1. INTRODUCTION
This research was initiated by observing the experiment results of the previous study. Strength behaviors of the three specimens were investigated through an experiment implemented by the steel structure lab. All of these specimens are the plate girders with high tension bolted connections. Two of the plate girders have the same specifications,however, one is with the horizontal stiffeners, while the other, horizontal stiffeners are omitted around the bolted connection.
The detailed specifications and shape of the test specimens are shown in Figure 1. Both of the specimens are the plate girder with the separated type of hightension bolted connection, which is that the moment splice plates and shear splice plates are separated in the web panel. In this case, the shear splice plate with the hightension bolts become responsibles of horizontal stiffeners and boosted the buckling strength of the web panel, as a result.
Therefore, it is possible to omit the horizontal stiffener around the bolted connection as in the Figure 1(b). The failure shapes of the both specimens after the experiments has been revealed in Figure 2.
Fig. 3 is experimental results of specimen1 and specimen2 in the relation of applied load(P) and displacement(δ) at the center of the girders. According to our results, the girder with the horizontal stiffeners doesn’t show the high strength performances while it’s comparing to the one without the horizontal stiffeners. The graph also shows that the specimens have the same strength behaviors in the elastic range, a slight difference behavior appear in the plastic range. Moreover, both test specimens showed the same loading capacity, yielding strength behaviors and finally, the ultimate strength of the girder were also the same.
After reviewing the two experimental results, it could be clearly noticed that the horizontal stiffeners around the hightension bolted connection since it doesn’t conduct the role of increasing the strength of the girder. In order to prove this hypothesis, the FEM analysis for the omission of the horizontal stiffener was proceeded.
2. OUTLINE OF ANALYSIS MODEL
2.1 Analysis Method
In order to efficiently investigate the behavior of the desired models, the standard FEM analysis program was used. The solid element was especially chosen over the thin shell element in order to support the accuracy of analysis results during the analysis process.
Specifically, the half model was used by considering the central plane of the model as the symmetric boundary plane in order to save the analysis period and reduce the errors during the analysis process. Moreover, the bolted load were considered for the boltedconnection, thus, the design bolt load which mentioned in the "Korean Highway Bridge Design Code (KHBDC, 2012)" was applied along with the axial of the hightension bolts. The detail boundary conditions and loading conditions of the analysis models are shown in the Figure 4.
The analysis model is considered as the SS400 steel, therefore, the mechanical properties of that is assigned to the model. The stressstrain relationship is calculated by using the steel composite equation in order to obtain the nonlinear stressstrain results of the analysis.
2.2 Verification of Analysis Method
In Figure 5, the comparison of the experimental results and analytical results can review in order to observe the validity of the analysis method. Here, the standard experimental results are obtained by the test results which is done by the Akiyama(1996) in his thesis named "A Study on the limit States of HSFG Bolted Joints."
According to the graph, experimental and analysis results show the same behavior in elastic and plastic ranges and also under the unloading condition. The slip behavior occurred at around the loading capacity of 610kN which is slightly earlier than the experimental results, that is caused by the difference in the friction resistance of experimental and analytical program. Although there is a slight difference in slip interval, yielding, elastic and plastic behaviors show that this analysis program has high vilidity.
2.3 Specifications of Analysis Models
In this study, the strength behavior of the plate girder is investigated by varying the aspect ratio(α ) and the web proportion(h/t_{w} ) independently in order to analyzed the effects of the horizontal stiffeners on the strength of the girder.. In the Table 1, the specifications of the analysis model can be observed.
The research proceeded by analyzing the models with different web proportion(h/t_{w} ), and the aspect ratio(α ) varies as 0.4, 0.7 and 1 for each model. The detail specifications of the analytical models can be observed in the Table 2 and the shape of the model can be seen in the Figure 6.
3. ANALYSIS RESULT
3.1 Effect of Aspect Ratio(α )
Fig. 7 shows the effect of the aspect ratio on the strength of the girder. The results are in the relationship of the displacement of the loading capacity at the center of Ishaped girder and the ratio of the analytical moment to the theoretical yield moment.
According to the results, the yielding of the girder occurs at the moment ratio (M /M_{y} ) of 1.0 while aspect ratio(α ) is 0.4, then, the yielding point occurs at the moment ratio (M /M_{y} ) of 0.9 while the aspect ratio(α ) is 1.0. Therefore, results manifest that the aspect ratio is inversely proportional to the strength of the girder. The effect that the larger the aspect ratio, the lower the strength of the girder can obviously be seen through this graph.
3.2 Effect of Web Proportion(h/t_{w})
In the Fig. 8, the effect of the webthickness ratio (h/t_{w}) on the strength of the girder can be seen in the relationship of the plastic moment ratio(M /M_{y} ). Herein, the models with the same aspect ratio while varying the h/t_{w} from 140 to the maximum 260, which is the maximum design limit in the "Korean Highway and Bridge Design Code (KHBDC,2012)" are analyzed through the same program.
According to the Fig. 7, yield point occurs at the plastic moment ratio(M /M_{y} ) at 0.9 for the designed (h/t_{w} ) of 140, while it presents at 0.7 when the (h/t_{w} ) designed as 200, while it’s found at 0.55 when the (h/t_{w} ) designed as 260, however, the aspect ratio was kept to be constant at 0.4 in all the aforementioned cases. Here, the effect that the larger (h/t_{w} ), the more reducing the strength of the girder can be clearly reviewed.
3.3 Slip Strength Behavior
As it is mentioned before, this analysis method used the solid element for the parts of the model, therefore, the occurrence of slip behavior at the hightension bolted connection can be investigated. The slip behavior can be reviewed in the Fig 8.
According to the Fig.9, the slip strength of the hightension bolted connection does not effect by the aspect ratio and it is only effected by the h/t_{w} . Thus, the interval between the splice plates and the vertical stiffener does not related to the slip strength of the bolted connection. Therefore, the slip strength can be controlled by designing the h/t_{w} .
3.4 Omission of Horizontal Stiffener
In the Fig. 10, the FEM analytical results in the relationship of aspect ratio (α ) and the ratio of the ultimate moment of the analytical to the theoretical yielding moment(M_{u}/M_{y}) are provided.
Based on results, when the aspect ratio is design as 0.4∼0.7, and the h/t_{w} designed as equal or lower than 180, then, the M_{u}/M_{y} is above 1. This means that the buckling moment at the web panel is effectively secured in that range. And also the M_{u}/M_{y} is above 1 when the aspect ratio is at 1 and h/t_{w} is equal or lower than 140. Consequently the web moment can secure the yield moment within that range.
The relationship of h/t_{w} and the M_{u}/M_{y} can be reviewed in the Fig. 10. When the aspect ratio is 0.4∼ 0.7 and web proportion is equal or lower than 160, the ultimate moment in the web exceeded the yielding moment, thus, it is possible to omit the horizontal stiffener within that range. Similarly, the ultimate moment of the web panel exceeded the yield moment when the aspect ratio is 1 and h/t_{w} is equal or lower than 140, and the omission of the horizontal stiffener is possible.eqs. 1
Equation 1 is the suggested design equation for the omission of the horizontal stiffener which is configured by reviewing the omission range in Fig.10 and Fig.11. Fig. 12 is the graph of the analytical results and the results calculated by eqs.1.
4. CONCLUSION
In this study, the strength behavior of the Ishaped plate girder was investigated through FEM analysis. The range to omit the horizontal stiffener safely around the hightension bolted connection is also investigated and the suggested equation is configurated. The slip strength behavior of the hightension bolted connection also explored in this study.
The following statements are organized by reviewing through this study.

(1) The aspect ratio(α) and the web slenderness ratio (h/t_{w} ) are reversely proportional to the strength of the girder. The larger the aspect ratio(α) and h/t_{w} , the lower the strength of the girder.

(2) The more substantial web proportion, the lower rigidity of the girder and thus, the aspect ratio effect more on the girder with more substantial web proportion. Therefore, the web must be thoroughly designed to have the strongest or more rigid girder.

(3) The slip at the bolted connection is only affected by the slenderness of the web (h/t_{w} ). However, it is not affected by the aspect ratio(α ). If h/t_{w} is designed as the maximum and the aspect ratio is at 1, the yielding of the girder occurs before the slip behavior at the bolted connection appear.

(4) The horizontal stiffener can be omitted when the h/t_{w} is lower or equal to 180 and the aspect ratio is 0.4. If the aspect ratio is larger than 0.4 and lower than 0.7 and h/t_{w} is equal or lower than 160, then, the horizontal stiffener can also be omitted. Finally, the horizontal stiffener can omit when the aspect ratio is design between 0.8 to 1.0 and the h/t_{w} is 140 or lower.
If the plate girder is designed by the eqs.1, the horizontal stiffener around the bolted connection can be omitted in the ranged which mentioned above. As a result, more economical and feasible girder can be obtained. This study can be referenced for designing the more portable plate girder which can give easy and advanced workability in the construction sites.