Slab Thickness Research Articles

Fire Resistance of Prestressed Multispan Steel Truss Composite Slab

Prestressed steel truss composite slab is composed of a precast prestressed bottom slab, a steel truss, and a postcast concrete layer. In order to investigate the fire resistance performance of prestressed multispan steel truss composite (STPC) slabs under the coupled effect of high temperature and load, four specimens of such composite slab containing two spans with various postcast concrete layer thicknesses were fabricated. Fire experiments were conducted following the ISO 834 standard temperature–time curve. Two of the specimens underwent two-span fire experiments, while the other two underwent single-span fire experiments. During the experiment, the bottom of the multispan STPC slabs exhibited serious bursting under fire and the precast concrete layer at the bursting locations fell off. The experiment result showed that the degree of bursting was much higher than that of nonprestressed composite slabs and single-span slabs. Although bond failure was observed at the composite interface where horizontal cracks developed, the STPC slabs still performed well in terms of load bearing, which could be attributed to the contribution of the steel truss. Under the coupled action of high temperature and load, concrete cracks were prone to occurring at the cut-off position of the top reinforcement near the supports; therefore, the anchorage length of these reinforcing bars should be appropriately extended. The damage to the STPC slab specimens after fire was found to be more serious for those with a less-think postcast concrete layer. In the single-span fire experiments, the structural performance of the unfired span was not prominently affected. Due to the bursting of the precast layer, the thickness of the STPC slabs was reduced, resulting in decreases in the thermal insulation and the fire resistance limit. The fire resistance limits of the STPC slabs with 60 mm and 80 mm postcast concrete layers were 90 min and 130 min, respectively. When a high fire resistance limit of the STPC slabs is required in a design, it is recommended that the thickness of the postcast concrete layer be no less than 60 mm.

Propagation loss in polyfluorene waveguides due to nanometer-roughness at their interfaces, studied by amplified spontaneous emission measurements

The propagation loss in single-mode asymmetric waveguides due to interface nanometer-roughness was studied using amplified spontaneous emission (ASE) measurements. Poly(9,9-dioctylfluorene) (F8) was used as the organic gain medium and the structure of the asymmetric waveguide was quartz glass substrate/F8/air. The propagation loss was measured at the ASE wavelength (447 nm) of amorphous F8, and the surface roughness of the substrate and F8 was measured using an atomic force microscope. The propagation losses of F8 waveguides with different F8 slab thicknesses were in good agreement with those calculated using an analytical expression for single-mode asymmetric waveguides with nanometer-roughness interfaces. The results presented herein will be useful for the design of high-performance organic lasers and organic optoelectronic integration systems.

Free Vibrations of Sustainable Laminated Veneer Lumber Slabs

In this paper, the results of dynamic laboratory tests of four laminated veneer lumber (LVL) slabs of different thicknesses, widths, and types were presented. In three of the tested slabs, LVL with all veneers glued lengthwise was used (LVL R). In one LVL slab, a fifth of the veneers were glued crosswise (LVL X). Laminated veneer lumber slabs are engineering wood products with several important performance characteristics, making them a sustainable and preferred solution in civil engineering. To ensure the safe operation of a building with LVL structural elements, it is important to know their dynamic properties. The basic dynamic characteristics of the slabs obtained from experimental tests made it possible to validate the numerical models of the slabs. The slab models were developed in the Abaqus program using the finite element method. The elastic and shear moduli of laminated veneer lumber used in the four slabs were identified through an optimization process in which the error between the analyzed frequencies from the laboratory tests and the numerical analyses was minimized. In the case of slabs that possess the same thickness and are composed of different LVL types, the elastic modulus of LVL R in the longitudinal direction was 1.16 times higher than the elastic modulus of LVL X in the same direction. However, the elastic moduli of LVL R in tangential and radial directions were lower than the elastic moduli of LVL X in the same directions. The above was the result of the fact that the 45 mm LVL X slab had 3 out of 15 veneers glued crosswise. In the case of slabs possessing different thicknesses but the same width and type, the elastic modulus of the thicker panel was 1.13 times higher than that of the thinner panel. After validating the models, the numerical analyses yielded results consistent with the experimental results. The numerical models of the LVL slabs will be used to develop numerical models of composite floors with LVL panels in future research. Such models will allow for the analysis of floor dynamic characteristics and user-generated vibrations, which is required when verifying the serviceability limit state.

Collisionless shock acceleration of protons in a plasma slab produced in a gas jet by the collision of two laser-driven hydrodynamic shockwaves

We have recently proposed a new technique of plasma tailoring by laser-driven hydrodynamic shockwaves generated on both sides of a gas jet [Marquès et al., Phys. Plasmas 28, 023103 (2021)]. In a continuation of this numerical work, we study experimentally the influence of the tailoring on proton acceleration driven by a high-intensity picosecond laser in three cases: without tailoring, by tailoring only the entrance side of the picosecond laser, and by tailoring both sides of the gas jet. Without tailoring, the acceleration is transverse to the laser axis, with a low-energy exponential spectrum, produced by Coulomb explosion. When the front side of the gas jet is tailored, a forward acceleration appears, which is significantly enhanced when both the front and back sides of the plasma are tailored. This forward acceleration produces higher-energy protons, with a peaked spectrum, and is in good agreement with the mechanism of collisionless shock acceleration (CSA). The spatiotemporal evolution of the plasma profile is characterized by optical shadowgraphy of a probe beam. The refraction and absorption of this beam are simulated by post-processing 3D hydrodynamic simulations of the plasma tailoring. Comparison with the experimental results allows estimation of the thickness and near-critical density of the plasma slab produced by tailoring both sides of the gas jet. These parameters are in good agreement with those required for CSA.

Slab Reinforcement Contributions to Negative Moment Strength of Reinforced Concrete T-Beam with High Strength Steel at Exterior Beam-Column Joints

Previous studies have revealed that the contribution of slab reinforcement to the T-beam flexural strength in negative moment regions are not negligible for the seismic capacity design. An effective slab width (i.e., effective width of flanged section) has been proposed, within which the slab reinforcement needs to be included in the calculation of the beam nominal flexural strength in negative moment regions. These studies mainly focused on the cases using normal-strength steel in moment resisting frames. However, recently high-strength steel has been widely used in reinforced concrete moment resisting frames in high seismic regions to avoid congestion near beam-column joints. The use of high-strength steel may affect the beam stiffness due to the fact that it will require less amount of reinforcement, and result in a different normal stress distribution compared to the case with normal-strength steel. Therefore, this paper investigates the slab reinforcement contribution to the flexural strength of the reinforced concrete T-beam designed with high-strength steel in negative moment regions at exterior beam-column joints, for which nonlinear pushover analyses were conducted. Beam reinforcement grade was considered as a primary parameter with several other design variables including slab thickness, height, and span length of the beam. Analytical results show that the use of high-strength steel can result in a wider effective slab width than the case of normal-strength steel for calculating the beam nominal flexural strength under the negative moment. Based on these results, new design equations were proposed.

Finite element investigation on the post-fire behavior of reinforced composite NSC-HPC slabs

Purpose Even though it is widely used, reinforced concrete (RC) is susceptible to damage from various environmental factors. The hazard of a fire attack is particularly severe because it may cause the whole structure to collapse. Furthermore, repairing and strengthening existing structures with high-performance concrete (HPC) has become essential from both technical and financial points of view. In particular, studying the postfire behavior of HPC with normal strength concrete substrate requires experimental and numerical investigations. Accordingly, this study aims to numerically investigate the post-fire behavior of reinforced composite RC slabs. Design/methodology/approach Consequently, in this study, a numerical analysis was carried out to ascertain the flexural behavior of simply supported RC slabs strengthened with HPC and exposed to a particularly high temperature of 600°C for 2 h. This behavior was investigated and analyzed in the presence of a number of parameters, such as HPC types (fiber-reinforced, 0.5% steel, polypropylene fibers [PPF], hybrid fibers), strengthening side (tension or compression), strengthening layer thickness, slab thickness, boundary conditions, reinforcement ratio and yield strength of reinforcement. Findings The results showed that traction-separation and full-bond models can achieve accuracy compared with experimental results. Also, the fiber type significantly affects the postfire performance of RC slab strengthened with HPC, where the inclusion of hybrid fiber recorded the highest ultimate load. While adding PPF to HPC showed a rapid decrease in the load-deflection curve after reaching the ultimate load. Originality/value The proposed model accurately predicted the thermomechanical behavior of RC slabs strengthened with HPC after being exposed to the fire regarding load-deflection response, crack pattern and failure mode. Moreover, the considered independent parametric variables significantly affect the composite slabs’ behavior.

Performance of Reinforced Concrete Flat Slabs Having GFRP Gratings

A thorough study of the literature indicated that there is not much relevant research on the application of GFRP gratings. Otherwise, extensive study has been done on FRP bars, laminates, sheets, strips, and rods. This study proposes a novel approach to improve the punching shear resistance of flat slab column connections by inserting GFRP gratings across the slab thickness. The results of seven specimens tested under vertical static loading are presented, considering the influence of the grating’s characteristics. All specimens were tested as simply supported slabs under one point of static loading. Experimental results, including crack patterns, slab deflection, concrete compressive strain, tensile steel strain, GFRP grating strain, and failure load, were recorded using extensive electric instrumentation. Test results revealed an enhancement in the failure load ranging between 9.03% and 27.67% for the specimens provided with the GFRP grating. In addition, a nonlinear finite element numerical model analysis was carried out using the ANSYS 15 program. Correlational studies based on the load-deflection response and crack patterns were utilized, resulting in a good agreement between numerical simulations and experimental results with differences ranging from 1.0% to 8.0%.

3D-printed stepped structure based on graphene-FeSiAl composites for broadband and wide-angle electromagnetic wave absorption

The design and preparation of absorbers with ultra-wide bandwidth and wide-angle absorption characteristics are crucial technologies for addressing electromagnetic (EM) pollution. In this paper, a stepped structure absorber was fabricated of graphene (GR)-FeSiAl/polylactic acid (PLA) composite by 3D printing technology. The absorber contains four layers, the bottom layer being a slab with periodic square holes, and the upper layer is a periodic distribution of three cubes with equal thickness and gradient changes in side length. It is shown that the stepped structure achieves a minimum reflection loss (RLmin) of −36.01 dB, with an effective absorption bandwidth (EAB, corresponding to the bandwidth of RL < −10 dB) of 12.75 GHz. These results were obtained when the unit cell had a side length of 22.5 mm, the slab thickness was 1.5 mm, and the cube had a thickness and edge length difference of 2.5 mm and 4.0 mm, respectively. Furthermore, the value of EAB is greater than 10 GHz for both transverse electric (TE) polarization and transverse magnetic (TM) polarization when the incident angle changes from 0° to 50°. The broadband and efficient EM wave (EMW) absorption characteristics of this absorber can be attributed to integration of excellent impedance matching and the multi-scale loss mechanisms.

Floor slab composite action effects on hysteresis behaviors of steel-framed-tube structures with shear links

The utilization of spandrel beams with a low span-to-depth ratio in a Steel-Framed Tube (SFT) structure can potentially diminish its ductility and energy dissipation characteristics. Conversely, integrating an SFT with end-plate-connected, replaceable low-yield-point steel shear links (SFT-RLYPSL) may significantly enhance its seismic response. This study introduces a prototype SFT-RLYPSL configuration designed to mitigate the premature separation of a reinforced concrete (RC) slab from the spandrel beams, a phenomenon observed in prior research. A series of finite element (FE) models were established, utilizing the prototype structure as a basis, to systematically investigate the impact of various parameters, including the presence and thickness of the RC slab, concrete strength, shear link length, and initial spandrel beam stiffness, on the cyclic behavior of an SFT-RLYPSL substructure module. Additionally, the failure mechanisms of the substructure module were assessed. The findings of this study reveal that the utilization of T-shaped connectors can effectively delay the pull-out of studs from the RC slab, especially under substantial vertical displacement of the spandrel beam. The initial elastic stiffness and load-carrying capacity of the substructure module can be significantly enhanced through the promotion of RC slab composite action. An optimal shear link length ratio falls within the range of 0.95 to 1.25, and given the assumption of LYP225 steel shear links with length ratios of 0.95 to 1.25 in the SFT-RLYPSL, the recommended minimum thickness and concrete grade for the RC slab, based on numerical simulation results, are 120 mm and C30, respectively. It is further recommended to employ C30 concrete for an RC slab with a thickness of 120 mm. Finally, a restoring force model is proposed, accurately reflecting the observed mechanical behaviors of the SFT-RLYPSL substructure module.

Photon tunneling mechanism of internal plasmon polaritons between two thick slabs under near-field radiation excitation

Internal plasmon polariton (IPP), featuring localization of electromagnetic fields in the interior of material, is recently revealed to be supported in slabs with gradient carrier density distribution under near-field thermal excitation. However, the dispersion relation and photon tunneling mechanism of IPP have not been fully elucidated. To address the issues, in this paper, we investigate the photon tunneling mechanism of IPPs both in the symmetric and asymmetric gradient systems of two thick slabs at the near-field configuration with thermal excitation. It is revealed that infinite modes of IPP are supported in the gradient slabs. The frequencies of these IPP modes are highly space-dependent. They poorly couple to each other and collectively contribute to the photon tunneling with respective trade-off wavevectors and tunneling probabilities. For asymmetric systems where the slab at one side is replaced by that of uniform carrier density, we find the resonance locking effect of IPP. Moreover, the photon tunneling spectrum can be tailored by the gradient layer and the vacuum gap sizes. The mechanism outlined here deepens our understanding of IPPs as well as offers guidance for the design of nanoscale devices with tunable carrier density.

Measurement and modelling of the moisture distribution in early-age concrete in the joint of composite beam and hollow core slab

The building moisture in concrete can damage the surface material if applied too early before the excess moisture has dried out. The composite beam forms an abnormal structure at the joint of the hollow-core slab, in which the thickness of the structural concrete is almost the thickness of the entire slab. For this reason, the joint of the beam and hollow core slab must be taken into account when assessing the adequate drying of concrete structures. The considered composite beams are steel casing beams, which are casted full of concrete. To achieve a composite structure, there are holes in the sides of the casing, through which moisture from the concrete transfers to the surrounding structure. However, the drying of the concrete inside the beam is significantly limited. The level of relative humidity of the concrete inside the beam remains moderately high for a long time, depending on the quality of the concrete and, consequently, the self-desiccation of the concrete. When using concrete with a low water binder ratio, drying occurs at a level of about 85%RH as a result of self-desiccation. In the study, relative humidity in the joint was measured continuously and with instantaneous measurements. The relative humidity in the joint concrete was also monitored after the surface structure layers were installed. In addition, humidity was measured from below the surface material and continued until equilibrium was reached. The structure was simulated as a 3D model and studied using a concrete material model which takes into account the self-desiccation and the thermal dependence of the sorption. A good agreement was found to describe the effect of temperature changes on the relative humidity of concrete that can be observed in continuous measurement. In addition, a suitable prediction of relative humidity below the surface material can be achieved based on modelled relative humidity distribution before the installation of the surface structure.

ANALISIS EVALUASI STRUKTUR GEDUNG SD UMMU AIMAN KECAMATAN LAWANG KABUPATEN MALANG MENGGUNAKAN METODE RANGKA MOMEN PEMIKUL KHUSUS

The increasing number of new students studying at SD Ummu Aiman has resulted in a shortage of space in the school building. Therefore, the addition of a new building is required to address this issue. However, the region of Indonesia, especially Java Island, is prone to earthquakes, making it necessary for all infrastructure development to consider earthquake resistance. SD Ummu Aiman's building is no exception, thus requiring special design and supervision to reduce the risk of losses due to earthquake loads that could affect the structure. This case study report will discuss the planning and design of a three-story building made of reinforced concrete for SD Ummu Aiman. In the preparation of this report, the emphasis will be on load analysis, SAP 2000 modeling, and reinforcement control analysis to understand the results of the preliminary structural design and analyze the reinforcement of beam structures using the special moment frame method. The results of the structural design include a 10 cm and 12 cm thick slab with main reinforcement of Æ8-100, the size of the main beams is 35/25 with main reinforcement of 2Æ16 2Æ14 and shear reinforcement of Æ8-150, 25/20 with main reinforcement of 2Æ16 2Æ14 and shear reinforcement of Æ8-120, and the size of secondary beams is 25/20 with main reinforcement of 3Æ25 2Æ25 and shear reinforcement of Æ8-200. The column size is 30/30 with main reinforcement of 4 D16 2 D12 and shear reinforcement of Æ8-150, and 25/25 with main reinforcement of 4 D12 and shear reinforcement of Æ8-150.

Relationship between non-destructive inspection and heavy-weight floor impact noises in a box-type test building

This study investigated the relationship between floor impact noise performance and non-destructive inspection methods for use in construction quality control prior to installing resilient floor-topping materials. The study measured floor impact noise characteristics using heavy-weight impact sources in a box-type test building with a 180-mm thick bare slab. The study employed impact echo and ultrasonic tomography methods to estimate concrete thickness and other mechanical properties. The results showed that the highest impact noise levels were observed at the central area in the frequency bands of 25 Hz to 50 Hz. However, the frequency bands of 63 Hz to 80 Hz showed different results as a peak characteristic at the middle area in the long direction. The study estimated the average slab thickness as 175 mm and 172 mm, respectively, using the impact echo and ultrasonic tomography methods. The standard deviation of the thickness was up to 9.3 mm and 6.6 mm, respectively, depending on the impact position. Furthermore, the study analyzed the correlation between concrete thickness and impact noise performance by frequency bands and discussed the application directions of the mechanical properties to manage noise performances during construction.

Performance of floor mats for heavy-weight impact noise reduction in a 210 mm-thick bare slab apartment houses

This study aims to understand the noise reduction performance of floor mats used to cover living room areas to reduce impact noise from children's jumping or walking. Several types of floor mat products, chosen based on their material and thickness, were selected from the market. The thickness of the mats ranged from 20 mm to 40 mm. The floor impact noise characteristics of a 210- mm thick bare slab in an actual apartment house were measured before and after the installation of the floor mat. The results showed that the highest noise reduction performance of up to 5 dB was observed when using a heavy-weight impact source with a bang machine. However, the highest noise reduction performance of up to 8 dB was observed when using a rubber ball as the heavy-weight impact source. The impact of a rubber ball dropped from a height of 40 cm, which simulates frequent living noise, resulted in a maximum reduction of up to 12 dB. In addition, the study discussed standardized methods for rating the heavy-weight impact noise performance of floor mats based on the measurement results.

Heavy-weight floor impact sound in the state of coupled vibration of floor slab and girder of a pure framed structure

Examples of poor heavy-weight floor impact sound insulation performance of pure framed structures with reinforced concrete were observed relative to the floor slab thickness. To investigate the cause of the poor performance, the floor vibration characteristics of actual pure framed structures were measured during heavy-weight impact. As a result, the floor vibration characteristics of the displacement of girders and the coupled vibration of the girders and floor slabs not seen in conventional floor structures surrounded by girders with reinforced concrete walls were observed. The propagation of the vibration of the floor slab was observed in more than the range surrounded by girders and in the next slab beyond the girders owing to the vibration of the girder itself. It was confirmed that these physical phenomena can be evaluated using a numerical calculation method. The effect of the changes in girder depth on the coupled vibration of the girder and floor slab was also investigated analytically. As a result, the coupled vibration of the girder and floor slab specific to pure framed structures that contribute to heavy-weight floor impact sound insulation performance was clarified physically.

A literature review of floor impact noise characteristics in wooden apartment buildings using cross-laminated timber slab

In this study, the floor impact noise characteristics of wooden apartment buildings made of cross-laminated timber (CLT) slabs were analyzed through a literature review. Data on heavy-weight impact noise performance was gathered, including information on floor components such as floor topping materials and ceiling finishes. The collected data was primarily analyzed in terms of CLT slab thickness. The results showed that 150 mm-thick bare CLT slabs had a single number rating of 70 to 77 dB when tested with a rubber ball, but this decreased to 64 dB for a 210 mm-thick bare slab. The addition of lower ceiling finishes and floor-topping materials could reduce the heavy-weight impact noise level to around 50 dB. However, results using a bang machine indicated 5 dB higher levels than those obtained with the rubber ball. The floor impact noise characteristics of CLT structures were also compared to those of concrete structures. The paper concludes by discussing directions for improving the floor impact noise isolation performance of CLT buildings.

Natural Frequency of Lightweight Composite Slabs Based on Experimental Study and Numerical Modelling

Recently, lightweight composite slabs have become increasingly popular. Lightweight composite slabs are an innovation that provides a better and more convenient construction method for floor systems. Under dynamic loads, lightweight composite slabs may experience meagre inertia forces due to poor stiffness or low mass. Compared to conventional composite slabs, lightweight composite slabs are 40% lighter and more susceptible to structural resonance. Therefore, the vibration behaviour must be controlled to avoid discomfort issues. This study investigates the natural frequency of lightweight composite slabs through experimental study and numerical modelling. In the experimental study, lightweight composite slabs were prepared for the hammer-impact test. The slab thickness ranges from 100 mm to 200 mm. In numerical modelling, lightweight composite slabs were modelled in SAP2000 using a unique technique called the simplified equivalent plate model. The effective material properties were derived from the rule of mixtures and depend exclusively on elastic properties with strength characteristics. The results of the experimental study and numerical modelling agree positively. The natural frequency decreased with slab thickness, signifying that the natural frequency is dominated by mass rather than stiffness. Overall, the natural frequency of lightweight composite slabs is around 27.23Hz to 31.45Hz.

Study on the relationship of design parameters and damage modes for RC slabs subjected to large-scale hard missile impacts base on task-driven approach

This study proposes a novel hybrid ensemble learning (EL) model that integrates CatBoost and SMOTE-NC algorithms to evaluate the damage modes of reinforced concrete (RC) slabs under large-scale hard missile impacts, overcoming the limitations of conventional approaches. To develop the optimization model, a database was constructed using publicly published experimental data from 304 large-scale missile impact tests conducted on RC plates. Furthermore, the SMOTE-NC oversampling algorithm is employed to optimize the database and address the issue of class imbalance. Subsequently, four ensemble machine learning models and empirical formulas are assessed. The findings indicate that the hybrid ensemble learning model combining CatBoost and SMOTE-NC exhibits superior performance, showcasing robustness and efficacy. Furthermore, through the application of SHAP analysis, it was revealed that velocity, thickness, concrete compressive strength, missile mass, reinforcement ratio, and missile diameter are the most influential variables, and they interact with each other in significant ways. Notably, the analysis indicated that once the concrete compressive strength reaches a certain value, further improvements may have a detrimental effect on penetration resistance. Additionally, the impact of yield strength on slab performance becomes more pronounced as the slab thickness decreases. Drawing upon these findings, a proposed approach for damage assessment and protection design utilizing an interpretable hybrid EL model was introduced. However, it is crucial to acknowledge that the applicability of this model is confined to RC targets with finite thickness, specifically engineered to withstand large-scale hard missile impacts.

Flexural performance of rectangular CFST composite T-beams: Experimental, numerical, and theoretical investigation

Steel-concrete composite beams find extensive application in bridge construction, offering adaptability to complex terrains and structural advantages. Nevertheless, a persistent challenge lies in local instability, especially in steel beams with large aspect ratios. This study proposes stirrup-confined concrete-filled steel tube (CFST) composite beams as a solution to enhance structural performance by mitigating local instability. The research comprises comparative tests, numerical simulations, and theoretical examinations of rectangular CFST composite beams. Results demonstrate a significant improvement, with a 40% increase in flexural stiffness and a 10% increase in ultimate bearing capacity compared to traditional composite beams. Stirrup confinement effectively limits cross-section slip between the steel tube and infilled concrete, resulting in slip measurements of 0.72 mm at the end of loading. Examination of aspect ratios reveals substantial enhancements, showing a 65.6% increase in flexural stiffness and a 54.7% increase in ultimate bearing capacity as aspect ratios increase. Concrete strength grade exhibits minor effects, with slight improvements as the grade increases. Steel yield strength significantly influences ultimate bearing capacity, with a maximum 24.4% increase in higher-strength steel. Moreover, the steel content ratio enhances both flexural stiffness (up to 40.2%) and ultimate bearing capacity (up to 34.6%) with an increased steel ratio. Increased concrete slab thickness leads to improvements of up to 18.3% in flexural stiffness and up to 10.1% in ultimate bearing capacity. Formulas for predicting the flexural stiffness and bearing capacity of rectangular CFST composite T-beams are developed, offering practical guidance for optimizing their performance in structural engineering applications.

Determination of critical collapse resistance of steel framed-structure: Fast manual calculation

This paper proposes a fast manual calculation method for determining the critical collapse resistance (CCR) of steel frame structures caused by an edge column loss. The critical collapse deformation (CCD) of the frame structure in an edge column loss is determined prior to calculating the CCR. Systematic parametric analysis is performed to examine the impacts of floor aspect ratio, slab rebar, slab thickness, beam depth, and beam span on the CCD of the frame structure. It is found that the CCD of the frame structure caused by the edge column loss can be determined by the beam depth, beam span and floor aspect ratio. When the beam span is increased by one beam depth, the CCD of the frame structure is increased by 0.2 times of the beam depth. The slab rebar and slab thickness have minimal effects on the CCD of the frame. When the rebar diameter and slab thickness are decreased by 50 % and 30 % respectively, the change of the CCD of the frame structure is within 10 %. A hardening factor is introduced to calculate the CCR of the frame in an edge column loss, defined as the ratio of the CCR to the yield resistance of the frame. Through more than 20,000 parametric analyses, it is found that the hardening factor can be determined by the normalized CCD (NCCD, the ratio of CCD to the yielding deformation) and the span-to-thickness ratio (STR) of the slab. For the STR of 40 and NCCD of 32, the hardening factor of the frame structure in an edge column loss is more than 3.0. A detailed process for calculating the CCR of the frame structure in an edge column loss is given. The results in the case study demonstrate that the error between the proposed method and the numerical analysis is within 10 %.