High impact force attenuation of reinforced concrete systems

Transcription

1 Structures Under Shock and Impact XII 273 Hgh mpact force attenuaton of renforced concrete systems Y. Km, T. El-Korch & K. S. Arsava Department of Cvl and Envronmental Engneerng, Worcester Polytechnc Insttute (WPI), Worcester, MA, USA Abstract Ths paper presents the applcaton of smart control technology to renforced concrete systems for hgh mpact force attenuaton. The smart renforced control system s developed through the ntegraton of renforced concrete beams, smart control devces, sensors, and sgnal processors. Varous combnatons of nput and output sgnals are appled to the smart renforced concrete beams: mpact forces and current sgnals are used as nput sgnals whle acceleratons and dsplacements are used as output sgnals. Based on the set of nput-output sgnals, a nonparametrc model s developed to predct the nonlnear behavour of smart concrete beam systems. It s demonstrated from the expermental studes that the proposed model s effectve n predctng the nonlnear mpact responses of the renforced concrete systems. Keywords: hgh mpact forces, mpact force attenuaton, renforced concrete systems, smart control technology, system dentfcaton, structural control, fuzzy logc model, magnetorheologcal (MR) damper. 1 Introducton The use of concrete systems as structural components, such as brdge grders, has become wde-spread due to superor strength to weght ratos [1]. However, the use of optmzed concrete systems ntroduces new concerns about the vbraton, fre resstance and endurance of such structural members [2, 3]: for example, wheel loads on brdge spans wth standard bolted ral onts can produce mpact loads that may exceed the desgn load as shown n Fgure 1. A collson-nduced mpact and/or a fuel tanker accdent on a brdge or under an overpass wll affect the structural ntegrty of members as shown n Fgure 2 [4]. WIT Transactons on The Bult Envronment, Vol 126, do: /su120241

2 274 Structures Under Shock and Impact XII Fgure 1: Traffc-nduced vbraton of concrete brdges. Fgure 2: Collson-nduced mpact forces of waterway vessel. Several such ncdents have occurred on maor nterstate hghways, beltways, brdges and overpasses n the US. In such scenaros, the mpact led to a weakenng of the long span concrete systems, by reducng the stffness of structural grders and beams and possbly resultng n the collapse of brdge structures. However, such damage mechansms of structures can be sgnfcantly reduced through hgh mpact force attenuatons, usng smart control systems [5, 6]. It s also expected that the reduced damage (e.g. less crackng n concrete) results n delayed stress ncrease wthn the structural components. In addton, mproved dynamc behavor wll result n reduced mantenance and an extended servce lfe of concrete brdges. However, one of the most challengng but mportant tasks n the smart control system desgn for the mpact force attenuatons s the development of an accurate explct mathematcal model of the dynamcal systems under hgh mpact loads to be controlled. The reason s that the mathematcal nformaton related to the dynamc system s used for calculaton of control forces [7]. However, there s no avalable approach n the lterature about how to model an ntegrated structure-mr damper system under hgh mpact loads (ncludng the nteracton effects between a structure and MR dampers). Wth ths n mnd, a mathematcal model for descrbng the nonlnear behavor of the ntegrated concrete-mr damper systems under hgh mpact loads s developed. The paper s organzed as follows: Secton 2 dscusses about the system dentfcaton process usng a Takag-Sugeno fuzzy modellng framework. Expermental studes and modellng results are descrbed n Secton 3. Concludng remarks are gven n Secton 4. 2 System dentfcaton 2.1 Takag Sugeno (TS) fuzzy model In 1985, Takag and Sugeno [8] developed a systematc methodology for a fuzzy reasonng usng lnear functons n the consequent part. Because the TS-fuzzy

3 Structures Under Shock and Impact XII 275 model uses lnear functons n the consequent part, the defuzzfcaton procedure s not requred. A typcal fuzzy rule for the TS fuzzy model has the form R : If z s p and z s p and and z s p 1 2 FZ 1, FZ 2, FZ, n k k k Then, y a y b u,,, 1 1 m (1) where R s the th rule of the fuzzy model; z FZ s the premse varable; u(k) and y(k) are the nput and output, respectvely; a, and b, are the consequent parameters to be estmated; n and m are the number of delay steps n the output and nput sgnals, respectvely. The TS fuzzy model-based reasonng s to smply compute weghted mean values y fnal Nr 1 wy( k) Nr 1 w, (2) where Nr s the number of the fuzzy rules and n 1, FZ w z, (3) where, ( zfz) s the grades of membershp of z FZ. In ths paper, the premse parameters are determned usng the fuzzy C-means clusterng algorthm [9] whle the consequent parameters are optmzed va the backpropagaton neural network algorthm [10]. 2.2 Identfcaton of hgh mpact responses Fgure 3 shows the confguraton of the structural system equpped wth nonlnear hysteretc actuators. In ths study, two MR dampers are mplemented nto the structural system for mpact force attenuatons. In ths paper, a two-nput and sngle output TS fuzzy model s developed such that the fuzzy model effectvely predcts the mpact responses of the smart structures. The hgh mpact force and current sgnals are used as the 1 st and 2 nd nput sgnals whle ether dsplacement or acceleraton responses are used as the output sgnal.

4 276 Structures Under Shock and Impact XII Fgure 3: Nonlnear system dentfcaton process of ntegrated structurecontrol system under hgh mpact loads. 3 Expermental study 3.1 Expermental setup To demonstrate the effectveness of the TS fuzzy modellng framework, an expermental setup s establshed n order to generate many sets of nput and output data as shown n Fgure 4(c) to (d). Renforced concrete beams measurng cm were constructed as shown n Fgure 4(a). The longtudnal steel (a) (b) (c) Fgure 4: (d) Confguraton of smart concrete beam constructon and data acquston system setup to study dynamc behavor of structures equpped wth MR dampers.

5 Structures Under Shock and Impact XII 277 conssted of deformed bars havng a yeld of 248MPa wth 7.5 cm n dameter. Three longtudnal bars were placed n the tenson and compresson zone. Strrups conssted of 0.25 cm steel wre spaced between 5, 7.5 and 10 cm for dfferent beams. Portland cement concrete mxtures wth a maxmum aggregate sze of 6.5 mm were used as shown n Fgure 4(b). The concrete beams were cured n a curng room for over three weeks. At tme of testng, the compressve strength of the concrete was 26 MPa and the modulus of elastcty E was 15 GPa. 3.2 Results Fgure 5 compares the measured data wth the predcted model. It s clearly seen that the proposed TS fuzzy model effectvely predcts nonlnear behavor of the structural concrete system equpped wth MR dampers. Ths demonstrates the feasblty of the TS fuzzy model for structural health montorng and structural control system desgn. Fgure 5: Comparson of the orgnal data wth the TS fuzzy model under the hgh mpact loads. 4 Conclusons Ths paper presents the applcaton of smart control technology to concrete system desgn under hgh mpact loads. Nne concrete beams are desgned and manufactured and then those are ntegrated wth magnetorheologcal (MR) dampers. Based on the set of nput and output data collected from the ntegrated concrete-mr damper system subected to hgh mpact forces, a TS fuzzy model was developed. It s shown from the smulaton that the TS fuzzy model effectvely predcts nonlnear mpact responses of smart concrete beam systems equpped wth MR dampers. References [1] K. Hong, S. Lee, Y. Km, H. Chun, J. Lee and S. Km (2012), Precast Concrete Both-end Cantlevered Beam employng X-bracng Rebars, Materals and Structures, n revew.

6 278 Structures Under Shock and Impact XII [2] Z. Huszar (2008), Vbratons of Cracked Renforced and Prestressed Concrete Beams, Archtecture and Cvl Engneerng, 6, [3] V. Motevall and T. El-Korch (2006), Investgaton of Fre Performance of Structural Members Incorporatng Fber Renforced Plastc Compostes used Scaled Expermental Enclosure Fres, 4 th Internatonal Workshop Structures n Fre-SF 06, Avero, Portugal, May [4] G.R. Consolazo, M.T. Davdson, D.J. Getter (2010), Vessel Crushng and Structural Collapse Relatonshps for Brdge Desgn, Florda Department of Transportaton, Fnal Report. [5] Y. Km, R. Langar and S. Hurlebaus (2009) Semactve Nonlnear Control of a Buldng wth a Magnetorheologcal Damper System, Mechancal Systems and Sgnal Processng, 23, [6] R. Mtchell, Y. Km and T. El-Korch (2012a) Wavelet-based Neuro-Fuzzy Controller for Vbraton Mtgaton of Hgh-rse Buldngs, Journal of Vbraton and Control, n press. [7] Y. Km, R. Langar and S. Hurlebaus (2011) MIMO Fuzzy Identfcaton of Buldng-MR damper System, Internatonal Journal of Intellgent and Fuzzy Systems, 22, [8] T. Takag and M. Sugeno (1985), Fuzzy Identfcaton of Systems and Its Applcatons to Modelng and Control, IEEE Transactons on Systems, Man, and Cybernetcs, 15, [9] J.S. Km, Y. Km and T. El-Korch (2012), Fuzzy Identfcaton of Sesmcally Excted Smart Systems, Structural Sesmc Desgn Optmzaton and Earthquake Engneerng: Formulatons and Applcatons, IGI-Global, Inc., Nkos Lagaros (ed.), [10] R. Mtchell, Y. Km and T. El-Korch (2012b) System Identfcaton of Smart Structures usng Wavelet Neuro-Fuzzy Model, Smart Materals and Structures, n press.