• Proceedings of the Korea Concrete Institute Conference
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• 1998.10a
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• pp.438-443
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• 1998

Softening os the name used for decreasing bending moment at advanced flexural deformation. To accommodate softening deformation in analysis, it is assumed that a hinge has finite length. The softening analysis of R/C frames relies on the primary assumption that softening occurs over a finite hinge length and that the moment-curvature relationship for any section may be closely described by a trilinear approximation. A stiffness matrix for elastic element with softening regions are derived and the stiffness matrix allows extension of the capability of an existing computer program for elastic-plastic analysis to the softening situation. The effect of softening on the collapse load of R/C frame is evaluated.

• Structural Engineering and Mechanics
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• v.5 no.6
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• pp.785-801
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• 1997

Reinforced Concrete beams with tension and compression softening material constitutive laws are studied. Energy-based and non-local regularisation techniques are presented and applied to a R.C. element. The element characteristics (sectional tangent stiffness matrix, element tangent stiffness matrix restoring forces) are directly derived from their symbolic expressions through numerical integration. In this way the same spatial grid allows us to obtain a non-local strain estimate and also to sample the contributions to the element stiffness matrix. Three examples show the spurious behaviors due to the strain localization and the stabilization effects given by the regularisation techniques, both in the case of tension and compression softening. The possibility to overestimate the ultimate load level when the non-local strain measure is applied to a non softening material is shown.

• Computers and Concrete
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• v.3 no.4
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• pp.213-233
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• 2006

Over the past years techniques for non-linear analysis have been enhanced significantly via improved solution procedures, extended finite element techniques and increased robustness of constitutive models. Nevertheless, problems remain, especially for real world structures of softening materials like concrete. The softening gives negative stiffness and risk of bifurcations due to multiple cracks that compete to survive. Incremental-iterative techniques have difficulties in selecting and handling the local peaks and snap-backs. In this contribution, an alternative method is proposed. The softening diagram of negative slope is replaced by a saw-tooth diagram of positive slopes. The incremental-iterative Newton method is replaced by a series of linear analyses using a special scaling technique with subsequent stiffness/strength reduction per critical element. It is shown that this event-by-event strategy is robust and reliable. First, the model is shown to be objective with respect to mesh refinement. Next, the example of a large-scale dog-bone specimen in direct tension is analyzed using an isotropic version of the saw-tooth model. The model is capable of automatically providing the snap-back response. Subsequently, the saw-tooth model is extended to include anisotropy for fixed crack directions to accommodate both tensile cracking and compression strut action for reinforced concrete. Three different reinforced concrete structures are analyzed, a tension-pull specimen, a slender beam and a slab. In all cases, the model naturally provides the local peaks and snap-backs associated with the subsequent development of primary cracks starting from the rebar. The secant saw-tooth stiffness is always positive and the analysis always 'converges'. Bifurcations are prevented due to the scaling technique.

• Earthquakes and Structures
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• v.14 no.5
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• pp.459-465
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• 2018

Reducing response of buildings during earthquakes by mass dampers, has been examined in many articles and books. Nowadays, many researchers are trying to realistically examine this type of dampers by new methods of performance. In this paper, for the better study of tuned mass damper (TMD), two schematic models are presented for a passive TMD with softening stiffness (softening TMD) and a passive TMD with hardening stiffness (hardening TMD). Then by modeling and analysis of the damper on a single degree of freedom (SDOF) structure and an 11-story steel building, the dampers performance was evaluated. State space was used for damper and structure modeling and to solve nonlinear equations, the Newton-Raphson method was used. The results show that when the structure is subjected to the Chi-Chi earthquake, response of the sixth floor in the system without TMD reduces 54.0% in comparison to the structure with softening TMD. This percentage of reduction for hardening TMD is 55.0%. Also for the Tabas earthquake, reduction in the RMS acceleration of the sixth floor in the system with hardening TMD is 96.2% more than the structure without TMD. This percentage of reduction for hardening TMD is 96.3%.

• Computers and Concrete
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• v.22 no.3
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• pp.305-317
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• 2018

Steel reinforced Engineered Cementitious Composite (ECC) components have been proposed for seismic structural applications, for example in coupling beams, infill panels, joints, columns, and flexural members. The development of strain in the steel reinforcement of cementitious components has been shown to vary based on both the steel reinforcement ratio and the applied deformation history. Strain in the steel reinforcement of reinforced ECC components is an important structural response metric because ultimate failure is often by fracture of the steel reinforcement. A recently proposed bond-slip model has been successfully calibrated to cyclically tested reinforced ECC beams wherein the deformation history contained monotonically increasing cycles. This paper reports simulations of two-dimensional finite element models of reinforced ECC beams to determine the appropriateness and significance of altering a phenomenological bond-slip model based on the applied deformation history. The numerical simulations with various values of post-peak bond-slip softening stiffness are compared to experimental results. Varying the post-peak bond-slip softening stiffness had little effect on the cracking patterns and hysteretic response of the reinforced ECC flexural models tested, which consisted of two different steel reinforcement ratios subjected to two different deformation histories. Varying the post-peak bond-slip softening stiffness did, however, affect the magnitude of strain and the length of reinforcing bar that strain-hardened. Overall, a numerical model with a constant bond-slip model represented well various responses in reinforced ECC beams with multiple steel reinforcement ratios subjected to different deformation histories.

• Structural Monitoring and Maintenance
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• v.5 no.1
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• pp.15-38
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• 2018

Negative stiffness dampers (NSDs) have been proven an efficient solution to vibration control of stay cables. Although previous studies usually assumed a linear negative stiffness behavior of NSDs, many negative stiffness devices produce negative stiffness with nonlinear behavior. This paper systematically evaluates the impact of nonlinearity in negative stiffness on vibration control performance for stay cables. A linearization method based on energy equivalent principle is proposed, and subsequently, the impact of two types of nonlinear stiffness, namely, displacement hardening and softening stiffness, is evaluated. Through the Hilbert transform (HT) of free vibration responses, the effects of nonlinear stiffness of an NSD on the modal frequencies, damping ratios and frequency response functions of a stay cable is also investigated. The HT analysis results validate the accuracy of the linearization method.

• Structural Engineering and Mechanics
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• v.65 no.1
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• pp.91-98
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• 2018

Three structure-dependent integration methods with no numerical dissipation have been successfully developed for time integration. Although these three integration methods generally have the same numerical properties, such as unconditional stability, second-order accuracy, explicit formulation, no overshoot and no numerical damping, there still exist some different numerical properties. It is found that TLM can only have unconditional stability for linear elastic and stiffness softening systems for zero viscous damping while for nonzero viscous damping it only has unconditional stability for linear elastic systems. Whereas, both CEM and CRM can have unconditional stability for linear elastic and stiffness softening systems for both zero and nonzero viscous damping. However, the most significantly different property among the three integration methods is a weak instability. In fact, both CRM and TLM have a weak instability, which will lead to an adverse overshoot or even a numerical instability in the high frequency responses to nonzero initial conditions. Whereas, CEM possesses no such an adverse weak instability. As a result, the performance of CEM is much better than for CRM and TLM. Notice that a weak instability property of CRM and TLM might severely limit its practical applications.

• Structural Engineering and Mechanics
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• v.5 no.6
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• pp.729-741
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• 1997

Cracked reinforced concrete in compression has been observed to exhibit lower strength and stiffness than uniaxially compressed concrete. The so-called compression softening effect responsible is thought to be related to the degree of transverse cracking and straining present. It significantly affects the strength, ductility and load-deformation response of a concrete element. A number of experimental investigations have been undertaken to determine the degree of softening that occurs, and the factors that affect it. At the same time, a number of diverse analytical models have been proposed by various this behavior. In this paper, the softened truss model thoery for low-rise structural shearwalls is employed using the principle of the stress and strain transformations. Using this theory the softening parameters for the concrete struts proposed by Hsu and Belarbi as well as by Vecchio and Collins are examined by 51 test shearwalls available in literature. It is found that the experimental shear strengths and ductilities of the walls under static loads are, in average, very close to the theoretical values; however, the experiment shear strengths and ductilities of the walls under dynamic loads with a low (0.2 Hz) frequency are generally less than the theoretical values.

• Proceedings of the Korea Concrete Institute Conference
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• 1990.10a
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• pp.7-12
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• 1990

This paper presents an equation for balanced-steel ratio in longitudinal and transverse direction throughout analysis based on a space truss model introducing the concept of concrete softening effect. This paper also presents as equation for postcracking torisonal stiffness throughout analysis considering the equilibrium conditions and compatibility conditions based on shear panel. Correlation between predicted postcracking torsional stiffness, and experimental results was good, not only for beams tested in this paper but also for others in the literature.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1995.10a
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• pp.185-193
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• 1995

The softening behaviors of concrete have been the object of numerous experimental and numerical studies, because the load carrying capacity of cracked concrete structure is not zero. Numerical studies are devoted to the investigation of three-dimensional softening behaviors of concrete on the basis of a viscoplastic theory, which may be able to represent the effects of plasticity and also of rheology. In order to properly describe material behaviors corresponding to different stress levels, two surfaces in stress space are adopted; one is a yield surface, and the other is a failure or bounding surface. When a stress path reaches the failure surface, it is considered that the softening behaviors are initiated as micro-cracks coalesce and are simulated by assuming that the actual strain increments in the post-peak region are less than the equivalent viscoplastic strain increment. The experimental studies and the finite element analyses have been carried out under the displacement control. Numerically simulated results indicate that the model is able to predict the essential characteristics of concrete behaviors such as the non-linearity, stiffness degradation, different behaviors in tension and compression, and specially dilatation under uniaxial compression.