بررسي رفتار برشي و مدل‌كردن تيرهاي عميق بتن مسلح به روش اجزا محدود

Investigation of Shear Behavior and Modeling of Deep Beams using the Finite Element Method

در اين نوشتار رفتار چند تير عميق بتني مسلح به روش اجزا محدود مطالعه و با نتايج مدل هاي آزمايشگاهي گزارش‌شده‌ي عربزاده و ليونارد- والتر مقايسه شده است. تيرهاي عميق بتني در سدها، اسكله هاي دريايي، بدنه‌ي مخازن مستطيلي، پل ها و ساختمان هاي بلند كاربرد دارند. اين تيرها توسط آيين نامه هاي مختلف، براساس نسبت دهانه (يا دهانه‌ي برشي) به عمق تير (به طور متداول 5/2) تعريف مي شوند. در اين نوشتار، نتايج تحليل اين تيرها با استفاده از برنامه‌ي NAOC (نوشته‌شده به زبان بيسيك) كه قادر به درنظرگرفتن عواملي مانند حالت خميري بتن در فشار، ترك خوردگي بتن در كشش، خردشدن بتن در فشار و حالت خميري ميلگردهاست، ارايه شده اند. در قسمت تحليل غيرخطي، نتايج شامل منحني بار- تغييرمكان قايم، الگوي ترك خوردگي و بار نهايي براي تيرهاي عميق ارايه شده‌اند. مقايسه‌ي نتايج برنامه با نتايج آزمايشگاهي موجود، دقت، كارايي و قدرت برنامه را در ارزيابي مقاومت برشي تيرهاي عميق آشكار ساخته است.

In this paper, the behavior of several reinforced concrete deep beams has been studied by means of finite element analysis, and the results are compared with experimental results reported by Arabzadeh, Leonard and Walter. Reinforced Concrete deep beams are structural elements used in dams, offshore piers, rectangular tanks, bridges, floors, diaphragms and high rise buildings. The definition of a reinforced concrete deep beam, by various codes, is based on the span to height ratio of the beam. Generally, the span to height ratio of deep beams is required to not be greater than 2.5. These beams have four different modes of failure: 1) Flexural, 2) Flexural-Shear, 3) Shear, and 4) Bearing. Since the ratio of width to height of deep beams is small and concrete acts unsymmetrically against tension and compression, a plain-stress model and nonlinear analysis are used in the study of these beams. In this paper, a finite element program is presented for the nonlinear analysis of two-dimensional and asymmetrical problems. In the case of reinforced concrete structures, the plasticity of concrete in compression, the yielding of reinforcement and the cracking of concrete under tension are accounted for. A new algorithm for embedding curved reinforcement in concrete elements is used in the program. NAOC software is a program written in “Visual Basic”, which has considerable capability for graphical presentation of input data and output results. In the nonlinear analysis section, program results include the vertical load versus vertical displacement curve, the crack pattern and the ultimate load of analytical models. Solving different examples with the NAOC program, the obtained results were compared with available test results. The comparisons validated the accuracy, efficiency and ability of the NAOC program to investigate shear strength in RC deep beams. Nonlinear stress analysis of reinforced concrete may also be conducted by the finite element method, although careful modeling of the reinforcement and cracking behavior regarding shear effects is needed.