The effects of different load paths on the stress-strain behaviors of the FRP confined concrete columns


Elastic materials and fiber reinforced polymers are predominantly used today to strengthen concrete members due to their strength and other advanced material properties. Existing stress-strain relationships of concrete columns confined by these materials major on concentric loading as compared to eccentric loading. For eccentric loading, these models mainly focuse on the load carrying capacity rather than stress-strain relationship of the concrete columns.

The stress-strain relationship in such columns under concentric loading is however different from that under eccentric loading. Eccentric loading has different load paths such as increasing axial load at constant load eccentricity and vice versa. The stress-strain characteristics of eccentrically loaded columns are affected by the different load paths which have led to a lot of research work with the aim of getting more insight on the behaviors of such columns.

Eccentrically loaded columns exhibit three typical load paths. The load path I comprise constant load eccentricity with increasing axial load and is mainly prevalent in structures under gravitational loading. Load Path II exhibits increasing load eccentricity or bending moment with constant axial force and occurs when the structures loaded gravitationally gets subjected to additional horizontal loading like a seismic load. Lastly, load path III is associated with increasing axial force with constant bending moment. It is rarely experienced in columns.

In a recent collaboration Professor Yu-Fei Wu from RMIT University in Australia with Dr Yugui Cao from the Wuhan University of Technology and Dr. Cheng Jiang from The Hong Kong Polytechnic University developed a stress-strain model for concrete columns confined with fiber reinforced polymers under increasing load eccentricity with constant axial loading. This was in a bid of validating the assumption drawn from the previously constructed models that the stress-strain behavior of concrete columns confined with FRP is independent of the different load paths. Additionally, the authors investigated the effects of different load paths on the stress-strain behaviors of the FRP confined concrete columns. Their research work is published in the research journal, Composites Part B.

The authors successfully observed that the stress-strain behaviors of the FRP confined concrete column vary depending on the different load paths. For instance, different load paths resulted in differences in stress-strain behavior which occurred in the nonlinear deformation stage. Small stress in the elastic deformation range resulted in small difference of stress-strain curves under different load paths. The difference increases when strain increases. This is because small dilation, and hence confinement, was experienced in the linear deformation stage as compared to the non-linear deformation stage.

According to the authors, columns under increasing bending and constant axial force exhibited post-peak stress-strain slopes that increased with increase in the axial force ratio, and decreased with increase in load eccentricity. However under another load path of increasing axial force and constant load eccentricity, load eccentricity hardens the stress-strain curve and axial force ratio has insignificant effect on the stress-strain curve. The differences in the dilation of the concrete were the cause of the differences observed in the stress-strain curves under different load paths. Generally, the dilation property depended on the load path. The confinement pressure largely determined the resistance of the concrete.

The effects of different load paths on the stress-strain behaviors of the FRP confined concrete columns. Advances in Engineering

The effects of different load paths on the stress-strain behaviors of the FRP confined concrete columns. Advances in Engineering

The effects of different load paths on the stress-strain behaviors of the FRP confined concrete columns. Advances in Engineering


About the author

Yugui Cao is currently Associate Professor in the Hubei Key Laboratory of Roadway Bridge and Structure Engineering, Wuhan University of Technology, Wuhan, China. He received his PhD both from City University of Hong Kong and Huazhong University of Science and Technology, China. He received his MS degree from the Wuhan University of Technology and his BS degree from the Anhui University of Science and Technology. His research interests include FRP confined concrete structures and steel-concrete composite structures.

About the author

Yu-Fei Wu is currently a Professor in Infrastructure Engineering in the School of Engineering at RMIT University in Australia. He obtained his BSc in 1983 and MSc in 1986 from Zhejiang University, China. He received MEng from National University of Singapore in 1994 and completed his PhD in 2002 at the University of Adelaide, Australia. He has more than ten years of industry working experience in structural engineering as a professional engineer in consulting firms in China, Singapore and Australia and is a chartered professional engineer of New Zealand and Australia (FIEAust, CPEng, NER, MIPENZ). He worked in Shanghai Jiao Tong University from 1989 to 1992 as a lecturer. Prior to joining RMIT University, he was an Associate Professor in the Department of Architecture and Civil Engineering at City University of Hong Kong (2004-2015).

His research interests lie in the broad field of structural engineering, including concrete structures, structural design, composite structures, FRP structures and structural rehabilitation.
Professor Wu has published more than 200 technical works, including 120 SCI indexed journal papers with an H index of 34 (Google Scholar) and 28 (ISI Web of Science). Professor Wu has received numerous research awards including the Moisseiff Award from American Society of Civil Engineers. He is the inventor of numerous new structural technologies with six US patents, including (1) the theorems for flexural design of reinforced concrete, (2) the experimental method that can directly measure shear strength components in RC member tests, (3) the compression yielding structural design concept to increase the ductiliy of RC members, and (4) the experimental facility for concrete test under passive 3-dimensional confinement stresses.

About the author

Cheng Jiang is currently a postdoctoral fellow in the Department of Civil and Environmental Engineering at The Hong Kong Polytechnic University in Hong Kong SAR. He received his BSc in 2011 from Southeast University, China. He completed his PhD in 2017 from City University of Hong Kong. He has visited Marquette University (USA) and RMIT University (Australia) as a visiting scholar from 2016 to 2017. Apart from these visits, he has nearly three years full-time working experiences conducting both research and consultancy activities at City University of Hong Kong (2011.9-2013.4), PolyU Technology and Consultancy Co. Ltd (2017.6-2017.8), and The Hong Kong Polytechnic University (2017.8-now).

His research involves concrete structures, structural rehabilitation and FRP structures. Dr. Jiang has authored more than 30 technical works. He has been involved as a guest editor of one special issue in the journal of Sensors in 2018.


Cao, Y., Wu, Y., & Jiang, C. (2018). Stress-strain relationship of FRP confined concrete columns under combined axial load and bending moment. Composites Part B: Engineering, 134, 207-217.

Go To Composites Part B: Engineering

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