Peak Bending Moment Research Articles

Prediction of pile response to lateral spreading by 3-D soil–water coupled dynamic analysis: Shaking in the direction perpendicular to ground flow

The 1995 Kobe earthquake seriously damaged numerous buildings with pile foundations adjacent to quay walls. The seismic behavior of a pile group is affected by movement of quay walls, pile foundations, and liquefied backfill soil. For such cases, a three-dimensional (3-D) soil–water coupled dynamic analysis is a promising tool to predict overall behavior. We report predictions of large shake table test results to validate 3-D soil–water coupled dynamic analyses, and we discuss liquefaction-induced earth pressure on a pile group during the shaking in the direction perpendicular to ground flow. Numerical analyses predicted the peak displacement of footing and peak bending moment of the group pile. The earth pressure on the pile in the crustal layer is most important for the evaluation of the peak bending moment along the piles. In addition, the larger curvatures in the bending moment distribution along the piles at the water side in the liquefied ground were measured and predicted.

Effects of Spatial Constraints on Trunk Kinematics during a Dependent Transfer on an Aircraft

A concern related to air travel by people with disabilities is the risk of low-back injuries while transferring the traveler to or from the aircraft seat. Potential contributing factors to this risk are the spatial constraints imposed by the aircraft's interior. This study investigated the effects of such constraints on the trunk angles, angular velocities, and load moment arm during a two-person dependent transfer between a wheelchair and an aircraft seat. Trunk kinematics were recorded as 33 pairs of subjects transferred a dummy to and from an aircraft seat under unconstrained and constrained conditions. The constraints primarily affected the front transferor, increasing peak trunk flexion, lateral bending, twisting, and load moment arm. Effects on the rear transferor were small and appeared to have offsetting effects on injury risk. The results suggest that the row spacing on an aircraft contributes to low-back injury risk during dependent transfers of travelers with disabilities.

Stiffener debonding mechanisms in post-buckled CFRP aerospace panels

This paper describes the fractographic analysis of five CFRP post-buckled skin/stringer panels that were tested to failure in compression. The detailed damage mechanisms for skin/stiffener detachment in an undamaged panel were characterised and related to the stress conditions during post-buckling; in particular the sites of peak twist (at buckling nodes) and peak bending moments (at buckling anti-nodes). The initial event was intralaminar splitting of the +45° plies adjacent to the skin/stiffener interface, induced by high twist at a nodeline. This was followed by mode II delamination, parallel to ±45° plies and then lengthwise (0°) shear along the stiffener centreline. The presence of defects or damage was found to influence this failure process, leading to a reduction in strength. This research provides an insight into the processes that control post-buckled performance of stiffened panels and suggests that 2D models and element tests do not capture the true physics of skin/stiffener detachment: a full 3D approach is required.

Influence of the crash pulse shape on the peak loading and the injury tolerance levels of the neck in in vitro low-speed side-collisions

The aim of the present in vitro study was to investigate the effect of the crash pulse shape on the peak loading and the injury tolerance levels of the human neck. In a custom-made acceleration apparatus 12 human cadaveric cervical spine specimens, equipped with a dummy head, were subjected to a series of incremental side accelerations. While the duration of the acceleration pulse of the sled was kept constant at 120 ms, its shape was varied: Six specimens were loaded with a slowly increasing pulse, i.e. a low loading rate, the other six specimens with a fast increasing pulse, i.e. a high loading rate. The loading of the neck was quantified in terms of the peak linear and angular acceleration of the head, the peak shear force and bending moment of the lower neck and the peak translation between head and sled. The shape of the acceleration curve of the sled only seemed to influence the peak translation between head and sled but none of the other four parameters. The neck injury tolerance level for the angular acceleration of the head and for the bending moment of the lower neck was almost identical for both, the high and the low loading rate. In contrast, the injury tolerance level for the linear acceleration of the head and for the shear force of the lower neck was slightly higher for the low loading rate as compared to the high loading rate. For the translation between head and sled this difference was even statistically significant. Thus, if the shape of the crash pulse is not known, solely the peak bending moment of the lower neck and the peak angular acceleration of the head seem to be suitable predictors for the neck injury risk but not the peak shear force of the lower neck, the peak linear acceleration of the head and the translation between head and thorax.

The effects of initial lifting height, load magnitude, and lifting speed on the peak dynamic L5/S1 moments

The purpose of this study was to quantify the peak dynamic bending moments on the spine during sagittal plane lifting as a function of the load's initial height above the floor, the load's magnitude, and the lifting speed. Ten male subjects participated in a repeated measures experiment in which 24 lifts were performed. The boxes lifted by the subjects contained loads that were 20, 100, 200, and 300 N. The lifts originated from three vertical locations (7.5 cm or “floor” level, knee level, and knuckle level), and were lifted at two qualitatively defined lifting speeds (“normal” and “fast”). All lifts were symmetric about the body's mid-sagittal plane and the boxes were gripped with both hands using the handles. Kinetic and kinematic data were used in a “bottom-up” linked segment dynamic model to determine the peak sagittal bending moment experienced by the subjects during each lift. The peak moments were significantly greater when lifting from lower lift heights ( p<0.001), at faster lifting speeds ( p<0.001), and with heavier loads ( p<0.001). Moreover, the peak moments were dependent upon the combination of these three factors. Based on these data, a regression model was developed to predict the peak dynamic moment given the load magnitude, the starting height, and a qualitative estimate of lifting speed. This model was then used to assess whether the current National Institute for Occupational Safety and Health's (NIOSH's) model can control the peak bending moments acting on the spine as the limits for safe lifting are adjusted according to changes in the initial lifting height. It was found that the current NIOSH guidelines under-represent the increased bimechanical load experienced during low-level lifting. Relevance to industry This work indicates the importance of controlling the height from which lifts originate when attempting to reduce the spinal loads experienced by employees. Moreover, this paper suggests that the NIOSH models under-estimate the increases in spine load that accompany lifts from progressively lower heights.

Wind-Induced Peak Bending Moments in Low-Rise Building Frames

We present a procedure for estimating peaks of non-Gaussian processes representing fluctuating internal forces induced by wind in low-rise building frames. The procedure is designed for inclusion in computer programs that use surface pressure databases to obtain peak internal forces in frames. In general, the processes of interest are non-Gaussian, and we apply translation models to estimate the distribution of their peaks. To illustrate the procedure we calibrate a translation model to the record of a 1 h time history of the bending moment at the upwind bent of a low-rise frame.

When do Bending Stresses on the Spine Rise to Damaging Levels?

Experiments on cadaver spines have quantified the bending stresses (bending moment) required to cause overload injury or fatigue failure to the lumbar spine. This paper reviews subsequent experiments in living people which sought to identify the circumstances that cause spinal bending to rise to potentially damaging levels in life. Healthy volunteers performed various bending and lifting activities in the laboratory, and peak bending moment was quantified from measurements of lumbar flexion, obtained using the 3-Space Isotrak. Bending stresses approached or even exceeded estimated fatigue limits in some subjects when they performed lifting tasks in the early morning (when the spine's bending stiffness is increased), and following fatigue of the back muscles. Individuals with a small range of lumbar flexion were particularly likely to exceed safe limits. These findings may explain why repeated bending and lifting are so closely associated with low back problems.

Sudden and unexpected loading generates high forces on the lumbar spine.

A cross-sectional study of spinal loading in healthy volunteers. To measure the bending and compressive forces acting on the lumbar spine, in a range of postures, when unknown loads are delivered unexpectedly to the hands. Epidemiologic studies suggest that sudden and unexpected loading events often lead to back injuries. Such incidents have been shown to increase back muscle activity, but their effects on the compressive force and bending moment acting on the spine have not been fully quantified. Furthermore, previous investigations have focused on the upright posture only. In this study, 12 volunteers each stood on a force plate while weights of 0, 2, 4, and 6 kg (for men, 40% less for women) were delivered into their hands in one of three ways: 1) by the volunteer holding an empty box with handles, into which an unknown weight was dropped; 2) by the same way as in 1, but with volunteer wearing a blindfold and earphones to eliminate sensory cues; or 3) by the volunteer sliding a box of unknown weight off a smooth table. Experiments were carried out with participants standing in upright, partially flexed, and moderately flexed postures. Spinal compression resulting from muscular activity was quantified using electromyographic signals recorded from the back and abdominal muscles. The axial inertial force acting up the long axis of the spine was calculated from the vertical ground reaction force. The bending moment acting on the osteoligamentous spine was quantified by comparing measurements of lumbar curvature with the bending stiffness properties of cadaveric lumbar spines. The contribution from abdominal muscle contraction to overall spinal compression was small (average, 8%), as was the axial inertial force (average, 2.5%), and both were highest in the upright posture. Peak bending moments were higher in flexed postures, but did not increase much at the moment of load delivery in any posture. Peak spinal compressive forces were increased by 30% to 70% when loads were suddenly and unexpectedly dropped into the box, and by 20% to 30% when they were slid off the table, as compared with loads simply held statically in the same posture (P < 0.001). The removal of audiovisual cues had little effect. Sudden and alarming events associated with manual handling cause a reflex overreaction of the back muscles, which substantially increases spine compressive loading. Manual handling regulations should aim to prevent such events and limit the weight of objects to be lifted.

Repetitive lifting tasks fatigue the back muscles and increase the bending moment acting on the lumbar spine

During manual handling, the back muscles protect the spine from excessive flexion, but in doing so impose a high compressive force on it. Epidemiological links between back pain and repetitive lifting suggest that fatigued muscles may adversely affect the balance between bending and compression. Fifteen volunteers lifted and lowered a 10 kg weight from floor to waist height 100 times. Throughout this task, the bending moment acting on the osteoligamentous lumbar spine was estimated from continuous measurements of lumbar flexion, obtained using the 3-Space Isotrak. Spinal compression was estimated from the electromyographic (EMG) activity of the erector spinae muscles, recorded from skin-surface electrodes at the levels of T10 and L3. EMG signals were calibrated against force when subjects pulled up on a load cell, and correction factors were applied to account for changes in muscle length and contraction velocity. Fatigue in the erector spinae muscles was quantified by comparing the frequency content of their EMG signal during static contractions performed before, and immediately after, the 100 lifts. Results showed that peak lumbar flexion increased during the 100 lifts from 83.3±14.8% to 90.4±14.3%, resulting in a 36% increase in estimated peak bending moment acting on the lumbar spine ( P=0.008). Peak spinal compression fell by 11% ( p=0.007). The median frequency of the EMG signal at L3 decreased by 5.5% following the 100 lifts ( p=0.042) confirming that the erector spinae were fatigued, but measures of fatigue showed no significant correlation with increased bending. We conclude that repetitive lifting induces measurable fatigue in the erector spinae muscles, and substantially increases the bending moment acting on the lumbar spine.

Time-dependent changes in the lumbar spine's resistancc to bending

Objective. To show how time-related factors might affect the risk of back injury. Design. Mechanical testing of cadaveric lumbar motion segments. Background. High bending stresses acting on the lumbar spine are associated with injuries to the intervertebral discs and ligaments. Since these soft tissues are viscoelastic, the bending stress (‘bending moment’) must depend on the speed of movement and the duration of loading, but this has not previously been quantified. Methods. Forty-five cadaveric lumbar segments, consisting of two vertebrae and the intervening disc and ligaments, were loaded in combined bending and compression in order to simulate movements and postures in living people. The relationship between flexion angle and bending moment was determined at different loading rates, and after sustained loading in bending and in compression. Results. Rapid flexion movements increased the peak bending moment by 10–15% compared to slow movements. On average, repeated flexion over a period of 5 min reduced the peak bending moment by 17%, and 5 min of sustained flexion reduced it by 42%. Two hours of compressive creep loading reduced the height of the intervertebral discs by 1.1 mm, increased the range of flexion by 12%, and reduced peak bending moment by 41%. Conclusions. The scale of these changes suggests that, in life, the risk of bending injury to the lumbar discs and ligaments will depend not only on the loads applied to the spine, but also on loading rate and loading history.

Influence of lumbar and hip mobility on the bending stresses acting on the lumbar spine

Bending and lifting activities are associated with injury to the lumbar discs and ligaments, and cadaveric experiments suggest that this damage is most attributable to a high bending moment (bending stress) acting on the osteoligamentous spine. We examined the hypothesis that people with poor sagittal mobility in the lumbar spine and hips apply higher bending stresses to their spines during everyday lifting activities. Forty-nine subjects performed a series of simple forward bending and lifting exercises while their lumbar flexion was measured continuously using a skin-surface technique ( 3-space isotrak). Peak flexion angles were compared with the bending properties of cadaveric osteoligamentous spines in order to calculate the peak bending moment (bending stress) acting on the lumbar spine during each exercise. All subjects flattened or reversed their lumbar lordosis when lifting, and most came close to or exceeded their static in vivo limit of lumbar flexion in many of the activities. The bending moment acting on the lumbosacral junction rose to about 30 Nm, which is about 50% of that required to cause injury in a single lift. Bending moments were significantly lower in subjects who had good sagittal mobility in the lumbar spine. Good hip mobility was similarly associated with a reduction in bending moment, but this reached significance only in subjects who reported a history of low back pain.

Fracture of reinforced concrete: Scale effects and snap-back instability

Remarkable size-scale effects are theoretically predicted and experimentally confirmed in low reinforced high strength concrete beams. The brittleness of the system increases by increasing size-scale and/or decreasing steel area. On the other hand, a physically similar behaviour is revealed in the cases where the non-dimensional number: N p= ƒ y·b 1 2 K IC · A S A is the same, ƒ y being the steel yield strength, K IC the concrete fracture toughness, b the beam depth and A s / A the steel percentage. The tensile strength and toughness of concrete, usually disregarded, are so high in some cases that the peak bending moment overcomes the bending moment of limit design (hyperstrength). The drop in the loading capacity can hide a virtual softening branch with positive slope (snack-back), which is detected if the loading process is controlled through the crack width.

Model Experiments for Span-Vehicle Dynamics

The transient dynamics of multiple-span beam-type bridges responding to constant speed, sprung and unsprung vehicle loads are investigated experimentally. Both instrumentation and the severe problems of dynamic modeling of realistic prototypes are considered. Scaling parameters such as vehicle mass to span mass ratio, passage frequency to bridge frequency ratio, vehicle suspension frequency ratios, and loading length to span length ratio are defined and applied to the design of a laboratory test facility. Considered are problems of data retrieval for the bridge dynamics and for the vehicle heave acceleration. The latter data, needed to design safe and comfortable vehicle suspension systems, are essential in future urban and interurban transportation systems. Span data are presented in nondimensional form, suitable for design purposes. Typical data for a six-span bridge show that the peak bending moments may exceed four times their respective static moments for a vehicle at its crawl speed.