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CONTENTS
Volume 80, Number 4, November25 2021
 


Abstract
This paper presents a theoretical study of the free vibration of functionally graded beam which has variable material properties along its length and thickness. These properties are also assumed to be temperature-dependent. The beam is supposed to be simply supported and resting on several kinds of foundations. The governing equations are found analytically using a quasi-3D model that contains undetermined integral forms and involves few unknowns to derive. Navier's method is employed to determine and compute the vibration characteristics of bidirectional functionally graded (BDFG) beam on foundation. The accuracy of the present method for BDFG beam with temperature-dependency has been validated. Then the effects of the grading indexes, geometrical properties, temperature-dependent material properties, type of foundations and other parameters on the free vibration of BDFG beam are analyzed and discussed via a detailed parametric study.

Key Words
bidirectional functionally graded beams; different foundation; quasi-3D model; temperature-dependent materials

Address
Ismail Benaberrahmane: Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Algeria
Mohamed Mekerbi: Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Algeria; Department of Civil Engineering, University of Ferhat Abbas Sétif 1, Algeria
Rabbab Bachir Bouiadjra: Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Algeria; Department of Civil Engineering, University Mustapha Stambouli of Mascara, Algeria
Samir Benyoucef: Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Algeria
Mahmoud M. Selim: Department of Mathematics, Al-Aflaj College of Science and Humanities, Prince Sattam bin Abdulaziz University, Al-Aflaj 710-11912, Saudi Arabia
Abdelouahed Tounsi: Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Algeria; YFL (Yonsei Frontier Lab), Yonsei University, Seoul, Korea; Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals,
31261 Dhahran, Eastern Province, Saudi Arabia
Muzamal Hussain: Department of Mathematics, Govt. College University Faisalabad, 38000, Faisalabad, Pakistan

Abstract
A slender steel pedestrian bridge suffers from excessive vibration under walking-induced excitations, which include vertical and lateral dynamic loads. Meanwhile, a slender footbridge may also be sensitive to the wind excitation. Excessive vibration will not only cause a serviceability problem, but also even a safety problem. Tuned mass dampers (TMDs) have been applied in slender steel bridges widely for vibration control. However, a passive TMD is sensitive to the frequency deviation. Though a semi-active TMD (STMD) can improve the control effect of a passive TMD to a great degree, there is no STMD and related research that can simultaneously control vertical and lateral walking and wind-induced vibrations of pedestrian bridges. To fill this blank, in this paper, a two-dimensional air spring based STMD (TDAS-STMD) is proposed. The TDAS-STMD is connected to the bridge through two vertical air springs and two lateral air springs, and the stiffness of each air spring can be retuned through adjusting its air pressure by an air pump. At the same time, the damping of TDAS-STMD can be adjusted in real time through changing the air gap between the conductor plate and permanent magnets by a step putter. The mechanical detail of TDAS-STMD and the combined variable stiffness and damping control algorithm are introduced firstly. Then, a simply supported steel footbridge which is sensitive to both vertical and lateral walking and wind-induced excitations is proposed as a case study. In the numerical simulation, the bridge is simplified as a Euler-Bernoulli beam with a constant section. A group of two optimized passive TMDs which implemented in vertical and lateral directions respectively are presented for comparison. Single pedestrian walking-induced vertical and lateral vibration, wind-induced lateral vibration, and a low-density random crowd-induced vertical and lateral vibration coupled with the wind-induced lateral vibration are both considered in the case study. Numerical results indicate that the TDAS-STMD can control vertical and lateral vibrations of the beam effectively and always has the best performance.

Key Words
air spring; semi-active control; steel footbridge; tuned mass damper; walking-induced vibration; windinduced vibration

Address
Yang Wang: School of Economics and Management, Shanghai University of Electric Power, Shanghai, 200090, P.R. China
Liangkun Wang, Weixing Shi: Department of Disaster Mitigation for Structures, Tongji University, Shanghai, 200092, P.R. China

Abstract
There are many mode shape damage localization methods but a few of them assess damage severity. In this paper a crack size prediction method using damaged beam mode shape is presented. The beam damaged sections are modelled by massless rotational springs, whose constants are calculated by the first and the second derivate of the mode shape using numerical differentiation. The method utilizes the relationship between the rotational spring constant and the size of an open single-sided crack with uniform depth in a rectangular cross section beam. The predicted crack depths are compared with the actual data from finite element models. The results obtained demonstrate that the proposed method correctly predicts the crack size in beam structures with single or multiple damages.

Key Words
cantilever beam; crack depth; mode shape; open single-sided crack; rectangular cross-section; rotational spring; simply supported beam

Address
Dimitrina D. Kindova-Petrova: Department of Technical Mechanics, University of Architecture, Civil Engineering and Geodesy, 1 Hristo Smirnenski Blvd, Sofia 1164, Bulgaria

Abstract
This paper presents quasi-static cyclic loading tests of reduced scale reinforced concrete Eccentrically Steel Brace (ESB) retrofitted and bare portal frames. A hollow square steel brace was attached to the beam diagonally at a distance of LBeam/8 from the beam ends for enhancing the seismic performance of deficient frames. Results indicated promising behavior of ESB retrofitted frame opposed to the bare frames and shifted the damage mechanism from severe shear cracking and column flexural hinging to beam flexural cracking. ESB retrofitted frame also increased lateral force-displacement capacity, stiffness and hysteretic damping compared to the bare frames. The test results were also used to calibrate a nonlinear modeling technique proposed using a finite element based program. Additionally, a nonlinear dynamic acceleration time history analysis were carried out for two-story ESB retrofitted and bare frames and inter-story drift limits were identified for each structure. The study also confirms the importance of joint detailing's and its beneficial role in improving the seismic performance of frames under earthquake ground motions.

Key Words
beam-column joint; cyclic loading test; nonlinear modeling; RC frames; seismic retrofitting; steel braces

Address
Abdul Basit, Muhammad S. Khan and Naveed Ahmad: Department of Civil Engineering, University of Engineering & Technology Peshawar, 25120, Khyber Pakhtunkhwa, Pakistan

Abstract
This research work presents a comparison of the dynamic response of the functionally graded sandwich cylindrical shell panels (FGSCS) using a new layerwise method. The layerwise method developed assumes a first-order shear deformation theory (FSDT) for top and bottom facesheets and a third-order shear deformation theory for the core. The strain-displacement relation for FGSCS panels is obtained using Sander's first approximation. Two different sandwich configurations are considered, one having a pure metallic core with top and bottom facesheets made of functionally graded material (FGM) and the other one having an FGM core with top and bottom facesheets made of pure ceramic and pure metal, respectively. Material properties of the FGM layers for the two configurations are varied along the thickness direction according to the power-law (P-FGM) and the sigmoid models (S-FGM) respectively. The newly developed layerwise finite element model in conjunction with Hamilton's principle is employed to obtain the governing differential equation. Subsequently, the Newmark-Beta time integration scheme is used to obtain the dynamic response of P and S functionally graded sandwich cylindrical shell (P and S-FGSCS) panels for two configurations. The results obtained are first compared with the exact analytical results available in the literature. Numerical results are presented to investigate the effect of volume fraction index, loading conditions, core-to-facesheet thickness ratio, curvature ratio and boundary conditions on the transient response of P and S-FGSCS panels. The analysis reveals by selecting optimum parameters and gradation model, the amplitude and frequency of dynamic response of P and S-FGSCS panels can be controlled substantially.

Key Words
dynamic analysis; finite element method; layerwise method; power law; sandwich shell panel; sigmoid model

Address
Abhilash Karakoti, Shashank Pandey and Vishesh Ranjan Kar: Department of Mechanical Engineering, National Institute of Technology Jamshedpur, Jamshedpur 831014, India

Abstract
Prefabricated steel connections are one of the innovations in the area of prefabricated steel frames that have been proposed by many researchers. In beam-to-column rigid connections, joining a beam with different angles to the column is difficult so that connecting more than four beams to the box column becomes impossible. In this study, a prefabricated steel rigid connection is proposed that allows to connect beams in a rigid form with any angle to columns using a through plate panel zone system. To this aim, several analyses were performed on the proposed connection using ABAQUS. To verify the finite element (FE) results, firstly, a prefabricated steel connection was modeled in ABAQUS and the results were then compared with the experimental model. Design formulations were also presented and validated by comparing them with finite element modeling. Afterward, the effect of different connecting angles and the number of connected beams were investigated under monotonic and cyclic loading. The results indicated that all models were able to withstand 0.04 rotation without undergoing a significant decrease in the resisting moment which demonstrates the high ductility of this connection.

Key Words
ABAQUS; HSS column; modular prefabricated steel moment connection; monotonic and cyclic loading; through-plate panel zone system (TPPZ)

Address
Hadi Askarian, Mohammad Reza Sohrabi: Civil Engineering Department, University of Sistan and Baluchestan, Zahedan, Iran
Seyed Morteza Kazemi: Department of Civil Engineering, Kashmar Branch, Islamic Azad University, Kashmar, Iran

Abstract
This study proposes an enhanced single-degree-of-freedom (SDOF) system for a two-way all-fixed reinforced concrete (RC) slab. Thus, this study aims to improve the performance of the conventional SDOF system to the level of finite element (FE) analysis. The conventional SDOF system makes incorrect prediction about structural dynamic deflections when a damage occurs during SDOF analysis, because a resistance of the conventional SDOF system cannot reflect stiffness and strength degradation due to damages. In other words, the conventional SDOF model utilizes the inelastic model regardless of its damage occurrence, as the hysterical model. Therefore, it is essential to enhance the SDOF system to minimize the errors. To this end, this study newly utilizes a Modified Plastic-Damage Hysteretic Model (MPDHM) as a resistance function of the SDOF system. Since the MPDHM can reflect stiffness and strength degradation due to damages, the enhanced SDOF system can conduct more reliable predictions than the conventional SDOF system. In order to apply the MPDHM in the SDOF system, its parameter estimation should be preferentially performed based on a number of reference data. For this reason, a series of FE analyses are carried out utilizing commercial S/W (i.e., AUTODYN). The performance of the enhanced SDOF system is numerically validated about a two-way all-fixed RC slab under the different stand-off distances with an identical explosive weight.

Key Words
AUTODYN; modified plastic-damage hysteretic model; numerical simulation; SDOF system blast loads

Address
Seung-Hun Sung and Haein Lee: Agency for Defense Development, P.O. Box 35, Yuseong-gu, DaeJeon, 34186, Korea

Abstract
For the first time, the finite Fourier integral transform approach is extended to analytically solve the free vibration problem of rectangular thin plates with two adjacent edges rotationally-restrained and others free. Based on the fundamental transform theory, the governing partial differential equations (PDEs) of the plate is converted to ordinary linear algebraic simultaneous equations without assuming trial function for deflection, which reduces the mathematical complexity caused by both the free corner and rotationally-restrained edges. By coupling with mathematical manipulation, the analytical solutions are elegantly achieved in a straightforward procedure. In addition, the vibration characteristics of plates under classical boundary conditions are also studied by choosing different rotating fixed coefficients. Finally, more than 400 comprehensive analytical solutions were well validated by finite element method (FEM) results, which can be served as reference data for further studies. The advantages of the present method are that it does not need to preselect the deformation function, and it has general applicability to various boundary conditions. The presented approach is promising to be further extended to solve the static and dynamic problems of moderately thick plates and thick plates.

Key Words
finite Fourier integral transform method; free edges; free vibration; rotationally-restrained edges; thin rectangular plate

Address
Jinghui Zhang: Key Laboratory of Green Construction and Intelligent Maintenance for Civil Engineering of Hebei Province, Yanshan University, Qinhuangdao 066004, China; Hebei Province Low-Carbon and Clean Building Heating Technology Innovation Center, Yanshan University, Qinhuangdao 066004, China
Jiale Lu: Faculty of Infrastructure Engineering, Dalian University of Technology, Dalian 116024, China
Salamat Ullah: Department of Civil Engineering, Abasyn University, Islamabad, 44000, Pakistan
Yuanyuan Gao: Key Laboratory of Green Construction and Intelligent Maintenance for Civil Engineering of Hebei Province, Yanshan University, Qinhuangdao 066004, China
Dahai Zhao: Key Laboratory of Green Construction and Intelligent Maintenance for Civil Engineering of Hebei Province, Yanshan University, Qinhuangdao 066004, China
Arshad Jamal: Department of Civil and Envirnmental Engineering, King Fahd University of Petroleum and Minerals,
KFUPM Box 5055, Dhahran, 31261, Saudi Arabia
Ömer Civalek: Research Center for Interneural Computing, China Medical University, Taichung, Taiwan

Abstract
Although it is well known that masonry walls are vulnerable to seismic loadings, they are still widely deployed for dwellings in many countries. Therefore, research on masonry walls has been extensively conducted. However, compared to studies on reinforced concrete or steel structures, research on masonry walls is still insufficient. Thus, in this study, the seismic performances of unreinforced unconfined and confined masonry walls were appraised experimentally. The large-scale confined masonry (CM) wall with toothed tie columns demonstrated 82.7% higher load-carrying capacity and 178.7% larger total dissipated energy than the unconfined masonry (UM) wall. In addition, numerical models for both UM and CM walls were developed using a discrete-finite element modelling (DFEM) with the use of a fracture-energy based interfacial tractionseparation law that was developed employing the user-subroutine VUINTERACTION of ABAQUS. The numerical results were in good agreement with the test results with respect to hysteresis loops and overall behavior, especially rocking behavior of the UM wall. Using the developed numerical models, the effects of the wall-base friction on hysteresis behaviors of UM and CM walls were investigated as a parametric study. The developed numerical models can be deployed for various studies on the seismic performances of UM and CM walls.

Key Words
confinement; discrete-finite element modelling; masonry walls; rocking; toothed tie column

Address
Young-Chan You: Department of Living and Built Environment Research, Korea Institute of Civil Engineering and Building Technology, Gyeonggi-Do, South Korea
Dongkeun Lee: Department of Civil and Environmental Engineering, Southern University and A&M College, Baton Rouge, Louisiana, USA
Terry Y.P. Yuen, Yi-Tso Chou, Trissa Deb: Department of Civil Engineering, National Yang Ming Chiao Tung University, Hsinchu, Taiwan ROC; Department of Civil Engineering, National Chiao Tung University, Hsinchu, Taiwan ROC

Abstract
In this paper, we propose three practical methods for directly evaluating stability in a local structural part of a large structure (local structure). The local stability is assessed by investigating global external load, local internal force, local strain energy, and local displacement, all calculated through nonlinear finite element (FE) analysis. A great advantage of the proposed methods is that they do not require local finite element analysis of the target local part and are applicable to arbitrarily-shaped local parts of a global structure. In addition, unlike previously developed methods, the proposed methods fully consider complicated interactions between local and global structures. The three evaluation methodologies are presented, and their practical effectiveness is demonstrated through several numerical examples.

Key Words
buckling; local stability; nonlinear finite element analysis; resistance capacity; strain energy variation

Address
Min-Han Oh: Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, 291 Daehak-ro, Yuseong-gu, Daejeon 34141, Republic of Korea; Load and Response Research Department, Hyundai Heavy Industries, 75 Yulgok-ro, Jongno-gu, Seoul 03058, Republic of Korea
Hyo-Jin Kim, Kyungho Yoon: Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, 291 Daehak-ro, Yuseong-gu, Daejeon 34141, Republic of Korea; Load and Response Research Department, Hyundai Heavy Industries, 75 Yulgok-ro, Jongno-gu, Seoul 03058, Republic of Korea
Phill-Seung Lee: Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, 291 Daehak-ro, Yuseong-gu, Daejeon 34141, Republic of Korea


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