مطالعه تجربی و عددی رفتار سازه ای ستونهای GFRP بطور غیر معمول بارگذاری شده

Glass fiber reinforced polymer (GFRP) pultruded profiles are being increasingly used in civil engineering applications. Although they offer several advantages over traditional materials, such as high strength, lightness and non-corrodibility, GFRP profiles present low elasticity and shear moduli, which together with their slender walls makes them very prone to buckling phenomena. Several previous studies addressed the global and local buckling behavior of GFRP pultruded members under concentric loading. However, little attention has been given to the effect of small eccentricities, which may arise from material geometrical imperfections or construction errors. This paper presents results of experimental and numerical investigations about the structural behavior of GFRP pultruded columns subjected to small eccentric loading about the major (strong) axis. To accomplish such goal, three series of 1.50 m long GFRP I-section (120×60×6 mm) columns were tested in compression applied with the three following eccentricity/height of the cross-section ratios: e/h=0.00, 0.15 and 0.30. It was found that such small eccentricities are of major importance for the behavior of GFRP pultruded columns. Although the initial axial stiffness of eccentrically loaded columns was similar to that of concentrically loaded ones, for increasing loads the stiffness considerably decreased due to bowing and second-order P–δ effects. Furthermore, results show that the load capacity of columns subjected to loads applied within the kern boundaries is reduced up to 40% at an approximately linear trend. Results obtained from the experimental campaign were compared with analytical predictions and numerical simulations using (i) the finite element method (FEM) and (ii) the generalized beam theory (GBT). In general, a very good agreement was obtained between experimental data and analytical and numerical results.

During the last decades the costs related to strengthening and maintenance of civil engineering structures made of traditional materials (such as steel or reinforced concrete) have been rising considerably. Moreover, there has been an even greater demand for lighter and faster construction [1]. Due to their low self-weight, high strength, high durability and reduced maintenance requirements, fiber reinforced polymer (FRP) pultruded profiles are becoming a competitive option as structural materials. However, the use of FRP pultruded profiles is being hindered by their high deformability (serviceability limit states), buckling sensitivity (ultimate limit states) and lack of consensual design codes. The structural behavior of FRP pultruded profiles is different from that exhibited by traditional materials (steel and reinforced concrete). They are considered to have linear elastic and orthotropic behavior until failure, which occurs generally in a brittle failure mode [2]. Conventional FRP pultruded profiles, usually made of glass fibers embedded in a polyester or vinylester polymeric matrix (GFRP), are particularly susceptible to local buckling when compressed due to their low in-plane moduli and high wall width-to-thickness ratio. Such phenomenon has been studied by many researchers using experimental, numerical and analytical tools. For instance, Tomblin and Barbero [3] studied such phenomenon on GFRP compressed members. The analytical results obtained from the modified Southwell method fitted very well the experimental values. Turvey and Zhang [4] also performed experimental and numerical studies aiming at studying the initial failure of post-buckled GFRP short columns, with length-to-radius of gyration ratios (from now on referred to as slenderness) varying from 4.7 to 19.0. A phenomenological failure criterion was proposed (Tsai–Wu criterion) and incorporated in the FE models to simulate the web–flange junction initial failure, providing good correlation with the experimental results. Regarding the global buckling phenomenon, there are several studies addressing the behavior of both beams and columns made of GFRP. Correia et al. [5] and Silva et al. [6] studied the structural behavior of GFRP cantilevers by both experimental and numerical means. Nguyen et al. [7] performed a numerical study about the influence of the load height as well as of the boundary conditions and geometric imperfections on the lateral–torsional buckling of FRP beams. Zureick and Scott [8] studied the short-term behavior under axial compression of GFRP slender members, with slenderness varying from 19.2 to 85.0. Several specimens with different slendernesses were tested and their critical loads were then compared with analytical predictions obtained from (i) Euler's buckling equation and (ii) the equation proposed by Engesser [9], which takes into account the shear deformation (often relevant in orthotropic materials with EL ⪢GLT). Results showed good agreement between experimental data and analytical predictions (relative differences between 1% and 15%). The authors also provided a step-by-step design guideline and a sample calculation for GFRP slender members under compression. The interaction between local and global buckling in GFRP columns was also studied by several authors. Hashem and Yuan [10] proposed a criterion to distinguish short from long GFRP columns, based on a critical slenderness ratio. A total of 24 full-scale specimens with different cross-sections and slendernesses ranging from 3.79 to 78.9 were tested. Experimental results were then compared to predictions provided by Euler's buckling equation and the classical plate theory showing that such critical slenderness ratio is about 50. Barbero and Tomblin [11] proposed a design equation that takes into account the interaction between local and global buckling in FRP columns. The experimental verification of such equation was also performed by Barbero et al. [12]. While each isolated local or global buckling mode has a stable post-critical path, the coupled mode arising from interaction at similar buckling loads is unstable and highly sensitive to imperfections. Such equation was also used by Correia et al. [13] and it gave satisfactory predictions of buckling loads of FRP pultruded short columns. The literature regarding the structural behavior of GFRP eccentrically compressed members is very scarce. Barbero and Turk [14] carried out an experimental study regarding the effect of eccentric loading about the minor (weak) axis of WF and I-section profiles. Results showed that the main factors controlling failure in beam-columns are the eccentricity, the member length and the specimen's mechanical and geometrical properties. The authors considered only one eccentricity (e=25.4 mm, corresponding to an eccentricity/height ratio (e/h) of 0.125–0.25 for the different cross-sections tested), and unfortunately they did not perform any numerical simulations to study the effect of different eccentricities. Mottram et al. [15] carried out an experimental study regarding the effect of eccentric loading about the major (strong) axis and moment gradient in GFRP members with WF cross-section. They analyzed different levels of high eccentricity, with e/h ranging from 0.5 to 2.0, aiming at studying the influence of combined compression and bending when joints in braced frames are simple to semi-rigid. In this investigation, numerical simulations were not performed. According to the authors' best knowledge, no studies were reported up to present on the effect of small eccentricities1 about the major (strong) axis in GFRP compressed members. Although in structural design the axial loading in columns may be assumed to be concentric, such eccentricities often exist due to both (i) geometrical imperfections of the materials and (ii) construction errors (e.g., member axis misalignment). This paper presents results of experimental and numerical investigations on the structural behavior exhibited by GFRP pultruded columns subjected to small eccentric loading. To accomplish such goal, three series of GFRP I-section columns were tested in compression applied with the three following eccentricity/height ratios (e/h=0.00, 0.15 and 0.30). Results obtained from the experimental campaign were compared to numerical simulations using (i) the finite element method (FEM) and (ii) the generalized beam theory (GBT).

This paper presented an experimental and numerical study on the effect of small eccentric loading (e/h=0.00, 0.15 and 0.30) about the major axis of GFRP pultruded I-section columns. The following main conclusions are drawn: 1. Results obtained for non-braced (series NBC) and braced (series BC) columns under concentric loading outlined the importance of designing lateral bracing systems in compressed GFRP members. 2. Results obtained for braced columns under concentric (BC) and eccentric (EBCI and EBCII) loading showed that small eccentricities that may arise from both geometrical imperfections of the materials and construction errors are of major importance for the behavior of GFRP pultruded members under compression. 3. Columns subjected to loads applied within the kern boundaries exhibited similar initial axial stiffness compared to concentrically loaded columns; however, for increasing load levels, their axial stiffness decreased due to bowing and second-order P–δ effects. Eccentrically loaded columns proved to be highly sensitive to those small eccentricities with an approximately linear load capacity decrease up to 40%. 4. In non-braced columns global buckling around the minor axis occurred. In braced columns failure was caused by local bucking, which triggered web–flange separation followed by material crushing. This failure mode is due to high shear stresses in the web–flange junction near inflection points of the buckled shape. In eccentrically loaded columns, such material crushing developed in the most compressed flange and was followed by the global buckling of the columns. 5. Estimates for the global and local buckling loads of series NBC and BC obtained using respectively Euler's and Kollar's equations provided very good agreement with the experimental data (relative differences of 6% and 2.5%, respectively). 6. The linear elastic analyses performed using both GBT and ABAQUS provided good agreement with experimental results of series NBC and BC. 7. GBT results showed that the combination of local modes 5 (symmetric configuration) and 6 (anti-symmetric configuration) changes with the eccentricity. For increasing eccentricity, the less compressed flange twists less than the most compressed flange and this effect is given by the increasing participation of mode 6 (anti-symmetric) and decreasing participation of mode 5 (symmetric). It was interesting to note that the variation of mode 6 participation with the eccentricity level (e/h) was nearly linear inside the cross-section kern. Noting that the participation of this mode is nearly 50% for pure bending (e/h→∞), this variation should be highly non-linear for higher eccentricity levels (outside the cross-section kern). 8. Results obtained from the nonlinear analysis performed with ABAQUS, in terms of axial strains and axial shortening, were very consistent with experimental data. Using the Tsai–Hill criterion, it was found that longitudinal stresses have a prevalent contribution to the failure index in the linear elastic stages. However, as the load increases to levels closer to the local buckling load, the cross-section starts to deform and flange twisting emerges, thus leading to a key role of the shear stress components. At failure, their contribution to the index failure is always higher than the longitudinal stress counterpart, regardless of the eccentricity level. The above mentioned findings are part of an ongoing investigation at the Technical University of Lisbon, aiming to study the structural behavior of pultruded profiles and develop design guidance. Hopefully, further research is needed to prove the findings reported in this paper, namely using other cross-section shapes and eccentricity levels.