Izračun torzijskega vztrajnostnega momenta poljubnega preseka

Sepin, Jon (author), Nagode, Marko (mentor), Šeruga, Domen (co-mentor)

Za preračun deformacije nosilca, ki je obremenjen s čisto torzijo, moramo poznati torzijski vztrajnostni moment preseka obravnavanega nosilca. V primeru bolj preprostih oblik preseka lahko to storimo analitično s pomočjo splošnih obrazcev, v primeru bolj zahtevnih geometrijskih oblik pa je analitični izračun zelo težaven oz. nemogoč, zato uporabljamo numerične metode. Zaključna naloga predstavlja zasnovo in izvedbo algoritma za numerično računanje torzijskega vztrajnostnega momenta preseka poljubne geometrije, ki temelji na podlagi metode končnih razlik. Prikazani so rezultati algoritma za primere polnega in votlega kvadratnega preseka ter polnega okroglega preseka. Za namene preverjanja natančnosti algoritma so dobljeni rezultati primerjani glede na vrednosti analitičnih izračunov.

• Language: Slovenian
• Keywords: torzijski vztrajnostni moment, torzija, numerične metode, presek nosilca, metoda končnih razlik, numerični algoritem.
• Work type: Bachelor thesis/paper
• Organization: FS - Faculty of Mechanical Engineering
• Year: 2018
• PID: 20.500.12556/RUL-100840
• Publication date in RUL: 18.04.2018

Secondary language

• Language: English
• Title: Calculation of the torsion constant of any cross section

Abstract

To calculate the deformation of a beam, which is subjected to pure torsion, we require the torsional constant of the beam cross section. In the case of simpler cross section shapes, this can be done analytically by means of general terms, while in the case of more demanding geometric shapes, analytical calculation is either immensely difficult or even impossible. It is for this reason that we utilise numerical methods. This final thesis includes the design and implementation of an algorithm for the numerical calculation of the torsional constant of a cross section of an arbitrary shape based on the finite difference method. Shown within this thesis are the results of the algorithm for a full and hollow square cross section as well as a full circular cross section which are, for the purposes of verifying the algorithm's accuracy, compared against values obtained via analytical calculations.

• Keywords: torsion constant, torsion, numerical methods, profile cross section, finite difference method, numerical algorithm.