ارائه روشی تحلیلی از ترکیب المان قابی بتن مسلح فیبری شبه تیموشنکو و تئوری میدان فشاری

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشگاه فردوسی مشهد، دانشکده مهندسی، گروه عمران, ایران

2 عضو هیئت علمی

3 عضو هیئت علمی، دانشکده مهندسی، گروه عمران، دانشگاه فردوسی مشهد، ایران

چکیده

ارزیابی دقیق رفتار یک سازه با روش تحلیلی، بایستی توانایی تخمین مناسبی از سختی اولیه سازه، بیشینه ظرفیت و شکل پذیری‌های محلی و کلی را داشته باشد. در این پژوهش به منظور شبیه‌سازی رفتار غیرخطی سازه‌های بتنی مسلح تحت بارگذاری یکنوا، یک المان تیرستونی فیبری با روش کنترل جابه‌جایی مبتنی بر روش طول قوس خطی شده توسعه داده شده است. فرمول‌بندی این المان بر مبنای ترکیب تئوری تیر اویلر- برنولی و تیموشنکو به همراه اثرات اندرکنشی محوری، خمشی و برشی در دامنه هر المان پیاده‌سازی شده است. در جریان حل غیرخطی، سطح مقطع هر المان در نقاط گوسی، با مجموعه فیبرهای گسسته با رفتار تک محوری معادل می‌شود. همچنین به منظور در نظرگرفتن تغییر شکل برشی المان، رویکرد ترک پخشی چهارجهته و تئوری میدان فشاری اصالح شده (MCFT )در قالب تحلیل غیرخطی برشی به روش الگوریتم کنترل تغییر مکان مستقیم در زیربرنامه اصلی مورد توجه قرار گرفته است. در این پژوهش مبنای فرمول‌بندی عددی پیکربندی مرجع، پیکربندی گام قبل و پیکربندی تغییرشکل نیافته اولیه به صورت همزمان در نظر گرفته شده است و رویکرد تحلیلی الگوریتم، توانایی تغییر فرموالسیون لاگرانژی به روز شده به لاگرانژی کل منطبق با الگوریتم حاکم بر مسأله را نیز دارد. المان فیبری توسعه داده شده توسط آزمایش‌های تجربی متعددی مورد اعتبارسنجی شده و ارزیابی روش تحلیلی ارائه شده مورد آزمون قرار گرفته است. روش ارائه شده با فرض‌های صورت گرفته، در سازه‌های با مودهای ترکیبی حاکم خمشی- برشی تقریب نسبتا مناسب و روند همگرایی قابل قبول با سرعت پردازش تحلیلی باال را در مسائل را نتیجه می‌دهد.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

A Mixed Analytical Approach based on Semi-Timoshenko Planar Fiber Frame Element and Modified Compression Field Theory in RC Structures

نویسندگان [English]

  • Behrooz Yousefi 1
  • Mohammadreza Esfahani 2
  • Mohammad Reza Tavakolizadeh 3
1 Civil Engineering Department, Ferdowsi University of Mashhad, Mashhad, Iran
2 Department of Civil Engineering, Ferdowsi Unversity of Mashhad
3 Civil Engineering Department, Ferdowsi University of Mashhad, Mashhad, Iran
چکیده [English]

An accurate assessment of the behavior of structures by an analytical method should be able to estimate the initial stiffness of the structure, the maximum capacity and the local and global ductility. In this research, in order to simulate the nonlinear behavior of reinforced concrete structures under monotonic loading, a new fiber beam-column element was developed with a displacement control method using linearized arc-length approach. The formulation of the implemented element was based on the combination of Bernoulli and Timoshenko’s theory along with the axial, flexural, and shear interaction effects of each element. The cross-sectional area of each element in Gaussian points was equivalent to a set of discrete fibers with uniaxial constitutive behavior in the process of nonlinear solution. Also, in order to consider the elemental shear deformation, the four-way smeared cracked approach and the modified compression field theory (MCFT) was considered in nonlinear shear analysis using the direct-displacement control algorithm in the main sub-program. The reference configuration of numerical formulation was considered according to the configuration of the previous step and the initial configuration, simultaneously. The analytic approach of the algorithm had the ability to change the updated Lagrangian formulation to the total Lagrangian in accordance with the problem-solving convergence. The developed fiber element was validated by numerous experimental experiments and the evaluation of the proposed analytical method was tested. The proposed method led to an appropriate solution and an acceptable convergence process with high processing speed for problems with mixed combinational mechanisms.

کلیدواژه‌ها [English]

  • Fiber Beam-Column Element
  • Displacement Control
  • Linearized Arc-Length
  • Timoshenko's Theory
  • Modified Compression Field Theory

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نشریه مهندسی عمران امیرکبیر
دوره 51، شماره 4
مهر و آبان 1398
صفحه 733-748

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