Stiffness Reduction Coefficient Research Articles

Experimental and numerical investigations on flexural behavior of stress-laminated timber-concrete composite decks with butt joints

Stress-laminated timber (SLT) products are increasingly used in the field of timber bridges. However, existing butt joints and significant vibrations of SLT greatly hinder its application. Allying a concrete slab on the top of an SLT deck to form a composite structure can effectively ameliorate these deficiencies. In this study, the flexural behavior of SLT-concrete composite decks (SCCD) was investigated via four-point bending tests. The test parameters include prestress level, butt joint frequency, and concrete slab thickness. Comparative analysis against the SLT deck revealed substantial improvements in the load-carrying capacity and initial bending stiffness of SCCD, with increases of 30.2 % and 86.2 %, respectively. Additionally, the improvement is more significant when the concrete slab thickness increases. The presence of butt joints reduces the structural performance of SCCD, and its stiffness reduction degree is slightly greater than that of the SLT deck at the same butt joint frequency. Furthermore, a finite element (FE) model for the SCCD was established, and the numerical simulation showed good agreement with the test results in terms of failure modes and bending performance. Finally, the bending stiffness reduction coefficient for the SCCD was recommended by considering various butt joint frequencies based on tests and numerical simulations, which can serve as a reference for practical engineering.

Transfer from defective bridge information model to defect analysis model based on industry foundation classes

Bridges, as an important part in modern infrastructure networks, suffer from increasingly severe aging issues in recent years. Road agencies and authorities conduct regular inspections for their bridges and identify defects and deteriorations for condition assessment. Such defect information cannot be efficiently used for analysis in the structural domain. This study proposes an Industry Foundation Classes-based method to allow for the transfer from a defective bridge information model to a defect analysis model. The architectural model of bridge is first converted into analytical model and then the impacts of defects on structural properties are quantified with a stiffness reduction coefficient. Case studies are conducted to validate the applicability of the proposed method for defect analysis and a range of coefficients are tested on an illustrative case bridge. The results prove that the proposed method can generate instructive and informative knowledge on the safety and reliability of the entire structure. This study narrows the gap between the empirical condition assessment scheme and the numerical structural analysis scheme for bridge management and manages to make full use of inspection-related information within Building Information Modelling (BIM) environment.

The influence of infill ALC walls on the seismic performance of prefabricated PEC T-column frames

Autoclaved lightweight concrete (ALC) is characterized by its light weight, high strength, fire resistance, and sound insulation, and has been widely used in industrial and civil construction. Partially encased concrete (PEC) columns exhibit good load-bearing performance, energy dissipation performance, and outstanding prefabrication performance. In order to study the influence of embedded prefabricated ALC wall panels on the seismic performance of assembled PEC T-shaped column frames, this study conducted low-cycle reversed loading tests on a two-story PEC T-shaped column pure frame and a two-story assembled PEC T-shaped column frame with ALC wall panels. This paper draws detailed comparisons between the failure modes and skeleton curves of the two frames. Analysis of the experimental results indicates that the stiffness contribution of infill walls is primarily affected by local compression and exhibits a negative correlation with the wall-frame lateral stiffness ratio. Furthermore, the presence of ALC walls can significantly increase the initial stiffness of the assembled frame. Therefore, based on the existing theoretical basis, a calculation model and method based on the interaction between infill wall panels and frames are proposed. The frame was numerically simulated using finite element software to study the factors affecting the initial stiffness of the frame, and a relationship formula for the wall stiffness reduction coefficient aw was obtained. The calculated lateral stiffness obtained from the formula was compared with the experimental results of this paper and other studies, proving that the model provides a safe result for the design and application of PEC T-shaped column frames filled with ALC walls, and can provide a reference for engineering practice.

Experimental Research on Fatigue Behavior of Reinforced UHPC-NC Composite Beams under Cyclic Loading.

Ultra-high-performance concrete (UHPC), a new cement-based material that offers high mechanical strength and good durability, has been widely applied in construction and rehabilitation projects in recent years. An optimum bending system is achieved by positioning the UHPC layer at the bottom tensile zone of the composite beam and placing the normal-strength concrete (NC) layer at the upper compression zone, which is described as the UHPC-NC composite beam. The fatigue behavior of reinforced UHPC-NC composite beams was described in this study, with an emphasis on the effects of UHPC layer thickness and fatigue load level on the fatigue life of the beam, deformation of the interface between UHPC and NC layers, as well as the bending stiffness of the beam. A total of 9 reinforced UHPC-NC composite beams were tested under cyclic loading. The test variables include UHPC layer thicknesses (zero, 200, and 360 mm), reinforcement ratios (1.184% and 1.786%), and the upper load levels (0.39~0.65). The results showed that good bonding had been achieved without delamination between UHPC and NC layers prior to the final fatigue failure of the beam, and the bending stiffness of the composite beam experienced a three-stage reduction under cyclic loading. Furthermore, an equation was proposed to predict the stiffness reduction coefficient of UHPC-NC composite beams under cyclic loading.

Corrosion initiation life and lateral bearing capacity of RC square piles considering different corrosion zones

This paper analyzes the differences in the corrosion initiation life and lateral bearing capacity of reinforced concrete (RC) square piles in different marine corrosion zones. A chloride diffusion model is presented by considering the effect of environmental factors on the chloride apparent diffusion coefficient. Different surface chloride concentration models in different corrosion zones are used to predict the corrosion initiation life of RC square piles. The time-dependent degradation law of bending stiffness of RC square piles in different marine corrosion zones is investigated. The lateral bearing capacity of RC square piles with different bending stiffness reductions in different corrosion zones is analyzed. The analysis results show that the corrosion initiation life of RC square piles decreases sequentially in the atmospheric zone, submerged zone, and tidal and splash zones. At the same exposure time, the stiffness reduction coefficient in the tidal and splash zones is the smallest, compared with atmospheric zone and submerged zone. The maximum lateral displacement, bending moment and negative shear force of RC square piles with variable stiffness are greater than those of invariable stiffness piles in different corrosion zones.

Simultaneous identification of impact force and structural local damage under pre-segmentation of structural elements

Identifying dynamic force and structural damage is often mathematically treated as an optimization problem. The number of optimization variables is closely related to the complexity and calculation amount of the identified problem. To reduce the number of optimization variables during the solution process and emphasize the localized characteristics of structural damage, a novel output-only method is proposed to address the problem of simultaneous identification under a pre-assumption of structural damage locations. The main idea is to decompose the identified problem into a series of subtasks. For each task, only part of a structure rather than the whole will be updated to reduce the discrepancy between the calculated responses and the measured ones. To realize this idea, the structure is simulated via a finite element (FE) model, and then the structural elements are divided into several groups. Each group is used to generate one identified task, in which the identified problem is formulated as a constrained optimization problem. Stiffness reduction coefficients of the elements, which are contained in the corresponding element group, are regarded as the optimization variables, while the impact force reconstructed via sparse regularization is mathematically formulated as a constraint for the optimization problem. The gradient descent method combined with a greedy strategy is introduced for solving the optimization problem of each task. The identified results obtained from all the tasks are regarded as candidates for a final one. To comprehensively consider the residual errors of structural responses and the sparsity of identified results, the Bayesian information criterion (BIC) is introduced for determining the final identified result. Numerical simulations and experimental studies are carried out. The illustrated results demonstrate that the proposed method is capable of simultaneously identifying the impact force and structural local damage, even though it still has shortcomings such as relatively poor robustness of identified damage and great subjectivity of group division for structural elements. Some relative issues are discussed as well.

Investigation on the Influence of Fiber Bundle Undulating Architecture on Tensile Behavior of Filament Wound Composite Laminates.

In filament wound composites, fiber bundles cross each other and form an undulating architecture, which may significantly affect the mechanical behavior of composites. In this study, the tensile mechanical behavior of filament wound laminates was studied experimentally and numerically, and the influences of the bundle thickness and winding angle on the mechanical behavior of the filament wound plates were also explored. In the experiments, tensile tests were carried out on filament wound plates and laminated plates. It was found that, compared to laminated plates, filament wound plates had lower stiffness, greater failure displacement, similar failure loads, and more obvious strain concentration areas. In numerical analysis, mesoscale finite element models, which take into account the fiber bundles' undulating morphology, were created. The numerical predictions correlated well with the experimental ones. Further numerical studies have shown that the stiffness reduction coefficient of filament wound plates with a winding angle of ±55° decreased from 0.78 to 0.74 as the bundle thickness increased from 0.4 mm to 0.8 mm. The stiffness reduction coefficients of filament wound plates with wound angles of ±15°, ±25°, and ±45° were 0.86, 0.83, and 0.8, respectively.

Research on Residual Bearing Capacity Calculation Method and Changing Law of Prestressed Concrete Box Girder with Damage

Due to the simple design and convenient construction of prestressed concrete box girder bridges, it is widely used in bridge construction in China. At present, the load test of bridge is the most direct and effective method to evaluate the actual bearing capacity of the structure. However, this method has barriers including high cost, long time, and unfriendly to the damaged structure. Besides, the calculation method of the ultimate bearing capacity of damaged structures is relatively subjective and uncertain. Therefore, this study combines the full-size model test results of a newly built 30 m prestressed concrete box girder, and the mechanical properties of the test beam under three different working states (elastic, elastic-plastic, and plastic stage) are obtained. The stiffness degradation and bearing capacity change law of precast prestressed concrete box girder during failure are investigated. Two different stiffness damage reduction coefficients are defined. Combined with the structural characteristics of this kind of precast prestressed concrete box girder and the calculation formula of flexural rigidity of cracked members given by the code, the calculation formula of the actual residual bearing capacity of members is proposed based on the stiffness damage reduction coefficient. The results show that the reduction coefficients of flexural stiffness defined by the two methods have the same variation trend. The stiffness reduction effect of the box girder after damage is evident. The stiffness reduction of the box girder from the cracking damage to the ultimate bearing capacity state is about 40%, and the stiffness reduction of the two adjacent sections can be approximately linear distribution. The deviation between the residual bearing capacity calculated based on the stiffness damage reduction coefficient and the test value is less than 5%. Combined with the distribution law of the stiffness reduction coefficient along the longitudinal section of the box girder, the distribution law of the actual residual bearing capacity along the longitudinal section of the box girder after the damage occurred in the midspan section can be calculated. This calculation method changes the previous assessment method of structural technical condition from qualitative assessment to quantitative assessment, which can be the reference for evaluating the technical condition of damaged bridges and the calculation of residual bearing capacity in engineering.

Modification of Segment Structure Calculation Theory and Development and Application of Integrated Software for a Shield Tunnel

From the aspect of calculation theory, the beam–spring model method and modified routine method of shield tunnel segment structure calculation were improved, and an efficient integrated software system for segment structure calculation of shield tunnel was developed. The beam–spring method is generally calculated according to the assumption of continuous displacement between beams and joints, and the existing modified routine method assumes that the lateral pressure gradient is constant generally, which does not consider the variation in lateral pressure gradient caused by the difference in the lateral pressure coefficient of soil layers or the water level height, which has a certain deviation from the actual situation. The existing beam–spring method and modified routine method theory were improved, the discontinuous displacement between beams and joints in the beam–spring method was taken into account, and the problem of lateral pressure gradient change in the modified routine method was solved. The calculation software system developed by C# and python programming language was proposed to improve the accuracy and efficiency of segment structure calculation. Based on the actual monitoring data of the internal force of the shield tunnel segment and the adjacent shield tunnel segments under construction in Changsha, China, the segments of the shield tunnel with different cross-section sizes and different hydrogeological conditions are calculated to verify the reliability of the calculation software system. At the same time, combined with the calculation results of the software system and field test data, the stiffness reduction coefficient and equivalent foundation resistance coefficient in the modified routine method were derived to further improve the accuracy of the calculation results, which provided a new idea for the calculation of segment structure of shield tunnel with different diameters under different hydrogeological conditions.

Double-Cell Prefabricated Utility Tunnel Composed of Groove-Shaped Elements: An Extended Study of Stiffness Reduction Method

Based on the semi-rigid characteristics of a double-cell prefabricated utility tunnel composed of groove-shaped elements (PUTCGE), this paper proposes an extended study of a stiffness reduction method for PUTCGEs by introducing the stiffness reduction and bending moment adjustment coefficients of the sidewalls. The effects of the joint stiffness ratio, the aspect ratio of width to height, the coefficient of subgrade reaction, and the embedment depth of the utility tunnel on the stiffness reduction and bending moment adjustment coefficients were investigated, and calculation formulas were established. The results showed that the stiffness reduction coefficient increased with the increase in the joint stiffness ratio, while the bending moment adjustment coefficient decreased with the increase in the joint stiffness ratio. The stiffness reduction coefficient increased with the decrease in the aspect ratio of width to height, while the effect of the aspect ratio of width to height on the bending moment adjustment coefficient was found to be very small. It was also found that neither the coefficient of subgrade reaction nor the embedment depth had a significant effect on the stiffness reduction and bending moment adjustment coefficients. The stiffness reduction method for the PUTCGE was validated through comparison with a full-scale physical model test. The proposed method can provide a reference for designing PUTCGEs for underground construction.

Dynamic analysis of multilayer-reinforced concrete frame structures based on NewMark-β method

Abstract The analysis method of the simplified structure formation model provides the basis for the analysis of the reinforced concrete (RC) structure under earthquake and dynamic load, which has important significance for seismic analysis of RC structure. In this paper, the three-layer RC frame structure is simulated and analyzed by MATLAB based on the NewMark-β method, considering the influence of time-varying simple harmonic loads and seismic waves on acceleration, displacement, and velocity of RC structure. The vibration response of the RC structure is analyzed by introducing the stiffness reduction coefficient. The results show that NewMark-β method provides a new idea for the seismic response of RC frame structures, making the seismic analysis of frame structures more practical; the variation range of its elastic modulus is obtained through the analysis of the constitutive model of RC, which provides the basis for the value of the stiffness coefficient; the application of the top load and the bottom load has different structural responses to the RC frame structure, and the impact of the load on the structure is more adverse when the load acts on the bottom; with the change of time, the binding stiffness coefficient will also change, and the stability of the structure will decrease greatly; the function relationship between the acceleration of the third floor and the reduction coefficient of rigidity is obtained by taking different values of the reduction coefficient of rigidity.

Nondimensionalized Bouc–Wen model with structural degradation for Kalman filter–based real-time monitoring

The Bouc–Wen model is one of the most widely accepted models for describing seismic hysteretic behavior owing to its versatility. However, in structural monitoring applications, implementing the Bouc–Wen model often causes an over-fitting problem because the phenomenological property includes redundant parameters. In this paper, the Bouc–Wen model is reexamined, and its nondimensionalized form is derived. The proposed nondimensionalized model describes hysteretic behavior with yield displacement, and the nondimensional hysteresis displacement is bounded between −1 and 1. In the proposed model, the dissipated energy is almost equivalent to the displacement per cycle and can be interpreted as the dissipation per an equivalent number of cycles. This interpretation enables us to assign a physical meaning to the degradation per cycle. The applicability of the proposed model was experimentally validated based on an unscented Kalman filter–based parameter identification technique. The identification results show that the nondimensionalized Bouc–Wen model can eliminate the over-fitting problem by converting one hysteresis variable into a variable that can be physically specified as the yield displacement. The convergence rate in estimating the strength and stiffness reduction coefficients was increased as a result of the proposed nondimensionalization.

Two-Stage Damage Detection of Beam Structure Based on Improved PSO Algorithm

In order to solve the problem of damage location and degree identification of beam structure under multiple damage and small damage condition, a two-stage recognition method based on the improved particle swarm optimization (PSO) algorithm was proposed. Firstly, the first stage damage localization is carried out. The D-S evidence theory fusion algorithm is used to fuse element damage variable and element stiffness reduction coefficient. Then, the improved PSO algorithm is used to update the location results and accurately quantify the damage. The results of simulation and experiment show that the two-stage recognition method can identify the damage locations and detect the damage extent precisely for multi-damage and small damage, and has the advantage of good anti-noise performance.

Stiffness Reduction Coefficient of Steel Plate-Reinforced Concrete Composite Coupling Beams

Stiffness Reduction Coefficient of Steel Plate-Reinforced Concrete Composite Coupling Beams

Assessment of Existing Bridge’s Beam Bending Stiffness Using Crack Characteristics

At present, the bearing capacity evaluation is mainly based on load detection, which requires closed traffic and has certain risks. With the increase of service time, the cracks of reinforced concrete beam bridge will gradually develop and the stiffness will reduce, resulting in the decrease of bearing capacity. Therefore, in this paper, the calculation of stiffness reduction coefficient by using crack characteristic parameters, which provides basic data for bearing capacity evaluation, has been studied. In this paper, using regression analysis through fracture characteristics of four model beam observation and test load-displacement curve characteristic parameters, crack flexural rigidity of the beam bridge relationship has been set up. The qualitative assessment based appearance of cracks in the structure of checks has been converted to quantitative assessment. And compared with the test results of a real bridge, comparative results show that the assessment is objective and reliable. It makes the assessment more objective and scientific. A new way of Quantitative assessment of the structural performance has been provided for a large number of existing reinforced concrete beam bridge.

Analysis of Stiffness Reduction Coefficient of Conventionally Reinforced Concrete Coupling Beams on the Bias of Strut-and-Tie Model

Stiffness reduction coefficient of coupling beams (κ) can reflect the stiffness degradation degree at yield and significantly affect the seismic response and the internal force distribution. However, existing calculation methods do not consider the influencing factors comprehensively and have a limited application scope. To effectively predict the stiffness reduction coefficient of conventionally reinforced concrete coupling beams (CCBs), a simplified analysis model was established, and analysis and parameter modification were also implemented. Then, an equation with comprehensive consideration, wide application, and high accuracy was proposed. The proposed equation was verified by comparison with existing test data and calculation methods, and parametric analysis was performed to investigate the independent factors, including the span–depth ratio, longitudinal reinforcement ratio, stirrup ratio and concrete compressive strength. Results show that the independent factors are related to each other, and the span–depth ratio has the greatest influence on the stiffness reduction coefficient of CCBs. Furthermore, κ significantly increases with the longitudinal reinforcement ratio when the coupling beam has a large span–depth ratio, but the stirrup ratio has a bigger role when the span-depth ratio is small. Finally, on the basis of the analysis results, suggestions are made to improve the stiffness reduction coefficient of CCBs. The study results provide a reference for the design and optimization of shear wall and core tube structures.

Seismic Reliability of Concrete Buildings considering Probabilistic Distribution of Crack

One of the effective factors in the analysis of concrete structures is consideration of the effect of cracking on the structural elements, which directly affects the calculation of the natural periods, the story displacement and other response parameters. In different codes for design of concrete structures, cracking effect is considered as a mean and constant coefficient for each element, while clearly the condition of various components will be different based on loading situation and specifications. In this paper, reliability of stiffness reduction coefficients of the beams and columns due to cracking of concrete in the ACI code is investigated under random distribution of floor live loads using Monte Carlo simulation method, By considering 1,000 modelling loops, calculating accurate crack coefficients of beams and columns and applying them in each model, the reliability of cracking coefficients has been obtained. The results show that the reliability index of these coefficients is very low. Also, other results of this modeling and applying accurate cracking coefficients show that the story displacements and the time period of first and second modes decrease about 40–55% and 20–30%, respectively, and the reaction forces of the elements, especially the axial and torsional forces increase about 20–30%.

Transverse inhomogeneity of laminated cylindrical panel influence on post-buckling behaviour

The present paper concerns the influence of transverse heterogeneity caused by layer stacking sequence in laminated cylindrical panels under compression on their stability and post-buckling behaviour. According to the classical laminated plate theory (CLPT) this inhomogeneity causes not trivial coupling matrix B terms. A method of the modal solution to the nonlinear buckling problem within Koiter’s asymptotic theory, using the semi-analytical method (SAM) and the transition matrix method, was applied in the analysis. Post-buckling behaviour of laminated shallow cylindrical panel within the first- and second-order non-linear approximation were determined when the coupling matrix B was included or neglected. Additionally for model 1D the dimensionless stiffness reduction coefficient values were estimated which already in the phase of composite structure design process makes it easier to assess the influence of coupling matrix on stability. Just like in the case of plate elements, when the value of these coefficients is close to 1, the effect of couplings on stability is negligible. If the value of these coefficients is significantly less than 1, then the effect of the coupling matrix terms on stability increases.

Seismic response of tunnel lining structure in a thick expansive soil stratum

The seismic response of a tunnel lining structure is essential for its safety design and construction. The objective of this study is to investigate the seismic response of a tunnel lining structure embedded in a thick expansive soil stratum. First, the deformation and internal force characteristics of tunnel lining structure under seismic action are evaluated from a theoretical perspective. Second, a finite element (FE) analysis is carried out of the seismic responses of the tunnel lining structure and ground stratum. In the FE analysis, the bolted connections in the tunnel lining structure are simulated using the local stiffness reduction method (LSRM). The LSRM reduces the stiffness of the lining segments affected directly by the bolted connections using a stiffness reduction coefficient (SRC), while leaves the stiffness of the rest of the lining segments to remain to be unchanged. The results indicate that under the effect of transversal waves propagating in the direction perpendicular to tunnel axis, the transversal displacement characteristics of the tunnel lining structure are almost identical to that of the surrounding soil stratum. They both decrease with an increase in buried depth. The circumferential distributions of shear force, bending moment, and axial force in lining segments are varied, but the magnitudes of them increase with an increase in SRC.

Non-linear stability and load-carrying capacity of thin-walled laminated columns in aspects of coupled buckling and coupled stiffness submatrix

To assess a load-carrying capacity of compressed thin-walled plate structures in the paper the coupling buckling phenomenon of compressed columns was analyzed. The columns were of open cross-sections and made of coupled laminate. Selected configuration of laminate layers enables different types of coupling between membrane and bending states which describes the coupling stiffness submatrix B. Element values of stiffness matrix ABD were determined with application of classical laminate plate theory CLPT.The main aim of the work is to estimate an influence of chosen submatrix B elements on buckling, postbuckling and load-carrying capacity of analyzed thin-walled structures. The problem was solved with the Koiter’s theory application. The detailed computations were performed for uniformly compressed lip channel and top hat channel. The dimensions of both columns were chosen in a way which allowed to observe the strong coupling effect among different buckling modes. It were two laminate configurations considered which differed in value of stiffness reduction coefficients.