Abstract:

ESDU 90026 introduces a program for calculating the loadings on a beam of solid or hollow polygonal section that give a defined maximum allowable extreme fibre tensile (or equal compressive) stress or strain. When two loads are specified (out of a possible three: two orthogonal bending moments and an offset end load), the output is the two values of the third. One load and the ratio of the other two may be input; the output in each limiting case is then the values of the two unknown loads. Alternatively, the beam may be constrained to deflect in a given direction; with one given load the output is then the constraining moment and the other load. The stresses and strains at each vertex are output in each case, and can be output at loading increments between the limiting cases; a strength analysis option also allows them to be output for an input of any loading combination. An elastic solution is given, and the program indicates whether the loading combination is valid when loads are applied consecutively or only simultaneously (the program cannot treat the unloading of yielded material). The location of the neutral axis and of the centroid, the cross-sectional area and second moment of area, and radius of curvature of the beam are also output. The material stress/strain curve is 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. The program assumes a linear strain distribution under the action of a moment, with a non-linear stress variation, and that plane sections remain plane. No account is taken of instability. The input and output formats are explained through worked examples, and the testing and validation of the program are discussed. The Fortran program is provided as ESDUpac A9026.