Redalyc.Structural Reliability of the Tampico Bridge Under Wind Loading

Ciencia Ergo Sum ISSN: 1405-0269 [email protected] Universidad Autónoma del Estado de México México León, David de; Manjarrez, Lorena; Ang, Alfredo H-S. Structural Reliability of the Tampico Bridge under Wind Loading Ciencia Ergo Sum, vol. 15, núm. 2, julio-octubre, 2008, pp. 161-166 Universidad Autónoma del Estado de México Toluca, México Available in: http://www.redalyc.org/articulo.oa?id=10415207 How to cite Complete issue Scientific Information System More information about this article Network of Scientific Journals from Latin America, the Caribbean, Spain and Portugal Journal's homepage in redalyc.org Non-profit academic project, developed under the open access initiative Structural Reliability of the Tampico Bridge under Wind Loading David de León*, Lorena Manjarrez* y Alfredo H-S. Ang** Recepción: 25 de septiembre de 2007 Aceptación: 3 de abril de 2008 *Facultad de Ingeniería, Universidad Autónoma del Confiabilidad estructural del Puente de Abstract. A highway bridge located in Estado de México, México. Tampico bajo cargas de viento Tampico, on the east coast of Mexico, is Correo electrónico: [email protected] Se analiza un puente carretero analyzed to determine its structural reliability **School of Engineering, University of California at Resumen. Irvine. localizado en Tampico, en la costa este de against wind loading. The inherent variabilities We thank the Communications and Transportation México, para determinar su confiabilidad of the random wind force and of the Secretary in Mexico for the information provided about the Tampico bridge. estructural ante cargas de viento. Las mechanical properties of steel constitute variabilidades inherentes a las fuerzas aleatorias the aleatory uncertainty; this contributes to de viento y a las propiedades mecánicas del the probability of failure of the steel girder. acero constituyen las incertidumbres aleatorias, The idealization of the loading and of the y esto contribuye a la probabilidad de falla bridge structure, and the analysis of the de las vigas de acero. La idealización de la structural response to wind loading, contribute carga y la estructura del puente, así como to additional uncertainty of the epistemic el análisis de la respuesta estructural ante la type, which leads to a range of possible carga de viento, contribuyen a que exista una (or distribution of) failure probabilities. The incertidumbre adicional, de tipo epistémico, design with the minimum expected life-cycle que deriva en un rango (o distribución) de cost is the optimal design. However, for this posibles probabilidades de falla. El diseño optimal design, the 90% value (or the mean con el mínimo del costo esperado en el ciclo plus one standard deviation value) of the de vida se asocia con el diseño óptimo. Sin corresponding failure probability or safety embargo, para este diseño óptimo, es posible index may be selected for a risk-aversive seleccionar el percentil 90, por ejemplo, (o design. The proposed criteria constitute a new la media más una desviación estándar) de la approach to make conservative decisions and probabilidad de falla o índice de confiabilidad involve the epistemic uncertainty on the bridge correspondiente, para administradores con design and assessment process. aversión al riesgo, lo cual constituye una Key words: bridge reliability, expected life-cycle decisión conservadora. El criterio propuesto cost, optimal design, wind loading, epistemic constituye una nueva aproximación para tomar uncertainty. decisiones conservadoras e involucrar a la incertidumbre epistémica en el proceso de diseño y evaluación de puentes. Palabras clave: confiabilidad de puentes, costo esperado en el ciclo de vida, diseño óptimo, cargas de viento, incertidumbre epistémico 1. The Tampico bridge In particular, the Tampico bridge, which was built over the Pánuco river in 1988 serves as a link between the Tamaulipas Bridges are important infrastructure because of its intended and Veracruz states and joins Tampico to the highway to function to provide communication between urban centers Mexico City. and to allow the flow of products and goods that determine The bridge structural system is composed by a cable the progress of economic and industrial growth of a region. stayed steel orthotropic box sustained by concrete piers and CIENCIA ergo sum, Vol. 15-2, julio-octubre 2008. Universidad Autónoma del Estado de México, Toluca, México. Pp. 161-166 161 CIENCIAS EXACTAS Y APLICADAS piles with a total length of 1543m and a central span of 360 life-cycle cost E[Ct] is expressed in terms of the initial cost m. The total width is 18.10m for four lanes of traffic, two Ci and the expected damage cost E[Cd] in each direction. See Fig. 1 for a view of the bridge. A new risk-based approach is proposed to assess the E[Ct ] = Ci + E[Cd ] (1) failure consequences and incorporate them into the design where: or evaluation process in an objective and explicit way. E[ C d ] = PV F [ C d ] P f (2) 2. Theoretical background in which: Modern codes intend to protect important infrastructure works against strong and unpredictable natural events (AAS- PVF = present value factor, Pƒ = annual failure probability, HTO, 2002 and Agarwal, 2003). In addition to the vehicle and the damage cost Cd is composed by the costs of the live loads, bridges are exposed to strong winds whenever consequences. they are located on coastal zones under strong wind hazard. Besides, because of its height and the openness of the C d = C r + C f + C e (3) area the exposure may be especially critical. Therefore, in these cases the bridge reliability assessment requires a careful in which: consideration of the failure probability associated with the Cr = bridge restitution cost, aleatory uncertainty, and the range (or error bound) in the Cƒ = cost related to fatalities and injuries, calculated probability as a result of the epistemic uncertainty Ce = economic loss due to the interruption of service. (Ang and De León, 1997; 2005 and Ang et al., 1984). The assessment considers the failure event as the worst The effects of the uncertainties on the bridge design possible scenario. Instead of repair, the term Cr involves the and maintenance are discussed from the standpoint of the cost of the whole bridge restitution. expected life-cycle costs and its expected failure proba- PVF is expressed as a function of the net annual discount bility (De León et al., 2004; Frangopol et al., 2007 a and rate r and the structure life T: 2007b). As a consequence of the epistemic uncertainty the mean damage index becomes a random variable and, PV F = [ 1 − ex p( − rT )] / r (4) given that the failure probability and the expected life-cycle cost depend on the damage index, they also are random If the initial cost Ci is expressed in terms of the failure variables. probability As proposed for many important structures (Ang et al., 1984; Cornell, 1969 and Stahl, 1986), the bridge expected Ci = C1 − C2 ln(Pf ) (5) Figure 1. General view of Tampico bridge. the optimal failure probability is obtained (Stahl, 1986) from ∂E[Ct ]/ ∂Pf = 0 : Pf = C 2 /[ PV F ( C d )] (6) From the optimal annual Pƒ, the optimal annual reliability index b is obtained. C1 and C2 are the cost due to just a gravity loading design, without wind resistance, and the cost of increasing the structural reliability by “e”, the base of natural Logarithms. As several designs, with corresponding different costs Ci, will be proposed, a reference is made to the actual design, whose cost is Co. The cost of damage consequence, Cd, is expressed (De León, 2006) as a ratio to the cost of the actual design Co. Given that the Tampico bridge is located over the Panuco River, the 162 DE LEÓN, D. ET AL. STRUCTURAL RELIABILITY OF THE TAMPICO BRIDGE... CIENCIAS EXACTAS Y APLICADAS only navigation route to the port, its failure would bring very consequences: repair, fatalities and business interruption adverse consequences not just for the land communication which are also assumed to be normally distributed. These but for the port and maritime commercial operations of the assumptions are typical from previous studies (De León, region. Therefore, Cd has been estimated to be thousands 2006a and Manjarrez, 2008). of time the actual design cost Co (Manjarrez, 2008) (see The reliability index is calculated as figure. 2). The curve represents that expensive structures, with se- = E { G } / G (11) rious damage consequences, demand a larger reliability as a design requirement. In particular, bridges are important where G is the limit state for the critical cross section: infrastructure whose damage consequences justify a reliability specification on the order of 4 or 5. G = 1 − { P a / P r + M a / M r } (12) 3. Proposed formulation And Pa, Pr, Ma and Mr are the applied axial force, axial force capacity, applied moment and moment capacity, respec- 3.1. Uncertainty on failure probability and tively in the most critical column. Failure is conservatively life-cycle cost defined as the event when the interaction ratio in the most According to previous studies (De León et al., 2004), and given critical column exceeds one. Shear forces are not included that the epistemic uncertainty on the mean value of maximum because the preliminary model analyses revealed they are wind velocity, E [v], makes the failure probability become a not critical for the studied bridge. The preliminary analyses random variable, the expected value and variance of the failure enlighten that the critical structural member is one of the probability are: central piles remarking the low redundancy of the bridge structural system and, therefore, the need of more detailed ∞ = (7) assessment and design procedures. E[Pf ] ∫[Pf ¦ E[v]] f E[v] (E[v])dE[v] 0 Finally, the histograms of the failure probability and the The above convolution involves the product of the con- expected life-cycle cost are estimated.

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