Quasi-static Cyclic Loading Tests Research Articles

Enhanced seismic performance: A novel cable brace with bending energy dissipation for semi-rigid steel frames

Ordinary braces upon experiencing compressive buckling, reach a fully plastic state, rendering them ineffective against further seismic action. Moreover, their post-earthquake repair and reinforcement pose significant challenges. Addressing these issues, this research introduces an innovative lateral force-resisting element: the bending energy dissipation-cable brace. This novel design utilizes steel cables in a unique tension-only arrangement, effectively dissipating seismic energy by inducing bending in a steel plate. A semi-rigid steel frame was constructed, incorporating two variations of the cable brace, differentiated by the thickness of their energy-dissipating frames. These were subjected to quasi-static cyclic loading tests to evaluate their hysteretic behavior, deformation pattern, load-bearing capacity decay, and energy dissipation capacity. The experimental results reveal the superior seismic performance of the bending energy dissipation-cable brace, evidenced by a 22 % enhancement in energy dissipation and a 38 % increase in stiffness when the thickness of the energy-dissipating frame is doubled. These results offer a promising solution to the current limitations in energy dissipation and difficulty of application of the combined brace of steel cable and bending yielding energy dissipation devices.

Experimental study on seismic performance of replaceable shear links with low-yield-point steel

Based on the design concept of controllable seismic damage during earthquakes and rapid functional recovery after earthquakes, a replaceable shear link with low-yield-point steel was proposed. Quasi-static cyclic loading tests and numerical analysis were conducted on six specimens. The failure mode, seismic performance, energy dissipation behavior, and shear distribution of each specimen were carefully considered to investigate the effects of web steel, web stiffening configuration and stiffener-plate stiffness ratio. The results showed that the stiffened specimens showed full-sectional shear yielding behavior, while the non-stiffened specimens exhibited coupling behavior of web yielding and buckling. Specimens with reasonable design parameters had excellent ductility and energy dissipation capacity, with the plastic shear angle exceeding 0.157 rad and the maximum equivalent viscous damping coefficients greater than 0.51 (80% of the theoretical maximum value). Owing to the cyclic strengthening of the low-yield-point steel web and the contributions of stiffeners and flanges, the specimens showed obvious overstrength behavior, with the overstrength factor ranging from 1.99 to 2.39. The cross-stiffening configuration was conducive to enhancing the seismic performance of shear links. Smaller web width-to-thickness ratios were recommended to match with smaller stiffener-plate stiffness ratios. Extended cross stiffeners and diagonal stiffeners resulted in earlier cracking of the web welds, which adversely affected the ductility of the specimens.

Study on seismic failure mechanism and damage model of unconstrained adobe block walls

Through the quasi-static cyclic in-plane loading test of three kinds of unconstrained adobe block walls, namely plain adobe wall, modified mud adobe wall and modified adobe wall, the failure mode and seismic performance of each specimen were clarified. Using residual deformation and cumulative energy dissipation as failure parameters, a two-parameter seismic damage model of unconstrained adobe block walls was established. and a calculation method for the adjustment coefficients of energy consumption items was provided. The results showed that the failure mode of the typical unconstrained adobe block wall under earthquake action was not affected by the modification of adobe materials, and the final failure mode was shear failure along the mud crack and the inclined crack extending through the block. Furthermore, the proposed seismic damage model can well reflect the evolution law of earthquake damage of adobe block walls, and the recommended damage index boundary values for five performance levels were given, providing a reference for performance-based seismic design and damage assessment of adobe block walls.

Quasi-static cyclic tests of FRP-confined steel-reinforced HPFRCC circular columns

This study presents a novel composite component comprising of steel-reinforced high-performance fiber reinforced cementitious composites (HPFRCC) circular columns confined by fiber-reinforced polymer (FRP), with the goal of improving the mechanical behavior of conventional reinforced concrete (RC) columns. Quasi-static cyclic loading tests were conducted to investigate various aspects of the column specimens, including failure phenomena, load-displacement response, sectional compression-bending performance, plastic hinge length, and lateral strain distributions in the FRP jacket, etc. A self-designed frictional force measurement device was employed to accurately measure the actual force borne by the specimen. The experiment results revealed that FRP confinement effectively improved the load-bearing capacity and deformation capacity of the specimens and delayed the deterioration of the sectional compression-bending performance. The superior tensile ductility of HPFRCC led to increased yielding displacement and peak load compared to FRP-confined concrete specimen, although this enhancement was limited. Furthermore, the peak load of the FRP-confined HPFRCC specimen increased with axial load, while the sectional compression-bending performance after the peak load remained relatively stable until approaching the collapse prevention (CP) limit state.

Local scour effects on seismic behavior of pile-group foundations in cohesionless soils: Insights from quasi-static tests

Local scour has been reported as a common phenomenon for pile-group foundations in marine, coastal, and riverine sites, while its effects on the seismic behavior of pile-group foundations are yet to be well documented. This paper reported a pair of quasi-static cyclic loading tests on 2 × 3 scoured pile-group foundation specimens, one in global scour and the other in local scour, to understand the influence of local scour on the seismic behavior, particularly in terms of soil-pile interaction features and failure mechanisms. Test results indicate a flexural failure mode for both specimens. Local scour does not change the order of limit states but postpones the occurrence of concrete cover cracking and rebar yielding due to the reduced lateral stiffness of the locally scoured piles. Moreover, local scour rarely changes the aboveground damage regions at the top of outer piles (one time the side length of squared pile section, D), but significantly aggravates and deepens the underground damage regions at outer piles (from 4 ∼ 5D for global scour to 3.7 ∼ 6D for local scour). Besides, local scour reduces the displacement ductility factor from 2.50 to 1.25 for the Easy-to-Repair limit state, resulting in adverse impacts on pile-group foundations in general.

Seismic performance assessment of RC bridge piers with variable hysteresis performance dampers

A novel variable hysteresis performance damper (VHD)—multi-stage slip friction damper is developed and applied to implement multi-level seismic resistance of structures. Different from the conventional slip friction dampers, which feature only a single type of slip friction surface, this innovative damper incorporates two types: a flat slip surface and a wedge slip surface. The quasi-static cyclic loading tests of the VHD were carried out to investigate its variable hysteresis performance. The test results revealed that the developed damper presented excellent adaptive performance, and its hysteresis behavior changed from a complete rectangle with efficient energy dissipation to a flag-shaped curve with exceptional self-centering capacity as deformation increases. Subsequently, the developed VHD with unique adaptive performance was applied in RC bridge piers (BP) to improve the seismic performance. Nonlinear time history and fragility analysis methods were employed to assess the seismic performance of the RC bridge piers with VHDs (BP-VHD) in deterministic and probabilistic manners, considering maximum and residual deformations as performance indicators. For comparison, seismic responses of RC bridge piers with traditional buckling restrained braces (BRBs) and self-centering energy dissipation braces (SCEBs) were also presented. The analysis and comparison results demonstrate that the developed VHD is as effective as BRB in reducing maximum deformation at small PGAs, meanwhile, it can effectively reduce the residual deformation of the structure to allowable values when the PGA is large. Furthermore, the failure probability of BP-VHDs is lower compared to piers with BRBs and SCEBs, particularly concerning maximum and residual drift ratios as performance indicators. The application of the VHD can effectively achieve the goal of multi-level seismic resistance for RC bridge piers.

Experimental and Analytical Investigation of Self-Centering Precast Composite Walls with Sloped Plane Friction Dampers.

To reduce the damage to reinforced concrete shear walls in earthquakes and repair costs, a self-centering wall with sloped plane friction dampers (SPFDs) is proposed. In addition to the SPFDs, the proposed wall includes a precast composite wall, steel wall toes, and post-tensioned (PT) tendons. The steel wall toes embedded in the base of the precast wall were used to improve its strength, and the SPFDs installed in the steel toes were used to increase its energy dissipation capacity. To investigate the effect of the initial PT force and prestressing clamping force of the friction bolt on the seismic performance of the wall, quasistatic cyclic loading tests were carried out on three precast wall specimens. The damage to the self-centering walls was slight, the residual drift was small, and the energy dissipation met the specification requirements. The wall with the greater initial PT force showed higher self-centering and bearing capacity, and the wall with higher prestressing clamping forces showed greater energy dissipation capacity. Additionally, a calculation method for the bearing capacity of the precast wall, which was verified by comparison with the test results, is suggested.

Shear performance of four-corner connected shear wall considering plate-frame connection ratio

The four-corner connection is an innovative way to connect the wall plate and frame of the steel plate shear wall (SPSW). Differing from the traditional four-side connected SPSW, this method mitigates the dependence of the wall plate on boundary elements. Through quasi-static cyclic loading tests, a comparison is made between a four-side connected SPSW with a plate-frame connection ratio of 100% and a four-corner connected SPSW with a plate-frame connection ratio of 65%. Subsequently, using finite element (FE) models validated by experiments, the impact of the connection ratio and the flexural stiffness of vertical boundary elements (VBEs) on structural mechanics is explored. Formulas for calculating the shear bearing capacity of the four-corner connected SPSW and the minimum flexural stiffness of VBEs considering the connection ratio are proposed and validated by FE results. The test results indicate that, when the connection ratio decreases to 65%, the ultimate bearing capacity, yield bearing capacity, initial stiffness and cumulative energy dissipation decrease by 32.7%, 28.8%, 27.9% and 35.3%, respectively. Additionally, The FE results demonstrate that decreasing the connection ratio effectively mitigates adverse effects on internal forces and deflection of VBEs.

Seismic behaviour of self-centring hybrid steel frames equipped with SMA plates under mainshock–aftershock sequences

This paper focuses on the mechanical behaviour, seismic application in steel frame connections and steel structure of shape memory alloy (SMA) plates. This study commenced by examining the hysteretic response of SMA plates subjected to cyclic tension tests, considering two different loading paths. Subsequently, a self-centring steel frame connection equipped with SMA plates and washers (SC-PW) was examined via quasi-static cyclic loading tests, and comparatively satisfactory self-centring behaviour was observed. However, the degradation of the initial stiffness of the SC-PW due to an initial imperfection was observed. An improvement strategy was proposed to overcome the degradation of the hysteretic behaviour (e.g., initial stiffness) of the SC-PW. Disc springs with a larger stiffness and preloads were introduced to overcome the degradation of the initial stiffness of the SC-PW, and the validation was confirmed via detailed finite element (FE) analyses. To improve the computation efficiency, a simplified FE model was developed to reproduce the hysteretic responses of the connection. Based on the simplified FE model, a six-storey prototype structure, i.e., a self-centring hybrid steel frame (SCHSF), equipped with the improved connection was developed, and the structural dynamic responses were investigated via nonlinear response history analyses, where mainshock–aftershock sequences were considered. The influence of the SMA material properties on the seismic behaviour of the prototype structure was investigated.

Ground shock attenuation performances of wire-rope-based meta-isolators

In this research, two types of novel meta-isolators were designed based on traditional wire-rope isolators and made by embedding mass-spring resonators into the wire-rope isolator. Measurement methods to reveal attenuation abilities of these meta-isolators were suggested through quasi-static cyclic loading tests, shaking table tests, and in-field explosion experiments. In the quasi-static tests, meta-isolators have greater hysteresis area under the same excitation displacement, which represents much greater energy consumption. Using shaking table tests and measurement, the vibration attenuation ability of the meta-isolators is improved in the designed resonant frequency, and the response amplitudes are significantly reduced compared with the conventional wire-rope isolators. Blast-induced ground shock experiments reveal that the meta-isolators indeed have an advantage over the conventional isolators in the aspect of shock resistance and the attenuation efficiency exceeds 98 %, providing a new idea and reference for protective engineering.

Research on bond behavior of CFRP-concrete interface under quasi-static cyclic loading

In order to investigate the bond behavior of CFRP-concrete interface under quasi-static cyclic loading, static and quasi-static interface shear tests were conducted on three different adhesive layer thicknesses and two concrete strength grades. From these results, it can be seen that the load-slip envelope curves of the quasi-static cyclic loading specimen is similar to the quasi-static monotonic loading curves. As the adhesive thickness increases, the interface bearing capacity increases, the maximum strain of CFRP plate increases, and the effective bond length slightly increases. The interface failure mode is related to concrete strength. The failure mode of C30 concrete bonded with CFRP plate is cohesive failure of concrete surface layer, while the failure mode of C50 interface specimen is adhesive failure between CFRP and adhesive layer interface. As the thickness of the adhesive layer and the strength of the concrete increase, the interfacial bond strength and maximum strain of CFRP plate increase. It can be seen that the bond-slip envelope curves of the quasi-static cyclic loading specimen coincide well with the curves of the quasi-static monotonic loading specimen. As the magnitude of the cyclic loading increases, the unloading/reloading stiffness degradation, residual slip at zero load increases, and the dissipated energy increases. The fitting resulted in a degradation model of interfacial stiffness during quasi-static cyclic loading.

Hysteretic behavior and resilience analysis of a new self-centering buckling restrained braces

The self-centering buckling restrained braces (SC-BRBs) are capable of dissipating energy through BRBs elements during seismic events and restoring to their initial positions after the earthquake, thus reducing residual deformations in structures. The traditional design of the SC-BRBs has a complex structure with dual/three steel load transfer tubes and prestressed tendons anchored by steel end plates as a prestressing system. The complexity of these structures and the possibility of errors in machining dimensions and interactions between components can result in uncertainties of the mechanical behavior of the traditional SC-BRBs. As a consequence, a new design has been developed that uses the brace component as the inner load transfer tube for improved stability and load transfer capabilities in this paper. The structural features and mechanics of the new SC-BRB are first described. Then, to examine the performance of new SC-BRB, a quasi-static cyclic loading test was conducted on one scaled model specimen. The results showed that the new SC-BRB exhibited a consistent flag-shaped hysteretic response, with maximum residual strain of 0.15% within the target design drift of 2%. Nonlinear finite element analyses using ABAQUS were conducted to examine the influence of initial prestress magnitude and properties of prestressing tendon materials on the performance of the new SC-BRBs. The findings indicate that pretension is crucial for full self-centering capabilities of the new SC-BRB. When pretension exceeds the yield bearing capacity of the BRB core, it results in full self-centering and eliminates residual deformations. Additionally, the elastic elongation of the prestressing tendon material determines the deformation capacity of the new SC-BRB, while the elastic modulus of the material affects its post-yield stiffness.

Multiscale finite element analysis of earthquake-induced damage on underground RC culverts: The role of reinforcing bar corrosion

This study conducted finite element (FE) analysis to investigate the effect of corrosion in the sidewall on the damage to underground reinforced concrete (RC) culverts under an earthquake. The rationality of the numerical model was validated through the analysis of quasi-static cyclic loading tests of corroded RC culverts. Based on the validated FE model, a nonlinear dynamic analysis of an underground RC culvert subjected to an earthquake was performed. Further, the global and local responses that were changed not only by the corrosion of the sidewall reinforcement, but also by shear reinforcement in the sidewall and magnitude of the earthquake were discussed comprehensively. The analysis results show that the global deformation of the underground RC culvert increases with a higher degree of corrosion of the sidewall reinforcement and that severe local shear crack damage can be concentrated on the concrete web when corrosion cracks exist. In addition, extremely serious damage was induced in the RC culvert when corrosion occurred in the sidewall without proper seismic provisions. Therefore, steel corrosion in an aging underground RC culvert with insufficient shear reinforcement should be closely monitored to prevent its collapse in the event of earthquakes.

Experimental and analytical research on seismic performance of ECC-filled high-strength double skin steel tubular columns with out-of-code D/t ratios

Against the offshore construction requirement on light weight and high performance, using high-strength (HS) steel in concrete-filled double skin steel tubular (CFDST) members usually results in out-of-code diameter-to-thickness (D/t) ratios and performance uncertainty. A quasi-static cyclic loading test was therefore conducted to investigate the seismic performance of circular-in-circular ECC-filled high-strength double skin steel tubular (EFHDST) columns with out-of-code D/t ratios. Typical failure mode, hysteretic curves, bearing capacity and ductility were analyzed. Subsequently, the finite element (FE) model incorporating material damage effect was established and verified to conduct further parametric study. Influence of geometric parameters (e.g., wall thickness and hollow ratio), material strength and axial compression level was discussed in detail. Finally, a simplified restoring force model was developed to predict the seismic behavior of EFHDST columns. The result indicates that: the EFHDST columns fail by the ECC crushing, steel fracture and local buckling of double-skin tubes; the steel yield strength and thickness of outer tube, axial compression level and hollow ratio obviously affect the hysteretic performance (e.g., the bearing capacity and ductility) through the test and FE analysis, e.g., increasing hollow ratio from 0.54 to 0.82 the bearing capacity and ductility coefficient of test respectively decrease by 11.20% and 26.61%; the dimensionless skeleton curve, unloading stiffness degradation and hysteretic rule are proposed to form the restoring force model, where a strength model considering effect of ECC tension strength is included, and the reasonable agreement is achieved by the comparison results. The displayed research on EFHDST columns can provide significant references to its engineering applications.

Seismic performance of precast concrete walls with grouted sleeve connections using large-diameter bars

This paper proposes an innovative assembly technique using large-diameter bars anchored in several single-row, widely spaced grouted sleeves at the keyway-type horizontal joint to realize an indirect vertical connection between adjacent precast concrete (PC) walls, which has the advantages of high efficiency and ease of construction. To examine the effect of vertical connection strength (rebars' diameter at horizontal joints) on the seismic performance of PC shear walls, quasi-static cyclic loading tests on five full-size wall specimens, including one cast-in-place specimen and four PC specimens with grouted sleeve connections, are carried out. Seismic performance indicators in terms of failure modes, hysteresis characteristics, energy dissipation, ductility, and stiffness degradation of PC walls are investigated and compared with those of the cast-in-situ wall. Meanwhile, the method for predicting the bearing capacity of PC walls with large-diameter rebars is developed. The results show that the failure modes of cast-in-situ and precast walls are controlled by bending instead of shear, but there is an obvious difference in the crack propagation between the two types of walls. Carrying capacity, ductility factor, stiffness, and energy dissipation of PC walls are significantly enhanced by increasing the connection strength, by 44.1%, 23.9%, 72.1%, and 24.0%, respectively, when the connection strength reaches around 90%. Particularly, the PC wall's seismic performance is comparable to that of the cast-in-situ wall when the connection strength is 90%. The calculated results are well-matched with the experimental results, the proposed calculation method reliably predicts the bearing capacity of PC walls with large-diameter rebars. The assembly technique can be safely applied to multi-story PC wall panel structures in seismic zones.

Seismic fragility functions for RC As-built and eccentric steel brace frames

Quasi-static cyclic loading tests were performed on single-story reduced-scale reinforced concrete as-built (un-retrofitted) and eccentrically steel braced (retrofitted) frames. The frames damage mechanism, force–displacement hysteretic response and capacity backbone envelopes were studied and a damage scale was developed. A simplified numerical modeling technique was proposed in the finite element-based package SeismoStruct and the model was evaluated, calibrated and validated with the test data. The proposed modeling technique was employed further to perform incremental dynamic time history analysis on two-story as-built and eccentric steel braced frames. Fragility functions for the frames in terms of immediate occupancy, life safety and collapse prevention were developed using a probabilistic-based methodology. The as-built frame was more fragile in terms of immediate occupancy, life safety and collapse prevention damage states as opposed to the retrofitted frame.

Study on seismic behavior of CHS T-joints under quasi-static cyclic in-plane bending

This paper aim to study the in-plane flexural behaviors of circular hollow section (CHS) T-joints by quasi-static cyclic loading test and finite element (FE) analysis. Two specimens under cyclic in-plane bending (IPB) were carried out to investigate the effect of the brace-to-chord diameter ratios (a key parameter for the CHS joints and denoted as β) on the seismic behaviors of the T-joints. Moreover, finite element (FE) analysis were performed to study the effect of β, γ (another key parameter for the joints with name of the chord radius-to-thickness ratio) and the chord axial pressure on the in-plane flexural behavior of the T-joints. Test results showed that both two specimens failed in tearing of the chord wall at the heat-affected zone (WHAZ), and both two specimens exhibit good ductility and energy dissipation behavior. Both specimens mainly rely on the plastic development of the chord wall near brace/chord intersection and the crack propagation (after cracking) to dissipate energy input by the earthquake. Test results also found that the current specification conservatively predict the in-plane flexural strength of the T-joints (about 20 %–30 %), especially for the joints with larger β. Test and FE results also show that the increase of β (or the decrease of γ) will effectively improve the flexural strength, energy dissipation capacity and ductility ratio. The results also shows that chord pressure stress will adversely affect the in-plane flexural behavior of the T-joints, especially when the stress is larger than 0.6 times of the chord yield strength. A FE parametric study was performed to investigate the effect of β on the force transmission characteristics of the T-joints under IPB, and the force transmission characteristics in elastic state was further interpreted by a simple semi-circular arch analytical model.

A new approach for improving lateral performance of pile foundations in seasonally frozen regions

Ground freezing in cold areas can cause brittle damage to deep foundations during seismic loading. This paper presents a novel solution to this problem by replacing local soil around the pile with a temperature-insensitive composite material, namely polyurethane glue-bonded rubber particles-sand mixture (PolyBRUS). Three 1/12 scale reinforced concrete pile foundations embedded in unfrozen, frozen, and frozen with local replacement conditions were prepared, and quasi-static cyclic loading tests were conducted to reveal the adverse effects of seasonal freezing on pile foundations and verify the performance of the proposed solution. The model preparation, including model pile configuration, model construction, sensor configuration, and frozen soil formation, were described in detail. The pile foundation lateral performance data, including failure mode observations, lateral load-displacement hysteresis relations, and moment distributions, were presented. The evolution of secant stiffness and energy dissipation of the pile-soil system with lateral displacement were analyzed and discussed. It was found that the peak lateral load of the model pile in 20 cm-thick seasonal frost is 53% larger than the unfrozen conditions. In contrast, the ultimate displacement in seasonally frozen conditions is 25% less than that in unfrozen conditions. And seasonal freezing can render a pile from ductile to brittle failure. More importantly, the results show that the local replacement with the proposed material can ensure similar lateral behavior for the soil-pile system under both unfrozen and frozen conditions. It is concluded that the proposed local replacement approach offers excellent potential for mitigating the adverse effects of seasonal freezing on the lateral performance of deep foundations in cold regions. In future studies, local replacement zone optimization and large-scale field tests are recommended to further confirm this method's effectiveness and provide design parameters for pilot testing.

Experimental and numerical investigations into seismic behavior of corroded steel frame beams and columns in offshore atmospheric environment

With the strong promoting of “national carbon peak and carbon neutrality” strategy and the continuous deepening of “performance-based seismic design” concept, the seismic performance evaluation field of Chinese steel structures has developed rapidly. Nevertheless, previous studies are generally aimed at new building structures, ignoring the seismic performance degradation characteristics caused by the durability loss of existing structures under environmental erosion. Thus, in this paper, accelerated offshore atmospheric corrosion and quasi-static cyclic loading tests were carried out on five steel frame beams and four steel frame columns. The effects of corrosion level on the failure mechanism, hysteretic behavior, skeleton curve, bearing capacity, ductility, stiffness degradation and energy dissipation of steel frame members were revealed and analyzed in detail. The test results indicate that with an increase in corrosion level, the appearance of plate local buckling, steel cracking and final failure shows a forward tendency, and all seismic performance indexes significantly decrease. Moreover, the deterioration models of the maximum load, ultimate displacement and cumulative energy dissipation with weight loss rate for corroded steel frame beams and columns were proposed. In addition, a finite element analysis method for corroded steel frame members was established and validated, which considered the corrosion damage and introduced a nonlinear mixed hardening constitutive model and a stress triaxiality dependent ductile damage criterion. On this basis, the parametric analysis was further presented to systematically study the influence of corrosion level, plate width - thickness ratio and its assembly factors, and stress conditions on the mechanical performance of H-shaped steel members, then obtaining the regular expressions of bending capacity and plastic rotation capacity.

Hysteretic restoring force model of high damping rubber bearings including thermo-mechanical coupled effect

In the application of High Damping Rubber (HDR) bearings as seismic isolation devices for bridges in cold regions, there are concerns about the low temperature effect on the hysteresis performance of HDR bearings and the resulting deterioration in bridge performance under strong ground motions. The stiffness and damping ratio of the HDR bearing significantly increase at lower ambient temperatures, and the stiffness reduces as the inner temperature of the bearing increases due to the self-heating of rubber material under repeated cyclic loading, resulting in a complicated thermo-mechanical coupled hysteresis behavior which is not expressed by the currently available restoring force models of HDR bearings. In this study, a simplified thermo-mechanical coupled hysteretic restoring force model of HDR bearings is newly developed. The model parameters are identified from the shear strain–stress curves of HDR bearings obtained in quasi-static cyclic loading tests at three different ambient temperatures. Accuracy of the improved model is verified by comparing the numerical result of seismic response analysis of a bridge model using the proposed restoring force model with the result of hybrid simulation of the same bridge model including the HDR bearing loading test under low-temperature conditions.