Limit analysis of masonry arches and domes with finite strength: funicular analysis versus stability area method

IF 1.9 3区 工程技术 Q3 MECHANICS
Danila Aita, Matteo Bruggi, Alberto Taliercio
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Abstract

This study, framed within the context of the lower bound theorem of limit analysis, aims to assess the anti-funicular equilibrium of masonry arches and domes using a computational approach based on the constrained force density method. In contrast to the commonly adopted classical Heyman’s assumptions, the approach proposed here considers the effects of finite compressive strength in the material. Assuming a fixed plan projection for a network with independent sets of branches, a suitable set of local constraints is enforced at each joint to account for the limit bending moment resulting from the material’s assumptions, including limited compressive strength and zero tensile strength. Additionally, the stereotomy of the voussoirs is considered by assigning a geometric law to the joint inclination. The collapse load is determined by formulating a multi-constrained maximization problem. The method is validated using a modern version of the semi-analytical Durand-Claye’s method. For benchmark case studies, such as symmetric masonry arches and domes with specific stereotomies subjected to axi-symmetrical load conditions, the set of statically admissible solutions compatible with equilibrium and strength requirements is graphically determined in terms of the horizontal thrust and its eccentricity at the crown, examining the shape of the stability area. Assuming an infinite value for the friction coefficient, the collapse condition is reached when the stability area shrinks to a single point. The results obtained from both of these methods are in excellent agreement. The influence of compressive strength on the bearing capacity of the structures is also discussed.

Abstract Image

具有有限强度的砌体拱和穹顶的极限分析:漏斗分析法与稳定面积法的比较
本研究以极限分析下限定理为框架,旨在使用基于约束力密度法的计算方法,评估砌体拱和穹顶的反船形平衡。与通常采用的经典海曼假设不同,本文提出的方法考虑了材料中有限抗压强度的影响。假设具有独立分支集的网络具有固定的平面投影,则在每个关节处强制执行一套合适的局部约束,以考虑材料假设(包括有限抗压强度和零抗拉强度)所产生的极限弯矩。此外,通过为连接倾斜度指定一个几何定律,考虑了榫槽的立体结构。坍塌荷载是通过提出一个多约束最大化问题来确定的。该方法使用现代版的半分析杜兰-克雷方法进行验证。对于基准案例研究,如对称砌体拱和穹顶在轴对称荷载条件下的特定立体结构,根据水平推力及其在顶部的偏心率,以图形方式确定了符合平衡和强度要求的静态可接受解集,并检查了稳定区域的形状。假设摩擦系数为无限值,当稳定区域缩小到一个点时,就达到了坍塌条件。这两种方法得出的结果非常吻合。此外,还讨论了抗压强度对结构承载能力的影响。
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来源期刊
Meccanica
Meccanica 物理-力学
CiteScore
4.70
自引率
3.70%
发文量
151
审稿时长
7 months
期刊介绍: Meccanica focuses on the methodological framework shared by mechanical scientists when addressing theoretical or applied problems. Original papers address various aspects of mechanical and mathematical modeling, of solution, as well as of analysis of system behavior. The journal explores fundamental and applications issues in established areas of mechanics research as well as in emerging fields; contemporary research on general mechanics, solid and structural mechanics, fluid mechanics, and mechanics of machines; interdisciplinary fields between mechanics and other mathematical and engineering sciences; interaction of mechanics with dynamical systems, advanced materials, control and computation; electromechanics; biomechanics. Articles include full length papers; topical overviews; brief notes; discussions and comments on published papers; book reviews; and an international calendar of conferences. Meccanica, the official journal of the Italian Association of Theoretical and Applied Mechanics, was established in 1966.
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