ESDU 90004
Maximum inelastic bending moments and end loads in fixed ratio for beam sections of general polygonal shape (computer program).
Abstract:
ESDU 90004 introduces a computer program for calculating the combination of the pair of orthogonal bending moments and an end load, in the same ratios to each other as in an initial loading combination, that gives a defined maximum allowable extreme fibre stress or strain. The beam may be of any general solid or hollow polygonal section and the allowable stress or strain may be above the limit of proportionality of the material. The material stress/strain curve is represented by the generalised form of ESDU 76016 input to the program as an elastic modulus and either any two inelastic stress/strain values or the two characteristic values that define the generalised equation. Also required are a specification value for the 0.2 per cent proof stress and the ultimate tensile strength. The program gives the location of the neutral axis, the radius of curvature of the deflected beam, and the stress and strain at each vertex under the maximum loads. Corresponding data for an elastic solution with the 0.2 per cent proof stress at the extreme fibre are also output. Additionally, values are given for the crosssectional area, the second moment of area, and the position of the centroid. An option allows the beam to be constrained in one direction and the output is then the maximum moment in the other direction and end load in the same ratio as the input, together with the value of the restraining moment. The program assumes a linear strain distribution under the action of the moment, with a nonlinear stress variation, and that plane sections remain plane. No account is taken of any instability and it is assumed loads are applied simultaneously maintaining their ratios. The input and output formats are fully explained through worked examples (one of which represents a circular tubular section by a 50sided polygon), and the testing and validation of the program are discussed. The program is provided as ESDUpac A9004.Indexed under:
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Data Item ESDU 90004  

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