Mathematics. — "An application of the theory of integral equa- 

 tions on the determination of the elastic curve of n beam, 

 elastically supported on its lohole length". By Pi-of. C. B. 

 BiEZENO. (Communicated by Prof. J. C. Kluijver). 



(Communicated at the meeting of March 24, 1923). 



In his well-known treatise „Voiiesungen iiber Technische Mecha- 

 nik" (Vol. Ill, ^ 48) Föppi- describes a construction, by wliich the 

 elastic curve of a beam, elastically supported on his whole length, 

 might been approximated. 



If in tlie differential equation of this elastic curve 



Ely"" + ky = q 



[EI = coefficient of stiffness of the beam, k = coefficient of stifftiess of 



the supporting ground, q := specific continuous loading) tlie function y 



where known, it would be possible to refind this function by 



,, . , q — ky 



mtegrating tour times the expression — wf'- 



This integration would graphically correspond to the construction 

 of the elastic curve of a beam, wbicli carries only well-known forces. 



It is obvious, therefore, first to make a supposition about the 

 elastic curve — in such a way, of course, that the reaction-forces 

 of the supporting ground will be in equilibrium with the external 

 forces of the beam — , then to integrate graphically the expression 



, and finally to controll, if the before-mentioned accordance 



Mil 



takes place. 



,,Im allgemeinen — such is the opinion of Foppl — wird man 

 zunachst eine starke Abweichung in der Gestalt beider Kurven 

 finden. Dann andert man die zuerst gezeichnete Belastungsfiache 

 so ab, dasz sich die Lastverteilung jetzt der Gestalt der gefundenen 

 elastischen Linie nahert und wiederholt das Verfahren fur diese zweite 

 Annahme. Die Uebereinstimmung zwischen Belastungstliiche und 

 zugehoriger elastischen Linie wird jetzt besser werden und nach 

 mehrmaliger Wiederholung findet man mit hinreichender Genauig- 

 keit die wirkliche Druckverteilung." 



16* 



