Overall Stability Behavior Of Monosymmetric I-Section Overhanging Beams And Two-Span Continuous Beams

The flexural-torsional buckling is an important failure mode of the steel beams. The buckling modes and stability capacities are significantly influenced by the variations in the section shape, condition of support and the type of loading. From the end of nineteen century, experimental investigation and theory analysis on all kinds of beams are being carried by many scholars. The researches on the overall stability capacity of the single span beams under various conditions are already very mature, and the formulas for calculating this capacity are also similar to in the design codes among different countries.Until now, the simple and convenient methods of calculating the buckling loads of the overhanging beams and continuous beams have not been presented, because this problem is considerably complex. Some tests were conducted on the double-symmetric I-section continuous beams by the foreign scholars, but the related experiment data have not been found in the domestic. Actually the proposed formulas for calculating the overall stability capacity mostly focus on the double-symmetric I-section beams, and in which the influence of the loading position and the monosymmetry section constant have not been fully accounted for. Therefore the overall stability behavior and the methods of calculating the overall load-carrying capacity of the monosymmetric I-section overhanging beams and continuous beams still need to be further investigated.Tests and theoretical analysis on the overall stability behavior of the monosymmetric I-section overhanging beams and two-span continuous beams were systematically conducted in this paper. Based on above, the simplified formulas for calculating the critical moment and ultimate moment have been proposed, in which the section shapes and the loading positions are all considered.Because of lack of the experimental data about the overhanging beams and continuous beams in the domestic, a total of 8 tests on the overall stability capacity of monosymmetric I-section beams, including 5 overhanging beams and 3 continuous beams, were performed under concentrated load applied on the top flange. As indicated from the experimental results: when the dominative stability portion of the overhanging beam is at the simply supported segment and greater portion of the top flange is compressed, the ultimate load of the beam with the enhanced flange at the top is greater than the beam with the enhanced flange at the bottom under the same conditions. When the position of the load acting at the free end of the beam is constant, the restraint to the simply segment by the overhanging segment is gradually enhanced with the position of the concentrated load acting at the simply segment closing to the support of the overhanging segment, and the ultimate load-carrying capacity of the overhanging beam is also gradually increases. For the continuous beams, if the span of the critical segment keeps invariable, the decrease in the buckling load is greater and greater as the span of the restraining segment gradually increases, due to the interactions between the segments becoming gradually lower. The interactions between the segments are the lowest when the load acting at the restraining segment is zero. The fairly accurate critical load can be obtained by using the Southwell plot method, consequently the more experimental data can be received from the elastic tests by using the limited specimens.The residual stresses of the welded monosymmetric I-section are measured by the sectioning method. According to the measured results, the simplified residual stress patterns of the monosymmetric I-section which are close to the test distribution have been proposed. The programs which can automatically create the initial stress file have been also compiled using FORTRAN. The initial stress file can be inputted in the non-linear buckling analysis by using ANSYS, the calculated ultimate loads fit together well with the test results. It is observed that the results of finite element analysis (FEA) in which the residual stresses are not considered are quite different with the test results.Based on the tests, large amounts of finite element parametric analysis were performed for the monosymmetric I-section overhanging beams and two-span continuous beams. The stability behaviors of these members were investigated by changing the section shapes, the section dimensions, the span lengths, the ratio of the span lengths, the load position and so on. It is observed that, the restraining actions between adjacent segments of the overhanging beams under concentrated loads acting at the bottom flange increase as the increase ofη(the ratio of overhanging length to span length of the simply segment) or the decrease of R (the ratio of the loads between the simply segment and the overhanging segment); the restraining actions between adjacent segments of the overhanging beams under concentrated loads acting at the top flange increase as the increase ofηwhen R is bigger, whereas the restraining actions between adjacent segments decrease as the increase ofηwhen R is smaller. The restraining actions between adjacent segments of the overhanging beams under the distributed loads increase as the increase ofη. The effect of the R is not as much asηwhen the overhanging beams carry distributed loads comparing with the concentrated loads. For the two-span continuous beams, the restraining actions between adjacent segments gradually decrease as the increase of the span length of the restraining segment.Taking the FEA results as the reference, the investigation about the ratio of the critical moments between the monosymmetric I-section overhang beams or two-span continuous beams under concentrated loads (or distributed loads) and the simply supported beams under the same conditions Mc/Mce (or Md/Mde) were conducted. It is found that the interrelation between the ratios of critical moments, Mc/Mce (or Md/Mde), and the coefficients of torsional stiffness of the dominative segment, K1, agree with the parabolic pattern, therefore the formulas for the critical moment of the monosymmetric I-section overhanging beams and two-span continuous beams can be obtained. The relation equations between the ultimate moment and critical moment are also obtained by using the regression analysis for the results of inelastically flexural-torsional buckling simulation.The studies about the effect of the residual stress on the overall stability capacity of the monosymmetric and double-symmetric I-section two-span and single-span beams were carried out. The influence of the loading type, the loading position, the monosymmetry section constant and the ratio of the distribution area between the tensile and the compress residual stress in the flange were all considered. The relation equations between the ultimate moment allowing for the residual stress and normalized slenderness have been proposed. It is shown that the ultimate bearing capacities of the beam with larger normalized slenderness may increase by the residual stress when the ratio of the distribution area between the tensile and the compress residual stress in the flange is greater than 1, and the increment should not be neglected. It is quite close to the test results of this paper.