By Edoardo Benvenuto
This booklet is among the best i've got ever learn. to write down a foreword for· it truly is an honor, tough to just accept. we all know that architects and grasp masons, lengthy prior to there have been mathematical theories, erected constructions of impressive originality, power, and sweetness. lots of those nonetheless stand. have been it now not for our now acid surroundings, shall we count on them to face for hundreds of years extra. We appreciate early architects' obvious good fortune within the distribution and stability of thrusts, and we presume that grasp masons had ideas, maybe held mystery, that enabled them to show architects' daring designs into truth. we all know that rational theories of energy and elasticity, created centuries later, have been encouraged by way of the wondrous constructions that males of the 16th, 17th, and eighteenth centuries observed day-by-day. Theorists be aware of that once, ultimately, theories began appearing, architects distrusted them, partially simply because they typically omitted information of significance in genuine building, partially simply because not anyone yet a mathematician might comprehend the purpose and func tion of a mathematical thought designed to symbolize a side of nature. This e-book is the 1st to teach how statics, energy of fabrics, and elasticity grew along latest structure with its millenial traditions, its host of successes, its ever-renewing kinds, and its quite a few difficulties of upkeep and service. In reference to reports towards fix of the dome of St. Peter's via Poleni in 1743, on p.
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Extra info for An Introduction to the History of Structural Mechanics: Part II: Vaulted Structures and Elastic Systems
5. 13. 341 342 10. " For church vaults "of uniform thickness," the author advises following the well-known rule taken from funicular equilibrium, warning builders to vary the weights acting on the rope in case the load on the vault should not be uniform. At the end of the work, Couplet faces the problem of the centerings, which H. Pitot had discussed (wrongly) in 1726. We shall return to this question later, in discussing Leonardo Salimbeni's treatise. Couplet concludes, correctly if there are many voussoirs, that "the voussoirs that weigh on the centering are placed within 60 degrees [from the key], and those which do not weigh on it [are placed within] 30 degrees from the horizontaL"27 Couplet's second memoir faces the problem of the adherence between voussoirS.
The effect of this force is a "strike" (ictus, small displacement) in the direction of the beam. The strength of this force is proportional to the sine of the angle of incidence of the displacement and the pier wall: Thus the lesser inclination of AV compensates the greater length of AM; as MA pushes the wall AG more sideways, according to angle MAY, and V A pushes more directly according to angle V AY, it follows that the pushing force due to M A is in proportion to the pushing force due to V A as the sine of angle MAY is to the sine of angle V AY.
57. B. concinnatae et collectae ab anna 1677, Basle University Library, ms. Ia 3. The reworked version can be found in Jakob Bernoulli, "Varia posthuma," Opera, Vol. 2 (1744) pp. 1119-1123. 330 10. •, I \ II •\ .... " ... 5. James Bernoulli's figure for calculating the curvature of an arch whose parts support each other without using mortar (1704). From Truesdell, Rational mechanics. which is integrated to obtain dy/dx = s/a [where a is a constantlY Jakob Bernoulli also considers the hypothesis that, because of friction, every voussoir is kept from sliding forward and tends to rotate around its edge, but his treatment is imperfect.
An Introduction to the History of Structural Mechanics: Part II: Vaulted Structures and Elastic Systems by Edoardo Benvenuto