{"title":"Limit analysis of masonry arches and domes with finite strength: funicular analysis versus stability area method","authors":"Danila Aita, Matteo Bruggi, Alberto Taliercio","doi":"10.1007/s11012-024-01781-7","DOIUrl":null,"url":null,"abstract":"<p>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.</p>","PeriodicalId":695,"journal":{"name":"Meccanica","volume":null,"pages":null},"PeriodicalIF":1.9000,"publicationDate":"2024-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Meccanica","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1007/s11012-024-01781-7","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MECHANICS","Score":null,"Total":0}
引用次数: 0
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.
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.