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CONTENTS
Volume 25, Number 3, March 2020
 

Abstract
In the study, a new, simple and alternative formula is proposed to calculate numerically crack widths of concrete on a finite element (FE) model. By considering more general tension softening behavior of concrete, the proposed expression is derived irrespective of any tension softening model given in the literature or design codes. The test results of six reinforced concrete (RC) deep beams having different geometrical and material properties selected from a recent existing experimental study of the authors are used to verify the accuracy and reliability of the proposed formula and the created numerical FE models of the specimens. Moreover, the crack width results obtained from the FE models are compared with the test results to see the performance of the proposed formula. The results of the study demonstrate that the proposed formula gives very accurate results in a comparison with the test results. The ratios of errors on the results stay commonly at an acceptable level as well. Consequently, the proposed formula is quite simple, unique, and robust to determine crack widths of RC deep beams on an FE model.

Key Words
crack width formula; numerical determination of crack width; tension softening; concrete damage plasticity; reinforced concrete deep beam

Address
Aydin Demir and Naci Caglar: Department of Civil Engineering, Faculty of Engineering, Sakarya University, Esentepe Campus, 54050 Serdivan, Sakarya, Republic of Turkey

Abstract
Cytoskeleton components in living cell bear large compressive force and are responsible in maintaining the cell shape. Actually these filaments are surrounded by viscoelastic media within the cell. This surrounding, viscoelastic media affects the buckling behavior of these filaments when external force is applied on these filaments by exerting continuous pressure in opposite directions to the incipient buckling of the filaments. In this article a mechanical model is applied to account the effects of this media on the buckling behavior of intermediate filaments network of cytoskeleton. The model immeasurably associates; filament\'s bending rigidity, adjacent system elasticity, and cytosol viscosity with buckling wavelength, buckling growth rate and buckling amplitude of the filaments.

Key Words
intermediate filaments; viscous cytosol; Euler beam theory

Address
Muhammad Taj: Department of Mathematics, The University of Azad Jammu and Kashmir, Muzaffarabad 13100, Pakistan
Muhammad Safeer: Department of Mathematics, The University of Azad Jammu and Kashmir, Muzaffarabad 13100, Pakistan; 2Department of Mathematics University of Poonch, Rawalwkot 12350, Azad Kashmir, Pakistan
Muzamal Hussain: Department of Mathematics, Govt. College University Faisalabad, 38000, Faisalabad, Pakistan
Muhammad N. Naeem: Department of Mathematics, Govt. College University Faisalabad, 38000, Faisalabad, Pakistan
Manzoor Ahmad: Department of Mathematics, The University of Azad Jammu and Kashmir, Muzaffarabad 13100, Pakistan
Kamran Abbas: Department of Statistics, The University of Azad Jammu and Kashmir, Muzaffarabad 13100, Pakistan
Abdul Q. Khan: Department of Mathematics, The University of Azad Jammu and Kashmir, Muzaffarabad 13100, Pakistan
Abdelouahed Tounsi: Materials and Hydrology Laboratory, University of Sidi Bel Abbes, Algeria Faculty of Technology Civil Engineering Department, Algeria; Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia

Abstract
In the present study, according to the important of porosity in low specific weight in comparison of high stiffness of carbon nanotubes reinforced composite, buckling and free vibration analysis of sandwich composite beam in two configurations, of laminates using differential quadrature method (DQM) is studied. Also, the effects of porosity coefficient and three types of porosity distribution on critical buckling load and natural frequency are discussed. It is shown the buckling loads and natural frequencies of laminate 1 are significantly larger than the results of laminate 2. When configuration 2 (the core is made of FRC) and laminate 1 ([0/90/0/45/90]s) are used, the first natural frequency rises noticeably. It is also demonstrated that the influence of the core height in the case of lower carbon volume fractions is negligible. Even though, when volume fraction of fiber increases, the critical buckling load enhances smoothly. It should be noticed the amount of decline has inverse relationship with the beam aspect ratio. Investigating three porosity patterns, beam with the distribution of porosity Type 2 has the maximum critical buckling load and first natural frequency. Among three elastic foundations (constant, linear and parabolic), buckling load and natural frequency in linear variation has the least amount. For all kind of elastic foundations, when the porosity coefficient increases, critical buckling load and natural frequency decline significantly.

Key Words
buckling and vibration analysis; DQM; variable

Address
Mohammad Mehdi Nejadi and Mehdi Mohammadimehr: Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran

Abstract
The influence of boundary conditions on the bending and free vibration behavior of functionally graded sandwich plates resting on a two-parameter elastic foundation is examined using an original novel high order shear theory. The Hamilton\'s principle is used herein to derive the equations of motion. The number of unknowns and governing equations of the present theory is reduced, and hence makes it simple to use. This theory includes indeterminate integral variables and contains only four unknowns in which any shear correction factor not used, with even less than the conventional theory of first shear strain (FSDT). Unlike any other theory, the number of unknown functions involved in displacement field is only four, as against five, six or more in the case of other shear deformation theories. Galerkin\'s approach is utilized for FGM sandwich plates with six different boundary conditions. The accuracy of the proposed solution is checked by comparing it with other closed form solutions available in the literature.

Key Words
sandwich plates; functionally graded materials; new four-unknown refined shear deformation theory and various boundary conditions

Address
Mohammed Cherif Rahmani: Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria
Abdelhakim Kaci: Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria; Facultede Technologie, Deartement de Geie Civil et Hydraulique, UniversiteDr Tahar Moulay, BP 138 CiteEn-Nasr 20000 Saida, Algeie
Abdelmoumen Anis Bousahla: Facultede Technologie, Deartement de Geie Civil et Hydraulique, UniversiteDr Tahar Moulay, BP 138 CiteEn-Nasr 20000 Saida, Algeie
Fouad Bourada: Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria; Deartement des Sciences et de la Technologie, Centre Universitaire de Tissemsilt, BP 38004 Ben Hamouda, Algeie
Abdeldjebbar Tounsi: Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria
E.A. Adda Bedia: Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals,
31261 Dhahran, Eastern Province, Saudi Arabia
S.R. Mahmoud: GRC Department, Jeddah Community College, King Abdulaziz University, Jeddah, Saudi Arabia
Kouider Halim Benrahou: Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria
Abdelouahed Tounsi: Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria; Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia

Abstract
Vibrational analysis in microtubules is examined based on the nonlocal theory of elasticity. The complete analytical formulas for wave velocity are obtained and the results reveal that the small scale effects can reduce the frequency, especially for large longitudinal wave-vector and large circumferential wave number. It is seen that the small scale effects are more significant for smaller wave length. The methods and results may also support the design and application of nano devices such as micro sound generator etc. The effects of small scale parameters can increase vibrational frequencies of the protein microtubules and cannot be overlooked in the analysis of vibrating phenomena. The results for different modes with nonlocal effect are checked.

Key Words
microtubules; nonlocal theory of elasticity; vibration analysis; small scale effects

Address
Muhammad Taj: Department of Mathematics, University of Azad Jammu and Kashmir, Muzaffarabad, 1300, Azad Kashmir, Pakistan
Afnan Majeed: Department of Mathematics, University of Azad Jammu and Kashmir, Muzaffarabad, 1300, Azad Kashmir, Pakistan
Muzamal Hussain: Department of Mathematics, Govt. College University Faisalabad, 38000, Faisalabad, Pakistan
Muhammad N. Naeem: Department of Mathematics, Govt. College University Faisalabad, 38000, Faisalabad, Pakistan
Muhammad Safeer: Department of Mathematics, University of Azad Jammu and Kashmir, Muzaffarabad, 1300, Azad Kashmir, Pakistan; Department of Mathematics, University of Poonch, Rawalwkot 12350, Azad Kashmir, Pakistan
Manzoor Ahmad: Department of Mathematics, University of Azad Jammu and Kashmir, Muzaffarabad, 1300, Azad Kashmir, Pakistan
Hidayat Ullah Khan: Department of Mathematics, University of Malakand at Chakdara, Dir (Lower), Khyber Pakhtoonkhwa, Pakistan
Abdelouahed Tounsi: Materials and Hydrology Laboratory, University of Sidi Bel Abbes, Algeria Faculty of Technology Civil Engineering Department; Department of Civil and Environmental Engineering, King Fahd University of Petroleumand Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia

Abstract
This study presents comparation of fixed and viscos boundary condition effects on three-dimensional earthquake response and performance of a RCC dam considering linear and non-linear response. For this purpose, Cine RCC dam constructed in Aydin, Turkey, is selected in applications. The Drucker-Prager material model is considered for concrete and foundation rock in the nonlinear time-history analyses. Besides, hydrodynamic effect was considered in linear and non-linear dynamic analyses for both conditions. The hydrodynamic pressure of the reservoir water is modeled with the fluid finite elements based on the Lagrangian approach. The contact-target element pairs were used to model the dam-foundation-reservoir interaction system. The interface between dam and foundation is modeled with welded contact for both fixed and viscos boundary conditions. The displacements and principle stress components obtained from the linear and non-linear analyses are compared each other for empty and full reservoir cases. Seismic performance analyses considering demand-capacity ratio criteria were also performed for each case. According to numerical analyses, the total displacements and besides seismic performance of the dam increase by the effect of the viscous boundary conditions. Besides, hydrodynamic pressure obviously decreases the performance of the dam.

Key Words
demand-capacity ratio; performance analysis; roller compacted concrete (RCC) dam; viscos boundary conditions

Address
Muhammet Karabulut: Department of Civil Engineering, Zonguldak Bulent Ecevit University, Zonguldak, Turkey
Murat E. Kartal: Engineering Faculty, Izmir Democracy University, Izmir, Turkey

Abstract
This paper investigates the effect of crumb rubber (CR) on compressive behaviour of crumb rubber concrete filled steel tube (CRCFST) stub columns. Therefore, experiments on 16 stub columns subjected to axial loading are carried out. The results show that the failure modes of CRCFST stub columns with different CR replacement ratios and CR size are similar, manifested the buckling of the outer steel tube. The axial bearing capacity and stiffness both decrease with an increase in CR replacement ratio, and with decreasing CR size.

Key Words
crumb rubber; concrete; axial; compressive behavior; stub columns

Address
Dawei Liu, Jiongfeng Liang: Jiangxi Engineering Research Center of Process and Equipment for New Energy, East China University of Technology, Nanchang, P.R. China; Faculty of Civil and Architecture Engineering, East China University of Technology, Nanchang, P.R. China
Guangwu Zhang, Jianbao Wang: Faculty of Civil and Architecture Engineering, East China University of Technology, Nanchang, P.R. China

Abstract
A new seismic design methodology for precast concrete diaphragms has been developed and incorporated into the current American seismic design code. This design methodology recognizes that diaphragm inertial forces during earthquakes are highly influenced by higher dynamic vibration modes and incorporates the higher mode effect into the diaphragm seismic design acceleration determination using a first mode reduced method, which applies the response modification coefficient only to the first mode response but keeps the higher mode response unreduced. However the first mode reduced method does not consider effects of diaphragm flexibility, which plays an important role on the diaphragm seismic response especially for the precast concrete diaphragm. Therefore this paper investigated the effect of diaphragm flexibility on the diaphragm seismic design acceleration for precast concrete shear wall structures through parametric studies. Several design parameters were considered including number of stories, diaphragm geometries and stiffness. It was found that the diaphragm flexibility can change the structural dynamic properties and amplify the diaphragm acceleration during earthquakes. Design equations for mode contribution factors considering the diaphragm flexibility were first established through modal analyses to modify the first mode reduced method in the current code. The modified first mode reduced method has then been verified through nonlinear time history analyses.

Key Words
diaphragm flexibility; seismic design; precast concrete diaphragm; modal analysis; nonlinear time history analysis

Address
Dichuan Zhang: School of Engineering and Digital Sciences, Narzarbayev University, Kazakhstan
Robert B. Fleischman: Department of Civil Engineering and Engineering Mechanics, University of Arizona, USA
Deuckhang Lee: Department of Architectural Engineering, Chungbuk National University, Korea

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