含鋼板阻尼器構架最佳化設計研究

Optimization of Steel Panel Damper for Moment Resisting Frame Designs

張舉虹(Chu-Hung Chang)

指導教授 ： 蔡克銓

國立臺灣大學/工學院/土木工程學研究所/碩士(2018年)

https://doi.org/10.6342/NTU201803137

摘要

在抗彎構架中配置鋼板阻尼器(Steel Panel Damper, SPD)，能有效提升構架側向勁度、強度與韌性。本研究之鋼板阻尼器為三段式寬翼構件，中段為非彈性核心段(Inelastic Core, IC)，上下兩段為彈性連接段(Elastic Joint, EJ)。在地震作用下SPD主要透過核心段反覆受剪來達到消能之目的。在核心段配置加勁板，可延緩SPD挫屈之時機，使受力變形遲滯消能行為飽滿。SPD之剪力強度由IC段剪力面積與剪降伏應力控制，因此可在SPD強度不變下，增加其勁度。然增加SPD或邊界梁勁度，皆能提升整體構架勁度；傳統多以試誤法設計含SPD構架，無法保證最經濟之設計。本研究根據反曲點，從構架中取出SPD與邊界梁十字子構架，在選定SPD降伏強度下，以滿足耐震設計及提升十字子構架側向勁度為條件，研究最少用鋼量之設計。
本研究利用MATLAB的最佳化工具箱，結合模擬退火法(Simulated Annealing, SA)與梯度下降法成混合式演算法(Hybrid Algorithms)，應用於構件最佳化設計。所探討之SPD配置於梁跨中心，上下層SPD斷面相同，僅探討SPD、邊界梁與其交會區之設計，以SPD、加勁板、邊界梁全長、交會區疊合板與連續板的總用鋼量為目標函數；SPD斷面、加勁板尺寸、邊界梁斷面與交會區疊合板厚為設計變數；以滿足SPD、邊界梁與交會區容量設計法、SPD核心段加勁板設計及防止斷面局部挫屈與側向扭轉挫屈等作為限制條件。
在已知樓高、邊界梁淨跨距、梁未支撐長度、SPD降伏強度、SPD與邊界梁材料，透過最佳化演算法找到符合安全性、韌性與穩定性等條件下，最少用鋼量之設計斷面為「基本設計」。另根據所提之十字子構架各變形分量，計算基本設計SPD降伏時十字子構架的層間位移角，以子構架側向勁度增加50%為新增限制條件，再次進行最佳化設計，稱最少用鋼量之斷面為「1.5倍十字架勁度之設計」。
研究顯示在滿足強度、韌性與斷面及構件穩定性要求下，只需增加約13%用鋼量，即可使子構架側向勁度增加50%。為了提高子構架勁度，寬翼斷面以增加深度與腹板厚較有效，其中又以增加邊界梁深與梁腹厚較為有效，但此將導致梁強度增大約為基本設計之1.4倍，影響強柱弱梁設計；因此另對邊界梁強度做不可大於基本設計1.25倍的限制，發現需增加約20%用鋼量，才可使子構架側向勁度增加50%；此外，亦導致邊界梁深度過深，深度甚至須增至1200 mm，恐影響建築使用效益；故另對梁深設上限，發現需增加約34%用鋼量，才可使子構架側向勁度增加50%，其中變數改以增加翼板寬與腹板厚為主。以梁跨9 m，SPD降伏強度1500 kN為例，欲使十字子構架側向勁度增加50%，梁強度為基本設計的1.4倍，梁深增為1200 mm，「1.5倍十字架勁度之設計」單位重量勁度為5.5/mm；對梁強度做1.25倍限制後，梁深為1175 mm，「1.5倍十字架勁度之設計」單位重量勁度為5.4/mm；對梁深度做800mm之上限後，梁強度為基本設計的1.2倍，「1.5倍十字架勁度之設計」單位重量勁度降為3.4/mm；上述變數皆為連續型設計結果。另探討實際工程應用之離散設計變數結果，以梁跨9 m，SPD降伏強度為700 kN為例，欲使子構架側向勁度增加50%，需比基本設計增加約44%之用鋼量。
另提出考慮邊界梁受垂直載重造成額外彎矩之容量設計法，並應用於最佳化設計中；分析五種配置SPD於構架中的形式，可發現SPD邊界梁與小梁垂直配置時，將導致邊界梁承受較大垂直載重彎矩，故建議小梁應盡量與SPD邊界梁平行配置。

關鍵字

鋼板阻尼器 ； 耐震設計 ； 容量設計 ； 挫屈束制 ； 最佳化設計 ； 模擬退火法 ； 有限元素模型分析

並列摘要

The strength, stiffness and ductility of the lateral force resisting frame can be enhanced by incorporating the steel panel dampers (SPDs) into a moment resisting frame (SPD-MRF). The proposed 3-segment SPD is a steel wide-flange section,which consists of one middle inelastic core (IC) and two end elastic joints (EJs). During the earthquake, the two EJs of the same cross-sectional property, are designed to remain elastic while the IC could undergo large inelastic shear deformation thereby dissipating seismic energy. In order to sustain a large deformation and delay the shear buckling of the IC web, stiffeners must be properly deviced. The shear strength of the SPD can be determined from the shear area and yield stress of the IC web. Therefore, the stiffness and strength of SPD can be decoupled. The lateral stiffness of the SPD-MRF can be enhanced by either increasing the stiffness of the SPD or boundary beams. Thus, the stiffness of the two half-height SPDs connected to the boundary beam subassembly can be defined and analyzed by using the four inflection points. In this study, optimization algorithm is adopted to design the SPD-MRF members, and to achieve the minimum steel weight design. The results, comply with the seismic design requirements and the specified lateral stiffness enhancement of SPD-to-beam subassembly for a wide range of SPD strengths and beam spans.
In this study, it is assumed that two identical SPDs are attached to the mid-span of the boundary beam. The focus of the study is the designs of the SPD, the boundary beam and the SPD-to-beam panel zone. The MATLAB optimization toolbox combined the simulated annealing algorithm with the gradient descent method is adopted to find the minimum steel weight design. The objective function is the total weight of the SPD, the boundary beam and the panel zone. The design variables are SPD’s sectional properties of the SPD, the boundary beam and the doubler plate thickness. Constraints must be the capacity design of the SPD, boundary beam and panel zone, the stiffeners of the IC web, compact section and lateral torsional buckling limit state design requirements.
While consider the story height, beam clear span, unbraced beam length, SPD shear strength, steel grade of SPD and beam as given parameters, the lightest SPD and beam sections meeting the aforementioned constraints can be found through optimization algorithm. These lightest sections which regarded as the ‘‘basic design’’. Then, the inter story drift ratio (IDR) of the PD-to-beam subassembly taken form the “basic design” are evaluated at a shear when the SPD reaches yield strength. Subsequently, an increace of 50% more stiffness of the subassembly as the new constraints, the optimization designs were conducted again. Results are defined as the‘‘1.5 times stiffened designs’’.
While complying with the aforementioned constraints, steel weight is increased by about 13% to achieve a 50% stiffened design. The stiffness of subassembly is found enhanced mostly by increasing beam depth and web thickness. However, this also leads to an increase of the beam flexural strength by about 40%. This obviously is not favorable to the strong column weak beam design. Thus, as an additional constraint, beam strength is limited to no greater than 1.25 times of that in the basic design. As the result, the steel weight would increase by about 20% to achieve the specified 50% stiffened design. In addition, it may also result in a 1200 mm deep beam depth, which could impact the ceiling height. Thus, limit the beams to the specified depths for different SPDs are set as a constraint. The resulting steel weight increases by 34% to achieve the 50% stiffeded subassembly. Taking the 9-meter long beam and the 1500-kN SPD for example, beam strength would be 1.4 times of the basic design, beam depth would be 1200 mm to achieve the 50% stiffened subassembly, and the stiffnes to weight ratio (SWR) is 5.5/mm. When the constraint of no greater than 1.25 times the basic beam strength is imposed, beam depth would be 1175 mm to achieve 50% stiffened subassembly, and the SWR would be 5.4/mm. While constraining the beam depth to 800 mm, beam strength would be 1.2 times of the basic design to achieve the 50% stiffened design, but the SWR would be only 3.4/mm. Finally, optimized designs using discrete design variables are discussed. Taking the 9-meter long beam and the 700-kN SPD for example, the steel weight increases by 44% to achieve the 50% stiffened subassembly.
Effects of the gravity loads on the capacity design of the boundary beam is also investigated. According to the five different configurations of SPDs in the MRFs, gravity beams frame into the boundary beam could result in a large gravity moment in the boundary beam. Therefore, it is suggested that gravity beams be oriented parallel to the boundary beam.

並列關鍵字

steel panel damper ； seismic design ； capacity design ； buckling restrained ； optimization design ； simulated annealing ； finite element model analysis

參考文獻

1. AISC 341-10 (2010). “Seismic Provisions for Structural Steel Buildings.” American Institution of Steel Construction, Chicago.

2. ASCE 7-10 (2010). “Minimum Design Loads for Buildings and Other Structures” American Society of Civil Engineers.

3. Chen, Z., Ge, H., Usami, T. (2006). “Hysteretic Model of Stiffened Shear Panel Dampers.” Journal of structural engineering, 132, 478-483.

4. Chen, Z., Ge, H., Usami, T., YUAN, Y. (2011). “Ultimate shear strength of shear panel damper under cyclic load” Journal of Shenyang University of Technology, Vol. 33, No. 2

5. Chusilp, P., & Usami, T. (2002). “New Elastic Stability Formulas for Multiple-Stiffened Shear Panels.” Journal of Structural Engineering, 128(6), 833-836.