al frequency of the bridge. The UHPC pedestrian cable stayed bridge experimented in this study was constructed as a cantilevered structure following the impossibility to install bearings or anchoring systems in the existing buildings connected by the bridge. Such structural characteristics and the slim structure achieved through the application of UHPC render inevitably the bridge vulnerable to vibration. To confirm this fact, users complained of their discomfort and loss of convenience caused by the vibration of the pedestrian bridge and led to the consideration of vibration control. Comparative analysis of the dynamic behavior of the bridge was conducted through analytic and experimental methods to evaluate the vibrational serviceability of the bridge and establish a solution for vibration control .
5.2. Dynamic Characteristics under Pedestrian Loads
Pedestrian load is influenced by various factors including the weight of the pedestrian or his walking frequency, speed, walking form, and personal walking habit. Such
Table 3. Mix composition of KICT-UHPC.
Figure 6. Installation of UHPC deck.
load can be thus expressed by means of various load-time history models. In order to evaluate whether sufficiently large dynamic responses are generated by these pedestrian load models, free vibration analysis was conducted using the commercial program SAP2000 on the 3-dimensional model of the bridge. Frame elements were used for the edge girder, deck and pylon, and truss elements were adopted to provide simplified model of the cables.
The analysis results can be summarized as follows:
- Structural mass: 225.91 kN·sec2/m;
- 1st mode natural frequency: 2.05 Hz;
- 1st mode frequency: 0.49 sec;
- 1st mode mass participation ratio: 94.80 %;
- 1st modal mass: 214.16 kN·sec2/m.
The first natural frequency of 2.05 Hz predicted by the analysis results was very close to the frequency of the pedestrian load caused by users walking at regular step. Accordingly, high risk of resonance to occur for the pedestrian bridge could be forecast. Since the dynamic behavior of the actual pedestrian bridge depends on a larger set of factors including the tension of the cable, its real natural frequency may differ from the analytically obtained value. Therefore, test was performed to evaluate exactly the natural frequency and comparison with the analysis was done to evaluate the resonance frequency of the pedestrian cable stayed bridge. The natural frequency and maximum vibrational acceleration as well as the dynamic deflection at the end of the deck were measured through loading test (Figure 7). Being a pedestrian bridge, the natural frequency was estimated under loaded condition according to the walking and jumping of users. The testing method is described in Table 4. The natural frequency under running of two people was 1.91 Hz (Figure 8). Since the load frequency of a walking pedestrian runs around 2 Hz, it appeared that the installation of TMD was required to prevent resonance.
6. Solution for Vibration Control
The current UHPC cable stayed pedestrian bridge experienced excessive vertical vibrational accelerations larger than the limit value of 0.1 g (Manual for the De-
Figure 7. Acceleration response (2 pedestrians running).
Table 4. Initial forced vibration test.
Figure 8. PSD (2 pedestrians running).
sign, Construction and Maintenance of Facilities). The measurement results of the initial forced vibration test revealed that the maximum vibrational acceleration reached about 0.11 g. Accordingly, Tuned Mass Dampers (TMDs) were installed on the parapet of the pedestrian bridge to improve its serviceability by reducing the vertical acceleration below 0.1 g. The installation process of the TMDs was conducted according to the following sequence.
1) Decision and fabrication of TMDs
- Design (dimensions) and fabrication conducted after 3-D structural analysis and initial forced vibration test
- Test of fabricated TMDs at factory;
- Selection of installation locations of TMDs;
2) Installation of TMDs on the pedestrian cable stayed bridge.
- A total of 4 units installed at a rate of 2 units per side at the parapet of the bridge.
3) Performance verification test.
6.2. Vertical Vibration Control Device (TMD)
TMD applies the principle of the dynamic vibration absorber traditionally applied in mechanical engineering to civil structures. This device absorbs the vibration of the bridge by tuning the natural frequencies of the bridge and device. The weight of the TMD is generally set to approximately 1% of that of the host structure. TMD as a passive vibration control device offers the advantages of not requiring separate supply of electric power and being semi-permanent. Examples of its application can be found among others in Millennium Bridge in London, UK, Bellagio Pedestrian Bridge in Las Vegas, Nevada USA, Yokohama Bay Bridge in Yokohama, Japan. The TMD for footbridge enhances the serviceability by reducing the vibration of the bridge through the efficient absorption of the energy transmitted by the external load (pedestrian load) to the bridge. TMD is a typical passive vibration control device, which exploits the inertial force and featured by the needlessness of electric power and stable behavior. TMS is essentially composed of masses, springs, damper, frame and various types of substructure. TMD should be installed at the location exhibiting the largest vibration in the host structure to develop maximum vibration control .
The movable mass of the TMD was computed to be 0.5% of the 1st modal effective mass.
- Movable mass of vibration reducing device: 214.16 × 0.005 = 1.0708 kN·sec2/m;
- 4 TMDs installed at a rate of 2 units at each end of the pedestrian bridge;
- Mass of each TMD: 1.0708/4 = 0.2677 kN·sec2/m;
- Movable mass of vertical TMD: 0.2677 × 9.806 = 263 kgf.
The design movable mass of TMD was determined to be 264 kgf per unit considering the workability of steel.
- Modified mass ratio (m) : m = 1.0708/214.16 = 0.005
- Frequency ratio of vertical TMD (fR):
fR = 1/(1 + μ) = 0.995;
- Optimal damping ratio of vertical TMD (zT): zT = 0.04 (Table 5 and Figure 9).
6.3. Analysis of Vibration Control Effect by Dynamic Loading Test
The forced vibration tests distinguished regular walking, fast walking, running and jumping considering 1, 2, 5 and 10 pedestrians so as to conduct the tests under diverse loading cases. By varying the speed, pace and load, each load case was performed twice and comparison was done of the measurements collected under operation and shut off of the TMDs. Walking tests were carried out at speeds of 2.16 km/h for regular walking, 5.4 km/h for fast walking, and 8.1 km/h for running while maintaining constant speed and spacing. Figures 10 and 11 illustrate the walking test and Figures 12-14 plot the dynamic responses.
Under operation of the TMDs, for Load Case 4 (2 people walking regularly), 2 people averaging a mass of 167 kg walked at slow speed of 2.16 km/h, i.e. pace of 60 cm/s, at spacing of 60 cm to each other through a course starting from the main building to the new building and returning to the main building. The corresponding maximum displacement and maximum acceleration reached respectively 1.97 mm and 0.0244 g at DT1. Under shut off of the TMDs, the maximum displacement and maximum acceleration increased slightly with respective values of 2.05 mm and 0.0316 g for LC4. Since LC4 repre-
Table 5. Characteristics of vertical TMD.
Figure 9. Dimension and view of TMD.
Figure 10. Walking test (numerous pedestrians running).
Figure 11. Walking test (2 pedestrians jumping).
Figure 12. Displacement response (2 pedestrian walking): (a) TMD on; (b) TMD off.
Figure 13. Displacement response (2 pedestrian walking rapidly): (a) TMD on; (b) TMD off.
Figure 14. Acceleration response (2 pedestrian jumping): (a) TMD on; (b) TMD off.
sents the most common way of walking, the maximum acceleration can be said to be 0.0244 g falling below the limit value. In the future, more detailed analysis related to the serviceability of the UHPC pedestrian cable stayed bridge needs to be performed.
A pedestrian cable stayed bridge using 200 MPa class UHPC developed by KICT has been designed and erected for the first time in the world. KICT-UHPC with a design compressive strength larger than 180 MPa can resist to large compressive forces and is a material enabling to minimize the thickness of the cross-section owing to its large resistance to tension and shear. Besides, UHPC is also featured by large autogenous shrinkage which presents the risk of early cracking in the case of structures with complex shape. Considering these characteristics of UHPC, the pedestrian UHPC cable stayed bridge was constructed in the site of KICT. Measures to prevent the occurrence of early autogenous shrinkage cracks were derived through a trial construction and the dynamic characteristics of UHPC members were evaluated by means of static loading tests on full-scale specimens. These findings enabled to verify the applicability of UHPC not only to pedestrian cable stayed bridges but also to common highway cable stayed bridge structures. In-depth tasks for further studies were also derived. In addition, a first series of forced vibration tests made it possible to evaluate the dynamic characteristics of the pedestrian bridge through measurement of its natural frequency, vibrational acceleration and dynamic displacement responses. The test results revealed that the pedestrian bridge secures satisfactory dynamic characteristics for most of the load cases. However, responses appeared to exceed the limit values in the case of jumping impact by users. Accordingly, TMDs were installed on the parapet of the pedestrian bridge to reduce vibration. Verification tests showed that the maximum acceleration response of 0.186 g measured before the installation of the TMDs under standing jump of two people reduced effectively by more than 49% to drop down to 0.095 g after the installation of the TMDs and fell within the limit value of 0.1 g. Moreover, the vibration effect reducing effect of the TMDs could also be verified in the case of 2 people walking at regular pace by a decrease of 30% of the maximum acceleration response from 0.0316 g to 0.0244 g. Future studies will apply various test variables for diversified vibration tests and analyses to evaluate the vibrational characteristics of the pedestrian bridge such as the maximum acceleration, dynamic deflection and mode shapes. Furthermore, it is believed that reliable data related to the vibration serviceability of the pedestrian cable stayed bridge according to the installed TMDs could be secured through more precise verification tests, dynamic analyses and lateral vibration tests.
This research was supported by a grant from a Strategic Research Project (Development of design and construction system technology for hybrid cable stayed bridge) funded by the Korea Institute of Construction Technology.