{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:45:19Z","timestamp":1760168719875,"version":"build-2065373602"},"reference-count":23,"publisher":"MDPI AG","issue":"18","license":[{"start":{"date-parts":[[2021,9,7]],"date-time":"2021-09-07T00:00:00Z","timestamp":1630972800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51578158"],"award-info":[{"award-number":["51578158"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>Theoretical or numerical progressive collapse analysis is necessary for important civil structures in case of unforeseen accidents. However, currently, most analytical research is carried out under the assumption of material elasticity for problem simplification, leading to the deviation of analysis results from actual situations. On this account, a progressive collapse analysis procedure for truss structures is proposed, based on the assumption of elastoplastic materials. A plastic importance coefficient was defined to express the importance of truss members in the entire system. The plastic deformations of members were involved in the construction of local and global stiffness matrices. The conceptual removal of a member was adopted, and the impact of the member loss on the truss system was quantified by bearing capacity coefficients, which were subsequently used to calculate the plastic importance coefficients. The member failure occurred when its bearing capacity arrived at the ultimate value, instead of the elastic limit. The extra bearing capacity was embodied by additional virtual loads. The progressive collapse analysis was performed by iterations until the truss became a geometrically unstable system. After that, the critical progressive collapse path inside the truss system was found according to the failure sequence of the members. Lastly, the proposed method was verified against both analytical and experimental truss structures. The critical progressive collapse path of the experimental truss was found by the failure sequence of damaged members. The experimental observation agreed well with the corresponding analytical scenario, proving the method feasibility.<\/jats:p>","DOI":"10.3390\/ma14185135","type":"journal-article","created":{"date-parts":[[2021,9,7]],"date-time":"2021-09-07T10:24:25Z","timestamp":1631010265000},"page":"5135","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Progressive Collapse Safety Evaluation of Truss Structures Considering Material Plasticity"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8936-5123","authenticated-orcid":false,"given":"Sheng-En","family":"Fang","sequence":"first","affiliation":[{"name":"School of Civil Engineering, Fuzhou University, Fuzhou 350108, China"},{"name":"National & Local Joint Engineering Research Center for Seismic and Disaster Informatization of Civil Engineering, Fuzhou University, Fuzhou 350108, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chen","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Civil Engineering, Fuzhou University, Fuzhou 350108, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiao-Hua","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Civil Engineering, Fuzhou University, Fuzhou 350108, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Li-Sen","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Civil Engineering, Fuzhou University, Fuzhou 350108, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhi-Bin","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Civil Engineering, Fuzhou University, Fuzhou 350108, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qing-Yi","family":"Zeng","sequence":"additional","affiliation":[{"name":"Xiamen Jiahe Construction Co., Ltd., Xiamen 361022, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,9,7]]},"reference":[{"key":"ref_1","first-page":"73","article-title":"Preventing Progressive Collapse in Concrete Buildings","volume":"25","author":"Baldridge","year":"2003","journal-title":"Concr. Int."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1163","DOI":"10.1016\/j.istruc.2021.02.045","article-title":"Performance of typical plan concrete buildings under progressive collapse","volume":"31","author":"Panahi","year":"2021","journal-title":"Structures"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Haitao, Z., Yigang, Z., Feng, F., and Jinzhi, W. (2020). Collapse Mechanism of Single-Layer Cylindrical Latticed Shell under Severe Earthquake. Materials, 13.","DOI":"10.3390\/ma13112519"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"2662","DOI":"10.3390\/ma14102662","article-title":"Effects of Corrosion on Compressive Arch Action and Catenary Action of RC Frames to Resist Progressive Collapse Based on Numerical Analysis","volume":"14","author":"Lu","year":"2021","journal-title":"Materials"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Bilow, D.N., and Kamara, M. (2004). U.S. General Services Administration Progressive Collapse Design Guidelines Applied to Concrete Moment-Resisting Frame Buildings. Struct. Congr.","DOI":"10.1061\/40700(2004)156"},{"key":"ref_6","unstructured":"Marchand, K.A., Stevens, D.J., Crowder, B., and Campbell, T. (2009, July 14). UFC 4-023-03, Design of Buildings to Resist Progressive Collapse. Available online: https:\/\/www.wbdg.org\/FFC\/DOD\/UFC\/ufc_4_023_03_2009_c3.pdf."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1016\/S0167-4730(02)00068-1","article-title":"Vulnerability of structural systems","volume":"25","author":"Agarwal","year":"2003","journal-title":"Struct. Saf."},{"key":"ref_8","first-page":"102139","article-title":"Robustness-oriented optimal design for reinforced concrete frames considering the large uncertainty of progressive collapse threats","volume":"39","author":"Praxedes","year":"2021","journal-title":"Struct. Saf."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"679","DOI":"10.1016\/j.engstruct.2017.05.063","article-title":"Probabilistic progressive collapse analysis of steel frame structures against blast loads","volume":"147","author":"Yang","year":"2017","journal-title":"Eng. Struct."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2361","DOI":"10.1016\/j.istruc.2021.06.008","article-title":"Finite element analysis and experimental validation of progressive collapse of reinforced rubberized concrete frame","volume":"33","author":"Alshaikh","year":"2021","journal-title":"Structures"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"499","DOI":"10.1061\/(ASCE)0733-9445(2008)134:3(499)","article-title":"System Safety Performance Metrics for Skeletal Structures","volume":"134","author":"Avinash","year":"2008","journal-title":"J. Struct. Eng."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"230","DOI":"10.1061\/(ASCE)CF.1943-5509.0000236","article-title":"Progressive Collapse Analysis and Safety Assessment Method for Steel Truss Roof","volume":"26","author":"Jiang","year":"2012","journal-title":"J. Perform. Constr. Facil."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1252","DOI":"10.1016\/j.istruc.2020.09.039","article-title":"Progressive collapse design of reinforced concrete frames using structural optimization and machine learning","volume":"28","author":"Esfandiari","year":"2020","journal-title":"Structures"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Qiang, Z., Yangang, Z., Kolozvari, K., and Lei, X. (2020). Simplified model for assessing progressive collapse resistance of reinforced concrete frames under an interior column loss. Eng. Struct., 215.","DOI":"10.1016\/j.engstruct.2020.110688"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"238","DOI":"10.1016\/j.jcsr.2016.03.024","article-title":"An evaluation method to predict progressive collapse resistance of steel frame structures","volume":"122","author":"Chen","year":"2016","journal-title":"J. Constr. Steel Res."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1016\/j.proeng.2017.06.190","article-title":"Robustness and Vulnerability of Flat Slab Structures","volume":"193","year":"2017","journal-title":"Procedia Eng."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"242","DOI":"10.1016\/j.engstruct.2015.01.008","article-title":"Robustness evaluation of RC frame buildings to progressive collapse","volume":"86","author":"Alessandro","year":"2015","journal-title":"Eng. Struct."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1016\/j.jcsr.2015.08.009","article-title":"Novel pin-jointed connection for cold-formed steel trusses","volume":"116","author":"Mathieson","year":"2016","journal-title":"J. Constr. Steel Res."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"109741","DOI":"10.1016\/j.engstruct.2019.109741","article-title":"Failure mechanism and bearing capacity of cold-formed steel trusses with HRC connectors","volume":"201","author":"Mathieson","year":"2019","journal-title":"Eng. Struct."},{"key":"ref_20","first-page":"204","article-title":"Importance coefficients of components in evaluation of structure robustness","volume":"27","author":"Yang","year":"2008","journal-title":"Chin. J. Rock Mech. Eng."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"320","DOI":"10.1016\/j.apm.2019.12.015","article-title":"An iterative elastic SBFE approach for collapse load analysis of inelastic structures","volume":"81","author":"Mellati","year":"2020","journal-title":"Appl. Math. Model."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Lu, J., Zhan, H., and Wu, X. (2021). Experimental study on collapse behaviour of truss string structures under cable rupture. J. Constr. Steel Res., 106864.","DOI":"10.1016\/j.jcsr.2021.106864"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1016\/j.engstruct.2016.03.060","article-title":"Constitutive model for full-range elasto-plastic behavior of structural steels with yield plateau, Calibration and validation","volume":"118","author":"Fangxin","year":"2016","journal-title":"Eng. Struct."}],"container-title":["Materials"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1996-1944\/14\/18\/5135\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:58:10Z","timestamp":1760165890000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1996-1944\/14\/18\/5135"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,9,7]]},"references-count":23,"journal-issue":{"issue":"18","published-online":{"date-parts":[[2021,9]]}},"alternative-id":["ma14185135"],"URL":"https:\/\/doi.org\/10.3390\/ma14185135","relation":{},"ISSN":["1996-1944"],"issn-type":[{"type":"electronic","value":"1996-1944"}],"subject":[],"published":{"date-parts":[[2021,9,7]]}}}