BEHAVIOR OF FRP PEDESTRIAN BRIDGES UNDER HUMAN INDUCED EXCITATION

The prediction of the dynamic response of pedestrian bridges under humaninduced excitation is a challenge in the design of pedestrian bridges, caused by the wide range of variables and the complex interaction effects. The use of new, lightweight materials, like FRP, and the trend to design long span and slender constructions lead to structures more sensitive to dynamical impact, which caused some vibrational problems at newly built bridges in the recent past. This brought increased attention to this topic. The present thesis aims to analyze the dynamic properties of the new material fiber reinforced polymer (FRP), to estimate the changes they cause in the dynamic response of respective constructions and to validate the current guidelines. The first part of the research includes a literature review in terms of pedestrian loading, their interaction with the structure, the characteristics of FRP and the specification of the current guidelines. In order to analyze the dynamic properties and the effects on the dynamic response, the second part presents a parametric analysis of simplified bridge structures and their dynamic response to different loads induced by pedestrians. In order to classify the new composite material, the estimated mechanical properties and dynamic characteristics are compared to the traditional material steel. FRPs are significantly lighter and less stiff than steel. The first property leads to a higher fundamental frequency, the later one counteracts this effect. The actual fundamental frequency of the unloaded system, which is also the main component in the dynamical evaluation specified in the AASHTO guideline, depends on the ratio stiffness to weight. In contrast to steel, FRP is more sensitive to human-induced loads. The additional mass of the pedestrians changes the fundamental frequency of the system significantly, due to the high ratio of live load to construction weight. This circumstance is disregarded by the current guidelines, which might have led to the vibrational problems at newly built pedestrian bridges. Furthermore, the lateralsynchronization-phenomenon, which is also not mentioned in the guidelines, has a significant impact on lively footbridges. A general approach for the consideration of the additional impact is introduced.


Significance of the Study
Pedestrian bridges sometimes span considerably long distances and, in combination with the advantage of comparatively low design loads and the recent aesthetic request for greater slenderness and lightness, they present an opportunity for innovative architectural and engineering design, using new systems and materials.
Therefore, common features of recent footbridges are "long span, light materials and increasing slenderness" [27]. All three of these attributes result in a reduced natural frequency of the structure. The reduced natural frequency, in turn, causes a higher sensitivity of the structure to dynamic forces induced by pedestrians, because the natural frequency of the structure drops into the range of frequencies of human walking. "For the design of slender footbridges, the vibration serviceability under pedestrian excitation is often the governing criterion" [55]. Consequently, this should be given special attention during the design process and should also be acknowledged in the corresponding guidelines and design codes. Predicting the response of pedestrian bridges to human-induced excitation is an exceedingly complex process, including the variability of human walking parameters and effects of human-structure and human-human interaction.
In order to simplify the design process, current guidelines (AASHTO) are limited to general restrictions of the structural natural frequency [1,2,3]. By doing this, the guidelines neglect the complexity of the phenomena appearing during a humaninduced excitation of bridges.
Some codes of practice (e.g. OHBDC, BS5400, Eurocode 5, Setra) [4] propose instead a deterministic moving force model, which is also insufficient to describe all aspects of the system. The true importance and complexity of the topic have been brought to the attention of civil engineers by an increasing number of reported vibration serviceability problems in newly built pedestrian structures under pedestrian loading.
A number of pedestrian-excited laterally unstable bridges reported all over the world over the past decades, including the London Millennium Footbridge and the Clifton Suspension Bridge, focused the attention towards the actual human walking mechanisms and the unique human-structure interaction. It also started a series of researches with the aim of identifying the underlying mechanisms leading to dynamic instability [47]. Extensive research in several fields over more than a decade has improved the understanding of the problem and has enabled the development of better modeling and simulation tools. The main component in these new models, which has been neglected in earlier approaches and is responsible for the vibration problems, is the human-structure interaction (HSI). The influence of this component increases with a higher ratio of live load to construction weight, which grows automatically due to the low density of the new materials and the increased slenderness of the structures.
The HSI includes changed dynamical properties of the structure due to the additional weight and damping effects of the pedestrians as well as interdependency of the structural movement and the induced pedestrian load. The latter one occurs particularly in the lateral direction. It is also known as synchronized lateral excitation and leads to unusually high loads and great lateral displacements. The effects of the dynamic components of the pedestrian load are significantly higher at slender and light constructions, like, for instance, constructions out of fiber reinforced polymer.
Composite materials, like "Fibre-Reinforced Polymers (FRPs) are an increasingly popular option for the construction of bridges as they possess high strength to weight properties and good durability qualities" [40]. However, the advantage of the reduced weight compared to traditional materials in combination with the also reduced stiffness is regarding the dynamic properties a detrimentthe structure is more sensitive to human-induced oscillations.

Methodology
Predicting the response of pedestrian bridges to human-induced excitation is an exceedingly complex process, including the variability of human walking parameters and effects of human-structure and human-human interaction. Even though approaches for the modeling of the multi-physics system of a bridge loaded by a crowd of pedestrians are available, the proposing of such a model is not the aim of this

Structure
The present thesis follows a simple structure. The second and third chapters include a literature review. The second chapter deals with fiber reinforced polymer and presents the production and composition, the properties and characteristics, and the applications of these materials. The third chapter gives an overview of the pedestrian walking loads. It is divided into three parts: individual level, collective level, and multi-physics level, which present the different considerable aspects of dynamic loads induced by a crowd on a flexible structure. The fourth chapter presents the requirements of the design code, which is the base for the model development.
During the fifth chapter, the development of the computer model and the choice of variables are explained and general settings are described. The results are presented and evaluated in chapter six. It points out the specifications of FRPs and the differences between FRPs and steel. Furthermore, a validation of the current guidelines is performed and an improved approach is presented. A summary of the research as well as an outlook for the possible future of this field of study is part of the conclusion in chapter seven.

Composites
Composite materials have been used for 6000 years and the trend is still developing and increasing.

Materials
"Polymer matrix-based composites are essentially composed of fibres embedded in polymeric matrices." [38]. For both of these phases, polymer matrices and fibres, different materials are availablewith changing material characteristics and combinability. The properties of the final materials are controlled by the properties of the initial materials, but also by the bonding conditions between them. Therefore, the interface area can be seen as the third phase. There are numerous materials available; however, this chapter is focused on the fiber-reinforced polymer materials used in bridge engineering.  [8] Thermosets in general are brittle at room temperature, that is why there is a need for reinforcement, but they have also a number of useful characteristics. Unlike thermoplastics, the properties of thermosets improve with increasing temperature, at least until a certain temperature threshold, at which the properties starts to degrade.
However, this threshold is significant higher than the corresponding degradation point for thermoplastics. [8,10,14] Common materials are polyester thermoset resins, phenolic resins, vinyl ester resins and epoxy resins. "Polyester is one of the earliest types of thermoset and is widely used in FRP composites" [8]. Due to their great mechanical properties and their high resistance to environmental degradation, epoxy resins are the most important polymers in structural civil engineering. Another advantage of epoxy resins is the absence of styrene, which minimises the toxic emission during the production process For polymers, to reach their full mechanical properties, it is essential that they have reached a nearly complete polymerisation. Therefore, it is important that the correct mix ratio is obtained between the resin and its curing agent. Since the curing reaction is influenced by heat, the site temperature should be given some attention.
Once the reaction is finished, the resins do not melt, soften upon reheating or dissolve in solvents. [8,57]

Reinforcement materials
The main function of the reinforcement is the strengthening of the matrix material by carrying the load along its length. "A wide range of amorphous and crystalline materials can be used to form fibres, but in bridge engineering the three fibres which are generally used are the glass fibre, the aramid fibre and the carbon fibre." [8]. A main component for the properties of the composites is the aspect ratio (length/diameter) of the fibers used as reinforcement and their orientation and fraction.
The choice for type, amount, length, orientation and other properties depend on the matrix characteristics, the intended application and the necessary load capacity. One distinction to categorize reinforcements is the size of the used fibers. It can be differed between macro-, micro-and nanoscale reinforcement. Macroscale reinforcement is the most common type of reinforcement. Glass fibers, carbon fibers and aramid fibres are widely used to reinforce polymers for the application in the field of civil engineering.
Usually they are used as CF fiber bundles (tows), glass fiber bundles (rovings), continuous strand mats and nonwoven surfacing veils. Glass fibers can be produced with tailored properties to meet specific applications. CF have also attractive properties "such as low weight, high strength and high modulus, fatigue resistance and vibration damping, corrosion resistance, good friction and wear qualities, low thermal expansion, and thermal and electrical conductivity" [8]. All three types of fibers have slightly different characteristics and can be chosen with respect to particular application. It is also possible to use a mix of different types of fibers to combine their advantages. [8,15,44] Independently of type and material of the used reinforcement, it is most important to adapt matrix and reinforcement to each other. The bonding between the two phases is decisive to ensure that the composite system as a whole gives satisfactory performance. [8,15,22,24]

General Characteristics
Accompanying the great importance of traffic and transportation, there is a growing concern with respect of the maintenance of the related infrastructure. The reparation, rehabilitation and replacement of old bridge structures is one of the main tasks in the field of civil engineering. The deterioration of reinforced concrete and steel bridges, especially when exposed to aggressive and hostile environments that are invariably encountered to traffic related constructions, lead to the need for durable, high strength and high stiffness materials. The result was the establishment of advanced composite materials as structural material in civil engineering. "These materials can provide significant advantages over conventional materials for the construction of bridges" [8]. Advanced composites have a higher resistance to oxidation than steel and a better freeze-thaw resistance than concrete, which might have been the initial reason for the introduction of FRP composite materials into the field of civil engineering. Nevertheless, FRPs provide a wide range of convenient characteristics, which led to a fast establishment of these materials. The resistance to corrosion and the freeze-thaw resistance result in low maintenance requirements and an enhanced service live. This applies also for harsh and corrosive environments, common at traffic related structures. The durability is even further improved, because also the fatigue performance is good. The high durability and resistance reduces the live cycle costs and is especially useful for areas with limited access. On the other hand, one of the main disadvantages is also related to this topic, which is the reprocessing. The high resistance of the material makes the reprocessing through either mechanical or chemical recycling difficult. In these days this is an important aspect which has to be considered during the planning of respective constructions.
FRPs provide a reduction of the dead load and a subsequent increase in live load rating. Related to this point is the advantage of a faster installation. Due to the reduced weight, the components are light and can be assembled easy and fast. Prior to shaping FRPs are liquids with low viscosity. As a result, their processing is relatively cheap and easy and they can be produced with complex shapes. It enables also the production of complete structural components under factory conditions, because they can be easily transported and installed. In comparison to concrete FRPs have also a good creep behavior that facilitates the design and planning process. [8,21,30,46] Another advantage of FRPs is the high versatility that means the possibility of adapting the material properties perfectly to the requirements of the intended application and function. Materials can be obtained with high strength, stiffness, and excellent impact strength. The actual stiffness is lower than the one of steel or concrete, but due to the reduced weight, the stiffness-weight ratio is better. Even the requirements for fire-and high-temperature-resistance of construction materials are fulfilled by the composites satisfactory, "due to their resistance to burning and minimal smoke and toxic fumes production" [8]. Additional tailorable characteristics are acoustic and thermal insulation as well as thermal conductivity. On the other hand, higher initial costs of materials can be considered as disadvantage, but considering the higher strength and the whole-life costs, these costs are more than compensated.
However, "composite materials are often predominantly composed of the most expensive construction materials." [8] The relation of mechanical properties and costs of the most commonly used constructional materials are presented in the following figure. It can be seen, that composites are relatively expensive, but provides better mechanical properties than most of the other available materials.

Mechanical Properties
It has been previously established that FRPs are highly versatile. This fact complicates the determination of general, or even average mechanical properties.
Depending on the used materials, the composition and the manufacturing process a wide range of mechanical properties, as Young's modulus, density and tensile stress capacity, are possible to create. "The mechanical properties of FRP composites are dependent upon the ratio of fibre and matrix material, the mechanical properties of the constituent materials, the fibre orientation in the matrix, and ultimately the processing and methods of fabrication" [8].
Not all of these attractive properties can be achieved at the same time; therefore, the design should be done carefully, since it can be efficiently optimized in contribution to the individual application. A main factor for the actual realisation are the costs. This factor limits the range of properties of FRPs used for constructions.

Introduction
Determining live loads correctly is a main challenge in the design of each human build structure. The dimensions should be in an economic range and the safety of the users still has to be assured. Unlike dead loads, the distribution of live loads is not However, the peculiarity of live loadsmoving, varying, and temporarymakes a generalization tedious. A compromise has to be found to assure a safe structure, without making it an uneconomical design, due to an overestimation of the load and the following dimensions. It gets even harder when, additional to the amount, the duration, impact and dynamic effects have to be considered. Traffic loads are especially hard to describe sufficient, due to the fact that they consist of an accumulation of many individual elements.
Because of the great importance and the major size of their shares at the live loads on bridges and other traffic areas, there is a great database for the impact of motorized traffic on structures. Numerous tests and studies regarding this topic have been conducted and led to a well-established model to compute traffic loads. All three levels are presented in the following paragraphs.

General Characterization
There are various types of dynamic loads produced by human activities. Both, Generally, the Gaussian probability density function is assumed the best fit for the measured data [59]. The median in combination with the standard deviation is sufficient as the base for a detailed and realistic simulation of the load.
Nevertheless, it is worth stressing that the geographical location of the structure should be taken into closer consideration, due to the fact, that even the average values vary strongly between different countries and cultural regions. [25,36] For instance, "Japanese people are expected to walk with a higher frequency than European, as a consequence of both their different lifestyle and smaller average body dimension." [15]. In the following the parameters necessary to describe the walking process sufficient are described and the average values for these parameters, collected from data out of a series of publications, are presented.

Frequency
Since pedestrian walking is a periodic load, the main parameter to describe walking is the frequency fp. Sometimes it is also referred to as pacing rate fs and is  As shown in Table 2, the walking frequency ranges between 1.5 and 2.5 Hz.
Consequently, the mean (μ) of the Gaussian normal distributions is often assumed as

Stride Length
Another way to describe the pedestrian propagation is the step or stride length ls.
It is normally given in m. Like the other parameters it varies due to a number of influence factors, but above all it is depending on the biometric characteristics, like body height and weight, the length of the legs and the walker's fitness. The stride length is the walking parameter to whose statistical description the smallest number of works are devoted. [43] 0.75 0.07 Wheeler [54] 0.75 n.a. Ricciardelli et al. [39] 0.768 0.098 This might be because the three parameters, frequency, velocity and step length, are coupled by the fundamental law [49] and therefore just two of them are necessary to describe the walking process sufficient. [7,49] 3.

Correlation
The law describes how two of the parameters determine the third one, but caused by the complexity of the walking behavior it is difficult to find relationships between the three walking parameters. Nevertheless, relations between frequency and velocity have been proposed by Butz et al.: [11] by Ricciardelli et al.: [39] and by Bertram and Ruina: [48] Ojeda et al. gave the relation between velocity and stride length as [33] where a and b are subject-specific constants. Even though these relations are not well established, the walking velocity is generally assumed as related to the walking frequency, as well as walking velocity and step length, while step length and walking frequency can be considered as uncorrelated. [49] Based on test results and average correlations can be estimated, as presented in the following figure.

Walking Loads
During walking, the pedestrian exerts dynamic forces on the ground. These forces  With an increasing walking frequency width the trough between the two maxima is shrinking so that this particular "feature disappears with increasing pacing rate and degenerates to a single maximum of sharp rise and descent when the person is running." [7]. At a really slow pacing rate the function has the shape of a block, caused by the decreasing impact factor. The slow loading of the foot eliminates the amplification of the load caused by the step and push off movement, that is why the load-time function stays even during the foot is loaded.
The maximum load: With an increasing walking frequency, the load maximum increases. This is caused by the load impact factor. A rapidly applied load causes generally larger stresses than those that would be produced if the same load would have been applied gradually. This dynamic effect of the load is referred to as impact and the ratio between the weight of the element and its dynamically increased load is referred to as impact factor. With a rising pacing rate the speed of the foot stepping on the ground is also increasing, therefore the impact factor rises and maximum load ascends.  Duration of foot contact: The last considerable characteristic is the contact duration of the single foot and the ground contact considering both feet. During walking, at each time one of the feet is touching the ground. In case of the load-time function this can be seen by the overlapping of the contact duration and load. One foot is being unloaded while the other one is being loaded, before the now unloaded foot is moved for the next step.
This leads to a time variation of the total dynamic load during walking, which has components in the 2 nd and 3 rd harmonicmaxima of the function appears also at the double and triple of the pacing rate. In contrast to the walking behavior, the behavior during running is characterized by an interrupted ground contact. The contact times of the two feet are separated by periods with no contact to the ground. [29] For one approach of the mathematical idealized formulation of the dynamic load, they differ between 'continuous ground contact' and 'discontinuous ground contact'.
The load, excited by walking, which exhibits an overlap of the individual contact times of either foot and produces therefore a continuous ground contact, can be idealized by the following expression: [11] where: G = weight of the person (generally assumed to G = 800 N) If the 2 nd and 3 rd harmonics are considered, both force components are often assumed as with the approximated phase angle of . [11] It is also possible to describe the function in a more general form as a Fourier series: [11] where: G = weight of the person (generally assumed to G = 800 N) In the case of the discontinuous ground contact, the description of the load-time function within one period has to be differentiated between the duration with contact to the ground and without contact to the ground. The former one, "generally characterized by a single load maximum, can be expressed by a sequence of semisinusoidal pulses" [49]. The function within one period is given by: [49] with: kp = Fp,max/G = dynamic impact factor

General Aspects
"Crowd modelling can be distinguished into microscopic-level and macroscopiclevel, based on the level at which crowd analysis is being performed." [42] The former describes how each individual within a crowd reacts to its surrounding and therefore to the surrounding individuals and their behavior. In addition, described in latter level, group dynamics can be observed, which leads to "a complex and coordinated collective behavior" [25] and indicates an interaction that exceeds the reaction of an individual to its surrounding. This phenomenon is known as emergent behavior. Among others, it is responsible for the formation of walking lanes and the prevention of collisions. Besides the description of the behavior of an average crowd, coincidentally compounded of independent individuals, it is worth to consider public events like demonstrations or city marathons. Because of the shared goal or walking purpose, the cohesiveness within the crowd and the interaction between the individuals gets stronger and influences also the resulting walking load. [10,9,2] All of the three cases are briefly described in the following paragraphs.

Microscopic-Level
The individuals in a crowd interact with their environment; "they unconsciously alter their behavior in line with the response of neighbouring entities" [25]. This interaction, even though it is unconscious, follows a set of simple rules to assure the realisation of the personal goals without a discrepancy with the social norms. An average walking pedestrian moves towards a goal destination and aims to stay as close as possible to the shortest route between his origin and the aspired destination. Inside a train station, individuals tend to move towards an entry or exit, walking on a bridge, they head to the other side. Even though each individual has his own goal destination and motion tendency, on their way they keep a distance to persons and obstacles in order to prevent collisions and, out of comfort, they avoid sudden changes in direction and velocity. The pedestrians have to adjust their routs according to these rules and the walking parameters are affected by them.
In contrary to the free speed, the walking parameters, especially the velocity, of a person moving in a crowded area are not determined by the person's abilities and wishes, but additionally by the crowd density (number of pedestrians per unit of area) and the general velocity of the crowd. With an increasing crowd density, each pedestrian has less space to its disposal, the strived distance to each other is not realisable anymore and the walking velocity has to be reduced to avoid collisions.
In addition, assuming a crowded scenario, passing of the foregoing pedestrian is not possible; the pedestrian with the lowest walking velocity determines the speed of the whole crowd or at least the people behind him. In conclusion, the average walking velocity in a crowded scenario is smaller than the average free speed. The other walking parameters, correlated to the velocity, might change too, but not necessarily on the same scale. [25] 3.

Macroscopic-Level
Even though each individual is self-organized and its walking behavior inside a crowd seems to follow just the described rules to avoid collision, forming a crowd, they appear to share common motion dynamics and together "they portray a complex and coordinated collective behavior" [25]. An example for these crowd dynamics is the forming of uniform walking lanes in crowds with groups of opposite moving directions, even without communication or a leadership. This emergent behavior is the subject of several researches with the purpose to investigate the underlying mechanism that allow this unity in the crowd. Collective crowd behavior arises in swarms or crowds with certain class of entities (e.g. insects, human, animals, etc.) and follows some physical laws. That is why there are models in both fields, biology and physics, available.
From the biology point of view, individuals in a crowd resemble the entities in a swarm. They observed that each entity acts independent and conform to a set of rules, while as a whole the swarm acts in a sophisticated way and forms something like a collective 'group-mind', which helps individuals to reach their goals. One aspect of this model is the "natural reflect that is deeply rooted in each entity (specifically human) to conform to social norm" [25].
On the contrary, associating crow behavior with the laws of physics, the crowd is assumed as a homogenous mass of bodies. "The idea of relating the motion of crowd with fluid, liquid or electrons in aerodynamics, hydrodynamics or continuum mechanics respectively, has generated many research in crowd analyses since the past years. Accordingly, physics-inspired studies assume that the individual in a crowd tends to follow the dominant flow of the crowd and thus, the motion of highly dense crowd resembles fluid. Hence, theories and methods in fluid mechanics are adopted to comprehend the flow of human crowd. In another physics-inspired example, the kinetic theory of gases is applied to model the sparse and random interaction forces amongst individuals in a crowd." [25]. In the field of physics the individuals are characterized as non-thinking particles whose motions are dictated by external forces.
Both approaches gain convincing results and share similar understanding and perspectives. Nevertheless, existing models are insufficient in understanding the interaction between individuals and their environment in total. Additionally, they do not take the possibility of subgroups and their influence on the crowd behavior into consideration. [25] Social interactions such as walking in pairs or in groups and the resulting harmonization of the walking parameters to each other leads in average to a smaller velocity.

Special events
The accumulation of the walking loads of a group of pedestrians is coincidental.
The maxima and minima of the individual load-time functions are randomly shifted to each other and the result is a nearly constant load function, because the peak values compensate each other. A higher risk for line-like structures poses crowds marching in step, because in that case, the accumulation is not coincidental anymore and the maximum of the resulting load function is the sum of the single load function maxima.
Therefore, the synchronization of the pedestrians within a crowd is a hazard, which has to be considered during the dynamic analysis.
There have been some accidents in history, where soldiers marched in step over slender bridges and combination of the summed loads and a marching frequency close to the natural frequency of the structure led to a resonance response and eventually to the collapse of the structure. Nowadays the risk of people marching in step is still existing, even though it is likely that they are not soldiers but demonstrators or participants of an big event, supported with music or drums and marching in step with the music. Even a bridge that has been designed to carry motorized traffic and therefore great loads can be affected by such an event. [49] Another kind of public event that should be considered is sport events, especially marathons. The risk of these is not the synchronization but the changed walking mode.
Jogging and running produce higher amplitudes in the load function than walking and an accumulation of these loads might result in considerable high loads. However, the crowd density in this scenario is noticeable lower, because the increased speed demands greater distances to surrounding peoples. As a result, the summed load would not be significant higher. In an approach for a simplified dynamic analysis of slender bridges, the scenarios of special and public events and the resulting loads should be included. [7] "In order to complete the introductory overview of the topic of interest, an additional issue to be considered arises by the onset of panic conditions, which substantially modify the crowd dynamics." [49]. In addition to aspects of a save evacuation panic conditions can lead to an increased crowd density and hence to higher loads. However, since synchronization does not occur in panic conditions and a high crowd density restricts the movement of individuals it is less a dynamic but more a general load problem and hence this issue is not of particular interest in this text.

Simplifications
In the field of structural engineering, especially for a structural analysis, the detailed analysis of a microscopic level is not expedient. The used measurements for walking parameters found in literature usually refer to averaged quantities and within a crowd occurs a assimilation. Additionally, the focus is normally at the general crowd behavior and if it has influence on the resulting load. "One of the main feature of crowd behaviour is that the walking velocity is affected by the crowd density, namely the higher the crowd density, the lower the walking velocity. Many studies have been directed to the determination of a law that links the walking velocity to the crowd density." [49]. Looking at the diagram some relevant quantities regarding crowd behavior can be identified: -Until the critical density ρc is reached the pedestrians are unimpeded and walk with constant free speed vM.
-For higher densities ( ) the walking speed decreases with increasing density.
-The highest flow occurs at the combination of a capacity speed vca and a capacity density ρca.
-ΡM is the maximum admissible density corresponding to null speed and flow.
"  Another approach introduces factor to account for the influence on the walking velocity of both psychology and physiological level. [50] where: (jam density) (surface occupied by motionless ped) (average free speed)  All the relations refer to a one-directional flow. Adding a contrariwise flow leads to a reduction of the flow capacity, due to passing pedestrians. [49] 3.4 Multi-Physic Level: Human-Structure Interaction

General Characterization
The interaction between human and structure is a sophisticated process in which approach, which applies also on walking people, another approach to explain the effect has been published. It claims, that the "humans' inability to synchronise their pace with vertically moving surfaces causes the vibration to diminish." [49]. The actual effect might be a combination of both theories. [11,20,49] In each case it is important to account for the effect within a dynamical analysis, because neglecting to do so "may result in an overestimation of the dynamic response of a structure, and as a result, a more costly structural design." [41] It is of great importance, because experiments demonstrate that the described effect, meaning occupants at a bridge, can change the damping factor of the system by a factor of 10.
The difficulties are in the estimation of the applicable values for specific cases, since they depend on several parameters, among others on the relative ratio of the average walking frequency of the occupants to the natural frequency of the empty structure and the relative ratio of the mass of the occupants to the structure. It is worth stressing out that the effect of additional damping applies in this form just on the vertical direction.
In the lateral direction contrary effects can occur. When a bridge is loaded with a crowd of pedestrians small lateral motion might occur, caused by the random lateral walking forces. The human body is sensitive to lateral motions and automatically he attempts to re-establish the balance by moving his body in the opposite direction. This reaction leads to changes in the walking behavior of the pedestrian. Firstly, the lateral width between the feet increases, because the pedestrian has to counteract the lateral acceleration of the pavement, and that leads to higher lateral forces. Secondly, the pedestrian synchronise his walking to the swaying frequency, that is the natural frequency, of the structure.
The enlarged load, adjusted to the resonance frequency, causes in turn an increased motion of the structure. The threshold at which a pedestrian starts to synchronize with the oscillation varies from person to person, which is why the number of synchronized people growth gradually. Consequently, the motion of the structure increases respectively. "Of course, because of adaptive nature of human being, the girder amplitude will not go to infinity and will reach a steady state." [17] Mainly, the induced force is restricted by the physiological limitation of the step width and characteristic of humans to stop walking when the motion is high enough to scare them.
The requirements for a synchronous lateral excitation are a natural frequency of the structure close to the average walking velocity and initial motions higher than the thresholds. In case of the vertical direction and therefore for a frequency around 2 Hz the threshold is 8-12 mm. For lateral vibrations with a frequency of about 1 Hz the threshold seems to be 4-6 mm [6]. This consonance to the research of Arup [32] following the Millennium Bridge incident. The low lateral threshold confirms the human sensitivity to lateral vibrations and underlines the importance of this effect, because even massive concrete bridges can be affected. The graph confirms also the trend that people synchronize with each other, even when there is no pavement motion.
"They also found that the lateral forces of the feet-apart gait are phase synchronized to the structure and approach 300N amplitude per person, which these researchers pointed out is four times the Eurocode DLM1 value of 70N for normal walking." [32]. The general conclusion to this topic is to avoid natural structural frequencies in the range of the walking frequency and its third harmonic. This rule might not be adequate, because it leads to unnecessary heavy and costly constructions, Figure 9: Probability of Synchronization [49] and eliminates innovative designs and the use of new materials. A model to consider this effect has to be found. [5,6,17,32,49]

General Aspects
Design codes and guidelines formulate requirements for buildings and constructions to ensure their structural safety and durability as well as serviceability.
Their aim is to establish standards for the design of structures and a general level of

Definition and Application
The AASHTO (American Association of State Highway and Transportation Officials) claims that pedestrian bridges "shall be designed for specified limit states to achieve the objectives of safety, serviceability, including comfort of the pedestrian user (vibration), and constructability with due regard to issues of inspectability, economy, and aesthetics" [3] and their formulated requirements are meant to reach this goal.
The Guide Specifications apply for pedestrian bridges, which is defined as a bridge "intended to carry, primarily pedestrians, bicyclists, equestrian riders and light maintenance vehicles, but not designed and intended to carry typical highway traffic" [3]. Consequently, the bridges has to be designed considering both a live load representing a dense pedestrian crowd and a maintenance vehicle. The configuration of the latter one can be determined by the Operating Agency; alternatively, there are design values available in the guidelines. The vehicle load has to be applied, even without a vehicle allowance, but it can be neglected, provided vehicular access is physically prevented. [1] Bicyclists are not expected to induce design-controlling loads that is why they are not further considered within the guidelines. The equestrian load is also not expected to control the design of the total structure, but can produce a significant patch load due to a high hoof pressure during a canter of the horse, which may control only the deck design. [3] Thus is why this load case can be also neglected within this research.

Pedestrian Live Load
The guidelines demand the application of a uniform pedestrian loading to the walkway area. "This loading shall be patterned to produce the maximum load effects." [3]. The actual values vary within the different specifications and guidelines, but are generally based on the maximum credible pedestrian load. Due to physical limits, the maximal load induced by pedestrians is restricted. It depends on the compounding of the crowed and if individual movement is still possible. Are standing crowd can have a high pedestrian density that cannot be reached within pedestrian traffic. 85 psf (4.07 kN/m²), which is proposed in [1], is considered "a reasonably conservative service live load that is difficult to exceed with pedestrian traffic" [1]. Other guideline specifications provide higher values, but allow reductions based on loaded length or area, considering the lower probability that a big area is crowded on a maximum level.
In cases of special events or locations, for instance close to stadiums with big sport events, this reduction might not be appropriate and includes an unnecessary risk. The following  The combination of pedestrian and vehicle load can be neglected. The considered Truck has to be placed to produce the maximum load effects.

Wind Load
Regarding the considered guidelines, the wind loads are the only live loads, which has to be applied in the horizontal direction. The wind load has to be applied in a 90° angle to the longitudinal direction of the structure and "shall be applied to the projected vertical area of all superstructure elements, including exposed truss members on the leeward truss." [1]. The following intensity should be used for the

Design Details
Besides the recommendations for design loads the guidelines provides also requirements for design details, like deflection limitations and instructions regarding vibrations, to assure the structural safety and serviceability.

Deflection
The present guideline formulates limitation for deflections in relation to the corresponding span to assure users and observer a secure feeling and restrict the stresses in secondary construction members due to the movement. "Members shall be designed so that the deflection due to the service pedestrian load does not exceed 1/500 of the length of the span." [1]. The same value applies for cantilever arms due to the pedestrian live load and for the horizontal deflection due to lateral wind load.
These values are more liberal than the AASHTO highway bridge values (1/1000), recognizing the differences between vehicle and pedestrian loads. While the maximum load, which is applied for the calculation of the maximum deflection, is expected to appear frequently, the maximum loading due to pedestrians and the resulting deflection is expected to be exceptional. [1] The limitation of maximal deflections correlates also with the vibration sensitivity of the structure. The structural stiffness, which is required to reach minimal deflections, ensures at the same time the fulfilment of the demanded vibration limitations. The reduction of the vertical deflection criterion for bridges out of traditional materials such as steel, concrete, wood, and aluminum, would cause a drop of the structural natural frequency, potentially below the threshold of 3 Hz, which represents the "comfort level of pedestrians and runners" [1]. Due to the reduced weight of FRP in comparison to traditional materials, one can satisfy the minimum vertical natural frequency criterion even with a more liberal deflection criterion.
Nevertheless, due to the serviceability in terms of observable high deflections, the limitation of the maximal deflection applies unmodified to FRP pedestrian bridges.

Vibrations
The avoid the second harmonic." [1]. In the horizontal direction the fundamental frequency of the pedestrian bridges should be higher than 3 Hz to avoid issues due lateral motion involving the first and second harmonics. Additionally, the aspect ratio (length/width), which also influences the lateral dynamic response of the construction, higher than 20 should be avoided. Finally, the fundamental frequencies in horizontal and vertical direction should be different "to avoid potential adverse effects associated with the combined effects from the first and second harmonics in these directions" [1].
If the aimed fundamental frequency cannot be reached by changes at structural level, for instance by changing stiffness, construction weight etc., additional effective measures to reduce the vibrations are "stiffening handrails, vibration absorbers, or dampers" [1].

General Aspects
The

General System
One part in the process of the model development was the simplification and generalization of the bridge structure. The aim was to find a model, which represents the characteristics of an average pedestrian bridge. Several parameters have to be chosen during the design of bridges, including the construction type, the number, profile and dimensions of the main girders, the cross-sectional beams and the deck and pavement design. Especially the first two points made a generalization of bridge properties complicated. Consequently, the final analysis has been made with an simplified girder system. The common structural system of pedestrian bridges is a single span, traversed by two main girders, connected by secondary crossbeams, carrying the deck construction including pavement and handrails. Since the deck construction has a minor influence on the structural properties considered in this research and has, on the other hand, a wide range of variables in design and composition independent from the girder material, the analyzed system has been reduced to a girder system, consisting out of two main girders and the connecting crossbeams. In order to identify the dynamical properties of FRP pedestrian bridges this reduction to the main constructional members has been necessary to determine the particular specifications of this material without the influences of deck constructions and materials and other design components, which might have changed the results.

Load Application
As presented in chapter 3 the load induced by pedestrian crowds on a flexible structure is a complex phenomenon, which includes several interactions and countless variables. To model this phenomenon sufficiently a multi-physical and extensive model is necessary. The development of such a model falls outside the scope of this paper. The aim of the research is to identify the different components of the dynamic response and the evaluation of the guideline requirements. In order to do this, the load is applied separately for the different components and, in order to estimate the maximum values, a uniform distributed and an harmonic load is assumed. The latter one does not represent an average pedestrian loading, but it represents a maxima crowd load, with pedestrians walking in step, which represents the conditions of the 'worst case' in terms of a dynamic response.

Materials
The bridge models are designed for the use of three different materials.

Boundary Conditions
The abutments are placed beneath the ends of each main girder. The aim is to prevent movement in all of the three directions without producing any constraints.
Vertical displacement is restricted at each abutment, two abutments provide support in lateral direction and two of the abutments prevent the longitudinal displacement. The following graphic presents the disposition of the boundary conditions.

General Aspects
In order to determine the dynamic properties of the different materials and the relating bridge models the analysis includes several steps to determine the single effects and influences. The following paragraphs describe briefly the proceeding and the respective settings used in the ABAQUS simulation.

Step 1: Natural Frequency
During the first step, the natural frequency of the modelled structure is estimated.
In order to identify the influences of the material properties on the fundamental frequency of the structure no further loads or preconditions are applied. To see the development of the frequencies and modes this analysis step is made for all spans and materials and includes the first seven modes of the structures. It is expected that the development follow the general laws of structural dynamics. This step provides also a first classification in terms of the range of fundamental frequencies and therefore a base for the following steps.

Step 2: Additional Mass
As mentioned in the chapter 3, the additional mass of the pedestrians changes the properties of the single degree of freedom system and therefore, the fundamental frequency of the structure. This effect is analyzed by a stepwise-applied mass and the calculation of the respective fundamental frequencies. The applied mass represents a load, which ranges between 0 kN/m² and 4 kN/m². The highest values equals the maximal pedestrian load. The load is assumed uniformly and an even distribution over the two or three girders is considered.

Step 3: Dynamic Response (harmonic loading)
To test for the dynamic response to the pedestrian loading the steady state of the structure is estimated, over a wide range of frequencies and with a stepwise applied dynamic load. The initial condition of this step is a maximal loaded (4.0 kN/m²) structure, to acknowledge the changed fundamental frequency, and stepwise a dynamic load, considering the impact factor related to different walking frequencies, is applied. In vertical direction, the first applied dynamic load is 0.8 kN/m², which is equivalent to an impact factor of 1.2, which correlates to walking frequencies of 1.

General Aspects
Considering a single-degree-of-freedom (SDOF) system, meaning a system with a single displacement variable, the rate at which the system chooses to oscillate in this direction is called natural or fundamental frequency. The natural frequency is governed by the mass and stiffness of the system. In terms of an undamped system the relation can be described as where k is the stiffness and m is the mass of the system. A bridge structure is much more complicated, it has several motion variables and therefore, it has to be approximated as a multi-degree-of-freedom (MDOF) system. In the case of MDOF systems, each degree of freedom is related to its own natural frequency. Each of these modes of vibration is associated with a particular deformation shape known as the  The comparison of the natural frequencies of the unloaded systems gives a first overview of the dynamical properties of the different materials. The table A5 with the detailed data is included in the appendix. The following graphs present the development, with increasing span, of the natural frequencies of the first lateral, vertical and torsional mode, respectively, which represents the first three modes of the structure. The curves for the three materials are printed in the same graph, in order to simplify the comparison. The natural frequencies of the structures depends mainly on the parameters mass and stiffness. The mass consists of the construction weight and depends on the mass distribution. The stiffness of the applied system consists of the mechanical material properties, the characteristics of the profile, type and span of the structural system.
The effects of three of these parameters can be seen in these graphs.
The first considerable parameter is the span. The curves of all three materials have similar shapes, because the dependency of the natural frequency to span is material independent. The dependency is in general complex, since the span influences more than one included parameter. The stiffness of a dynamical system can be calculated as [18] Where α is a factor depending on the statically system. Thus, the natural frequency is dropping with increasing span. Since the moment of inertia I is also estimated based on the span length L (see chapter 5.3.3.1 Main Girder), the interdependency between the stiffness and the length L is even more complicated.
Additionally the span also dictates the mass, since the construction weight is closely related to the span, because of both, the span and the resulting profile dimensions. The continuity with which the curves of all materials develop shows that the proceeding to model comparable systems has been sufficient. Minor discontinuities can be explained by the stepwise increase of the moment of inertia and the changes in the cross beam spacing.
The next considerable parameter, which is in order to estimate the material depending dynamical properties of greater importance, is the stiffness of the material, namely the Young's modulus E. The equation above shows, the stiffness of the structure is proportional to the Young's modulus. However, it has to be considered that the moment of inertia depends also on the material properties, so the actual correlation is not linear. An increase of the structure's stiffness leads to higher natural frequencies. This can be easily observed in the direct comparison of the two FRP materials, whose properties differ just in terms of stiffness. This aspect requires consideration during the design process of FRP constructions, because advanced composite materials vary strongly regarding their mechanical properties and a reduced natural frequency can cause resonance related problems.
Although the FRP materials have significant smaller Young's moduli than steel, the model structures built out of these materials have still higher natural frequencies than the respective ones out of steel. This circumstance is caused by the third considerable parameter, the mass. The assumed materials have significantly differing densities, which is decisive for the mass to be applied. The actual mass of the dynamical system is the product of span, profile area and density. The span is for all material the same, profile area and density are material depended. FRP 2 and steel have similar stiffnesses and have therefore similar profiles. In conclusion, their main difference is the density. As it can be seen clearly, this property has a major influence on the structure's natural frequency. A reduced density causes an increased natural frequency, which can be seen as a major advantage of advanced composite materials, because it counteracts the effects of the reduced stiffness. Since the factor between the materials' densities is higher than the one of the stiffness, the influence of the density is higher, which is the explanation, why the natural frequencies of the FRP materials are higher than the one of steel.
One additional aspect can be seen in these curves regarding the construction form itself. The constructions out of FRP 1 are designed with three instead of two girders.
This has not a big influence in vertical direction, because the structure's stiffness is the sum of the individual girders. In horizontal direction, the impact of this change of construction is much higher. Due to the reduced spacing and the reduced length of the crossbeams, the connection between the individual girders increases which leads to an improved stiffness in this direction. The respective position of the corresponding curve is therefore higher in the lateral direction than in the vertical.
The development and relation to each other of the different modes respectively for the different materials are presented in the following graphs. The significant similarity proves the comparability of the used models, which is important for the following analysis steps. Even though the mechanical properties of fiber reinforced polymer lead to increased natural frequencies, which is positive in terms of the resistance against human induced excitations, FRP constructions are still more sensitive to these loads, due to high live load to construction weight ratios.
Unlike wind or earthquake live loads, pedestrian live loads add an additional mass to the dynamical system. When pedestrians enter a bridge construction, their weight is added to the oscillating mass; they become a part of the system. This changes in turn the dynamical properties of this system. As it is shown above, the fundamental frequency of a dynamical system is directly correlated to its mass.  As shown in the graphs, the fundamental frequency of the structure drops significantly due to the additional load. The maximum load of 4 kN/m2 reduces the frequency of the structure in all materials by a factor of 2, or in the case of FRP 2 by a factor of 4. Even though the actual values are not representative for actual bridge constructions, because the ratio of construction weight to load and therefore the change of mass would be smaller due to the neglected deck and additional construction elements, but the influence of this effect is still decisive and cannot be neglected. Due to the small density of FRP, the ratio of construction weight to applied load is much higher, which causes the respectively great change of the frequencies. The influence on the FRP 1 material is smaller than the one on FRP 2, because the additional girder used in the first case increases the construction weight and therefore decreases the ratio of construction weight to live load. The relationship between the different materials can be seen in the following graphs.  with that of the applied loading, and will continue for as long as the loading." [56] Pedestrian loading can be classified as long duration load. The transient response can be neglected, at least in terms of a general analysis. The greatest hazard due to a dynamical load is an effect called resonance. If the exciting frequency of the harmonic loading is close to natural frequency of the respective structure, the amplification factor of the equivalent static load is growing significantly. The natural frequency of a structure and its relation to the loading frequency is therefore of decisive importance in the design process. The difficulty of pedestrian loading is the high variability. The load applied by a crowd of pedestrians is normally not harmonic, due to the individual parameters of the pedestrians. In the case of randomly distributed walking parameters and phase angles, the dynamic part of the load does not have a great impact, because the minima and maxima of the individual pedestrian loads compensate each other.
However, in the case of synchronously walking, intentional (marching) or unintentional (lateral synchronisation), the load amplitudes accumulate and the resulting load is near a harmonic load. This scenario causes the greatest deformations and therefore, the analysis deals with harmonic, uniformly distributed loads, as an approximation of a uniformly distributed crowd walking in step. In this way, the "worst case" is presented.  As expected the maximum values appear at the frequencys equal to the fundamental frequencys of the structure. It can be seen, that the natural frequency of the loaded FRP 2 structure dropped to the same value as the one of the steel structure, even though the natural frequency of the unloaded system is much higher. The importance of this fact can be seen in this graphs. Since the girder profiles in vertical direction are dimensioned for equal displacements, the similar maximum values are also as expected. The differences of the FRP 1 material can be justified by the changed stiffness parameters as a consequence of the additional girder.

Guideline Evaluation
The results and conclusions of the previous paragraphs enables to identify some insufficiencies in the current guidelines, regarding the handling of human induced excitations on FRP pedestrian bridges. As it is shown above, the effects of the material characteristics of advanced composite materials on the dynamic properties of respective structures equalize each other. Since the reduced density leads to higher frequencies, it compensates the drop of the frequency due to the smaller stiffness of FRP materials. The final natural frequency depends on the ratio of stiffness to density.
The fundamental frequencies of FRP bridge constructions, at least of the applied models, are in the same range as respective steel structures, or even higher.
The guidelines require for FRP constructions, as well as for steel structures, fundamental frequencies higher than 5 Hz and 3 Hz for the vertical and lateral direction, respectively. This limitation is meant to avoid great displacements due to a resonance response. It applies to the unloaded structure, which, regarding the results of this research, seems to be inefficient. The additional mass induced by a crowd of pedestrians can causes a drop of the natural frequency by a factor of 2 to 4.
Consequently, even an apparently safe structure with a natural frequency higher than 5 Hz, could drop into the critical frequency range close to the walking frequency, due to the additional mass applied by pedestrians.
The guideline is in the case of steel structures well established, what might imply that in the threshold of 5 Hz a sufficient amount of redundancies is included. In the case of FRP structures, the impact of the additionally applied load is much bigger, due to the reduced construction weight and the resulting high live load to construction weight ratio. The neglecting of this effect might be part of the problem, which led to the vibration related serviceability problems in the recent past, and a revision of the respective guidelines should be considered.
The lateral component of the walking load is small, comparatively to the vertical component, and, due to the connection between the girders and the additional construction elements, the stiffness in lateral direction is often higher. Nevertheless, the main part of the recent vibrational problems appeared in lateral direction. The problem refers to bridges with great spans, which is why the present research does not present considerable resultsthe major deformations appear in the vertical direction.
However, it can still be recognized, that, based on the recent past, the elision of lateral, pedestrian live loads cannot be justified.

Summary
In order to keep guidelines efficient and practicable, they have to be adjust continuously to recent trends and developments. It has to be an ongoing process, in which the current requirements are evaluated and verified or improved. This applies especially to the field of civil engineering, because these constructions involve high investments and include a high hazard in the case of failure. This research points out that the current guideline regarding FRP pedestrian bridges under human induced excitation requires such an adjustment.
This circumstance has been indicated by several oscillation problems all over the world and has been confirmed by the estimated data. Depending on the density to stiffness ratio of the used material, the dynamical properties of FRP bridges are similar to the ones of steel structuresthe natural frequency is in the same range.
Nevertheless, FRP pedestrian bridges are more sensitive to dynamical pedestrian loading, due to the high impact of additional load on the natural frequency. The additional mass of the pedestrians changes the dynamical properties of the construction and the natural frequency drops in the range of human walking, what might lead to high deformations due to resonance.
The current guideline limits the natural frequency of the unloaded system and neglect the human-structure interaction. It also does not cover all aspects of the complex pedestrian loading, particularly the lateral component of the load, which leads to the most vibrational issues in the recent past, is not included in the guideline's requirements. Therefore, an adjustment of the guidelines is suggested.

Future Work
The phenomenon of a pedestrian crowd walking on a bridge structure is extremely complex, hard to simulate sufficient and still not completely understood.