Shake Table Test of Long Span Cable-Stayed Bridge Subjected to Near-Fault Ground Motions Considering Velocity Pulse E ﬀ ect and Non-Uniform Excitation

Featured Application: The research conclusion on the velocity impulse e ﬀ ect and non-uniform excitation in this paper can be used to guide the seismic design of cable-stayed bridges. Abstract: This paper presents the results of shake table tests of a scaled long span cable-stayed bridge (CSB). The design principles of the scaled CSB are ﬁrst introduced. The ﬁrst six in-plane modes are then identiﬁed by the stochastic subspace identiﬁcation (SSI) method. Furthermore, shake table tests of the CSB subjected to the non-pulse near-ﬁeld (NNF) and velocity-pulse near-fault (PNF) ground motions are carried out. The tests indicated that: (1) the responses under longitudinal uniform excitation are mainly contributed by antisymmetric modes; (2) the maximum displacement of the tower occurs on the tower top node, the maximum acceleration response of the tower occurs on the middle cross beam, and the maximum bending moment of the tower occurs on the bottom section; (3) the deformation of the tower and girder subjected to uniform excitation is not always larger than that subjected to non-uniform excitation, and therefore the non-uniform case should be considered in the seismic design of CSBs.


Introduction
For a long time, the cable-stayed bridge (CSB) has been the main bridge type scheme for long-span bridges. Among them, many CSBs are located in earthquake-prone zones. Owing to their flexibility and slenderness, CSB can dissipate a major portion of the earthquake forces [1]. However, when suffering from strong earthquakes, CSBs experience large displacements and internal forces [2]. For example, the tower of Chilu bridge was seriously damaged during the CHICHI earthquake in 1999 [3]. As transportations hubs, any damage to a bridge during an earthquake may lead to serious problems.
To reveal the seismic response of long span CSBs, many studies have been carried out. Xu and Duan discussed the seismic design strategy of CSBs subjected to strong ground motion [4]. Yi and Li studied the seismic-induced bearing uplift of CSBs subjected to strong ground motions [5]. Bayraktar et al.

Shake Table System
This test is carried out on the shake tables system of Fuzhou University (China), shown in Figure  2. The shake tables system is capable of 3-freedom motions with maximum acceleration is up to 1.5 g. The effective operation frequency band is 0.1-50 Hz. The shake tables system consists of one middle tables and two side tables. The middle table is 4 m × 4 m, while the side table is 2.5 m × 2.5 m. The maximum payload of middle table and side table are 25 t and 10 t respectively. The two side tables are movable in longitudinal direction with the maximum length of 24 m. All three tables can work together or independently, which can simulate uniform excitation and non-uniform excitation separately. Other parameters of the shake tables of Fuzhou University are listed in Table 1.

Shake Table System
This test is carried out on the shake tables system of Fuzhou University (China), shown in Figure 2. The shake tables system is capable of 3-freedom motions with maximum acceleration is up to 1.5 g. The effective operation frequency band is 0.1-50 Hz. The shake tables system consists of one middle tables and two side tables. The middle table is 4 m × 4 m, while the side table is 2.5 m × 2.5 m. The maximum payload of middle table and side table are 25 t and 10 t respectively. The two side tables are movable in longitudinal direction with the maximum length of 24 m. All three tables can work together or independently, which can simulate uniform excitation and non-uniform excitation separately. Other parameters of the shake tables of Fuzhou University are listed in Table 1.  Table 1. Performance specifications of the shake tables system. For the test bridge, the towers and piers are made of polymethyl methacrylate (PMMA), as that is easy to be fabricated. The cross-sections of towers and piers are designed strictly following the geometric scaling factors of 1/100. Figure 3 shows the elaborated tower and pier.
As the towers is the most important components of CSB, the similitude ratios of the whole CSB are determined according to tower. Based on the Buckingham theorem of dimensional analysis [20],  Table 1. Performance specifications of the shake tables system.

Similitude Ratio
For the test bridge, the towers and piers are made of polymethyl methacrylate (PMMA), as that is easy to be fabricated. The cross-sections of towers and piers are designed strictly following the geometric scaling factors of 1/100. Figure 3 shows the elaborated tower and pier.

Girder and Stayed Cables
In the prototype bridge, the deck is flat, thin walled steel box with many U shape shear key. It would be very difficult to manufacture the deck if the cross-section were scaled in ratio of 1/100 stickily. Therefore, it is simply designed according similitude ratios of bending stiffness in Table 2.
The aluminum is selected as the material of girder for the characteristics of low elastics modulus, simply processed and installed. Figure 4 shows the size, area and moment of inertia of the cross section. The section stiffness EIz and EIz are calculated as 4.72e-06 m 4 and 1.50e-07 m 4 . The actual bending stiffness ratios of EIz and EIz are 6.91E+08 and 5.00E+08. They are about 1.86 times and 2.56 times of target similitude ratios of bending stiffness in the Table 2. As the towers is the most important components of CSB, the similitude ratios of the whole CSB are determined according to tower. Based on the Buckingham theorem of dimensional analysis [20], the similitude ratios of other parameters were calculated, shown in Table 2. All other components of the test CSB are designed based on the similitude ratios in the table.

Girder and Stayed Cables
In the prototype bridge, the deck is flat, thin walled steel box with many U shape shear key. It would be very difficult to manufacture the deck if the cross-section were scaled in ratio of 1/100 stickily. Therefore, it is simply designed according similitude ratios of bending stiffness in Table 2.
The aluminum is selected as the material of girder for the characteristics of low elastics modulus, simply processed and installed. Figure 4 shows the size, area and moment of inertia of the cross section. The section stiffness EI z and EI z are calculated as 4.72e-06 m 4 and 1.50e-07 m 4 . The actual bending stiffness ratios of EI z and EI z are 6.91E+08 and 5.00E+08. They are about 1.86 times and 2.56 times of target similitude ratios of bending stiffness in the Table 2.  The high-strength steel wire was used to fabricate stayed cables. The diameters of cables were calculated strictly followed similitude ratio of axial stiffness in Table 2. In the model, diameters of the steel wires are 0.4 mm for C1-C8, 0.6 mm for C9-C14 and 0.9 mm for C15-C21. Material tests of the polymethyl methacrylate (PMMA) and other materials were conducted, and the average properties are shown in Table 3.  (table 1#), and #4 tower, #5, #6 and #7 piers were placed on the right-side table (table 2#). All the towers and piers were fixed on the tables by high stress bolts. Figure 5c shows the elaborate roll bearings installed between the tower and girder. The bearings can roll freely in longitudinal direction, but is restrained in the lateral direction. The high-strength steel wire was used to fabricate stayed cables. The diameters of cables were calculated strictly followed similitude ratio of axial stiffness in Table 2. In the model, diameters of the steel wires are 0.4 mm for C1-C8, 0.6 mm for C9-C14 and 0.9 mm for C15-C21. Material tests of the polymethyl methacrylate (PMMA) and other materials were conducted, and the average properties are shown in Table 3.  (table 1#), and #4 tower, #5, #6 and #7 piers were placed on the right-side table (table 2#). All the towers and piers were fixed on the tables by high stress bolts. Figure 5c shows the elaborate roll bearings installed between the tower and girder. The bearings can roll freely in longitudinal direction, but is restrained in the lateral direction.

Additional Masses
The additional mass is calculated according to the similitude ratio of mass in table 2. In order maintain the rigidity of the bridge, the additional mass is realized by a series of discrete mass blocks. Steel blocks of different weights were prefabricated, such as 1 kg and 0.5 kg. For each tower, steel blocks with a total weight of 294 kg are fixed, shown in Figure 6a. For each pier, steel blocks with a total weight of 66 kg are fixed, shown in Figure 6b. For girder, steel blocks with a total weight of 114 kg are fixed on the deck, shown in Figure 6c.

Additional Masses
The additional mass is calculated according to the similitude ratio of mass in table 2. In order maintain the rigidity of the bridge, the additional mass is realized by a series of discrete mass blocks. Steel blocks of different weights were prefabricated, such as 1 kg and 0.5 kg. For each tower, steel blocks with a total weight of 294 kg are fixed, shown in Figure 6a. For each pier, steel blocks with a total weight of 66 kg are fixed, shown in Figure 6b. For girder, steel blocks with a total weight of 114 kg are fixed on the deck, shown in Figure 6c.

Sensors Arrangement
The responses of the bridge model were measured by 128 channels transducers collecting (made by Dewetron Co., Grambach, Austria) with a sampling frequency of 512 Hz. The displacements and accelerations for the decks, towers, and piers were measured by two displacement transducers and 23 accelerometers, respectively. The strains in the towers and piers were measured by 54 strain gauges, which were stacked on the surface of the critical sections, such as the bottom sections of the towers and piers. Figure 7 shows all the sensors arrangement.

Sensors Arrangement
The responses of the bridge model were measured by 128 channels transducers collecting (made by Dewetron Co., Grambach, Austria) with a sampling frequency of 512 Hz. The displacements and accelerations for the decks, towers, and piers were measured by two displacement transducers and 23 accelerometers, respectively. The strains in the towers and piers were measured by 54 strain gauges, which were stacked on the surface of the critical sections, such as the bottom sections of the towers and piers. Figure 7 shows all the sensors arrangement.

Dynamic Characteristics of the Test CSB
White noise excitation with bandwidth of 0.1~50 Hz was used to excite the dynamic characteristics of test CSB. The stochastic subspace identification method (SSI) [21] is used to identify the stochastic state space model from the recorded accelerations. Figure 8 shows the estimated inplane modal shapes and frequencies of first six modes. The first mode is dominated by longitudinal sway of the girder. The 2 nd mode shows vertical antisymmetric vibration of girder combining longitudinal bending vibration of tower. The 2 nd , 4 th and 6 th modes are antisymmetric around the vertical axis, while the 3 rd and 5 th modes are symmetric.

Dynamic Characteristics of the Test CSB
White noise excitation with bandwidth of 0.1~50 Hz was used to excite the dynamic characteristics of test CSB. The stochastic subspace identification method (SSI) [21] is used to identify the stochastic state space model from the recorded accelerations. Figure 8 shows the estimated in-plane modal shapes and frequencies of first six modes. The first mode is dominated by longitudinal sway of the

Input Ground Motions
In this paper, two near fault (NF) ground motions, recorded at stations within 20 km of the fault, are selected as input motions. The first one is EL-Centro wave, recorded in El Centro Array #9 station with epicentral distance of 6.09 km during the Imperial Valley earthquake in 1940. The ratio of PGV/PGA is 0.11. The other motion is recorded at station TCU052 with an epicentral distance of 1.84 km during the 1999 CHICHI earthquake. The PGV/PGA ratio is 0.43.
The algorithm proposed by Shahi and Baker [22] can identify pulses at arbitrary orientations. The procedure has been widely used to classify ground motions in the Next Generation Attenuation-West2 database [23]. Based on the above method, TCU052 is identified by an obvious velocity pulse, while the El-Centro motion has no velocity pulse.
During the shake table test, the PGA of both recorders are adjusted to 2.08 m/s 2 . According to the similitude ratio of time in Table 2, the recorder motions are scaled in time domain. The adjusted El-Centro wave and TCU052 wave are renamed as ScEL and ScTCU respectively. Figure 9a shows the acceleration time history of two motions. Figure 9b shows the acceleration Fourier amplitudes spectrum. It can be seen that the ScEL has more energy in the frequency range of [10 Hz,20 Hz], while the ScTCU has higher energy in the low frequency band of f < 10 Hz. For comparison, the identified frequencies of the first six modes are marked in Figure 9b. It is obvious that the frequencies of the first two modes are close to the predominant frequency of the ScTCU. Figure 9c,d show the velocity and displacement time histories of two motions. It shows the ScTCU has significant higher velocity than ScEL (2.89 cm/s). Besides, the maximum displacement value of ScTCU is much larger than ScEL, shown in Figure 9d. In conclusion, the ScTCU is stand for the PNF ground motion, while the ScEL can be seen as NNF ground motion.

Input Ground Motions
In this paper, two near fault (NF) ground motions, recorded at stations within 20 km of the fault, are selected as input motions. The first one is EL-Centro wave, recorded in El Centro Array #9 station with epicentral distance of 6.09 km during the Imperial Valley earthquake in 1940. The ratio of PGV/PGA is 0.11. The other motion is recorded at station TCU052 with an epicentral distance of 1.84 km during the 1999 CHICHI earthquake. The PGV/PGA ratio is 0.43.
The algorithm proposed by Shahi and Baker [22] can identify pulses at arbitrary orientations. The procedure has been widely used to classify ground motions in the Next Generation Attenuation-West2 database [23]. Based on the above method, TCU052 is identified by an obvious velocity pulse, while the El-Centro motion has no velocity pulse.
During the shake table test, the PGA of both recorders are adjusted to 2.08 m/s 2 . According to the similitude ratio of time in Table 2, the recorder motions are scaled in time domain. The adjusted El-Centro wave and TCU052 wave are renamed as ScEL and ScTCU respectively. Figure 9a shows the acceleration time history of two motions. Figure 9b shows the acceleration Fourier amplitudes spectrum. It can be seen that the ScEL has more energy in the frequency range of [10 Hz, 20 Hz], while the ScTCU has higher energy in the low frequency band of f < 10 Hz. For comparison, the identified frequencies of the first six modes are marked in Figure 9b. It is obvious that the frequencies of the first two modes are close to the predominant frequency of the ScTCU. Figure 9c,d show the velocity and displacement time histories of two motions. It shows the ScTCU has significant higher velocity than ScEL (2.89 cm/s). Besides, the maximum displacement value of ScTCU is much larger than ScEL, shown in Figure 9d. In conclusion, the ScTCU is stand for the PNF ground motion, while the ScEL can be seen as NNF ground motion.

Shake Table Test Cases
When subjected to longitudinal earthquakes, CSBs respond to the significant internal force of the tower and large displacement of the girder [24]. It is usually one of the control cases of the seismic design of cable-stayed bridges [25]. Although lateral and vertical ground motions will also have a non-negligible effect on the seismic response of the CSB. However, when considering multidirectional seismic excitation, the seismic responses of the CSB are more complicate as multidirectional excitations maybe coupled. It is unfavorable to study the influence law of velocity pulse effect or wave passage effect. In order to avoid the complexity caused by multi-directional seismic excitations, this experiments only focuses on seismic responses of CSB subjected to longitudinal seismic excitation. The schematic diagram of input excitations and sensors are shown in Figure 10.
Besides, the seismic response of the CSB subjected to non-uniform excitation are studied. It should be noted that the non-uniform excitation in this paper only considers wave passage effects, while local site effects and incoherence effects are not considered. In the test, the wave passage effect is realized by the time delay (dt) between two tables, shown in Figure 10.
The delay time dt can be calculated by following formula: L stands for the distance of two points; Vapp stands for the apparent wave velocity. In this paper, different Vapp is studied, such as 480 m/s, 240 m/s and 120 m/s; St stands for the similitude ratios of time, that is 0.0707 in table 2. As the main span of the CSB is 680 m, delay time dt in the test is calculated as 0.1 s, 0.2 s and 0.4 s, listed in Table 4.

Shake Table Test Cases
When subjected to longitudinal earthquakes, CSBs respond to the significant internal force of the tower and large displacement of the girder [24]. It is usually one of the control cases of the seismic design of cable-stayed bridges [25]. Although lateral and vertical ground motions will also have a non-negligible effect on the seismic response of the CSB. However, when considering multi-directional seismic excitation, the seismic responses of the CSB are more complicate as multi-directional excitations maybe coupled. It is unfavorable to study the influence law of velocity pulse effect or wave passage effect. In order to avoid the complexity caused by multi-directional seismic excitations, this experiments only focuses on seismic responses of CSB subjected to longitudinal seismic excitation. The schematic diagram of input excitations and sensors are shown in Figure 10.  Figure 10. Schematic diagram of input excitations and sensors.
As mentioned above, the ScEL and ScTCU are adopted as input motions for comparing the different seismic responses due to the NNF the PNF motion. Table 4 shows the shake table test cases.  Besides, the seismic response of the CSB subjected to non-uniform excitation are studied. It should be noted that the non-uniform excitation in this paper only considers wave passage effects, while local site effects and incoherence effects are not considered. In the test, the wave passage effect is realized by the time delay (dt) between two tables, shown in Figure 10. The delay time dt can be calculated by following formula: L stands for the distance of two points; V app stands for the apparent wave velocity. In this paper, different V app is studied, such as 480 m/s, 240 m/s and 120 m/s; S t stands for the similitude ratios of time, that is 0.0707 in table 2. As the main span of the CSB is 680 m, delay time dt in the test is calculated as 0.1 s, 0.2 s and 0.4 s, listed in Table 4. As mentioned above, the ScEL and ScTCU are adopted as input motions for comparing the different seismic responses due to the NNF the PNF motion. Table 4 shows the shake table test cases. Figure 11a shows the accelerations recorded on the shake tables under the uniform excitation of ScEL. It shows the longitudinal movement of both tables are in the same order. Figure 11b shows the acceleration Fourier amplitudes comparison of the two tables. The result indicates the identical Fourier amplitudes distribution of both tables. In the other test cases, similar result can be observed. Generally, the measured data shows shake table system of Fuzhou University has a good reproduction accuracy for earthquake motions.

Accelerations Responses
In the tests, the accelerometers are assembled on the key nodes of tower, such as on the lowerbeam (T2), middle cross-beam (T3) and top node (T4). Figure 12a,b show the longitudinal acceleration responses of tower when subjected to uniform excitation of ScEL and ScTCU. As shown, the acceleration responses time histories of the different nodes are various. However, the peak time seem the same for all nodes. When subjected to NF excitations with same PGA (2.08 m/s 2 ), maximal accelerations subjected to NNF motion (ScEL) seems a little larger than the PNF motion (ScTCU). The phenomenon can be explained by the response Fourier spectrum, such as Figure 13a,b. As operation frequency limitation of the test system, the frequency range of 0~50 Hz are shown in the figures. It is obviously the energy of tower top node (T4) are mainly at 6.9 Hz, 13.8 Hz, 27 Hz, which are close to

Accelerations Responses
In the tests, the accelerometers are assembled on the key nodes of tower, such as on the lower-beam (T2), middle cross-beam (T3) and top node (T4). Figure 12a,b show the longitudinal acceleration responses of tower when subjected to uniform excitation of ScEL and ScTCU. As shown, the acceleration responses time histories of the different nodes are various. However, the peak time seem the same for all nodes. When subjected to NF excitations with same PGA (2.08 m/s 2 ), maximal accelerations subjected to NNF motion (ScEL) seems a little larger than the PNF motion (ScTCU). The phenomenon can be explained by the response Fourier spectrum, such as Figure 13a,b. As operation frequency limitation of the test system, the frequency range of 0~50 Hz are shown in the figures. It is obviously the energy of tower top node (T4) are mainly at 6.9 Hz, 13.8 Hz, 27 Hz, which are close to the frequencies of the 2 nd , 4 th , 5 th modes. Among them, the 2 nd mode dominate the acceleration response of tower top node. However, the response of mid cross beam (T3) has more energy than top node (T4). For f = 6.9 Hz, the peak amplitude is 0.05 m/s 2 for tower top node, while that is 0.15 m/s 2 for mid cross beam. In addition, there are an energy crest around 20 Hz, which is close to the frequency of the 5 th mode. In the result, the acceleration response of tower mid cross beam is larger than top node. As shown in Figure 13b, the very similar phenomenon can be found in the tower response subjected to ScTCU.  Figure 14 shows the maximum tower acceleration distribution of the 3# tower and 4# tower. For the both towers, the maximum acceleration happens on middle cross beam (T3), rather than the tower top node (T4). The reason is the tower top node is effectively restricted by stayed-cables. In the result, the vibration on tower top node always smaller than mid cross beam under the longitudinal excitation. In general, from the point of view of longitudinal seismic response, the tower can be equivalent to a cantilever column with limited restriction on top node. When subjected to the ScEl, the acceleration responses seem a little larger than ScTCU. It should be noted that the acceleration for the same node of the two towers seems a little different. This may come from the manufacturing differences between the two towers or bearings.  Figure 14 shows the maximum tower acceleration distribution of the 3# tower and 4# tower. For the both towers, the maximum acceleration happens on middle cross beam (T3), rather than the tower top node (T4). The reason is the tower top node is effectively restricted by stayed-cables. In the result, the vibration on tower top node always smaller than mid cross beam under the longitudinal excitation. In general, from the point of view of longitudinal seismic response, the tower can be equivalent to a cantilever column with limited restriction on top node. When subjected to the ScEl, the acceleration responses seem a little larger than ScTCU. It should be noted that the acceleration for the same node of the two towers seems a little different. This may come from the manufacturing differences between the two towers or bearings.  Figure 15a,b show the absolute displacements of tower subjected to different excitations. As the towers are fixed on the shake table, the recorded movement on node T1 is approximately equal to the input excitation. It is obvious that the displacement of node T2 is similar to the node T1, while the node T3 and T4 are quite different to the base node. The similar phenomenon can be found in displacement responses subjected to the ScTCU in Figure 15b. The displacement response subjected to the ScTCU is significant larger than ScEL.

Displacements Responses
Based on the response of the node T1, the relative displacement of tower key nodes can be calculated. Figure 16a,b shows the relative displacement response of tower subjected to different excitations. For the both NNF and PNF excitations, the relative displacements on the node T3 and node T4 are significant larger than the node T2. It can explain why the displacement of node T3 and node T4 are different from that of node T2 in the Figure 15.
For comparison, the maximum displacements and relative displacements of 3# tower are extracted and compared in Figure 17a,b. Both for displacement and relative displacement, the maximum values happen on the tower top node. However, the response values subjected to ScTCU are significant larger than ScEL. For the top node, the displacement and relative displacement subjected to ScTCU are 31.8 mm and 30.8 mm, while those are 1.6 mm 1.9 mm subjected to ScEL.
It shows the velocity pulse has great impact on displacement and relative displacement responses, while have little effect on the acceleration response.  Figure 15a,b show the absolute displacements of tower subjected to different excitations. As the towers are fixed on the shake table, the recorded movement on node T1 is approximately equal to the input excitation. It is obvious that the displacement of node T2 is similar to the node T1, while the node T3 and T4 are quite different to the base node. The similar phenomenon can be found in displacement responses subjected to the ScTCU in Figure 15b. The displacement response subjected to the ScTCU is significant larger than ScEL. Based on the response of the node T1, the relative displacement of tower key nodes can be calculated. Figure 16a,b shows the relative displacement response of tower subjected to different excitations. For the both NNF and PNF excitations, the relative displacements on the node T3 and node T4 are significant larger than the node T2. It can explain why the displacement of node T3 and node T4 are different from that of node T2 in the Figure 15. For comparison, the maximum displacements and relative displacements of 3# tower are extracted and compared in Figure 17a,b. Both for displacement and relative displacement, the maximum values happen on the tower top node. However, the response values subjected to ScTCU are significant larger than ScEL. For the top node, the displacement and relative displacement subjected to ScTCU are 31.8 mm and 30.8 mm, while those are 1.6 mm 1.9 mm subjected to ScEL.

Strains and Bending Moment
The strain of 3# tower bottom section on both sides subjected to ScEL excitation are shown in Figure 18a. The strain responses on different sides (Sec T3-1E and Sec T3-1W) are changing nearly oppositely due to the bending effect. The maximum strain for Sec T3-1E is 24.1 µƐ. Based on strain response on the section edge, we can calculate the section bending moment, shown in Figure 18b. It shows the maximum bending moments of 3# tower is approach to 32 N·mm. It shows the velocity pulse has great impact on displacement and relative displacement responses, while have little effect on the acceleration response.

Strains and Bending Moment
The strain of 3# tower bottom section on both sides subjected to ScEL excitation are shown in Figure 18a. The strain responses on different sides (Sec T3-1E and Sec T3-1W) are changing nearly oppositely due to the bending effect. The maximum strain for Sec T3-1E is 24.1 µ . Based on strain response on the section edge, we can calculate the section bending moment, shown in Figure 18b. It shows the maximum bending moments of 3# tower is approach to 32 N·mm. Based on the above process, the maximum bending moments on other critical sections are calculated and shown in Figure 19a,b. For the sections above the girder, such as Sec T3-3, Sec T3-4, Sec T3-5, the bending moment are very small when subjected to the ScEL motions. However, the moments increase obviously from 11 N·mm to 32.8 N·mm for the tower below the lower cross-beam. On the contrary, when subjected to the ScTCU, the moments of section below the lower cross-beam also are large. For example, the moment reaches to 85 N·mm for secT3-3 subjected to ScTCU. Figure  19b shows the bending moments of the 4# tower. The similar conclusion can be drawn in the figure.
Comparing the seismic response subjected to different NF motions, the bending motions subjected to the PNF (ScTCU) are significant larger than that of NNF (ScEL), about 2.98-4.50 times. This means the bending moments of tower are sensitive to the velocity pulse. Based on the above process, the maximum bending moments on other critical sections are calculated and shown in Figure 19a,b. For the sections above the girder, such as Sec T3-3, Sec T3-4, Sec T3-5, the bending moment are very small when subjected to the ScEL motions. However, the moments increase obviously from 11 N·mm to 32.8 N·mm for the tower below the lower cross-beam. On the contrary, when subjected to the ScTCU, the moments of section below the lower cross-beam also are large. For example, the moment reaches to 85 N·mm for secT3-3 subjected to ScTCU. Figure 19b shows the bending moments of the 4# tower. The similar conclusion can be drawn in the figure. As we can see, the bottom sections is the most critical section for all piers. Table 5 shows the maximum bending moments of piers bottom sections. The largest responses happen on piers on the edge, such as 0# and 7#. For the 0# pier, bending moment subjected to ScEL and ScTCU are 10.23 N·mm and 13.84 N·mm respectively.

Longitudinal Responses
When the bridge is excited only in longitudinal direction, the longitudinal and vertical vibration are significant. Figure 20a shows the longitudinal acceleration of girder subjected to the ScEL and ScTCU. It is obviously the maximum acceleration subjected to ScTCU reaches 0.89 m/s 2 , which is larger than 0.58 m/s 2 when subjected to ScEL. Figure 20b shows the Fourier amplitude of the longitudinal acceleration subjected to different type of NF motions. When subjected to the PNF (ScTCU), the Fourier amplitudes of the first and second order modes are significant larger than the NNF (ScEL). In the result, when subjected to ScTCU motion, the larger acceleration response of girder are recorded, shown in Figure 20a. Comparing the seismic response subjected to different NF motions, the bending motions subjected to the PNF (ScTCU) are significant larger than that of NNF (ScEL), about 2.98-4.50 times. This means the bending moments of tower are sensitive to the velocity pulse.
As we can see, the bottom sections is the most critical section for all piers. Table 5 shows the maximum bending moments of piers bottom sections. The largest responses happen on piers on the edge, such as 0# and 7#. For the 0# pier, bending moment subjected to ScEL and ScTCU are 10.23 N·mm and 13.84 N·mm respectively.

Longitudinal Responses
When the bridge is excited only in longitudinal direction, the longitudinal and vertical vibration are significant. Figure 20a shows the longitudinal acceleration of girder subjected to the ScEL and ScTCU. It is obviously the maximum acceleration subjected to ScTCU reaches 0.89 m/s 2 , which is larger than 0.58 m/s 2 when subjected to ScEL. Figure 20b shows the Fourier amplitude of the longitudinal acceleration subjected to different type of NF motions. When subjected to the PNF (ScTCU), the Fourier amplitudes of the first and second order modes are significant larger than the NNF (ScEL). In the result, when subjected to ScTCU motion, the larger acceleration response of girder are recorded, shown in Figure 20a.

Vertical Response
The girder vertical vibration in different locations, such as 1/4 span (G2), 1/2 span (G3) and 3/4 span (G4) subjected to different type NF motions are shown in Figures 21 and 22.  The maximum vertical acceleration of girder in 1/4 span, mid-span and 3/4 span are 2.88 m/s 2 , 0.88 m/s 2 , 2.70 m/s 2 separately. It is obviously that the vertical acceleration on the G2 and G4 are significant larger than node G3 on the mid-span when subjected to the ScEL. The amplitude spectrum of the accelerations time histories was analyzed by FFT method, shown in Figure 21b. The predominant frequency of the girder vertical vibration is about 13.9 Hz. which corresponds to the 4 th vibration mode, shown in Figure 8d. The mode is a typical antisymmetric mode. In the result, the vibrations of the G2 and G4 are larger than the mid-span.
However, when subjected to the ScTCU, the vertical accelerations on the G2 and G4 are slight larger than the G3. The acceleration amplitude spectrums are shown in Figure 22b. We can find the contributions of the several modes are at a similar level, such as the 2 nd , 3 rd , 4 th and 5 th vibration mode. In the result, the peak accelerations on the G2, G3 and G4 are close.
For easier comparison, the peak vertical accelerations of different critical nodes of girder are shown in Figure 23a. The acceleration peak envelope curves subjected to both ground motions present "inverted W shape". However, the maximum accelerations subjected to the ScEL are significant larger than the ScTCU.
The displacements response of girder were computed from the accelerations by double integration and baseline correction. The maximum displacements of girder are drawn in Figure 23b. Similarly, both vertical displacement envelops are inverted 'W' shape, rather than 'U' shape. When subjected to the PNF motion (ScTCU), the maximum displacements are larger than the NNF motion.
in Figure 23b. Similarly, both vertical displacement envelops are inverted 'W' shape, rather than 'U' shape. When subjected to the PNF motion (ScTCU), the maximum displacements are larger than the NNF motion.   Figure 24a shows the relative displacement between girder and tower. The maximum value subjected to ScTCU is 30 mm, which is far larger than ScEL. The amplitude spectrums of the relative displacement are shown in Figure 24b. It is dominated frequency is 0.79 Hz.

Comparison of the Seismic Response
The magnitude responses of towers and girder subjected to both excitations are listed in Table 6 and Table 7. It can be drawn from above tables that the accelerations amplitude of tower are very similar when subjected to both motions. The acceleration of girder subjected to ScTCU are smaller than ScEL. However, the displacement of both tower and girder subjected to ScTCU are great larger than ScEL.
The acceleration time histories and Fourier amplitudes are shown in Figure 12, Figure 13, Figure  21 and Figure 22. From the acceleration Fourier amplitudes, the accelerations of both tower and girder are contribution by several different modes. Therefore, the acceleration responses are mainly

Comparison of the Seismic Response
The magnitude responses of towers and girder subjected to both excitations are listed in Tables 6 and 7. It can be drawn from above tables that the accelerations amplitude of tower are very similar when subjected to both motions. The acceleration of girder subjected to ScTCU are smaller than ScEL. However, the displacement of both tower and girder subjected to ScTCU are great larger than ScEL.
The acceleration time histories and Fourier amplitudes are shown in Figures 12, 13, 21 and 22. From the acceleration Fourier amplitudes, the accelerations of both tower and girder are contribution by several different modes. Therefore, the acceleration responses are mainly determined by the several vibration modes of CSB and energy distribution of ground motions. From Figure 9b, the ScTCU has advantage in low frequency band, while the ScEL has more energy on the frequency band of [10 Hz,30 Hz]. In the result, the acceleration responses subjected to both excitation are similar.
On the other hand, the displacement responses subjected to the ScTCU are significant larger than ScEL. There are two mainly reasons: the first is the quite different PGD of both input motions. Although the PGA of both motions are the same, the PGV and PGD are very different, shown in Figure 9c,d. The PGD of ScEL and ScTCU are 1.3 mm and 22.8 mm, respectively. The other reason is the energy of ScTCU concentrates in the low frequency band, shown in Figure 9b. Meanwhile, the displacement response of CSB are mainly contributed by the long period component, shown in Figure 15a,b. In summary, the displacement response induced by the ScTCU are significant larger than the ScEL.

Non-Uniform Test Cases
In these tests, only the wave passage effect, which is caused by the different arrival times of the same ground motions, is considered. Therefore, for the non-uniform test cases, the excitations of two tables are the same, however, the excitation on the 2# table is delayed by dt, shown in Figure 10. The tested non-uniform cases are shown in Table 4.
Taking the non-uniform ScEL with dt = 0.1 s (Case3 in Table 4) for example, the recorded input longitudinal displacement of two shake tables are shown in Figure 25a. As the figure shows, the displacement of two tables almost the same, except a time delay of 0.1 s. It shows the multi-tables system have reproduced the wave passages excitation accurately with the expectant delay time.

Non-Uniform Test Cases
In these tests, only the wave passage effect, which is caused by the different arrival times of the same ground motions, is considered. Therefore, for the non-uniform test cases, the excitations of two tables are the same, however, the excitation on the 2# table is delayed by dt, shown in Figure 10. The tested non-uniform cases are shown in Table 4.
Taking the non-uniform ScEL with dt= 0.1 s (Case3 in Table 4) for example, the recorded input longitudinal displacement of two shake tables are shown in Figure 25a. As the figure shows, the displacement of two tables almost the same, except a time delay of 0.1 s. It shows the multi-tables system have reproduced the wave passages excitation accurately with the expectant delay time.
When subjected to the non-uniform ScEL with dt = 0.1 s, the displacements of tower top nodes are shown in Figure 25b. The test results shows the displacement of two towers seems consistent as effective restraint of stayed-cables.

Seismic Responses Subjected to the Non-Uniform Excitations
During the tests, six non-uniform cases were carried out, shown in Table 4. The delay times are 0.1, 0.2 and 0.4 s, respectively. Based on the measured accelerations time history, we can get the displacement time histories through direct integration and baseline correction. The relative displacement is the displacement to tower base, which can be calculated by displacement subtracting in time history. The tower relative displacements envelopes are shown in Figure 26a,b. When subjected to the uniform excitations, the relative displacements on both tower tope nodes are consistent. While the tower relative displacements are quite different when subjected to the time delayed excitations. For non-uniform cases with different delay time (dt), the responses also seems quite different. However, the relative displacement responses excited by different dt seems to have no obvious rules to follow.   When subjected to the non-uniform ScEL with dt = 0.1 s, the displacements of tower top nodes are shown in Figure 25b. The test results shows the displacement of two towers seems consistent as effective restraint of stayed-cables.

Seismic Responses Subjected to the Non-Uniform Excitations
During the tests, six non-uniform cases were carried out, shown in Table 4. The delay times are 0.1, 0.2 and 0.4 s, respectively. Based on the measured accelerations time history, we can get the displacement time histories through direct integration and baseline correction. The relative displacement is the displacement to tower base, which can be calculated by displacement subtracting in time history. The tower relative displacements envelopes are shown in Figure 26a,b. When subjected to the uniform excitations, the relative displacements on both tower tope nodes are consistent. While the tower relative displacements are quite different when subjected to the time delayed excitations. For non-uniform cases with different delay time (dt), the responses also seems quite different. However, the relative displacement responses excited by different dt seems to have no obvious rules to follow.   Figure 27a, when non-uniform excited by ScEL, the vertical deformation on the mid-span (G3) are larger than uniform excitation. The reason is the symmetrical modes, such as the 4 th , 6 th modes, are more seriously excited by the non-uniform excitations. Secondly, comparing the non-uniform cases with different dt, the deformation on the G4 is more sensitive than G2. It means wave passage effect has a greater impact on the nodes located farther away, such as G4, when the excitation is propagating from G1 to G5. Figure 27b shows the girder deformation when subjected to the PNF ground motions (ScTCU). Similar to the previous Figure, the deformation on the node G4 is significant various for different non-uniform cases. In order to explain this rule more clearly, Figure 28 shows the deformation response time history diagrams subjected to different non-uniform cases. For the uniform case, the maximum deformation on the node G4 is larg   Figure 27a, when non-uniform excited by ScEL, the vertical deformation on the mid-span (G3) are larger than uniform excitation. The reason is the symmetrical modes, such as the 4 th , 6 th modes, are more seriously excited by the non-uniform excitations. Secondly, comparing the non-uniform cases with different dt, the deformation on the G4 is more sensitive than G2. It means wave passage effect has a greater impact on the nodes located farther away, such as G4, when the excitation is propagating from G1 to G5.
Appl. Sci. 2020, 8, x FOR PEER REVIEW 27 of 28 er than the node G2. However, for non-uniform with dt = 0.4 s, the maximum deformation on node G4 is significant reduced. Further, the peaking time is also different to the uniform cases. In contrast, the deformation response of node G2 is less different for different non-uniform cases.  Figure 27b shows the girder deformation when subjected to the PNF ground motions (ScTCU). Similar to the previous Figure, the deformation on the node G4 is significant various for different non-uniform cases. In order to explain this rule more clearly, Figure 28 shows the deformation response time history diagrams subjected to different non-uniform cases. For the uniform case, the maximum deformation on the node G4 is larger than the node G2. However, for non-uniform with dt = 0.4 s, the maximum deformation on node G4 is significant reduced. Further, the peaking time is also different to the uniform cases. In contrast, the deformation response of node G2 is less different for different non-uniform cases.

Conclusions
To evaluate the seismic response of CSBs subjected to NF ground motions, a scaled CSB was designed and fabricated. Two NNF and PNF motions were selected as the input excitations. The shake table test of scaled CSB subjected to uniform and non-uniform excitations were carried out. The following conclusions can be made based on the test results: (1) The first six modes and the corresponding frequencies of the scaled CSB were identified using the SSI method. The fundamental mode shows as girder and tower longitudinal vibration with a frequency of 0.79 Hz. The 2nd mode shows as girder vertical antisymmetric vibration combing tower longitudinal bending with a frequency of 6.61 Hz. In the first six in-plane modes, the 2 nd , 4 th and 6 th modes are antisymmetric, while the 1 st , 3 rd and 5 th modes are symmetric. (2) The maximum displacement of the tower occurs on the tower top node, the maximum acceleration response of the tower occurs on the middle cross beam, and the maximum bending moment of the tower occurs on the bottom section (3) The deformation of the tower and girder subjected to uniform excitation is not always larger than that subjected to non-uniform excitation, and therefore the non-uniform case should be considered in the seismic design of CSBs.