JOURNAL OF BRIDGE ENGINEERING / JULY/AUGUST 2001 / 285 FINITE-ELEMENT MODEL UPDATING FOR THE KAP SHUI MUN CABLE-STAYED BRIDGE By Q. W. Zhang, 1 T. Y. P. Chang, 2 and C. C. Chang 3 ABSTRACT: This paper presents the implementation of the finite-element model updating for the Kap Shui Mun Bridge, a 430 m main span double-deck cable-stayed bridge in Hong Kong. The dynamic characteristics of the bridge have been studied through both three-dimensional finite-element prediction and field vibration measurement previously. In this paper, the developed finite-element model is updated based on the field measured dynamic properties. A comprehensive sensitivity study to demonstrate the effects of various structural parameters (including the connections and boundary conditions) on the modes of concern is first performed, according to which a set of structural parameters are then selected for adjustment. The finite-element model is updated in an iterative fashion so as to minimize the differences between the predicted and the measured natural frequencies. The final updated finite-element model for the Kap Shui Mun Bridge is able to produce natural frequencies in good agreement with the measured ones, and can be helpful for a more precise dynamic response prediction. FIG. 1. Schematic Representation of the Kap Shui Mun Bridge: (a) Elevation; (b) Typical Cross Section of the Composite Deck; (c) Typical Cross Section of the Prestressed Box Girder; (d) Three-Dimensional Fi- nite-Element Model INTRODUCTION The Kap Shui Mun Bridge (Fig. 1), located between the islands of Lantau and Mawan in Hong Kong, is the world’s longest cable-stayed bridge that carries both road and railway traffic. To ensure its structural integrity and operational safety, the bridge has been equipped with a fairly sophisticated mon- itoring system that includes instruments such as accelerome- ters, displacement transducers, level sensors, strain gauges, temperature sensors, and anemometers (Lau and Wong 1997). The dynamic characteristics of the bridge have been studied through finite-element prediction and field vibration measure- ment by Chang et al. (2001). A three-dimensional finite-ele- ment (FE) model was constructed using linear elastic beam elements for the towers and the deck, truss elements for the cables, and elastic or rigid links for the connections and the boundary constraints [Fig. 1(d)]. The bridge deck, which con- sists of steel/concrete frames in the central portion of the main span and trapezoidal box girders for the remaining portions, is modeled using a single spine passing through the shear cen- ters of the deck. Since the cross sections are nonmonolithic, a virtual and equivalent monolithic material is used to represent the composite deck. This is achieved by making the mass and stiffness properties of the monolithic deck equivalent to those of the composite deck. Details on the computation of the cross- sectional moduli can be found in the report by Chang (1998). The cables, on the other hand, are modeled using linear elastic truss elements. The nonlinear effect due to cable tension and sagging is taken into account by linearizing the cable stiffness using the concept of an equivalent modulus of elasticity. The finite-element model consists of 464 beam elements, 176 truss elements, and 615 nodes, and has a total of 1,536 degrees of freedom. Generally, the finite-element modeling gives a detailed de- scription of the physical and modal characteristics of the bridge, while the field vibration test serves as a valuable source of information for evaluating the drawing-based (idealized) fi- 1 Assoc. Prof., Dept. of Bridge Engrg., Tongji Univ., Shanghai, People’s Republic of China. 2 Prof., Dept. of Civ. Engrg., Hong Kong Univ. of Sci. and Technol., Clear Water Bay, Kowloon, Hong Kong, People’s Republic of China. 3 Assoc. Prof., Dept. of Civ. Engrg., Hong Kong Univ. of Sci. and Technol., Clear Water Bay, Kowloon, Hong Kong, People’s Republic of China. Note. Discussion open until January 1, 2002. To extend the closing date one month, a written request must be filed with the ASCE Manager of Journals. The manuscript for this paper was submitted for review and possible publication on April 28, 1999; revised September 27, 2000. This paper is part of the Journal of Bridge Engineering, Vol. 6, No. 4, July/ August, 2001. ASCE, ISSN 1084-0702/01/0004-0285–0293/$8.00 + $.50 per page. Paper No. 20842. nite-element model. The finite-element results and the field vibration test show reasonable correlation in terms of the nat- ural frequencies and the mode shapes of the bridge. However, significant discrepancies can still be seen between the pre- dicted and the measured frequencies for the higher modes. The possible sources that may cause these discrepancies include the following. Differences between Finite-Element Model and Actual Bridge In the finite-element modeling, the geometric, elastic, and inertial parameters as well as the connections and boundary conditions of the Kap Shui Mun Bridge were estimated from the engineering drawings, which are highly idealized. The dis- crepancies between the finite-element prediction and measure- ment of the bridge vibration may be caused by the following factors in connection with the finite-element modeling: (1) in- accuracy in the analytical model discretization; (2) uncertain-