Analysis and Design of a Complex⁃Shaped High⁃Rise Cantilevered Steel Structure
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摘要: 本工程为铸铜人物雕像,整体外形呈高层悬挑状,其结构形式为异形空间桁架结构。该人物雕像主要分为竖直身体部分及水平悬挑披风两部分。竖直身体部位高度为32 m,采用层高约为2 m的竖向叠放空间钢桁架。悬挑披风的悬挑长度为24 m,采用宽度约为2 m沿水平排列布置的空间钢桁架。考虑到各部分杆件的受力特征及施工便利性,竖向部分钢桁架的上下弦杆采用工字型截面、腹杆采用圆钢管,悬挑部分钢桁架的杆件均采用圆钢管。鉴于本结构的特殊性,采取了抗震性能化设计与稳定验算相结合的整体结构分析方法,并且针对重要节点开展了有限元分析,从而有效确保结构设计结果的安全性。根据结构的特性确定了本结构的抗震性能目标,竖向部分的抗震性能目标为设防地震弹性、罕遇地震不屈服,水平部分的性能目标为多遇地震弹性、设防地震不屈服、罕遇地震部分屈服。多遇地震弹性分析结果表明,在充分考虑铸铝蒙皮效应时,本结构的位移满足JGJ 7—2010《空间网格结构技术规程》要求。设防地震等效弹性分析结果显示,竖向部分的杆件应力比均在0.85范围之内,水平大部分杆件的应力比处于0.7范围之内,满足设防地震性能目标。本结构的弹塑性时程分析结果显示,披风处构件的延性系数可达0.96,身体部分构件的延性系数最大值为0.78,底层柱的延性系数均小于0.2,均满足罕遇地震抗震性能目标。采用特征值屈曲分析法和双非线性稳定分析法开展了整体结构的稳定验算。特征值屈曲分析结果表明前3阶屈曲模态集中于悬挑披风竖向变形屈曲,该屈曲模态符合悬挑结构的结构特征。双非线性稳定分析的荷载工况分别为恒载+满布活载(工况1)、恒载+半布活载(工况2)、恒载+风载(工况3),计算结果表明3种工况的临界荷载系数分别为2.1、2.7、3.2,均大于规范限值2.0。水平披风跨中和竖向身体腹部的部分杆件均进入塑性阶段,即率先屈服部位的杆件将是本结构失稳破坏的薄弱环节。竖向部分关键节点采取设防地震弹性荷载设计值,水平部分关键节点选用设防地震不屈服荷载设计值,基于此,建立典型节点有限元模型。通过有限元分析得到了关键节点在设防目标荷载设计值作用下的应力状态:竖向部分关键节点的最大应力为264.4 MPa,水平部分关键节点的最大应力为292.97 MPa,均保持在弹性阶段,满足抗震性能目标。Abstract: This project is a cast bronze statue with an overall shape of a high-rise cantilevered form, and its structural system is a special-shaped spatial truss structure. The statue is mainly divided into two parts: the vertical body section and the horizontal cantilevered cloak. The vertical body section has a height of 32 m and adopts a vertically stacked spatial steel truss with a story height of approximately 2 m. The cantilevered cloak has a length of 24 m and employs a horizontally arranged spatial steel truss with a width of approximately 2 m. Considering the stress characteristics and construction convenience of the members in each part, the upper and lower chords of the vertical section of the steel truss use I-shaped sections, the web members use round steel tubes, and the members of the cantilevered section of the steel truss also use round steel tubes. In view of the particularity of this structure, an overall structural analysis method combining seismic performance design and stability verification was adopted. A finite element analysis was carried out for critical joints to effectively ensure the safety of the structural design results. Firstly, the seismic performance objectives of the structure were determined according to its characteristics: the vertical members were designed to remain elastic under moderate earthquakes and non-yielding under major earthquakes, while the horizontal members were designed to remain elastic under minor earthquakes, non-yielding under moderate earthquakes, and partially yielding under major earthquakes. The results of the elastic analysis under minor earthquakes showed that the displacements of the structure met the code requirements when the effects of the cast aluminum cladding was fully considered. The equivalent elastic analysis results for moderate earthquakes showed that the stress ratios of vertical members were within 0.85, and those of most horizontal members were within 0.7, meeting the performance target for moderate earthquakes. The elastic-plastic time-history analysis results of the structure showed that the ductility coefficient of the members at the cloak reached 0.96, the maximum ductility coefficient of the body part members was 0.78, and the ductility coefficients of the bottom columns were all less than 0.2, which met the seismic performance objectives for major earthquakes. Then, the eigenvalue buckling analysis method and the dual nonlinear stability analysis method were used to carry out the stability check of the overall structure. The eigenvalue buckling analysis results showed that the first three buckling modes were concentrated in the vertical deformation buckling of the cantilevered cloak, and this buckling mode conformed to the structural characteristics of the cantilevered structure. The load cases of the dual nonlinear stability analysis were dead load + full live load (Case 1), dead load + semi-distributed live load (Case 2), and dead load + wind load (Case 3), respectively. The calculation results showed that the critical load coefficients for the three cases were 2.1, 2.7, and 3.2, all of which exceeded the specification limit of 2.0. Some members in the span of the horizontal cloak and in the belly of the vertical body had entered the plastic stage, meaning that the members at the first yielding position would become the weak link in structural instability and failure. The design value of the elastic load for moderate earthquakes was adopted for the critical joints in the vertical part, while the design value of the non-yielding load for moderate earthquakes was adopted for the critical joints in the horizontal part. The finite element model of typical joints was established. Through finite element analysis, the stress state of critical joints under the design value of the fortification target load was obtained. The maximum stress of the critical joints in the vertical part was 270 MPa, and that of the critical joints in the horizontal part was 300 MPa. Both remained in the elastic stage, meeting the seismic performance objectives.
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