Uncoupled approaches for walking-induced vertical vibration of a lively footbridge

The recent trend towards the design of flexible footbridges, characterized by a low ratio between permanent and variable load, has made them more sensitive to dynamic forces induced by pedestrians. While walking, the pedestrian moves on the flexible structure adapting his gait to the bridge motion and interacting with the footbridge. At contact points, the pedestrian transmits contact forces to the bridge that, in turn, imposes a set of displacements and velocities to the pedestrian’s feet. The pedestrian is here described with an increasing accuracy. Neglecting the interaction with the bridge, the pedestrian is described with a refined force model, that simulates the force pattern transmitted by each foot. The position of the two forces reproduces the sequence of single and double support phases, typical of the human gait. Interaction is accounted for when both systems are described as mechanical systems (having proper mass, stiffness and damping matrices). In this work a newly proposed bipedal pedestrian mass-spring-damper model is adopted, sharing with the force model the same type of locomotion. The mechanical system is excited by an equivalent bio-mechanical force and its equation of motion takes into account the interaction with the bridge. The coupled equations of motion of the bridge-pedestrian system are then derived; with a forced uncoupling of the equations, the two systems can be analyzed separately. The case study concerns a lively footbridge, whose dynamic response is computed with the different modeling approaches

Walking-induced vibration of a footbridge

In the last years, the need for structures able to link the functional and aesthetic role has led engineers and architects to design footbridges characterized by long span, light materials and increasing slenderness. The low ratio between permanent and variable loads makes recent footbridges more sensitive to the dynamic loads, such as the forces transmitted by pedestrian. Excessive vibrations may arise when the bridge natural frequencies are very close to those characterizing the human activities: walking, jogging and running. This issue became relevant after the Millenium Bridge inauguration, when an excessive lateral sway motion was triggered by the synchronization between bridge and pedestrian movements. The dynamic behavior of a lively footbridge over-passing the Serio river near Seriate (about 50 km far from Milan), Italy, is investigated in this paper. The suspension bridge, 63.75 m long, is composed of a timber deck on a steel grid. The footbridge model, based on the as-built design data, is implemented in the ANSYS framework. The numerical frequencies computed through the FE model match those identified from the results of the experimental campaign of ambient vibration measurements in a fully satisfactory way. Since the bridge displays several frequencies in the range excited by human activities, its response to crossing pedestrians is investigated. The dynamic interaction pedestrians-footbridge is analyzed for different classes of traffic with two approaches. First, the FE model developed in ANSYS is excited by the distributed harmonic load model for a pedestrian stream, applied on the bridge coherently with the corresponding mode shape, as suggested by the Hivoss Guideline. Second, an ad-hoc developed numerical code is adopted to compute the bridge dynamic response to moving forces. This code reads as input data the structural matrices computed in ANSYS and integrates the equations of motion of a system in which the pedestrian is modeled as a constant vertical travelling force along the footbridge deck. The vibration serviceability under the vertical component of pedestrian load is assessed by comparison to comfort criteria. The results of the Hivoss guideline show accelerations exceeding the value of comfort. The transient analysis predicts lower values within the limits. The two sets of values can be interpreted as an upper and lower bound of the actual response

Pedestrian-Footbridge Dynamic Interaction: A Probabilistic Assessment of Vibration Serviceability

Recent footbridges are characterized by long span, light materials and increasing slenderness, which make them more sensitive to dynamic forces induced by pedestrians. The vibration serviceability under human-induced dynamic forces is the governing criterion for the design of these slender structures. To assess serviceability, the bridge response must be computed accounting for human-structure interaction, adopting reliable estimates of expected loading scenarios, accurate models representing pedestrians and suitable integration techni¬ques. The present contribution investigates the dynamic response of a lively footbridge due to a group of pedestrians described as bipedal mechanical systems able to reproduce the human gait. Based on a numerical procedure previously developed, extensive simulation activity is performed in order to characterize the structural response in a probabilistic way. The step frequencies of the pedestrians are considered as correlated random variables, where correlation is based on mutual distance among pedestrians

FE modelling of the Streicker Footbridge

The Streicker footbridge was completed in 2010 at the Princeton University Campus, over the Washington Road. It is about 104 m long and consists of a central main span supported by a steel arch and four lateral approaching legs. The deck is a post-tensioned high-performance concrete girder. Steel columns with “Y” shape support four lateral legs that connect the bridge to the lateral bearings on the ground and the whole system results a slender varying cross section main girder. The original shape in the horizontal plane provides horizontal stability to the footbridge despite the intrinsic slenderness of the steel supporting columns. Vertical stability is provided also by the arch in the central main-span and by the supporting columns under the legs. Cross section width increases from the midpoint of the main span to the connections with the legs and then remains constant up to the ground bearings. This work is focused on the development of a finite element analysis of the footbridge at different levels of refinement from the essential implementation of beam elements to more refined FE solutions for the prestressed concrete deck. The models are identified with respect to the available operational modal parameters. This deck discretization could further allow simulating the motion of a running/walking pedestrian along different trajectories

Assessing Background Values of Regulated Parameters in Groundwater Bodies of Sardinia (Italy)

Abstract The groundwater bodies in the European Union should be classified on the basis of their chemical status according to the European regulations. To this purpose, the background values for electrical conductivity, chloride, sulfate, fluoride and lead in groundwater bodies hosted in carbonatic rocks in Sardinia (Italy) were estimated. Background values were dependent on geological (lithology and mineralization) and geographical (distance from the coast) features of aquifers. Results indicate that statistical methods should be integrated with hydrogeochemical investigations for a correct assessment of the background values

NON-LINEAR DYNAMIC ANALYSES OF AN RC FRAME BUILDING COLLAPSED DURING L’AQUILA 2009 EARTHQUAKE

This study focuses on the partial seismic collapse of a building during the earthquake of L'Aquila (Italy) on April 6th 2009. Designed in the early â60s, the 7-story building has a reinforced concrete frame structure. In elevation, above a first basement and a ground floor, three wings rise. The collapse affected the North wing, where three separate collapse mechanisms were identified. All the columns at ground story failed with a weak-story mechanism in North-South direction. Three columns, located near the interface with the other wings, failed on the full height. In the same area, subjected to strong distortions due to the difference in vertical displacements following the weak-story mechanism, at stories 1-4 a third collapse mechanism involved a beam supporting a non-structural wall inserted in recent renovation works. Previous investigations carried out with both pushover and nonlinear dynamic analyses explained why the collapse was confined to the North wing, the collapse sequence and the role of the non-structural wall. Based on nonlinear dynamic analyses on a refined 3D FE model, this study focuses on the role of the East and West wings that survived the earthquake. The subdivision of the base shear among the three wings at the collapse onset confirms that only few elements in the East and West wings contributed to resist horizontal forces in the North-South direction where the weak story mechanism took place

Association of kidney disease measures with risk of renal function worsening in patients with type 1 diabetes

Background: Albuminuria has been classically considered a marker of kidney damage progression in diabetic patients and it is routinely assessed to monitor kidney function. However, the role of a mild GFR reduction on the development of stage 653 CKD has been less explored in type 1 diabetes mellitus (T1DM) patients. Aim of the present study was to evaluate the prognostic role of kidney disease measures, namely albuminuria and reduced GFR, on the development of stage 653 CKD in a large cohort of patients affected by T1DM. Methods: A total of 4284 patients affected by T1DM followed-up at 76 diabetes centers participating to the Italian Association of Clinical Diabetologists (Associazione Medici Diabetologi, AMD) initiative constitutes the study population. Urinary albumin excretion (ACR) and estimated GFR (eGFR) were retrieved and analyzed. The incidence of stage 653 CKD (eGFR < 60 mL/min/1.73 m2) or eGFR reduction > 30% from baseline was evaluated. Results: The mean estimated GFR was 98 \ub1 17 mL/min/1.73m2 and the proportion of patients with albuminuria was 15.3% (n = 654) at baseline. About 8% (n = 337) of patients developed one of the two renal endpoints during the 4-year follow-up period. Age, albuminuria (micro or macro) and baseline eGFR < 90 ml/min/m2 were independent risk factors for stage 653 CKD and renal function worsening. When compared to patients with eGFR > 90 ml/min/1.73m2 and normoalbuminuria, those with albuminuria at baseline had a 1.69 greater risk of reaching stage 3 CKD, while patients with mild eGFR reduction (i.e. eGFR between 90 and 60 mL/min/1.73 m2) show a 3.81 greater risk that rose to 8.24 for those patients with albuminuria and mild eGFR reduction at baseline. Conclusions: Albuminuria and eGFR reduction represent independent risk factors for incident stage 653 CKD in T1DM patients. The simultaneous occurrence of reduced eGFR and albuminuria have a synergistic effect on renal function worsening

Coupled analysis of footbridge-pedestrian dynamic interaction

In this work, an analytical formulation for the vibration response of a bridge due to walking pedestrians is proposed to the aim of modelling the human-structure interaction (HSI) in the vertical direction. Bridge and pedestrians are described as mechanical systems having a finite number of degrees of freedom (DOFs). A new single DOF model of a bipedal pedestrian is proposed, that reproduces the alternation of single and double support phases of human gait and the related ground reaction forces. The finite element method is adopted to model the 3D geometry of the bridge. The coupled equations of motion are derived based on the key assumption that contact points between the pedestrians and the bridge deck are massless. However, the structural matrices of the coupled system are time varying due to the pedestrian motion along the bridge. An uncoupled solution strategy is devised to reduce the computational burden, allowing for the separate integration of the bridge and the pedestrian sub-systems. The coupled formulation is uncoupled and associated with an iterative procedure that restores compatibility and equilibrium at contact points. The pedestrian model and the analytical procedure are implemented in a research code where input data are the bridge structural matrices computed with a commercial FE code. The modelling and analysis procedure is applied to a case study, a lively footbridge in Seriate, Italy. A first validation of the code is obtained by comparison with a closed form solution for a 1D beam. For the loading scenarios analyzed here, a maximum of two iterations per step are necessary to achieve convergence within a prescribed tolerance. Loading scenarios encompassing groups of pedestrians in different transverse positions highlight the importance of the 3D bridge modelling. The comparison with a few experimental results clarifies the role of the modelling assumptions. Conclusions discuss novelties, advantages, limits and future developments of the proposed approach

Numerical Simulation of Seismic Collapse of a RC Frame Building: a Case Study

The paper investigates the partial collapse (during the April 6, 2009 earthquake of L’Aquila, Italy), of a seven-story reinforced concrete building designed in 1965. The three-wing building underwent a partial collapse in one of them. Within the affected wing, two collapse mechanisms developed, one in a horizontal plane and the other in vertical direction. The former was a soft/weak story mechanism at the ground floor, the latter involved the failure of three columns (and of the supported beams) at all the levels from the ground floor to the roof. Casualties are all due to this second mechanism, as nobody was trapped in the soft-story collapse. The three columns were located at the interface with the remaining building, in the zone undergoing a severe distortion because of the dramatic difference in vertical displacements due to the soft–story mechanism. At levels from 1 to 4, one of the columns was supporting a beam that was in turn carrying, on half of its span, a non-structural wall added during a refurbishment work. The beam failed in shear, approximately at midspan, at the end cross-section of the wall. A previous study, based on linear analyses only, showed that the lack of flexural strength of ground story columns was the main cause of the collapse. Through non-linear static analyses, the paper investigates the collapse sequence and the role played by the non-structural wall (and by the related shear failure of beams). A refined numerical model of the structure, including the reinforcement layout, has been developed to find the reasons for the disproportionate effects that the partial softstory collapse had. The results clarify the role of the added wall and of the lack of beam shear strength on the collapse of the three columns

Numerical Simulation of the Partial Seismic Collapse of a 1960s RC Building

This study focuses on the partial seismic collapse of a building during the earthquake of L'Aquila (Italy) on April 6, 2009. Designed in the early 1960s, the seven-story building has a reinforced concrete frame structure. In elevation, above a first basement and a ground floor, three wings rise. The collapse affected the north wing, where all the columns at ground story and three columns, located at the interface with the other wings, failed on the full height. In the same area, subjected to strong distortions, a third collapse mechanism involved (at stories 1-4) a beam supporting a nonstructural wall inserted in recent renovation works. Previous investigations explained why the collapse was confined to the north wing, providing (and based on) the knowledge of the building to the date of the earthquake in terms of geometry, material properties, acting loads, and seismic input to the site. This study aims to simulate the structural response during the earthquake to investigate the sequence of the different mechanisms and their possible interdependence. Nonlinear dynamic analyses on OpenSees adopt a refined three-dimensional finite element model with beam-columns fiber elements and the components of the ground motion at site. Results up to the collapse onset (1) satisfactorily simulate the identified collapse mechanisms; (2) clarify the interaction and the likely sequence among the different mechanisms; and (3) highlight the negative role of the nonstructural wall in the collapse. Conclusions provide comprehension of the past design procedures and of the possible flaws affecting the structures of the time