Study Of Thin-walled Structure Including The Effect Of Shear Lag

There will be shear lag effect existing in the thin-walled structure when it is suffered from bending load. Many eyes are focused on shear lag effect and some achievements have been obtained. But there are still some engineering problems not solved wholly. Based onΠ-shaped cross section cable-stayed bridge, concrete box beam and composite box girder with corrugated steel webs, the effect of shear lag on the static and dynamic character of thin-walled structure were studied. The main achievements are as followings.(1) With the help of finite element method, the shear lag effect of aΠ-shaped cross section cable-stayed bridge was discussed. The credibility of the finite-element model was validated by comparison of its results with the test results of the bridge. A parametric study using finite element analysis was carried out, in which the parameters such as prestress, transverse slope of bridge deck and little longitudinal beams were considered. Also, the effect of shear lag on the dynamic character ofΠ-shaped cross section cable-stayed bridge was discussed. The results show that shear lag effect is more serious at the root of theΠ-shaped cross section girder than that at its mid-span. The axial stress distribution curve of all sections has several knee points and so it is difficult to describe the shear lag with one parameter. Presstress and transverse slope of the girder have much effect on the shear lag, and it should not be neglected during calculation. And transverse slope is another important factor that influencing the shear lag, especially for the longitudinal normal stress near the middle area of the deck. It also shows that longitudinal girders can improve the stress distribution obviously. The analysis of dynamic character indicates that the vibration frequencies will decrease due to shear lag effect. The decrease will be more obviously with the increasing of frequency order.(2) Based on energy variational principle, a new method to analyze the vibration of simply supported box girder was proposed, in which the effect of shear lag was considered, and the closed-form solutions of the fundamental frequency were derived. The example shows that the accuracy and effectiveness of this new method is much improved compared with the conventional beam theory. Furthermore, the frequency formula was extended to calculate all orders of frequencies of box girder, in which both the effect of shear lag and shear deformation were taken into consideration, and the accuracy was improved. The parameters affecting the vibration frequencies were discussed in detail. The parametric study shows that the natural frequencies of simply supported box girder will decrease when the effects of shear lag or shear deformation is taken into account, especially for the high order frequencies' calculation. The main parameters that affect the frequencies decrease include inertia moment ratio(I_s/I), the width span ratio(l/2b), shear factor(k) and span high ratio(l/r), in which the width span ratio is the most important parameter.(3) An analytic formula of the natural frequencies of simply supported box girder with corrugated steel webs was deduced, in which both the effects of shear lag and shear deformation were taken into consideration. The natural frequencies of a composite box girder model with corrugated steel webs were tested and compared with the results of the elementary beam theory, formula of this dissertation and the 3D finite element model. The results show that the effects of shear lag and shear deformation on vibration are so pronounced that it should not be neglected in the frequencies calculation. The frequencies of composite box girder with corrugated steel webs will decrease when the effect of shear lag and shear deformation are taken into consideration. Compared with the concrete box girder, the effect on composite box girder is more pronounced. And the effects increase sharply with the increase of the frequency order. The formula proposed in this dissertation can take the effects of shear lag and shear deformation into consideration; furthermore, it is simple and accurate.(4) A practical method was proposed to calculate the forced vibration of simply supported box girder bridge, and the effect of shear lag is included in this method. Based on the forced vibration theory of elementary beam, the dynamic stress amplification factor of a simply supported box girder under harmonic load was deduced, in which the effect of shear lag was considered. The comparison of it with the results of solid finite element model shows the method of this dissertation is feasible. As for the earthquake calculation, equivalent elastic modulus method was proposed to analyze the effect of shear lag according to response spectrum method and time history method. Example shows that the equivalent elastic modulus method is feasible.(5) Based on energy variational principle, the closed-form formula of stability critical force of cantilever box girder was deduced, in which the effect of shear lag was included. A cantilever box section pier was taken as example, and the comparison between elementary beam theory and solid finite element model shows that the formula is more simple and accurate. The critical force will decrease when shear lag is taken into consideration, so elementary beam theory would lead to non-conservative result. The formula introduced in this dissertation can improve the accuracy while the formula is as simple as elementary beam theory's.