تحلیل پایداری دینامیکی ستون‌های قاب تحت اثر جرم متمرکز و میرایی ذاتی با روش اجزای محدود

نوع مقاله : مقاله پژوهشی

نویسندگان

گروه مهندسی عمران، دانشکده فنی و مهندسی، دانشگاه بین‌المللی امام خمینی (ره) قزوین، ایران.

چکیده

تحلیل پایداری در ستون‌ها به‌عنوان اصلی‌ترین عضو سازه‌ای از جایگاه ویژه‌ای در تحقیقات مهندسی برخوردار است. در عمدة تحقیقات گذشته، عموماً پژوهشگران به مطالعه بارکمانشی استاتیکی در ستون‌های (منشوری یا غیر منشوری) در (قاب‌های ساختمانی یا سولة صنعتی) پرداخته‌اند. بارکمانشی استاتیکی تنها بیانگر ظرفیت بار بحرانی استاتیکی اعضا تحت بار ثقلی است. برای طراحی ایمن سازه لازم است که پایداری دینامیکی ستون‌ها در قاب‌های ساختمانی تحت بار قائم زلزله نیز بررسی گردد. در مقالة حاضر در مدلی جامع اثر توأمان میرایی ذاتی، جرم طبقه و بار قائم زلزله بر پایداری دینامیکی ستون‌ها در قاب‌های خمشی مهارنشده بررسی می‌شود. در واقع روش پیشنهادی تلفیقی از  مدل‌سازی استاتیکی ژولیان - لارنس و مدل‌سازی دینامیکی بولوتین برای لحاظ اثرات دینامیکی در ستون‌های قاب بر مبنای روش اجزاء محدود است. در گام نخست، با استفاده از روش همیلتون معادله متشکله استخراج می‌شود. در گام بعدی، پاسخ معادله با استفاده از روش اجزا محدود با توابع میان‌یابی از نوع درجه سه هرمیتی به‌ازای 50 جزء بررسی می‌شود. نتایج بیانگر این است که میرایی ذاتی، جرم متمرکز و سختی دورانی اتصالات نیمه‌سخت تأثیر قابل‌توجهی بر مقادیر فرکانس تشدید، طول مؤثر و ضریب بار دینامیکی بی‌بُعد دارند. با افزایش میرایی ذاتی، سختی دورانی و جرم متمرکز نمودار تغییرات طول موثر به سمت چپ محور فرکانس تحریک منتقل می‌شود. لحاظ اثر میرایی ذاتی و جرم متمرکز در مدلسازی به ترتیب 7% و 81 % بر تغییرات فرکانس تشدید تاثیرگذار است. تطابق قابل قبولی بین نتایج مقاله‌ی حاضر و تحقیق‌های پیشین برقرار است.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

Analysis of Dynamic Stability of Frame Columns under The Effect of Concentrated Mass and Inherent Damping by Finite Element Method

نویسندگان [English]

  • Amir Hossein Taherkhani
  • Majid Amin Afshar
Structural Engineering, Department of Civil Engineering, Imam Khomeini International University, Qazvin, Iran
چکیده [English]

Analysis of stability in columns as the main structural member has a special place in engineering research. In most of the past research, generally, researchers have studied the static buckling in columns (prismatic or non-prismatic) in building frames or industrial beams. Static load capacity only expresses the static critical load capacity of members under gravity load. For the safe design of the structure, it is necessary to check the dynamic stability of the columns in the building frames under the vertical load of an earthquake. In this article, in a comprehensive model, the combined effect of inherent damping, floor mass, and vertical earthquake load on the dynamic stability of columns in unrestrained moment frames is investigated. In fact, the proposed method is a combination of Julian-Lawrence static modeling and Bolotin dynamic modeling to consider the dynamic effects in the frame columns based on the finite element method. In the first step, the constitutive equation is extracted using Hamilton's method. In the next step, the response of the equation is checked using the finite element method with Hermitian three-degree interpolation functions for 50 components. The results show that the inherent damping, concentrated mass, and rotational stiffness of semi-rigid joints have a significant effect on the resonance frequency, effective length, and dimensionless dynamic load factor. With the increase in inherent damping, rotational stiffness, and concentrated mass, the graph of effective length changes is shifted to the left side of the excitation frequency axis. Considering the effects of inherent damping and concentrated mass in the modeling, 7% and 81%, respectively, affect the resonance frequency changes. There is an acceptable agreement between the results of the present article and previous research.

کلیدواژه‌ها [English]

  • Dynamic Buckling
  • Dynamic Stability
  • Effective Length
  • Critical Load Capacity
  • Analysis Eigenvalue

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نشریه مهندسی عمران امیرکبیر
دوره 57، شماره 5
1404
صفحه 765-792

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