Analysis of serviceabilty limit state of pedestrian bridges regarding vibrations induced by pedestrians

The advanced engineering technologies and the development of construction materials have brought the new trends in the design and construction of pedestrian bridges. Contemporary footbridges are slender and lightweight long span structures. As a consequence of the small mass and stiffness of the structure, reduction in the fundamental natural frequency of the bridge, results in greater sensitivity to dynamic loadings, especially the human-induced ones. Therefore, a more detailed dynamic analysis becomes necessary in the design of pedestrian bridges. For evaluation of the serviceability limit state of a footbridge, it is necessary that the superstructure response to human-induced vibration is known. As vibration analysis of bridges is very complex, the simplest solutions of vibration problem are the most acceptable to designers. For these reasons, using modal analysis, solutions such as a time depending response of the bridge superstructure were performed in the dissertation. Pedestrian-induced actions are modelled as deterministic forces, defined using the Fourier transform, and their position on the bridge is defined using the Dirac function, Heaviside function and Hermite polynomials. The response function is determined using the author’s algorithms and programs written in Mathematica. The dissertation presents three algorithms, which includes all girder structural systems. For dynamic analysis they are modeled as continuous or discrete oscillatory systems. Moreover, the superstructure of the bridge can be of a constant or a variable mass and flexural stiffness along the span. The response functions for the vertical and horizontal direction of vibration are defined using the same algorithms, with the introduction of the modal characteristics of the structure for the respective direction. The required response can present vertical displacement, horizontal displacement, velocity or acceleration, as well as stress and strain of the observed cross section, since the algorithms include such an option. The possibility option of response presentation trough time histories, significantly simplifies the qualitative and quantitative analysis. This is particularly important for the variation of the parameter, for example, intensity of the constant force, intensity of the amplitude and frequency of the time varying force, speed of the force, damping, and the position of the cross section of interest. The efficiency of the proposed dynamic analysis, carried out according to the above response functions, is shown for three pedestrian bridges of different structural systems and materials applied. The proposed analytical solutions to the vibration problem are easily applicable for various dynamic actions, so that they can represent a great help for designers to estimate the dynamic behavior of pedestrian bridges, which is a prerequisite for a contemporary and acceptable footbridge design principle and, with modern technologies, their quality construction

Modelling of a bridge stay cable for individual strand tensioning

U radu su, na osnovi predloženog matematičkog modela kosog mostovskog kabela, izvedeni analitički izrazi za određivanje potrebne sile zatezanja u užadima i odgovarajuće deformacije kabela pri postupku višecikličnog zatezanja. Za ovaj postupak koriste se lake hidraulične preše (eng. monostrand jacks), pri čemu se u svakom ciklusu užad zateže pojedinačno silom istog intenziteta. Broj ciklusa zavisi od geometrijskih i mehaničkih karakteristika kabela, od intenziteta konačne sile zatezanja, kao i pomaka točaka oslonaca kabela. Efikasnost predloženog analitičkog postupka prikazana je na numeričkom primjeru.Analytical expressions for determining the required tensioning force in strands, and the corresponding deformation of cables during the multi-cycle tensioning process, are derived in the paper based on the proposed mathematical model of a bridge stay cable. Monostrand jacks are used in this procedure and, at that, strands are tensioned in each cycle by individual application of force of the same intensity. The number of cycles depends on geometrical and mechanical properties of the cable, on the final tensioning force intensity, and on the moveability of the cable support points. The efficiency of the proposed analytical procedure is illustrated by a numerical example

Global Analysis of Steel Constructions with Semi-Rigid Connections

In this paper, original extension of classic deformation method for global elastic analysis of steel construction with semi-rigid connections is developed. The original calculation for steel frame structures with semi-rigid connections as a function of rotational rigidity of connection, a realistic parameter for determination of both tension and deformation fields of connection as well as entire construction, has been derived in detail. Due to its generality, simplicity and straight-forward calculation, the method developed in this paper is convenient for both computational utilization and hand calculations. For introduced rotational rigidity of realistic connections, the expressions for determination of bending moments at ends of semi-rigidly connected elements have been derived as well as conditional equations for determination of deformation-unspecified values at static load by first-order theory. The obtained results are illustrated in detail on a numerical example. Their comparison with the results of FEM analysis was provided

COMPARATIVE ANALYSIS OF USING DEGREE OF RIGIDITY AND ROTATIONAL STIFFNESS OF CONNECTIONS IN STRUCTURAL DESIGN

Using classical formulation of stiffness method, impact of semi-rigid connections on the stresses and strains can be analyzed by the degree of rigidity or by rotational stiffness of connections. In this paper, functional dependence between the degree of rigidity and rotational stiffness of connections is formulated and the comparative analysis of these two approaches in the analysis of semi-rigid connections behavior of members in real structures, is implemented

Analysis of material non-linearity of steel girders subjected to patch loading

U radu se daje analiza ponašanja limenih nosača (nosači od zavarenog čelika I) pod lokalnim opterećenjem. Koncentrirano ili jednoliko raspoređeno opterećenje na maloj udaljenosti od prirubnice i u ravnini mreže, poznato je kao lokalno opterećenje (patch loading). Analiziralo se ponašanje nosača u nelinearnom području kao i učinak kritičnog opterećenja, koji se manifestira izvijanjem. Za modeliranje nosača primijenjen je softver ANSYS Workbench 15 [1]. U skladu s važećim propisima EN 1993-1-5 [2] i BSK 07 [3], tijekom numeričke analize korišteno je šest različitih modela materijala. Dobiveni rezultati uspoređeni su s eksperimentalno dobivenim rezultatima.The paper presents an analysis of behaviour of plate girders (welded steel I girders) under patch loading. Concentrated or uniformly distributed loading on a short length of the flange, and in the plane of web is known as patch loading. Behaviour of the girder in non-linear area, as well as the ultimate load capacity, which is manifested by buckling in the loaded zone were analysed. Girder modelling was performed in ANSYS Workbench 15 software [1]. In accordance with the standing regulations EN 1993-1-5 [2] and BSK 07 [3], in the course of the numerical analysis, six different material models were employed. The obtained results were compared to the experimentally obtained results

DESIGNING OF SUPPORT ZONES OF CONCRETE BRIDGES TO WITHSTAND ACTION OF STATIC AND DYNAMIC LOAD UDC 624.21:624.042.1+624.042.8(045)=111

Abstract. In the paper are presented some of the acquired experiences in designing and construction of bridge structures in several countries, with a special attention to the analysis of support zones and expansion joints behavior of a number of road bridges. During destruction or damage of bridges, there is a small probability, but still there, that the human lives might be endangered (Kobe, Japan 17 th January 1995); what is likely, however, is that it will be very difficult to help the injured in the region. Considering that the characteristics of removal of supports has a great influence on the behavior of the entire bridge structure, the design of support joints and connections must be paid due attention. In the recent decades, efforts are made to enhance research of all engineering structure, and thus the bridge structures and their weak points. Key words: bridges, bearings, expansion devices, design. 1

MODELIRANJE PEŠAČKOG OPTEREĆENJA U ANALIZI GRANIČNOG STANJA UPOTREBLJIVOSTI PEŠAČKIH MOSTOVA

The last few decades new trends in the design of pedestrian bridges have resulted in lighter and more slender structures. This leads to a reduction in natural frequencies and increased flexibility, and thus a greater possibility for structures to become more exposed to excessive vibrations caused by pedestrians. The lager amplitudes of vibrations occur if the pace frequency of excitation load approaches one of natural frequency of footbridge. The vibration of high proportions may cause pedestrians to feel uncomfortable, sick or unsafe while crossing the bridge. In modern pedestrian bridge design, human-induced vibrations have become an important issue. Footbridge vibrations occur in vertical, lateral and longitudinal direction, and torsion of the bridge deck is also possible. The main types of pedestrian action on the bridge are walking and running, while jumping, bouncing, swaying are considered to be intentional, or sometimes even vandal excitation. Pedestrian-induced loads are difficult to model since pedestrians may have different weight, various number in the groups randomly distributed over the bridge deck. Also, the walking velocity may vary from a pedestrian to a pedestrian. The load models appropriately set up are of great importance for understanding the response of the bridge. Principles of modeling of the human-induced load and some characteristic models of pedestrian loads, described in proposals and codes, are presented in this paper. Some results of Serviceability Limit State analysis, in terms of human-induced vibration, of the pedestrian bridge over the Nišava River in Niš, are also presented.Novi trendovi u projektovanju pešačkih mostova, koji uglavnom proizilaze iz zahtevnih estetskih kriterijuma i mogućnosti korišćenja savremenih građevinskih materijala, doveli su do vitkih i fleksibilnijih konstrukcija. Kao posledica toga, lagani pešački mostovi su skloniji da vibriranju sa amplitudama velikih proporcija i na taj način izazivaju nelagodnost kod pešaka. S toga je dinamička analiza pešačkih mostova postala neizbežna, a određivanje modela opterećenja je neophodno za njeno sprovođenje. U radu su date osnove modeliranja vremenski zavisnog opterećenja pešaka korišćenjem Furijeove transformacije i prikazana je njihova upotreba u važećoj regulativi. Treba naglasiti da je opsežno istraživanje na ovu temu još uvek u toku, kako bi se poboljšali postojeći i predložili pouzdaniji modeli dinamičkog opterećenja. Prikazan je i deo analize graničnog stanja upotrebljivosti pešačkog mosta preko Nišave u Nišu. Pokazano je da je odziv konstrukcije za opterećenje izazvano kretanjem pešaka u granicama preporučenim važećom regulativom

DEFORMACIJSKA NEODREĐENOST U GLOBALNOJ ANALIZI ČELIČNIH KONSTRUKCIJA SA POLU-KRUTIM VEZAMA

This paper shows the procedure for determination of deformation indeterminacy within global analysis of steel constructions with semi-rigid joints, as well as the analysis of deformation indeterminacy within the approximate deformation method. In this paper there has been a detailed comparative analysis with criteria of cinematic system stability and division on steel frame with semi-rigid connections to systems with movable and immovable joints.U ovom radu prikazan je postupak za određivanje deformacijske neodređenosti u globalnoj analizi čeličnih konstrukcija sa polu-krutim vezama kao i analiza deformacijske neodređenosti u približnoj metodi deformacija. U radu je detaljno izvršena komparativna analiza sa kriterijumima o kinematičkoj stabilnosti sistema i podeli na čelične ramovske nosače sa polu-krutim vezama na nosače sa pomerljivim i nepomerljivim čvorovima

INFLUENCE OF GEOMETRICAL AND STRUCTURAL IMERFECTIONS OF STEEL PLATE GIRDERS

Abstract. The girders or parts of the girders are not ideally flat in terms of their geometry. The deviations that occur are defined as geometric imperfections. Also, in the material from which the girder is made, a certain deviation may occur during factory production or for some other reason, which is known as structural imperfection.  We will introduce the case of a plate girders (welded steel I girders), with and without stiffening and loaded with patch loading. The results were obtained by numerical simulation in the ANSYS for models with included geometric imperfections. The model was performed in accordance with the recommendations for different behavior curves of materials from Eurocode 3. The limit load obtained by numerical simulation corresponded to the experimental results from the literature. Stress values for girders with and without geometric imperfections for the same load value were compared

On the Optimal Design of Steel Shells with Technological Constraints

This paper is concerned with determining the optimum conditions of steel cylindrical shells with technological limitations and one behavioral constraint, related to a specific constitutive law for limiting load-carrying capacity. The optimum structural design in the plastic range of circular cylindrical full shells composed of rings of variable thickness is given. A numerical procedure for determining the optimal dimensions of shell rings is given. A shell collapse mechanism is assumed in the kinematic part, which satisfies requirements. Within the optimum conditions, the power of the dissipation energy of rings assuming the hexagon Hodge condition of plasticity are derived. A series of numerical solutions and results of optimal structural designs for a shell that is simply supported at the ends are presented. In one example of optimally calculated shells, the length X1 of one ring was varied