Vertical Dynamic Loads on Footbridges Generated by People Running

Vehicle traction control is the cornerstone for enhancing driving performance, ensuring road safety, and enabling intelligent driving. For off-road vehicles, variable road roughness imposes varying degrees of vertical dynamic loads on the wheels and affects changes in vehicle traction. Through simulation experiments, this paper found that the slip rate control performance of vehicle traction control systems traditionally designed for static loads exhibited significant variations when dynamic loads were introduced. To address this issue, vertical dynamic wheel load data under different vehicle speeds and road classifications were subjected to clustering, leading to the determination of three as the optimal number of clusters. The integration of the immune whale algorithm for the design of corresponding traction control systems for different dynamic load categories, and their subsequent comparison with traditional controllers, revealed a significant enhancement in slip rate control performance. Under Class I dynamic loads, the control performance on all road surfaces achieved the best results, reaching a maximum of 63.4%. Consideration of the dynamic variations in dynamic loads caused by changes in vehicle speed led to the design of a global controller capable of adapting to different dynamic load conditions, based on the aforementioned classification controller. The final simulation verification confirmed the maintained excellent control performance of this adaptive controller under various operating conditions.

Introduction: Tibial stress fracture is a common and destructive musculoskeletal issue for military, particularly female, personnel. Common military tasks, such as walking and running with body borne load, reportedly lead to lower limb biomechanics that elevate tibial stress fracture risk. Yet, it is unknown if similar increases are evident when running with heavy load – particularly over varied terrain personnel commonly navigate during military exercises. Purpose: This study sought to quantify vertical ground reaction force (GRF) and tibial compression while participants ran with body borne load over challenging surfaces, and determined whether they differed between sexes. Hypothesis: Participants will exhibit a significant increase in vertical GRFs and tibial compression with the addition of body borne load, but increases will be dependent of the surface. Females will exhibit larger increases in vertical GRFs and tibial compression than males. Methods: Eighteen (9 Male and 9 Female) participants had 3D lower limb biomechanics quantified while running (4.0 m/s) with and without a 15 kg load over four surfaces (flat, squishy, firm, and rocky). Statistical Analysis: Stance phase vertical GRF and tibial compression measures were submitted to a two-way repeated measures ANOVA to test the main effect and interaction between load (0 kg, 15 kg) and surface (flat, soft, firm, rocky). Alpha was p < 0.05. Results: Running with body borne load led to greater peak, impact peak and VLR of vertical GRF, and maximum and impulse of tibial compression (all: p < 0.001). Surface impacted both vertical GRF and tibial compression measures (all: p < 0.001). Specifically, peak vertical GRF, and maximum and impulse of tibial compression were greatest on the rocky surface (all: p < 0.001), while peak vertical GRF was larger on the squishy and firm foam compared to flat surface (p = 0.025; p = 0.006). Sex did not impact any vertical GRF or tibial compression measure (p > 0.05). Conclusion: Running with body borne load may elevate tibial stress fracture risk by leading to larger tibial compression and larger, faster vertical GRFs. Additionally, running over challenging surfaces may alter injury risk, but the specific changes in vertical GRF and tibial compression that increase injury are dependent on the specific surface. Males and females exhibited no significant difference in tibial compression or vertical GRF measures during the loaded running over challenging surfaces.

Almost all of road damage can be caused by dynamic loads of vehicles that fluctuate according to the type of vehicle that passes through. This study aims to calculate the vertical dynamic load of the vehicle actually occurs on road construction by the mechanism of vehicle wheel suspension. Pneumatic cylinders driven by pressurized air directly load the spring and shock absorber installed on the wheels of the vehicle. The load fluctuations of the medium weight categorized vehicles are determined by the regulation of the amount of pressurized air that enters into the pneumatic cylinder chamber, pushing the piston and connecting rods. The displacement that occurs during compression on the spring and shock absorber, is substituted into the equation of vehicle dynamic load while taking into account the spring stiffness constant, and the fluid or damper gas coefficient. The results show that the magnitude of the displacement when the compression force works has significant influences to the amount of vertical dynamic load of the vehicle that overlies the road construction. The presence of dynamic load of vehicles that fluctuates and repeats, also affects on the reduction of road ability to receive the load. Experimental results using pneumatic actuators instead of real dynamic vehicle loads illustrate the characteristics of the relationship between work pressure and dynamic load. If the working pressure of P2 (bar) is greater, the vertical dynamic load Ft (N) that overloads the road structure is also greater. The associate graphs show that the shock absorber has a greater ability to reduce dynamic load vertically that burden the road structure when compared with the ability of screw spring.

The measurement of ground reaction force (GRF) is important in biomechanical analysis for clinical gait assessment and gait research. The GRF measured by the force plate, along with the gravity, are the only significant external forces acting on the body during gait. The purpose of this study is to show the effects of walking speed on vertical ground reaction force (VGRF) F z using Kistler quartz force platform embedded on the floor. Since considerable differences in the gait of normal subjects arises due to ‘constrained’ walking, so subject are made to walk with their self selected walking speed in the walkway. Vertical component of the GRF was analysed from the recorded data using Bioware software. It was clearly observed that with increasing walking speed VGRF increased at F z 1 and F z 3 whereas decreased at F z 2 .

Center of pressure is a valuable biomechanical variable, predicting joint loading contributions during movement and giving insight into compensatory patterns. The purpose of this study was to assess the validity and reliability of force insoles in calculating vertical ground reaction force and center of pressure during return-to-sport jump testing. Ten healthy individuals performed double- and single-leg vertical and horizontal jumps on an instrumented treadmill while wearing instrumented force insoles. Vertical ground reaction force and anterior-posterior and medial-lateral center of pressure were collected at peak vertical ground reaction force from both devices. Repeat testing occurred 7 ± 5 days following the initial session. Force insoles were valid for measuring vertical ground reaction force (mean absolute error (MAE): 4.34 N/kg) and anterior-posterior center of pressure (MAE: 10% foot length) but were not valid for medial-lateral center of pressure (MAE: 50% foot width). During double-leg vertical, single-leg vertical, double-leg horizontal, and single-leg horizontal jumps, force insoles demonstrated good reliability for measurements of vertical ground reaction force (ICC: 0.89, 0.75, 0.89, and 0.91), anterior-posterior center of pressure (ICC: 0.88, 0.89, 0.94, and 0.97), and medial-lateral center of pressure (ICC: 0.72, 0.09, 0.82, and 0.73). Force insoles are a valid and reliable alternative to evaluating vertical ground reaction force and anterior-posterior center of pressure during return-to-sport jump testing.

To address the frequent occurrence of rock burst disasters in areas with wide coal pillars during mining in the western mining area of China, the wide coal pillar area of the Tingnan coal mine in Shanxi Province was used as the research background. Theoretical analysis, numerical simulation, and field tests were used to establish the mechanical criterion and the energy criterion for the dynamic instability of wide coal pillars. The process and mechanism of wide coal pillar dynamic instability under dynamic and static load disturbances were revealed, and a wide coal pillar rock burst prevention and control scheme was proposed. The results indicated that when the load above a coal pillar reached the stress failure index and the energy failure index was met, the coal pillar reached the critical conditions for rock burst. With increasing static load, the stress, energy, and range of the plastic zone all showed increasing trends on both sides of the coal pillar. Under a given dynamic load, the stress and plastic zone range of the coal pillar significantly increased compared to those without a dynamic load. Under a given static load, the greater the dynamic load, the more likely the coal pillar was to undergo dynamic instability. The evolution of coal pillar dynamic instability was divided into three stages: energy accumulation, local instability, and dynamic instability. When the critical stress and energy conditions for coal pillar dynamic instability are exceeded, rock burst will occur. To reduce the static and dynamic loads of coal pillars, a rock burst prevention and control scheme of energy release and load reduction was proposed and applied onsite. The monitoring results showed that this control plan effectively reduced the stress of the coal pillar and the dynamic load generated by the fracture of the overlying rock layer, indicating safe mining in this area of wide coal pillars.

PurposeThe safety assessment of engineering structures under repeated variable dynamic loads such as seismic and wind loads can be considered as a dynamic shakedown problem. This paper aims to extend the stress compensation method (SCM) to perform lower bound dynamic shakedown analysis of engineering structures and a double-closed-loop iterative algorithm is proposed to solve the shakedown load.Design/methodology/approachThe construction of the dynamic load vertexes is carried out to represent the loading domain of a structure under both dynamic and quasi-static load. The SCM is extended to perform lower bound dynamic shakedown analysis of engineering structures, which constructs the self-equilibrium stress field by a series of direct iteration computations. The self-equilibrium stress field is not only related to the amplitude of the repeated variable load but also related to its frequency. A novel double-closed-loop iterative algorithm is presented to calculate the dynamic shakedown load multiplier. The inner-loop iteration is to construct the self-equilibrated residual stress field based on the certain shakedown load multiplier. The outer-loop iteration is to update the dynamic shakedown load multiplier. With different combinations of dynamic load vertexes, a dynamic shakedown load domain could be obtained.FindingsThree-dimensional examples are presented to verify the applicability and accuracy of the SCM in dynamic shakedown analysis. The example of cantilever beam under harmonic dynamic load with different frequency shows the validity of the dynamic load vertex construction method. The shakedown domain of the elbow structure varies with the frequency under the dynamic approach. When the frequency is around the resonance frequency of the structure, the area of shakedown domain would be significantly reduced.Research limitations/implicationsIn this study, the dynamical response of structure is treated as perfect elastoplastic. The current analysis does not account for effects such as large deformation, stochastic external load and nonlinear vibration conditions which will inevitably be encountered and affect the load capacity.Originality/valueThis study provides a direct method for the dynamical shakedown analysis of engineering structures under repeated variable dynamic load.

Most runners strike the ground with a rearfoot strike (RFS) pattern, 25% of runners land with a midfoot strike (MFS) pattern, and less than 1% land with a forefoot strike (FFS) pattern. RFS patterns are characterized by a transient vertical impact peak (IP), which is associated with high average and instantaneous vertical loading rates (AVLR, IVLR). When excessive, these have been shown to be associated with a number of running related injuries. It has been well-documented that impact loading is significantly reduced in a FFS pattern. This reduction has been attributed, in part, to a shorter (SL). Our previous research suggests that loading during a MFS pattern is not reduced from a RFS pattern. However, the study only included runners who naturally run with a RFS pattern. PURPOSE: To investigate impact loading variables in runners with a natural MFS pattern. It was hypothesized that these runners would have reduced impact loading, as well as a shorter SL, compared to runners with a natural RFS pattern. METHODS: This is an ongoing study of which 15 runners, 10 with a natural RFS and 5 with a natural MFS have been recruited to date. Subjects ran with their natural pattern on an instrumented force treadmill at a self-selected speed (RFS=2.96±0.4, MFS=3.0±0.4 m/s) for 5 min. IP, AVLR, IVLR and SL, were extracted from the analog data. RESULTS: IP, AVLR and IVLR were reduced between 12-16% in the natural MFS condition. Surprisingly, the SLs were fairly similar between MFS and RFS. CONCLUSIONS: These preliminary results suggest that habitual MFS running is associated with reduced impact loading. This may provide justification to recommend a MFS pattern for injured runners with high impact loading. ACKNOWLEDGEMENTS: NIH 1 S10 RR022396, DOD W911NF-05-1-0097

Measurements of multi-axial Ground Reaction Force (GRF) can provides quite useful information for monitoring abnormalities of gait during Activities in Daily Living (ADL). Measuring multi-axial GRF using ambulatory GRF sensing systems is difficult due to the height of sensor and the number of sensors used. Therefore, we developed a wireless GRF sensing system having the low height (12 mm) and the capability of sensing simultaneously lateral and vertical GRF using only four optical sensors. The proposed biaxial force sensor showed the low interference rate (less than 0.1 %) and excellent repeatability (0.6 %). We extracted the lateral and vertical GRFs via Bluetooth communication during normal and pronated/supinated walking and presented a three dimensional vector diagram employing center of pressure and GRFs to provide visualization of the ratio between the lateral and vertical GRFs according to the amount of foot pronation. In healthy subjects, the lateral forces were observed less than 10 % of their bodyweights, while large lateral forces were observed in over pronated/supinated walking up to 20 %.

Predicting timing of foot strike during running, independent of striking technique, using principal component analysis of joint angles

The stability control of surrounding rock for large or super-large section chamber is a difficult technical problem in deep mining condition. Based on the in-site geological conditions of Longgu coal mine, this paper used the dynamic module of FLAC3D to study the response characteristics of deep super-large section chamber under dynamic and static combined loading condition. Results showed that under the static loading condition, the maximum vertical stress, deformation and failure range are large, where the stress concentration coefficient is 1.64. The maximum roof-to-floor and two-sides deformations are 54.6 mm and 53.1 mm, respectively. Then, under the dynamic and static combined loading condition: (1) The influence of dynamic load frequency on the two-sides is more obvious; (2) The dynamic load amplitude has the greatest influence on the stress concentration degree, and the plastic failure tends to develop to the deeper; (3) With the dynamic load source distance increase, the response of surrounding rock is gradually attenuated. On this basis, empirical equations for each dynamic load conditions were obtained by using regression analysis method, and all correlation coefficients are greater than 0.99. This research provided reference for the supporting design of deep super-large section chamber under same or similar conditions.

This paper evaluates the impact of dynamic loads (induction motors) on the damping of Subsynchronous Resonance (SSR) based on load location and aggregate load inertia for the IEEE 68 bus network simulated in DIgSILENT. The severity of SSR oscillations is shown to increase in the presence of Subsynchronous Resonance Load Interactions (SSRLI), whereby dynamic loads may contribute towards negative damping under certain network topologies. This change in severity is investigated for each load location by replacing the static (constant impedance) load model, traditionally used in SSR studies, with a 50% static and 50% dynamic load model. The paper shows that the torsional damping and thus the severity of SSR is sensitive to the location and aggregate inertia of the dynamic load. These results establish the sensitivity of torsional damping to dynamic load location, size and aggregate inertia. In the absence of accurate knowledge of load composition, 50% static and 50% dynamic load composition can be used as a recommendation for the modelling of load during EMT studies of SSR, to avoid conservative results and over/under design of protection or mitigation strategies.

Heavy Vehicles speeds and dynamic loads are critical factors to bridge’s structure fatigue and rapid deterioration. The proposed paper addresses the modeling and simulation of dynamic loads of heavy vehicles, such as trucks and buses, on bridges and the effects of their speed on frequency response. In light of the above analysis, this paper proposes a method on how to minimize the structural vibrational of the combined vehicle and bridge system using semi-active suspension control. The vehicle dynamic load is minimized through an optimization scheme to yield an impact force with negligible bridge lateral deflection. The dynamic coupling between the vehicle and bridge are studied by examining the modes that are most likely to be excited by the vehicle speed and the roughness of the bridge surface. The models consist of a bridge and a heavy vehicle. The bridge is modeled as continuos, lightly damped beam with different supports defined by the boundary conditions. The vehicle is a multi-degree of freedom (MDOF) system undergoing motion in one plane. The methods of solution consist of a simple supported beam that closely simulates the first three beam modes of the Kishwaukee Bridge in Rockford, Illinois. The surface of the bridge generates some random excitation that serves as input to the vehicle, this is commonly known as the roughness of the bridge surface. The heavy vehicle is moving from left to right of the simply supported beam. The system is analyzed and optimized by semi-active control algorithms. Close form numerical solution is obtained by a set of second order differential equations for the bridge-vehicle system. Experimental data obtained from the vibration testing of Kishwaukee Bridge (Illinois) were collected and validated with a FEM model. Only the first three beam modes were used due to the experimental limitations and the actual structural condition of the bridge. Using MATLAB a simulation is obtained by inputting the linear time-variant equations and optimizing the system. Simulations of bridge vertical motion under different dynamic load conditions were examined and the results of bridge structure response were analyzed by comparing the effects of passive versus semi-active suspension controls. The method shows effectively how we can reduce the dynamic load force magnitude and its frequency of impact. The latter is usually associated with structural damage caused to the bridge.

This research aims to develop principles for assessing the impact of mega-cyclic vibrodynamic loads on the reliability of construction structures. The relevance of the reasons for the development and improvement of algorithms for numerical modeling of multicycle dynamic loads on building structures is due to the steadily increasing intensity of such loads on buildings and structures in megacities, as well as the acute practical problem of significant differences in the dynamic characteristics of buildings and structures obtained as a result of mathematical modeling and determined by experimental methods. The article presents research materials on computational equivalent models of dynamic load sources for numerical modeling of the behavior of construction structures under their influence, using the method of vibroacoustic analogies. The article examines models of sources of dynamic impact on construction sites. Algorithms and final formulas for computational modeling of the simplest sources of dynamic load are developed using the method of vibroacoustic analogies. The dynamic properties of the simplest dynamic load sources were analyzed. A significant difference between the computational models of real and ideal dynamic load sources. The article presents research and development results intended for calculating the distribution of dynamic loads on elements of construction structures in industrial and civil engineering projects located in areas with high levels of transport vibrodynamic impacts. An important property of the proposed computational equivalent models of sources of dynamic impact on building structures is the possibility of computational verification of critical elements, points, or nodes of load-bearing structures of buildings and structures under dynamic overloads. The position of these critical elements, points, and nodes of load-bearing structures under dynamic loads can differ significantly from their position determined using static and quasistatic computational modeling methods.

It continues to be argued that a forefoot (FF) strike pattern during running is more economical than a rearfoot (RF) pattern; however, previous studies using one habitual footstrike group have found no difference in running economy between footstrike patterns. We aimed to conduct a more extensive study by including both habitual RF and FF runners. The purposes of this study were to determine whether there were differences in running economy between these groups and whether running economy would change when they ran with the alternative footstrike pattern. Nineteen habitual RF and 18 habitual FF runners performed the RF and FF patterns on a treadmill at 3.0, 3.5, and 4.0 m/s. Steady-state rates of oxygen consumption (Vo2, ml·kg(-1)·min(-1)) and carbohydrate contribution to total energy expenditure (%CHO) were determined by indirect calorimetry for each footstrike pattern and speed condition. A mixed-model ANOVA was used to assess the differences in each variable between groups and footstrike patterns (α = 0.05). No differences in Vo2 or %CHO were detected between groups when running with their habitual footstrike pattern. The RF pattern resulted in lower Vo2 and %CHO compared with the FF pattern at the slow and medium speeds in the RF group (P < 0.05) but not in the FF group (P > 0.05). At the fast speed, a significant footstrike pattern main effect indicated that Vo2 was greater with the FF pattern than with the RF pattern (P < 0.05), but %CHO was not different (P > 0.05). The results suggest that the FF pattern is not more economical than the RF pattern.