Element Size in Longitudinal Direction near Supporting Point

Element size in the longitudinal direction near supporting point is basically set as one-half of an interval of stirrups and is 125 mm long. However, since an interaction between RC girder and the steel beam set on the upper surface of the girder for protecting jump up may influence to the numerical analysis on impact response behavior, numerical accuracy due to element size in the longitudinal direction was investigated, in which the element size in the region of 500 mm long back and forth of supporting point was considered. Here, three kinds of element size were taken as listed in Table 4, which are corresponding to those defined in the longitudinal direction of the RC girder, and element size for each four and eight division is the same for the elements near supporting part and the mid-span part, respectively, as shown in Figure 6.

Figure 7 shows the comparisons of analytical results for each response wave in case varying the mesh size of concrete elements near supporting point with the experimental results. From Fig­ures 7(a) and 7(b), it is understood that the impact force wave at the beginning of impact can not be influenced by the element size near supporting point, but second dominant wave after 30 ms passed from the beginning of impact tends to be high amplitude with decreasing down of element size. From Figures 7(c) and 7(d), it is confirmed especially from Figure 7(d) that reaction force wave at the one supporting point tends to be high amplitude for high frequency component waves corresponding to element size decreasing and maximum amplitude in case of eight division was almost similar to that of the experimental results. From the comparison for displacement waves at the points D — 1/2 shown in Figures 7(e) and 7(f), it is observed that the wave during impact load surcharging behaves almost similar in spite of the element size near supporting point. Then, it is

Fig. 6. FE division near 500 mm supporting point in longitudinal direction.

Fig. 7. Comparison of each response waveforms in case varying element size near support point.

confirmed from this investigation that the element size near supporting point will influence to the response of reaction force and maximum amplitude can be corresponded to the experimental results by dividing the 500 mm region near supporting point into eight elements in the longitudinal direction, in which the longitudinal length of those elements is the same to a quarter of an interval of stirrups.

Table 5. Analytical case for investigating numerical accuracy by yield criterion for concrete.

Concrete yield

Division near


Damping constant


support point

concrete modeling

von Mises Drucker-Prager

8 Division

Beam element