Elastic critical moment of beams with sinusoidally corrugated webs Gonçalo Correia Lopes, Carlos Couto ⁎, Paulo Vila Real, Nuno Lopes RISCO, Department of Civil Engineering, University of Aveiro, Portugal abstract article info Article history: Received 20 June 2016 Received in revised form 10 October 2016 Accepted 4 November 2016 Available online xxxx This paper approaches the elastic critical moment of web-corrugated beams (WCB), either subjected to a uniform bending moment, gradient bending moments, or a uniformly distributed load. Previous research on the subject of lateral-torsional buckling (LTB) of WCB is presented and critically reviewed. Based on earlier studies on the cross- section properties of beams with trapezoidal corrugations, a new method is proposed to obtain the warping or torsional constant of WCB with sinusoidal corrugation. Furthermore, based on an extensive numerical study for a wide range of different corrugation proﬁles and lengths, it is demonstrated that the present design formulae for the moment modiﬁcation factor for ﬂat web beams (FWB) could be improved, in order to predict satisfactorily the buckling capacities of WCB under non-uniform bending distributions. Therefore, a new closed-form expres- sion for the moment modiﬁcation factor is proposed and successfully veriﬁed. Finally, by comparing the analyt- ical results with those obtained from a linear buckling analysis (LBA) carried out using shell ﬁnite elements, it is demonstrated that the proposed modiﬁcations lead to an accurate prediction of the buckling strength of WCB. © 2016 Elsevier Ltd. All rights reserved. Keywords: Steel structures Corrugated web beams Lateral-torsional buckling Elastic critical moment 1. Introduction The use of web-corrugated beams (WCB) has been increasing con- siderably during the last years for various structural applications, espe- cially in industrial/commercial buildings and bridges, due to their high load-carrying capacity in relation to the material usage. The major asset of this structural solution lies in taking advantage of the increase of rigidity provided by the corrugated web, that leads to an higher resis- tance against local buckling and to an improved shear capacity, com- bined with a weight reduction up to 30% [1], when compared to beams with ﬂat webs. Furthermore, due to their intrinsic properties, it is possible to achieve adequate out-of-plane stiffness and lateral tor- sional buckling (LTB) resistance without the need to increase the thick- ness of the web plate [1] or the need to use additional transversal and/or longitudinal stiffeners. Since the ﬁrst developments of WCB, especially in Germany and Austria in the 1990's, a considerable number of researchers have per- formed experimental, analytical and numerical studies on the behav- iour of these beams under different loading conditions to investigate their response against shear, bending and compressive patch loads. Concerning the ﬂexural and torsional behaviour of WCB, the most cited studies could be summarized as follows; Elgaaly et al. [3], found that the web could be neglected in the calculation of the bending resis- tance and that the load-carrying capacity should be based on the ﬂange yield strength. Abbas et al. [4,5], stated that the ﬂexural capacity of WCB cannot be analysed by the conventional beam theory alone, since under in-plane loading an additional torsional moment is produced resulting in an out-of-plane twist simultaneously with the in-plane deﬂection. Lindner [6], based on the study of the lateral-torsional behaviour of these beams, has developed a formula to calculate the warping constant of WCB, letting the remain cross-sectional constants considered equal to those used for ﬂat web beams (FWB). In the same publication, it was concluded that, for such conditions, the interaction between local plate buckling and overall LTB needs to be taken into account. Moon et al. [7], have proposed approximated methods for locating the shear centre and calculating the warping constant; Nguyen et al. [2,8] pro- posed new general formulae for the cross-sectional properties (mo- ments and product of inertia), also for locating the shear centre and to calculate the warping constant, as well as for the determination of the moment modiﬁcation factors of WCB under moment gradients. Since the corrugated web is not supposed to resist axial forces due to the so-called accordion effect [7], WCB subjected to bending are de- signed considering that only the ﬂanges resist to the bending moment. On the other hand, such beams have a considerably higher LTB capacity than that of FWB, owing to an increased rigidity, which translates into a higher elastic critical moment for lateral-torsional buckling, M cr . How- ever, Eurocode 3 [9,10] does not provide information on how to com- pute M cr , only stating that it should be based on the gross cross- sectional properties and take into account the loading conditions, the real moment distribution and the lateral restraints without further ref- erence for WCB. Therefore, it is paramount to ﬁnd an analytical expres- sion to predict the buckling strength of WCB. In this context, the main difference in the existing expressions to calculate M cr for I-beams with ﬂat webs, is the inﬂuence of the torsion and warping constants, which Journal of Constructional Steel Research 129 (2017) 185–194 ⁎ Corresponding author. E-mail addresses: gclopes@ua.pt (G. Correia Lopes), ccouto@ua.pt (C. Couto), pvreal@ua.pt (P. Vila Real), nuno.lopes@ua.pt (N. Lopes). http://dx.doi.org/10.1016/j.jcsr.2016.11.005 0143-974X/© 2016 Elsevier Ltd. All rights reserved. Contents lists available at ScienceDirect Journal of Constructional Steel Research