Variable Axial Load Research Articles

Effects of Soil Simulation on the Interaction Analyses of Framed Structures Under 2-D and 3-D Conditions

The effects of some important factors on the development of differential settlements and flexural moments were investigated in the context of interaction analyses for two hypothetical building structures founded on a grid of strip footings. Geometrical simulations included 2-D and 3-D building models in order to identify possible differences when applying the simple 2-D simulation as against the more difficult 3-D one. Furthermore, in order to investigate the applicability of the simple linearly elastic soil model, comparisons were attempted between results obtained on the basis of linearly elastic and elastoplastic according to Mohr–Coulomb’s failure criterion interactive analyses. The variation of differential settlements (or rotations), bending moments and axial loads of the superstructure and foundation were studied versus the elastic modulus E or versus the global safety factor. Detailed conclusions were deduced based on representative diagrams. The comparisons between corresponding results obtained by 2-D and 3-D simulations indicated significant differences especially in cases of high relative rigidity, influenced by the thickness of the compressible soil layer. The comparisons between linearly elastic and elastoplastic soil simulation showed the important role of the relative rigidity in the interaction problem, especially for low values of the global safety factor.

Dynamic response of steel-reinforced concrete-filled circular steel tubular members under lateral impact loads

Abstract In this study, dynamic response of steel-reinforced concrete-filled circular steel tubular (SRCFST) members was experimentally studied under lateral impact loads. Eighteen SRCFST specimens were prepared and tested by the drop hammer impact test system. Various parameters, namely, cross-section of profiled steel, impact velocity and impact direction for I section profiled steel were considered to examine their influences on the failure mechanism, impact force, impact duration, displacement response and energy absorption. Since the beams may be of different constraints at boundary and the columns are axially loaded, boundary condition and axial load level were also considered. The experimental results show that the energy dissipation ratios (Eab/Ek) of all tested specimens except CIFP2-0 are more than 85% and the maximum energy dissipation ratio reaches 97.5%, indicating SRCFST members can absorb large amounts of input energy. Moreover, the inserted profiled steel can effectively enhance impact resistance while reduce energy absorption. It is also found that the peak value (Fmax) of impact force is very sensitive to the variation of impact velocity. The plateau value (Fplateau) of impact force and displacement response are very sensitive to the variation of boundary conditions and axial loads, which can significantly change the lateral flexural stiffness of specimens. Given the same impact energy input, SRCFST members with cruciform section profiled steel under fixed-fixed boundary conditions exhibit the best impact resistance performance with the lowest mid-span displacement.

Seismic Performance of Steel Fiber Reinforced Concrete Beam-Column Joints under the Variation of Column Axial Load

Seismic Performance of Steel Fiber Reinforced Concrete Beam-Column Joints under the Variation of Column Axial Load

Static stability and of symmetric and sigmoid functionally graded beam under variable axial load

This manuscript presents impacts of gradation of material functions and axial load functions on critical buckling loads and mode shapes of functionally graded (FG) thin and thick beams by using higher order shear deformation theory, for the first time. Volume fractions of metal and ceramic materials are assumed to be distributed through a beam thickness by both sigmoid law and symmetric power functions. Ceramic–metal–ceramic (CMC) and metal–ceramic–metal (MCM) symmetric distributions are proposed relative to mid-plane of the beam structure. The axial compressive load is depicted by constant, linear, and parabolic continuous functions through the axial direction. The equilibrium governing equations are derived by using Hamilton\'s principles. Numerical differential quadrature method (DQM) is developed to discretize the spatial domain and covert the governing variable coefficients differential equations and boundary conditions to system of algebraic equations. Algebraic equations are formed as a generalized matrix eigenvalue problem, that will be solved to get eigenvalues (buckling loads) and eigenvectors (mode shapes). The proposed model is verified with respectable published work. Numerical results depict influences of gradation function, gradation parameter, axial load function, slenderness ratio and boundary conditions on critical buckling loads and mode-shapes of FG beam structure. It is found that gradation types have different effects on the critical buckling. The proposed model can be effective in analysis and design of structure beam element subject to distributed axial compressive load, such as, spacecraft, nuclear structure, and naval structure.

Axial Load Monitoring for Concrete Columns Using a Wearable Smart Hoop Based on the Piezoelectric Impedance Frequency Shift: A Feasibility Study

Concrete columns are critical in supporting the weight of an entire structural frame and also play a key role in force transferring among structural members. Therefore, integrity of the columns, especially their axial load bearing capacity, directly affects the stability and safety of the entire structure. In this study, a wearable smart hoop is designed to monitor the axial load of the concrete columns. The smart hoop measures the shift in impedance frequency of its integrated piezoelectric transducer and correlates the frequency to the structural state of the column. In order to validate the feasibility of the smart hoop, an experiment on two concrete columns with different dimensions is carried out. The smart hoop is installed on each column. Then, an increasing axial load was applied onto the specimen, and the admittance of the PZT patch is acquired under different load levels by using an impedance analyzer. Finally, frequencies corresponding to the peak and trough in the susceptance of the admittance signal are collected as the monitoring index to estimate the axial load variation on the specimen. The experimental results demonstrated a downward shift in frequency corresponding to an increase of axial load. The results validate the feasibility of the wearable smart hoop in monitoring axial load for concrete columns and show potential for retrofit on existing columns.

Experimental Evaluation and Numerical Modeling of Wide-Flange Steel Columns Subjected to Constant and Variable Axial Load Coupled with Lateral Drift Demands

This paper presents results from an experimental evaluation on the pre- and post-buckling behavior of 12 steel wide-flange cantilever columns under axial load and lateral drift demands. The influence of several loading and geometric parameters, including the cross-sectional local web and flange slenderness ratios, applied axial load, and lateral and axial loading history on the performance of these columns is thoroughly examined. The test data indicate that cross-sectional local buckling is highly asymmetric in steel columns under variable axial load. A relatively high compressive axial load can significantly compromise the steel column seismic stability and ductility, but this also depends on the imposed lateral loading history. The AISC axial load–bending moment interaction equation provides accurate estimates of a steel column’s yield resistance. However, the same equation underestimates by at least 30% the column’s peak resistance, regardless of the loading scenario. Measurements of column flange deformation, axial shortening, flexural resistance, and lateral drift are combined in a single graphical format aiding the process of assessing steel column repairability after earthquakes. The test data suggest that current practice-oriented nonlinear component modeling guidelines may not provide sufficient accuracy in establishing both the monotonic and first-cycle envelope curves of steel columns. It is also shown that high-fidelity continuum finite-element models should consider geometric imperfections of proper magnitude, in addition to the steel material inelasticity, to properly simulate the inelastic buckling of wide-flange steel columns and generalize the findings of physical tests. Issues arising due to similitude are also discussed to properly limit steel column instability modes in future studies.

Development of collapse‐consistent loading protocols for experimental testing of steel columns

SummaryIn order to effectively utilize results from quasi‐static cyclic testing on structural components for the earthquake‐induced collapse risk quantification of structures, the need exists to establish collapse‐consistent loading protocols representing the asymmetric lateral drift demands of structures under low‐probability of occurrence earthquakes. This paper summarizes the development of such protocols for experimental testing of steel columns prone to inelastic local buckling. The protocols are fully defined with a deformation‐ and a force‐controlled parameter. They are generally applicable to quantify the capacity and demands of steel columns experiencing constant and variable axial load coupled with lateral drift demands. Through rigorous nonlinear earthquake collapse simulations, it is found that the building height, the column's local slenderness ratio, and ground motion type have the largest influence on the dual‐parameter loading protocol indexes. Comprehensive comparisons with measured data from full‐scale shake table collapse tests suggest that unlike routinely used symmetric cyclic loading histories, the proposed loading protocol provides sufficient information for modeling strength and stiffness deterioration in steel columns at large inelastic deformations.

Investigation on seismic behavior of bridge piers with thin-walled rectangular hollow section using quasi-static cyclic tests

This study aims to investigate the seismic behavior of thin-walled rectangular hollow reinforced concrete (RC) bridge piers through quasi-static cyclic tests. For this purpose, two identical 1:12 scale specimens were designed and tested under different loading protocols. One specimen was subjected to displacement-controlled cyclic lateral loading with a constant axial load, and the other to the same lateral loading history, but with a variable axial load. The behavior of both specimens was evaluated in terms of the damage progression and failure mode, concrete crack width, hysteretic response, backbone curve, and residual displacement. The results revealed that both specimens experienced a mixed flexure-shear damage progression from the first crack through collapse. Flexural cracks were first observed in the flange surfaces, followed by the development of shear diagonal cracks in both web surfaces. Meanwhile, both specimens exhibited stable hysteretic behavior. Then, concrete spalling and longitudinal bar buckling were concentrated at the corners of the flanges due to the shear lag effect. Eventually, both specimens collapsed as a result of the flange local compression buckling. In addition, the specimen under a variable axial load collapsed much severer than the one under a constant axial load. Ultimate drifts of the specimens under a constant or variable axial load were 2.25% and 2%, respectively. This experiment provides valuable dataset for validating advanced numerical modeling techniques for thin-walled rectangular hollow RC piers, especially the data points in the collapse stage.

Soil-pile-superstructure interaction effects in seismically isolated bridges under combined vertical and horizontal strong ground motions

This paper presents a deterministic analysis carried out to study the influence of coupled vertical and horizontal ground motions on the response of an isolated bridge (or soil-pile-bridge system) considering soil-pile-superstructure effects. Towards this end, an advanced 3D finite element model is developed to evaluate the effects of combined Vertical Component (VC) and Horizontal Component (HC) of ground motion on the structural elements of the bridge including Soil Structure Interaction (SSI). Non-linear time-history analysis is carried out under strong ground motions using an advanced soil plasticity model for non-liquefiable soil. Three different bridge configurations consisting of (i) simply-supported girders (SSERB), (ii) continuous girder with fixed bearing (CFB) and (iii) continuous girder with elastomeric bearing (CERB) are considered. Ground motion selection procedure was applied among 21,000 records to select suitable ground motions for nonlinear time-history analysis. Critical damage parameters in the structural elements under the combined HC and VC of the ground motion are compared with those under only the HC of the ground excitation. Results indicate that the vertical components produce significant amplification in the pier's axial load with different lower and upper bounds for different seismic isolation systems. The Influence of higher modes on results of Incremental Dynamic Analysis (IDA) are presented for the different structural elements in a deterministic framework. The variations of shear capacity and demand are presented by IDA and the combined spectral acceleration is implemented as an Intensity Measure (IM) due to the inclusion of higher order modes. The simply-supported and continuous girder with elastomeric bearings have a trend for a higher drift ratio than the continuous girder with the fixed-bearings system under vertical excitation. Furthermore, the variation of axial loads and pile-cap displacements are highlighted with and without VC for piles at piers and abutments. In addition, pile-cap displacements, influence of bridge higher modes and VC effects on Soil-Pile-Superstructure Interaction (SPSI) relations are investigated with respect to frequency content of the ground motion. The kinematic and inertial SPSI effects on seismic isolation systems including VC are also explored comparatively. The influence of elastomeric bearing on SSI reduction was investigated by comparing the relative response of the superstructure, Free-Field and Foundation Input Motion (FIM) at the pile head in the frequency domain. The new information presented in this paper will be useful for realistic design of bridges in seismic areas considering coupled HC and VC of the seismic excitation.

Fatigue and fracture analysis of a seven‐wire stainless steel strand under axial and bending loads

AbstractFatigue failure of cables and strands is a common and complex problem. Failure is typically caused by different combinations of time‐variable bending and axial forces. In addition to these loads, contact stresses between wires may play an important role in the fatigue failure of cables. The present work aims to provide deep insight into the fatigue failure of a seven‐wire stainless steel strand subjected to a combination of variable axial and bending loads. To avoid side effects in the analysis, fatigue failure of the strand close to the clamps is prevented. Several tests were performed with a new device specifically designed to avoid failure near the clamps. Thus, failure is always produced at the middle length of the specimen. Test simulations were performed by employing the finite element method. The numerical results were validated via comparisons with experimental data. Finally, life prediction curves were obtained.

Effect of axial load and transverse reinforcements on the seismic performance of reinforced concrete columns

The aim of this research is to assess the seismic performance of reinforced concrete columns under different axial load and transverse reinforcement ratios. These two parameters are very important as for the ductility, strength, stiffness, and energy dissipation capacity for a given reinforced concrete column. Effects of variable axial load ratio and transverse reinforcement ratio on the seismic performance of reinforced concrete columns are thoroughly analyzed. The finite element computer program Seismo-Structure was used to perform the analysis of series of reinforced concrete columns tested by the second author and other researchers. In order to reflect the reality and grasp the actual behavior of the specimens, special attention was paid to select the models for concrete, confined concrete, and steel components. Good agreements were obtained between the experimental and the analytical results either for the lateral force-drift relationships or for the damage progress prediction at different stages of the loading.

New fatigue device for testing cables: Design and results

AbstractThe fracture of cables is often caused by fatigue phenomena. To analyse the fatigue behaviour of these elements, a device has been designed, manufactured, and validated. This machine can produce different load states for the specimens, combining variable axial loads and variable bending moments. The testing machine has been designed to achieve two goals: to avoid the fracture of the cable in the vicinity of the clamps and to assure that the fracture of the cable is in the middle of the length of the specimen. The type of failure will be due to a combination of global stresses and fretting fatigue phenomena. This work also shows the results of different fatigue tests for a specific strand configuration. Finally, the fracture and contact surfaces of the strand have been analysed with a scanning electron microscope (SEM). The results obtained with this device show that it is adequate for testing cables and strands subjected to different combinations of axial loads and bending moments.

A New Geometrically Exact Model for Buckling and Postbuckling Statics and Dynamics of Beams

In this study, a new geometrically exact nonlinear model is developed for accurate analysis of buckling and postbuckling behavior of beams, for the first time. Three-dimensional nonlinear finite element analysis is conducted to verify the validity of the developed model even at very large postbuckling amplitudes. It is shown that the model commonly used in the literature for buckling analysis significantly underestimates the postbuckling amplitude. The proposed model is developed on the basis of the beam theory of Euler–Bernoulli, along with the assumption of centerline inextensibility, while taking into account the effect of initial imperfection. The Kelvin–Voigt model is utilized to model internal energy dissipation. To ensure accurate predictions in the postbuckling regime, the nonlinear terms in the equation of motion are kept exact with respect to the transverse motion, resulting in a geometrically exact model. It is shown that even a fifth-order truncated nonlinear model does not yield accurate results, highlighting the significant importance of keeping the terms exact with respect to the transverse motion. Using the verified geometrically exact model, the possibility of dynamic buckling is studied in detail. It is shown that dynamic buckling could occur at axial load variation amplitudes as small as 2.3% of the critical static buckling load.

A new approach for free vibration analysis of nonuniform tall building structures with axial force effects

SummaryDynamic analysis of beam‐like structures is significantly important in modeling actual cases such as tall buildings and several other related applications as well. This article studies free vibration analysis of tall buildings with nonuniform cross‐section structures. A novel and simple approach is presented to solve natural frequencies of free vibration of cantilevered tall structures with variable flexural rigidity and mass densities. These systems could be replaced by a cantilever Timoshenko beam with varying cross‐sections. The governing partial differential equation for vibration of a nonuniform Timoshenko beam under variable axial loads is transformed with varying coefficients to its weak form of integral equations. Natural frequencies can be determined by requiring the resulting integral equation, which has a nontrivial solution. The presented method in this study has fast convergence. Including high accuracy for the obtained numerical results as well. Numerical examples including framed tube as well as tube‐in‐tube structures are carried out in the study and compared with available results in the literature, and also with the results obtained from finite element analysis in order to show the accuracy of the proposed method in the study. Obtained results indicate that the presented method in this study is powerful enough for the free vibration analysis of tall buildings.

Three-to-one internal resonance of inclined marine riser

In this paper, we investigate the three-to-one internal resonance of an inclined marine riser. The model accounts for the flexural rigidity of the riser, variable axial load, nonlinear geometry, and initial static deflection due to self-weight. The applied tension with the static deflection are tuned such that the ratio between the fifth and first natural frequencies is three. Then, the multiple time scales (MTS) perturbation method is applied to study the internal resonance interactions when the structure is harmonically excited. The system equation is solved using a multi-mode Galerkin model and its results are compared to the perturbation results showing good agreement. Moreover, the frequency response curves of the fifth and first modes amplitudes exhibit Hopf and saddle node bifurcations. In addition, the interaction of the fifth mode with the first mode during internal resonance results into new emerging solutions and states. These phenomena are well observed in the force response curves and confirmed by the time history of the response of the structure, which can lead to complex dynamics that hinder the life of the riser by fatigue failure.

Phenomenological Model of Rubber Bearings With Variable Axial Loading

Seismic base isolation systems protect thousands of structures and infrastructures all over the world. Their effectiveness for seismic protection is widely recognized owing to acceleration reduction with a consequent minimization of the structural damage and of the ‘panic’ effect for the occupants. This work deals with the development of a model for simulating the horizontal response of rubber bearings, extending an existent procedure to the case of variable axial loading. A consolidated procedure from literature, demonstrated able to correctly reproduce the complex mechanical behavior of rubber bearing isolation devices under constant axial loading, represents the starting point. Available laboratory cycling tests at variable axial load allow to illustrate the new numerical formulation. An optimization process, based on both automatic and user-driven procedures, is used to identify at different loading conditions the model parameters and the functions to model their variation. The proposed formulation overcomes the limits of the original model in this respect. The developed new version of the bearing model is shown to be capable of simulating with reasonable accuracy the experimentally observed cyclic behavior under coupled vertical-horizontal loading conditions, and the consequences in terms of the device response in the case of a seismic vertical-horizontal concurrent excitations are highlighted.

Analytical prediction of seismic behavior of RC joints and columns under varying axial load

In this study, an analytical model for predicting nonlinear behavior of exterior reinforced concrete (RC) beam-column joints under varying axial load was developed. The main focus was given on the assessment of the effect of axial load variations on the response of RC joints and columns. During seismic actions, overturning moments are produced by lateral loads that are translated as axial loads in the columns. It leads to compressive axial force on one side of the structure along with tensile on the opposite. It can overwhelm nonlinear behavior associated with axial, flexural, shear stresses of RC columns and joints. To simulate and evaluate these nonlinearities, a beam- column joint model consisted of rotational springs were developed. The characteristics of joint spring could be computed using principle tensile stress-joint rotation relation (pt versus θj) in the joint core depending on the type of the beam bar anchorage. Therefore, for the joints with various beam bar anchorage details, pt versus θj relations in the joint core were proposed. A new theoretical methodology was also developed to consider the effect of the axial load variations in determining characteristics of rotational springs. To assess the accuracy and reliability of the analytical model, it was compared through experimental data available in the literature. The results showed that the proposed analytical model could predict the experimental response of poorly detailed RC beam-column joints under varying or constant axial loads with reasonable precision. Furthermore, parametric studies were carried out to highlight the overwhelming effect of axial load variations on RC beam-column joints and columns. The simple analytic procedure would make the model sufficiently suitable for practical applications.

FUNCTION OF THE MENISCI IN THE LOAD TRANSFER WITHIN THE KNEE JOINT

The aim of the study was to conduct strength analysis of a knee joint in order to experimentally determine the destructive fatigue loading under the conditions of cyclic compression. Animal joints were used as the study material. They were periodically subjected to variable axial loading. The degree of joint deformity and damage to articular surfaces and menisci were globally determined after isolation of the joint structures. The application of the variant of axial loading without slip and rolling results in the rupture of the medial meniscus, which is an important biotribological structure. Fatigue testing of the joints allowed for the determination of the parameters of biomechanical extortions, which lead to the loss of normal lubrication conditions and the degradation of the meniscus and cartilage structures on the femoral condyles.

Influence of seismic loading on axial load variation in reinforced concrete columns

Influence of seismic loading on axial load variation in reinforced concrete columns

Effects of High Strain Rates on the Response of Glulam Beams and Columns

AbstractA material predictive model that accounts for strain-rate effects and captures the effect of variable axial load on the dynamic response of glulam structural members subjected to combined l...