Cyclic Softened Membrane Model Research Articles

New OpenSees material model for simulating reinforced concrete shear walls subjected to coupled axial tension and cyclic lateral loads

In high-rise buildings, reinforced concrete (RC) shear walls, particularly those forming part of coupled wall systems or core wall systems, may be subjected to coupled axial tension and cyclic lateral loads during strong seismic events. A new two-dimensional material model named the “Fixed Angle Model Considering Crack Sliding” (FAM-CS) was proposed for simulating the nonlinear behavior of RC walls subjected to axial tension and cyclic lateral loads. The proposed model was implemented in the OpenSees platform. Nonlinear constitutive models for shear aggregate interlock effects of concrete and dowel action of rebars were incorporated into the proposed model to represent the shear transfer mechanisms along concrete cracks. The proposed model was validated against the test data of six wall specimens subjected to coupled axial tension and cyclic lateral loads. The results indicated that the proposed model reasonably predicted the lateral strength capacity (an average error of 6.2 %) and the residual strength at the maximum drift loading (an average error of 12.3 %) of the specimens. For comparison, three other commonly used models, the Shear-Flexure Interaction Multiple-Vertical-Line-Element-Model, the multi-layer shell element model and the Cyclic Softened Membrane Model were adopted for the simulation of the specimens. Compared with the three existing OpenSees models, the newly implemented material model provided improved predictions of the wall hysteretic behavior with respect to lateral strength capacity, lateral strength degradation, pinching characteristics and cyclic stiffness degradation. In addition, the proposed model reasonably captured the localized failure pattern as well as the energy dissipation characteristics of the test specimens. Finally, a mesh sensitivity study was conducted to assess the robustness of the proposed model. The results revealed that the proposed model was robust regarding the lateral load-drift responses of RC walls, with a mesh size ranging from approximately one to three times the average crack spacing.

Experimental Study and Finite Element Modelling of Squat Shear Walls under Combined Cyclic Loads and High Axial Loads

Experimental observations on three reinforced concrete shear walls with small shear span-to-depth ratio (SDR) under combined high vertical axial load and horizontal cyclic loads are presented. The influence of high axial load ratio (ALR) on the failure mode, hysteretic behaviour, displacement ductility, shear strength and stiffness of the squat shear walls is investigated. In addition, a novel built-in strain gauges measuring system is employed for measuring the strain conditions in the reinforcements during the whole test process. Test results indicate that high axial load restrains the development of cracks and improves the shear load capacity, but that it also decreases ductility and energy dissipation and aggravates stiffness degradation. Concrete crush and out-of-plane buckling were observed in all specimens, resulting in the final failure of the specimens. According to the strain analysis, the section of the squat walls coincided well with the assumption of plane section under the condition of high ALR. With the increase of ALR, the depth of the compression zone of members increases, while the length of plastic hinge decreases. When the axial load is relatively small, the vertical and horizontal reinforcements provided almost equal contribution to the shear capacity of squat shear walls. However, under extremely high axial load, both vertical and horizontal reinforcements cannot provide full contribution to the shear capacity. The hysteretic behaviours of the tested shear walls were simulated by a cyclic softened membrane model (CSMM). Simulation results indicate that CSMM captured well the nonlinear characteristics of the squat shear wall under high axial load.

Nonlinear shear analysis of I-shaped beams with arbitrary inclination angles of shear reinforcement

We studied the effect of the inclination angle of stirrups and wire mesh on the web-crushing strength of reinforced concrete I-beams beams. Experimental studies were carried out in Kuban State Technological University. The variable parameters of the tested specimens included concrete compressive strength, level of prestressing, cross-sectional shape, shear span, shear reinforcement ratio and angles of inclination of stirrups or wire mesh. The strength of beams was calculated with the Cyclic Softened Membrane Model for reinforced concrete (CSMM), developed at the University of Houston and implemented in the OpenSees software package. The modeling of the web of the beams was fulfilled with quadrilateral finite elements with the assigned material FAReinforcedConcretePlaneStress. The flanges of the beams resisting the bending moment were modeled with nonlinear volumetric elements having fiber section. Uniaxial Kent-Scott-Park concrete material and uniaxial bilinear steel material were assigned to the flanges. Calculation results are close to experimental data having wide variation of the materials properties and structural parameters of beams.

Robustness evaluation of CSMM based finite element for simulation of shear critical hollow RC bridge piers

PurposeThe purpose of this study is to evaluate the effectiveness of two-dimensional (2D) cyclic softened membrane model (CSMM)-based non-linear finite element (NLFE) model in predicting the complete non-linear response of shear critical bridge piers (with walls having aspect ratios greater than 2.5) under combined axial and reversed cyclic uniaxial bending loads. The effectiveness of the 2D CSMM-based NLFE model has been compared with the widely used one-dimensional (1D) fiber-based NLFE models.Design/methodology/approachThree reinforced concrete (RC) hollow rectangular bridge piers tested under reversed cyclic uniaxial bending and sustained axial loads at the National Centre for Research on Earthquake Engineering (NCREE) Taiwan have been simulated using both 1D and 2D models in the present study. The non-linear behavior of the bridge piers has been studied through various parameters such as hysteretic loops, energy dissipation, residual drift, yield load and corresponding drift, peak load and corresponding drift, ultimate loads, ductility, specimen stiffness and critical strains in concrete and steel. The results obtained from CSMM-based NLFE model have been critically compared with the test results and results obtained from the 1D fiber-based NLFE models.FindingsIt has been observed from the analysis results that both 1D and 2D simulation models performed well in predicting the response of flexure critical bridge pier. However, in the case of shear critical bridge piers, predictions from 2D CSMM-based NLFE simulation model are more accurate. It has, thus, been concluded that CSMM-based NLFE model is more accurate and robust to simulate the complete non-linear behavior of shear critical RC hollow rectangular bridge piers.Originality/valueIn this study, a novel attempt has been made to provide a rational and robust FE model for analyzing shear critical hollow RC bridge piers (with walls having aspect ratios greater than 2.5).

FE simulation of cylindrical RC containment structures under reserved cyclic loading

The nuclear containment structure is one of the most important infrastructure systems ensuring the safety of a nuclear power plant. The structural behavior of a cylindrical containment structure made of reinforced concrete (RC) with large dimensions and numerous rebars is complex and difficult to predict. The complex behavior of the RC containment structure has been investigated in an international collaboration project between the National Center for Research on Earthquake Engineering (NCREE) in Taipei, Taiwan and the University of Houston (UH), Houston, Texas. At NCREE two 1/13 scaled cylindrical RC containment specimens were tested under reversed cyclic loads [1]. At UH, a finite element simulation of the two tested specimens was developed using a finite element analysis (FEA) program SCS [2]. In the program, a new shell element, the so-called CSMM-based shell element, was developed based on the Cyclic Softened Membrane Model [3] and the formulation of an 8-node Serendipity curved shell element [4] with a multi-layer approach [5]. The UH simulated seismic behavior was close to the NCREE experimental results. This paper presents the theoretical development of the FEA program SCS and the comparisons of its predictions with the experimental structural behavior of the two RC containment specimens. This simulation model and the FEA program are excellent tools to develop effective performance-based design provisions.

Effect of load history on shear strength of reinforced concrete I-Beams

A series of 32 reinforced concrete I-beams was tested to investigate the effect of existing inclined cracks on shear strength. Testing of beams consisted of two stages. At the preliminary stage, load large enough to cause a formation of a developed crack pattern in the web was applied with the primary shear span-depth ratio. After that, the load with breaking shear span-depth ratio was applied until failure of the specimen. The load applied during the preliminary loading stage was maintained with a full or partial value by a lever, or removed. The test variables include shear span, shear reinforcement ratio and angle of stirrups inclination. Pre-cracking was found to decrease the ultimate shear strength of beams by a maximum of 16 percent depending on the angle of stirrups. A corresponding reduction factor is suggested to the formula of the Russian code for the design of bridges. The finite element simulation of beams was fulfilled by using the program OpenSees. The webs of beams were simulated with a 2D element built on the Cyclic Softened Membrane Model to take into account the deterioration of concrete due to the previous loading. The accuracy of the proposed FE model was verified with the aforementioned tests and the results of several other studies.

Development of CSMM-based shell element for reinforced concrete structures

Reinforced concrete shell structures have been widely used in a variety of modern engineering applications. It is found from earthquake reconnaissance that reinforced concrete (RC) shell structures, such as nuclear containments, cooling towers, roof domes, shear walls, etc., are the key elements in resisting earthquake disturbances. This paper presents the development of a finite element analysis (FEA) program, SCS-3D, to predict the inelastic behavior of RC shell structures. In the program, a Cyclic Softened Membrane Model (CSMM)-based shell element is developed based on the degenerated shell theory with a layered approach and taking into account the CSMM developed at the University of Houston. To form the FEA program, the constitutive relation modules and the analysis procedure were implemented into a finite element program development framework, OpenSees developed at UC Berkeley. Several large-scale structural tests were employed to validate the developed FEA program, including RC panels subjected to a combination of shear and bending, three-dimensional RC shear wall and cylindrical RC tanks subjected to reversed cyclic loading.

Structural integrity of steel plate ultra high-performance concrete modules

Modular construction techniques allow for faster onsite construction, reduce cost and time, increase security, and facilitate flexible designs. In this study, steel plate concrete (SC) modular design benefits have been maximized by incorporating ultra high-performance concrete (UHPC). For a steel plate ultra high-performance concrete (S-UHPC) module to behave effectively, structural integrity of steel plate and UHPC is necessary. Different forms of construction for SC modules have been proposed in the past. Cross-ties method is considered to be one of the most efficient forms of construction of an SC module and has been proven to play an important role in ensuring the integrity of the module. This study investigates the structural integrity of S-UHPC modules. In addition, this paper focuses on finite element simulation (FEM) of the S-UHPC beams with emphasis on shear and bond slip behaviour. A new constitutive model is proposed to account for the bond slip behaviour of steel plates. The Cyclic Softened Membrane Model is utilized to simulate the shear behaviour of UHPC with embedded shear reinforcement. Both constitutive models are implemented into a finite element analysis programme based on the framework of OpenSees. The proposed FEM is able to capture the behaviour of the tested S-UHPC beams.

Simulation of post-tensioned bridge columns under reversed-cyclic loads

Thin-walled prestressed concrete structures such as bridge columns can be subjected to large magnitudes of dynamic loads. It is essential to develop a robust model to accurately predict the nonlinear behavior of these structures and thereby ensure their structural integrity under extreme loading conditions. A research project was performed to study the properties of prestressed concrete (PC) elements under shear loads using the Universal Panel Tester built at the Structural Engineering Lab of University of Houston. The test results were used to develop the softened membrane model for prestressed concrete (SMM-PC) (Wang, Constitutive relationships of prestressed concrete membrane elements, 2006). SMM-PC has been extended to the cyclic softened membrane model for prestressed concrete (CSMM-PC) by using the cyclic softened membrane model (CSSM) for reinforced concrete (Mansour and Hsu, J Struct Eng 131:44–53, 2005, J Struct Eng 131:54–65, 2005) CSMM-PC has been implemented into a finite element program to simulate the non-linear behavior of PC structures under cyclic loads. The program thus developed was named simulation of concrete structures (SCS). SMM-PC has been previously validated by tests on prestressed concrete beams under monotonic loading (Laskar et al., 12th international conference on engineering, science, construction, and operations in challenging environment, earth and space, 2010). In this paper CSMM-PC incorporated in SCS has been validated by tests on precast post-tensioned axisymmetric bridge columns under reversed cyclic loading. The analysis results of the bridge columns using SCS showed good agreement with the test results in terms of the primary backbone curves and the hysteretic loops including the energy dissipation and the strength degradation in the post-peak region. The damage and residual drift of the specimens were also closely predicted from the analysis results. Based on the accuracy of the analytical results it can be concluded that CSMM-PC implemented in SCS is an effective tool to simulate the cyclic non-linear behavior of thin-walled prestressed concrete structures and can be used for simulation of 3D actions of these type of structures through proper implementation.

Multiscale modeling of reinforced/prestressed concrete thin-walled structures

Reinforced and prestressed concrete (RC and PC) thin walls are crucial to the safety and serviceability of structures subjected to shear. The shear strengths of elements in walls depend strongly on the softening of concrete struts in the principal compression direction due to the principal tension in the perpendicular direction. The past three decades have seen a rapid development of knowledge in shear of reinforced concrete structures. Various rational models have been proposed that are based on the smeared-crack concept and can satisfy Navier's three principles of mechanics of materials (i.e., stress equilibrium, strain compatibility and constitutive laws). The Cyclic Softened Membrane Model (CSMM) is one such rational model developed at the University of Houston, which is being efficiently used to predict the behavior of RC/PC structures critical in shear. CSMM for RC has already been implemented into finite element framework of OpenSees (Fenves 2005) to come up with a finite element program called Simulation of Reinforced Concrete Structures (SRCS) (Zhong 2005, Mo et al. 2008). CSMM for PC is being currently implemented into SRCS to make the program applicable to reinforced as well as prestressed concrete. The generalized program is called Simulation of Concrete Structures (SCS). In this paper, the CSMM for RC/PC in material scale is first introduced. Basically, the constitutive relationships of the materials, including uniaxial constitutive relationship of concrete, uniaxial constitutive relationships of reinforcements embedded in concrete and constitutive relationship of concrete in shear, are determined by testing RC/PC full-scale panels in a Universal Panel Tester available at the University of Houston. The formulation in element scale is then derived, including equilibrium and compatibility equations, relationship between biaxial strains and uniaxial strains, material stiffness matrix and RC plane stress element. Finally the formulated results with RC/PC plane stress elements are implemented in structure scale into a finite element program based on the framework of OpenSees to predict the structural behavior of RC/PC thin-walled structures subjected to earthquake-type loading. The accuracy of the multiscale modeling technique is validated by comparing the simulated responses of RC shear walls subjected to reversed cyclic loading and shake table excitations with test data. The response of a post tensioned precast column under reversed cyclic loads has also been simulated to check the accuracy of SCS which is currently under development. This multiscale modeling technique greatly improves the simulation capability of RC thin-walled structures available to researchers and engineers.

Seismic simulation of RC wall-type structures

Reinforced concrete (RC) wall-type structures are crucial to the safety and serviceability of buildings subject to earthquakes. The shear strength of elements in walls depends strongly on the softening of concrete struts in the principal compression direction due to the principal tension in the perpendicular direction. By studying the shear behavior of isolated membrane elements, this softening phenomenon has been clarified for monotonic loading in the Softened Membrane Model (SMM) [Hsu TTC, Zhu RRH. Softened membrane model for reinforced concrete elements in shear. Struct J Amer Concrete Institute 2002; 99(4):460–9]. Recently, SMM was extended to cyclic loading, resulting in the Cyclic Softened Membrane Model (CSMM) [Mansour M, Hsu TTC. Behavior of reinforced concrete elements under cyclic shear: Part 1 — experiments. J Struct Eng, ASCE 2005; 131(1):44–53; Mansour M, Hsu TTC. Behavior of reinforced concrete elements under cyclic shear: Part 2–theoretical model. J Struct Eng, ASCE 2005;131(1):54–65]. In the present paper, the CSMM for elements is first formulated and then implemented in a finite element program, called Simulation of Concrete Structures (SCS), to predict the behavior of RC wall-type structures. SCS is based on the framework of OpenSees [Fenves GL. Annual workshop on open system for earthquake engineering simulation. Berkeley: Pacific Earthquake Engineering Research Center, UC; 2005]. The accuracy of the modeling technique is confirmed by comparing simulated responses with experimental data on nine framed shear walls reported by [Gao XD. Framed shear walls under cyclic loading. Ph.D. dissertation. Houston (TX): Department of Civil and Environmental Engineering, University of Houston; 1999]. This new modeling technique gives engineers greatly improved simulation capabilities.

Stiffness, Ductility, and Energy Dissipation of RC Elements under Cyclic Shear

A new Cyclic Softened Membrane Model (CSMM) was recently developed to predict the stiffness, ductility, and energy dissipation of reinforced concrete (RC) elements subjected to reversed cyclic shear. Using the nonlinear finite element analysis, we can integrate these responses of elements to predict the behavior of a whole structure, such as a low-rise shear wall, subjected to earthquake action. This study of CSMM summarizes systematically the effects of the two primary variables: the steel bar angle with respect to the direction of the applied principal stresses and the steel percentage. The results clearly show that RC structures under cyclic shear stresses could be designed to be very ductile, have large stiffness, and possess high energy-dissipation capacities (just like flexural-dominated elements), if the steel bars are properly oriented in the directions of principal stresses and if the steel percentages are kept within certain limits.

Behavior of Reinforced Concrete Elements under Cyclic Shear. II: Theoretical Model

In order to design reinforced concrete (RC) structures in earthquake regions, a cyclic softened membrane model (CSMM) is presented to predict the load–deformation behavior of RC membrane elements subjected to reversed cyclic shear stresses. This model is an extension of the softened membrane model for monotonic shear behavior. Both models are rational because they satisfy Navier’s principles of mechanics of materials (stress equilibrium, strain compatibility, and constitutive laws of materials). Three new components of material laws were required in developing CSMM: the stress–strain relationships for concrete and steel in the unloading and reloading regions, the modifications of the envelope curve for compressive concrete, and the Hsu/Zhu ratios for cyclic loading. In order to verify the CSMM as a valid theoretical model, this study focused on comparing the predictions of CSMM with actual test results reported in the companion paper. We conclude from this comparison study that the CSMM can indeed predict the hysteretic loops and their pinched shapes, and that the “pinching effect” was the result of steel bar direction deviating from that of the principal stresses. The “pinching mechanism” and the “failure mechanism” are logically explained using Mohr’s circles of stresses and strains.

Performance Simulation of Nuclear Containments for Security

Under blast loading, nuclear containment structures are subjected to cyclic flexural, axial, and shear forces. Less attention has been paid to modeling the cyclic behavior of reinforced concrete elements in which shear deformations are significant, such as in nuclear containments. Research has demonstrated that the strength of concrete in the principal compression direction is softened by tension in the lateral direction. This interaction has been considered for monotonic loading for many years. To consider this interaction for cyclic loading, the material laws recently derived by Mansour et al. in 2001 for the cyclic softened membrane model (CSMM) can be used. Both fire and explosion effects resulting from blast loading can also be incorporated into the constitutive models of concrete and reinforcing bars. This paper presents a method to implement the CSMM model, so that it can be used to simulate the performance of nuclear containments for security by the design communities.