Copyright © 2018 Authors. This is an open access article distributed under the Creative Commons Attribution License , which permits unrestrict- ed use, distribution, and reproduction in any medium, provided the original work is properly cited. International Journal of Engineering & Technology, 7 (4.26) (2018) 153-158 International Journal of Engineering & Technology Website: www.sciencepubco.com/index.php/IJET Research paper Theoretical Bending Collapse of Hat-Section Tubes Hafizan Hashim 1 *, Hanita Hashim 2 , Arif Affendi Jamal 3 , M.A.M. Jusoh 4 1 Faculty of Mechanical Engineering, Universiti Teknologi MARA (UiTM), 40450 Shah Alam, Selangor, Malaysia 2 Faculty of Engineering and Life Sciences, Science and Biotechnology Cluster, Universiti Selangor (UNISEL), Jln Timur Tambahan, 45600 Bestari Jaya, Selangor, Malaysia 3 Insitute of Product Design & Manufacturing, Universiti Kuala Lumpur (UniKL), 56100 Cheras, Kuala Lumpur, Malaysia *Corresponding author E-mail: hafizandes@gmail.com Abstract This paper presents an attempt to modify an existing theoretical model to predict the bending collapse response of hat-section tubular structures. The analytical collapse model was based on Kim and Reid. Additional hinge lines created during deformation of the tube were examined and integrated with existing model to forming a modified analytical solution. Variation of the hinge moments were solved using limit analysis technique. Procedure for developing the finite element (FE) models of tube specimens was also presented. Moment- rotation characteristics from pure bending simulation were compared with analytical model and good agreement was achieved. The aver- age of differences between simulation and calculation were found to be <5% within plastic region. In conclusion, the modified analytical solution has adequate capability to predict the moment-rotation relationship of hat-section tubes subject to pure bending. . Keywords: Bending; Hat-section; Hinge mechanism;Finite element. 1. Introduction Thin-walled structure is a kind of typical energy absorbers used in many applications such as automotive, naval, and aerospace. Over the past decades, many efforts have been made to improve their crashworthiness, however axial progressive collapse succeeded only in laboratory and fails in the real crash. Under external im- pact load, a thin-walled beam tends to bend due to instability and minimal energy absorption. Real crash scenario shows that almost 90% of structural members involved in an accident failed in bend- ing collapse mode [1]. Therefore, study on the bending behaviour of thin-walled energy absorbers is essential for their improvement. Among vehicular structural members is a generic form of steel profiles known as hat-section tube. They are used due to their excellent light weight to protect occupant and other assets against impact loads. During impact, bending deformation is a basic de- formation exhibited by hat-section tube. It becomes a theoretical basis for body structure design that is studied under bending col- lapse theory. The study of bending behaviour of thin-walled tubular structures was first reported by Abramowicz and Wierzbicki [2] and Kecman [3]. Both approaches involved nonlinear geometrical problems in plasticity. The mathematical equations derived by Kecman [3] relate hinge moment and rotation angle during post collapse that involve stationary and moving plastic hinge lines. The bending moment of the whole sections showed a good agreement between theoretical predictions and experiment results. Wierzbicki et al. [4] proposed a collapse model based on the moving hinge lines within a small angle range. This model was further improved by Kim and Reid [5] by introducing a new kinematically admissible folding mechanism to predict bending collapse of square and rectangular cross section tubes. It closely resembles Kecman’ s model [3] with inclusion of some in-plane deformation and introduced two addi- tional free parameters from total plastic work. Compared with typical thin-walled tubes, the hat-section tubes with the same parameter possess higher flexibility in terms of manufacturability and workability. Related studies showed that the hat-section tubes are versatile and reflect the actual application in real world with higher hybrid ability [6-10]. Nevertheless, study on the collapse behaviour and analytical approach to estimate moment-rotation relationship has received less attention [11]. This paper re-examines the bending collapse mechanism of hat-section tubes and suggests an analytical solution to determine the mo- ment-rotation relationship. The collapse model is based on Kim and Reid [5] which is originated from Kecman [3] and Weizbicki et al. [4] by addressing some issues found in both previous models. This work includes development of finite element (FE) model using an explicit non-linear FE programme, ABAQUS. The vali- dated model was used to simulate pure bending in order to verify the modified analytical results. Comparison results show good agreement and the modified analytical approach is therefore vali- dated. 2. Bending Collapse Mechanism: Kim and Reid’s Approach For applying this analytical approach, an idealized collapse mechanism for present collapse modal is considered. Fig. 1 shows a theoretical collapse model of a hat-section tube subject to pure bending. During the hinge development, there are about four phases describe the actual bending collapse mechanism of a hat- section tube. The first phase occurs by a protruding bulge in the webs at a fixed location without rolling deformations. It follows by the second phase when the bulge starts to roll along yield lines GA, AK, and their symmetric counterparts. In the next phase, the rolling deformation due to the moving bulge was put to the end when jamming mechanism initiated from the creation of the sec- ondary hinge and the hinge continues to develop in the final phase