تعیین بار کمانش جانبی-پیچشی تیرهای جدار نازک الاستیک دو سر مفصل با مقطع نامتقارن با استفاده از روش اختلاف محدود

نوع مقاله : مقاله پژوهشی

نویسندگان

1 گروه مهندسی عمران، دانشگاه کاشان، کاشان، ایران

2 دانشکده مهندسی عمران دانشگاه صنعتی خواجه نصیرالدین طوسی، تهران، ایران

چکیده

تیرهای جدار نازک المان بسیار مهمی در سازه‌های فولادی هستند. در این اعضا، با توجه به نحوه بارگذاری جانبی و همچنین بر اساس تقارن و یا عدم تقارن سطح مقطع عضو، امکان وقوع کمانش جانبی-پیچشی وجود دارد. لذا در این پژوهش به بررسی پایداری تیرهای جدار نازک با نیم‌رخ نامتقارن در برابر کمانش جانبی-پیچشی پرداخته شده است. بدین منظور، در اولین گام در تحلیل پایداری جانبی تیرها، با استفاده از روابط حاکم بر تغییر شکل اعضای جدار نازک و اصل پایستگی انرژی پتانسیل، معادلات دیفرانسیل تعادل تیر با سطح مقطع نامتقارن تحت بارگذاری جانبی تعیین می‌گردد. معادلات پایداری جانبی بدست آمده در حضور پارامترهای لنگر خمشی، نامتقارنی سطح مقطع و زاویه پیچش، یک دستگاه معادلات دیفرانسیل وابسته است. سپس با استفاده از شرایط مرزی حاکم بر خمش، معادله تعادل پیچش مستقل گشته و معادله دیفرانسیل مرتبه چهار با ضرایب متغیر حاصل شده تنها وابسته به پارامتر تغییر شکل پیچشی عضو جدار نازک خواهد بود. در ادامه، با استفاده از روش عددی تقریبی اختلاف محدود مرکزی و فرضیات حاکم بر این روش معادله دیفرانسیل مرتبه چهار بدست آمده حل می‌گردد و در نهایت، با توجه به شرایط مرزی حاکم بر تیرهای دو سر مفصل و با استفاده از روش حل مقادیر ویژه مقدار بار بحرانی کمانش محاسبه می‌شود. نتایج بدست آمده از روش معرفی شده با مقادیر ارائه شده توسط محققان دیگر و مقادیر حاصله از نرم افزار Ansys مقایسه گشته‌اند.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

Determination of Lateral-Torsional Buckling Load of Simply Supported Prismatic Thin-Walled Beams with Mono-Symmetric Cross-Sections Using the Finite Difference Method

نویسندگان [English]

  • M. Soltani 1
  • B. Asgarian 2
1 Department of Civil Engineering, University of Kashan, Isfahan, Iran
2 Earthquake Engineering Department, Faculty of Civil Engineering, K.N. Toosi University of Technology, Tehran, Iran
چکیده [English]

In this paper, the lateral-torsional stability of simply supported thin-walled beams with mono-symmetric section subjected to bending loads has been studied by means of a numerical method based on the finite difference method (FDM). To fulfill this purpose, the equilibrium equations for elastic thin-walled members with linear behavior are derived from the stationary condition of the total potential energy. In the applied energy method, effects of initial stresses and load eccentricities from shear center of cross-sections are also considered. Finite difference method is one of the most powerful numerical techniques for solving differential equations especially with variable coefficients. Between various computational methods to solve the equilibrium equation, finite difference method requires a minimum of computing stages and is therefore very suitable approach for engineering analysis where the exact solution is very difficult to obtain. The main idea of this method is to replace all the derivatives presented in the governing equilibrium equation and boundary condition equations with the corresponding central finite difference expressions. Finally, the critical buckling loads are then derived by solving the eigenvalue problem. In order to present the accuracy of the proposed method, several numerical examples including lateral-torsional behavior of prismatic beams with mono-symmetric sections are considered. In order to illustrate the correctness and performance of FDM, the evaluated results are compared to the finite element simulations and other available methods.

کلیدواژه‌ها [English]

  • Thin-Walled Beams
  • Lateral-Torsional Buckling
  • Mono-Symmetric Sections
  • Simply Supported
  • Finite Difference Method

مراجع

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نشریه مهندسی عمران امیرکبیر
دوره 50، شماره 1
فروردین و اردیبهشت 1397
صفحه 61-72

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