• Structural Engineering and Mechanics
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• v.69 no.2
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• pp.155-162
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• 2019

It is very common to find an empirical formulation in an earthquake design code to calculate fundamental vibration period of a structural system. Fundamental vibration period or frequency is a key parameter to provide adequate information pertinent to dynamic characteristics and performance assessment of a structure. This parameter enables to assess seismic demand of a structure. It is possible to find an empirical formulation related to reinforced concrete structures, masonry towers and slender masonry structures. Calculated natural vibration frequencies suggested by empirical formulation in the literatures has not suits in a high accuracy to the case of rest of the historical masonry bridges due to different construction techniques and wide variety of material properties. For the listed reasons, estimation of fundamental frequency gets harder. This paper aims to present an empirical formulation through Mean Square Error study to find ambient vibration frequency of historical masonry bridges by using a non-linear regression model. For this purpose, a series of data collected from literature especially focused on the finite element models of historical masonry bridges modelled in a full scale to get first global natural frequency, unit weight and elasticity modulus of used dominant material based on homogenization approach, length, height and width of the masonry bridge and main span length were considered to predict natural vibration frequency. An empirical formulation is proposed with 81% accuracy. Also, this study draw attention that this accuracy decreases to 35%, if the modulus of elasticity and unit weight are ignored.

• Earthquakes and Structures
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• v.10 no.2
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• pp.483-494
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• 2016

Historical structures that function as a bridge from past to present are the cultural and social reflections of societies. Masonry bridges are one of the important historical structures. These bridges are vulnerable against to seismic action. In this study, linear and non-linear dynamic analyses of historical Nadir Bridge are assessed. The bridge is modelled with three dimensional finite elements. For the seismic effect, artificial acceleration records are generated considering the seismic characteristics of the region where the bridge is located. Seismic response of the bridge is investigated.

• Geomechanics and Engineering
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• v.31 no.1
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• pp.31-52
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• 2022

Investigating and evaluating the long-term creep behavior of historical buildings built on seismic zones is of great importance in terms of transferring these structures to future generations. Furthermore, assessing the earthquake behavior of historical structures such as masonry stone bridges is very important for the future and seismic safety of these structures. For this reason, in this study, earthquake analyses of a masonry stone bridge are carried out considering strong ground motions and various water levels. Tokatli masonry stone arch bridge that was built in the 10th century in Turkey-Karabük is selected for three-dimensional (3D) finite difference analyses and this bridge is modeled using FLAC3D software based on the three-dimensional finite difference method. Firstly, each stone element of the bridge is modeled separately and special stiffness parameters are defined between each stone element. Thanks to these parameters, the interaction conditions between each stone element are provided. Then, the Burger-Creep and Drucker-Prager material models are defined to arch material, rockfill material for evaluating the creep and seismic failure behaviors of the bridge. Besides, the boundaries of the 3D model of the bridge are modeled by considering the free-field and quiet boundary conditions, which were not considered in the past for the seismic behavior of masonry bridges. The bridge is analyzed for 6 different water levels and these water levels are 0 m, 30 m, 60 m, 70 m, 80 m, and 90 m, respectively. A total of 10 different seismic analyzes are performed and according to the seismic analysis results, it is concluded that historical stone bridges exhibit different seismic behaviors under different water levels. Moreover, it is openly seen that the water level is of great importance in terms of earthquake safety of historical stone bridges built in earthquake zones. For this reason, it is strongly recommended to consider the water levels while strengthening and analyzing the historical stone bridges.

• Geomechanics and Engineering
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• v.18 no.2
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• pp.141-151
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• 2019

In this paper, it is aimed to present a detail investigation about the comparison of static and dynamic behavior of historical masonry arch bridges considering different arch curvature. $G{\ddot{o}}derni$ historical masonry two-span arch bridge which is located in Kulp town, Diyarbakir, Turkey is selected as a numerical application. The bridge takes part in bowless bridge group and built in large measures than the others. The restoration projects were approved and rehabilitation studies have still continued. Finite element model of the bridge is constituted with special software to determine the static and dynamic behavior. To demonstrate the arch curvature effect, the finite element model are reconstructed considering different arch curvature between 2.86 m-3.76 m for first arch and 2.64 m-3.54 m for second arch with the increment of 0.10 m, respectively. Dead and live vehicle loads are taken into account during static analyses. 1999 Kocaeli earthquake ground motion record is considered for time history analyses. The maximum displacements, principal stresses and elastic strains are compared with each other using contour diagrams. It is seen that the arch curvature has more influence on the structural response of historical masonry arch bridges. At the end of the study, it is seen that with the increasing of the arch heights, the maximum displacements, minimum principal stresses and minimum elastic strains have a decreasing trend in all analyses, in addition maximum principal stresses and maximum elastic strains have unchanging trend up to optimum geometry.

• Earthquakes and Structures
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• v.18 no.1
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• pp.83-96
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• 2020

The main structural elements of historical masonry arch bridges are arches, spandrel walls, piers and foundations. The most vulnerable structural elements of masonry arch bridges under transverse seismic loads, particularly in the case of out-of-plane actions, are spandrel wall. The vulnerability of spandrel walls under transverse loads increases with the increasing of their length and height. This paper computationally investigates the out-of-plane nonlinear seismic response of spandrel walls of long-span and high masonry stone arch bridges. The Malabadi Bridge with a main arch span of 40.86m and rise of 23.45m built in 1147 in Diyarbakır, Turkey, is selected as an example. The Concrete Damage Plasticity (CDP) material model adjusted to masonry structures, and cohesive interface interaction between the infill and the spandrel walls and the arch are considered in the 3D finite element model of the selected bridge. Firstly, mode shapes with and without cohesive interfaces are evaluated, and then out-of-plane seismic failure responses of the spandrel walls with and without the cohesive interfaces are determined and compared with respect to the displacements, strains and stresses.

• Structural Engineering and Mechanics
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• v.53 no.5
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• pp.897-919
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• 2015

In this study, the effects of ground shocks due to explosive loads on the dynamic response of historical masonry bridges are investigated by using the multi-point shock response spectrum method. With this purpose, different charge weights and distances from the charge center are considered for the analyses of a masonry bridge and depending on these parameters frequency-varying shock spectra are determined and applied to each support of the two-span masonry bridge. The net blast induced ground motion consists of air-induced and direct-induced ground motions. Acceleration time histories of blast induced ground motions are obtained depending on a deterministic shape function and a stationary process. Shock response spectrums determined from the ground shock time histories are simulated using BlastGM software. The results obtained from uniform and multi-point response spectrum analyses cases show that significant differences take place between the uniform and multi-point blast-induced ground motions.

• Smart Structures and Systems
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• v.16 no.6
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• pp.1069-1089
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• 2015

Arch bridges consist of some important components for structural behavior such as arches, sidewalls, filling materials and foundations. But, arches are the most important part for this type of bridges. For this reason, investigation of arch is come into prominence. In this paper, it is aimed to investigate the arch thickness effect on the structural behavior of masonry arch bridges. For this purpose, Goderni historical arch bridge which was located in Kulp town, Diyarbakir, Turkey and the bridge restoration process has still continued is selected as an application. The construction year of the bridge is not fully known, but the date is estimated to be the second half of the 19th century. The bridge has two arches with the 0.52 cm and 0.69 cm arch thickness, respectively. Finite element model of the bridge is constructed with ANSYS software to reflect the current situation using relievo drawings. Then the arch thickness is changed by increasing and decreasing respectively and finite element models are reconstructed. The structural responses of the bridge are obtained for all arch thickness under dead load and live load. Maximum displacements, maximum-minimum principal stresses and maximum-minimum elastic strains are given with detail using contours diagrams and compared with each other to determine the arch thickness effect. At the end of the study, it is seen that the maximum displacements, tensile stresses and strains have a decreasing trend, but compressive stress and strain have an increasing trend by the increasing of arch thickness.

• Structural Engineering and Mechanics
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• v.62 no.5
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• pp.643-649
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• 2017

Masonry walls are amongst the oldest building systems. A large portion of the research on these structures focuses on the load-bearing walls. Numerical methods have been generally used in modelling load-bearing walls during recent years. In this context, macro and micro modelling techniques emerge as widely accepted techniques. Micro modelling is used to investigate the local behaviour of load-bearing walls in detail whereas macro modelling is used to investigate the general behaviour of masonry buildings. The main objective of this study is to investigate the elastic behaviour of the load- bearing walls in masonry buildings by using micro modelling technique. In order to do this the brick and mortar units of the masonry walls are modelled by the combination of plane truss elements and plane frame elements with no shear deformations. The model used in this study has fewer unknowns then the models encountered in the references. In this study the vertical frame elements have equivalent elasticity modulus and moment of inertia which are calculated by the developed software. Under in-plane static loads the elastic displacements of the masonry walls, which are encountered in literature, are calculated by the developed software, where brick units are modelled by plane frame elements, horizontal joints are modelled by vertical frame elements and vertical joints are modelled by horizontal plane truss elements. The calculated results are compatible with those given in the references.