Cyclic Loading Histories Research Articles

Tensile strength of compacted rammed earth materials

A rammed earth technique is a traditional architectural technique to build soil structures by compacting geo-materials in a form. In this study, tensile strength properties of rammed earth materials and effects of test conditions are evaluated by conducting direct tension tests and splitting tests on several specimens. It is inferred from the result of these test that the direct tension test should be used to evaluate tensile strength of a layer interface, while the splitting test might evaluate the strength related to the tensile strength inside a compaction layer. When rammed earth structures are constructed, the results from the experiments indicate that it is important to scarify interfaces during compaction in order to prevent reduction and variation of the tensile strength of the layer interfaces. The tensile strength of the rammed earth specimens made of compacted soils without lime increased with the decrease in their water contents. The tensile strengths of the specimens represent 5.0–12.5% of corresponding values of unconfined compression strength at the same water content range. The tensile strength of rammed earth specimens made of lime-mixed soil was in the range of 15–20% of the corresponding unconfined compression strength at 28 days curing. In the series of cyclic tensile loading test, no significant reduction of tensile strengths was observed even after undergoing the cyclic loading history.

Investigation of Limit States Specified for Reinforced Concrete Column Members in TEC–2007

In this study, the deformation based limit states stipulated for reinforced concrete members in the Turkish Earthquake Code (TEC) were experimentally investigated. Thus four RC cantilever columns which have low concrete compressive strengths and have not adequate confinement, were subjected to constant axial load and cyclic lateral load history. In the study, firstly, the strain values representing the damage limits were converted to top of the column lateral displacements by using fundamentals of structural mechanics. Subsequently the column damages corresponding to the displacement demands were observed, hence limit states were evaluated. After conducting all column tests, it was noted that no column damage was observed for the immediate occupancy (IO) performance level defined in the code. For the life safety (LS) and collapse prevention (CP) performance levels, though somewhat residual deformations occurred on the critical regions, the column members can pretty much sustain their lateral load capacities. It was also observed for all columns that significant damages and strength losses occurred beyond the collapse prevention level. The results of experimental study indicate that the evaluation procedure in the TEC is still in good relationship with the limit states even if the columns have not adequate compressive strength and confinement.

Linear matching method for design limits in plasticity

In this paper a state-of-the-art numerical method is discussed for the evaluation of the shakedown and ratchet limits for an elastic-perfectly plastic body subjected to cyclic thermal and mechanical load history. The limit load or collapse load, i.e. the load carrying capacity, is also determined as a special case of shakedown analysis. These design limits in plasticity have been solved by characterizing the steady cyclic state using a general cyclic minimum theorem. For a prescribed class of kinematically admissible inelastic strain rate histories, the minimum of the functional for these design limits are found by a programming method, the Linear Matching Method (LMM), which converges to the least upper bound. By ensuring that both equilibrium and compatibility are satisfied at each stage, a direct algorithm has also been derived to determine the lower bound of shakedown and ratchet limit using the best residual stress calculated during the LMM procedure. Three practical examples of the LMM are provided to confirm the efficiency and effectiveness of the method: the behaviour of a complex 3D tubeplate in a typical AGR superheater header, the behaviour of a fiber reinforced metal matrix composite under loading and thermal cycling conditions, and effects of drilling holes on the ratchet limit and crack tip plastic strain range fora centre cracked plate subjected to constant tensile loading and cyclic bending moment.

Application of Small Punch Test in Predicting the Axial Fatigue Life of 304 Stainless Steel Sheets

The application of small punch test (SPT) for predicting the axial fatigue life of 304 stainless steel is examined. The results of SPT on predamaged 304 stainless steel sheets show that the increase in fatigue damage decreases the maximum punch load. However, the change in the maximum punch load can be translated into the change in the ultimate strength of the specimen according to the literature. Using the Palmgren–Miner model then, a cyclic load history is estimated that is found to be in good agreement with the actual loading. Consequently, the SPT is suggested as a fatigue life estimating technique where the past loading history is not available. In other words, this study proposes an SPT-based assessment of the remaining fatigue life of used components.

A 3D multiscale cohesive zone model for quasi-brittle materials accounting for friction, damage and interlocking

A three-dimensional (3D) two-scale Cohesive Zone Model (CZM), which is based on a multiplane approach and couples damage with friction and interlocking, is presented for analysing crack propagation in quasi-brittle materials along structural interfaces where formation of cracks is expected. The main idea of the 3D multiplane formulation herein exploited is to describe the asperities of the interface in the form of periodic patterns of inclined planes, denominated Representative Interface Elements (RIE). The interaction within each plane of the RIE is governed by the interface formulation proposed by Alfano and Sacco in earlier work. After reporting details of the formulation and of its algorithmic implementation, the sensitivity of the macroscopic mechanical response to the specific selection of the RIE is analysed and reported with a general numerical assessment of the 3D interface mechanical response to monotonic and cyclic loading histories. A fundamental issue addressed in this paper is the identifica...

A generalised method for ratchet analysis of structures undergoing arbitrary thermo‐mechanical load histories

SummaryA novel approach is presented based upon the Linear Matching Method framework in order to directly calculate the ratchet limit of structures subjected to arbitrary thermo‐mechanical load histories. Traditionally, ratchet analysis methods have been based upon the fundamental premise of decomposing the cyclic load history into cyclic and constant components, respectively, in order to assess the magnitude of additional constant loading a structure may accommodate before ratcheting occurs. The method proposed in this paper, for the first time, accurately and efficiently calculates the ratchet limit with respect to a proportional variation between the cyclic primary and secondary loads, as opposed to an additional primary load only. The method is a strain‐based approach and utilises a novel convergence scheme in order to calculate an approximate ratchet boundary based upon a predefined target magnitude of ratchet strain per cycle. The ratcheting failure mechanism evaluated by the method leads to less conservative ratchet boundaries compared with the traditional Bree solution. The method yields the total and plastic strain ranges as well as the ratchet strains for various levels of loading between the ratchet and limit load boundaries. Two example problems have been utilised in order to verify the proposed methodology. Copyright © 2015 John Wiley & Sons, Ltd.

On the experimental and numerical study of braced steel shear panels

Steel shear panels in combination with bracing are a novel form of steel shear walls that eliminate large distributed loads to impose on primary beams along with columns. This paper presents the results of a comparative experimental program on two types of steel shear panels with and without stiffeners. For this purpose, the proposed quasi-static cyclic loading history of Federal Emergency Management Agency(FEMA) 461 was applied on two full-scale specimens. Structural steel was selected as the material of the panels, which were welded to the surrounding boundary elements. In addition, using finite element models, performed tests were simulated and scaling effects were investigated. This study identified that steel shear panels have acceptable hysteretic behavior in addition to excellent ductility, which cause more dissipation of induced seismic energy. Comparison of seismic performance of two types of steel shear panels and high cost of setting up stiffeners demonstrate that unstiffened shear panel is a reliable selection for seismic-resisting systems. The results of numerical study show that acceleration-based similitude laws have acceptable estimation for responses of scaled models. Copyright © 2015 John Wiley & Sons, Ltd.

Small- and large-strain behaviour of a cement-treated soil during various loading histories and testing conditions

The effects of loading histories on small-strain and large-strain stiffness of a compacted cement-mixed well-graded gravelly soil were evaluated by consolidated drained triaxial compression (TC) tests. Various cyclic loading histories were applied during otherwise continuous monotonic loading at different confining pressures, σhs, and multiple-step loading with stepwise increase or decrease of σh. To evaluate small-strain stiffness, minute unload/reload cycles were applied during TC loading. The value of peak-to-peak secant modulus from a minute unload/reload cycle was defined as the equivalent Young’s modulus, Eeq. The average of Eeq values measured during continuous monotonic loading at low deviator stresses was rather close to the elastic modulus, Ee. As the Ee increased with an increase in the axial stress, the Eeq value increased first and then decreased due to an increase in creep strains. The stress–strain behaviour after the start of a large-scale yielding and the peak shear strength is not noticeably affected by the previous cyclic loading with relatively large stress amplitude. However, the large-strain stiffness during reloading is significantly affected by the following factors controlled by pre-cyclic loading history; (a) strain hardening; (b) strain nonlinearity; (c) hysteresis effect; (d) viscous effect; and (e) damage to bonding by immediately preceding large unloading. The tangent stiffness, Etan, at a given stress level during reloading becoming larger with an increase in the effects of factor (a) and smaller by the effects of factors (b), (c), (d) and (e). In addition, increase of σh has a negative effect on stiffness of primary loading curves and a positive effect on stiffness of reloading curves. The effect of loading history on the small-strain stiffness in terms of equivalent Young’s modulus, Eeq, was found to be significant. This effect depends on various factors. Four factors—axial stress level, strain-hardening effect, creep effect by the viscous properties and damage due to a loading history—were identified to be responsible for equivalent Young’s modulus, Eeq variations. Axial stress increase and strain-hardening effect both increase Eeq, making Eeq closer to the Ee. However, creep strains by the viscous properties and damage due to a loading history both decrease Eeq.

Inflow Parameter Effects on Wind Turbine Tower Cyclic Loading

Wind turbine towers are fatigue-critical structures subjected to a variety of atmospheric wind regimes at onshore installations. At a commercial wind farm in Southwestern Ontario, the structural steel supporting tower of a multi-megawatt horizontal-axis turbine has been instrumented with a fiber Bragg grating strain gauge array. A nearby meteorological mast allows wind conditions to be classified on the basis of horizontal turbulence intensity and vertical wind shear. Data has been collected over a measurement campaign spanning multiple months, and a sample of the tower's cyclic loading history has been compiled. Comparisons are drawn between accumulated hourly loading cycle spectra for operation across different upwind inflow parameters.

Stress–strain–temperature relation for cyclically-damaged structural mild steel

Experimental results suggest that the mechanical properties of mild steel at elevated temperatures are affected by the cyclic load history previously applied to the material. This has great implications when it comes to post-earthquake fire analyzes. Therefore, it is desirable to establish the relationship for each mechanical property, not only as a function of temperature but also the damage induced by the cyclic load history. To achieve this goal, a special class of functions known as Bézier curves have been utilized in this research. These functions are used for the construction of stress–strain curves that depend on temperature and the amplitude of the previously applied strain cycles. Actual experimental results are used throughout the process for calibration and validation purposes. The proposed model proves to be highly versatile in the sense that it can successfully take the effect of temperature and pre-induced strain cycles into account, making it applicable to post-earthquake fire analyzes.

Cumulative Deformation Capacity of Steel Braces under Various Cyclic Loading Histories

AbstractThe postbuckling behavior of seismic-resistant braces in steel frames under a cyclic axial force is often evaluated by time–history analyses; however, brace fracture is seldom considered. The authors previously proposed a physical model for predicting the moment of fracture of circular-tube braces after buckling using phenomenological hysteresis. However, the accuracy of that model was confirmed only against the test results of the gradually increasing amplitude loading protocol, and its applicability under other loading histories has not yet been verified. In this study, cyclic loading tests were carried out until fracture on circular-tube and H-section braces under various loading histories, followed by FEM analyses. The validity of the proposed formulas for evaluating the strain-concentration index under various loading histories was examined. The proposed method was used for predicting the moment of fracture and the cumulative deformation capacity until fracture, and the predictions agreed wel...

Influence of cyclic loading history on small strain shear modulus of saturated clays

Small strain shear modulus Gmax is an essential parameter in soil dynamics, and it is usually estimated based on the Hardin and Richart equation. However, many previous researches on sands have indicated that the Hardin and Richart equation does not consider the influences of cyclic loading history on Gmax. In this paper, effects of cyclic loading history on Gmax of saturated clays under undrained conditions are studied using a combination device of piezoelectric-ceramic bender element system and cyclic triaxial apparatus. The dynamic pre-loading includes both relatively high amplitudes of cyclic stresses and cyclic strains. Gmax without cyclic loading history is also investigated for the comparison purpose. Test results show that, at the same effective stress, both cyclic strain history and cyclic stress history will induce reduction of Gmax compared to the corresponding Gmax values with non-cyclic loading effects. In strain-controlled tests, the reduction of Gmax is slight and relatively stable; while in stress-controlled tests, the reduction of Gmax increases suddenly and remarkably when the effective stresses degrade to a certain degree. The comparison between double amplitude axial strain and residual excess pore water pressure behaviors show that the remarkable reduction of Gmax can demonstrate the cyclic failure of saturated clays.

Modeling of Cyclic Shear-Flexure Interaction in Reinforced Concrete Structural Walls. II: Experimental Validation

This paper presents the experimental calibration and validation of the analytical wall model that incorporates interaction between shear and flexural responses under cyclic loading conditions described in the companion paper. The model is calibrated and validated against detailed experimental data obtained from tests on five moderately slender reinforced concrete wall specimens that experienced significant levels of shear-flexure interaction. Test measurements were processed to allow for detailed comparisons between the predicted and measured wall responses at various locations and response levels. Response comparisons reveal that the proposed analytical model captures the experimentally measured nonlinear shear deformations and their coupling with flexural deformations throughout the cyclic loading history. In addition, the analytical results successfully represent various experimentally measured responses, such as lateral-load versus wall-top-displacement relations, magnitudes and distributions of deformations associated with shear and flexure, and local responses including flexural rotations, vertical strains, and concrete crack orientations. Based on the comparisons presented, model capabilities are assessed and future model improvements are suggested.

Experimental analysis on friction materials for supplemental damping devices

In this paper, the friction coefficient and the cyclic response of different interfaces for friction devices are investigated by means of experimental tests under displacement control. In particular, six interfaces have been tested: steel–steel, brass–steel, sprayed aluminum–steel and three different rubber based friction materials adopted, respectively, in automotive applications, electrical machines and applications requiring low wearing.Static and kinetic friction coefficients have been evaluated and the influence of the interface pressure has been analyzed. The variation of the sliding force during the cyclic loading history has been investigated by comparing also the response coming from the use of different washers: circular flat washers and cone shaped annular disc springs.The work is aimed at the investigation of friction materials to be applied within the connecting elements of beam-to-column joints according to the double split tee configuration with friction pads.

Element mesh, section discretization and material hysteretic laws for fiber beam–column elements of composite structural members

A fiber beam–column element for nonlinear analysis of composite structural members is developed in this paper. The programing of complex material uniaxial constitutive laws and the implementation of the developed element into a general commercial standard finite-element package are discussed. Intensive parametric studies on the modeling strategies of element mesh, section discretization and material hysteretic laws are carried out to develop fiber element with sufficient accuracy, efficiency, stability and practicality for composite structural members. Rational element mesh scheme is recommended to capture the sharp jump of the curvature value at the plastic hinge region and to effectively overcome the numerical difficulty of pathological mesh-sensitivity brought about by the strain softening effect. Efficient section discretization schemes are proposed to give results of sufficient accuracy for the hysteretic behavior of composite members under complex cyclic load histories. The Bauschinger effect of the steel is found to be the most significant factor dominating the accuracy, and the hysteretic law of the concrete can be simplified by ignoring the complex strength and stiffness degradation effects with little influence on the accuracy. Finally, the developed program COMPONA-MARC and the recommended modeling strategies are validated by extensive experimental results of composite structural members.

A Residual Stress Decomposition based Method for the Shakedown analysis of structures

In the attempt to extend the life of a structure, or a component, which is subjected to cyclic loading history it is important to provide safety margins against excessive inelastic deformations. Direct methods and in particular shakedown analysis provide the only means towards this end. Most of the approaches in shakedown analysis are based on the two theorems of plasticity and are tuned with the solution of optimization algorithms. In this paper a new method is presented which approaches the problem in a different way. The method makes use of a recently published direct method, called the Residual Stress Decomposition Method (RSDM), which assumes the decomposition of the residual stresses into Fourier series in time. The RSDM may predict any cyclic elastoplastic state for a given cyclic loading history. With the present approach a loading of prescribed limits is converted to an equivalent loading which has a prescribed time history. The procedure approaches the shakedown loading from above starting from a loading factor that makes the whole structure plastic. The procedure generates a descending sequence of loading factors which shrinks the load domain until the only remaining term of the Fourier series is the constant term. It is formulated within the finite element (FE) method and an elastic-perfectly plastic material with a von Mises yield surface is assumed. It may be directly implemented in any FE code. The versatility of the approach is shown through examples of application.

Effects of drained cyclic loading history on small strain shear moduli and liquefaction strength of Toyoura sand

Effects of drained cyclic loading history on small strain shear moduli and liquefaction strength of Toyoura sand

Mechanical properties of cyclically-damaged structural mild steel at elevated temperatures

The mechanical response of a structural element not only depends on the inherent properties of the materials which constitute the element, but also on the history of any loads it had been previously subjected to. An important instance of this is the response of steel structures under post-earthquake fire. This research aims to investigate the potential changes that the mechanical properties of structural grade mild steel experience under such a loading sequence. The experimental results presented in this paper indicate that a prior history of cyclic loading significantly affects the proceeding ductility and strength of grade 300 steel at high temperatures. This implies that any history of cyclic loading should be included in the post-earthquake fire-resistant design of structures.

Experimental and Analytical Evaluation of Concrete-Filled Crisscross Steel Tubular Columns Subjected to Earthquake Loads

Concrete-filled steel tubular columns have been studied extensively worldwide. Such columns provide stable energy dissipation, which is ideal for earthquake engineering application. However, most applications use rectangular steel tubular sections. In the location of wall intersections, these sections often create sharp corners, which are architecturally displeasing. In some facilities such as schools and correctional facilities, sharp corners are even prohibited due to their potential hazard to occupants. To resolve the issue, concrete-filled crisscross steel tubular columns (CCSTCs) have been proposed. Three half-scaled specimens were constructed and tested under cyclic displacement loading history. The experimental results were used to calibrate numerical models of the components and further used to examine the seismic behavior of a three-story prototype office building located in Los Angeles. The results showed the proposed CCSTC has excellent energy dissipation and postearthquake performance, and hence it can be used as an alternative lateral force resisting system for seismic applications.

Damage Mechanics and Critical Plane Approach to Multiaxial Fatigue

The mechanical behaviour of structural components subjected to multiaxial fatigue loading is very important in modern design. Several approaches have been introduced in recent decades to analyse this problem. The so-called critical plane approach, based on the stresses acting on the plane where the crack nucleation is expected to occur, is widely used. This criterion can give us a fatigue damage measurement, which can be used to evaluate fatigue life. On the other hand, fatigue life under general multiaxial stress histories can also be assessed by applying the damage accumulation method. In such a method, a scalar damage parameter is quantified through the damage increments which develop during the fatigue process up to the critical damage value corresponding to the final failure of the structures. The damage increment approach to fatigue has recently been discussed and connected to the classical crack propagation approach. In the present paper, the interpretation of the critical plane approach based on the continuum damage mechanics concepts is examined. In particular, the physical meaning of the critical plane approach is shown, that is, such an approach can be interpreted as a damage method which takes into account the scalar damage parameter evaluated along preferential directions. Finally, the fatigue behaviour of a metallic material under multiaxial cyclic load histories is analysed through the two above approaches.