Y. Liu. 2009. Int. J. Vehicle Structures & Systems, 1(1-3), 45-49 ISSN: 0975-3060 (Print), 0975-3540 (Online) doi: 10.4273/ijvss.1.1-3.06 © 2009. MechAero Foundation for Technical Research & Education Excellence International Journal of Vehicle Structures & Systems Available online at www.ijvss.maftree.org 45 Dynamic Crushing Behaviour of Box Section Steel Beams Yucheng Liu Department of Mechanical Engineering University of Louisiana, Lafayette, LA 70504, USA Email: yucheng.liu@louisiana.edu ABSTRACT: As a popular energy absorber, steel box-sectional beams are widely used in various engineering structures. In this paper, the dynamic crushing behaviours of steel beams with box cross sections are investigated and outlined. Systematic parametric studies were conducted in order to study the effect of material properties, including strain hardening ratio and strain rate effect, length of the beam, and initial impact velocity on the crushing behaviours of the steel beams. A series of numerical models were constructed with various sets of parameters and used for crashworthiness analyses. Maximum crushing force, mean force, and specific energy absorption were recorded after analyses and compared to reveal the influences of parameters. Empirical equations were also developed based on the analyses results using nonlinear regression method, which can predict the effects of the initial impact velocity on the peak crushing forces of steel beams with box sections. KEYWORDS: Steel beam, Box section, Crushing behaviour, Strain rate, Strain hardening CITATION: Y. Liu. 2009. Dynamic Crushing Behaviour of Box Section Steel Beams, Int. J. Vehicle Structures & Systems, 1(1-3), 45-49. 1. Introduction Nowadays, thin-walled box-sectional beams are extensively used as energy absorbers in civil engineering, automotive engineering, shipbuilding and other industries because of their excellent energy absorption capacity during impacts. Such beams are commonly made of steel, which is a strain rate sensitive material [1]. Jones [1] and Han et al. [2] discussed the effects of strain hardening and stain rate sensitivity on crash responses of circular steel tubes. In this paper, the strain hardening and strain rate effects on steel box- sectional beams are examined. Crushing behaviour of box section beams under axial compression has been thoroughly illustrated in previous research [3-5]. In those literatures, researchers indicated that the mean crushing force could be evaluated based on beam’s material properties (ultimate stress) and cross-sectional dimensions (side length and wall thickness). According to our experience, the peak crushing force is also related to the beam’s total length and initial impact velocity as well as the beam’s material and cross-sectional dimensions. One objective of this study is to reveal the effects of beam length and initial velocity on the peak crushing force. In this study, a series of finite element (FE) models are created for the steel box-sectional beams with different lengths. These FE models are used for crashworthiness analysis, during which different initial impact velocities are assigned. The effects of the material strain hardening ratio and strain sensitivity rate are firstly discussed. Next, for the steel beams with box sections, which have both strain hardening and rate sensitivity, the effects of beam length and impact velocity on the beam’s crushing behaviours are demonstrated. This is based on the results of peak crushing force, mean crushing force and specific energy absorption (SEA). Finally, empirical equations are developed using a non-linear regression method to reflect the relationship between the beam length and the peak crushing force. ANSYS is used to create CAD beam models and LS-DYNA is employed to generate the FE models and run the numerical analyses. 2. FE Modelling and Numerical Analysis Finite element models are created for the steel box- sectional beams with fixed cross-section (Side length (a) 45mm×45mm and wall thickness (t) is 2.0mm, where the side 45mm is measured between the centrelines of the section thickness) and various lengths, which vary from 200mm to 400mm. The commercial explicit code, LS- DYNA, is used for generating the FE models as well as running the dynamic analyses [6]. As shown in Fig. 1, the FE models are meshed with 4-node Belytschko-Tsay shell elements with five integration points through its thickness. Material model 3 of LS-DYNA (MAT_ PLASTIC_KINEMATIC) is selected to model such beams. The material properties of the mild steel are: density ρ = 7830kg/m 3 , Young’s modulus E = 207GPa, Poisson’s ratio υ = 0.3, yield stress σ y = 200MPa. According to the classic material theories [1], strain rate sensitivity is a material property where the plastic flow of some materials is sensitive to the strain rate ε  . Strain