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A method is derived whereby warping shear stresses due to restraints or the variation of torque along a bar can be computed using finite elements. For completeness, it is also indicated how the restrained warping longitudinal stresses are calculated. In this paper, the effects of nonuniform torsion are incorporated into Herrmann.s solution for the case of thin-walled open sections.

Simple infinite beams on an elastic foundation have presented few problems, in fact they are usually easier to solve than beams of finite length. For some time it has been possible to analyze with relative ease finite beams with arbitrary loading and foundations. The transfer matrix method is particularly useful in the static, stability, and dynamic study of beams with many changes in cross-sectional and support properties. Most available techniques encounter difficulties when applied to very long beams. It is the purpose of this paper to show how the transfer matrix method for beams of finite length can be extended to encompass beams of infinite length. With this approach it is possible to analyze, without encountering numerical instability, infinite or semi-infinite beams with any loading or arbitrary changes in properties along the beam.

Large rectangular openings on the strength deck are a major concern of the designers of commercial and military ships. Currently used methods are inaccurate for the prediction of stress concentration factor (SCF). There is no commonly accepted criterion for the maximum stress. The current design method cannot be used to explain the behaviors of the structure when the stress at a small area is calculated as greater than the ultimate strength of the metal. Nor can it explain the failures that occur at relatively low nominal stress. All these problems can be better explained and analyzed by the concept of fatigue strength and fatigue life. This paper proposes some new methods for the prediction of SCF, approximate methods for the prediction of fatigue strength reduction factor due to stress concentration, and fatigue life of openings. Validation of the new method is also included.

A general, computationally efficient approach for treating mooring line static and dynamic response problems is presented. The technique is a form of incremental linearization. An initial equilibrium configuration is obtained from explicit integration of the nonlinear equations including only the dominant loading. Other loadings are then considered as increments in the equations which are linearized for each load. The line solution or transfer matrix formulation is used to compute the small deformation due to each increment. Changes in mooring line properties and loads are accommodated. Nomenclature A = cross-sectional area of the mooring line Cn - drag coefficient of the mooring line for flows normal to the line elements D(R, myv = added mass components per unit length of mooring line R - normal component of the hydrodynamic force arising from the current per unit length of the mooring line S = unstretched length of the mooring line t = time T = tension of the mooring line v = increment of the relative velocity V = relative velocity of the water current w = increment of buoyant weight of the mooring line W = buoyant weight of the mooring line (x,y) = increment of the components of the location (X, Y) = coordinate components of the location A£ = increment of the tension 0 = increment of the angle $ = angle between the tangent of the trajectory of the mooring line and the x axis

The theory of beams supported by elastic foundations has been shown to be particularly well-suited to the analysis of grillage beams [1, 2, 3[.2 This theory leads to a far more general formulation regarding the types of structures amenable to analysis than that offered by the orthotropic plate theory. As compared to the methods of finite element theory, the theory of beams supported by elastic foundations decreases the computer time by an order of magnitude, thus making the analysis particularly valuable as a design tool. This paper shows that the measurement of the grillage beam analysis based upon the elastic foundation concept can be further simplified by certain matrix transformations that uncouple the deflection equations. The problem has, in fact, been simplified to such an extent that many large grillages can be analyzed with the aid of a desk calculator. Whenever comparison with results obtained from finite element methods has been possible, it has been found that, for all practical purposes, complete correlation exists.

The transfer matrix method provides a simple approach for the analysis of grillages under general conditions. In contrast to other efficient methods, no simplifying assumptions are made; the transfer matrix approach is exact within the framework of the classical theory of bending and torsion of bars. The technique accepts arbitrary loading, nonprismatic beams, arbitrary spacing, in-span conditions such as supports and releases, and arbitrary boundary conditions. The special features in ship structures such as deck openings, stanchion supports, and various brackets can be easily handled. The theory is readily grasped and implemented in full generality for computer solution.

A general method for obtaining the stability criteria of a grillage is presented. Axial loads in both sets of intersecting beams are considered. Properties and arrangements of beams are fairly arbitrary, as are permissible boundary conditions. However, the analysis is restricted to include only initially straight compression members.