Damping Constant h

In the impact response analysis for prototype RC girders, system damping effects of the structure should be considered as well as the hysteretic damping effects of concrete and rebar material. Here, an appropriate viscous damping constant, h (hereinafter, damping constant) was determined with referring to the first natural vibration frequency. In this study, four cases were considered: h =

Table 6. In case of varying damping constant for concrete.

Damping constant

Division near


Concrete yield

support point

concrete modeling






8 Division

Beam element


0. 005, 0.01, 0.015, and 0.02 with the design parameters as listed in Table 6. Figure 9 shows the comparison of impact response waves obtained varying damping constant h with those from the experimental results. From Figures 9(a) through 9(d), it is seen that: (1) maximum amplitudes of impact force and reaction force at one supporting point are hardly influenced by damping constant h; and (2) phase of the second dominant wave of impact force and reaction force wave during impact load surcharging tends to be large with increasing of damping constant h. From Figures 9(e) and 9(f) for the comparison of displacement waves at points D — 1/2, it is confirmed that maximum displacement and residual displacement tend to be large with decreasing of damping constant h and an appropriate damping constant may be h = 0.015.

3. Conclusions

To establish a simple elasto-plastic impact analysis method of flexure-failure-type RC girder, a

falling-weight impact test and three-dimensional FE analyses were conducted for full-scale RC

girder. The results obtained from this study are as follows:

(1) Changing yield criterion for concrete material from von Mises model to Drucker-Prager model, and applying system damping constant of h = 0.015, the maximum amplitudes and the con­figuration of primary wave for three waves: weight impact force; reaction force; and mid-span displacement, can be better simulated;

(2) To better simulate the characteristics of mid-span displacement wave, the region near supporting point should be modeled with fine mesh which is the same to a quarter of an interval of stirrups;

(3) Stress-strain relation of concrete assumed for analysis of small-scale RC beams can be applic­able for the analysis of large-scale RC girders; and

(4) However, the initial gradient of weight impact force wave and frequency of secondary displace­ment wave cannot be properly estimated whatever any parameter is changed.