تخمین عدم‌قطعیت در مدل‌سازی سازه‌های فولادی توسط تیر تیموشنکو

نوع مقاله : علمی - پژوهشی

نویسندگان

دانشکده مهندسی عمران، دانشگاه صنعتی شریف

چکیده

این مقاله به کمی‌سازی عدم‌قطعیت ناشی از مدل‌سازی سازه‌های فولادی توسط تیر تیموشنکو می‌پردازد. یکی از روش‌های مرسوم در تحلیل دینامیک سازه‌ها، مدل کردن سازه‌های ساختمانی توسط مدل‌های تیر پیوسته است. استفاده از تیر تیموشنکو، به‌عنوان یک کلاس از مدل‌های تیر پیوسته، به‌جای یک مدل اجزای محدود به تسریع محاسبات منجر می‌شود. این کاهش محاسبات، امکان شناسایی احتمالاتی برخط سازه‌های ساختمانی و تشخیص سریع خرابی در آن‌ها را پس از یک رویداد لرزه‌ای فراهم می‌سازد. لازمه شناسایی سازه‌ها به این روش، کمی‌سازی عدم‌قطعیت ناشی از تقریب سازه با یک تیر پیوسته است که هدف اصلی این پژوهش را تشکیل می‌دهد. بدین منظور با توسعه یک سیستم خودکار، تعداد 1000 مدل اجزای محدود سازه ساختمانی طراحی شده و تحت تحلیل مقدار ویژه قرار می‌گیرند تا بسامد و شکل مودی طبیعی آن‌ها تعیین شود. برای هر سازه، تیر تیموشنکوی معادل آن تعیین می‌شود. سپس، خطای ناشی از ارضا نشدن معادله مشخصه تیر تیموشنکو به‌ازای بسامد و شکل مودی ناشی از مدل دقیق اجزای محدود محاسبه می‌شود. با تحلیل آماریِ این خطاها برای سیستم‌های مختلف، مشخصات توزیع احتمال خطا، از جمله شکل توزیع، میانگین و انحراف معیار آن تعیین می‌شود. نتایج نشان می‌دهد که میزان خطا حساسیت اندکی به طول، عرض و ارتفاع سازه دارد، اما به سیستم سازهای بسیار وابسته است. بر اساس این نتایج، انحراف معیار خطا برای سازه‌هایی با سیستم قاب خمشی فولادی 5/3 برابر کمتر از سازه‌هایی با سیستم مهاربندی فولادی است. بنابراین، کلاس مدل تیر تیموشنکو تقریب بهتری از سیستم‌های قاب خمشی فولادی ارائه می‌کند.

کلیدواژه‌ها


عنوان مقاله [English]

Uncertainty Quantification in Modeling of Steel Structures using Timoshenko Beam

نویسندگان [English]

  • Mahdi Naderi
  • Mojtaba Mahsuli
Department of Civil Engineering, Sharif University of Technology
چکیده [English]

This paper quantifies the uncertainty emanated from modeling steel structures using a Timoshenko beam. Using continuous beams to model building structures is a conventional approach in structural dynamic analyses. The use of Timoshenko beams, as a class of continuous beam models, in lieu of finite element models significantly expedites the computations. In turn, the reduction in the computational cost facilitates probabilistic, online identification and rapid damage detection of building structures in the aftermath of a seismic event. The prerequisite for structural identification using this method is the quantification of uncertainties that arise as a result of approximating the structure with a continuous beam, which is the primary objective of this research. To this end, an automated system is developed and subsequently employed to design 1000 finite element models of building structures followed by eigen-analyses to determine their natural frequencies and mode shapes. Thereafter, the residual of the eigen-equation of the Timoshenko beam given the frequency and mode shape from the exact finite element model is computed for each structure. Statistical analysis of these residuals for various structures leads to the distribution type, mean, and standard deviation for the probability distribution of the model error. The results show that the error is nearly insensitive to the height and dimensions of the plan, but is heavily dependent on the structural system. The results also show that the error standard deviation for steel moment-resisting frame systems is 3.5 times smaller than that of the steel concentrically-braced systems. This indicates that the Timoshenko beam model class provides a better estimation of steel moment-resisting frame systems.

کلیدواژه‌ها [English]

  • Timoshenko beam
  • Characteristic equation
  • Probabilistic analysis
  • Bayesian identification
  • Finite Element
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