Dynamic Modification and Damage Propagation of a Two-Storey Full-Scale Masonry Building

The progressive change of modal characteristics due to accumulated damage on an unreinforced masonry (URM) building is investigated. The stone URM building, submitted to five consecutive shakings, has been experimentally studied on the shaking table of EUCENTRE laboratory (Pavia, Italy). The dynamic characteristics of the test specimen are analytically estimated using frequency and state-space modal identification from ambient vibration stationary tests carried out before the strong motion transient tests at various levels of damage. A singular value (SV) decomposition of the cross-correlation matrix of the acceleration response in the frequency domain is applied to determine the modal characteristics. In the time domain, the subspace state-space system identification is performed. Modal characteristics evolve from the initial linear state up to the ultimate collapse state in correlation with accumulated damage. Modal frequencies shorten with increasing intensity, whereas modal damping ratios are enhanced. Modal shapes also change with increasing level of accumulated damage. Comparing the evolution of modal characteristics, it is concluded that modal damping ratio shift can be better correlated with the system's actual performance giving a better representation of damage than that of natural frequency shift ratio or the modes difference

A Note on Gradient/Fractional One-Dimensional Elasticity and Viscoelasticity

An introductory discussion on a (weakly non-local) gradient generalization of some one-dimensional elastic and viscoelastic models, and their fractional extension is provided. Emphasis is placed on the possible implications of micro-and nano-engineering problems, including small-scale structural mechanics and composite materials, as well as collagen biomechanics and nanomaterials

A practice-oriented model for pushover analysis of a class of timber-framed masonry buildings

Timber-Framed (TF) masonry is a structural system characterized by high complexity and diversity. Limited experimental and analytical research has been carried out so far to explore their earthquake response, partly due to the complexity of the problem and partly due to the scarcity of TF buildings across the world. Here, a new practice-oriented non-linear (NL) macro-model is presented for TF masonry structures, based on the familiar diagonal strut approach with NL axial hinges in the struts. The constitutive law for the hinges (axial force vs. axial deformation) is derived on the basis of an extensive parametric analysis of the main factors affecting the response of TF masonry panels subjected to horizontal loading. The parameters studied are related to the geometric features of the panel and the strength of wood as well as the connections of the timber elements. The parametric analysis is performed using a micro-model based on Hill-type plasticity and it is shown that in the studied X-braced walls the masonry infills do not make a significant contribution to the lateral load resistance. Empirical expressions are proposed for the yield and maximum displacement and shear of a horizontally loaded TF panel. The model is verified against available experimental data, and is found to capture well the envelopes of the experimental loops. The model is readily applicable to NL static analysis (pushover) analysis for the assessment of the lateral load capacity of TF masonry buildings, as the number of input parameters for deriving the constitutive law has been limited to only five

Assessment of the seismic behaviour of timber-framed masonry buildings

This doctoral dissertation deals with the non-linear behaviour under seismic loading and the seismic vulnerability of structures made of traditional timber-framed masonry (ΤF). Firstly, the development of a non-linear model able to capture the response of TF masonry structures is implemented. Τimber-framed masonry panels with two diagonal braces are investigated. The simulation is based on an elastoplastic finite element model for wood members using the orthotropic Hill's yield criterion and an associative flow rule. The hardening of the material is considered isotropic. Contact elements have been used to simulate the contact between diagonals and the surrounding frame. Contact is modelled using Mohr-Coulomb's law without cohesion as the bond achieved by the iron elements is unreliable. Masonry infills are not directly included in the model but they contribute to the total response with their weight, in the stability and the hysteretic and the viscous -through sliding- damping, but not to strength. This model is validated against two experimental programmes from the literature; the one is carried out with specimens extracted from a real building and the other with specimens constructed in the laboratory. A very good match is noticed of the non-linear pushover curve of the timber framed walls with the skeleton curves of the tests. This model being highly non-linear as it has two sources of non-linearity (material and geometrical non-linearity), is difficult, if at all feasible, to apply to entire buildings and large structures. Consequently, a simplified approach is proposed, meant for a wide range of applications, which is based on an equivalent diagonal strut with a NL (non-linear) axial point hinge, involving solely beam elements. This simplified approach is developed in two alternative forms; in the first version a proposed set of empirical equations determine the NL law of the plastic hinge. These equations have been derived using an extensive parametric analysis of the main parameters affecting the response of the frame. Nevertheless, when the geometry does not meet the limitations of the previous parametric analyses, or when there are other geometry parameters not having been taken into account, the second version of the simplified approach should be applied. Both simplified models have been validated against the experimental results and the almost bilinear pushover curves match reasonably well the key features of the skeleton monotonic curves of the tests. Using the aforementioned simplified models the NL analysis of three typical buildings of Lefkas (Greece) is carried out. The fundamental characteristic of the Lefkas buildings is their dual structural system. The primary system consists of a stone masonry ground storey, while all upper storeys are made of TF masonry walls. Timber posts in the ground floor a few centimetres apart from the stone masonry form the secondary structural system which is connected to the upper floors. From the NL analysis of the buildings pushover curves are derived and are subsequently converted to capacity curves using the characteristics of the fundamental mode. On this curve four damage states are quantified using quantitative criteria of the response of the structures. According to this definition fragility curves in terms of spectral displacement are generated adopting a log-normal statistical distribution. Then, these fragility curves are expressed in terms of peak ground acceleration using the Eurocode-8 spectrum for high seismicity areas. Using the latter, a pilot scenario of seismic risk for the Lefkas city is developed and compared to the available damage statistics from the 2003 earthquake.Η διδακτορική αυτή διατριβή πραγματεύεται την ανελαστική συμπεριφορά υπό σεισμικά φορτία και την σεισμική τρωτότητα των κτιρίων από ξυλόπηκτη φέρουσα τοιχοποιία (ΞΤ). Κατ’ αρχήν γίνεται η ανάπτυξη ενός ανελαστικού μοντέλου για την ΞΤ. Εξετάζεται ΞΤ τα φατνώματα της οποίας έχουν δύο χιαστί διαγώνιες, για την οποία διατίθεται επαρκής πειραματική τεκμηρίωση. Η προσομοίωση που προτείνεται αποτελείται από ένα ελαστοπλαστικό μοντέλο πεπερασμένων στοιχείων για τα ξύλινα μέλη, που βασίζεται στο ορθότροπο κριτήριο Hill και έχει συσχετισμένο νόμο διαρροής. Η κράτυνση του υλικού θεωρείται ισότροπη. Με στοιχεία επαφής έχει προσομοιωθεί η επαφή των διαγωνίων με το περιβάλλον πλαίσιο. Η επαφή υπακούει στον νόμο Mohr-Coulomb αλλά χωρίς αρχική συνοχή διότι είναι σαφές από τη βιβλιογραφία ότι η σύνδεση των διαγωνίων με το περιβάλλον πλαίσιο είναι αναξιόπιστη. Η παρουσία των τοιχοπληρώσεων είναι έμμεση καθώς στο μεγαλύτερο τμήμα της απόκρισης των τοίχων συμβάλλουν στο βάρος, στην ευστάθεια και στην απόσβεση του συστήματος αλλά όχι στην αντοχή. Το μοντέλο αυτό εξετάσθηκε με δύο σειρές πειραματικών δοκιμίων από τη βιβλιογραφία· η μία σειρά αποτελείται από τρία δοκίμια που ελήφθησαν από πραγματικό κτίριο, ενώ η δεύτερη σειρά από δοκίμια που κατασκευάσθηκαν στο εργαστήριο. Διαπιστώθηκε πολύ καλή σύμπτωση των αναλυτικών με τα πειραματικά αποτελέσματα. Το μοντέλο αυτό είναι έντονα μη-γραμμικό (μη-γραμμικότητα υλικού και γεωμετρίας) και έτσι είναι δύσκολο, αν όχι αδύνατο, να ληφθούν αποτελέσματα για εκτεταμένα κτίρια. Συνεπώς, προτείνεται ένα απλοποιημένο μοντέλο ισοδύναμης διαγωνίου με μία αξονική πλαστική άρθρωση που υλοποιείται με δύο διαφορετικούς τρόπους. Με τον πρώτο τρόπο για την αξονική πλαστική άρθρωση προτείνονται σχέσεις που καθορίζουν τον ανελαστικό νόμο της. Οι σχέσεις αυτές έχουν προκύψει από μία εκτεταμένη παραμετρική ανάλυση και λαμβάνουν υπ' όψιν τους τις βασικές παραμέτρους από τις οποίες επηρεάζεται η απόκριση των φατνωμάτων. Ο δεύτερος τρόπος είναι κατάλληλος για περιπτώσεις όπου θα κριθεί ότι τα φατνώματα δεν εμπίπτουν στους περιορισμούς ή ακριβώς στην γεωμετρία των προηγουμένων σχέσεων. Τα απλοποιημένα αυτά μοντέλα συγκρινόμενα με τα πειραματικά αποτελέσματα δίνουν διγραμμικές καμπύλες απόκρισης με ικανοποιητική προσέγγιση των βασικών μεγεθών. Εφαρμόζοντας το παραπάνω απλοποιημένο μοντέλο γίνεται η ανάλυση τριών τυπικών κτιρίων της Λευκάδας υποθέτοντας ότι αυτά αποτελούνται από φατνώματα ξυλόπηκτης τοιχοποιίας με δύο χιαστί διαγώνιες. Επιπλέον, γίνεται μία διερεύνηση όσον αφορά στην θεμελίωσή τους. Το σημαντικό χαρακτηριστικό των κτιρίων της Λευκάδας είναι ότι αποτελούνται από δύο φέροντα συστήματα. Το κύριο σύστημα αποτελείται από λιθοδομή στο ισόγειο και ΞΤ στους ορόφους, ενώ το δευτερεύον σύστημα στο ισόγειο έχει ξύλινα υποστυλώματα και συνδέεται με την ΞΤ των ορόφων. Από την ανάλυση προκύπτουν οι καμπύλες αντιστάσεως των κτιρίων, οι οποίες μετατρέπονται σε καμπύλες αντιστάσεως του ισοδυνάμου μονοβαθμίου ταλαντωτή. Στην συνέχεια γίνεται ορισμός των σταθμών βλάβης, οι οποίες είναι τέσσερις πέραν της στάθμης χωρίς βλάβες, ώστε να συνδεθούν με όσο το δυνατόν αντικειμενικά κριτήρια της απόκρισης των κατασκευών. Βάσει αυτών των ορισμών εξάγονται καμπύλες τρωτότητας ως προς την φασματική μετακίνηση και στην συνέχεια μετατρέπονται βάσει του φάσματος του Ευρωκώδικα σε καμπύλες τρωτότητας βάσει της μέγιστης εδαφικής επιταχύνσεως. Με αυτές τις τελευταίες αναπτύσσεται ένα πιλοτικό σενάριο σεισμικής διακινδυνεύσεως των ξυλοπήκτων κτιρίων της Λευκάδας και συγκρίνεται με τα διαθέσιμα στατιστικά δεδομένα βλαβών του σεισμού του 2003

A gradient elastic homogenisation model for brick masonry

The elastic macro-mechanical properties of masonry are investigated herein by taking into account the presence of a weakly non-local heterogeneity, within a simple gradient elasticity model. Masonry has a heterogeneous structure composed of masonry units bound by mortar. The homogenisation of masonry walls is a challenging task but also a very appealing method for modelling heterogeneity effects exhibited by masonry elements. In particular, it allows the use of smeared mechanical properties, thus avoiding the need of knowing the exact unit-to-unit and joint-to-joint geometry. Current codes provide very simplified empirical expressions to estimate an isotropic elastic modulus of masonry on the basis of its strength properties. The respective equations which do not take into account the anisotropy of masonry, present high scatter resulting in ambiguous safety. The homogenization argument employed in this work is based on a simple procedure utilising Aifantis gradient elasticity (GradEla) model. The GradEla model is a straight-forward extension of Hooke’s law by enhancing it with the addition of the Laplacian of the classical expression of the Hookean stress multiplied by an internal length accounting for the local heterogeneity. It has been successfully used to eliminate singularities from dislocation lines and crack tips, as well as in interpreting size effects. However its use in masonry structures has not yet been explored. A first step in this direction is attempted in this paper with emphasis on obtaining practical easy-to-use results rather than exhausting all other possibilities and complexities encountered in GradEla and its generalisation as well as in more involved homogenisation procedures. In our analysis uniform vertical, horizontal and shear loads are assumed to act on the boundaries of the representative volume/surface element. The components of masonry are assumed to follow a gradient elastic stress distribution resulting in a gradient elastic homogenised model (GREHM). GREHM comprises a set of closed-form concise equations which estimate the elastic moduli in the longitudinal and transverse directions, the shear modulus and the Poisson’s ratio. The aforementioned orthotropic material properties are verified using experimental results and also, compared to other homogenisation models. The validation shows that the proposed equations can effectively estimate with considerable precision the elastic properties of masonry walls. To illustrate the resulting estimation of the orthotropic elastic properties, normalised graphs are provided.JRC.E.4-Safety and Security of Building

A Note on Gradient/Fractional One-Dimensional Elasticity and Viscoelasticity

An introductory discussion on a (weakly non-local) gradient generalization of some one-dimensional elastic and viscoelastic models, and their fractional extension is provided. Emphasis is placed on the possible implications of micro- and nano- engineering problems, including small-scale structural mechanics and composite materials, as well as collagen biomechanics and nanomaterials