIN FORCE BITE CORRECTOR

Pelo fato das consequências do uso de aparelhos ortopédicos fixos sobre o periodonto ósseo vestibular e lingual ainda serem uma incógnita para o ortodontista clínico e pesquisador, este estudo teve como objetivo avaliar, por meio de tomografia computadorizada de feixe cônico (TCFC) as alterações em espessura das tábuas ósseas vestibulares e linguais em primeiros molares superiores e incisivos e caninos inferiores, após a utilização de aparelhagem fixa e dos aparelhos Twin Force (grupo A) e Forsus (grupo B) para o tratamento da maloclusão de Classe II, 1ª divisão. Para tanto, obteve-se uma amostra de 22 pacientes jovens adultos, divididos em dois grupos, de acordo com o aparelho propulsor da mandíbula. Grupo experimental A: 11 pacientes, 6 masculinos e 5 femininos, com idade média de 15,09 anos na instalação do Twin Force, e 11 pacientes, 7 masculinos e 4 femininos, com idade média de 15,45 anos na instalação do Forsus. O tempo médio de uso do aparelho Twin Force foi de 3,73 meses e do Forsus, 7,09 meses. O grupo A realizou TCFC antes do início do tratamento (T1), antes da instalação do Twin Force (T2), após a remoção do Twin Force (T3); e o grupo B somente antes da instalação do Forsus (T2) e após a remoção do Forsus (T3). Para comparação entre os tempos T2 e T3 foi utilizado o teste t pareado e entre os tempos T1, T2 e T3 foi utilizada a Análise de Variância (ANOVA) a um critério e o teste post-hoc de Tukey. Para comparação entre os grupos foi utilizado o teste t . Na comparação intergrupos os resultados evidenciaram que não houve diferença estatisticamente significante entre as alterações das espessuras das tábuas ósseas vestibular e lingual; por outro lado, na avaliação intra-grupo, de 48 medidas avaliadas, no grupo A houve reduções estatisticamente significantes nos terços cervical e médio por vestibular, nos dentes anteroinferiores e nos primeiros molares superiores e aumento nos terços cervical e médio, por lingual nos dentes anteriores inferiores, totalizando 25 medidas significantes. Já no grupo B, houve aumento significante da tábua óssea lingual nos dentes anteriores inferiores e redução em vestibular nos molares superiores, totalizando apenas sete medidas significantes, mas com mais medidas significantes de redução óssea vestibular em terços cervical e médio nos primeiros molares superiores, em comparação com o grupo A. Não houve diferença significante entre as medições obtidas com voxel 0,2 mm e 0,4 mm e nem dimorfismo entre os gêneros. As reduções em espessura óssea alveolar, principalmente em terços cervicais e médios vestibulares nos dentes avaliados neste estudo são um alerta ao clínico, para que realize essa abordagem diagnóstica periodontal antes de iniciar o tratamento ortodôntico.

Discriminating ambulation using a smart sensing plate

The automated sensing scheme described in this paper has the potential to automatically capture, discriminate and classify transients in gait. The mechanical simplicity of the walking platform offers advantages over standard force plates. There is less restriction on dimensions offering the opportunity for multi-contact and multiple steps. This addresses the challenge of patient targeting and the evaluation of patients in a variety of ambulatory applications. In this work the sensitivity of the distributive tactile sensing method has been investigated experimentally. Using coupled time series data from a small number of sensors, gait patterns are compared with stored templates using a pattern recognition algorithm. By using a neural network these patterns were interpreted classifying normal and affected walking events with an accuracy of just under 90%. This system has potential in gait analysis and rehabilitation as a tool for early diagnosis in walking disorders, for determining response to therapy and for identifying changes between pre and post operative gait. Copyright © 2009 by ASME.