Increase In Initial Stiffness Research Articles

Punching shear behavior of ultra-high-performance fiber-reinforced concrete and normal strength concrete composite flat slabs

This paper presents the results of tests on flat slabs with partial application of ultra-high-performance fiber-reinforced concrete (UHPFRC) mixtures to improve the punching shear capacity of slab-column connections. One normal strength concrete (NSC) slab and two UHPFRC slabs were tested as a reference for tests on 12 UHPFRC-NSC composite slabs with full depth UHPFRC in the center area of the NSC slab. The main test parameters were the steel fiber volume (0.8 % and 1.6 % volume fractions) and the dimensions of UHPFRC mixtures. The load-column displacement curves, crack patterns, slab rotations at failure, and failure loads are presented and discussed. The failure loads are compared with estimates obtained following the yield line analysis, design codes, and other theoretical models. Test results showed that the use of UHPFRC mixtures led to an increase in initial stiffness, punching shear strength, and deformation capacity, along with a change in the slab failure mode. The shear capacity of the slab improved proportionally to the increase in the dimension of the UHPFRC. These tests confirmed the effectiveness of the UHPFRC mixtures as an alternative to enhance the punching shear capacity for slab-column connections.

Mechanical deviation in 3D-Printed PLA bone scaffolds during biodegradation

Large or carcinogenic bone defects may require a challenging bone tissue scaffold design ensuring a proper mechanobiological setting. Porosity and biodegradation rate are the key parameters controlling the bone-remodeling process. PLA presents a great potential for geometrically flexible 3-D scaffold design. This study aims to investigate the mechanical variation throughout the biodegradation process for lattice-type PLA scaffolds using both experimental observations and simulations. Three different unit-cell geometries are used for creating the scaffolds: basic cube (BC), body-centered structure (BCS), and body-centered cube (BCC). Three different porosity ratios, 50 %, 62.5 %, and 75 %, are assigned to all three structures by altering their strut dimensions. 3-D printed scaffolds are soaked in PBS solution at 37 °C for 15, 30, 60, 90, and 120 days both unloaded and under dead load. Water absorption, weight loss, and compression stiffness are measured to characterize the first-stage degradation and investigate the possible influences of these parameters on the whole biodegradation process. The strength reduction stage of biodegradation is simulated by solving pseudo-first-order kinetics-based molecular weight change equation using FEA with equisized cubic (voxel-like) elements.For the first stage, mechanical load does not have a statistically significant effect on biodegradation. BCC with 62.5 % porosity shows a maximum water absorption rate of around 25 % by the 60th day which brings an advantage in creating an aquatic environment for cell growth. Results indicate a significant water deposition inside almost all scaffolds and water content is determined to be the main reason for the retained or increased compression stiffness. A distinguishable stiffness increase in the initial degradation process occurs for 75 % porous BC and 50 % porous BCC scaffolds. Following the quasi-stable stage of biodegradation, almost all scaffolds lost their rigidity by around 44–48 % within 120 days based on numerical results. Therefore, initial stiffness increase in the quasi-stable stage of biodegradation can be advantageous and BCC geometry with a porosity between 50% and 62 % is the optimum solution for the whole biodegradation process.

Silk-inspired architectured filament with enhanced stiffness and toughness for Fused deposition modelling (FDM)

Architectured materials, those capable of manipulating the spatial configurations of two or more material phases, have recently gained substantial attention, primarily due to their unprecedented material properties (e.g., exceptional strength-to-weight ratio and intriguing negative Poisson's ratio). Most architectured materials draw inspiration from the microstructure of natural solutions. One of fascinating examples are spider silk and cocoon silk. Their multimaterial core-shell fibrous structure exhibits remarkable mechanical properties—high stiffness, strength, and toughness. In this study, silk-inspired dual-phase Core-Shell Architectured Filament (CSAF), which combines a rigid Polylactic Acid (PLA) core with a soft Thermoplastic Polyurethane (TPU) shell, was developed as feedstock for additive manufacturing. The mechanical testing of dual-phase CASF printed samples reveal intriguing results. Notably, the optimized CASF in this study, whose volume fraction of rigid core was set as 52 %, was observed a substantial improvement of the printed specimens in initial stiffness and energy absorption capacity—up to a remarkable 14-fold increase in initial stiffness and a ∼9 % enhancement in energy absorption when compared to the pure TPU filament. To gain a deeper understanding of the synergistic effects arising from geometrical and material configurations on the structure's damage mechanism, a theoretical model of this core-shell structure was developed. Computational models have been built to validate theoretical model, and the results from finite element analysis are in excellent agreement with experimental results. These discoveries offer valuable insights to enhance mechanical performance of the feedstock for additive manufacturing.

Failure characterization of fully grouted rock bolts under triaxial testing

Confining stresses serve as a pivotal determinant in shaping the behavior of grouted rock bolts. Nonetheless, prior investigations have oversimplified the three-dimensional stress state, primarily assuming hydrostatic stress conditions. Under these conditions, it is assumed that the intermediate principal stress (σ2) equals the minimum principal stress (σ3). This assumption overlooks the potential variations in magnitudes of in situ stress conditions along all three directions near an underground opening where a rock bolt is installed. In this study, a series of push tests was meticulously conducted under triaxial conditions. These tests involved applying non-uniform confining stresses (σ2 ≠ σ3) to cubic specimens, aiming to unveil the previously overlooked influence of intermediate principal stresses on the strength properties of rock bolts. The results show that as the confining stresses increase from zero to higher levels, the pre-failure behavior changes from linear to nonlinear forms, resulting in an increase in initial stiffness from 2.08 kN/mm to 32.51 kN/mm. The load-displacement curves further illuminate distinct post-failure behavior at elevated levels of confining stresses, characterized by enhanced stiffness. Notably, the peak load capacity ranged from 27.9 kN to 46.5 kN as confining stresses advanced from σ2 = σ3 = 0 to σ2 = 20 MPa and σ3 = 10 MPa. Additionally, the outcomes highlight an influence of confining stress on the lateral deformation of samples. Lower levels of confinement prompt overall dilation in lateral deformation, while higher confinements maintain a state of shrinkage. Furthermore, diverse failure modes have been identified, intricately tied to the arrangement of confining stresses. Lower confinements tend to induce a splitting mode of failure, whereas higher loads bring about a shift towards a pure interfacial shear-off and shear-crushed failure mechanism.

Hysteretic and rotational performance study of outwardly extending shape-steelprefabricated beam-column joints

This paper proposes fully-bolted extending shape steel prefabricated beam-column joints to achieve rapid construction and reliable connection of the precast reinforced concrete frame. The prefabricated component uses steel tube-concrete composite structures with outwardly extended shape steel, which achieves efficient installation and internal force transfer. Horizontal hysteresis tests were conducted on four components to determine the joint mode of failure and seismic performance index. The results show that the joint exhibits a “double plastic” failure mode, with plastic deformation occurring at the end of the reinforced concrete beam and buckling deformation at the shaped steel. Compared to cast-in-place joints, the new joints have a 30% increase in yield load, a 51% increase in peak load, an approximately 50% increase in initial stiffness, a 33% increase in equivalent viscous damping coefficient, and a ductility coefficient greater than 4.0. Analysis of strain showed that the stiffness of the connection area was too high, which will have a significant extrusion effect on the concrete at the end. Reducing the thickness of the steel plate in the joint space and weakening the shape stee by opening holes can significantly improve the rotational deformation capacity of the joint - further developing the plastic zone of reinforced concrete beams to improve the mechanical performance of the joint. Finally, the finite element model of the joint is established, and the numerical calculation is in good agreement with the experimental results. The research in this paper can provide technical support for the engineering application of the prefabricated joint.

Stress distributions of infinite strip steel reinforced elastomeric isolators with a rubber core

Lead-rubber bearings contain a lead core that provides an advantageous increase in initial stiffness and increased energy dissipation during earthquake events. Despite these advantages, the inclusion of the lead core is an environmental and health concern and can be costly. The use of rubber cores in lieu of lead cores has been proposed as an alternative and shown to achieve excellent energy dissipation. The inclusion of the rubber core also decreases the weight of the isolator through the partial removal of the steel reinforcement or the replacement of lead with a lighter material. In this paper, the inclusion of a rubber core in an infinite strip steel-reinforced elastomeric isolator was investigated. An analytical solution was developed based on the assumptions of the pressure solution including and excluding the compressibility of the elastomer for the compression and bending properties. Finite element analysis was subsequently conducted to verify the analytical solution. The analysis considered three different shape factors and a rubber core up to 90% of the width of the isolator. The models were used to determine the elastic moduli as well as the normal and shear stress distributions under pure bending and rotation. The verified analytical solution is an important tool for designers.

Seismic Performance of Reinforced Concrete Columns Retrofitted with Hybrid Concrete Jackets Subjected to Combined Loadings.

In the existing reinforced concrete columns where they are insufficient seismic details, critical failure mode such as shear failure can be observed under seismic loads. One strategy for the retrofitting of existing concrete columns is to use concrete jacketing. Concrete jacketing consists of a new concrete layer with longitudinal and transverse reinforcements, and can improve seismic resistance capacity. In this paper, a detail of concrete jacket that can be expected for easy construction and improved adhesion performance of longitudinal and transverse reinforcement was proposed. Additionally, a combined cyclic loading test was conducted to consider the seismic load with multiaxial characteristics. The concrete jacket details utilize three components: Steel Grid Reinforcement (SGR), Steel Wire Mesh (SWM), and Steel Fiber Non-Shrinkage Mortar (SFNM). One RC column with non-seismic details and two jacketed RC columns were fabricated to demonstrate the construction efficiencies and structural capacities of the jacketed columns. Two details of jacketed section were considered as variables. It was observed that the specimens retrofitted with concrete jacket resisted torsional load more than the un-retrofitted specimen in terms of crack and failure mode. The experimental results showed that the maximum load of retrofitted specimens was increased by more than 8 times compared to the un-retrofitted specimen, regardless of the jacket details. Newly designed concrete jacket effectively increased the strength. Compared with the un-retrofitted column, the columns retrofitted with the proposed details achieved significant increase in initial stiffness and energy dissipation.

Parametric Analysis of the Static Behavior for Stainless-Steel Beam-Column Connections

To study the influence of geometric parameters on flexural capacity and stiffness of beam-column connections using stain-steel S31608 and get the key influence parameters, on the basis of test data, using the finite element analysis software ABAQUS, parameter analysis on three main geometrical parameters of flexural capacity and stiffness of stain-steel beam-column connections was conducted. The analysis results show that when flange thickness of I-shaped bars increases, bearing capacity and initial stiffness of the joints increase with large amplitude; when slipping coefficient increases, bearing capacity and initial stiffness of the joints increase with small amplitude; when weld ac-cess hole changes, bearing capacity increases and initial stiffness increase with small amplitude, but can decrease stress concentrate phenomenon; when “Dog-bone” is used, the position of plastic hinge appearance will out-shift, but bearing capacity and initial stiffness decrease with large amplitude. Using the weld access hole of FEME350 and increasing the flange thickness of I-shaped bars is a good way to improve the static behavior of stain-steel beam-column connections.

Experimental investigation on the seismic behavior of self‐stressing steel slag CFST column

AbstractTo fully use the expansion property of steel slag, an experiment on 10 self‐stressing steel slag concrete‐filled steel tube (SSSCFST) columns and four steel slag concrete‐filled steel tube (SSCFST) columns subjected to low cyclic loading are implemented, the effects of the expansion ratio of the steel slag concrete, axial compression ratio, diameter‐thickness ratio, and shear span ratio on the seismic properties of SSSCFST components are analyzed. The outcomes present that the failure mode of specimens changes from bending failure to bending‐shear failure as the shear span ratio reduces. With the improvement of the axial compression ratio, the initial stiffness, strength degradation degree, and the growth rate of energy dissipation capacity increase, while the ductility decreases. With the decrease in diameter‐thickness ratio, there is no significant change in other seismic performance except for the increase in initial stiffness. Compared with the SSCFST columns, the seismic performance indexes of SSSCFST columns are advanced. The study on the seismic behavior of SSSCFST columns can provide the basis for engineering application.

Biomechanical comparison of sacral and transarticular sacroiliac screw fixation.

A detailed finite element analysis of screw fixation in the sacrum and pelvis. To biomechanically assess and compare the fixation performance of sacral and transarticular sacroiliac screws. Instrumentation constructs are used to achieve fixation and stabilization for the treatment of spinopelvic pathologies. The optimal screw trajectory and type of bone engagement to caudally anchor long fusion constructs are not yet known. A detailed finite element model of the sacroiliac articulation with two different bone densities was developed. Two sacral and one transarticular sacroiliac screw trajectories were modeled with different diameters (5.5 and 6.5mm) and lengths (uni-cortical, bi-cortical and quad-cortical purchase). Axial pullout and flexion/extension toggle forces were applied on the screws representing intra and post-operative loads. The force-displacement results and von Mises stresses were used to characterize the failure pattern. Overall, sacroiliac screws provided forces to failure 2.75 times higher than sacral fixation screws. On the contrary, the initial stiffness was approximately half as much for sacroiliac screws. High stresses were located at screw tips for the sacral trajectories and near the cortical bone screw entry points for the sacroiliac trajectory. Overall, the diameter and length of the screws had significant effects on the screw fixation (33% increase in force to failure; 5% increase in initial stiffness). A 20% drop in bone mineral density (lower bone quality) decreased the initial stiffness by 25% and the force to failure by 5-10%. High stresses and failure occurred at the screw tip for uni- and tri-cortical screws and were close to trabecular-cortical bone interface for bi-cortical and quad-cortical screws. Sacroiliac fixation provided better anchorage than sacral fixation. The transarticular purchase of the sacroiliac trajectory resulted in differences in failure pattern and fixation performance.

Behavior of Circular CFST Columns Subjected to Different Lateral Impact Energy

Forty-eight circular concrete-filled steel tube (CFST) columns subjected to lateral impact were tested to investigate the behavior of circular CFST columns under axial compressive load. Analyses of effects of concrete compressive strength, impact location and impact energy on residual ultimate axial capacity, ductility and initial stiffness are provided in this paper. It is found that lateral impact has negative effects on residual ultimate axial capacity of circular CFST columns from test results. Residual ultimate axial capacity decreases as impact energy increases and impact location comes close to the end of the specimen. It is also found that increasing concrete compressive strength can reduce the negative effects of impact location on residual ultimate axial capacity. Ductility and the initial stiffness of circular CFST columns decrease as impact energy increases. Ductility and the initial stiffness increase as impact location varies from middle-length to the end of specimens. When impact energy and impact location are constant, the ductility of the specimen with 30 MPa of concrete compressive strength is better than that of other specimens with different compressive strength. Besides, analyses of strain developments for 12 typical specimens to investigate failure modes under axial compressive load are provided in this paper. Strain developments have indicated that the steel at impact location becomes plastic faster than that at other locations. Based on the test results, a calculation formula is presented to predict the residual ultimate axial capacities of circular CFST columns subjected to lateral impact, and good agreement with experimental results has been achieved.

Seismic retrofitting of timber framed walls

After the 1755 earthquake that destroyed Lisbon, an innovative anti-seismic structural system was developed consisting of a timber skeleton, that included timber framed masonry walls. After more than 250 years these structures need rehabilitation to face the present demands. The research presented in this paper aimed at experimentally characterizing the cyclic behaviour of timber framed walls reinforced with three different methods, namely: (i) elastic-plastic dampers on diagonal braces, (ii) reinforcement of timber connections with steel plates, (iii) application of a reinforced rendering. The elastic-plastic damper showed an unsymmetrical behaviour and some difficulties to implement in practice. The strengthening with reinforced render led to an initial stiffness increase but showed a limited deformation capacity. The walls with reinforcing steel plates at the timber connections showed the best behaviour in terms of strength, stiffness and energy dissipation.

Improved time-zero biomechanical properties using poly-L-lactic acid graft augmentation in a cadaveric rotator cuff repair model

Rotator cuff repair failure rates range from 20% to 90%, and failure is believed to occur most commonly by sutures cutting through the tendon due to excessive tension at the repair site. This study was designed to determine whether application of a woven poly-L-lactic acid device (X-Repair; Synthasome, San Diego, CA) would improve the mechanical properties of rotator cuff repair in vitro. Eight pairs of human cadaveric shoulders were used to test augmented and non-augmented rotator cuff repairs. Initial stiffness, yield load, ultimate load, and failure mode were compared. Yield load was 56% to 92% higher and ultimate load was 56% to 76% higher in augmented repairs. No increase in initial stiffness was found. Failure by sutures cutting through the tendon was reduced, occurring in 17 of 20 non-augmented repairs but only 7 of 20 augmented repairs. Our data show that application of the X-Repair device significantly increased the yield load and ultimate load of rotator cuff repairs in a human cadaveric model and altered the failure mode but did not affect initial repair stiffness.

Influence of Frequency on the Behaviour of Plate Anchors Subjected to Cyclic Loading

This article reports the response of embedded circular plate anchors to varying frequencies of cyclic loading. The effects of time period of loading cycles and pre-loading on movement of anchors and post-cyclic monotonic pullout behavior are studied using a model circular (80 mm diameter) plate anchor, buried at embedment ratio of six in a soft saturated clay. The frequencies of loading cycles have showed considerable effect on movement of anchors. For given duration of loading, higher frequency cycles cause more movement of anchor than lower frequency cycles. Pre-loading reduces the movement of anchors in subsequent loading stages. When anchors are recycled at a load ratio level less than the pre-cycling load, the movement of anchor in recycling phase are very much reduced, but if the recycling is done at a higher load ratio level, the effect is not that much pronounced and the anchors behave as if they were not subjected to any cycling load in the past. Anchor subjected to cyclic loading and then monotonic pullout shows an increase in initial stiffness, whereas the peak pullout load was found to decrease marginally over that of an anchor not subjected to any cyclic loading. For the present test conditions, the relative post-cyclic stiffness of anchors is found to vary from 1.169 to 1.327.

Micromechanics and macromechanics of carbon nanotube-enhanced elastomers

The effects of carbon nanotubes on the mechanical behavior of elastomeric materials is investigated. The large deformation uniaxial tension and uniaxial compression stress–strain behaviors of a representative elastomer are first presented. This elastomer is then reinforced with multi-wall carbon nanotubes (MWNTs) and the influence of weight fraction of MWNTs on the large deformation behavior of the resulting composite is quantified. The initial stiffness and subsequent strain-induced stiffening at large strains are both found to increase with MWNT content. The MWNTs are also found to increase both the tensile strength and the tensile stretch at break. A systematic approach for reducing the experimental data to isolate the MWNT contribution to the strain energy of the composite is presented. A constitutive model for the large strain deformation behavior of MWNT-elastomer composites is then developed. The effects of carbon nanotubes are modeled via a constitutive element which tracks the stretching and rotation of a distribution of wavy carbon nanotubes. The MWNT strain energy contribution is due to the bending/unbending of the initial waviness and provides the increase in initial stiffness as well as the retention and further enhancement of the increase in stiffness with large strains. The model is shown to track the stretching and rotation of the CNTs with macroscopic strain as well as predict the dependence of the macroscopic stress–strain behavior on the MWNT content for both uniaxial tension and uniaxial compression.

Durability performance of RC beams strengthened with epoxy injection and CFRP fabrics

Cracks in reinforced concrete (RC) should be repaired if they present the potential for durability related problems such as corrosion of reinforcing steel. One way to repair extensive cracks is the use of epoxy injection. Another repair technique to enhance shear or flexural strength in deficient RC members is the utilization of externally bonded carbon fiber reinforced polymer (CFRP) fabrics. The effect of environmental conditioning on crack injection with or without CFRP strengthening is of interest in this investigation. Test results showed that the crack injection provided an increase in initial stiffness for un-strengthened RC beams. An increase in initial stiffness and ultimate strength was achieved in CFRP strengthened RC beams. Surface roughness combined with crack injection significantly increased the flexural capacity of the specimens. Environmental conditioning significantly affected the bond performance of the epoxy injection. The presence of sustained load during environmental conditioning resulted in reduced section capacity and ductility.

Seismic Resistance of Wood Shear Walls with Large OSB Panels

Results are presented from studies on the seismic resistance of wood shear walls sheathed with large (2.4 × 2.4 m) and standard (1.2 × 2.4 m) size oriented strand board (OSB) panels. Comparisons were made among twelve 2.4 × 2.4 m walls tested under quasi-static monotonic and cyclic, as well as dynamic, loads. In push-over tests, all walls reached a drift of approximately 2.5% at maximum load. A 26% increase in shear capacity was achieved using large panels. The nails that would be at internal seams in walls with standard panels were redistributed around the exterior edges of some large panel walls. They also showed a 104% increase in shear capacity and a 30% increase in initial stiffness. These walls performed significantly better when tested dynamically, using the east-west motion recorded at Joshua Tree Station during the 1992 Landers, Calif., earthquake. Their maximum drift was reduced by approximately 25% over standard walls. Damage incurred during dynamic tests consisted mainly of nail pullout and tear out. Renailing at these locations is simple and can restore the wall to a satisfactory performance level.

Characteristics of pullout failure in conical and cylindrical pedicle screws after full insertion and back-out

Background context: Biomechanical studies show that bone-mineral density, pedicle morphology, and screw thread area affect pedicle screw pullout failure. The current literature is based on studies of cylindrical pedicle screw designs. Conical screws have been introduced that may provide better “fit and fill” of the dorsal pedicle as well as improved resistance to screw bending failure. However, there is concern about loss of fixation if conical screws must be backed out after insertion.Purpose: To determine that conical screws have comparable initial stiffness and fixation strength compared with standard, cylindrical screws, and to assess whether conical screw fixation deteriorates when screws are backed out from full insertion. Study design/setting: This biomechanical analysis compared pullout strength of cylindrical and conical pedicle screw designs, using porcine lumbar vertebrae in a paired testing format. Methods: Porcine lumbar vertebrae were instrumented with conical and cylindrical pedicle screws with the same thread pitch, area and contour, and an equivalent diameter at the pedicle isthmus, 1.2 cm distal to the hub. Axial pullout was performed at 1.0 mm/minute displacement. Pullout loads, work and stiffness were recorded at 0.02-second intervals. Conical versus cylindrical screws were tested using three paired control configurations: fully inserted, backed out 180 degrees and backed out 360 degrees. Fully inserted values were compared with each set of back-out values to determine relative loss of fixation strength. Screw pullout data were analyzed using a Student's t test. Results: Pullout loads in these porcine specimens were comparable to data from healthy human vertebrae. Conical screws provided a 17% increase in the pullout strength compared with cylindrical screws (P<.10) and a 50% increase in initial stiffness (P<.05) at full insertion. There was no loss in pullout strength, stiffness or work to failure when conical or cylindrical screws were backed out 180 or 360 degrees from full insertion. Conclusions: Conical screws offer improved initial fixation strength compared with cylindrical screws of the same size and thread design. Our results suggest that appropriately designed conical screws can be backed out 180 to 360 degrees for intraoperative adjustment without loss of pullout strength, stiffness or work to failure. Intraoperative adjustments of these specific conical screws less than 360 degrees should not affect initial fixation strength. These results may not hold true for screws with a smaller thread area or larger minor diameter.

Long-Term Oven-Aging Effects on Fatigue and Initial Stiffness of Asphalt Concrete

An investigation of the effects of long-term oven aging (LTOA) on initial stiffness and fatigue of asphalt concrete was made using two typical California asphalts, known to have different aging characteristics, in mixes with one aggregate. Asphalt content, air-voids content, and days of LTOA were varied independently. Stiffness and fatigue were evaluated using the controlled-strain flexural beam test developed by the Strategic Highway Research Program Project A-003A. The results indicated that both mixes exhibited an increase in initial stiffness with LTOA periods of up to six days. The sensitivity of beam fatigue life to LTOA depended on the asphalt. Beams containing Valley asphalt had virtually no change in fatigue life due to LTOA, whereas beams with Coastal asphalt showed some sensitivity to LTOA. For both asphalts, the average reduction in fatigue life from 6 days of LTOA was less than that caused by a 3 percent increase in air-void content or a 1 percent decrease in asphalt content. Simulations of thick and thin pavement structures were performed to reconcile the effects of LTOA, asphalt content, and air-void content on mix fatigue life and stiffness by evaluating their combined effects on predicted pavement fatigue life. The simulations indicated that aging, as induced by LTOA, increased fatigue life for all cases except one.

Cyclic Compression-Flexion Loading of the Human Lumbar Spine

The present study was designed to investigate the biomechanical behavior of the lumbar spine under controlled complex physiologic situations with chronic input. The objective was to determine the response of the human cadaver lumbar spinal column under repetitive compression-flexion forces. Studies have been conducted in the past to determine the biomechanical response of the spine under uniaxial or pure forces. There is no methodology that can be used to apply and continuously quantify the fatigue response of the lumbar spinal column under controlled combined complex loading vectors (e.g., compression flexion). Intact cadaver lumbar columns (L1-L5) were mounted with the superior end in contact with a ball-transfer mount, inducing a flexion load to the spine while allowing multiple degrees of freedom. The distal portion of the specimen was attached to a six-axis load cell to quantify the force sustained by the specimen during the entire loading cycle. The applied load and piston deformation and the generalized six-axis force histories were gathered as a function of time using a digital data acquisition system. The stiffness versus number of cycles (K-N) response exhibited nonlinear characteristics. The stiffness increased initially and then stabilized after 1,000-2,000 cycles of loading, delineating the viscoelastic characteristics of the spine. The initial stiffness increase before stabilization was found to be significantly different (P < 0.025) compared to the stiffness beyond 2,000 cycles. The data suggest that the fatigue response can be understood by cyclically loading the ligamentous lumbar spine preparation to approximately 2,000 cycles.