A History of the Theory of Structures in the Nineteenth by T. M. Charlton
By T. M. Charlton
The outstanding buildings of this present day, resembling huge suspension bridges, are the results of clinical rules proven in the course of the new iron age of the 19th century. The ebook is worried with an in depth and demanding account of the advance and alertness of these ideas (including statics and elasticity) via humans of exceptional expertise in utilized arithmetic and engineering. They have been, in fact, customarily encouraged through the calls for of the railway, building increase. one of the notable examples selected through the writer is Robert Stephenson's use of novel ideas for the layout and erection of the Britannia tubular iron bridge over the Menai Straits. A background of the idea of buildings within the 19th Century is a uniquely complete account of a century of the improvement of the speculation; an account which skilfully blends the personalities and the good works and that is enlivened through little-known bills of friendship and controversy.
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Extra info for A History of the Theory of Structures in the Nineteenth Century
Clebsch While railway engineers developed theory of continuous beams, a significant treatment of the problem was produced by the mathematician Clebsch (1862) within his researches into theory of elasticity. It does not seem, however, to have become either well known or advantageous in engineering but it bears some similarity to Scheffler's method (1857; 1858c). Clebsch's elegant use of the differential equation of bending seemed to be unknown in Britain until the method was published in 1919 independently, it is believed, by Macaulay and subsequently termed 'Macaulay's method'.
The equations for the deflexion, due to bending of the free end of an arch, encastre at the opposite end and loaded such that there is a bending moment Af, at any element of length ds and flexural rigidity El, whose location is defined by coordinates y, z with reference to the free end, are given as follows: The elastic centre 45 As r66\ Fig. 18. After Culmann (1866). 16)] Thus the resultant of the forces is equivalent to a couple Uug = Mg, together with a force U through the elastic centre G, and the total angle of elastic bending $ depends only on that couple.
26)] where / and /i are the second moment of area and weight per unit length of CD, and p3 is the reaction at C. 6 tons per ft; / = 1584 (ft)4; and /2 (for DE) = 962 (ft)4. It is interesting to note that no account is taken of the fact that in making the joint at D the original angle of separation was not completely eliminated, because the bending of DE due to its self-weight was neglected. The value of the angle of separation at C obtained from this analysis is used to determine the height through which BC should be raised at B for complete closure and it is noted that it was actually raised by little more than half that amount when the joint at C was completed.