Dynamic properties of cable-stayed system

It is well known that non-linear vibrations of long span cables present a considerable problem of lightweight structures like suspended roofs, cable stayed bridges and cable stayed masts. In the analysis of global structural behaviour, cables are often modelled as equivalent tendon elements. The importance of modelling coupled cable-structure dynamics has been demonstrated by a number of researchers. Dynamic response of non-linear systems can lead to internal or auto-parametric resonance in the case of integer frequency ratio. The analysis of cable-stayed system frequency spectra can show parameter values for which integer frequency ratio condition is fulfilled. In this paper an analytic model of simplified cable-stayed system is formulated. Parabolic cable is modelled using the assumption of quasi-static stretching, while the structure is modelled as Euler-Bernoulli beam. Equations of motions are derived by Hamilton’s principle and then linearized around a static equilibrium configuration. Differential equations of motion are solved by the method of variable separation. System deformation is described using analytical functions. Equations of motions together with boundary conditions are solved in closed form to obtain a characteristic equation. For chosen system parameters, the eigenvalue spectra are determined. Parametric analysis of dynamical properties is carried out and integer frequency ratios along with the associated modes are pointed out. Analytic solutions are verified with finite element modelling

Cable oscillations due indirect excitation

U radu je formuliran analitički model oscilacija kabela za nehomogene rubne uvjete pri čemu su uzete u obzir kvadratne i kubne nelinearnosti sustava. Oblikovan je reducirani sustav koji je riješen numeričkom integracijom, te za slučaj prisilnih i parametarskih oscilacija perturbacijskom metodom višestrukih skala. Dobivena rješenja uspoređena su s rješenjima numeričkog modela pri čemu je korištena metoda konačnih diferencija i algoritam prediktor-korektor za vremensku integraciju sustava jednadžbi.An analytical cable oscillation model is formulated for inhomogeneous boundary conditions taking into account quadratic and cubic nonlinearities of the system. The reduced system is solved by numerical integration and, for the case of external and parametric oscillations, by the multiple scales perturbation method. The comparison of solutions with numerical model results is based on the finite difference model and the predictor-corrector algorithm for time integration of equation systems

Post-earthquake damage assessment of buildings – procedure for conducting building inspections

Procjene oštećenja i uporabljivosti građevina u Hrvatskoj, iskočile su u prvi plan nakon potresa u Zagrebu 22. ožujka 2020. S obzirom na manjkavosti pripremne faze, pri čemu nije provedena edukacija stručnjaka prije potresa, nego u hodu, procjene su sadržavale dozu subjektivnosti i interpretacije na temelju znanja, iskustva, ali i intuicije pojedinaca. U radu je detaljno prikazana metodologija koja može pomoći u brzim procjenama te kod detaljnih inženjerskih pregleda koji se moraju napraviti prije obnove. Prikazana metodologija se može iskoristiti u slučaju novoga razornog potresa koji se može dogoditi već sutra.Assessments of building damage and usability were of primary importance after the Zagreb earthquake of 22 March 2020. Due to deficiencies of preparatory phase, where education of experts was not carried out before the earthquake, but later on, the assessments contained certain subjectivity and interpretations, based on knowledge and experience, but also on intuition of individuals. Detailed methodology, which should improve rapid assessments and detailed engineering inspections to be performed before reconstruction, is highlighted in the paper. This methodology may be utilized if another devastating earthquake occurs, which could happen already tomorrow

Zagreb earthquake of 22 March 2020 – preliminary report on seismologic aspects and damage to buildings

U radu su opisane bitne značajke i glavne posljedice potresa magnitude 5,5 koji je u jeku pandemije virusa COVID-19 zadesio Zagreb i okolicu. Premda je potres, seizmološki gledano, bio umjerene magnitude, prouzročio je gubitak jednoga života i veliku materijalnu štetu. Napravljen je pregled stanja prije trešnje te prikaz lokacije, seizmičke aktivnosti i organizacije pregleda zgrada. Grubo su razvrstani podaci o oštećenjima, s težištem na povijesnoj jezgri i četvrtima blizu epicentra. Na kraju su istaknute nužne aktivnosti koje je odavno trebalo provesti, s nadom da će ih ovaj potres potaknuti.Significant characteristics and main consequences of the 5.5 magnitude earthquake that struck Zagreb and its surroundings in the midst of the COVID-19 pandemic are presented in the paper. Although, from the seismologic aspect, the earthquake was of moderate magnitude, it caused the loss of one life and considerable material damage. An overview of the situation before the quake is given, and information about the location, seismic activity, and organisation of building inspection activity, is presented. The data on damage are roughly classified, with the focus on historic core of the city and districts situated close to the epicentre. A strong emphasis is placed on indispensable activities that should have been carried out a long time ago, in the hope that they will be prompted by this earthquake

Seismic Retrofitting of Dual Structural Systems—A Case Study of an Educational Building in Croatia

On 29 December 2020, a devastating Mw6.4 earthquake struck near the town of Petrinja, Croatia. The main earthquake was preceded by a Mw4.9 foreshock the day before. The earthquakes caused extensive damage to buildings, especially historic buildings made of unreinforced masonry but also to buildings of other typologies and to critical infrastructure. Today, recovery efforts in Croatia focus primarily on reconstruction and seismic retrofitting. Family homes and public, cultural, educational, and other facilities are top priorities. In this paper, a comprehensive study of existing building in the educational sector is presented as a case study. The seismic performance of the building is evaluated using numerical methods, first for the as-built condition and then for the retrofitted building. For each condition, the collapse mechanisms of the building were determined and critical structural elements were identified. The presented retrofit strategy of the dual structural system consisting of RC frame system and masonry walls aims to reduce the displacements of the RC frame system to a level sufficient to prevent the early brittle failure of the concrete. Additionally, the discrepancies when using different modelling approaches are discussed

Damage Evaluation and Seismic Assessment of a Typical Historical Unreinforced Masonry Building in the Zagreb 2020 Earthquake: A Case Study—Part I

The city of Zagreb, the national capital and economic hub of Croatia, is situated in a seismically active region and hosts a significant array of historical buildings, from the medieval to Austro-Hungarian periods. These buildings possess varying but generally high degrees of vulnerability to seismic loading. This was highlighted in the Zagreb earthquake of 22 March 2020, emphasizing the need for seismic retrofitting in order to preserve this architectural heritage. In this paper, the seismic capacity of one such unreinforced masonry building is considered through a number of analysis methods, including response spectrum, pushover, and out-of-plane wall failure analyses. Given the advantages and disadvantages of the individual methods, their applicability and value in a seismic analysis is considered. Ambient vibration measurements before and after the Zagreb 2020 earthquake, used for model calibration, are also presented. Conclusions are drawn from each individual analysis and later compared. In conclusion, no single analysis method considers all relevant failure modes, and a combination of nonlinear static or dynamic analysis and out-of-plane analysis is recommended. Due to the large volume of the material, it is published in two parts, with ground motion record selection, dynamic analysis, and a comparison of the results published in part two