Moment modification factor of I-girder with trapezoidal-web-corrugations considering concentrated load height effects Ngoc Duong Nguyen a , Seung-Ryong Han a , Gyu-Sei Lee b , Young-Jong Kang a, ⁎ a School of Civil, Environmental & Architectural Engineering, Steel Structural Laboratory, Korea University, 5-1 Anam-dong, Sungbuk-ku, Seoul 136-701, South Korea b Sun Moon University, Chungnam 336-708, South Korea abstract article info Article history: Received 22 February 2011 Accepted 16 May 2011 Available online 14 June 2011 Keywords: Moment modification factor End restraint conditions Trapezoidal web corrugations Load height effects I-girder Moment modification factors of the I-girder with trapezoidal web corrugations subjected to concentrated load, applied at different heights on the cross section and various end restraint conditions, are investigated. The moment modification factors are obtained by finite element buckling analyses. The new FEM program is developed by using beam elements and new general formulas of cross-section properties as well as a new warping constant of the I-girder with trapezoidal web corrugations. The theoretical results of moment modification factors are compared with commercial finite element software (ABAQUS) using shell elements. A series of finite element analyses with different corrugation profiles and lengths is performed. Through comparative numerical studies, the theoretical results are successfully verified. The moment modification factors from the SSRC Guide are compared with present FEM results. The new values of the variable C b , the moment modification factor, in the SSRC Guide are proposed as the variable C b,c to improve the accuracy of lateral–torsional buckling strength. © 2011 Elsevier Ltd. All rights reserved. 1. Introduction Corrugated steel beams are built up using two flange plates and corrugated steel webs. The use of corrugated steel webs signifi- cantly increases their buckling resistance and can reduce the thickness of webs by replacing the stiffened steel plates of plate girders. Moreover, previous research indicates that the weight of the I-girder with vertical corrugated webs can be 10.6% less than the weight of the original I-girders with the same static capacity [1]. Therefore, the cost of beam fabrication is reduced. Studies about the behavior of the I-girder with corrugated webs have been carried out by Lindner [2,3], Elgaaly et al. [4,5], Elgaaly and Seshadri [6,7], Sayed-Ahmed [8], Ibrahim et al. [9,10], Abbas et al. [11–13], Driver et al. [14], Yi et al. [15], Eldib [16], and Moon et al. [17]. Lateral–torsional buckling is one of the limit states of structural usefulness. The elastic critical moment is directly affected by the following factors [3]: material properties; geometrical properties of the cross-section, such as the torsional constant, warping constant, and moment of inertia about the minor axis; unbraced length of the beam; end restraint conditions, such as lateral bending and warping re- strictions at supports; and loading conditions, such as the bending moment distribution and transverse loading position with respect to the section shear center. In spite of the importance of lateral–torsional buckling phenomenon, studies on this behavior for the I-girders with trapezoidal web corrugations are scarce. Most recently, Moon et al. [18] suggested approximated methods for locating the shear center and calculating the warping constant using the concept of the average corrugation depth, d avg . A simple method was proposed for calculating the lateral–torsional buckling strength of the I-girder with trapezoidal web corrugations under uniform bending. Nguyen et al. [19] proposed the general formulas for the cross-section properties and a new warping constant of the I-girder with trapezoidal web corrugations based on the numerical equations and numerical method. Their studies showed that the elastic lateral–torsional buckling strength under uniform moment is determined by taking the average elastic lateral–torsional buckling strength at d =0 and d =d max (d is depth of corrugation and d max is maximum depth of corrugation) using their proposed formulas. The critical moment used in their study is the same as simple formula of lateral–torsional buckling strength of an I-girder with flat webs [20]. However, the recent studies of Moon et al. [18] and Nguyen et al. [19] have concentrated on a simply supported I-girder with trapezoidal web corrugations under uniform moment. For a doubly symmetric and monosymmetric I-girder with flat webs, many researchers have carried out studies on the moment modification factor, C b . Nethercot and Rockey [21] recommended a method for modifying the C b value to account for load height effects in a doubly symmetric I-girder with four types of end restraints (simply supported, warping fixed, lateral-bending fixed, and completely fixed) and two types of transverse loads (concentrated load and uniformly distributed load). Helwig et al. [22] presented the simplified C b values for simply supported monosymmetric I-girders subjected to transverse loads applied at different heights on the cross-section. Suryoatmono and Ho [23], using a finite difference method, proposed closed-form expressions of C b obtained for some linear and nonlinear moment diagrams for the Journal of Constructional Steel Research 67 (2011) 1773–1787 ⁎ Corresponding author. Tel.: +82 2 3290 3317; fax: +82 2 921 5166. E-mail address: yjkang@korea.ac.kr (Y.-J. Kang). 0143-974X/$ – see front matter © 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.jcsr.2011.05.002 Contents lists available at ScienceDirect Journal of Constructional Steel Research