Construction Effects on the Mechanical States of a Truss Structure

The Harbin railway station is located in Harbin, Heilongjiang Province, which is known as one of the largest transportation hubs in Northeast China. The roof of the elevated train station is constructed using a steel structure roof with dimensions of $162.15\times 72\times 13.25\mathrm{m}$. The construction of the steel structure roof is divided into two phases, and the completed second-phase structure has dimensions of $93.9\times 72\times 13.25\mathrm{m}$.

As shown in Fig. 1, the steel structure roof is composed of transverse principal trusses and transverse secondary trusses arranged along the longitudinal direction, which are connected by longitudinal trusses. The completed second-phase structure consists of 13 transverse arch trusses and 4 longitudinal vertical trusses. As shown in Fig. 2, the trusses are composed of top chords, bottom chords, and web members, which are all constructed with steel hollow pipes of different section dimensions. The section dimensions are listed in Table 1. The steel used in the truss structure is Q345B, and its mechanical properties are listed in Table 2. The entire structure is mounted on the concrete structure of the lower part with horizontal elastic supports and vertical rigid supports.

As shown in Fig. 3, the second-phase truss structure is divided into three parts, which are assembled and welded on the floor of the 9-m-high waiting hall of the station. Each part contains four, seven, and two transverse trusses. During the hoisting stage, the first and second parts are lifted from the floor of the waiting hall to the roof height of 22 m by fixed hydraulic jacks, as shown in Fig. 4. The third part of the truss is lifted by a crane truck. The three parts are successively elevated to the same height and mounted on the concrete structure and supported by welded steel pipes. The connections at the supports are shown in Fig. 5. Finally, the three parts are connected to each other with the longitudinal trusses.

During the unloading stage, the methods of unloading large trusses in practical projects are mainly divided into synchronous and asynchronous unloading methods. For a large-span steel structure with high integrity and symmetry, the synchronous unloading method of unloading the whole structure at the same time is usually chosen. For a large-span steel structure with clear regional structural division and a relatively independent structure or more supporting points before the completion of the whole structure, the partition synchronous unloading method is usually used to carry out synchronous unloading of each part of the structure separately. Asynchronous unloading is a construction method that dismantles and unloads the same structure at different unloading points in a certain sequence, which is seldom used in engineering (Pan 2015).

In the study presented in this paper, the synchronous unloading method is adopted for the first part of a truss structure, and the asynchronous unloading method is adopted for the second part. Because the first and second parts of truss structures are relatively similar, the finite-element analysis of synchronous unloading of the second part of the truss structure is carried out. And the results show that the stress of each member of the main and secondary truss is similar to that of the first part of the truss in synchronous unloading, and the strain variation trend is the same, as is the strain state in the final stress state. Therefore, this paper directly compares the first part of the truss structure, where synchronous unloading is used, with the second part of the truss structure, where asynchronous unloading is used.

The first part of the truss structure is connected to the hydraulic jacks by four groups of steel strands. The connection positions are located on the bottom chords of the two principal trusses. Each group has eight strands. After all the principal and secondary trusses are welded to the supports through connecting rods, the steel strands in each lifting position are cut to complete the process of fixing the trusses. The connections between the strands and the bottom chords are shown in Fig. 6.

The second part of the truss structure is connected to hydraulic jacks by six groups of steel strands, and each group has eight steel strands. After the truss structure is elevated to a predetermined height, the rods connected to the supports are welded to each of the principal trusses in a certain sequence, as shown in Fig. 7. The determination of the welding sequence should meet the following principles. First, ensure that the structure in the construction process of the overall deformation is small. Second, ensure that the internal forces of key components are always within the elastic range during the construction process so as to avoid any structural strength damage or instability caused by the destruction of local components. Finally, ensure that the internal force and displacement of the structure change slowly during construction. When the welding of the connecting rods at certain positions is completed, the steel stands are cut off. After all the principal trusses are fixed to the supports and the steel strands are cut, the connecting rods are welded to the secondary trusses, and the process of fixing the truss structure is complete.

In terms of environmental factors, the effect of the slight wind on the truss structure in Harbin during the construction process may be ignored. The construction processes of the first and second parts of the truss structure were performed on August 19, 2018 and August 27–28, 2018, respectively. The daytime temperature varied from 19°C to 28°C and 20°C to 26°C. Owing to the slight temperature difference during the construction process, the effects of temperature on the structure could be ignored. Therefore, the effects of the construction methods became the main factors that altered the internal force of the truss members.

For arch truss structures, axial forces are the main form of bearing and transmitting loads. For the first part of the truss structure, all the bottom chords of the principal trusses are compressed. The trusses deform in the transverse direction under gravity, and the steel strands deviate by small angles from a vertical position. Therefore, the axial pressures on the bottom chords of the principal trusses are generated by the steel strands. Since the effect of axial pressure on strain is stronger than that of the bending moment caused by upward shearing forces, the entire bottom chords are compressed. Under the constraints of the steel strands, the weight of the top chords is transferred to the bottom chords through the compressed web members. Because of the bending moments caused by the downward shearing force from the web members, the parts partially located on the bottom chords are obviously compressed, as shown in Fig. 9. The axial pressures at the ends of the bottom chords are stronger than those at midspan. The bending moments caused by the upward shearing forces from the steel strands are more obvious in the midspan of the truss. Thus, the compression degree on the upper surface of the bottom chords increases gradually from the middle of the bottom chords to the end. The position with the largest compressive strain appears in the lifting position. For the top chords of the principal trusses, the connections between the web members and the top chords in the midspan part are clearly in compression. The weights of the secondary trusses are transferred to the principal trusses through the longitudinal trusses. Since the longitudinal trusses are directly connected to the top chords of the principal trusses, the bending moments in the midspan of the top chords caused by the downward shearing force are relatively large. Consequently, for the midspan part of the top chords, the compressive strains on the upper surface are large. Owing to the small axial pressure of the top chords and the absence of external constraints, the compression degree of the members is gradually weakened from the middle to the end of the span.

For the secondary trusses of the first part of the truss, the weight is transferred to the principal trusses by four longitudinal trusses. Since the secondary trusses and the longitudinal trusses are not connected to the steel strands, their deformations are more obvious than those in the first part of the truss structure. Fig. 11 shows the vertical displacements of the secondary trusses under the effect of the self-weight (the unit is meters). Consequently, the bottom chords are tensioned in the midspan area, and the entire top chords are compressed.

Trusses 17 and 23 are on the same sides of the structure in the longitudinal direction as Trusses 13 and 16. Therefore, the strain states of the top and bottom chords of Trusses 17 and 23 are the same as those of Truss 16. As shown in Fig. 3, owing to the slight difference in the distances between the adjacent principal trusses of the second part, the strains of Trusses 17 and 23 exhibit a slight asymmetry. Truss 20 is further loaded owing to the middle position of the structure. The FEM analysis shows that the steel strands connecting Truss 20 are subjected to the largest tension. Owing to the stronger axial pressure caused by the strands, the compressive strains of the bottom chords are larger than those of the other principal trusses. The longitudinal trusses transfer more load to Truss 20, and the bending moments caused by the downward shearing forces of the top chords are obvious. Consequently, the degree of compression of the top chords of Truss 20 is more obvious than that of the other principal trusses, as shown in Fig. 10.

For the secondary trusses of the second part, the strain states are the same as those of Truss 15. Owing to the construction aisles on the four secondary trusses, the weights of the secondary trusses increase; thus, the compression strains on the upper surface of the bottom and top chords are larger than those of Truss 15. The vertical displacements of the secondary trusses are shown in Fig. 12 (unit: meteres).

In this subsection, a finite-element model simulation and time history analysis are carried out for the truss structure during the unloading process. The mechanical behavior of the structure in the construction process belongs to the category of slow time-varying structural mechanics. The time history analysis of the structure can be selected based on the slow change of material properties, geometric shape, and boundary conditions of the structure with time. The changing structure can be divided into a series of static structures according to the time node, and the most unfavorable state of the structure in the construction process can be analyzed, or the relationship between the structure itself and the load in the time-varying process of the structure can also be considered and the strength of the structure in the construction process analyzed. In the construction stage of a long-span steel structure, the internal force and displacement of the structure in the previous construction stage will inevitably affect the next stage. It is necessary to superimpose the internal force and displacement of each stage to reflect the final stress state and displacement of the structure accurately.The structural state of any stage in the construction process can also be obtained considering the mechanical state of each construction stage (Hu 2016).

Based on the preceding discussion, influential factors, such as the wind and ambient temperature, are assumed to be invariable owing to their insignificant effects. Since the eight strands in each group are cut off one after another, the weight of the truss structure is gradually transferred to the supports. The entire construction process is analyzed by the numerical simulation software.

Since boundary conditions change during the construction process, the internal structural forces are redistributed and can be reflected by the strains. Fig. 14 shows the strain variations for typical elements of members with a time step. It can be seen from the figure that the force of each member of the truss structure is stabilized after a redistribution of internal forces. In the 0.25th time step, the Link 180 unit exits work, and the strain of each selected unit tends to stabilize. The positions of the elements are shown in Fig. 13. Since the main function of the web members is to transmit the forces, the strain variations of the web members are not discussed.

In the time step, the load of the structure is transferred from the steel strands to the supports. With the continuous shearing of the steel strands, the web members gradually transfer the weight of the bottom chords to the top chords and finally to the supports. Owing to the change in the boundary conditions, the axial pressures of the bottom chords decrease. The direction of the bending moments caused by the shearing forces of the web members reverses. For the bottom chords, owing to the more obvious effects of the bending moments caused by the shearing forces, the degree of compression is weakened. Noticeably, the trends of the strain variations are similar for different positions on the bottom chords. For the top chords, the two ends are constrained horizontally and longitudinally. According to Fig. 14, the degree of compression for the top chords increases with increasing axial pressure and bending moment caused by supports. Moreover, owing to the greater axial pressures caused by the supports at the end of the top chords, the degree of compression increases from the midspan of the top chords to the ends.

The supports of the secondary trusses have the same form as those of the principal trusses. After the boundary conditions of the principal and secondary trusses change, the top chords bear their main weight. Therefore, the degree of compression on the top chords of the principal and secondary trusses increases. However, before the hydraulic jacks are unloaded, the secondary trusses are supported by four longitudinal trusses, and the supporting positions are dispersed. Thus, compared with the principal trusses, the strain variations of the top chords of the secondary trusses are smaller than those of the principal trusses. For the bottom chords, the supports enhance the transverse stiffness of the secondary trusses and inhibit the transverse deformation of the bottom chords. Therefore, the degree of compression of the bottom chords of the secondary trusses increases.

The strain variations of the rods that connect the trusses to the supports are shown in Fig. 14(c). Since the connecting rods bear the total weight of the structure after the hydraulic jacks are unloaded, the strains clearly change. According to the preceding discussions, the rods connecting the top chords become part of the top chords after being loaded; thus, the rods are obviously compressed. The rods connecting the bottom chords transfer part of the weight of the bottom chords to the supports; thus, the connecting rods are obviously in tension.

Based on the foregoing analysis, it can be concluded that strain variations of structural members are related to the construction methods and structural forms. The strains can directly or indirectly reflect changes in the structural internal forces. During the static construction process of the first part, the strains of the truss members vary uniformly and symmetrically. Since the stresses of the truss reflected by the strains are far less than the allowable stress of the structural steel, the structure remains in a stable state during the construction process.

For the second part of the truss structure, the strain variations of the members are complex owing to the asynchronous unloading method and the longitudinal asymmetry of the structure. Fig. 16 shows the strain variations for typical elements with time steps. During the six time steps, hydraulic jacks are unloaded in sequence. The positions of the elements are shown in Fig. 15. As shown in Fig. 16, the loaded supports have substantial effects on the trusses connected to them. Moreover, there are significant strain variations of the members near the unloading position. In the first and fourth time steps, the hydraulic jacks on both sides of Truss 20 are unloaded successively. For the elements on the bottom chords of Truss 20, Positions 20-1 and 20-5 exhibit maximum strain variations in the first and fourth time steps, respectively. The strain variation of Position 20-1 (82.403 με) in the first time step is lower than that of Position 20-5 (85.024 με) in the fourth time step. This is because the constraints of the structure in the first time step are less than those in the fourth time step.

For the principal trusses of the second part, the strain change tendencies of the bottom chords in the midspan are different from those of the nonmidspan positions and the bottom chords of the principal trusses of the first part. Since the secondary trusses of the second part are not connected to the supports during the unloading process, the weight of the second part is supported by the longitudinal trusses. Thus, the loads on the principal trusses increase. Because the two longitudinal trusses located in the middle of the transverse direction transfer most of the loads, there is a slight compression phenomenon in the midspan of the bottom chords. The tendencies of the strain variation of the top chords of the second part are the same as those of the top chords of the first part. It is worth mentioning that because Truss 20 is located in the middle of the second part and bears more load, the top chords of Truss 20 show the most significant strain variations compared to those of other trusses. In addition, since Trusses 17 and 23 are not completely symmetrical in the longitudinal direction, there are slight differences between their strain variations.

With the change in the boundary conditions, the internal forces of the principal truss members change substantially. Since the secondary trusses are only supported by the principal trusses through the longitudinal trusses and are not connected to the supports during the construction process, the strain of the secondary trusses varies slightly in value. Therefore, the secondary trusses are not analyzed in detail. Compared with Truss 15, the strain variations of all the members in each time step are relatively small, and there are no obvious differences, as shown in Fig. 16(b).

For the connecting rods, the trends of the strain variation are the same as those of the first part, as shown in Fig. 16(e). Since the second part has a larger weight and the secondary trusses are not supported during the construction process, the connecting rods are subjected to larger loads than those of the trusses. Consequently, the strain values of the connecting rods change more than those of the first part.

Analysis of the strain data lead one to conclude that the strains of different members have different variation degrees during the unloading process. When the hydraulic jacks on both sides of a truss are unloaded, the strain variations of the members are more obvious, and the tendencies of the variations are different. For Truss 23, the hydraulic jacks on both sides are unloaded in the third and sixth time steps, and the strains of the members change significantly during the two time steps.

For the second part of the truss structure, owing to the frequent changes of the structural constraints at different positions, the redistributions of the internal forces occur repeatedly in the structural members. The structure stays in an asymmetrical state, and the strains of the members exhibit complicated changes. Moreover, compared with the first part, the maximum strains of some members appear during the construction process rather than at the beginning or the end of the state.

During the unloading process, in addition to the nonobvious environmental factors, the internal forces of the truss structure are mainly affected by the construction factors. To monitor the real-time state of trusses to ensure that the structure is in a stable state, the axial strains on typical top chords and bottom chords are monitored. The layout of the monitoring positions is shown in Fig. 17. The selected typical sensors are located at the same positions as the partial elements chosen in the FEM results.

As shown in Fig. 18, optical fiber Bragg grating (OFBG) surface strain sensors were installed to collect the axial strains of the typical chords. The properties of the OFBG strain sensors are listed in Table 3. The sensors are installed during the process of the assembly and welding of the truss structure. The state of the entire structure is evaluated by collecting and analyzing the values of the strain variation of the members during each construction stage.

The monitoring results of the two unloading construction processes on August 19, 2018, are displayed in Fig. 19. For the four monitoring positions of Truss 16, before the unloading construction at 13:20, the strain basically remains in a stable state. The fluctuation of the strain is caused by construction factors, such as the welding of members on site. When the unloading construction begins, the four groups of strands are cut synchronously, and the strands of each group are cut one after another. The internal force of the first part changes abruptly, and the strains shown in Fig. 19 show obvious step differences. For Positions 16-1 to 16-4, the degree of compression at each location is weakened. Among the four monitoring positions, the strains of Positions 16-1 and 16-3 show the most and least significant changes. The strain variations of transversely symmetrical Positions 16-2 and 16-4 are different. This might be due to actual structural differences. After the unloading construction is complete, structural strains tend to stabilize. Since the surface strains of the members are greatly affected by construction and personnel factors, the monitoring results clearly fluctuate. The strain of Position 16-3 shows the most significant fluctuation, while that of Position 16-1 shows the least fluctuation. This indicates that the members farther away from the supports are more affected by construction factors than those close to the supports.

The overall variation trends of the strains for the bottom chords of Truss 16 are the same as the results of the FEM analysis. The monitored strain change is less than the simulated strain change. For a truss structure in the stable state before and after unloading construction, the measured strain change value of each sensor and the finite-element simulated strain change value are shown in Table 4.

It can be seen from Table 4 that the overall monitoring strain change is smaller than the numerical simulation strain change result, and the causes of this result are analyzed. In addition to the impact of site construction factors and actual truss structure differences on the monitoring data, the limitations of finite-element simulation also have a certain impact on the simulation results. In actual engineering, when a truss is hovering, it is only constrained by the vertical upward pulling force of the steel strand, and there is no restriction in the horizontal direction. The truss and the steel strand system are called mechanisms in engineering mechanics. In the finite-element simulation, it is impossible to make the structure reach a statically indeterminate state by applying only vertical constraints to the lifting points of the model, so the analysis can only be performed by applying corresponding constraints to the truss in the horizontal direction. Therefore, compared with the actual structure, the strain value in the initial state in the numerical simulation increases with the increase of the model’s constraints, so the strain change in the unloading process in the simulation result is slightly larger than the monitoring result. However, considering that the force distribution law of the truss are the same as the simulation analysis result, the strain change amplitude and trend of each monitoring position during the unloading process are consistent with the simulation conclusions, and after the truss is stabilized, the strain approaching the phenomenon of each monitored member is similar to the simulation result. Therefore, the finite-element simulation of simultaneous unloading construction is reliable to a certain extent. During the construction process, the strain variations of truss members are explicit, and the strain changes in the same direction. During unloading construction, the strains of the truss members have significant variations. Before and after unloading construction, environmental factors have little effect. The small fluctuations in strain are mainly caused by construction factors. Before unloading, construction personnel on the truss check the weld, spray steel anticorrosion paint on it, and repair the specific weld, which will cause small strain fluctuation. After unloading, the construction personnel cut the residual steel strand at the lifting position of the end of the bottom chord and the steel clamps welded there, which will also cause small strain fluctuation. Therefore, the collected data are reliable. Generally, the first part of the truss structure is in a stable state during the monitoring process.

The monitoring results for the two unloading construction processes on August 27–28, 2018, are displayed in Fig. 20. According to the figure, when the hydraulic jacks are unloaded, the welding construction of the connecting rods and the unloading construction at each support position are carried out continuously without a construction interval. Moreover, the construction processes at different support positions are independent. Thus, the monitored strain fluctuates during the total monitoring process. For Positions 17-1 and 17-2, when the closest hydraulic jack of Truss 17 is unloaded, the strain exhibits a large step mutation. When the hydraulic jack on the other side of Truss 17 is unloaded, the strain exhibits a small step mutation. Nevertheless, when the hydraulic jacks of other trusses are unloaded, the strain is basically unchanged. Since Position 17-3 is at midspan, the unloading of the hydraulic jacks on both sides of Truss 17 has similar effects on the strains, which are not significant. Similarly, the strain fluctuations of the members farther from the supports are more obvious than those of the first part.

Table 5 shows a comparison of the measured strain difference of each monitoring position of Truss 17 at the initial and final steady states of the overall unloading construction and the final strain difference of the numerical simulation results.

Table 5 shows that the overall monitored strain difference is less than the simulated difference, for the same reasons as given previously.

As in the preceding discussion, according to Fig. 21, for the bottom and top chords of Truss 20, the strain differences are obvious when the hydraulic jacks on both sides of Truss 20 are unloaded. Since Positions 20-1 and 20-2 are relatively close, the tendencies and values of the strain variation of the two positions are similar when the jacks are unloaded. It is worth mentioning that the strain variation of Position 20-1 is larger because Position 20-1 is closer to the support. For Position 20-5, which is located in the transversely symmetric position of 20-1, the value of the strain variation is larger when the jack on its side is unloaded than when it is loaded, as discussed earlier. Like Position 17-3, Position 20-3 exhibits obvious strain variations only when the hydraulic jacks on both sides are unloaded and the compression degree increases. For Positions 20-6 and 20-7, Position 20-6 show the maximum value of the strain variation of the seven monitoring positions when the jacks of Truss 20 are unloaded. When the boundary conditions change, the top chords near the support positions are subjected to substantial pressure, and the internal force changes significantly. Compared with Truss 17, the strain variation of Truss 20 is greater because it is located in the middle of the structure.

As shown in Table 6, the measured strain difference for the sensors of Truss 20 before and after unloading construction is always smaller than the final strain difference in the numerical simulation, except for the limitations imposed by the constraints. Compared with the material and construction defects of the finite-element model, the actual structure is also related to the wire stiffness simulation of the steel strand in the simulation process, so the monitoring results cannot fully meet the results of the finite-element analysis. However, during the unloading process, the strain change trend of each monitoring position during the unloading process is consistent with the simulation results, the main force-bearing members and force areas are the same as the simulation analysis, and the force distribution of each member before and after unloading basically conforms to the simulation force analysis results. Therefore, the finite-element simulation can be used to obtain relatively accurate strain trend and force characteristics of the truss structure under synchronous and nonsynchronous unloading and then compare the effects of the two unloading methods on the mechanical state of the truss structure.