Redistribution Of Internal Forces Research Articles

Elasto-Plastic Seismic Shear Distributions of Frame-Wall Structures

ABSTRACT In this study, theoretical and numerical methods were used to research seismic shear distributions of frame-shear wall structures under elasto-plastic conditions. The shear distributions of frame-shear walls were analyzed based on a simplified elasto-plastic analysis model of flexural shear. Based on a preliminary project, three groups of 2D models with different stiffness eigenvalues were designed and used to compare the shear distributions of whole structures and frames. The characteristics of the shear distributions of structures and frames and the development of plastic hinges were analyzed, and the rationality of shear adjustment based on Chinese standards was discussed from the perspectives of structural design, seismic performance and collapse resistance. The results revealed obvious differences between shear distributions of structures caused by strong vs. frequent earthquakes. For strong earthquakes, the shear distributions tended to be evenly distributed with respect to height, while the shear force of the bottom story was significantly larger than that of the upper stories. This was mainly caused by the redistribution of plastic internal forces due to the development of plastic hinges. The shear adjustment of the frame usually affected the reinforcement in the beams rather than in the columns, which contradicted the design concept of strong columns – weak beams. Additionally, shear adjustment had little effect on the seismic performance and collapse resistance of structures. This paper suggests that by ensuring the ability of strong columns, weak beams and plastic hinges to rotate, shear force adjustment can be prevented.

Experimental and numerical investigation on collapse performance of wooden drum-towers in southwest China

The drum-tower belongs to the category of towering structures, and the overall collapse is a common accident in such structures. In order to study the anti-collapse performance of drum-towers, this research used the bottom floor of a wooden drum-tower in the southwest China as a prototype, designing and producing a 1/3 scale structural model. The sudden-column-removal (SCR) method was employed to simulate the structural collapse process, observe collapse characteristics, and analyze the dynamic response of the structure. A finite element model was established, and on the basis of verifying its accuracy, a parameter expansion analysis was conducted. The study indicates that the ductility of wooden drum-towers is relatively poor, and the pulling out of mortise- tenon joints in adjacent components in the failure area is a primary factor for the progressive collapse of the structure. Due to the redistribution of internal forces, the load-bearing status of beams in the failure area changes, experiencing tension, bending moment, and torsion simultaneously, leading to the pulling out, compression, and splitting of mortise-tenon joints. After the failure of these joints, the structure undergoes progressive collapse under the influence of gravity. The dimensions of mortise-tenon joints and the friction coefficient have a significant impact on the anti-collapse performance of the structure. Larger dimensions and friction coefficients result in slower structural damage and more stable structural response. Among these factors, increasing the depth of mortise-tenon joints has the most significant effect.

Plastic Properties of Prestressed High-Strength Steel Reinforced Concrete Continuous Beams

In this paper, the plastic properties of prestressed high-strength steel reinforced concrete (PHSSRC) beams are studied, by performing static load tests on eight built-in Q460 and Q690 prestressed high-strength steel reinforced concrete continuous beams and one built-in Q355 prestressed steel reinforced concrete (PSRC) continuous beam. The design parameters of the specimens were the steel strength grade, the steel ratio, the comprehensive reinforcement ratio, and the stirrup ratio. The failure mode, load–deflection curve, internal force redistribution ability, curvature ductility, plastic hinge performance, and moment modification coefficient of continuous beams under the influence of various parameters were analyzed to measure the plastic performance of the continuous beams. These results show that after the plastic hinge is formed in the middle support and mid-span of the prestressed high-strength steel reinforced concrete continuous beam, the test beam eventually becomes a rotating mechanism and is destroyed with increasing load. The built-in high-strength steel can significantly improve the bearing capacity of the specimen, and the maximum increase in the bearing capacity is 37.3%. The specimen still has a high bearing capacity after reaching the ultimate bearing capacity. With a decrease in the steel ratio, the degree of internal force redistribution is deepened, the curvature ductility is improved, and the plastic performance is enhanced. Increasing the comprehensive reinforcement ratio and the stirrup ratio can improve the plastic performance of the specimen. The calculation formula of the equivalent plastic hinge zone length is proposed. The calculation formula of the moment modification coefficient, with the relative plastic rotation angle and relative compression zone height as independent variables, is established. When the relative plastic rotation angle is not greater than 0.829 × 10−5, the moment modification coefficient increases with increasing plastic rotation angle and is not greater than 0.37. In the range of 0.3~0.4, the moment modification coefficient decreases with increasing height of the relative compression zone.

Progressive Collapse Resistance Assessment of a Multi-Column Frame Tube Structure with an Assembled Truss Beam Composite Floor under Different Column Removal Conditions

To estimate the progressive collapse resistance capacity of a multi-column frame tube structure with an assembled truss beam composite floor (ATBCF), pushdown analysis and nonlinear dynamic analysis are conducted for such a structure using the alternate load path (ALP) method. The bearing capacities of the remaining structures under three different work conditions, which are the side middle column removal, the edge middle column removal, and the corner column removal, are individually studied, and the collapse mechanism of the remaining structures is analyzed based on the aspects of the internal force redistribution and the failure mode of the second defense line. Simultaneously, the influence of the column failure time on the dynamic response of the remaining structure and the dynamic amplification coefficient is discussed. The results indicate that the residual bearing capacity of the remaining structure following the bottom corner column removal is higher than that of the one following the side or edge middle column removal, while the latter has a stronger plastic deformation capacity. When the ALP method is adopted to operate the progressive collapse analysis, it is reasonable to take the column failure time as 0.1 times the period of the first-order vertical vibration mode of the remaining structure, and it is suitable to set the dynamic amplification coefficient as 2.0, which is the ratio of the maximum dynamic displacement to the static displacement of the remaining structure under the transient loading condition.

Fire research of joint between special-shaped CFST column and U-shaped composite beam

The steel-concrete composite joint plays an important role in the building structure of transmitting load and maintaining structural stability, and the research on fire performance of composite joints is significant. The special-shaped concrete-filled steel tube (SCFST) column and U-shaped steel-concrete composite beam (USCB) have good fire resistance which is proved by authors' previous fire tests. Therefore, the fire performance of the joint between SCFST column and USCB, the temperature distribution, failure mode, fire resistance, and internal force distribution of the joint under fire are investigated based on the fire tests results of column and beam component. The results showed that the temperature of the joint zone is lower than that of the non-joint zone, which ensured that the strength and stiffness of the joint zone are higher than that of the non-joint zone (beam and column). Then the two failure modes including beam failure and column failure occurred in the composite joint in fire conditions. Furthermore, the internal force analysis indicated that internal force redistribution happens during the elevated temperature. The parameter analysis expressed that fire resistance decreases with the increase of load ratio and the beam-column moment ratio and increases with the increase of the beam-column stiffness ratio and the fire protection layer thickness. Finally, the high-temperature calculation formula for the bearing capacity of beam-column joint was proposed.

Time-dependent response of continuous steel-concrete composite beams under sustained loading

Although the long-term behavior of composite beams raises critical concerns in their application, only a few investigations have been conducted on the time-dependent response of continuous composite beams (CCBs). Herein, long-term tests were conducted on four two-span CCBs with different loading ages. The shear stiffness and time-slip relationship of flexible shear connectors were evaluated by carrying out short-term and long-term push-out tests. The experimental results revealed that loading age substantially affected the development of deflection, interface slip, crack, and internal force redistribution of CCBs under sustained loads. A finite element model (FEM-2) of test specimens was developed, considering the damage evolution, creep and shrinkage of concrete slab, and stiffness degradation of connectors. After the FEM results were verified against the experimental data, the developed FEM-2 model was implemented to further investigate the influences of loading age and loading level on the long-term performance of CCBs.

Redistribution of Internal Forces in Reinforced Concrete Beams Subjected to Combined Load

Redistribution of Internal Forces in Reinforced Concrete Beams Subjected to Combined Load

Progressive collapse demolition of double-layer space truss under different demolition load conditions

Two double-layer space trusses (DLSTs) under different demolition load conditions were tested for progressive collapse demolition. The primary load-carrying members of the tested DLSTs were removed one by one according to a pre-designed demolition process. The global structural responses, including the strains of the members on the main force transmission paths and the vertical displacements of representative joints, were measured. The structures' internal force redistributions and load-carrying mechanisms were investigated based on the experimental results and the corresponding FE analysis. The results show that both the tested DLSTs achieved progressive collapse demolition as expected. The two tested DLSTs under different demolition load conditions followed the same internal force redistribution patterns and exhibited three identical mechanical characteristics: arch action, catenary action, and beam action. The removal of specific members will change the load-carrying mechanism of the DLST and lead to local or global collapse.

Review of the Main Mechanical Testing Methods for Interlayer Characterization in Laminated Glass

In the last decades, the use of structural glass has increased exponentially. The reliability of brittle structural glass elements is considerably improved if laminated glass elements are chosen because, in this case, a redistribution of internal forces is permitted once a limited breakage occurs. Thus, instead of monolithic glass, composite materials consisting of two or more glass plies bonded together using a polymeric film as an interlayer are used. In the event of glass failure, because of the chemical bond between the different materials, the adhesion to the interlayer prevents glass fragments from scattering. To design structural elements, the definition of the mechanical features of the interlayer is necessary. However, several standards and techniques can be applied, considering the characterization of either the interlayer itself or the laminated glass. The paper reviews the main existing methods and focuses on the standard suggested by the CEN/TS 19100:2021, analyzing in detail the effect of the different parameters involved. A numerical model is presented to account for the effect of the stress level, glass, and interlayer thickness. Although the standard leaves a certain degree of freedom in choosing those parameters, in some cases the results can differ.

Wind-Induced Responses of Corroded Angle-Steel Transmission Tower

Corroded transmission towers, whose load-bearing capacities are lowered, are suffering from wind-induced damage. By simulating the member corrosion through section thinning, the structural dynamic finite element model of an angle-steel transmission tower with a corrosion depth of 0 mm to 1.4 mm was established using ANSYS/LS-DYNA software. The incremental dynamic analysis method was used to study the collapse mode of the tower under different degrees of corrosion, as well as the effects of corrosion on structural self-vibration characteristics, wind-induced member stress, and tower-top displacement. The results show that with the corrosion deepening, the first three vibration frequencies decrease, and the torsional mode becomes the first mode. When the corrosion depth is smaller, the overall structure failure occurs under strong wind. The failure starts at the most unfavorable oblique rod between the upper and middle cross arm, then expands to the rods under the lower cross arm. When the corrosion depth is larger, the overall structure failure occurs restrictedly between the upper and middle cross arm. Internal axial force and bending moment redistribution happen when corrosion deepens. Under the critical failure state, the oblique rods are always at a high stress level, while the stresses of the main rods decrease. Corrosion has a stronger impact on component strength and stability than on structural stiffness.

Comparative study on failure mechanism of multi-storey planar composite frames with RC beams to CFST columns subjected to compartment fire

This paper presents a theoretical study of the failure mechanism of planar composite frames composed of reinforced concrete (RC) beams to concrete-filled steel tubular (CFST) columns subjected to compartment fire. The numerical analyses on the planar composite frames with multiple stories and spans are meant to reproduce the conditions of framed members in multi-storey composite structures in real buildings. A refined finite element model is established and calibrated against the thermal and mechanical results from physical testing and shows good reliability in general. Using this model, this study proposes comparative analyses on the failure mechanisms of three typical composite frames, and discusses the effects of two significant parameters: the beam-to-column linear stiffness ratio and the fire protection thickness of the composite column. The responses of the heated composite frames, including the rotational deformation and stiffness degradation of framed joints, the internal force redistribution within framed members, and the failure mode of framed structures are investigated and discussed. The results indicate that there are two important parameters should be considered in the design of composite frames in fire.

Study on progressive collapse demolition method of double-layer space truss

This paper conducted a demolition test of a double-layer space truss (DLST) to investigate more efficient, safe and environmentally friendly demolition methods of truss systems. The high-speed 3D displacements of representative joints and the global dynamic strain response of the structure were well collected. The internal force redistribution and load-carrying mechanisms of DLST structures during demolition were explored. The results indicate that new equilibrium states were sought in the DLST through local and global internal force redistribution. When the main force transmission members were removed, the load-carrying mechanism of the DLST underwent sudden changed, which resulted in a snap-through in the structural load-carrying capacity. The test DLST exhibited three load-carrying mechanisms in time sequence during the proposed demolition: arch action, catenary action, and beam action. The theoretical vertical load-carrying capacity provided by each load-carrying mechanism was investigated separately. Finally, a progressive collapse demolition method was presented for the engineering DLST structures subjected to certain demolition external loads.

Plastic redistribution capacity of stainless steel frames in fire

Stainless steel frames with compact cross-sections are capable of redistributing internal forces at room temperature and forming plastic failure mechanisms, which is reflected in the new generation of structural codes for stainless steel by allowing to carry out global plastic analyses on certain types of stainless steel if the joints conforming the structure are classified as full-strength joints. Nevertheless, the requirements for the fire design of stainless steel structures in current standards is still primarily based on the resistance of individual members, disregarding strain hardening effects and the redistribution of internal forces, mainly because the influence of the performance of stainless steel joints on the response of the frames under fire situation is yet unknown. On this basis, this paper presents a numerical study focused on stainless steel frames with compact rectangular hollow sections, both at room temperature and at elevated temperatures, to analyse the influence of full-strength joints on the frame's response by means of two joint modelling techniques, and to assess the plastic redistribution capacity of stainless steel frames, especially under fire situation. In addition, an exhaustive revision of the failure criteria for stainless steel frames under fire situation is carried out and a new failure criterion is proposed based on the results derived from the parametric study. The results demonstrate that stainless steel frames are also capable of redistributing internal forces and forming plastic collapse mechanisms under fire situations, suggesting a new procedure to predict the response of these structures under fire situation more accurately.

Deep learning-based bridge damage identification approach inspired by internal force redistribution effects

Damage identification has always been one of the core functions of bridge structural health monitoring (SHM) systems. Damage identification techniques based on deep learning (DL) approaches have shown great promise recently. However, DL methods still need to be improved owing to their poor interpretability and generalization performance. The fundamental reason lies in the separation between physics-based mechanical principles and data-driven DL methods. To address this issue, this paper proposes a physics-inspired approach combining the data-driven method and the internal force redistribution effects to perform efficient damage identification. Firstly, the mechanical derivation of internal force redistribution is given based on a simplified three-span continuous bridge. Then, two types of typical damage scenarios including segment stiffness decrease and prestress loss are simulated to formulate the damage dataset with monitored field data noise added. Next, a modified Transformer model with multi-dimensional output is trained to obtain the complex dynamic spatiotemporal mapping among multiple measurement points from the intact structure as a benchmark model. Finally, the relationship between multiple damage patterns and the corresponding output regression residual distribution is studied, based on which the flexible combinations of the sensors are proposed as the test set to characterize the internal force redistribution due to damage. Validation on the extended dataset showed that this approach is effective to realize preliminary identification of damage patterns and resist interference from noise at the monitoring site.

Area-loss effect analysis of pin-jointed structures

Corrosion will cause cross-sectional area loss of steel members, which will lead to redistribution of internal force and affect the performance of structures. In this paper, a generalized formula for the internal force variation of pin-jointed structures due to variation of external force, cross-sectional area, and initial length is derived. The area-loss sensitivity coefficient ( ASC) and the area-loss evenness coefficient ( AEC) based on statistical measures are then defined. By calculating these two coefficients, the influence of single member’s area-loss on the behavior of the structure as well as the evenness of internal force variation are evaluated. Besides, a method to determine the area-loss limit of pin-jointed structures is proposed based on the structural reliability theory and mathematical nonlinear programming. According to the above process, the effect of members’ area loss on structural properties is analyzed without complicated numerical approaches such as FEM, and then the safety of corroded structures is assessed preliminarily. The proposed method is verified by two numerical examples, and provides a convenient tool for pre-manufacturing, maintenance during service life, and structural health monitoring of pin-jointed structures.

Experimental research on the structural performance of continuous composite beams with uplift-restricted and slip-permitted connectors

The uplift-restricted and slip-permitted (URSP) connector technology is a new composite technology which achieves the purpose of reducing the tensile stress in concrete slab by releasing part of the composite action in the negative moment region. In this paper, it is found that arranging URSP connectors in continuous composite beams has an end-restraint effect, which has a significant impact on the force transfer mechanism of URSP composite beams. Previous studies on URSP technology seldom mention similar constraint effects, which cannot accurately reveal the mechanical behavior of URSP composite beams. In order to properly consider the influence brought by the end-restraint effect, this study uses continuous composite beams to carry out experimental research. Three two-span continuous composite specimens are fabricated and tested in this research. Six aspects of performance are compared and analyzed in detail, including ① cracking load, ② crack distribution and development pattern, ③ interfacial slip behavior, ④ deformation and stiffness, ⑤ internal force redistribution, and ⑥ strain distribution. It is found that the URSP connector can realize the release of part of the composite action, and has a significant effect on the crack control in the negative moment region. Meanwhile, the application of URSP connectors has little effect on the stiffness, bearing capacity and strain of steel beam.

Fatigue Experiment Study on Internal Force Redistribution in the Negative Moment Zone of Steel–Concrete Continuous Composite Box Beams

Due to the accumulated fatigue damage in steel-concrete continuous composite box beams, a plastic hinge forms in the negative moment zone, leading to significant internal force redistribution. To investigate the internal force redistribution in the negative moment zone and confirm structural safety under fatigue loading, experimental tests were conducted on nine steel-concrete continuous composite box beams: eight of them under fatigue testing, one of them under static testing. The test results showed that the moment modification coefficient at the middle support increases during the fatigue process. When approaching fatigue failure, an increase of 1.0% in the reinforcement ratio or 0.27% in the stirrup ratio results in a reduction of 13% in the moment modification coefficient. Furthermore, a quadratic function model was proposed to calculate the moment modification coefficient of a steel-concrete continuous composite box beam during the fatigue process, which exhibited good agreement with the experimental results. Finally, we verified the applicability of the plastic hinge rotation theory for steel-concrete continuous composite box beams under fatigue loading.

Building Response to Excavation-Induced Ground Movements from a Nonlinear-Inelastic Perspective

The nonlinear-inelastic response of reinforced concrete moment-resisting frame buildings due to an adjacent excavation in soft to medium clays is presented. An advanced numerical model is used to account for building-soil-excavation interactions, post-yielding behavior of the structural members, and solid-fluid coupled behavior of supporting soils. The effects of the excavation on the internal force redistributions of structural members, lateral and vertical distortions, ground surface settlements, and lateral wall movements are presented in terms of angular distortions and drifts, curvature ductility, axial forces, and flexural moments. Results showed how beams progressively developed plastic deformations as deep-seated movements occurred during the excavation of soft and medium clays, reaching maximum curvature ductility ratios larger than 2. As the excavation advanced, maximum curvature ductilities of up to 5 were computed in beams closer to the excavation, causing localized inelastic mechanisms in the building. This paper shows how even well-designed buildings to withstand large levels of lateral load demands using strong column–weak beam approaches can still be subjected to significant excavation-induced nonlinear-inelastic demands that can cause damage.

Study on Redistribution of Internal Force and Plastic Hinge Development of Mountainous Building Structures with Foundations at Two Different Elevations

This study was conducted to study the redistribution of internal force and the development of the plastic hinge of an MBS with foundations at two different elevations considering the torsional effect. The results indicate that the redistribution of the base shear of MBS is evident at different embedding ends, and the redistribution of story shear on different floors also took place. The redistribution of the shear force of columns is different at the upper- and lower-embedding sides, and the internal force redistribution is more prominent along the slope direction. Consequently, the redistribution of the internal force of MBS should be considered in practical seismic design. Furthermore, the damage of MBS is transferred from the floors above the upper-embedding end to the floors under the upper-embedding end with the increase in the seismic intensity, where the elements at the floors above the upper-embedding end suffer the most serious damage, and the damage is unevenly distributed in the upper-embedding story and the adjacent upper story. The lower-embedding column is more prone to hinge across the slope direction because of the torsional effect. With γintra changes, the redistributions of the shear force of the base, story, and column are different. A larger γintra would result in a weaker redistribution of base shear. The redistribution of the story shear of the 1st floor and its columns along the slope direction shows an increasing-decreasing tendency with the increase in γintra, and the redistribution is the most serious when γintra is 0.4. While across the slope direction, the redistribution of the story shear tends to be weakened as γintra increases. The forming of the plastic hinge of single-frames along the slope direction is related to γintra and γnon, especially the damage of the upper-embedding columns. The torsional effect has a significant influence on the damage of the single-frames across the slope direction. Some measures should be taken to improve the bearing capacity of the upper embedding columns and columns on floors under the upper-embedding end, as well as the drift ductility of the upper-embedding columns.

Closure Scheme Analysis of 3 × 70 m Bearingless Integral Rigid Frame Bridge of Fuzhou Xiamen High-Speed Railway

The hydrodynamic problems associated with the construction of the sea-crossing bridge were proposed. The deep-water approach bridge on both sides of the main bridge of Fuzhou Xiamen high-speed railway adopts the bearingless prestressed concrete integral rigid frame bridge for the first time in the domestic railway bridge design. The rigid frame bridge applies the hanging basket cantilever construction, and there are several options for closure. Because the bridge structure system changes before and after closure, which will cause the redistribution of bridge internal force, the results of internal force redistribution will be different with the sequence and position of closure, and sometimes, there will be great changes. In order to select the optimal closure scheme, this article establishes the finite element model of the whole bridge and analyzes the whole construction process according to the working conditions and the mechanical state of the bridge before closure is obtained. Based on this state, eight closure schemes are analyzed and studied, which provides a sufficient mechanical basis for the determination of the final closure construction scheme.