The Paper presents a numerical procedure for the static stress analysis of submarine pipelines during lay-barge installation. The pipeline is considered to be acted on by its submerged weight along its length and a horizontal tension at the barge end. The fourth order non-linear governing differentia1 equation of equilibrium in terms of vertical deflexions is solved using the finite difference method with the zero moment boundary condition at the sea bed end treated in a novel way. The resulting non-linear algebraic simultaneous equations are solved by the Newton Raphson method with the Jacobian matrix evaluated in an approximate manner. The validity of the computer program has been checked against an available solution. The example also shows that good agreement can be obtained with a relatively coarse mesh and that the convergence of the iterative method is quite rapid. Notationcoefficient matrix resulting from difference equations rhodulus of elasticity for the pipe depth of water at the stinger end moment of inertia of the pipe cross-section horizontal length between the two ends (stinger end and sea floor end) of the bending moment at a pipe section submerged weight of the pipe per unit length column vector representing the right-hand side of difference equations column vector representing the residuals length of the stinger tension applied at the barge end deflexion of the pipe measured from the stinger end co-ordinate axis slope of the stinger at the barge end slope of the pipe at the stinger end curvature of the pipe radius of curvature for the stinger pipeline

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The theory developed by the Authors and their computer program should be especially useful in making parametric studies of reinforced concrete columns and composite steel-concrete columns, for which torsion is effectively negligible, as assumed in the theory. Has the program already been used to check the validity of the existing design methods of reinforced concrete or composite steel columns?49. The Authors have pointed out that for columns in antisymmetrical bending 16-20 segments have to be used to obtain acceptable results, compared with the 8 segments sufficient for single curvature bending. I came to a similar result for biaxially restrained bare steel, beam columns. So, to increase the accuracy of the finite difference method, I made use of two half segments at the two extremities of the beam column as shown in Fig. 9. Although the corresponding finite difference expressions are slightly more inv~lved,'~ the number of segments, the size of matrices and the computer time could be reduced considerably.50. The sections selected by Gent and Milner17 are not truly representative of torsionally weak, rolled steel sections used in practice. Also, the loading conditionvery heavy axial load at failure-used in their experiments may not include all loading types that are encountered in reality. In effect, for most of the columns forming part of rigid jointed frames, the major axis bending moments will be proportionally more important. For such columns, as the sections become plastic there is a continuous shift in the shear centre, and a shift and rotation of the principal axes of the remaining elastic core under the combined influence of major and minor axis moments, residual stresses and initial crookedness. So, theoretically torsion effects cannot be dissociated from

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