| Abstract | Luk je zakrivljeni konstrukcijski element pretežno opterećen tlakom. Moment savijanja u luku je vrlo mali ili u idealnom slučaju ga nema, gdje se ravnoteža sila postiže tlačnim potiscima prema osloncima. Primjenjuje se u raznim područjima graditeljstva kao
u mostogradnji, tunelogradnji, branama, spomenicima i palačama. Jedan od prvih nosivih sustava građen u različitim oblicima i od različitih materijala kroz svoju bogatu povijest. Od kamenih i zidanih lukova antičkog i srednjovjekovnog svijeta izgrađeni tradicionalnim geometrijskim pravilima proporcionalnosti, iskustvom i usmenom predajom koji i danas svojom veličinom, estetikom i koncepcijom prkose uvjetima. Razne daljnje teorije i pretpostavke, elastičnosti i plastičnosti, stvorile su proračune lukova analitičkim metodama ravnoteže i posebno grafičkim metodama tlačne linije kojima se bavimo u ovom radu. Počelo je od Hookeove teorije primjene lančanice za prikaz osi luka, prvi prikaz tlačne linije koja je kasnije matematički dokazana. Na kraju Couplet-Heymanova teorija predstavlja konkretne pretpostavke, gdje ziđe nema vlačnu čvrstoću, ima beskonačnu tlačnu čvrstoću i postoji trenje u sljubnicama, te da do sloma dolazi zbog pojave plastičnih zglobova. Takvi zaključci su omogućili određivanje graničnih stanja i određivanje koeficijenata sigurnosti, značajno za usporedbu djelovanja okoline i otpornosti materijala danas. Tlačna linija je rezultantna krivulja hvatišta tlačnih sila u presjecima luka. Idealan položaj potporne linije je takav da prolazi kroz os luka jer tada ne dolazi do pojave momenta savijanja, ali u realnosti je to nemoguće izvesti jer uvijek dolazi do nekog odstupanja ili u materijalu ili u opterećenju. Grafičko određivanje tlačne linije radi se pomoću iterativnog postupka. Podjelom luka na segmente, proračunom težišta i sila kroz isto, tvoreći poligon sila, graničnim horizontalnim potiscima sila određujući granične tlačne linije unutar kontura luka. Zaključno, luk i proračun lukova grafičkim postupkom nam je donijelo veliko razumijevanje ponašanja lukova i interakcija sila u njima, te i kako se prije teorija lukova skokovito mijenjala, sigurno će isto biti i u budućnosti. |
| Abstract (english) | The arch is a curved structural element predominantly loaded with pressure. The bending moment in the arc is very small or ideally absent, where a balance of forces is achieved by compressive thrust against the supports. It is applied in various areas of construction such as bridge construction, tunnel construction, dams, monuments and palaces. One of the first load-bearing systems built in different shapes and from different materials throughout its rich history. Made of stone and masonry arches of the ancient and medieval world, built with traditional geometric rules of proportionality, experience and oral tradition, which even today, with their size, aesthetics and concept, defy the environment. Various further theories and assumptions, of elasticity and plasticity, have created arc calculations by analytical equilibrium methods and especially by graphical pressure line methods which we deal with in this paper. It began with Hooke’s theory of the application of a chain to represent the axis of an arch, the first representation of a pressure line that was later mathematically proven. Finally, Couplet-Heyman's theory presents concrete assumptions, where masonry has no tensile strength, has infinite compressive strength and there is friction in the joints, and also that failure occurs due to the appearance of plastic joints. Such conclusions have made it possible to determine boundary conditions and to determine safety coefficients, significant for comparing environmental affects and material resistance today. The pressure line is the resultant curve of the grip of the compressive forces in the cross sections of the arc. The ideal position of the support line is such that it passes through the axis of the arch because then there is no bending moment, but in reality it is impossible to perform because there is always some deviation either in the material or in the load. Graphical determination of the pressure line is done using an iterative procedure. By dividing the arch into segments, calculating the center of gravity and forces through the same, forming a polygon of forces, boundary horizontal thrusts of forces determining the boundary pressure lines within the contours of the arch. In conclusion, the arch and the calculation of arches by the graphical process brought us a great understanding of the behavior of arcs and the interactions of forces in them and as before the theory of arches changed rapidly it will certainly change in the future. |
