Simplified Bilinear Model Research Articles

Failure prediction of butterfly-shaped steel plate shear keys under cyclic loadings

A novel energy dissipation shear key (BSP shear key) is proposed using multiple butterfly-shaped steel plates arranged in parallel for small-to-medium-span highway bridges. Two series of quasi-static experiments have been conducted to investigate the influence of loading protocols on the energy dissipation behavior of the BSP shear keys. Based on the test results, a simplified bilinear model is developed to represent the force-displacement skeleton curves of the BSP shear keys subjected to different loading protocols. And the force-displacement hysteretic curve of the BSP shear keys is decomposed into the skeleton part and the Bauschinger one. The energy dissipation capacity of the BSP shear keys can then be approximately calculated by adding the energies dissipated by the two parts respectively. The energy dissipation of the skeleton part can be determined using the simplified bilinear model and the one of the Bauschinger part is derived according to the loading protocols. The calculated energy dissipation capacity of the BSP shear key specimens can be validated by the test results with the maximum error of 13.9%. Finally, a flowchart is proposed to predict the failure of the BSP shear keys based on their energy dissipation capacity under cyclic loadings. The prediction results indicate that the proposed flowchart can capture with a satisfactory accuracy the failure of the BSP shear keys due to their energy dissipation capacity being exhausted. This study demonstrates that the failure prediction is feasible based on the energy dissipation capacity of the BSP shear keys.

Experimental investigation on the fracture properties of concrete under different exposure conditions

The fracture properties of concrete subjected to sulphate attack are investigated. First, concrete beams were subjected to different exposure conditions, i.e., full immersion, partial immersion and dry-wet cycling, for 90, 180 and 270 days, and a subsequent three-point bending test was conducted. A softening constitutive relationship of concrete was then derived and a simplified bilinear model was proposed for different exposure conditions. Finally, a chemical titration test was conducted to obtain the profiles of sulphate ion contents along the depth of concrete. The results indicate that, when concrete is subjected to different exposure conditions, the initial fracture toughness increases but the unstable fracture toughness decreases with the exposure duration. The stress-free crack opening displacement in the simplified bilinear model decreases significantly, indicating that concrete attacked by sulphate becomes more brittle. In addition, the sulphate ion content decreases rapidly along the depth and the sulphate ion content in concrete under dry-wet cycling is obviously higher than those under the other exposure conditions, demonstrating that dry-wet cycling results in the most serious sulphate attack on concrete.

Effects of Pounding and Abutment Behavior on Seismic Response of Multi-Span Bridge Considering Abutment-Soil-Foundation-Structure Interactions

This study aims to analyze the longitudinal seismic performance of a typical multi-span continuous girder bridge with seat-type abutments under earthquake excitation, especially accounting for different abutment behaviors. Three-dimensional finite element models of typical multi-span bridges are built considering the nonlinearity of the bridge columns, bearings, abutment-backfill interactions, pile-soil interactions, and the pounding at expansion joints. One of the models adopts a simplified bilinear model to express the force-displacement relationship of the abutment backwall. The other adopts a more practical multi-linear model, and the abutment backwall is used as a sacrificial component to control the damage to the abutment’s foundation by changing the strength of the abutment backwall. Comparisons of the results of the analysis of two bridge models with and without a sacrificial backwall indicate that it is more favorable for bridges with a sacrificial backwall to protect the foundation, but it is likely to arouse a larger displacement response of the main beam and even cause the unseating of girders. The recommendation for a sacrificial abutment in seismic design is that the right yield strength of the backwall should be selected to reach the balance point of force and displacement, and a collapse-proof system could be employed to prevent the beam from unseating.

Flexural behavior and mechanical model of aluminum alloy mortise-and-tenon T-joints for electric vehicle

AbstractWith the development of electric vehicles, more and more high requirements for the lightweight design on EV body are put forward. This paper aims to study a new structure, aluminum alloy mortise-and-tenon structure, which is used for lightweight EVs. Two new types on aluminium alloy MT-T joint specimens are designed and tested under low-cycle reciprocating loading. And the failure characteristics, hysteretic curve, skeleton curve, restoring force model and energy dissipation curve are obtained by analyzing the experimental data. Moment and rotation angle relationship is conducted by joint geometric deformation and equilibrium relation. Based on theoretical model, a simplified bilinear model has been proposed for engineering calculation. When the beam bending performance is qualitatively analyzed, the theoretical model, simulation model and bilinear model are verified through experiments and finite element method simulations. The results show that mortise-and-tenon T joint main failure modes are plastic deformation caused by the upper contact area squeezed each other and the lower contact area divorced each other. Furthermore, it can be obtained from the theoretical model that MT-T joint deformation process consists of elastic segment and elastoplastic segment. Theoretical model, simulation model and bilinear model agree well with the experimental results. This fruit gives a useful reference to composite material used in EVs.

Full Debonding Process of Adhesively Bonded Composite and Metallic Pipe Joints under Torsion

Bonded joints are very common in many pipeline systems, in which the bond behavior of the joint interface is of crucial importance. This paper presents two analytical solutions for the debonding process of a pipe joint under torsion, assuming that the bond interface follows either an exponential softening bond-slip law or a simplified bilinear model. The solutions are general, applicable to composites and metallic and indeed other pipes. Based on the analytical solutions, the influences of the bond length and stiffness on the torque-displacement curve and ultimate load are investigated. The solutions can be used to explain the stress transfer mechanism, the interface crack propagation, and the ductility of the joint.

Drift Capacity of Lightly Reinforced Concrete Columns

This paper presents the findings of a research project investigating the lateral load drift behaviour of lightly reinforced concrete columns. Such columns of limited ductility are common in regions of low-moderate seismicity, and although their strength properties are well defined, the drift performance is less understood. The paper presents the results of an experimental study undertaken and the development of a theoretical model for predicting the lateral load-drift behaviour of lightly reinforced concrete columns together with a simplified bi-linear model for checking purposes. The test results are presented and clearly indicate the dramatic impact that the axial load ratio has on the drift performance of columns of limited ductility, particularly the significantly lower drift capacities that are available in compression dominated columns.

Drift capacity of lightly reinforced concrete columns

This paper presents the findings of a research project investigating the lateral load drift behaviour of lightly reinforced concrete columns. Such columns of limited ductility are common in regions of low-moderate seismicity, and although their strength properties are well defined, the drift performance is less understood. The paper presents the results of an experimental study undertaken and the development of a theoretical model for predicting the lateral load-drift behaviour of lightly reinforced concrete columns together with a simplified bi-linear model for checking purposes. The test results are presented and clearly indicate the dramatic impact that the axial load ratio has on the drift performance of columns of limited ductility, particularly the significantly lower drift capacities that are available in compression dominated columns.

Nonlinear adaptive filter-based simplified bilinear model for multichannel active control of nonlinear noise processes

To circumvent nonlinear distortions which occur in multichannel nonlinear active noise control (ANC) systems used for practical applications, a simplified bilinear leaky filtered-x least mean square (SBLFXLMS) algorithm for nonlinear adaptive filter is presented in this paper. The performance of the simplified bilinear adaptive filter is evaluated in terms of computational complexity and convergence characteristics. Computer simulations have been carried out to verify that the nonlinear adaptive filter with the SBLFXLMS algorithm is more effective in eliminating nonlinear distortions in multichannel nonlinear ANC systems than the linear FXLMS, second-order Volterra FXLMS (VFXLMS) and filtered-s LMS (FSLMS) algorithms. Furthermore, the analysis of the computational requirements and simulations results both show that the SBLFXLMS algorithm requires less computations without suffering from any performance degradation of mutichannel nonlinear ANC systems.

Steel–concrete composite flange plate connections — finite element modeling and parametric studies

Composite connections are defined as the regions where composite beam frames into a steel column. A composite flange plate connection with web cleats is studied here since it is expected to satisfy the seismic performance requirements at a reasonable cost. A modification of the traditional flange plate connection, termed as stiffened flange plate connection, is also studied and its merits over the flange plate connection are assessed. The flange plate and stiffened flange plate connections are analyzed by finite element method and the validity of the model developed established by comparing with the envelope of the cyclic moment–rotation curve and the failure mode obtained from tests. Parametric studies were done to understand the connection parameters influencing the moment–rotation behavior of the connections under hogging and sagging moments. Based on the results of the parametric studies, mathematical equations have been developed for predicting the initial stiffness, moment capacity and ultimate rotation under hogging and sagging moments, and thus the entire moment–rotation curve. A simplified bilinear model is also developed for use in semi-rigid frame analysis and dynamic analysis.

Confinement of concrete with hybrid FRP bistable structures

Abstract The ductility potential of concrete confined with fiber reinforced polymer (FRP) composites is limited by the low fracture strain and brittleness of the fiber and consequently poor energy dissipation in the system. To improve this aspect, a series of experiments were conducted to investigate the use of mechanism-based hybrid FRP bistable wraps, which consist of energy-absorbing “links” made of carbon and glass fabrics bonded together (with the main links designed as the primary load carrier and the waiting links as the secondary load carrier). The FRP bistable-confined concrete was found to have increased ductility and energy absorption with a controlled failure mode. The effect due to material type of the bistable links and core inserts was substantial in terms of load-carrying capacity and deformability. A two-step simulation method was developed for the FRP-confined concrete, where the FRP wrap was modeled with a material constitutive behavior obtained from a separate modeling step of the FRP bistable structure. A simplified bilinear model was also proposed for design purpose.

Pipe damper, Part I: Experimental and analytical study

In this paper the behavior of steel pipes, filled and unfilled with concrete, is studied under cyclic shear to examine the possibility of their use as a seismic damper. Two specimens of steel pipes filled inside with concrete are tested under monotonic and cyclic shear. Four other specimens of bare steel pipes are tested under fully reversed cyclic shear loading. The results show that the bare steel pipes are capable of absorbing a great amount of energy under a severe cyclic shear loading with a stable hysteretic behavior. This behavior is also simulated using the finite element method. Then, parametric studies are performed to investigate the effects of variations in geometrical properties of the pipe on its hysteretic behavior. A simplified bi-linear model is proposed to approximate the hysteretic behavior of the steel pipe as a metallic-yielding damper.

Cyclic Behavior of Single Angles for Ductile End Cross Frames

The cyclic inelastic behavior of single angle braces used in bridge cross frames is described in this paper. Based on the results from experiments, it is shown that steel angles can be designed to achieve a ductile response with large inelastic strains prior to failure under cyclic loading. Preventing fracture in the connections as well as satisfying limiting b/t and Kl/r ratios results in good cyclic behavior and maximum cyclic strains greater than 6%. The tensile yield force for the single angles can be confidently predicted. The buckling capacity is shown to be largely dependent on the effective length of the members which, in turn, is dependent on the type of end condition. Where plastic hinging is expected in the gusset plates an effective length factor of 1.0 can be assumed for the member, while if plastic hinging is expected in the member an effective length factor of 0.7 is appropriate, where the length is defined as the distance between the centroids of the connections. It is recommended that Kl/r for single angles in end cross frames of bridges be limited to 120 to preclude the use of slender members for which the buckling strength is sensitive to effective length. By limiting the slenderness ratio to 120, the members are treated like main members for seismic loads based on AASHTO provisions. The b/t ratio should be limited to those specified for special concentrically braced frames from the AISC Seismic Provisions for Structural Steel Buildings. An analytical model was developed to simulate the nonlinear response of the single angles and a simplified bilinear model was developed for design purposes.

Hysteretic Model of Stiffened Shear Panel Dampers

A properly designed two-way stiffened (stiffened both in longitudinal and transverse directions) shear panel can sustain large deformation without pinching and consequent strength degradation. Hence it can be used as an effective passive energy dissipating damper (PEDD) in building and bridge structures to absorb seismic energy. In this Technical Note, a series of steel shear panels with 1, 2, or 3 two-way stiffeners has been analyzed under cyclic loading by the general-purpose finite element program ABAQUS, in which a modified two-surface model is incorporated to trace the material nonlinearity. Slenderness of web, Rw, is employed as a key parameter to investigate the hysteretic performance of stiffened shear panels. The sensitivities of the ratio of stiffener rigidity to optimum stiffener rigidity, γs∕γs*, the ratio of flange thickness to web thickness, tf∕tw, and aspect ratio, α, are also investigated. Finally, a simplified bilinear model for stiffened shear panels acting as a PEDD is presented in this Technical Note based on FEM results. The proposed model is expected to get use in the time-history analysis of engineering structures that employ the PEDD to mitigate seismic hazard.

Tension-stiffening model for FRP-strenghened RC concrete two-way slabs

The main focus of this paper is to present a tension-stiffening model that is suitable for finite element analysis (FEA) aimed at investigating the effect of FRP strengthening on the tensile behaviour of concrete slabs. Available experimental results of the FRP-strengthened reinforced concrete slabs are used to calibrate the finite element model based on the ultimate load carrying capacity of the two-way slabs. The proposed tension-stiffening model is implemented into the constitutive concrete model defined in a general-purpose finite element code. Reinforced concrete behaviour in tension can signifcantly be changed due to strengthening. An overall increase in the post-peak stiffness based on the tensile stress-strain relationship is observed. A simplified bilinear model is introduced to define the behaviour of the FRP-strengthened concrete in tension. An expression of the fracture energy density is introduced to define the area under the concrete tensile stress-strain relationship. The tensile stress-strain relationship of concrete is referred to as the tension-stiffening model. It is shown numerically that the ultimate load capacity of two-way slab specimens is sensitive to the fracture energy density. Hence, a distinction has to be made between the definitions of the tension-stiffening model of FRP-strengthened and un-strengthened concrete. This distinction is the focus of this paper.