Contraflexure Research Articles

Experimental study on cyclic lateral response of piles in sandy sloping ground

This study aims to experimentally investigate the cyclic lateral responses of piles in sloping ground. The effects of slope angle θ, number of cycles n, and loading pattern (static or dynamic) on the pile responses (inc. unloading stiffness and residual displacement) were revealed by a series of laboratory (1-g) model tests considering the combined effects of slope and cyclic lateral loading. The measured responses indicated that all the pile head displacement, bending moment, lateral earth pressure, and unloading stiffness increase non-linearly with n. Thereinto, the pile head displacement x can be fitted by the function x = A(θ)n0.1 where the coefficient A(θ) is linearly related to tanθ; the residual displacement decays exponentially with the number of cycles. In addition, the slope effect would exacerbate the pile responses under cyclic loading, for instance, the maximum bending moment is linearly related to tanθ, and the depth of contraflexure point increases by 0.14 times the pile diameter when the slope angle increases by 1°.

EFFECT OF OUT-OF-PLANE LOADING CONDITIONS ON SHEAR BEHAVIOR OF RC SHEAR WALLS

Bi-directional loading tests on reinforced concrete walls were conducted with out-of-plane deformation and height of contraflexure point as parameters. The experimental results were discussed with FE analysis. The reduction of the in-plane load capacity due to out-of-plane loading was smaller when the wall was bent in single curvature compared to when in double curvature in the out-of-plane direction. An evaluation method of the in-plane shear capacity considering tri-directional loading proposed by the authors can capture the experimental results of the nine wall specimens with a margin of error ranging from -3 to +9%.

Site Measurement Study on Mechanical Properties of SMW Piles of Building Structures in Sandy Soil Areas

SMW (soil mixing wall) piles have been widely used in soft soil areas such as Jiangsu, Shanghai, Tianjin and so on, and they have many advantages, such as retaining the structures of foundation pits. In order to promote the application of SMW piles in sandy soil areas such as Henan province, SMW piles were used in a deep foundation pit project of a high-rise building in Zhengzhou. Three SMW piles in the middle area of the foundation pit were selected for site measurement to determine the mechanical properties of SMW piles in sandy soil areas. Several typical test sections were determined along the height of the pile. The vibrating string type of the reinforcement dynamometers were set on the H-shaped steel of each test section, and the stress distribution of the H-shaped steel along the depth of the pit was obtained via testing. The axial force, bending moment and shearing force of the H-shaped steel were further calculated, and the affecting factors and development laws of the internal force distribution of the H-shaped steel were analyzed in detail. The research shows that, at the stage of foundation pit excavation, the overall stress of H-shaped steel increases gradually. The axial force of H-shaped steel in an SMW pile is mainly affected by such factors as the weight of the H-shaped steel, the weight of the crown beam and the first support system, the weight of the breast beam and the second support system, and the frictional resistance of the cemented soil. The bending moment and shearing force of H-shaped steel are mainly affected by such factors as the lateral soil pressure and the concentrated forces of the two support systems. When the foundation pit was excavated to the base, the development of and changes in the law of internal force with regard to the H-shaped steel was analyzed. When the overall internal force of the H-shaped steel is at its maximum, the maximum absolute values in terms of the axial force, bending moment and shearing force are −481 KN, 371 KN·m and 123 KN. In the process of foundation pit excavation and backfilling, the point of contraflexure of the H-shaped steel moves down gradually, and the fixed end of corresponding SMW pile also moves down and stabilizes below the base. These results may provide a reference for the design and construction of SMW piles of building structures in sandy soil areas.

Experimental and theoretical research on relation between magnetic and mechanical property of structural I-steel column

As an ignored physical property, the metal magnetic memory signal has the potential for non-destructive testing in the future. To get the variation characteristic of magnetic signals under different loads, the normal components of surface spontaneous magnetic signals Hp(y) of the Q235 I-steel column were measured online. In this paper, the variation law of Hp(y) with stress was investigated in the position of the point of contraflexure and stress concentration. The physical mechanism between its magnetic property and mechanical property was established at the elastic and plastic stages. Experimental results show that Hp(y) reaches the extreme value in the position of stress concentration, where the magnetic field gradient K presents the zero-crossing phenomenon along with the peak–peak value phenomenon on the left and right sides. In the position of the point of contraflexure, when the Hp(y) curve reaches the extreme value, the corresponding equivalent uniaxial stress σeq is 54 MPa, which is in good agreement with the Jiles–Atherton (J–A) model. Characteristic parameters Kmax, ζ, and η can reflect the extent of damage of the specimen. In the position of stress concentration, Hp(y) values decrease sharply at the early plastic stage. The analysis shows that the distribution regularity of Hp(y) at the elastic stage is in good agreement with the J–A model. The modified J–A model is consistent with the experimental results at the plastic stage.

Evaluation Methodology of Laminar-Turbulent Flow State for Fluidized Material with Special Reference to Submarine Landslide

Submarine landslides have destroyed many ocean engineering facilities and induced catastrophic tsunamis, causing considerable loss of lives and properties. However, the evolution process of submarine landslides is highly complicated and difficult to describe with a unified mechanical framework. For fluidized landslides with wider influence ranges, faster migration velocities, and stronger impact forces, it is necessary not only to describe the constitutive model but also to determine the flow state. First, based on the essential rheological test for determining constitutive models, the relevant method and principle are thoroughly analyzed, and the formula for calculating the Reynolds number of fluidized submarine landslides in the entire shear process is derived. Taking the critical Reynolds number as the evaluation standard, a methodology to distinguish the flow state (laminar or turbulent) of fluidized landslides is quantitatively proposed. Second, through the low-temperature rheological test, the proposed formula and methodology are briefly applied to the natural submarine sediment samples in the South China Sea. In addition, the point of contraflexure of the rheological curve is consistent with the critical Reynolds number calculated by the formula, and the validity of this methodology is further verified. Finally, the mechanism of the flow-state transition is systematically analyzed by the internal evolution of the structure of the fluidized sediment samples in the shear process. This study provides important support for understanding the migration of fluidized submarine landslides.

Numerical investigation on the shear behavior of prestressed concrete beams with small rectangular openings

AbstractThe numerical investigation focused on the shear behavior of prestressed concrete (PC) beams with small rectangular openings, using the software ABAQUS. Three variables, including the prestressing force, the height of the opening and its length, were considered. The numerical results exhibited a good agreement with the previous experimental outcomes, and the parametric analysis was conducted to study the local internal force distribution of two chords during the loading process. The results indicate that for RC beams with openings, the shear proportion variation of the top chord is stable as the opening size changes, while it decreases almost linearly with the increase of prestressing force for PC beams with openings. The position of contraflexure point is found to be proportional to the root of the reinforcement ratio of the chord, and it moves towards the support with the increase of the prestressing force. Furthermore, the empirical equations to determine the shear proportions and the position of contraflexure point between chords are established.

Comparison of Fracture Test Methods for Evaluating the Crack Resistance of Asphalt Mixture

For the better understanding of fracture test method to evaluate the crack resistance of asphalt mixtures, the current test methods and evaluation indexes were theoretically and experimentally compared, including the indirect tensile test, single edge notch beam test, semicircular bending test (SCB) and disk-shaped compact tension test. The stress intensity factors for different tests were compared, and the appropriate range of notch depth was determined. The SCB was finally selected as the test method for evaluating the crack resistance of the asphalt mixtures. According to the relationship between the fracture energy and notch depths, the essential fracture energy of asphalt mixtures was calculated, and it was recommended as the evaluation index of asphalt mixtures for crack resistance. Furthermore, the failure process of the SCB was analyzed, and the contraflexure point on the load–displacement curve was found and defined. The fracture energy at the contraflexure point could be used to evaluate the ultimate crack resistance of the asphalt mixtures. The application of the essential fracture energy and the contraflexure point can correspond to the actuality of the asphalt pavement, which provides a reference for the crack resistance research of asphalt mixtures in the future.

Parametric analysis on punching shear resistance of reinforced-concrete continuous slabs

Punching shear resistance formulations provided by codes are usually calibrated on test results of isolated specimens that typically simulate the slab zone within the points of contraflexure around the column (hogging area). However, the behaviour of actual continuous flat slabs can be different to that of isolated specimens owing to the beneficial contributions of moment redistributions and membrane actions that cannot take place in isolated specimens. This paper presents a parametric study carried out to highlight the influence of the main geometrical features and the reinforcement layout affecting the punching shear resistance of continuous slabs around internal columns.

Experimental investigation on the blocking of groundwater seepage from a waterproof curtain during pumped dewatering in an excavation

The interaction between a waterproof curtain and withdrawal wells (or simply, the wall-well effect) is a key factor in controlling the environmental effects that occur during the dewatering of foundation pits. A series of laboratory investigations was conducted to study the changes in groundwater level during dewatering. The influence of the buried depth of the waterproof curtain placed in a dewatering confined aquifer (D), and the filter length of the pumping well (L), is investigated. Based on the laboratory test results, numerical simulations are used to analyse the ground settlement. The relationship between the approximate hydraulic gradients on both sides of the wall (Δi), or the ground settlement outside the excavation (S), using ratio RD (D divided by the thickness of the confined aquifer) or ratio RL (L divided by the thickness of the confined aquifer), can be simulated using a Boltzmann curve. The value of Δi increases while S decreases with an increase in RD, whereas Δi decreases while S increases with an increase in RL. The value of the contraflexure point of the Boltzmann curve is regarded as the effective value of RD or RL. Based on a comprehensive consideration, RD is suggested to be equal to or larger than the effective value, and RL is suggested to be equal to or lesser than the effective value.

Substitute Frame and adapted Fish-Bone model: Two simplified frames representative of RC moment resisting frames

This paper aims to develop simplified frame models applicable for Reinforced Concrete (RC) moment frames. For this purpose, the existing Modified Fish-Bone (MFB) model, which is usually used for steel moment frames, is adapted for RC moment frames using modified Ibarra-Medina-Krawinkler springs with deteriorating peak-oriented behavior. Pre-analysis demonstrates that the MFB model requires some modifications for RC moment frames to (a) eliminate the imposed redundant compressive forces to the single column which was caused by the unbalanced shear forces between two half-beams at each story, and (b) simulate the migration of contraflexure point in the beams of original RC frames. The challenges stem from (a) the different negative and positive moment capacities in RC beams, and (b) the peak-oriented hysteretic behavior of rotational springs representing beam plastic hinges. More detailed investigation indicates that eliminating the redundant compressive force is the most effective modification, but the migration of contraflexure point due to different negative and positive moment capacities and even the single curvature bending condition of original beams is not crucial. The reason is investigated using step-by-step incremental nonlinear analysis and illustrated that the contraflexure point is usually located in the mid-span at each step, except for a transient phase in the reverse loading. This minor effect is fundamentally based upon the peak-oriented hysteretic behavior of RC beams. Hence, two simplified models branch from the Modified Fish-Bone model: (i) the Adapted Fish-Bone (Adapted MFB) model in which the first crucial modification is applied, and (ii) the Substitute Frame in which both modifications are reflected and seems to be more compatible for RC moment frames. In the end, the accuracy of the proposed models is evaluated using two sets of far-fault and one set of near-fault ground motions. The comprehensive nonlinear dynamic analysis demonstrates that the two proposed models can estimate engineering demand parameters with high accuracy, while they greatly simplify the modeling process, computational effort and visualization of results.

Design against failure of structural concrete elements near points of contraflexure

In spite of the considerable number of reinforced-concrete structures invariably suffering earthquake damage in the regions of points of contraflexure of their beam or column elements, research on the subject to date has been sparse. This work discusses the causes of such damage and proposes a simple design method that does not require calibration through the use of experimental data. A comparison of the proposed method's predictions with experimental information and the predictions of typical current code methods not only demonstrates the validity of the proposed method, but also confirms the shortcomings of current design practice.

Analysis on Extension Length of Shape Steel in Transfer Columns of SRC–RC Hybrid Structures

Seismic performance of SRC–RC transfer column was analyzed based on the experiment of 16 transfer columns specimens under low cyclic reversed loading, which mainly focus on the extension length of shape steel. Analysis of ductility, bearing capacity, energy dissipation capacity and degeneration ratio of strength were completed. Displacement ductility promotes at first and then reduces with increasing of extension length of shape steel, reaching the peak value when extension length gets close to three fifths of column height. Extension length of shape steel has little effect on bearing capacity, while energy dissipation capacity of transfer columns is influenced by many factors. Three fifths of column height is the rational extension length of shape steel, of which specimens have advanced in energy dissipation, good stability of stiffness and strength. The bond performance between concrete and shape steel decreases with the increasing of extension length of shape steel, and hence the stability of strength decreases. Minimum extension length of shape steel was confirmed and the calculation method was proposed, which is mainly used to ensure the bend yielding of shape steel at bottom section. Moment at the truncation section leads to pull-out effect of steel bars, which enhances with increasing of the moment and section ratio of shape steel. Contraflexure point is at three fifths of column height. If the shape steel extends to contraflexure point, moment of steel truncation section will reach minimum. So the reduce the concrete damage with better deformation ability and mechanical behavior of transfer column.

Laboratory Study on Response of Single Pile Adjacent to Supported Cut

This paper presents the response of single pile against excavation induced soil movement by conducting model tests at unit gravity. The study involves a series of tests conducted on piles of three L/d ratios 10, 20 and 30 embedded in medium dense sand. From the test results it was found that the pile head deflection and bending moment of pile decrease exponentially with increasing distance between the pile and the sheet pile wall supporting the excavation. Analyses of the test results show that the shorter passive pile (L/d = 10) deflects more when compared to a long pile (L/d = 30) and a point of contraflexure for a long pile occurs in the pile section approximately at a depth close to the depth of excavation. The influence of soil movement on the lateral response of pile is also analysed through 3-dimensional finite element analysis. The numerical results thus obtained are validated with the results of experiments. The Mohr–Coulomb material model adopted to represent the soil characteristics predicts the response of pile reasonably and compares well with the response observed in the 1g model test. Design charts are included to predict pile head deflection and maximum moment in pile for the excavation depth ratio (De/Lr) = 0.5. These charts can be adopted to predict prototype pile behaviour by applying scaling law of Wood (Geotechnical modelling, Spon Press, London, 2001). The results of numerical and 1g model tests are validated with the design methods of Chen and Poulos (J Geotech Geoenviron Eng 123(9):802–811, 1997) and Xu and Poulos (Comput Geotech 28:349–375, 2001) and the design charts proposed in this study for deflection of passive pile and sheet pile wall support system are validated with centrifuge test results of Leung et al. (J Geotech Geoenviron Eng ASCE 126(11):947–954, 2000).

Lap Splice in GFRP-RC Rectangular Columns Subjected to Cyclic-Reversed Loads

This paper presents the experimental results of five full-scale glass fiber–reinforced polymer (GFRP) reinforced concrete (RC) columns with lap splices under axial and cyclic-reversed loads. One additional reference column was reinforced with steel bars and stirrups for comparison purposes. The column specimens had a 350-mm square cross section with 1,650-mm shear span. Each specimen represented the lower segment of a first-story column between the footing and the point of contraflexure. The test parameters included type of reinforcement, lap splice length of longitudinal reinforcement and transverse reinforcement spacing. Test results indicated that a splice length of 60 times the diameter of the longitudinal column bar was adequate in transferring the full bond forces along the splice length. In addition, lap-spliced GFRP-RC columns with closely spaced transverse reinforcement showed stable hysteresis response and achieved high levels of deformability, which far exceeded the limitations of the North American building codes.

Seismic Performance of GFRP-Reinforced Concrete Rectangular Columns

AbstractThis paper presents an assessment of the seismic performance of concrete columns internally reinforced with glass-fiber-reinforced polymers (GFRP) bars. Eight full-scale column prototypes with 1,650-mm shear span and 350-mm square cross-section were constructed and tested under combined lateral cyclic quasi-static and constant axial loading. The test specimens represent the lower portion of first-story columns between the footing and the contra-flexure point. The test parameters included longitudinal reinforcement type and ratio, level of axial load, and stirrup spacing. Test results showed that the drift capacity of GFRP-reinforced concrete (RC) rectangular columns at failure ranged between 8.5 and 12.5%, which exceeds the limitations of North American building codes. This indicates that the deformability of GFRP-RC column prototypes successfully replaced the ductility in steel–RC columns in dissipating the seismic energy in the presence of constant axial load. Furthermore, there was insignifican...

Self-equilibrating moments in FRP-reinforced continuous structures

In continuous steel or concrete structures with surface-mounted fibre reinforced polymer (FRP) plates as flexural reinforcement, self-equilibrating moments can influence the loads at first yield and at failure, the latter due to potential buckling of the FRP plate or to end-peel both on account of offsets between points of contraflexure and the nearby FRP curtailments. In this paper, expressions are derived for the total (including self-equilibrating) moments along 2-span continuous structures with differential settlement. The expressions show how moments depend on support-to-member stiffness ratios and on distributions of section stiffness for service and ultimate limit states. Thus, the analysis is generic, applicable to FRP-reinforced steel and concrete structures. This analysis is verified via test data (including observation of end-peel in FRP compression curtailment zones offset from nearby contraflexure) and is used to construct 3D plots that facilitate identification of stiffness ratios which lead to significant self-equilibrating moments and contraflexure offset effects. Use of the plots to assess influences of differential settlement on laboratory test specimens is discussed. The analysis is shown to lead to an unprecedented result, namely that a unique point of load application exists for which changes to the stiffness layout have no impact on the moment distribution.

Deformation of continuous reinforced concrete beams during patch repair

This paper describes an experimental and numerical investigation examining the effect of reinforcement exposure during the patch repair process on the behaviour of continuous beams. Particular attention is paid to moment transfer and change in strain patterns during concrete breakout. The test programme embraced a range of parameters including the length and position of breakout and a variety of reinforcement arrangements. Moment transfer during concrete breakout was monitored to assess whether breakout at one location would cause overstressing in other parts of the structure. Results from tests and numerical analysis show increases in section deformations away from the breakout were small when compared to those within the breakout length. It is surmised that there is little danger of overstraining in locations away from the breakout zone while breakout does not extend past a point of contraflexure.

Second-order inelastic analysis of composite framed structures based on the refined plastic hinge method

Composite steel-concrete structures experience non-linear effects which arise from both instability-related geometric non-linearity and from material non-linearity in all of their component members. This paper therefore presents a numerical procedure capable of addressing geometric and material non-linearities at the strength limit state based on the refined plastic hinge method. The refined plastic hinge approach models the elasto-gradual-plastic material non-linearity with strain-hardening under the interaction of bending and axial actions. This produces a benign method for a beam–column composite element under general loading cases. Another main feature of this paper is that, for members containing a point of contraflexure, its location is determined and a node is then located at this position to reproduce the real flexural behaviour and associated material non-linearity of the member. The formulation with the refined plastic hinge approach is efficacious and robust, and so a full frame analysis incorporating geometric and material non-linearity is tractable. Following development of the theory, its application is illustrated with a number of varied examples.

Extensible elastica solutions on the large deflection of fiber cantilever with circular wavy crimp. II. Classification of equilibrium configurations

The types of equilibrium shapes in the extensible elastica solutions of planar deflection of two-element crimped fiber cantilever with circular wavy crimp were classified for one end clamped boundary under concentrated, inclined and dead tip load. Material property of the fiber was also regarded linear elastic, while crimp was described as a combination of semicircular arcs smoothly connected with each other having constant curvature of all the same magnitude and alternative sign. Investigating the mathematical features of the previously obtained solutions shows that the possibility and variety of multiple equilibrium shapes originates from the following two reasons: the existence of Case 1/Case 2 type transformation, and the mathematical features of Case 1 type transformation. In two-element crimped fiber, there exist four different choices for Case1/Case2 type transformation. Regarding Case 2-Case 2 type equilibrium shape as the default and most probable one, other three types of equilibrium shape can be regarded as multiple equilibrium shapes. Moreover, Case 1 type transformation itself may lead to multiple configurations due to the possibility of the contra-flexure point after bending while Case 2 type transformation doesn’t allow such characteristics. Case 1-Case 1 type equilibrium shape shows maximum varieties in shape, while Case 2-Case 1 and Case 1-Case 2 type shapes occasionally leads to the identical results with different choice of the sign. Tables and shapes in each configuration were also presented.

Heat-straightening repairs to a steel road bridge

On 16 July 2002 a low-loader lorry carrying heavy machinery travelling eastbound on the A27 struck the underside of Brockhampton Road new bridge. The bridge suffered structural damage to the main beams and bracing. From an initial emergency inspection, the damage was found to be located close to the point of contraflexure in an area where the bottom flange was in tension. It was not considered necessary to impose immediate closures or traffic restrictions. A heat-straightening repair of the damaged beams was proposed. Detailed analysis using both hand calculations and the finite-element method confirmed the structural adequacy of the bridge to undergo the heat-straightening process. These checks encompassed the temporary conditions prior to, during and after the heating. The major heat-straightening process was successfully completed on site in ten days. Impact damage to the beams was repaired within acceptable tolerances and the straightened steel was subjected to hardness and magnetic particle investigation testing. The repairs to Brockhampton Road new bridge were concluded without undue disruption to the travelling public or local residents.