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Abstract
An analytical method for control of the strength of a grillage (gross panel) under unidirectional in-plane axial load is proposed. It allows us to solve the following tasks: (i) calculation of the critical stiffness of transverse girders, (ii) calculation of the maximum unidirectional in-plane compression load when the structure's scantlings are known (iii) and calculation of the required structure's scantlings when the unidirectional in-plane compression load is given. The proposed procedure is helpful in the application of probabilistic methods without employing specialised computer programmes, which is an advantage when fast (although approximate) evaluation is needed for the grillage critical buckling strength (e.g. ship's deck structure) before applying the finite-element method (FEM) analysis. Results of analytical approach are compared and confirmed using FEM data. A probabilistic method for control of the strength of ship's deck structure under unidirectional in-plane axial load is proposed. It allows us to assess the effect of deterioration due to corrosion on the deck's buckling strength while avoiding the use of specialised computer programmes.
Part A: Deterministic assessment of the critical buckling strength of deck structures: Nomenclature
| α, α 1 | = | Coefficients of pliability of deck transverses’ ends |
| ω | = | First natural frequency |
| ζ i | = | Coefficient representing boundary conditions at deck transverses’ ends |
| a | = | Spacing of deck transverses |
| b | = | Spacing of deck longitudinals |
| bc | = | Spacing of carlings |
| C.L. | = | Central line |
| CDF | = | Cumulative distribution function |
| E | = | Modulus of elasticity |
| FEM | = | Finite-element method |
| fC | = | Carling's cross-sectional area including attached plate |
| fr | = | ‘rth’ longitudinal's cross-sectional area including attached plate |
| ic | = | Carling's moment of inertia including attached plate |
| ir | = | ‘rth’ moment of inertia of deck longitudinals including attached plate |
| J | = | Moment of inertia of deck transverses including attached plate |
| j | = | Number of half-waves when deck longitudinals buckle |
| J1 | = | Moment of inertia of side frame including attached plate |
| Jcr | = | Critical moment of inertia of deck transverses |
| Kr | = | Spring constant of ‘rth’ deck transverse |
| kr | = | Coefficient of rigidity of the elastic foundation |
| l | = | Length of deck longitudinals |
| L | = | Length of deck transverses |
| LOC | = | Level of certainty |
| l1 | = | Side frame's length |
| Mr | = | Concentrated mass |
| m | = | Intensity of uniformly distributed mass |
| m1 | = | Number of deck longitudinals |
| n | = | Number of deck transverses |
| P | = | Compressive force on each deck longitudinal |
| P C | = | Compressive force on carling |
| P cr | = | Critical buckling force |
| = | Probability density function | |
| POE | = | Probability of exceedance |
| ϕ | = | Coefficient representing the effect of the deviations from Hook's Law on buckling strength |
| λr | = | Parameter representing the ratio between the buckling stress of the whole longitudinal and buckling stress of a one-span simply supported beam |
| μ | = | Parameter determining the natural frequency |
| σcr | = | Critical buckling stress on each longitudinal |
| σE | = | Euler buckling stress |
| σE,T | = | Theoretical Euler buckling stress |
| σy | = | Material's yield stress |