Mise en équation de la théorie des poutres par une approche purement expérimentale

Résumé du document

En mécanique des structures, la théorie des poutres permet de simplifier les problèmes rencontrés, en assimilant le solide étudié à une poutre, à savoir une structure élancée, dont une dimension est grande devant les deux autres. C'est ainsi que l'étude d'une aile d'avion, dont l'envergure est par exemple grande devant la corde, d'un fuselage ou de la semelle d'un pont peut être abordée par la théorie des poutres.

Celle-ci s'applique dans un domaine d'efforts permettant au matériau, homogène et isotrope, de demeurer linéaire et élastique, ce qui implique, entre autres, qu'après déformation, le solide reprend sa forme initiale. En effet, on négligera dans le cadre de cette étude l'usure du matériau, en particulier l'usure des jauges de mesures.

Cette étude a pour but de faire découvrir la théorie des poutres au travers d'une approche expérimentale. Toutes les expériences réalisées ne mettent en jeu que des matériaux linéaires et isotropes. Ainsi, nous pourrons confronter les résultats obtenus en appliquant les 4 types de sollicitations connues : un effort normal, une torsion, une flexion ou encore un effort tranchant avec les résultats théoriques étudiés en cours de mécanique des milieux continus et en élasticité en début d'année. Cela nous permettra de valider ou de restreindre certaines hypothèses.

Extraits

[...] The population explosion is responsible for countless tragedies throughout The South, with the widespread degradation of living standards, the constant demise of sanitation, the aggravation of malnutrition, increased disease spread, exacerbated unemployment and poverty, also increasing the pressure on the planet's already strained hydrological resources, but also leading to environmental catastrophes such as massive deforestation, soil erosion, desertification, extensive pollution Enumerating all the troubles brought by overpopulation is unnecessary to convey the strong sense of urgency implicit in the fact that the population explosion is considered to be one of the major challenges humanity will have to face in the forthcoming decades and is sadly a major characteristic of most countries of The South, exclusive certainly to developing nations. Indeed, birth rates remain high in The South, approaching 25 births per thousand on average, due to the number of young couples in age of having children. The fertility rate, although today decreasing, is still alarmingly high in developing nations, attaining three or four children per woman. [...]

[...] Stage 2 can last between ten and fifty years before announcing the real take-off, which constitutes Rostow's third stage of development. The take-off is characterized by a society driven more by economic processes than by tradition, a society where the norms of economic growth are solidly established. Rostow announces a transitional period of between fifty and one hundred years before the reaching of stage the age of maturity and rapid increase of industry. Economic development gradually necessitates the diversification of the economy, a vital step which leads to greatly reduced poverty rates associated to higher standards of living, as the society no longer needs to sacrifice wellbeing in order to strengthen all sectors of the economy. [...]

[...] With an annual population growth rate of between 1975 and 2003, estimates suggest a sharp decline to come, with a growth rate of between 2003 and 2015. Whereas the fertility rate was of 4.7 children per woman between 1970 and 1975, between the years 2000 and 2005 it plummeted to 2.3 births per woman, approaching the regeneration threshold of 2.1 that most developed nations have passed. Brazil, which therefore seems to have completed its demographic transition, appears once more as well on its way towards rejoining the developed North, contrasting and setting it apart once more from numerous nations of The South. [...]

[...] Most of these countries are in Sub-Saharan Africa. With even more alarm do we discover that more than 840 million people in the world are malnourished, and 799 million of them live in the developing world. In these basic statistics underlie once more the illustration of an immense developmental gap widening ever further the North South divide. Yet despite the overwhelming feeling emanating of such figures that tend to present the problems of hunger and poverty as inexorable plagues intrinsic to the human condition at certain stages of development, the eradication of widespread hunger and extreme poverty can be attained. [...]

[...] Each country in this position chooses its own balance between these three goals. Therefore according to this model, a nation can be considered as belonging to The South when it conforms to either stage or 4. Although many consider Sub-Saharan Africa as incompatible with the type of development countries of The North are enjoying today, we must remember that only a few decades ago Asia was in widespread opinion an un- developable continent, which paradoxically today withholds some of the world's most developed nations such as Japan, Singapore or South Korea. [...]