Bending of the Stiffened Plates Under Combined Lateral and In-Plane Loads
Authors: Mansour A. , Nagler R. 
Published: October 2008

ABSTRACT
In marine and ship structures, the basic structural element, which consists of a plate reinforced with stiffeners, is in general subjected to normal and in-plane loads. The behavior of this structural element, idealized by an equivalent orthotropic plate, is investigated. Solution of Huber's equation with boundary conditions that occur often in marine structures is obtained. In analysis, the solution is carried out in its most general form so that the results could be also applied to-any material that has orthotropic characteristics; for example, reinforced concrete, laminated plastics, etc. Design curves for nondimensional deflections and moments are obtained. Stresses in the actual stiffened plate are obtained from the moments and formulas are given for their determination. In general, the results include special cases, such as isotropic plates under combined loading, orthotropic and-isotropic plates under only uniform lateral loads and strips loaded with lateral load.

INTRODUCTION
This study is concerned with the analysis and design of the basic structural element in marine structures, i.e., the plate-stiffener combination. In general, this basic element is subjected to loads normal to its plane due to water pressure, deck loads, etc., and in-plane forces due to the bending of the structure or the vessel. The plate-stiffener combination can be effectively idealized by an equivalent orthotropic plate. The development of the orthotropic plate theory advanced by Huber1 has been under intensive study by Lichnitzky, 2 Pflügger3 and many others. The application of the theory has been recognized in many fields. It has been applied to bridge decks, reinforced concrete, plywood and laminated plastics. In ship structures the application of the theory which has been started by-Schnadel4 was considered by Schade, 5 Ando6 and Schultz. 7
A linearized or second-order theory of an orthotropic plate under uniform lateral and in-plane loads is considered in this study. Derivation of Huber's equations representing the defection surface can be readily obtained in a general form through consideration of force-equilibrium, strain-compatibility and their interrelation [Hook's law]. The relation between stress and. strain in the orthotropic case includes four independent elastic constants and may be represented by
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This relation implies two assumptions:normal stresses perpendicular to the plane of the plate are disregarded anddeflection is small relative to plate thickness.
The first assumption is satisfied when the plate thickness is small compared with other dimensions of the plate. This is usually the case in marine structural elements. The validity of the second assumption for the isotropic plates with reference to plate proportions normally used in marine structures is discussed by Bleich8. He concluded that the linearized theory implying Assumption 2 will always be valid for plates with clamped edges while for simply supported panels occasional values up to w/h. 0.8 might occur. This conclusion is then confirmed experimentally by A. G. Young. 9 It seems reasonable to extend the validity of this conclusion to orthotropic or stiffened plates where deflection is referred to some equivalent thickness of combined plate and stiffeners.