Journal of Constructional Steel Research最新文献_第5页

Investigation into welding residual stress of high-performance-steel Q500qE welded-joint 高性能钢 Q500qE 焊接接头的焊接残余应力研究

IF 4 2区工程技术 Q1 CONSTRUCTION & BUILDING TECHNOLOGY

Journal of Constructional Steel Research

Pub Date : 2024-11-19 DOI: 10.1016/j.jcsr.2024.109171

Bin Qiang , Qiang Xie , Dian Lei , Hong Yang , Jun Wu , Tihao Qin , Dongming Zhu , Yadong Li

This study investigates the welding residual stress (WRS) spatial distribution in a high-performance steel (HPS) Q500qE unequal-thickness butt-welded joint of steel bridge tower. The hole-drilling and contour methods were used to measure the initial residual stress (IRS) of the base material and WRS in the welded joint. Additionally, the welding process was simulated using ABAQUS, incorporating IRS of base material to study WRS of welded joint. The comparison between measured and simulated WRS showed good agreement, validating the simulation's effectiveness and accuracy. The results reveal that simulated longitudinal and transverse WRSs (LWRS and TWRS) on the top and bottom surfaces indicate high tensile stresses in the weld region, exceeding the measured yield strength of the Q500qE steel. These stresses decrease and transition to compressive states as the distance from the weld increases. LWRS contours show a high tensile stress region along the plate thickness in the weld. Away from the weld, the LWRS is compressive at the surface layer and tensile in the interior zone, especially in the 56 mm-thick base material. The simulated TWRS shows high tensile stress primarily at the weld surface layer, with compressive stress mainly in the surface layer of the 56 mm-thick base material. Compared to vertical WRS (VWRS), the simulated LWRS and TWRS with IRS show higher stress levels and significant stress gradients.

本研究探讨了高性能钢（HPS）Q500qE 不等厚对焊钢桥塔接头中焊接残余应力（WRS）的空间分布。采用钻孔法和等高线法测量了母材的初始残余应力（IRS）和焊接接头中的 WRS。此外，还使用 ABAQUS 模拟了焊接过程，并结合母材的 IRS 研究了焊接接头的 WRS。测量和模拟的 WRS 比较显示出良好的一致性，验证了模拟的有效性和准确性。结果显示，顶部和底部表面的模拟纵向和横向 WRS（LWRS 和 TWRS）表明焊接区域的拉伸应力很大，超过了 Q500qE 钢的实测屈服强度。随着与焊缝距离的增加，这些应力逐渐减小并过渡到压缩状态。LWRS 等值线图显示了焊缝中沿钢板厚度方向的高拉伸应力区域。在远离焊缝的地方，LWRS 在表层为压应力，而在内部区域为拉应力，尤其是在 56 mm 厚的母材中。模拟 TWRS 主要在焊缝表层显示出较高的拉应力，而压应力主要在 56 mm 厚母材的表层。与垂直 WRS（VWRS）相比，带有 IRS 的模拟 LWRS 和 TWRS 显示出更高的应力水平和明显的应力梯度。

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引用次数: 0

Experimental and numerical investigation on ductile fracture of Q235 cold-formed thin-walled steel Q235 冷弯薄壁型钢延性断裂的实验和数值研究

IF 4 2区工程技术 Q1 CONSTRUCTION & BUILDING TECHNOLOGY

Journal of Constructional Steel Research

Pub Date : 2024-11-18 DOI: 10.1016/j.jcsr.2024.109130

Liusi Dai , Jinchen Shi , Shen Yan , Chong Ren

In order to simulate the full-range moment-rotation characteristic of steel storage rack beam-to-upright connections incorporating material fracture, this paper presents experimental and numerical investigations into the fracture behaviour of Q235 cold-formed thin-walled steel (CFTWS) flat and corner materials. A total of 43 specimens derived from Q235 CFTWS plates were tested. Two different thicknesses (1.8 mm and 3.25 mm), three varied bend angles (0°, 70° and 90°), and five types of specimens representing different stress states, were considered. The load-displacement curves and fracture characteristics of each specimen were derived from tests. The refined numerical models were established and validated by the test data. Based on experimental and numerical simulation results, four commonly used ductile fracture models for metal materials were calibrated and compared. The results show that the verified LMVGM fracture model is applicable to Q235 CFTWS flat and corner materials, and then compiled into a USDFLD subroutine in numerical simulation models to predict the flexural behaviour of storage rack beam-to-upright connections. The comparison between test and numerical simulation results illustrates that the established ductile fracture model for Q235 CFTWS materials can accurately simulate the fracture related failure modes of beam-to-upright connections in CFTWS storage racks.

为了模拟包含材料断裂的钢制仓储货架梁对梁连接的全范围力矩旋转特性，本文对 Q235 冷弯薄壁型钢（CFTWS）平板和角钢材料的断裂行为进行了实验和数值研究。共测试了 43 个由 Q235 CFTWS 板材制成的试样。试验考虑了两种不同厚度（1.8 毫米和 3.25 毫米）、三种不同弯曲角度（0°、70° 和 90°）以及代表不同应力状态的五种试样。每个试样的载荷-位移曲线和断裂特征都是通过试验得出的。通过试验数据建立并验证了完善的数值模型。根据试验和数值模拟结果，对四种常用的金属材料韧性断裂模型进行了校准和比较。结果表明，经过验证的 LMVGM 断裂模型适用于 Q235 CFTWS 平面和转角材料，然后将其编译成数值模拟模型中的 USDFLD 子程序，用于预测仓储货架横梁与直梁连接的抗弯行为。测试结果与数值模拟结果的对比表明，已建立的 Q235 CFTWS 材料韧性断裂模型可准确模拟 CFTWS 仓储货架中梁对正连接的断裂相关失效模式。

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引用次数: 0

Triple-actuator apparatus for strength experiments of cold-formed steel members in combined loadings 用于冷弯型钢构件在组合载荷下进行强度实验的三驱动装置

IF 4 2区工程技术 Q1 CONSTRUCTION & BUILDING TECHNOLOGY

Journal of Constructional Steel Research

Pub Date : 2024-11-18 DOI: 10.1016/j.jcsr.2024.109150

Duy Khanh Pham , Cao Hung Pham , Gregory J. Hancock , Colin A. Rogers

Cold-formed steel members are likely to undergo complex combinations of loadings such as bending, shear, and compression. In the literature, numerous test rigs have been developed to test members subject to both isolated and combined actions. These apparatuses are commonly employed for testing combined two actions, such as shear-bending and bending-compression. However, as of today, there is no test rig specifically designed for more complex combined actions including compression, bending and shear. This paper introduces an innovative experimental apparatus namely a “Triple-Actuator Test Rig”, recently developed at the University of Sydney, with a focus on investigating the ultimate behaviour of cold-formed steel channel sections subjected to combined actions of shear, bending and compression. The combined shear and bending is conducted by using two vertical dual actuators, and the axial compression force is applied using an additional horizontal actuator. To elucidate the mechanism of the new apparatus in capturing various combinations of actions, linear static analyses are performed under different cases of combined loadings. Furthermore, detailed information on test controls and procedures is provided. An experimental validation is also conducted to demonstrate the performance of the test rig in investigating not only pure actions but also complex combinations of actions.

冷弯型钢构件可能会承受复杂的组合荷载，如弯曲、剪切和压缩。在文献中，已经开发了许多测试装置，用于测试承受孤立和组合作用的构件。这些设备通常用于测试两种组合作用，如剪切-弯曲和弯曲-压缩。然而，到目前为止，还没有专门针对更复杂的组合作用（包括压缩、弯曲和剪切）而设计的试验台。本文介绍了悉尼大学最近开发的一种创新实验设备，即 "三执行器试验台"，主要用于研究冷弯槽钢型材在剪切、弯曲和压缩等组合作用下的最终性能。剪切和弯曲联合作用通过两个垂直双推杆进行，而轴向压缩力则通过另一个水平推杆施加。为了阐明新仪器捕捉各种组合作用的机制，在不同的组合载荷情况下进行了线性静态分析。此外，还提供了有关测试控制和程序的详细信息。还进行了实验验证，以证明该测试装置不仅在研究纯动作，而且在研究复杂动作组合方面的性能。

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引用次数: 0

Cyclic behavior of steel self-centering prestressed beam-column connection with weakened FCP 削弱 FCP 的钢自定心预应力梁柱连接的循环行为

IF 4 2区工程技术 Q1 CONSTRUCTION & BUILDING TECHNOLOGY

Journal of Constructional Steel Research

Pub Date : 2024-11-17 DOI: 10.1016/j.jcsr.2024.109153

Zi-Qin Jiang , Zi-Yao Niu , Xiao-Feng Yang , Zhong-Shuai Yang , Taichiro Okazaki

A self-centering prestressed beam-column connection (SCPBCC) with weakened flange cover plate (FCP) is proposed to achieve self-centering features and post-earthquake recoverability at reasonable cost. The self-centering and energy dissipation capacity of SCPBCC are controlled respectively by the prestressed cable and FCP, and the bearing capacity of SCPBCC is controlled by adjusting the bearing ratio of the cable and FCP. Five SCPBCC specimens were subjected to large and small-amplitude, cyclic-loading tests. The test results demonstrated that the new SCPBCC can meet requirements of stiffness and strength, achieve excellent self-centering features, survive multiple aftershocks and allows for replacement. The connection can supply ample energy dissipation through cyclic yielding of the FCPs. Reasonable variable section and limited prestress can protect beams and the column from plastic deformation. The proposed design methodology ensures good bearing and self-resetting capacity for SCPBCCs.

本文提出了一种带有削弱翼缘盖板（FCP）的自定中心预应力梁柱连接（SCPBCC），以合理的成本实现自定中心功能和震后恢复能力。SCPBCC 的自定心和耗能能力分别由预应力拉索和 FCP 控制，而 SCPBCC 的承载能力则通过调整拉索和 FCP 的承载比来控制。对五个 SCPBCC 试件进行了大振幅和小振幅循环加载试验。试验结果表明，新型 SCPBCC 能够满足刚度和强度要求，具有出色的自定心功能，可经受多次余震并允许更换。通过 FCP 的周期性屈服，该连接可提供充足的能量消耗。合理的变截面和有限的预应力可以保护梁和柱不发生塑性变形。建议的设计方法可确保 SCPBCC 具有良好的承载能力和自复位能力。

引用次数: 0

An effective stress approach for the design of rectangular hollow section flexural members with slender elements 设计带有细长构件的矩形空心截面抗弯构件的有效应力法

IF 4 2区工程技术 Q1 CONSTRUCTION & BUILDING TECHNOLOGY

Journal of Constructional Steel Research

Pub Date : 2024-11-16 DOI: 10.1016/j.jcsr.2024.109143

Brendan Richards , Kamran Tayyebi , Min Sun , Kyle Tousignant

An evaluation of North American and European design provisions for rectangular hollow section (RHS) flexural members with slender elements is performed. Seventy-three non-linear finite element models, covering practical ranges of width-to-thickness, height-to-thickness, and aspect ratio are developed, validated, and analyzed. The results demonstrate that current Class 3 or non-compact limit(s) in CSA S16, AISC 360, and EN 1990 are accurate; however, the effective width methods used in the current nominal strength expressions are inconsistent across different RHS orientations, and conservative (up to 11 %). To address this, a new effective stress approach using gross-section properties was explored. The new approach is shown to increase (up to 9 %) the accuracy and precision of nominal strength predictions when compared to the current approach(es), for all orientations, and still meet/exceed target reliability indices based on an approximate first-order reliability method analysis.

本研究评估了北美和欧洲对带有细长构件的矩形空心截面 (RHS) 挠性构件的设计规定。开发、验证和分析了 73 个非线性有限元模型，涵盖了宽度-厚度、高度-厚度和长宽比的实际范围。结果表明，目前 CSA S16、AISC 360 和 EN 1990 中的 3 级或非紧凑型限制是准确的；但是，目前名义强度表达式中使用的有效宽度方法在不同的 RHS 方向上并不一致，而且比较保守（最多为 11%）。为了解决这个问题，我们探索了一种使用总截面特性的新有效应力方法。与目前的方法相比，新方法在所有方向上都能提高（高达 9%）名义强度预测的准确性和精确度，并且仍能达到/超过基于近似一阶可靠性方法分析的目标可靠性指数。

引用次数: 0

Machine learning for ULCF life prediction of structural steels with synthetic data 利用合成数据对结构钢的 ULCF 寿命进行机器学习预测

IF 4 2区工程技术 Q1 CONSTRUCTION & BUILDING TECHNOLOGY

Journal of Constructional Steel Research

Pub Date : 2024-11-16 DOI: 10.1016/j.jcsr.2024.109152

Mingming Yu , Shuailing Li , Xu Xie

Machine learning (ML) has gradually developed into an effective method for fatigue life prediction. However, training an accurate and robust ML model is challenging when the data points resulting from expensive tests are scarce. This study proposed and validated of using synthetic ultra-low cycle fatigue (ULCF) life data generated by tabular generative adversarial network (GAN) as input for ML models. The ULCF life prediction using synthetic data was conducted for structural steels through artificial neural network (ANN) and multi-fidelity deep neural network (MFDNN). The results demonstrated that the ANN_Syn model trained with original experimental data plus synthetic data possessed higher mean value and lower standard deviation of R² in ULCF life prediction, compared to the ANN model trained with original experimental data only. The pioneeringly constructed MFDNN model with synthetic data by tabular GAN can generally have good predictive performance. The synthetic data size had more significant influence on the predictive ability of MFDNN model than that of ANN_Syn model. The results of this study will promote the application of ML models on ULCF life prediction of structural steels, thereby greatly reducing the cost of parameters calibration of models for ULCF damage evaluation of steel structures.

机器学习（ML）已逐渐发展成为一种有效的疲劳寿命预测方法。然而，在昂贵的测试所产生的数据点稀缺的情况下，训练一个准确且稳健的 ML 模型具有挑战性。本研究提出并验证了使用表格生成式对抗网络（GAN）生成的合成超低循环疲劳（ULCF）寿命数据作为 ML 模型的输入。通过人工神经网络（ANN）和多保真度深度神经网络（MFDNN）使用合成数据对结构钢进行了超低循环疲劳寿命预测。结果表明，与仅使用原始实验数据训练的 ANN 模型相比，使用原始实验数据和合成数据训练的 ANN_Syn 模型在 ULCF 寿命预测中具有更高的 R2 平均值和更低的标准偏差。通过表格 GAN 利用合成数据率先构建的 MFDNN 模型总体上具有良好的预测性能。与 ANN_Syn 模型相比，合成数据的大小对 MFDNN 模型预测能力的影响更为显著。本研究的结果将促进 ML 模型在钢结构 ULCF 寿命预测中的应用，从而大大降低钢结构 ULCF 损伤评估模型参数标定的成本。

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引用次数: 0

Experimental Investigations on Structural Behaviour of Reusable Interlocking Steel column base Connection with Demountability 具有可拆卸性的可重复使用联锁钢柱底座连接结构行为的实验研究

IF 4 2区工程技术 Q1 CONSTRUCTION & BUILDING TECHNOLOGY

Journal of Constructional Steel Research

Pub Date : 2024-11-16 DOI: 10.1016/j.jcsr.2024.109146

Aswin Kumar Rajakala Jeyabalan , Sivaganesh Kanmani Selvaraj , Tak-Ming Chan

Implementing a circular economy in construction is one of the potential approaches to limit the natural resource consumption by the construction industry and construction waste generation after demolition. There exist necessities for constructing buildings with easier demountability and direct reusability. One of the key aspects of reuse is designing with structural connections for demountability after service life, rendering the buildings for reuse. Therefore, this study endeavours to develop a directly reusable interlocking hold-down type column base connection for steel structures through full-scale experimental and theoretical investigations. The new reusable column base connection consists of a connector plate to replace the anchor rods in the traditional exposed column base connections to connect the concrete footing with the steel column and base plate assembly. This paper investigates the structural behaviour of the new reusable column base connection subjected to monotonic lateral loading and determines the effective embedment depth required for the connector to avoid concrete failure. A loading protocol that signifies reuse through repeated loading sequences is adopted for this study. Thus, each specimen is loaded for three repeated reuse cycles. A theoretical method based on the traditional component model concept representing the connection components as a combination of spring assembly is developed to predict the initial elastic stiffness of the connection. This will consequently aid in estimating the lateral displacement occurring for the corresponding design load. The theoretically predicted stiffness values are in good correlation with the experimental results. The design example for stiffness calculation is also provided for industrial practical applicability.

在建筑业中实施循环经济是限制建筑业自然资源消耗和拆除后产生建筑垃圾的潜在方法之一。有必要建造便于拆卸和可直接重复使用的建筑。重复使用的一个关键方面是设计结构连接，使建筑物在使用寿命结束后可拆卸，从而实现重复使用。因此，本研究致力于通过全尺寸实验和理论研究，为钢结构开发一种可直接重复使用的联锁压紧式柱基连接。这种新型可重复使用的柱基连接由一个连接板组成，用来取代传统外露柱基连接中的锚杆，将混凝土基脚与钢柱和底板组件连接起来。本文研究了新型可重复使用柱基连接在单调侧向荷载作用下的结构行为，并确定了连接器为避免混凝土破坏所需的有效埋入深度。本研究采用了通过重复加载序列表示重复使用的加载协议。因此，每个试样要重复加载三个重复使用周期。研究开发了一种基于传统构件模型概念的理论方法，将连接构件表示为弹簧组件的组合，以预测连接的初始弹性刚度。这将有助于估算相应设计荷载下发生的横向位移。理论预测的刚度值与实验结果具有良好的相关性。此外，还提供了刚度计算的设计实例，供工业实际应用。

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引用次数: 0

Seismic performance of wall plate supported semi-rigid steel frames with a novel type of wall-beam connector 采用新型墙梁连接器的墙板支撑半刚性钢架的抗震性能

IF 4 2区工程技术 Q1 CONSTRUCTION & BUILDING TECHNOLOGY

Journal of Constructional Steel Research

Pub Date : 2024-11-16 DOI: 10.1016/j.jcsr.2024.109161

Wei Bao , Sheng Long , Dongying Liu , Zhiwei Yu , Jiaopeng Fang , Wenzhe Lin

This study focuses on investigating the seismic performance of semi-rigid steel frames (SSFs) reinforced with wall plates and a novel wall-beam connector (WBC). The aim is to address the inherent limitations of these frames regarding lateral resistance and susceptibility to local instability. To evaluate the effectiveness of the proposed reinforcement, three specimens were subjected to pseudo-static cyclic loading. One specimen represented a standard SSF without wall plates, while the other two specimens were supported by wall plates with WBCs of different thicknesses (3 mm and 5 mm). The comparative analysis of the three specimens revealed significant improvements in seismic performance and energy dissipation capacities resulting from the inclusion of the WBCs. The WBCs facilitated displacement deformation, effectively mitigating structural damage caused by seismic forces. Notably, the introduction of WBCs led to a substantial increase in initial stiffness (45.2 % for WBC1 and 111.3 % for WBC2) and a significant enhancement in ultimate bearing capacity (251.9 % increase for WBC2) compared to the standard SSF. The thickness of the WBCs emerged as a crucial factor in regulating the load-bearing capacity, stiffness, and energy dissipation of the structure. The integration of WBCs ensured stable load-bearing functionality for both the frame and wall plate, effectively utilizing the material properties of each component. This configuration enhanced the lateral stiffness and hysteretic behavior of the structure, facilitating staged and incremental yielding and plastic energy dissipation under varying inter-story drifts.

本研究的重点是调查用墙板和新型墙梁连接器（WBC）加固的半刚性钢框架（SSF）的抗震性能。目的是解决这些框架在抗侧能力和易受局部失稳影响方面的固有局限性。为了评估所建议的加固措施的有效性，对三个试样进行了伪静态循环加载。其中一个试样代表了不带墙板的标准 SSF，而另外两个试样则由带有不同厚度（3 毫米和 5 毫米）WBC 的墙板支撑。对这三个试样的对比分析表明，由于加入了有孔板，抗震性能和消能能力都有了显著提高。木筋混凝土促进了位移变形，有效减轻了地震力对结构造成的破坏。值得注意的是，与标准 SSF 相比，引入 WBC 后，初始刚度大幅增加（WBC1 增加 45.2%，WBC2 增加 111.3%），极限承载能力显著提高（WBC2 增加 251.9%）。在调节结构的承载能力、刚度和能量耗散方面，WBC 的厚度是一个关键因素。WBC 的集成确保了框架和墙板的稳定承重功能，有效利用了每个组件的材料特性。这种配置增强了结构的横向刚度和滞后行为，有利于在不同的层间漂移情况下分阶段、渐进式屈服和塑性消能。

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引用次数: 0

HGYF based ultimate bearing capacity analysis of rectangular CFST trusses 基于 HGYF 的矩形 CFST 桁架极限承载力分析

IF 4 2区工程技术 Q1 CONSTRUCTION & BUILDING TECHNOLOGY

Journal of Constructional Steel Research

Pub Date : 2024-11-15 DOI: 10.1016/j.jcsr.2024.109154

Weiwei Xie , Jian Wang , Yan Rong , Wei Zhang , LuFeng Yang

An efficient and high-precision linear elastic iterative method is proposed for ultimate bearing capacity analysis of rectangular concrete-filled steel tube (CFST) trusses, based on the homogeneous generalized yield function (HGYF). Firstly, a fiber model method is developed for evaluating the bearing capacity of rectangular CFST members under combined compression and bending. The influence of material strength and cross-sectional geometric parameters on HGYF of rectangular CFST members is investigated, and the main influencing factors are determined. Then, a HGYF for rectangular CFST members with wide applicability is formulated, based on which the element bearing ratio is defined and a linear elastic iterative method for ultimate bearing capacity analysis of rectangular CFST trusses is introduced on the basis of the elastic modulus reduction method. Finally, the results of the proposed method are compared with test data, generalized yield function (GYF) based results and the results from the traditional incremental nonlinear finite element method (INFEM). Results indicate that the presented HGYF can accurately predict the ultimate bearing capacity of rectangular CFST members while effectively addressing the limitations of GYF. Meanwhile, the proposed HGYF based method agrees well with the test results with high accuracy and efficiency, and can accurately identify the high and low bearing members of truss structure.

基于均质广义屈服函数（HGYF），针对矩形混凝土填充钢管（CFST）桁架的极限承载力分析，提出了一种高效、高精度的线性弹性迭代法。首先，开发了一种纤维模型方法，用于评估矩形 CFST 构件在压缩和弯曲联合作用下的承载能力。研究了材料强度和截面几何参数对矩形 CFST 构件 HGYF 的影响，并确定了主要影响因素。然后，提出了具有广泛适用性的矩形 CFST 构件 HGYF，在此基础上定义了构件承载比，并在弹性模量折减方法的基础上引入了矩形 CFST 桁架极限承载力分析的线性弹性迭代法。最后，将所提方法的结果与测试数据、基于广义屈服函数（GYF）的结果以及传统增量非线性有限元法（INFEM）的结果进行了比较。结果表明，所提出的 HGYF 可以准确预测矩形 CFST 构件的极限承载力，同时有效解决了 GYF 的局限性。同时，所提出的基于 HGYF 的方法与试验结果吻合度高、精度高、效率高，能准确识别桁架结构的高承载力构件和低承载力构件。

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引用次数: 0

A decomposition method for form-finding of circular hybrid cable-truss structures considering self-weight 考虑自重的圆形混合索-桁架结构形式求解分解法

IF 4 2区工程技术 Q1 CONSTRUCTION & BUILDING TECHNOLOGY

Journal of Constructional Steel Research

Pub Date : 2024-11-15 DOI: 10.1016/j.jcsr.2024.109160

Zhenhua Wang , Zhihong Zhang , Zhangli Peng , Xinran Wang , Jiankai Chen , Xinzan Hu

A hybrid cable-truss structure has been previously utilized in the Maracana Stadium. There are two ways to design the initial prestress distribution in the hybrid cable-truss structure, taking into account the functionality of the upper and lower hoop cables. This study proposes a decomposition method for determining the form-finding of circular hybrid cable-truss structures with two different prestress distributions. The hybrid cable-truss structure is decomposed into the inner and outer cable-truss structures. The PBS (partial balance strategy) method is employed to design the prestress and shape of both the inner and outer cable-truss structures with consideration of self-weight. A detailed prestress and shape design analysis of a circular hybrid cable-truss structure with two prestress distributions is conducted, and the precision of the initial prestress design is analyzed. The illustrative example presented herein demonstrates that the proposed method, combined with the PBS method, provides a simple and accurate approach for the form-finding of hybrid cable-truss roof systems subject to self-weight.

马拉卡纳体育场曾采用过混合索-桁架结构。考虑到上下箍索的功能，有两种方法可以设计混合索-桁架结构的初始预应力分布。本研究提出了一种分解方法，用于确定具有两种不同预应力分布的圆形混合索-桁架结构的成型。混合索-桁架结构被分解为内索-桁架结构和外索-桁架结构。在考虑自重的情况下，采用 PBS（部分平衡策略）方法设计内外索桁架结构的预应力和形状。对具有两种预应力分布的圆形混合索桁架结构进行了详细的预应力和形状设计分析，并对初始预应力设计的精度进行了分析。本文提供的示例表明，所提出的方法与 PBS 方法相结合，为受自重影响的混合索桁架屋顶系统的外形确定提供了一种简单而准确的方法。

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引用次数: 0