Stiffness Reduction Factor Research Articles

Evaluation of two crack models for reinforced concrete one-way slabs subjected to bending by means of modal tests

Cracks can affect a reinforced concrete (RC) structure and the evaluation of damage related to them is a typical application of structural health monitoring systems. This way, two RC one-way slabs with different reinforcement ratios were tested in laboratory in a four-line static load test scheme, followed by modal testing. Using modal testing data, finite element models of the cracked structures were prepared and calibrated for several cracked stages, to evaluate which crack model would present a better performance when compared to the experimental counterparts. Cracks were simulated via a reduction of flexural stiffness by penalizing the elastic modulus. Two continuous crack models were evaluated: Model 1 which employs reduction factors based on the ratio of moment of inertia after the cracking moment is reached and the moment of inertia of the uncracked section; Model 2 which is based on the stiffness reduction in the region of influence of each crack. The evaluation of both models was made using natural frequencies and mode shapes (through Modal Assurance Criterion-MAC indicator) as indicators, and Model 2 presented better results. An additional approach to globally reduce stiffness in the early stages of load before visible cracks appear and also in uncracked regions was shown necessary, to take into account the reductions on natural frequencies observed in the tests. By employing the stiffness reduction factors obtained for Model 2 it was possible to evaluate the crack depth evolution along the load stages.

Effect of Stress Anisotropy on the Efficiency of Large-Scale Destress Blasting

Large-scale panel destressing is a rockburst control technique that is used to create a stress shadow in the ore pillar to be mined. The technique aims to reduce the pillar burst proneness by deviating the major induced principal stresses away from the concerned zone of interest. The destress panels, situated in the pillar hanging wall, are choke-blasted with high explosive energy density, and the blast-induced damage in the panel is accompanied by stress dissipation and stiffness reduction due to fragmentation in the panel. These two effects are traditionally modeled holistically with stiffness and stress reduction factors α and β, respectively, applied to the destressed zone. This paper focuses on the interpretation of Phase 3 destress blasting results at Copper Cliff Mine (CCM) where a stress increase (rather than decrease) was detected in the ore pillar crown, while a stress decrease was recorded in the ore pillar sill (as expected). It is hypothesized that high mining-induced stress anisotropy in the pillar crown caused blast-induced fractures to propagate in the orientation of the major principal stress, a condition that would hinder the destressing effect in that orientation. To verify the hypothesis, a series of panel anisotropic rock fragmentation and stress dissipation factors are iteratively tested in a 3-dimensional back analysis of the Phase 3 destress blast. The analysis takes into consideration the stope extraction schedule per the mine plan to better replicate the mining-induced stress condition in the panel and the ore pillar. The results show good agreement with stress measurements taken in situ using borehole stress cells installed in the ore pillar prior to destressing. The paper discusses the implications of preferential fracture propagation orientation and how it might affect the efficiency of destress blasting.

Flexural stiffness reduction for stainless steel SHS and RHS members prone to local buckling

In this paper, flexural stiffness reduction factor formulations, applicable to stainless steel members with compact cold-formed square and rectangular hollow section (SHS and RHS), are extended to account for local buckling effects and initial localized imperfection (ω). Local buckling effects and the influence of ω are accounted for by means of reducing the gross section resistance using a strength reduction factor ρ. ρ, determined by the Direct Analysis Method, depending on cross-section slenderness, is adopted. For in-plane stainless steel elements with non-compact and slender sections, results determined by the extended flexural stiffness reduction factor coupled with Geometrically Nonlinear Analysis (GNA) are verified against those determined by Geometrically and Materially Nonlinear Analysis with Imperfections (GMNIA). It is found that GNA with the extended flexural stiffness reduction factor (using beam element) generally achieves the accuracy of GMNIA (using shell element). Probabilistic studies based on 3D models with random ω are carried out to evaluate the effect of uncertainty in ω on the accuracy of GNA with the extended beam-column flexural stiffness reduction factor.

Local Delaminations Induced by Interaction Between Intralaminar Cracking and Specimen Edge in Quasi-Isotropic CF/EP NCF Composites in Fatigue Loadings

Experimental results are presented on the onset and propagation of local delaminations caused by the interaction between specimen edges and intralaminar cracks in fiber bundles of 90° layers in quasi-isotropic [–45/90/45/0]s CF/EP noncrimp fabric (NCF) laminates subjected to tension-tension fatigue loadings. It is confirmed that the first damage mode is intralaminar cracking in 90° layers, which consists of intrabundle cracks and cracks in the matrix between bundles (often beginning from stitches). This damage mode triggers cracking in off-axis layers and local delaminations in positions where the 90° layer crack meets an adjacent layer. The process of local delamination is significantly enhanced at specimen edges, where the out-of-plane edge stresses contribute to the local delamination. During cyclic loadings, delaminations grow and coalesce along the edge and propagate towards the specimen center. These processes are quantified experimentally at different levels of cyclic load. In a low-stress fatigue, a very high number of cycles is required to detect small edge delaminations, and they stay at the edge. In high-stress cyclic tests, delaminations grow faster inside the composite: about 20% of the interface in the central zone can be delaminated. It is found that the reduction in the axial modulus is proportional to the relative delaminated area, proving that delamination is the major stiffness reduction factor in these laminates.

Experimental Investigation on the Force-Crack Quantification Model for HSRC Columns with Flexure\u2013Shear and Shear Failure Modes

A total of six full-scale high strength reinforced concrete (HSRC) columns were tested under axial and cyclic lateral loading. The specified concrete compressive strength was 70 MPa and the specified yield strength was 685 MPa and 785 MPa for the longitudinal and transverse reinforcements, respectively. The main variables considered in the study are the transverse reinforcements ratio and axial load ratio. Although such HSRC columns have gradually transformed in use and scope, the damage assessment method is less understood. The main purpose of this study is to propose a damage assessment model for HSRC columns. An analytical backbone curve model for predicting force–deformation behavior of HSRC columns is described. Column stiffness is also measured from the experiment to obtain stiffness reduction factors that are necessary to calculate member deformation. Based on experiment results, a new limiting value of residual crack width is defined to determine damage level. This study uses specified residual crack width of 0.15 mm, 0.30 mm, and 1.00 mm in the damage assessment model. The new limiting value of residual crack width is also used to determine the performance points of structural members. Finally, a new drift ratio limit of each damage level is also proposed. Experiment results are presented and used to investigate the application of the proposed damage assessment model.

Damage identification using time series analysis and sparse regularization

Time series models have been popularly used in structural damage identification because the model coefficients and residual errors are sensitive to structural damages. As the direct relationship between the time series model coefficients (or residual errors) and damage severity is hard to be established, these methods provide limited information about the location or severity of damage. This study theoretically derives the sensitivity of the autoregressive coefficients of autoregressive moving average model to structural stiffness reduction factors. The autoregressive coefficients of both the damaged structure and the undamaged structure are extracted for damage identification. Structural damage identification is an inverse problem, and an underdetermined set of equations is a common obstacle encountered in solving such problem. Afterwards, sparse regularization is used to solve the underdetermined set of equations. The location and severity of damage is identified using the solution. The effectiveness of the proposed method is verified through a laboratory test of a cantilever beam and the Experimental Phase II IASC-ASCE benchmark structure. In addition, the proposed time series analysis-based method is promising to be used in online structural health monitoring systems.

Advancements in the stability design of steel frames considering general non‐prismatic members

AbstractThis paper discusses an innovative approach to the design of planar steel frames composed of prismatic and/or non‐prismatic members. The method evaluates the member stability limit states using an inelastic eigenvalue buckling analysis configured with column, beam and beam‐column inelastic stiffness reduction factors derived from the ANSI/AISC 360‐16 Specification. The resulting procedure provides a relatively rigorous evaluation of all member strength limits accounting for moment and axial force variations along the member lengths, non‐prismatic geometry effects, general out‐of‐plane bracing conditions and beneficial end restraint from less‐critical adjacent, unbraced segments and/or from end conditions. The approach uses a geometric non‐linear pre‐buckling analysis based on the AISC direct analysis method to estimate the in‐plane internal forces. Given these forces, an eigenvalue buckling solution is conducted to evaluate the overall member stability. Other limit states are addressed through cross‐section strength checks using the internal forces determined from the geometric non‐linear load‐displacement analysis. Calculations using this approach are compared with results from recent experimental tests.

Geometrically non-linear analysis with stiffness reduction for the stability design of stainless steel structures: Application to members and planar frames

This paper focuses on the development of beam-column flexural stiffness reduction factor (τMN) applicable to the in-plane stability design of stainless steel beam-columns and frames with compact cold-formed square and rectangular hollow sections. The proposed τMN accounts for the deleterious influence of material non-linearity, residual stresses and member out-of-straightness. The use of a Geometrically Non-linear Analysis (GNA) with the proposed τMN eliminates the need for member buckling strength checks and thus, only cross-sectional strength checks are required. The proposed approach, aligned to AISC standards, is aimed at facilitating greater and more efficient use of stainless steel. Two types of τMN are proposed: analytical and approximate. The analytical τMN presumes knowing the maximum internal second order moment (Mr2) within a member. It is developed by means of extending the formulations for evaluating the elastic second order effects to the inelastic range. The accuracy of the analytical τMN is verified for beam-columns and sub-assemblages. Since in practical design Mr2 is not known in advance, an approximate expression of τMN, which is more likely to be used relative to the analytical τMN, is proposed by fitting variables to the analytically determined MN. The accuracy of the approximate τMN is verified for frames with different geometrical and loading configurations. Furthermore, the proposed approach is compared against the Direct Analysis Method (DM). Results show that, compared to the DM, GNA coupled with the approximate τMN provides improved estimations, since the proposed τMN can more accurately capture stiffness reduction resulted from material non-linearity and well capture additional second order effects due to material non-linearity.

Relationship between Corrosion of Reinforcement and Surface Cracking Width in Concrete

The durability of structure cannot be guaranteed when a corrosion expansion crack reaches the surface of the reinforced concrete member. In this paper, firstly, based on the existing theoretical model of steel corrosion degree, the calculation process of the model and the determination of the relevant parameters in the model were analyzed and discussed. Secondly, the stiffness reduction factor of concrete in the model was calculated according to the existing experimental data, and the engineering formula of the steel corrosion degree was established, which was related to the surface crack width of reinforced concrete. Moreover, the experiments of steel bar corrosion were carried out with different components of surface crack width, in which the parameters of the bar diameter, concrete protection layer thickness, and water‐cement ratio were taken into consideration. The experimental phenomena and results were further analyzed and discussed. Finally, comparing with the experimental data, the engineering formula presented in the paper was validated. The results show that the calculated values by the engineering formula are in better agreement with the experimental values than those by the existing model, which provide a theoretical basis for further study on the durability limit state of the structure.

Damage identification of a reinforced concrete frame at increasing damage levels by sensitivity-based finite element model updating

This paper presents the damage identification results of an experimentally tested half-scale reinforced concrete portal frame using the sensitivity-based finite element model updating method. Progressively increasing story drifts are imposed on the frame by a displacement-controlled hydraulic actuator using single-cycle quasi-static lateral loading along the frame’s in-plane direction. System identification is performed using an output-only system identification method at different damage levels. Dynamic tests used for system identification are conducted using an electro-dynamic shaker. The objective function used for damage identification is constructed by the difference between the experimentally identified and numerically predicted modal parameters. Damage identification is performed in two steps: (1) The initial numerical model is updated to obtain a reference model using the modal parameters corresponding to the undamaged frame and (2) the reference model is updated for increasing damage levels using the modal parameters corresponding to these levels to identify existence of damage, its location and extent. The condition of the optimization problem is improved by reducing the number of design parameters. Damage identification results are presented in terms of stiffness reduction factors assigned to the column(s) bottom and beam ends and they correlate very well with the visual damage inspections done during the quasi-static tests.

Study on the application of post-embedded piezoceramic transducers for crack detection on earthquake-damaged RC columns

In this study, the post-embedded piezoceramic transducers are used to perform structural health monitoring (SHM) and detect crack damage on the reinforced concrete (RC) column. The piezoceramic transducers are utilized as actuators and sensors, respectively. To investigate the use of the piezoceramic transducer in detecting crack damage in RC columns, SHM tests are performed on three full-size RC column specimens with various failure modes under cyclic loading. The sensors are installed at two depth ranges (40–50 and 70–80 mm) beneath the surface of the column to investigate the effect of the sensor depth on the damage index. In this study, the energy and amplitude-based damage indexes are developed. Both approaches follow the same trend under various drift ratios of the specimen. However, the value of energy-based damage index is much higher than the amplitude index for all peak drift ratio of the specimen. From different depth range of piezoceramic transducers, this study recommends a depth of 80 mm as optimal for post-embedded piezoceramic transducers, since it receive more stable signals in various frequencies. In the proposed health monitoring approach using piezoceramic transducers, the equation to predict the maximum residual crack width and damage index smart aggregates are developed. The normalized damage index equation which in this study is referred as ‘crack damage index’ is introduced and used to calculate the limiting value for each damage level. The suggested value of the crack damage index for each damage level is also provided. The energy, strength and stiffness reduction factors for each damage level, which correlate with the crack damage index, are also presented. These results demonstrate that the proposed post-embedded piezoceramic transducers has the potential to be used as a tool for SHM on an RC column.

Effect of Construction Type on Structural Behaviour of R.C Bubbled One-Way Slab

Using Bubbles in the slab is a revolutionary method of eliminating concrete from the middle of conventional slab as this concrete does not perform any structural function, thereby dramatically reducing structural dead weight. This research presents experimental study to investigate the effect of construction type on the strength and behaviour of bubbled one-way slabs. The experimental program consists of testing four slabs with dimensions of 1850mm×460mm×110 mm. One1of the tested slabs was conventional slab (without bubbles), two bubbled slabs with different types of construction (simple and filigree bubbled slabs) and the remaining one is filigree bubbled slab strengthened with steel cage. The bubbles were made of recycled plastic balls. The experimental results show that the stiffness reduction factor for all the bubbled slabs was (0.87), this leads to decrease the ultimate strength of bubbled slabs and to be smaller than that of the solid slab by 4.4% 69% and 1.7% respectively. Also an increase in deflection at yield load (∆y) by about (10% to 12%), at the same time the crack load is found to be decreased by (13% to 40%). The simple bubbled slab is more efficient when compared with filigree bubbled slab. Also the results show that the use of steel cage in filigree bubbled slab gives an increase in the ultimate load by 69% and an increase in the ultimate deflection by about 77% when compared with filigree bubbled slab without steel cage.

Research on Damage Identification of Grid Structure Based on Genetic Algorithm

This paper proposes a genetic algorithm based damage identification method for grid structures. The genetic algorithm is used to process the modal information of the structure, and the damage identification of the truss structure is carried out. The stiffness reduction factor of the structural member is used as the optimization variable. The objective function is constructed according to the frequency and vibration mode, and the fitness function is established. The binary coding method is used to improve the crossover and mutation operators. In this paper, a grid structure model is used for numerical simulation analysis and verified by experiments. In the experimental stage, the grid structure is excited by hammering method, and the response data of each node and the modal information of the structure are obtained. Numerical simulation and experimental analysis show that the damage identification method based on genetic algorithm can effectively judge the location and extent of damage.

Monotonic and cyclic performance of threaded reinforcement splices

This paper examines the fundamental uniaxial monotonic and cyclic response of reinforcement bars connected with threaded mechanical couplers. Based on a survey of available splicing forms, two types of threaded couplers with different geometric configurations, namely ‘parallel threaded couplers’ and ‘parallel threaded sleeve couplers’ are selected for detailed assessment. An experimental study consisting of twenty-four bare (in-air) and embedded (in-concrete) specimens incorporating threaded couplers and non-spliced counterparts, is described. The results enable direct assessment of strength as well as complete deformation characteristics, including the post-cracking and post-yield response, for both monotonic and cyclic conditions. After describing the material properties and specimen details, the main observations are reported based on detailed measurements of crack kinematics including crack width and spacing through a digital image correlation system. Complementary numerical studies, undertaken using nonlinear finite element procedures which are validated against the tests, enabled supplementary parametric investigations accounting for wider ranges of coupler geometries. The findings show that existing guidelines may be used for assessing the crack width and spacing, by accounting for the characteristic bond behaviour at the rebar and coupler regions. The complete deformational response may be obtained by using a suggested stiffness reduction factor that depends on the coupler geometry. Several ‘in-air’ performance parameters may also be used as a basis for the selection and implementation of couplers in applications requiring ductile member behaviour.

Combining interface damage and friction in cohesive interface models using an energy based approach

Cohesive zone models coupling interface damage and friction have been developed in the literature and are available in the commercial finite element package ABAQUS to consider the enhancing effect of through-thickness compression on interfacial fracture resistance. It is revealed in this paper that these models are extremely dependent on interface stiffness, because interface stiffness reduction factor is used to combine damage and friction in these models. The interfacial constitutive law converges but only when the interface is extremely stiff and an unrealistic evolution of the interface damage is produced. A new approach is then developed which uses a cohesive energy related parameter to combine interface damage and friction. The behaviour of the new coupled model is independent of the interface stiffness once the interface is moderately stiff. The new and existing damage/friction coupled models have been employed to simulate the shear failure of a composite specimen and the predictions are compared against the experimental data in the literature. The new model produces converged results over a wide range of interface stiffness and the predictions match the experiments quite well, better than the existing models.

Assessment of I-Section Member LTB Resistances Considering Experimental Test Data and Practical Inelastic Buckling Design Calculations

The current AASHTO and AISC Specification equations characterizing the lateral-torsional buckling (LTB) resistance of steel I-section members are the same, with minor exceptions, and are based in large part on unified provisions calibrated to experimental data. This paper takes a fresh look at the correlation of the flexural strength predictions from these equations with a large experimental data set compiled from research worldwide. To account fully for the moment gradient and end restraint effects present in the physical tests, the study employs practical buckling calculations using inelastic stiffness reduction factors (SRFs) based on the design resistance equations. The study focuses on uniform bending tests as well as moment gradient tests in which the transverse loads are applied at braced locations. Reliability indices are estimated in the context of building design. It is shown that a proposed modified form of the current resistance equations provides a more uniform level of reliability, as a function of the LTB slenderness, consistent with the target intended in the AISC Specification. The paper also calls attention to the limited experimental data pertaining to the inelastic LTB resistances in certain cases. The paper concludes by providing additional recommendations for LTB strength calculations in routine design, including illustrative plots conveying the impact of the proposed changes.

Experimental Assessment of Retrofitting RC Moment Resisting Frames with ADAS and TADAS Yielding Dampers

Due to the lack of sufficient concrete strength or change in design codes, some RC structures are in need of retrofitting. Retrofitting and reevaluating a building is only possible if the seismic characteristics of the new hybrid seismic system are specified. This study attempts to experimentally investigate the effect of using the Chevron brace with ADAS and TADAS yielding dampers in retrofitting RC moment resisting frames. Seven RC moment resisting frames were constructed and six of which were retrofitted with Chevron braces and a different number of ADAS or TADAS yielding dampers. The frames were subjected to cyclic loading and strength, crack expansion, stiffness, ductility, energy dissipation, and strength reduction factor of all the frames were evaluated. The results show that the yielding dampers not only increase the strength of the RC frame, they also elevate its strength reduction factor and ductility. The effect of the ADAS damper is better than the TADAS damper and in both cases, pinching in the hysteresis diagram has considerably decreased.

Unified equivalent frame method for post-tensioned flat plate slab structures

The post-tensioned (PT) flat plate slab system is commonly used in practice, and this simple and fast construction method is also considered to be a very efficient method because it can provide excellent deflection and crack control performance under a service load condition and consequently can be advantageous when applying to long-span structures. However, a detailed design guideline for evaluating the lateral behavior of the PT flat plate slab system is not available in current design codes. Thus, typical design methods used for conventional reinforced concrete (RC) flat plate slab structures have inevitably been adopted in practice for the lateral load design of PT flat plate structures. In the authors\' previous studies, the unified equivalent frame method (UEFM) was proposed, which considers the combined effect of gravity and lateral loads for the lateral behavior analysis of RC flat plate slab structures. The aim of this study is to extend the concept of the UEFM to the lateral analysis of PT flat plate slab structures. In addition, the stiffness reduction factors of torsional members on interior and exterior equivalent frames were newly introduced considering the effect of post-tensioning. Test results of various PT flat plate slab-column connection specimens were collected from literature, and compared to the analysis results estimated by the extended UEFM.

An application of finite element model updating for damage assessment of a two-story reinforced concrete building and comparison with lidar

This article investigates the performance of finite element model updating to identify the induced damage in a two-story reinforced concrete masonry-infilled building using vibration data as well as lidar (light detection and ranging) scans. The building, located in El Centro, California, was severely damaged due to the 2010 El Mayor–Cucapah (Baja California, Mexico) Earthquake, and it was planned to be demolished following a number of ambient and forced vibration tests. The forced vibration tests were performed using an eccentric mass shaker. During the testing sequence, damage was induced to the building by removing four exterior walls. The modal parameters of the structure are estimated using the ambient vibration and forced vibration measurements at the reference state and damaged state. Lidar data are also used to detect surface defects and quantify the temporal changes of surface defects caused by the wall removal and forced vibration tests. Based on site inspections, geometry measurements, and material test data, two initial finite element models are built, namely the un-tuned initial model and the tuned initial model. The tuned initial model implements stiffness reduction factors to account for the observed damage in the building at its reference state while the un-tuned model does not. Two sets of reference models are calibrated to represent the structure at the reference state using the un-tuned and tuned initial models. The reference models are then updated to fit the measured data at the damaged state of the building with damage being estimated as the loss of stiffness in updating substructures. The estimated damage is compared to the nominal value of induced damage and surface defects detected by lidar scans. The analysis of the results indicates that the un-tuned and tuned initial models provide similar updated models and damage identification results which are in good agreement with the nominal values of damage and lidar detection results.

Elevated temperature material behaviour of high-strength steel

This paper presents an experimental investigation into the behaviour of high-strength steel (HSS) structures (i.e. yield strength between 460 and 700 N/mm2) in fire conditions. The paper proceeds with a description of the experimental programme that includes two different grades of HSS with the aim of assessing (a) the mechanical properties at elevated temperature through tensile testing and (b) the effect of chemical composition and processing route on the microstructure through a detailed metallurgical investigation. The investigation takes a holistic view of the analysis whereby the effect of processing route and composition on the microstructure and hence mechanical properties are assessed. In this paper, following a detailed description of the tests under isothermal conditions, the results are analysed to determine strength and stiffness reduction factors at elevated temperatures and these values are compared with the literature and design standards.