Load Path Method Research Articles

Progressive Collapse Assessment: A review of the current energy-based Alternate Load Path (ALP) method

The Alternate Load Path (ALP) is a useful method that has generated a considerable recent research interest for the assessment of progressive collapse. The outcome of the ALP analysis can be assessed either using the force-based approach or the energy-based approach. The Unified Facilities Criteria (UFC- 4- 023-03) of progressive collapse guideline - have outlined that the force-based approach can either be analysed using static or dynamic analysis. The force-based approach using static analysis is preferable as it does not require a high level of skill and experience to operate the software plus no effort is required in scrutinising the validity of the analysis results output. However, utilising the static approach will eliminate the inertial effect in capturing the actual dynamic response of the collapsed structure. In recent years, the development of the energy-based progressive collapse assessment is attracting widespread interest from researchers in the field; as the approach can produce a similar structural response with the force-based dynamic analysis by only using static analysis. Most of the current energy-based progressive collapse assessments are developed following the requirements which are given in the progressive collapse guidelines provided by the Unified Facilities Criteria. However, little attention is given to the development of the energy-based approach using the Eurocode standards as a base guideline. This article highlights the merits of utilising the energy-based approach against the force-based approach for a collapsed structure and explains the collapse mechanism of a steel frame in the perspective of the energy concept. The state of the art of energy-based progressive collapse assessment for a structural steel frame is reviewed. The comprehensive review will include insights on the development of the energy-based method, assumptions, limitations, acceptance criterion and its applicability with the European standards. Finally, potential research gaps are discussed herein.

Experimental and Theoretical Investigations on Progressive Collapse Resistance of the Concrete‐Filled Square Steel Tubular Column and Steel Beam Frame under the Middle Column Failure Scenario

A static loading test was carried out on a 1/3‐scale concrete‐filled square steel tubular column‐steel beam frame (CFSTSBF) specimen with 2 spans to study its progressive collapse behaviors under the middle column failure scenario using the alternate load path method and to examine the failure mode and load transfer and main resistance mechanisms of the residual structure. Then, theoretical models of the specimen, involving the whole collapse process, were developed, and the resistance and deformation relationships of each model were calculated and validated with test results. The results indicated that the specimen collapse process includes the elastoplastic stage, plastic stage, transfer stage, and catenary stage, the beam mechanism and catenary mechanism were the principal mechanisms for the structure against progressive collapse, and catenary action can significantly strengthen structural resistance. The modified theoretical models with higher practical accuracy could be used to assess structural performances against progressive collapse.

Analysis of Anti-Collapse Performance of Beam–Column Substructure with Welded Flange-Bolted Web Connection in Minor-Axis Direction Under Different Span Ratios

The failure modes, mechanical properties, and resistance mechanisms of beam–column substructures with welded flange-bolted web connection in the minor-axis direction under different span ratios (1:0.6, 1:1.0, 1:1.4) were compared and analyzed under the condition of progressive collapse. The beam–column substructures included three columns and two beams, and monotonic static loading tests were conducted using the alternate load path method. The test results indicated that the specimens began to fracture at the beam tension flange; and then, part of the main internal force was transferred by the bolts on the web, followed by buckling of the compression flange at the beam end. Finally, specimens were deactivated by the shear failure of bolt holes or the fracturing of the web and junction plate. The joint with a welded flange-bolted web connection was found to have high redundancy, with sufficient rotational capacity after the fracture of the tension flange. As a result of the effective pulling force between the beam and column, combined with sufficient rotation of the beam end, the remaining structure could give full play to the catenary effect, which would play a leading role in the later stage of large deformation. The deformation of the beam–column joint increased rapidly, which was conducive to the beam–column substructure to bear the load by collaboration between the beam and column. The simplified model and the numerical simulation are proved to be reliable by test results. The results of numerical simulations and analyses of anti-collapse performances of beam–column substructures under different span ratios showed that the large beam-span ratio was beneficial to the development of ultimate failure displacement of the substructure and increase the ratio of ultimate to initial failure load. The resistance provided by catenary mechanism also increased, and the short beam developed a better catenary effect than the long one.

Performance of Low-yield Strength Plates in Beam-column Connections against Progressive Collapse

In many studies about progressive collapse in steel moment frames, the effect of connections in all of structural frames has not been investigated. This is while the connections can have a significant impact on structure behavior against abnormal loads. This study highlights the effect of mechanical and geometric properties of beam-column connections in steel moment frames against progressive collapse. For this purpose, variable parameters include beam-column connection type (Welded Flange Plate connection or WFP and Welded Unreinforced Flange-Welded web connection or WUF-W), mechanical properties of beam-column connection (St37 building steel and low-yield strength plates) and the column removal location in different stories (without removing column and removing column on the ground, first and second floors). Three-storey steel frames which are designed to withstand earthquakes are examined. Finite element ABAQUS software is used for simulation. Moreover, the alternative load path method in which the structure response is examined against the column removal is used to evaluate steel frames response against progressive collapse. The results show that the use of low-yield strength steel plates depending on connection type can be efficient in improving the behavior of steel moment frames against progressive collapse.

Progressive Collapse Analysis of SRC Frame-RC Core Tube Hybrid Structure

Steel reinforced concrete (SRC) frame-reinforced concrete (RC) core tube hybrid structures are widely used in high-rise buildings. Focusing on the progressive collapse behavior of this structural system, this paper presents an experiment and analysis on a 1/5 scaled, 10-story SRC frame-RC core tube structural model. The finite element (FE) model developed for the purpose of progressive collapse analysis was validated by comparing the test results and simulation results. The alternate load path method (APM) was applied in conducting nonlinear static and dynamic analyses, in which key components including columns and shear walls were removed. The stress state of the beams adjacent to the removed component, the structural behavior including inter-story drift ratio and shear distribution between frame and tube were investigated. The demand capacity ratio (DCR) was applied to evaluate the progressive collapse resistance under loss of key components scenarios. The results indicate that the frame and the tube cooperate in a certain way to resist progressive collapse. The core tube plays a role as the first line of defense against progressive collapse, and the frame plays a role as the second line of defense against progressive collapse. It is also found that the shear distribution is related to the location of the component removed, especially the corner column and shear walls.

Effects of different steel-concrete composite slabs on rigid steel beam-column connection under a column removal scenario

Trapezoidal and Reentrant are two ordinary deck profiles in modern steel-concrete composite floor system in China. The progressive collapse resistance of rigid steel beam-column connections with these two different composite deck profiles was experimentally investigated. This research addressed progressive collapse behavior of components evaluated by removing columns through the alternate load path method where the connections simulated the behavior of connections from a multi-bay steel moment-resisting frame. Also, collapse resistance of the connection above the removed column and the adjacent connection was considered. The results were compared with a bare steel subassembly, which has the same configuration but without composite slab, the load carrying capacity of the specimen with trapezoidal steel deck is improved by 28% and the specimen with reentrant steel deck is improved by 44%. The type of steel decks influenced the degree of restraint to the beam top flange and resistance of the connection. The specimen with trapezoidal steel deck had a higher plastic rotation capacity than the reentrant one, but the specimen with reentrant steel deck had improved composite behavior in the large deformation range and, therefore, developed more catenary action than the specimens with trapezoidal steel deck. Overall, the specimens with reentrant steel deck had a better performance under the progressive collapse situation, however, some constructional measures must be made to delay the bottom beam flange fracture.

A new method for progressive collapse analysis of steel frames

As a massive explosion happens inside a building, a number of structural members (columns, beams, slabs and so on) are damaged or failed, along side with non-zero initial conditions (displacement, velocity, acceleration and so on), and the progressive collapse of the building structures is most likely to occur. However, limited research works about blast load effect of structural members inside a building can be found. In view of this, based on the substructure model, a new method for progressive collapse analysis of steel frames under blast load is proposed. First, the massive explosion scenario inside a building is introduced. Then, the substructure model within effective areas of blast influence is established. After that, the calculation method of non-zero initial conditions and initial damage for structural members is given, and finally the specific steps of the proposed method are described. By way of example of a steel frame with 5 stories in height, 4 bays in the longitudinal direction, 3 bays in the transverse direction, direct simulation method, alternative load path method and proposed method are all employed to simulate the progressive collapse process, respectively. Through the example analyses, it is shown that blast load effect of structural members cannot be ignored on the ground floor, and it can be ignored on the other floors by the effect of the reinforced concrete slab. The non-zero initial conditions and initial damage of structural members can be predicted well by the substructure model, and the proposed method is also reliable and accurate.

Irregularity index for quick identification of worst column removal scenarios of RC frame structures

Irregular structures are known to be more prone to disproportionate collapse (DC) than structures with regular horizontal and vertical layouts. Despite this, many public, commercial and institutional buildings have to be designed with various irregularities in structural layout due to architectural and aesthetic considerations. While extensive experimental and numerical studies have been carried out to advance the basic understanding of DC behaviors of regular structures, limited research has been carried out on irregular structures. On the other hand, alternate load path method has been recommended by several design codes and standards for DC design, but the large number of potential column removal scenarios involved poses a real challenge for the wide use of the method. This paper presents a quantitative measure referred to as irregularity index, or Π, that can be used to quickly identify the worst column removal scenarios for design check of DC resistance of reinforced concrete (RC) frame structures. Based upon a solid understanding of various competing failure mechanisms and DC resistance of RC frame structures, the irregularity index was derived from the maximum load factors between the yielding load and the limit load at the end of tensile membrane action stage. For verification and validation of the proposed Π, a 3D nonlinear finite element model was developed in OpenSees and calibrated by beam-slab sub-assemblage experiments. Various numerical experiments were carried out to verify the effectiveness of the Π. The very high correlation coefficient between the calculated irregularity indices and DC resistance obtained from finite element analyses showed that the proposed irregularity index can quickly identify the worst column removal scenarios in various irregular structures including setback buildings and large-bottom-space structures. Sensitivity analysis further verified the reliability of the proposed irregularity index.

Study on Structural Robustness of Isolated Structure Based on Seismic Response

The qualitative analysis for structural robustness study subjected to severe earthquakes is unable to meet engineering requirements, and a quantitative analysis method for structural robustness is needed to be proposed. The existing analysis methods, such as Incremental Dynamic Analysis Method and Pushover method, only study the response of the structure directly from the macroscopic view, rather than focusing on the response of a single component on the structure. Especially for the construction of isolated structure, the impact of accidental bearing failure on the isolated structure and the impact of progressive collapse cannot be considered. In this paper, based on the Alternative Load Path Method, the quantitative analysis method for structural robustness analysis under earthquake is proposed. The structural robustness of some different vertical irregular isolated structures under different earthquakes is studied.

A simplified model for alternate load path assessment in RC structures

To assess the robustness of reinforced concrete structures under progressive collapses, alternate load path method by introducing a single column removal has been widely adopted by structural engineers. Numerical analyses of structures under several possibilities of single column removal may be time consuming, especially when non-linear finite element analyses are employed which require high computational costs and modelling skills. Towards this end, a simplified analytical model is proposed in this paper to facilitate engineers in predicting resistance of the affected substructure (frames or frame-slabs above the removed column), and allow them to perform a quick check on the adequacy of progress collapse resistance of the structure to stop or prevent the damage propagation to the remaining structure. The proposed model considers development of different bridging mechanisms in RC structures under a concentrated loading above the removed column, including compressive arch action, catenary action, and tensile membrane action. In addition to validation against test results, applications of the proposed analytical model to predict the bridging capacities of a 2-D two-storey frame and unsymmetrical double-span beams are also presented.

Dynamic response analysis for submerged floating tunnel with anchor-cables subjected to sudden cable breakage

Anchor-cables are critical bearing components of the submerged floating tunnel (SFT). As the accidental cable-breakage incident will seriously threaten the public safety, this paper investigates the global dynamic response of a SFT subjected to an abrupt anchor-cable failure by focusing on the post-breakage behavior. Firstly, an approximate theoretical approach is proposed, in which the analysis model of SFT is simplified and the alternate load path method (AP method) is adopted to simulate the cable-breakage process. Then, the differential equations of the SFT tube are established based on the Hamilton principle, and solved through the fourth order Runge-Kutta method. A finite element analysis in ABAQUS is also performed as a verification of the theoretical results, in which the VUSDFLD subroutine and ABAQUS/Aqua is employed to simulate the stiffness loss of the cable and apply the fluid loads respectively. A good agreement exists between the simplified theoretical model and FE simulation. Finally, the effects of some key parameters are discussed, such as the gravity-buoyance ratio and the damping ratio of the SFT, the breakage time and position of the broken cable, etc. The results show that the structural vibration is intensive after the sudden cable breakage. Also, the remaining anchor-cables close to the cable-loss position are most affected by the cable rupture. The change of gravity-buoyance ratio and damping ratio have notable effects on structural deformation. The SFT is most unfavorable when the cable breakage happens at the mid-span or near the two ends of the tunnel. The vibration amplitude attenuates significantly with the increase of the failure time of anchor-cable.

Progressive Collapse Analysis of Latticed Telecommunication Towers under Wind Loads

As the antenna-supporting structures, latticed telecommunication steel towers are considered as critical members of telecommunication infrastructures. It is necessary to perform progressive collapse analysis of lattice telecommunication towers under wind loads. The present study conducts a nonlinear dynamic analysis on 50 m high typical standard latticed telecommunication tripole tower and angle tower by alternative load path method. The finite element models for two towers subjected to design wind loads are developed by ABAQUS. The analysis results show that, for 50 m high standard tripole tower, the member failure in the first three tower sections from tower top would not trigger the collapse of the tower. From the fourth tower section to tower bottom, the member failure at certain wind direction may cause a collapse. For 50 m high standard angle tower, the single member failure in any tower section would not cause the collapse of the tower. A dynamic sensitivity index is proposed to identify the most unfavorable wind direction for tripole tower and angle tower. A progressive collapse fragile curve based on collapse probability of telecommunication tower under wind loads is proposed to assess the anticollapse performance of the towers.

Multi-axial fatigue life assessment of high speed car body based on PDMR method

This article mainly introduces a method of converting the acceleration signal of body bolster obtained by the circuit test into the load of the air spring seat of vehicle body. This method mainly decomposes the body's movement posture into the form of ups and downs, roll and nod. Then formulate the test plan according to the performance of the body fatigue test bench. The vertical and horizontal displacements and longitudinal force are used as control commands.Taking advantage of vehicle body fatigue test bench to reproduce these basic types of vibration. Establish the transfer function of the acceleration of the bolster and the displacement excitation of the air spring, and then obtaining the load of the air spring seat. Finally, the multi-axial fatigue life assessment of the vehicle body was performed using the obtained load combined with the Moment of Load Path Method and the Path-Dependent Maximum Range Method.

Progressive Collapse Analysis of Reinforced Concrete Structures: A Simplified Procedure

In this paper, a simplified analysis procedure to calculate the column removed point displacement at progressive collapse analysis of reinforced concrete structures is proposed. The energy absorption capacity under the column missing event is used for formulations. The approximate method is simple to utilize, user friendly, yet accurate. For progressive collapse analysis of structures, linear static analysis, nonlinear static analysis, linear dynamic analysis and nonlinear dynamic analysis can be performed. In this paper, the nonlinear static analysis from alternate load path method is used and the reason of initial local collapse has not been considered. In fact, an energy-based method by using load-displacement curve of RC frame and considering the effect of floor slab for the progressive collapse analysis is considered. The accuracy of the proposed method is demonstrated by comparing the results to three experimental and analytical results. Finally, the effects of the spans length, sections dimensions, material properties and the beams reinforcements of column removed spans on substructure behavior is studied, as well.

Progressive Collapse Analysis of Reinforced Concrete Structures: A Simplified Procedure

In this paper, a simplified analysis procedure to calculate the column removed point displacement at progressive collapse analysis of reinforced concrete structures is proposed. The energy absorption capacity under the column missing event is used for formulations. The approximate method is simple to utilize, user friendly, yet accurate. For progressive collapse analysis of structures, linear static analysis, nonlinear static analysis, linear dynamic analysis and nonlinear dynamic analysis can be performed. In this paper, the nonlinear static analysis from alternate load path method is used and the reason of initial local collapse has not been considered. In fact, an energy-based method by using load-displacement curve of RC frame and considering the effect of floor slab for the progressive collapse analysis is considered. The accuracy of the proposed method is demonstrated by comparing the results to three experimental and analytical results. Finally, the effects of the spans length, sections dimensions, material properties and the beams reinforcements of column removed spans on substructure behavior is studied, as well.

Robustness analysis of steel structures with various lateral load resisting systems under the seismic progressive collapse

Abstract Robustness is called to non-sensitivity of a structure to local damage. In the literature of Civil Engineering, the sensitivity of structures to the local damage which can cause a progressive collapse is called Robustness Index. After 9/11, progressive collapse drew the attention of researchers and since that time, increasing the Robustness Index in a structure has been considered as one of the factors in strengthening the structure against progressive collapse. The aim of this study is assessing the Robustness Indices of steel structures having various lateral load resisting systems. So, 8-story, 4-story and 15-story structures with Moment Frames, Concentrically Braced Frames and Eccentrically Braced Frames were modeled and assessed under Robustness analysis. For a progressive collapse analysis, the Alternative Load Path method was used and after emerging local damage, the potential of progressive collapse was assessed using the Robustness Index. First, Robustness analysis was carried out on the basis of Robustness Index assessment using Stiffness and Base Shear methods. Subsequently, it continued by introducing a simple method based on Energy. The results show that despite their simplicity, the methods which are based on Stiffness and the Base Shear, have lots of disadvantages. But, the Energy method has better capabilities for understanding the behavior of structure under seismic loads in progressive collapse scenario. Furthermore, structures which have bracing had a better reaction in progressive collapse scenario.

Assessment of Masonry Buildings Subjected to Landslide-Induced Settlements: From Load Path Method to Evolutionary Optimization Method

One of the main difficulties, when dealing with landslide structural vulnerability, is the diagnosis of the causes of crack patterns. This is also due to the excessive complexity of models based on classical structural mechanics that makes them inappropriate especially when there is the necessity to perform a rapid vulnerability assessment at the territorial scale. This is why, a new approach, based on a ‘simple model’ (i.e. the Load Path Method, LPM), has been proposed by Palmisano and Elia for the interpretation of the behaviour of masonry buildings subjected to landslide-induced settlements. However, the LPM is very useful for rapidly finding the 'most plausible solution' instead of the exact solution. To find the solution, optimization algorithms are necessary. In this scenario, this article aims to show how the Bidirectional Evolutionary Structural Optimization method by Huang and Xie, can be very useful to optimize the strut-and-tie models obtained by using the Load Path Method.

Resilience of tall steel moment resisting frame buildings with multi-hazard post-event fire

Infrastructure resilience is the ability of an infrastructure asset to limit the effect and duration of damaging extreme events. The four main components of the concept of resilience are robustness, resourcefulness, recovery and redundancy most of which are very difficult to be quantified. In addition to this difficulty, a careful study of extreme event cases can demonstrate that it is very common for an extreme event scenario to include cascading multi-hazard events such as blast, floods, earthquake, and fire. This paper studies the resilience of a multi-story steel frame with multi-hazard considerations which include a post-event fire scenario. The initiating extreme event is simulated through the threat-independent alternate load path method of analysis and a post-event fire is considered following the extreme event. The work in the paper combines previous work by the authors on stability-induced collapse of damaged steel structures and closed-form solutions for temperature predictions of wide-flange components during a fire scenario. For the purposes of the fire scenarios, new fire time-temperature curves are developed based on experimental data from the well-known Cardington fire tests. The results show that even when a structure can withstand an extreme event scenario, a post-event fire consideration is highly critical to evaluate the remaining time of survival of the structure before collapse. It is shown that the sequential method of multi-hazard analysis can lead to very short available time periods before the post-event fire leads to the complete collapse.

Studies on passive flexible protection to resist landslides caused by the May 12, 2008, Wenchuan earthquake

Summary The landslides caused by the 5.12 Wenchuan earthquake resulted in enormous casualties and property losses. Since the earthquake, more than 3,600 landslides have occurred, and 17 of them were catastrophic, each of which has killed more than 30 people. Meanwhile, passive flexible protection has gradually been introduced to resist landslides due to its significant advantages of economy, safety, and environmental protection. To resist landslides effectively, it is necessary to study the load path and design method of passive flexible protection under the action of landslides. In the design of passive flexible protection against landslides, determination of the landslide load is the primary task. In this paper, the formulas of the probability density function and distribution function of the landslide pressure are developed to obtain the value of the accumulated landslide pressure acting on the passive flexible protection, which can be used as the load input parameter in the design of passive flexible protection to resist landslides. Based on the case of the “Shiziliang” potential landslide for the 5.12 earthquake, the pressure data of the landslide are collected, the calculation formulas of the volume, and the pressure of the intercepted landslide are established, and the statistical parameters of the landslide pressure-loading sample are obtained. According to the Kolmogorov–Smirnov test method, the loading sample of the landslide pressure obeys an extreme-value type-I distribution, and then the load model of the landslide pressure is determined. Based on the reliability analysis method, the standard value of the landslide pressure with an over-95% assurance rate is obtained. These results can provide references for load confirmation to design the passive flexible protection to resist landslides.

Investigation of optimal layout of ties in STM developed by topology optimization

AbstractStrut‐and‐tie models (STMs) have been wildly used for the design of disturbed regions in structural concrete members. The STM developed based on the load path method or with the aid of stress trajectories is not unique and varies with the designer′s intuition and past experience. As a result, topology optimization methods have been adopted to generate STMs in reinforced concrete structures. However, such models are just a preliminary configuration and the detailed layout of ties in an STM cannot be determined by the optimal topology. This is because reinforced concrete is assumed to be a uniform elastic continuum. Therefore, the effect of the steel reinforcement on the load transmission cannot be considered in the optimization process. Recently, the criterion of minimum strain energy has been proposed to determine the optimal layout of STMs obtained by the modified optimization method. However, the strain energy criterion does not work when the minimum strain energy in ties is zero when evaluated by mathematical equations. To address this issue, the maximum stiffness criterion is proposed to discover the optimal layout of ties in STMs by evaluating the stiffnesses of strut ties.