Lateral-Torsional Buckling Strength of Two-Span Glass Fiber Reinforced Polymer Beams

This paper presents the outcome of a study of two-span glass fiber reinforced polymer (GFRP) I-section beams susceptible to lateral-torsional buckling when subjected to gradually increasing concentrated vertical load(s) in the presence of two different types of lateral bracing schemes. It is found that loading one span results in a smaller buckling load as compared with the cases with loading in both spans regardless of the type of bracing scheme used. Also, the study shows that the addition of midspan braces for the GFRP beams results in up to 5.5 times increase in the buckling load capacity. Index Terms — Glass Fiber Reinforced Polymer, I-Beams, Lateral-Torsional Buckling, Bracing.


I. INTRODUCTION 1
Pultruded glass fiber reinforced polymer (GFRP) I-section beams are often susceptible to lateral-torsional buckling when subjected to gradually increasing flexural loads about the cross-sectional major axis. The authors have previously published studies on lateral-torsional buckling behavior of laterally unbraced single-span GFRP beams [1], [4], [6]. In [3], the authors presented a practical solution for avoiding lateral-torsional buckling of single-span I-section beams by addition of lateral bracing. Amponin and Razzaq [5] presented a theoretical and experimental study of a threespan FRP beam under a gradually increasing concentrated load at the center of the middle span. Qiao et al [7] presented a lateral-torsional buckling study of GFRP I-beams including sectional distortions. Nguyen et al. [8] presented a lateral-torsional buckling design procedure for FRP beams. Corria et al studied both buckling and post-buckling behavior of I-section GFRP beams.
The present paper summarizes the outcome of an investigation of a two-span GFRP I-section beam with two different types of bracing systems. The effectiveness of the bracing systems is studied for two different types of loading conditions. Figure 1 shows four different cases of two-span beam problems investigated in this paper with various lateral bracing schemes and gradually increasing load W applied in one or both spans. In this figure, Case 1 represents a beam with a single concentrated load W at point D and lateral braces provided at the supports only, that is, at A, B, and C. The beam shown as Case 2 has the same brace locations as for Case 1, however, it is subjected to a pair of loads each of magnitude W. Cases 3 and 4 have braces not only at the (e-mail: Sirjani nsu.edu) supports but also at the middle of each span. Furthermore, the beam in Case 3 is loaded only in span AB while that in Case 4 has loads in both spans. Figure 2 shows the a typical cross section before and after lateral-torsional buckling, where u, v, and β are lateral, vertical, and torsional displacements.

II. BRACING AND LOADING CONDITIONS
In this exression, Mmax is the absolute value of the maximum bending moment, and MA, MB, and MC are the absolute values of the quarter-point moments between any consecutive pair of lateral braces. Table 1

V. CONCLUSIONS
Based on the lateral-torsional buckling analysis of the two-span GFRP beams shown in Figure 1, the following conclusions are drawn: 1. Loading one span results in a smaller buckling load as compared with the cases with loading in both spans regardless of the type of bracing scheme used. This is evident from the fact that the beam in Case 1 buckled at a load equal to 92.3 percent of the load for Case 2, and that in Case 3 buckled at a load of 69.2 percent of the load for Case 4.
2. Adding midspan braces results in a dramatic increase in the buckling load capacity when only one span is loaded. This can clearly be seen by the ratio 0.796/0.193 = 4.12 indicating a more than four times increase in the buckling capacity of the two-span beam owing to the addition of midspan braces.
3. When both spans are loaded in the presence of midspan braces, the buckling load is 5.5 times compared to that in the absence of such braces.