{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:02:15Z","timestamp":1760230935573,"version":"build-2065373602"},"reference-count":35,"publisher":"MDPI AG","issue":"16","license":[{"start":{"date-parts":[[2022,8,22]],"date-time":"2022-08-22T00:00:00Z","timestamp":1661126400000},"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":["52108464","2021997791"],"award-info":[{"award-number":["52108464","2021997791"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Professional Construction Support Plan of Sichuan Agricultural University","award":["52108464","2021997791"],"award-info":[{"award-number":["52108464","2021997791"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In seismic assessment of continuous girder bridges, plastic hinges form in bridge piers to dissipate seismic energy through nonlinear restoring forces. Considering temporal and spatial variations of ground motions, seismic evaluation of the bridges involves nonlinear stochastic vibration and expensive computation. This paper presents an approach to significantly increase the efficiency of seismic evaluation for continuous girder bridges with plastic hinges. The proposed approach converts nonlinear motion equations into quasi-linear state equations, solves the equations using an explicit time-domain dimension-reduced iterative method, and incorporates a stochastic sampling method to statistically analyze the seismic response of bridges under earthquake excitation. Taking a 3 \u00d7 30 m continuous girder bridge as an example, fiber beam-column elements are used to simulate the elastic\u2013plastic components of the continuous girder bridge, and the elastic\u2013plastic time history analysis of the continuous girder bridge under non-uniform seismic excitation is carried out. Results show that the computation time is only 5% of the time of the nonlinear time history approach while retaining the accuracy. This study advances the capability of rapid seismic assessment and design for bridges with localized nonlinear behaviors such as plastic hinges.<\/jats:p>","DOI":"10.3390\/s22166311","type":"journal-article","created":{"date-parts":[[2022,8,22]],"date-time":"2022-08-22T23:49:56Z","timestamp":1661212196000},"page":"6311","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Rapid Seismic Evaluation of Continuous Girder Bridges with Localized Plastic Hinges"],"prefix":"10.3390","volume":"22","author":[{"given":"Zhaolan","family":"Wei","sequence":"first","affiliation":[{"name":"School of Civil Engineering, Sichuan Agricultural University, Dujiangyan 611830, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mengting","family":"Lv","sequence":"additional","affiliation":[{"name":"School of Civil Engineering, Sichuan Agricultural University, Dujiangyan 611830, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Minghui","family":"Shen","sequence":"additional","affiliation":[{"name":"School of Civil Engineering, Sichuan Agricultural University, Dujiangyan 611830, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haijun","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Civil Engineering, Sichuan Agricultural University, Dujiangyan 611830, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qixuan","family":"You","sequence":"additional","affiliation":[{"name":"School of Civil Engineering, Sichuan Agricultural University, Dujiangyan 611830, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kai","family":"Hu","sequence":"additional","affiliation":[{"name":"School of Civil Engineering, Sichuan Agricultural University, Dujiangyan 611830, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shaomin","family":"Jia","sequence":"additional","affiliation":[{"name":"School of Civil Engineering, Sichuan Agricultural University, Dujiangyan 611830, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,8,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1016\/j.soildyn.2018.12.016","article-title":"Emulative seismic resistant technology for accelerated bridge construction","volume":"124","author":"Mashal","year":"2019","journal-title":"Soil Dyn. Earthq. Eng."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1016\/j.engstruct.2017.01.015","article-title":"Cyclic behavior of damaged reinforced concrete columns repaired with high-performance fiber-reinforced cementitious composite","volume":"136","author":"Li","year":"2017","journal-title":"Eng. Struct."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"109699","DOI":"10.1016\/j.engstruct.2019.109699","article-title":"Plastic hinge behavior and rotation capacity in reinforced ductile concrete flexural members","volume":"200","author":"Pokhrel","year":"2019","journal-title":"Eng. Struct."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"110225","DOI":"10.1016\/j.engstruct.2020.110225","article-title":"Experimental investigation on the seismic performance of low-level corroded and retrofitted reinforced concrete bridge columns with CFRP fabric","volume":"209","author":"Jia","year":"2020","journal-title":"Eng. Struct."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"398","DOI":"10.1061\/(ASCE)1084-0702(2008)13:4(398)","article-title":"Role of shear keys in seismic behavior of bridges crossing fault-rupture zones","volume":"13","author":"Goel","year":"2008","journal-title":"J. Bridge Eng."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1367","DOI":"10.1016\/S0141-0296(99)00076-0","article-title":"Analysis of cable-stayed bridges under multi-component random ground motion by response spectrum method","volume":"22","author":"Allam","year":"2000","journal-title":"Eng. Struct."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"314","DOI":"10.1016\/j.soildyn.2014.07.013","article-title":"Nonlinear dynamic analysis of base isolated cable-stayed bridge under earthquake excitations","volume":"66","author":"Atmaca","year":"2014","journal-title":"Soil Dyn. Earthq. Eng."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"04015160","DOI":"10.1061\/(ASCE)ST.1943-541X.0001440","article-title":"Framework of nonlinear dynamic simulation of long-span cable-stayed bridge and traffic system subjected to cable-loss incidents","volume":"142","author":"Zhou","year":"2016","journal-title":"J. Struct. Eng."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"500","DOI":"10.1016\/j.engstruct.2018.09.014","article-title":"Nonlinear dynamic response analysis of vehicle\u2013bridge interactive system under strong earthquakes","volume":"176","author":"Borjigin","year":"2018","journal-title":"Eng. Struct."},{"key":"ref_10","unstructured":"Nayfeh, A.H. (2008). Perturbation Methods, John Wiley & Sons."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1006\/jsvi.1999.2668","article-title":"Statistical linearization of the Duffing oscillator under non-Gaussian external excitation","volume":"231","author":"Sobiechowski","year":"2000","journal-title":"J. Sound Vib."},{"key":"ref_12","unstructured":"Roberts, J.B., and Spanos, P.D. (2003). Random Vibration and Statistical Linearization, Courier Dover Publications."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"102044","DOI":"10.1016\/j.strusafe.2020.102044","article-title":"Nonlinear stochastic dynamic analysis by evolutionary tail-equivalent linearization method","volume":"90","author":"Broccardo","year":"2021","journal-title":"Struct. Saf."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"04016053","DOI":"10.1061\/(ASCE)EM.1943-7889.0001106","article-title":"Tail-equivalent linearization of inelastic multisupport structures subjected to spatially varying stochastic ground motion","volume":"142","author":"Wang","year":"2016","journal-title":"J. Eng. Mech."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1016\/0022-460X(72)90600-1","article-title":"Digital simulation of random processes and its applications","volume":"25","author":"Shinozuka","year":"1972","journal-title":"J. Sound Vib."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"119","DOI":"10.12989\/eas.2014.7.2.119","article-title":"Efficient MCS for random vibration of hysteretic systems by an explicit iteration approach","volume":"7","author":"Su","year":"2014","journal-title":"Earthq. Struct."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2050054","DOI":"10.1142\/S0219455420500546","article-title":"Influence of random multi-point seismic excitations on the safety performance of a train running on a long-span bridge","volume":"20","author":"Wang","year":"2020","journal-title":"Int. J. Struct. Stab. Dyn."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1061\/JMCEA3.0002106","article-title":"Method for random vibration of hysteretic systems","volume":"102","author":"Wen","year":"1976","journal-title":"J. Eng. Mech. Div."},{"key":"ref_19","unstructured":"Truong, D.Q., and Ahn, K.K. (2012). MR fluid damper and its application to force sensorless damping control system. Smart Actuation and Sensing Systems-Recent Advances and Future Challenges, In Tech."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1243\/PIME_PROC_1994_208_148_02","article-title":"A precise time step integration method.","volume":"208","author":"Zhong","year":"1994","journal-title":"Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1002\/nme.5934","article-title":"Highly precise time integration method for linear structural dynamic analysis","volume":"116","author":"Xing","year":"2018","journal-title":"Int. J. Numer. Methods Eng."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1007\/s11803-012-0096-2","article-title":"Dynamic performance analysis of a seismically isolated bridge under braking force","volume":"11","author":"Yu","year":"2012","journal-title":"Earthq. Eng. Eng. Vib."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"657","DOI":"10.1785\/0120130094","article-title":"A low-dispersive symplectic partitioned Runge\u2013Kutta method for solving seismic-wave equations: II. Wavefield simulations","volume":"105","author":"Ma","year":"2015","journal-title":"Bull. Seismol. Soc. Am."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Rubinstein, R.Y., and Kroese, D.P. (2016). Simulation and the Monte Carlo Method, John Wiley & Sons.","DOI":"10.1002\/9781118631980"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Parsons, T. (2008). Monte Carlo method for determining earthquake recurrence parameters from short paleoseismic catalogs: Example calculations for California. J. Geophys. Res. Solid Earth, 113.","DOI":"10.1029\/2007JB004998"},{"key":"ref_26","unstructured":"(2018). Specifications for Design of Highway Reinforced Concrete and Prestressed Concrete Bridge and Culverts (Standard No. JTG 3362-2018). (In Chinese)."},{"key":"ref_27","unstructured":"(2020). Specifications for Seismic Design of Highway Bridges (Standard No. JTG\/T 2231-01-2020). (In Chinese)."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1616","DOI":"10.1080\/13632469.2019.1592791","article-title":"Effect of damping modeling and characteristics on seismic vulnerability assessment of multi-frame bridges","volume":"25","author":"Abbasi","year":"2021","journal-title":"J. Earthq. Eng."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"04020216","DOI":"10.1061\/(ASCE)ST.1943-541X.0002732","article-title":"Enhanced Rayleigh damping model for dynamic analysis of inelastic structures","volume":"146","author":"Salehi","year":"2020","journal-title":"J. Struct. Eng."},{"key":"ref_30","unstructured":"Clough, R.W., and Penzien, J. (2003). Dynamics of Structures, McGraw-Hill. [3rd ed.]."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1061\/(ASCE)1084-0702(2008)13:4(319)","article-title":"Stochastic response of bridges seismically isolated by friction pendulum system","volume":"13","author":"Jangid","year":"2008","journal-title":"J. Bridge Eng."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"4635","DOI":"10.1007\/s10518-017-0153-3","article-title":"An effective approach for simulating multi-support earthquake underground motions","volume":"15","author":"Liu","year":"2017","journal-title":"Bull. Earthq. Eng."},{"key":"ref_33","unstructured":"Yang, Q.S., and Tian, Y.J. (2008). Earthquake Ground Motions and Artificial Generation, Science Press."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"891","DOI":"10.1002\/eqe.562","article-title":"Physically compliant, conditionally simulated spatially variable seismic ground motions for performance-based design","volume":"35","author":"Liao","year":"2006","journal-title":"Earthq. Eng. Struct. Dyn."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"891","DOI":"10.1002\/eqe.4290140606","article-title":"Response of a rigid foundation to a spatially random ground motion","volume":"14","author":"Luco","year":"1986","journal-title":"Earthq. Eng. Struct. Dyn."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/16\/6311\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:13:35Z","timestamp":1760141615000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/16\/6311"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,8,22]]},"references-count":35,"journal-issue":{"issue":"16","published-online":{"date-parts":[[2022,8]]}},"alternative-id":["s22166311"],"URL":"https:\/\/doi.org\/10.3390\/s22166311","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2022,8,22]]}}}