Simplified analytical methods for the crashworthiness and the seismic design of lock gates

Abstract

2 AbstractThe design of navigation lock gates requires to account for accidental loads such as ship impacts or earthquakes, but it is quite difficult to handle with them. The most satisfactory way to investigate their effects is to perform numerical simulations. Such an approach can be justified at the late design stage, but it is quite commonly accepted that it is not well suited during the conception process. This may be justified by the calculation and modeling efforts that are usually prohibitive. Consequently, the aim of this thesis is to develop simplified methods to circumvent these difficulties. The dissertation is divided into two main parts.

Simplified Analytical Methods to Analyze Lock Gates Submitted to Ship Collisions and Earthquakes

“…By applying equation (2) to the four types mentioned here above, it is possible to find closed-form expressions in each case. As this operation is quite fastidious, it is not reported here, but additional information on this topic may be found in the literature (see references [5] to [10] for example). -a super-element remains inactive ( 0) as long as a geometrical contact is not established with the striking bow.…”

“…The latter may be directly expressed as a function of the mechanical and geometrical properties of the structure, but for convenience, they are simply denoted here by . More details about their analytical derivation can be found in references [10] and [16]. As is a force per unit of area, the corresponding external work is:…”

“…Of course, during this overall motion, each of the girders opposes an individual resistance , which can be simply evaluated by using the classical bending theory of beams in both the elastic and plastic regimes. For conciseness, the analytical derivation of will not be presented here but additional details may be found in [10]. Furthermore, as the horizontal girders are assumed to be independent, the global resistance may be again calculated by summing all the contributions .…”

“…In these two expressions, it is also worth mentioning that and translates the effects of the mass and the stiffness of the gate, while and are related to the flexible and rigid pressures. Of course, all these parameters may be evaluated analytically [10], but for conciseness, the corresponding detailed relations are not provided here. 18 Finally, in accordance with the virtual work principle, and may be equated to get a set of equations that may be written in the following matrix form: (20) in which is a vector containing the unknown coefficients .…”

“…Introducing (5) in equations (7) to (10), it is possible to get matrix formulations for and . If is the vector containing the unknown coefficients mentioned in equation (5), it could be shown that [10]:…”