Issue 48

E. Maiorana, Frattura ed Integrità Strutturale, 48 (2019) 459-472; DOI: 10.3221/IGF-ESIS.48.44 471 varies from 0.15 h to 0.25 h , depending on the relative rigidity of the system stiffener / plate (as confirmed in Bedair 1997 [7]). For   0, the optimal position is independent of  s and is a function of  . C ONCLUSIONS hree open cross-sections (Flat, T-shaped, L-shaped) and four closed ones (Triangular, Rectangular, Circular, Trapezoidal) longitudinal stiffeners, with equal area and differing second moment of area, were examined. Through linear buckling analysis, buckling coefficient k was used to compare stiffeners contribution in terms of weight per linear meter. The following conclusions are reached:  For  < 1.5, Rectangular cross-section shows the greater value while Circular cross-section appeared to be the best shape to stiffen the plate for 1.5 <   2.  Triangular cross-section makes the same contribution to stability with varying  .  Among the open-section stiffeners, the best characteristics were found in the profiles T-shaped and L-shaped cross- sections, which show higher second moments of area.  Flat cross-section makes the lowest contribution to the increase in buckling coefficient k .  Respect to open cross-sections of equal area, with Rectangular, Circular and Trapezoidal cross-sections, k decreases as  increases; local instabilities occur in closed cross-sections with greater slenderness.  With aspect ratio  = 1.5 and position of longitudinal stiffener h  / h = 0.2, the minimal value of buckling coefficient k is for Flat cross-section and maximum for Circular.  Comparing non-stiffened plates with closed cross-section ones, for the range  < 1, Trapezoidal cross-section is the best. Finally, longitudinal stiffeners, with optimal flexural stiffness,, set in various positions from the compressed edge were analysed and a useful practical law is given to correlate the best position with respect to variations in stress gradient  . The results of numerical analyses were compared with those in the literature, to validate the proposed formulation, and a good match was obtained. R EFERENCES [1] Timoshenko, S.P. and Woinowsky-Krieger, S. (1959). Theory of plates and shells. Mc-Graw-Hill Book Company. [2] Xie, M. and Chapman, J.C. (2004). Design of web stiffeners: local panel bending effects. J. Constr. Steel Res., 60(10), pp. 1425-1452. DOI 10.1016/j.jcsr.2004.03.001. [3] Lee, S.C., Yoo, C.H. and Yoon, D.Y. (2002). Behaviour of intermediate transverse stiffeners attached on web panels. J. Struct. Eng., ASCE, 128(3), pp. 337-345. [4] Alinia, M.M. (2005). A study into optimization of stiffeners in plates subjected to shear loading. Thin-Walled Struct., 43(5), pp. 845-860. DOI 10.1016/j.tws.2004.10.008. [5] Alinia, M.M. and Moosavi, S.H. (2009). Stability of longitudinally stiffened web plates under interactive shear and bending forces. Thin-Walled Struct., 47(1), pp. 53-60. DOI 10.1016/j.tws.2008.05.005. [6] Maiorana, E., Pellegrino, C. and Modena, C. (2011). Influence of longitudinal stiffeners on elastic stability of girder webs. J. Constr. Steel Res., 67, pp. 51-64. DOI 10.1016/j.jcsr.2010.07.005. [7] Bedair, Osama K. (1997). Influence of stiffener location on the stability of stiffened plates under compression and in- plane bending. Int. J. Mech. Sci., 39(1) pp. 33-49. DOI 10.1016 /0020-7403(96)00017-3 . [8] Graciano, C. and Casanova, E. (2005). Ultimate strength of longitudinally stiffened I-girder webs subjected to combined patch loading and bending. J. Constr. Steel Res., 61, pp. 93-111. DOI 10.1016/j.jcsr.2004.07.006. [9] Pavlovčič, L., Detzel, A., Kuhlmann, U. and Beg, D. (2007). Shear strength of longitudinally stiffened panels. Part 1: tests and numerical analysis of imperfections. J. Constr. Steel Res., 63, pp. 337-350. [10] G+D Computing, (2005). Strand7 User’s Manual, Sydney, Australia. [11] Maiorana, E. and Pellegrino, C. (2011). Linear buckling analysis of welded girder webs with variable thickness. Steel and Composite Struct., 11(6), pp. 505-524. DOI 10.12989/scs.2011.11.6.505. T