İnşaat Mühendisliği Bölümü Yayın Koleksiyonu
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Browsing İnşaat Mühendisliği Bölümü Yayın Koleksiyonu by Department "Çankaya University"
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Article Açılı Cfrp Ankrajlı Şeritler ile Beton Yüzey Arasındaki Gerilme Deformasyon Davranışı için Yeni Bir Model Önerisi(2020) Özgür, A. C. Anıl; Ghoroubi, Rahim; Mercimek, ÖmerBetonarme, çelik veya yığma yapılar birçok farklı nedenden dolayı güçlendirilmeleri veya onarılmaları gerekmektedir. Karbon takviyeli elyaf kumaşlar (CFRP) deprem performansı yetersiz yapıların onarım ve güçlendirme çalışmalarında son 20 yıldır yaygın olarak kullanılmaktadır. CFRP ile geliştirilen onarım ve güçlendirme detaylarında önemli olan tasarım kriterlerinden biri CFRP elemanların yüzeyden soyulmalarını geciktirmektir. Bu amaçla CFRP ile geliştirilen güçlendirme detaylarında ankrajların kullanılması artış göstermiştir. Güçlendirme detaylarında kullanılan fan tipi CFRP ankrajlı CFRP şeritler ile ilgili gerilme-kayma deplasmanı modellerinin ankrajsız CFRP şeritlere göre çok daha sınırlı sayıda olduğu görülmektedir. Bu konudaki sınırlı sayıdaki çalışmada ankrajlar CFRP şeritlere uygulanan eksenel çekme kuvvetine göre 90o açılı olacak şekilde yerleştirilmiştir. Yapılan literatür taramasında eksenel yüke göre değişik açılarda yerleştirilen ankrajlı CFRP şeritlerin eksenel kuvvet taşıma gücü ve gerilme kayma deplasmanı modelleri ile ilgili bir çalışmaya rastlanmamıştır. Bu nedenle deneysel bir çalışma düzenlenmiş ve 28 adet beton yüzeyine yapıştırılan açılı ankrajlı CFRP şerit deney elemanı eksenel çekme kuvveti etkisinde yazarlar tarafından tasarlanan bir deney düzeneği kullanılarak test edilmiştir. Deneysel çalışmada incelenen değişkenler CFRP şerit genişliği ve CFRP şeritler üzerindeki CFRP fan tipi ankrajların açılarıdır. Deneysel çalışma sonucunda açılı ankrajlı CFRP şeritlerin maksimum taşıma gücü değerlerinin hesaplanması için bir denklem ve yeni bir gerilme kayma deplasmanı modeli önerilmiştir.Article Ahşap Bağlantı Noktalarında Mekanik Ankraj Sayısı ve Yerleşim Şeklinin Kayma Gerilmesi-kayma Deplasmanı Davranışı Üzerindeki Etkilerinin Deneysel Olarak İncelenmesi(2021) Acehan, Ayşegül Özden; Mercimek, Ömer; Ghoroubi, Rahim; Anıl, ÖzgürAhşap yapılar ve yapı elemanlarında yapıştırıcı ve mekanik bağlantı elemanları ile bir araya getirilmiş birleşim bölgerinin genel yük-deplasman davranışı, kayma gerilmesi- kayma deplasmanı davranışları, yapısal sistemin kapasitesi ve göçme mekanizmaları üzerinde son derece etkilidir. Ahşap-ahşap bağlantı bölgelerinin davranışları, malzemenin mekanik özelliklerine, yapısına ve türüne göre çok büyük oranda değişim gösteren farklı kayma gerilmesi-kayma deplasmanı davranışları sergileyen, incelenmesi gerekli olan önemli bir konudur. Ahşap yapı elemanlarının yapıştırıcı ve yapıştırıcı ile birlikte mekanik ankrajlar ile birleştirilmesi durumunda genel yük-deplasman davranışlarının, bağlantı bölgesindeki gerilme dağılımları ile kayma gerilmesi - kayma deplasmanı davranışlarının incelendiği kapsamlı bir deneysel çalışmaya literatürde rastlanmamıştır. Bu nedenle deneysel bir çalışma planlanmıştır. Bu çalışma kapsamında birbirlerine yapıştırıcı ve yapıştırıcı ile birlikte mekanik ankrajlar ile bağlanmış olan, kenetlenme uzunlukları 180, 240 ve 350 mm olarak değişim gösteren ahşap bağlantı bölgelerinin, eksenel çekme yükü etkisi altındaki genel yük deplasman davranışları deneysel olarak incelenmiştir. Ayrıca çalışma kapsamında birleşim bölgesinde kullanılan mekanik ankraj sayısı ve yerleşiminin değişim göstermesinin, genel yük-deplasman davranışı ve kayma gerilmesi-kayma deplasmanı davranışları üzerindeki etkileri de araştırılmıştır.Article Citation - WoS: 7Citation - Scopus: 17An Analysis on the Relationship Between Safety Awareness and Safety Behaviors of Healthcare Professionals, Ankara/Turkey(Oxford Univ Press, 2020) Uzuntarla, Fatma; Kucukali, Serhat; Uzuntarla, Yasin; 20413Objectives: This descriptive study aims to examine the relationship between the safety awareness of healthcare professional and their safety behaviors. Methods: The study was carried out on 418 healthcare professionals working in a training and research hospital in Ankara/Turkey. The survey method was used as data collection tool. The questionnaire consisted of 3 sections and 18 questions. First section consisted of questions on sociodemographic characteristics and, second section consisted of the awareness scale and third section consisted of safety behaviors scale. Results: The safety awareness and safety behaviors are scored on a scale from 1 (completely disagree) to 5 (completely agree). The safety awareness and safety behaviors has an average score of 3.85 +/- 0.81 and 3.56 +/- 0.82, respectively. The safety awareness and safety behavior levels of healthcare professionals were found to be high. Conclusion: A significant positive correlation was found between safety awareness and safety behaviors and it was concluded that the increase in safety awareness led to an increase in safety behavior.Article Citation - WoS: 3Citation - Scopus: 4An Analytical Investigation of Rigid Plastic Beams Under Impact Loading(Gazi Univ, Fac Engineering Architecture, 2015) Gultop, Tekin; Gültop, Tekin; Yilmaz, Mahmut Cem; Alyavuz, Bahadir; 5168; İnşaat MühendisliğiBeams might be subjected to impact loading which is a particular type of dynamic loading during their service lives. In this study the behaviour of beams under low speed impact loading has been investigated analytically. Simply supported and fixed ended beams have been analyzed with the assumption of rigid plastic behaviour. The collapse mechanism has been assumed to emerge by the instant formation of plastic hinges, hence, a limit analysis has been performed under dynamic loading considering the conservation principles of energy and momentum. The behaviour of rigid plastic beams under impact loading has been compared to the behaviour of elastic beams under similar loading conditions.Article Citation - WoS: 11Citation - Scopus: 15Assessment of the Effectiveness and the Initial Cost Efficiency of Hot Recycled Asphalt Using Polymer Modified Bitumen(Elsevier, 2023) Almusawi, Ali; Shoman, Sarmad; Lupanov, Andrei P.The drastic increase in environmental concerns and increasing costs of road construction materials necessitate evaluating some alternative solutions. One of the most suitable alternatives is recycling old asphalt pavement to produce reclaimed asphalt pavement (RAP). The RAP materials have been commonly combined with asphalt mixtures during pavement construction. Incorporating RAP material should demonstrate an equivalent or better performance than conventional asphalt mixtures. Conversely, the inclusion of RAP mainly needs to improve performance compared to conventional asphalt mixtures. The key issue of using RAP is to restore the loss properties of aged materials and normally asphalt Agent Rejuvenator (ARA) was used. Also, adding polymers with RAP into the asphalt mixture becomes necessary to obtain the required performance. This study investigated the RAP effects of elastomeric polymer on the performance of the asphalt mixture following Russian standards (GOST). The impact of using PMB with RAP material on the asphalt mixture's performance was primarily considered by employing tests that can reveal the adhesion property. Additionally, the performance of the pavement was evaluated in terms of strength and low-temperature cracking. For this purpose, numerous test methods were implemented to appraise the asphalt performance, such as compressive strength, moisture susceptibility, shear resistance, tensile strength, porosity of the mineral particles, and residual porosity. The results indicated that the overall performance of the asphalt mixtures prepared with RAP and combined with polymer depicted a better performance. Moreover, the initial construction cost for each asphalt composition was estimated and compared. The utilization of PMB increased the cost of the asphalt mixture. However, such an increase in the cost would lead to an increase in the overall performance, especially for RAP mixtures.Article Citation - WoS: 81Citation - Scopus: 106Availibility of Renewable Energy Sources in Turkey: Current Situation, Potential, Government Policies and the Eu Perspective(Elsevier Sci Ltd, 2012) Kucukali, Serhat; Baris, Kemal; 20413This study aims to explore the availability and potential of renewable energy sources in Turkey as well as assessing related government policies, financial and environmental aspects of renewable energy projects. Turkey is a country which has the highest hydropower, wind and geothermal energy potential among European countries. As a European Union (EU) candidate several incentives were developed in Turkey for electricity generation from renewable energy sources by the enactment of Law No. 5346 in 2005 which was later restructured by Law No. 6094 in 2010. The most important ones are: ease of land acquisition and feed-in-tariffs which promise purchasing of electricity generated and domestic manufacturing of equipment by the private companies with a price of 5.30-9.69 and 0.3-2.55 (sic)c/kWh, respectively, depending on the type of the renewable and the equipment. However, feed-in tariff amounts take reservoir area into account instead of installed capacity for hydroelectric power plants. Moreover, Environmental Impact Assessment (EIA) report is not mandatory for all renewable energy plants. According to the multi-criteria analysis tool developed in this study to evaluate the renewable energy source (RES) technologies the most appropriate renewable energy alternative for Turkey is biomass, simply because of the highest social benefit among others. (C) 2011 Elsevier Ltd. All rights reserved.Article Citation - WoS: 22Citation - Scopus: 25Behavior of Glulam Timber Beam Strengthened With Carbon Fiber Reinforced Polymer Strip for Flexural Loading(Sage Publications Ltd, 2021) Isleyen, ummu K.; Ghoroubi, Rahim; Mercimek, Omer; Anil, Ozgur; Erdem, Recep TugrulIn the last 20 years, the use of wooden structures and their dimensions have gradually increased. The wood application has increased in different structures such as multistory buildings, sports, industrial facilities, road and railway bridges, power transmission lines, and towers. The widespread use and size of wood structures have increased the research on developing special types of wood products supported by composite materials. Laminated wood elements are the leading composite wood materials. Laminated wooden beams allow making much larger openings than standard solid wood structural elements. The development of the sizes and usage areas of wooden structures has increased the capacity of glulam structural elements and reveals the need to improve their performance. Carbon fiber reinforced polymers (CFRPs) are the most suitable options for increasing the bearing capacity values of glulam beams and improving general load-displacement behaviors. In this study, the use of CFRP strips in different layouts to increase glulam wooden beams and the application of CFRP fan-type anchors in the CFRP strip endpoints are the studied variables. Anchored and non-anchored glulam wooden beams reinforced with CFRP strips with different layouts were tested using a three-point bending test. The ultimate load capacity, initial stiffness, displacement ductility ratio, energy dissipation capacity, failure mechanisms, and general load-displacement behavior of wooden beam test specimens were obtained and interpreted as a result of the experiments.Article Citation - WoS: 4Citation - Scopus: 4Behaviour of Steel Beams Retrofitted With Anchored Carbon-Fibre Polymer Strips(Ice Publishing, 2022) Mercimek, Omer; Ghoroubi, Rahim; Baran, Mehmet; Anil, OzgurSteel bridge beams can be damaged due to increased traffic loads and environmental impacts. An experimental study on the use of bonded and mechanically anchored carbon-fibre-reinforced polymer (CFRP) strips was undertaken to assess the retrofitting of such steel beams. The number of mechanical anchors used in the ends of the bonded strips was varied from zero to eight. The steel beam samples were tested under four-point loading. Loading was applied as an increasingly high static load and a low repetitive fatigue load. The load-displacement behaviour under the effects of static and fatigue loading and the strain distributions along the strips were measured and interpreted. The results showed that retrofitting cracked steel beams with CFRP strips is an effective method. In addition, retrofitting with anchored strips increased the performance of cracked beams under the effects of both static and fatigue loading.Article Citation - WoS: 6Citation - Scopus: 7Crack Width - Seismic Intensity Relationships for Concrete Gravity Dams(Taylor & Francis Ltd, 2024) Soysal, Berat Feyza; Arici, Yalin; 157572Seismic assessment of plain concrete structures like gravity dams is generally conducted based on cracking. The responses of two types of gravity dams, i.e. the conventional and roller compacted concrete (RCC), were investigated in this study using a discrete element tool coupled with special reservoir elements. Using incremental dynamic analysis, the relationship between the seismic intensity measures and crack widths on the U/S face of the monolith was obtained. The damage accumulation on conventional and RCC dams was different: The cumulative cracking on the upstream face of the monolith correlated well to a seismic intensity measure representing base shear.Article Citation - WoS: 3Citation - Scopus: 2Critical Submergence for Single and Multiple Horizontal Intake Structures(Springer Heidelberg, 2023) Gogus, Mustafa; Gokmener, Serkan; 6062In this study, a series of experiments were carried out to investigate the variation of the critical submergence of air-entraining vortices with the related flow and geometric parameters at single and multiple horizontal intake structures. Three identical intake pipes were tested at a wide range of discharges with varying sidewall clearances under symmetrical and asymmetrical approach flow conditions. Experimental results indicated that increasing the number of intake structures in operation results in a more complicated flow pattern in front of the intake structures due to the mutual effects of the intakes on each other. Therefore, critical submergence values are higher for multiple intake structures than those of single water intake structures for a given Froude number. Dimensionless empirical equations were derived for each single, double and triple unit operation to calculate the critical submergence as a function of relevant flow and geometric parameters, and they were compared with the related equations available in the literature. These equations can be used to determine sufficient submergence to avoid air-entraining vortices at single and multiple horizontal intakes within the ranges of dimensionless parameters tested in this study.Article Citation - WoS: 8Citation - Scopus: 8Damage Limits for Ductile Reinforced Concrete Shear Walls(Turkish Chamber Civil Engineers, 2012) Gülkan, Hakkı Polat; Kazaz, Ilker; Gulkan, Polat; 5743; İnşaat MühendisliğiAlthough the strain based damage limits proposed in the existing Turkish Earthquake Code were adopted from reported studies of leading researchers, the appropriateness of these limit state definitions and corresponding values to evaluate the performance with the analytical tools and methods used in the displacement based design and assessment procedures has not been verified properly. The moment-curvature analysis based on the plane section hypothesis is severely violated especially for reinforced concrete walls. This indicates that a comprehensive investigation is required to investigate the validity of proposed damage limits for structural walls. This study is based on advanced and computationally rigorous numerical procedures to investigate the relation between drift ratio, plastic rotation and curvature, compressive strain in concrete and tensile strain in steel for rectangular reinforced concrete structural walls. Validity of the requirements related to deformation limits in the Turkish Seismic Code and other design guidelines is then evaluated. Modeling and acceptance criteria that are more accurate than the existing ones have been proposed for structural walls.Article Citation - WoS: 12Citation - Scopus: 15Debris Flow Modelling and Hazard Assessment for a Glacier Area: a Case Study in Barsem, Tajikistan(Springer, 2023) Dincer, A. Ersin; Kalpakci, Volkan; Ozturk, Sevki; Yilmaz, Kutay; 163874This study analyses a previous debris flow hazard as a consequence of emerging risks related to climate and regional physical changes. In addition to the increasing flood frequencies, there is an increasing risk of mud or debris flow due to increasing temperature and heavy precipitation resulting in glacier melting. One of the most recent dramatic examples of the debris flow incident took place in Barsem, Tajikistan, in 2015. As a result of heavy precipitation and excess temperature, the melting of glaciers caused debris flow which ended up with a catastrophic damage at Barsem Town. In this study, a methodology for modelling debris flow and related hazard is developed by examining the 2015 incident in detail with a commercially available software, Hydrological Engineering Centre-River Analysis System (HEC-RAS). Simulations and hazard assessment of the incident suggest that assessment of debris flow hazard can be implemented similar to flood hazard. Moreover, it is seen that debris flow inundation area can be predicted accurately by low-resolution free-source digital elevation models (DEMs), while in the present work they could not predict the debris flow hazard assessment accurately. Sensitivity results also reveal that free-source DEMs with higher resolutions do not necessarily give better predictions than free-source DEMs with lower resolutions.Article Citation - WoS: 24Citation - Scopus: 32Deformation Limits for Structural Walls With Confined Boundaries(Earthquake Engineering Research inst, 2012) Kazaz, Ilker; Gulkan, Polat; Yakut, Ahmet; 5743For accurate analytical assessment of performance and damage in reinforced concrete members, well-defined deformation limits at particular damage states are required. With advanced and computationally intensive finite element analyses, we establish deformation limits at yield and ultimate limit states for adequately confined rectangular reinforced concrete structural walls in terms of drift ratio, plastic rotation, and curvature. To investigate the deformation limits of structural walls, a parametric study on isolated cantilever wall models is performed. The primary variables of the parametric study are the shear-span-to-wall-length ratio, wall length, axial load ratio, normalized shear stress, the amount of horizontal web reinforcement, and the amount of longitudinal reinforcement at the confined boundary of structural wall models. Expressions and limit values are proposed for yield and ultimate deformation capacity of structural walls, based on the most influential parameters. The proposed equations are found to be promising when compared to results of experiments. [DOI: 10.1193/1.4000059]Book Part Design of a Versatile and Rapid Calculator for Oncological Computations(Nova Science Publishers, Inc., 2019) Dinçkal, Ç.; Dinçkal, Çiğdem; 26773; İnşaat MühendisliğiIn oncology, there exists many complicated and time-consuming computations for students, clinicians and medical researchers. Although many programs generated in Microsoft Excel have been studied many times, the improvements in design of programs are still an issue of concern. So design of calculator becomes essential for practical use. The objective of this study is to design a rapid and versatile calculator named as TGTSCalculator in Microsoft Excel for comprehensive computation of clonogenic cells amount when growth and irradiation for tumor occurred for all tumor growth models and the total amount of relative cells outliving the treatment schedule (in other words; survival fraction) after radiotherapy. Microsoft Excel with Visual Basics for Applications (VBA) has been employed since it is a high versatile and extensively used special spreadsheet program and easily accessible and available for biomedical scientists and clinicians for a wide range of applications. TGTSCalculator is so transparent and practical that any kind of users requires only requires clicking its macro or CALCULATE button in spreadsheet to manage the all computations effectively and simultaneously. © 2020 by Nova Science Publishers, Inc. All rights reserved.Article Citation - WoS: 4Citation - Scopus: 4Design of Integral Spreadsheet Calculator for Engineering Applications(Wiley, 2018) Dinckal, Cigdem; 26773Although Newton-Cotes integration formulas in engineering have been the subject of the study for a long time, the improvement in formulations is still object of interest. In this sense, design of calculators based on these formulations becomes significant. The purpose of this paper is to design an integral calculator for any engineering problems. Since the integral calculator, easy-to-understand and use, is aimed to be employed by any kind of users. Visual Basic for Applications (VBA) is the programming language of Excel. Excel spreadsheet with VBA is preferred for this purpose. In this study, a user interface input form is introduced. This form is composed of the embedded algorithm. This algorithm includes not only rules and formulations of each Newton-Cotes such as Composite Trapezoidal rule, Simpson's rules, Boole's rules, and Gauss Legendre formulations with 2, 6, 10, 16, and 24 points and exact result of any integral (if it exists) with computed true percent relative error for comparison purposes. This calculator is tested for civil, mechanical, and chemical engineering applications. The results and screenshots for each application obtained from calculator are presented. The present study allows design of an integral spreadsheet calculator for any integral given. If exact result of the integral cannot be obtainable, the calculator can perform only integral calculations numerically without exact solution and computed true percent relative error. Otherwise, user can solve the integrals completely with this tool easily and accurately again but this time by both numerically and analytically with true percent relative error calculations.Article Citation - WoS: 7Citation - Scopus: 9Determination of Hydraulic Characteristics of Flow Over a Triangular Sectioned Weir by Using Experimental and Numerical Modeling(Univ Tehran, Danishgah-i Tihran, 2021) Yildiz, Ali; Marti, Ali Ihsan; Gogus, Mustafa; 6062The spillways of hydraulic structures transfer excessive water from dam reservoir to the downstream in a safe and controlled manner. A labyrinth or triangular weir is a flat spillway folded in plain view. The labyrinth weirs provide an increase in crest length for a given channel width and increase the flow capacity for a given weir load. As a result of the increased flow capacity, the labyrinth and triangular weirs require less space in the dam body than the flat weirs. In this study, experiments were carried out on the labyrinth weirs containing triangles of different heights and numbers by using 3 different weir heights (P=20cm, 30cm, and 40 cm) and 4 different weir shapes. Each experiment was repeated for 30 different discharge values. The effects of weir height and weir shape on the total head over the weir (H-T) and discharge (Q) were investigated. In addition, the numerical models of all experimental setups were created by ANSYS-Fluent program using Computational Fluid Dynamics (CFD). By comparing the results obtained from the numerical models with the physical models, the accuracy of the numerical models was tested. According to the results, as the number of the triangles (N) of the weir increases, the discharge coefficient (Ca) decreases. The weir height (P) does not have a major effect on the discharge.Editorial Citation - WoS: 22Citation - Scopus: 26A Dispassionate View of Seismic-Hazard Assessment(Seismological Soc Amer, 2013) Gulkan, Polat; 5743Article Citation - WoS: 47Citation - Scopus: 62Ductility of Frp-Concrete Systems: Investigations at Different Length Scales(Elsevier Sci Ltd, 2013) Lau, Denvid; Tuakta, Chakrapan; Bueyuekoeztuerk, Oral; Gunes, Oguz; 160252Fiber reinforced polymer (FRP) materials have been increasingly used in the last two decades to improve various structural characteristics of reinforced concrete (RC) bridges, buildings and other structures. Ductility of the resulting FRP-concrete system plays an important role in structural performance, especially in certain applications such as earthquake resistant design of structures, where ductility and energy dissipation play a vital role. Wrapping RC columns with FRP has been shown to generally result in significant increase in ductility due to the confinement of concrete by the FRP. Other applications such as flexural strengthening of beams involve tradeoffs between ductility and the desired load capacity. Furthermore, environmental factors may adversely affect the FRP-concrete bond raising concerns about the ductility of the system due to possible premature failure modes. Characterization of these effects requires the use of more involved mechanics concepts other than the simple elastic or ultimate strength analyses. This paper focuses on characterizing ductility of the FRP-concrete systems at different length scales using a combined experimental/computational mechanics approach. Effects of several parameters on ductility, including constituent material properties and their interfaces, FRP reinforcement geometry at the macro- and meso-level, and atomistic structure at the molecular level are discussed. Integration of this knowledge will provide the basis for improved design strategies considering the ductility of FRP-concrete systems from a global as well as local perspective including interface bond behavior under various mechanical and environmental conditions. (C) 2012 Elsevier Ltd. All rights reserved.Article Citation - WoS: 8Citation - Scopus: 8Dynamic Shear Force Amplification in Regular Frame-Wall Systems(Wiley-blackwell, 2016) Kazaz, Ilker; Gulkan, Polat; 5743A parametric study is conducted to investigate the dynamic shear amplification factor (DAF) in low-to-mid-rise frame-wall systems in which the reinforcement curtailment along the height matches the required code strength. The level of frame-wall interaction is varied by changing the wall index, defined as the ratio of the total wall area to the floor plan area, in a generic frame-wall system, and its correlation with the DAF is investigated. Wall index values ranging in the 0.2% to 2% interval are selected. Walls with lengths of 3m, 5m and 8m are used in the design of model buildings of 4, 8 and 12 stories. Shear-flexure beam continuum formulation is used in design and modeling. The global behavior is analyzed using nonlinear response history procedure using spectrum compatible ground motions. It is found that the primary source of amplification is the level of inelastic demand on the system. Walls designed for code-specified force reduction factor R=6 experienced an average base shear force amplification in the order of 1.64 with standard deviation of 0.19 with respect to design shear force. Amplification diminishes with decreasing R. An expression for the dynamic amplification factor as a function of the number of stories and force reduction factor R is proposed. Copyright (C) 2015 John Wiley & Sons, Ltd.Conference Object Dynamic Stability of Planar Frames Supported by Elastic Foundation(Structural Stability Research Council (SSRC), 2016) Alemdar, B.N.; Dinçkal, Çiğdem; Dinçkal, Ç.; 26773; İnşaat MühendisliğiAn exact analytical solution for a vibrating beam-column element on an elastic Winkler foundation is derived. The solution covers all cases comprised of constant compressive and tensile axial force with restrictions of ks -mω1 > 0 and ks -ma>2 < 0. Closed form solutions of dynamic shape functions are explicitly derived for each case and they are used to obtain frequency-dependent dynamic stiffness terms. Governing dynamic equilibrium equations are not only enforced at element ends, but also at any point along the element. To this end, derived stiffness terms are exact and they include distributed mass effects and geometric nonlinear effects such as axial-bending coupling. For this reason, the proposed solution eliminates the need of further element discretization to obtain more accurate results. In absence of elastic foundation (i.e., ks → 0), exact dynamic stiffness terms for beam-columns are also derived and presented in this study. Derived stiffness terms are implemented in a software program and several examples are provided to demonstrate the potential of the present study.
