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U ovom radu je u okviru kombinirane metode konačno-diskretnih elemenata razvijen novi numerički model za simulaciju ponašanja zidanih konstrukcija izloženih statičkom, dinamičkom i seizmičkom opterećenju. U postojeći računalni program Y-2D koji se temelji na kombiniranoj metodi konačno-diskretnih elemenata implementiran je novi numerički model za simulaciju čeličnih klamfi i trnova u suho zidanim kamenim konstrukcijama. Model uključuje dva tipa klamfi i jedan tip trnova koji se najčešće koriste u kamenim konstrukcijama uzimajući u obzir mogućnost izvlačenja klamfe i trna iz kamenog bloka, mogućnost pucanja klamfi i trnova te cikličko ponašanje materijala. U sklopu ovog rada provedena je verifikacija ugrađenog modela te je prikazana njegova primjena u inkrementalnoj seizmičkoj analizi realnih kamenih konstrukcija. Također, razvijen je novi numerički model materijala za analizu nearmiranih zidanih konstrukcija. Model se sastoji od novog numeričkog modela kontaktnog elementa za simuliranje veze bloka i morta te novog modela ponašanja materijala u konačnom elementu. Model materijala u konačnom elementu uzima u obzir ortotropno ponašanje, mogućnost sloma u tlaku, pojavu tlačnog omekšanja te cikličko ponašanje materijala. Model ponašanja kontaktnog elementa za simulaciju veze morta i bloka uzima u obzir pojavu sloma u vlaku i posmiku, povećanje energije loma u posmiku uslijed povećanja predlačnog naprezanja, smanjenje koeficijenta trenja uslijed povećanja posmične deformacije te cikličko ponašanje veze morta i bloka. Valjanost modela je provjerena usporedbom dobivenih rezultata s numeričkim i eksperimentalnim rezultatima preuzetima iz literature. Prezentiran je također i novi numerički model za seizmičku analizu zidanih konstrukcija omeđenih armiranobetonskim serklažima koji se sastoji od sinteze novo razvijenog numeričkog modela materijala za analizu nearmiranih zidanih konstrukcija te prethodno razvijenog numeričkog modela za analizu armiranobetonskih konstrukcija. This thesis presents a new numerical model based on a combined finite-discrete element method, capable of predicting the behaviour of masonry structures under static, dynamic and seismic loads. A new numerical model of steel clamps and bolts in dry stone masonry structures is implemented in the available numerical cod Y-2D based on combined finite-discrete element method. Model includes several types of clamps and bolts which are frequently used in strengthening of dry stone masonry structures taking into account influence of the pulling out of the clamps and bolts from the stone block, cyclic behaviour, yielding and failure of the steel. The verification of the model and possibility of using this model in incremental dynamic analysis of real dry stone masonry structures is also shown. New material model for numerical analysis of unreinforced masonry structures was also developed. Model consists of new numerical model in contact element which simulates connection between block and mort, and new material model in finite element. Material model in finite element takes into account orthotropic behaviour, cyclic behaviour, possibility of failure and softening in pressure. Numerical model of contact element which simulate connection between block and mort take into account possibility of failure and softening behaviour in tension and shear, increasing of fracture energy in shear due to increasing precompression stress, decreasing friction coefficient due to increasing shear displacement as well as cyclic behaviour connection between mort and block. The verification of the model was performed on examples by comparing it with the results obtained with the known numerical and experimental results from literature. New numerical model for seismic analysis of reinforced masonry structures was also presented. Model consists of synthesis of new developed material model for unreinforced masonry structures and previously developed numerical model for analysing reinforced concrete structures.

Za zidani toranj sa satom koji se nalazi u pokrajini Ferrera u Italiji izvršene su seizmičke analize preko kombinirane metode konačno-diskretnih elemenata (FEM/DEM) za tri potresa na lokacijama (Petrovac, Campano Lucano, South Iceland) s četiri rubna uvjeta. Seizmičkom analizom su dobiveni rezultati. Iz tih rezultata utvrdilo se koji rubni uvjet je najpovoljniji za zidani toranj, koji je postigao najveća ubrzanja i najveće pomake, odnosno koji je izdržao najduže do konačnog urušavanja. For the masonry tower with cloak located in the province of Ferrera in Italy, seismic analyses were performed using the combined finite-discrete element method (FEM / DEM) for three earthquakes at locations (Petrovac, Campano Lucano, South Iceland) with four boundary conditions. The results were obtained by seismic analysis. From these results, it was determined which boundary condition is the most favourable for the masonry tower, which achieved the greatest accelerations and the greatest displacements, that is, which lasted the longest until the final collapse.

Cilj rada je izrada numeričkog modela koji prikazuje ponašanje konstrukcije uslijed potresnog djelovanja. Korištena su tri razorna potresa koja su se dogodila u povijesti Campano Lucano 1980. Italija, Petrovac 1979. Crna Gora i South Iceland 2000. (Island). Analiza se vršila na zidanoj konstrukciji izrađenoj u 17. stoljeću koja ima namjenu zvonika, a smještena je u pokrajini Rovigo u sjevero-istočnom dijelu Italije. Metoda proračuna korištena je kombinacijom konačnih i diskretnih elemenata. Kao rezultat rada dobiveni su rezultati krajnih stanja konstrukcije do potpunog sloma. The goal of this work was making of numerical model that shows construction behaviour during earthquake. Three destructible historical earthquakes were used: Campano Lucano 1980. Italy, Petrovac 1979. Montenegro and South Iceland 2000. Iceland. Analysis was conducted on a brick building constructed in 17th century that was used as bell tower, and it ́s placed in Italian northeast province of Rovigo. Calculation method was a combination of finite and discrete element method. Final results of this work where values of marginal states of construction until the final breakdown.

Za obrambeni zidani toranj koji se nalazi u dolini Pada u Italiji izvršene su seizmičke analize preko kombinirane metode konačno-diskretnih elemenata (FEM/DEM) za tri potresa na lokacijama (Petrovac, Campano Lucano, South Iceland) s četiri rubna uvjeta. Seizmičkom analizom su dobiveni rezultati. Iz tih rezultata utvrdilo se koji rubni uvjet je najpovoljniji za zidani toranj, koji je postigao najveća ubrzanja i najveće pomake, odnosno koji je izdržao najduže do konačnog urušavanja. For the defensive masonry tower located in the Po Valley in Italy, seismic analyzes were performed using the combined finite-discrete element method (FEM / DEM) for three earthquakes at locations (Petrovac, Campano Lucano, South Iceland) with four boundary conditions. The results were obtained by seismic analysis. From these results, it was determined which boundary condition is the most favorable for the masonry tower, which achieved the greatest accelerations and the greatest displacements, that is, which lasted the longest until the final collapse.

Prikaz proračun nosive konstrukcije zidane zgrade. Nosiva konstrukcija je zidana i omeđena serklažima. Međukatna konstrukcija je AB ploča. Građevina se nalazi u potresnoj zoni gdje se očekuje vršno ubrzanje podloge ag=0.2 g s povratnim periodom od 475 godina, II. području opterećenja vjetrom i području D opterećenja snijegom. Proračunom dokazati mehaničku otpornost i stabilnost konstrukcije. Proračun proveden prema europskim normama EC1, EC6, EC8, dopunjeno podacima o opterećenjima prema odgovarajućim hrvatskim normama i pravilnicima. The calculation of the load-bearing structure of a masonry building. The load-bearing structure is masonry and bounded by circles. Floor construction is AB . The building is located in the earthquake zone where the peak acceleration of the substrate is expected ag = 0.2 g with a return period of 475 years, II. wind load area and snow load area D. Prove the mechanical resistance and stability of the structure by calculation. Calculation carried out according to European standards EC1, EC6, EC8, supplemented with data on loads according to the relevant Croatian standards and regulations.

U radu je prikazan proračun nosive konstrukcije zidane građevine. Predmet proračuna je zgrada, sa prizemljem i tri kata, locirana u Splitu. Proračun sadrži dokaz nosivosti zidova na vertikalna opterećenja, dokaz nosivosti zidova na potres, proračun potrebne armature vertikalnih serklaža, određivanje širine temeljnih traka iz uvjeta nosivosti, te proračun međukatnih konstrukcija i određivanje potrebne armature u istim. This paper presents the calculation of the load bearing masonry structure. The subject of the calculation is a building with a ground floor and three floors, located in Split. The calculation contains proof of bearing capacity of walls to vertical loads, proof of bearing capacity of walls to earthquake, calculation of required reinforcement of vertical tie columns, determining the width of strip foundation from the load capacity conditions, and the calculation of floor structures and the required reinforcement of those structures.

Armirano betonska konstrukcija smještena u Splitu proračunata je na potresno djelovanje prema HRN EN 1998-1:2011 modalnim proračunom primjenom spektra odaziva. Konstrukcija zidnog sustava proračunata je za razred umjerene duktilnosti (DCM). Provedeni proračun i dimenzioniranje prikazano je za karakteristični zid. Naglasak je stavljen na detaljiranje lokalne duktilnosti zida i odabir armature kritičnog područja zida. Dodatno je proveden proračun i dimenzioniranje karakteristične međukatne ploče, stupa, grede i trakastog temelja. Također je izvršen proračun i ocjena fizikalnih svojstava zgrade u odnosu na racionalnu uporabu energije i toplinsku zaštitu. Rinforced concrete building located in Split was designed to an earthquake action. Calculation was preformed by modal response spectrum analyses all align towards rules of HRN EN 1998-1:2011. The building is wall system and calculation was done for the medium ductility class (DCM). The calculation, design and reinforcement selection was estimated for a caracteristic wall. The budget and the assessment of the physical properties of the building were compared to the rational use of energy and thermal protection.

Armirano betonska konstrukcija smještena u Splitu proračunata je na potresno djelovanje prema HRN EN 1998-1:2011 modalnim proračunom primjenom spektra odziva. Konstrukcija zidnog sustava proračunata je za razred umjerene duktilnosti (DCM) i razred visoke duktilnosti (DCH). Provedeni proračun i dimenzioniranje prikazano je za karakteristični zid. Naglasak je stavljen na detaljiranje lokalne duktilnosti zida i odabir armature kritičnog područja zida. Reinforced concrete building located in Split was designed to an earthquake action. Calculation was preformed by modal response spectrum analyses all align towards rules of HRN EN 1998- 1:2011. The building is wall system and calculation was done for the medium ductility class (DCM) and high ductility class (DCH). The calculation, design and reinforcement selection was estimated for a caracteristic wall. Emphasis is placed on detailing of local ductility and reinforcement selection for critical area of the wall.

Tema završnog rada je proračun zidane konstrukcije poslovne zgrade koja je smještena u Bjelovaru. Potrebno je izraditi proračun nosive konstrukcije zidane zgrade te dokazati mehaničku otpornost i stabilnost konstrukcije u cjelini, kao i nekih tipičnih elemenata. Proračuni se izvode prema Eurocode-a. The topic of this final work is design of masonry construction of a business building located in Bjelovar. It is necessary to draw up calculation of the supporting structure of the masonry building and to prove the mechanical resistance and stability of the structure as a whole, as well as some typical elements. The design is carried out according to Eurocodes.

U ovom diplomskom radu napravljen je numerički model s kojim se analiziraju različita djelovanja na štapne sustave, te se provodi kontrola svih dobivenih rezultata s analitičkim rješenjima i eksperimentalnim rezultatima. In this thesis, a numerical model was developed to analyze different effects on the beam structures, and control of all the results obtained with analytical solutions and experimental results, was performed.

Potrebno je izraditi proračun nosive konstrukcije zidane zgrade. Nosiva konstrukcija predmetne građevine je zidana, omeđena AB serklažima. Međukatne konstrukcije su AB ploče. Proračunom je potrebno dokazati mehaničku otpornost i stabilnost konstrukcije u cjelini, kao i nekih tipičnih elemenata. Građevina se nalazi u VIII potresnoj zoni i I području opterećenja vjetrom. Proračun provesti u svemu prema europskim normama EC1, EC6 i EC8, dopunjeno podacima o opterećenima prema odgovarajućim hrvatskim normama i pravilnicima. It is necessary to make a calculation of the supporting structures of the masonry building. The supporting structure of the building concerned is masonry, recessed with AB cuttings. Intermediate constructions are AB slabs. The calculation must demonstrate the mechanical resistance and stability of the construction as a whole, as well as some typical elements. The building is located in the VIII quake zone and the wind load area. The budget is implemented in all European EC1, EC6 and EC8 norms, supplemented by cargo data according to the relevant Croatian standards and regulations.

Potrebno je izraditi proračun nosive konstrukcije zidane zgrade. Nosiva konstrukcija predmetne građevine je zidana; omeđena AB serklažima. Međukatne konstrukcije su AB ploče. Proračunom je potrebno dokazati mehaničku otpornost i stabilnost konstrukcije u cjelini, kao i nekih tipičnih elemenata. Građevina se nalazi u VIII potresnoj zoni i I području opterećenja vjetrom. Proračun provesti u svemu prema europskim normama EC1, EC6 i EC8, dopunjeno podacima o opterećenima prema odgovarajućim hrvatskim normama i pravilnicima. It is necessary to make a calculation of the supporting structures of the masonry building. The supporting structure of the building concerned is masonry; recessed with AB cuttings. Intermediate constructions are AB slabs. The calculation must demonstrate the mechanical resistance and stability of the construction as a whole, as well as some typical elements. The building is located in the VIII quake zone and the wind load area. The budget is implemented in all European EC1, EC6 and EC8 norms, supplemented by cargo data according to the relevant Croatian standards and regulations.