Minimum cost design of an orthogonally stiffened welded steel plate with a deflection constraint

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An assembly desk is constructed as a square plate stiffened by an orthogonal grid of ribs. The residual welding deflection is calculated applying the Okerblom's method. When the ribs are tacked to each other and to the base plate before welding, then the deflection is decreased by grid effect. The base plate thickness and the dimensions of stiffeners are optimized to minimize the cost and to fulfil the deflection constraint. The optimization is performed with and without grid effect and it is shown that the grid effect decreases the cost significantly.

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A relatively simple method is proposed for the prediction of residual welding stresses and deformations, originally developed by Okerblom. The main formulae for the shrinkage and curvature of a beam due to one or more single- or multi-pass welds are derived. The calculated residual stress distributions are in good agreement with those published in recent literature. The derived formulae are applied for prediction of the correct welding sequence in the case of an asymmetric I-section beam with two longitudinal welds. The efficiency of welding in a clamping device without and with prebending is shown in the case of an asymmetric I-section beam with one eccentric longitudinal weld. Numerical examples illustrate the use of derived formulae.
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The basic formulae for the calculation of the negative thermal impulse due to the shrinkage of a circumferential weld are given as a function of welding parameters. A differential equation for the radial shell deformation is derived using the bending theory of cylindrical shells. The solution of this equation gives an approximate formula for the maximum radial deformation. Comparing this formula with the limiting deformation given by ECCS allows calculating the required shell thickness. Another thickness can be obtained using ECCS buckling formulae. Using an interpolation, a thickness can be calculated, which fulfils both constraints. Numerical examples illustrate the thickness design.