تحلیل مودال تیرهای بتن آرمه دارای ترک با استفاده از یک تکنیک جدید مبتنی بر روش اجزای محدود

نوع مقاله : علمی - پژوهشی

نویسندگان

1 گروه مهندسی مکانیک، واحد بندرانزلی، دانشگاه آزاداسلامی، بندرانزلی، ایران

2 مهندسی عمران، دانشکده فنی، دانشگاه گیلان، رشت، ایران

3 استادیار، دانشگاه گیلان

چکیده

در این مقاله، فرکانس های دو مود اول تیرهای بتن آرمه ی دارای ترک با استفاده از روش اجزای محدود بررسی می شود. مدل سازی ترک در تحقیق حاضر، بر مبنای شرایط پیوستگی، اصلاح گشتاور دوم سطح و تعیین ضریب شدت تنش در نقطه ی ترک انجام می گیرد. در این مطالعه، ترک در مود اول شکست (بازشدگی)، با یک فنر پیچشی متناظر، معادل می گردد. ضریب سختی این فنر به صورت تابعی از مولفه ی ضریب شدت تنش، مشخصات هندسی و مادی سطح مقطع ترک خورده استخراج می شود. در روش حاضر، ماتریس‌های سختی و جرم المان دارای ترک با استفاده از ماتریس های تبدیل مستخرج از اعمال شرایط پیوستگی در محل ترک، غنی سازی می گردند. با جایگذاری ماتریس های سختی و جرم اصلاح شده در معادله ی مقدار ویژه، فرکانس های طبیعی تیر دارای ترک تعیین می شوند. در این تحقیق، تاثیر مکان و عمق های مختلف ترک در شرایط مرزی متفاوت بر روی مودهای اول و دوم ارتعاش بررسی می شود. مقایسه و صحت سنجی نتایج فرکانس طبیعی تیر بتن آرمه ی دارای ترک با نتایج تحقیقات آزمایشگاهی مراجع معتبر و شبیه سازی کامل در نرم افزار آباکوس، نشان دهنده ی صحت و دقت مناسب روش حاضر برای تحلیل مودال تیرهای بتن آرمه ی دارای ترک می باشد. این مقایسه به وضوح دقت روش پیشنهادی برای تعیین فرکانس طبیعی تیرهای بتن آرمه ی دارای ترک را نشان می دهد.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

A new technique in the modal analysis of cracked reinforced concrete (RC) beams through the finite element method

نویسندگان [English]

  • Ali Alijani 1
  • Morteza Khomami Abadi 2
  • Javad Razzaghi 3
1 Department of Mechanical Engineering, Bandar Anzali Branch, Islamic Azad University, Bandar Anzali, Iran
2 Civil Engineering, Faculty of Engineering, University of Guilan, Rasht, Iran
3 Civil Engineering, Faculty of Engineering, University of Guilan, Rasht, Iran
چکیده [English]

In this paper, the natural frequency of the cracked reinforced concrete (RC) beams in the first and second modes are investigated using the finite element method. In this research, the modelling of the crack is made based on continuity conditions, the correction of the moment of inertia and considering the stress intensity factor (SIF) at the crack point. In this study, the crack in opening mode is corresponded to a rotational spring. The stiffness factor of the spring is derived as a function in terms of the stress intensity factor and geometric and material characteristics of a cracked cross-section. In the present technique, the stiffness and mass matrices of a cracked element are enriched using convert matrices obtained by applying continuity conditions in the crack point. Natural frequencies of the cracked reinforced concrete Euler-Bernoulli beam are determined by inserting enriched stiffness and mass matrices in the eigenvalue equation. The effect of different depths and positions of crack and various boundary conditions are studied on the first and second vibration modes. A comparison between the results of the present work with experimental results and fully simulation in Abaqus clearly demonstrates the accuracy of the proposed technique in the determination of the natural frequency of the cracked reinforced concrete beams.

کلیدواژه‌ها [English]

  • Modal analysis
  • Reinforced concrete beam
  • Crack
  • Finite element method
  • Rotational spring
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