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Showing 12 results for Stiffness

Amir Hamidi, S. Mohsen Haeri,
Volume 6, Issue 3 (9-2008)

The deformation and stiffness characteristics of a cemented gravely sand was investigated using triaxial equipment. The triaxial tests were conducted in both dry and saturated undrained conditions. Artificially cemented samples are prepared using gypsum plaster as the cementing agent. The plaster was mixed with the base soil at the weight percentages of 1.5, 3, 4.5 and 6. The applied confining pressure varied between 25 to 500 kPa in triaxial tests. The process of yielding of the soil was investigated for the considered soil and the bond and final yield points were identified for the cemented soil with different cement contents. The variations of deformation and stiffness parameters with cement content and confining stress were studied as well. Some of the parameters were determined for both drained and undrained conditions to investigate the effect of drainage condition on the stiffness and yield characteristics of the tested cemented gravely sand. According to the results, the difference between drained and undrained tangent stiffness decreases with increase in confining stress. Finally the effect of cement type was investigated as an important parameter affecting the stiffness at bond yield. The rate of increase in tangent stiffness at bond yield changes with cement content for different cementing agents.
T. Dahlberg,
Volume 8, Issue 1 (3-2010)

The track stiffness experienced by a train will vary along the track. Sometimes the stiffness variation may be

very large within a short distance. One example is when an unsupported sleeper is hanging in the rail. Track stiffness

is then, locally at that sleeper, very low. At insulated joints the bending stiffness of the rail has a discontinuity implying

a discontinuity also of the track stiffness. A third example of an abrupt change of track stiffness is the transition from

an embankment to a bridge. At switches both mass and stiffness change rapidly. The variations of track stiffness will

induce variations in the wheel/rail contact force. This will intensify track degradation such as increased wear, fatigue,

track settlement due to permanent deformation of the ballast and the substructure, and so on. As soon as the track

geometry starts to deteriorate, the variations of the wheel/rail interaction forces will increase, and the track

deterioration rate increases. In the work reported here the possibility to smooth out track stiffness variations is

discussed. It is demonstrated that by modifying the stiffness variations along the track, for example by use of grouting

or under-sleeper pads, the variations of the wheel/rail contact force may be considerably reduced.

A.r. Khaloo, I. Eshghi, P. Piran Aghl,
Volume 8, Issue 3 (9-2010)

In this paper the response of cantilevered reinforced concrete (RC) beams with smart rebars under static lateral loading has been numerically studied, using Finite Element Method. The material used in this study is SuperelasticShape Memory Alloys (SE SMAs) which contains nickel and titanium elements. The SE SMA is a unique alloy that has the ability to undergo large deformations and return to their undeformed shape by removal of stresses. In this study, different quantities of steel and smart rebars have been used for reinforcement andthe behavior of these models under lateral loading, including their load-displacement curves, residual displacements, and stiffness, were discussed. During lateral loading, rebars yield or concrete crushes in compression zone in some parts of the beams and also residual deflections are created in the structure. It is found that by using SMA rebars in RC beams, these materials tend to return to the previous state (zero strain), so they reduce the permanent deformations and also in turn create forces known as recovery forces in the structure which lead into closing of concrete cracks in tensile zone. This ability makes special structures to maintain their serviceability even after a strong earthquake

O. Omidi, V. Lotfi,
Volume 8, Issue 3 (9-2010)

 Neither damage mechanics model nor elastoplastic constitutive law can solely describe the behavior of concrete satisfactorily. In fact, they both fail to represent proper unloading slopes during cyclic loading. To overcome the disadvantages of pure plastic models and pure damage approaches, the combined effects need to be considered. In this regard, various classes of plastic-damage models have been recently proposed. Here, the theoretical basics of the plastic-damage model originally proposed by Lubliner et al. and later on modified by Lee and Fenves is initially presented and its numerical aspects in three-dimensional space are subsequently emphasized. It should be mentioned that a part of the implementation in 3-D space needs to be reformulated due to employing a hyperbolic potential function to treat the singularity of the original linear form of plastic flow proposed by Lee and Fenves. The consistent algorithmic tangent stiffness, which is utilized to accelerate the convergence rate in solving the nonlinear global equations, is also derived. The validation and evaluation of the model to capture the desired behavior under monotonic and cyclic loadings are shown with several simple one-element tests. These basic simulations confirm the robustness, accuracy, and efficiency of the algorithm at the local and global levels. At the end, a four-point bending test is examined to demonstrate the capabilities of the model in real 3-D applications.

H. Shakib, Gh. R. Atefatdoost,
Volume 12, Issue 1 (3-2014)

An approach was formulated for the nonlinear analysis of three-dimensional dynamic soil-structure interaction (SSI) of asymmetric buildings in time domain in order to evaluate the seismic response behavior of torsionally coupled wall-type buildings. The asymmetric building was idealized as a single-storey three-dimensional system resting on different soil conditions. The soil beneath the superstructure was modeled as nonlinear solid element. As the stiffness of the reinforced concrete flexural wall is a strength dependent parameter, a method for strength distribution among the lateral force resisting elements was considered. The response of soil-structure interaction of the system under the lateral component of El Centro 1940 earthquake record was evaluated and the effect of base flexibility on the response behavior of the system was verified. The results indicated that the base flexibility decreased the torsional response of asymmetric building so that this effect for soft soil was maximum. On the other hand, the torsional effects can be minimized by using a strength distribution, when the centre of both strength CV and rigidity CR is located on the opposite side of the centre of mass CM, and SSI has no effect on this criterion.
H. Liu, M. He, J. Guo, Zh. Hou, Y. Shi,
Volume 13, Issue 2 (6-2015)

Self-centering pier (SCP) has been viewed as a remarkable accomplishment which is able to sustain major lateral loading with reduced structure damage in seismic engineering. Stiffness deterioration observed in experiment is vital for the seismic performance of self-centering concrete pier. In this contribution, the associated stiffness deterioration with respect to the structural damage is modeled in a modified analytical model for SCP comprehensively. In the proposed modified theoretical model, the lateral force-displacement relation associated with the stiffness reducing is analyzed. Three damage factors are introduced in the stiffness deterioration analysis to illustrate the damage evolution caused by gradually increasing lateral displacement. The proposed modified quasic-static model with damage evolution or stiffness deterioration has been validated against an experiment we conducted, where a good agreement is clearly evident. Subsequently, a parametric investigation focusing on aspect ratio, initial pre-tension, and ratio of ED (Energy Dissipator) was conducted to evaluate the hysteretic behavior of SCP under quasi-statically cyclic loading.
A. Fooladi, Mo.r. Banan,
Volume 13, Issue 2 (6-2015)

Latticed columns are frequently used in industrial steel structures. In some countries these built-up columns might be even used in other types of steel structures such as residential and commercial buildings. Besides, latticed columns are parts of skeletons of many historic buildings all around the world. To analyze a steel structure with latticed columns a more accurate numerical model for such a column seems to be essential. The lay-out and connectivity of constructing main profiles of a latticed column leads to formation of many shear zones along the length of a column. Therefore, considering shear effects on the behavior of a lattice column is inevitable. This paper proposed a new super-element with twelve degrees of freedom to be used in finite element modeling of latticed columns. The cross sectional area, moments of inertia, shear coefficient and torsional rigidity of the developed new element are derived. To compute these parameters with less complexity a model using only beam elements is also introduced. A general purpose finite element program named LaCE is developed. This FE program is capable of performing linear and nonlinear analysis of 3D-frames with latticed columns, considering shear deformation. To show the accuracy of the proposed element, several cases are studied. The outcome of these investigations revealed that the current-in-practice model for latticed columns suffers from some major shortcomings which to some extends are resolved by the proposed super-element. The developed element showed the capability of modeling a lattice column with good accuracy and less computational cost.
S.m. Zahrai,
Volume 13, Issue 3 (9-2015)

Seismic retrofit of masonry slabs in existing steel or masonry buildings has found special significance in current codes as failure of unstable jack arch slabs has been reported as a major reason for collapsing structures in Middle East deadly earthquakes. In this paper, three retrofit schemes are investigated and compared. The proposed rehabilitation techniques consist of a single X strapping, SXS, a double X strapping, DXS, and a two-way jack arch slab supported by a steel grid. Using experimental studies, advantages and disadvantages of each scheme are evaluated. In-plane stiffness and capacity of the diaphragm are adopted as the seismic performance index of each rehabilitation scheme. According to the obtained results, the jack arch slab systems designed and constructed based on proposed retrofit methods provide an appropriate alternative to other forms of flooring in seismic zones. DXS can greatly improve diaphragm performance in terms of in-plane stiffness, capacity and even energy dissipation of the diaphragm compared with the other two techniques. The second place belongs to SXS while the steel grid scheme has a minor effect on the in-plane stiffness of the diaphragm.
I. Štimac Grandić, D. Grandić, A. Bjelanović,
Volume 13, Issue 3 (9-2015)

In this paper, evaluation of torsional stiffness in beam and slab bridge deck elements is presented. A beam and slab bridge decks structurally behave as a grillage. A grillage has an efficient transverse load distribution due to transverse asymmetric load. In the case of bridge deck without transverse beams in the span, transverse load distribution depends on the torsional stiffness of longitudinal beams, transverse beams over the supports and deck slab. The results of load testing conducted on series of bridges in Croatia are compared with results obtained on different numerical grillage models in which torsional stiffness of main structural elements was varied. Five different numerical models for each tested bridge are used. To evaluate torsional stiffness of main structural elements of the bridge the transverse distribution coefficients are introduced. The design value of the coefficients of torsional stiffness reduction for verification of the serviceability limit state (SLS), with assumption of normal probability distribution is determined. The same coefficient is calculated using recommendation for torsional stiffness reduction in concrete elements defined by Model code CEB-FIB 1990 (MC 90). According to conducted analyses the design value of the coefficient of torsional stiffness reduction for verification of the serviceability limit state of main structural elements of beam and slab bridge deck is proposed.
Saeid Sabouri-Ghomi, Barash Payandehjoo,
Volume 15, Issue 1 (1-2017)

Abstract The Drawer Bracing System (DBS) is a ductile bracing system that is developed to enhance the seismic performance of braced frames. The system is composed of three parallel plates that are attached together via transfer plates at right angle. Seismic energy is dissipated through the formation of flexural plastic hinges at the two ends of the transfer plates. The parallel plates must have adequate strength and stiffness to prevent global buckling and to remain elastic while transferring forces to transfer plates. Height, width, thickness and the number of the transfer plates may be varied to achieve the desired strength and stiffness of the system. In contrast to common bracing systems, the main advantage of a DBS is the conversion of the axial forces to flexural moments in the dissipating elements. In the present paper, the nonlinear shear response of the DBS is predicted via closed-form formulas for calculation of strength, stiffness and post-yield behavior of the system. These formulations are based on both experimental observations and theoretical analysis. The calculated force-displacement backbone curve is verified to be a very good approximation for predicting the nonlinear shear response of the system.

Krzysztof Sternik,
Volume 15, Issue 3 (5-2017)

Constitutive model for saturated cohesive soils based on the bounding surface plasticity notion with anisotropic hardening law is presented in the paper. The model predicts inelastic behaviour of overconsolidated cohesive soils. The projection centre is the only point in the stress space which represents elastic soil behaviour. Approximation of the plastic modulus within the preconsolidation domain is made using the radial mapping rule between a projection centre and a reflecting point on the bounding surface. The projection centre changes its position each time when stress path turns rapidly of more than 90°. The configuration of the elliptic bounding surface is governed by preconsolidation effective pressure pc which depends on change of plastic both volumetric and deviatoric strain. Associated flow rule has been assumed in the formulation. Integration of constitutive relations is done according to forward Euler scheme with error control proposed by Sloan. The effectiveness of the proposed model is illustrated in both monotonic and cyclic loading in the homogeneous triaxial drained and undrained conditions.

Volume 15, Issue 4 (6-2017)

Bridges normally undergo nonlinear deformations during a near field strong ground motion resulting in a critical deviation of their columns from the plumb state due to considerable residual deformations. These excessive residual deformations make a bridge, which has not collapsed, ‘irreparable’ and in turn ‘not operable.’ Therefore, reasonable prediction of these types of bridge piers deformations is of great importance in order to evaluate the serviceability of bridges subjected to a seismic scenario. Conventional hysteresis models formulated for typical concrete columns are normally used for this purpose which most of times fail to correctly predict the residual deformations occurred as a result of a one-sided or directivity pulse excitation. The present research aims at development of a peak oriented hysteresis model being able to regenerate residual deformations more reasonable compared to the conventional hysteresis models. This multi linear peak oriented model considers strength deterioration in each half cycle in addition to stiffness degradations in unloading cycles. Yielding points differ in both positive and negative sides of the hysteresis model that enables us to define a different elastic stiffness of both sides in asymmetric concrete sections. Another remarkable property of this model is breaking points and strength deterioration in unloading and reloading stages. This work also compares the obtained results to the conventional hysteresis models, namely bilinear, Clough, Q-Hyst, Takeda and Bouc-Wen in terms of prediction of residual nonlinear deformations in cyclic or dynamic analysis of reinforced concrete single-column bridge piers. The obtained results prove higher relative accuracy of the proposed model.

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