اثر شرايط تكيه‌گاهي در ارتعاش اعضا محوري (تيرهاي كش) و تحليل حساسيت پارامترهاي موثر در ارتعاش

Analytical Investigation of the Vibration Performance of Tie Rods with Sensitivity Analysis of Effective Factors on Beam Frequency

كاربرد المان‌هاي مهاري (كش‌ها) در ساختمان‌هاي تاريخي از گذشته رايج بوده است و براي تامين پايداري قوس‌ها، حد فاصل پاي قوس اجرا مي‌شود. بازبيني المان كش از نظر نيروي موجود براي بررسي نياز به تعويض آن با يك المان جديد در فرآيند كنترل سلامت سازه، امري ضروري است. در اين پژوهش ضمن بررسي ويژگي ديناميكي كش‌ها، تاثير شرايط تكيه‌گاهي، طول تير كش، سختي محوري و خمشي و نيروي محوري در بسامد ارتعاشي آن ارزيابي و گراف‌هاي كاربردي براي برآورد نيروي محوري موجود تير متناظر با شرايط تكيه‌گاهي مختلف تهيه شده است. از طرفي براي شرايط تكيه‌گاهي نامعلوم، نيروي محوري و سختي خمشي حاصل از روش تحليلي با مقادير آزمايشگاهي مندرج در مرجع]21[ مقايسه شده است. نتايج به‌دست‌آمده، نشان‌دهنده‌ي تاثير پارامترهاي مذكور در بسامد اصلي تير است. از طرفي نيروي محوري فشاري و كششي حاصل از روش تحليلي با نتايج آزمايشگاهي مرجع]21 [تطابق خوبي را نشان داده است. همچنين با افزايش نيروي محوري فشاري، سختي خمشي دو انتهاي تير از شرايط گيرداري كامل فاصله مي گيرد. به‌علاوه رابطه‌ي پيشنهادي نيومارك مي‌تواند تقريب قابل قبولي از نيروي محوري موجود در تير كش را ارايه كند.

The historical application of tie rods in historical buildings was used in the past to ensure the stability of arches and vaults against gravity and horizontal loads. Therefore, the necessity of tie rod health monitoring is a prevalent subject in the vulnerability assessment of historical buildings. The main purpose of this research is to evaluate the dynamic characteristics of tie rods. Also, the effect of several parameters, such as known and unknown boundary conditions, length and cross section, flexural stiffness and axial load, on fundamental frequency, has been evaluated. As a result, after a series of analytical modeling, practical graphs for three types of beam end connection have been developed. It is possible to calculate axial force with the fundamental frequency of in-situ testing with the proposed graphs. Results showed that the frequency is sensitive to all the aforementioned factors. For instance, under known boundary condition, the effect of the support type is more tangible for long span beams. Also, under constant tensile stress, changes in the boundary condition of tie rods with small cross sections did not affect the frequency considerably. Furthermore, length factors for a pinned-pinned beam with small tensile force are not sensitive in comparison with other support conditions. Comparison of analytical results of axial load and flexural stiffness with experimental data of reference 1, showed an acceptable conformity between them. The maximum error for tensile stress was calculated as 12%. This error was 5% for compressive stress. Furthermore, analytical flexural stiffness approached a full rigid support condition, while tensile force increased. This is due to the geometric effect of tensile force on the stiffness matrix of the beam. Also, for unknown boundary conditions, estimated buckling force, regarding Newmark’s analytical formulation, had 3.1% error, with the corresponding force from in-situ dynamic testing obtained from reference 1.