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1. Numerous methods have been devised for determining moment profiles1 in statically indeterminate structures. Most of these can be classified as either approximate or exact. The approximate methods are usually simple to apply, but when employing them it is necessary to specify numerical values for the dimensions and stiffnesses (or their ratios) of the structure involved. The exact methods consist in solving systems of linear equations obtained by setting up relations between generalized displacements or by the equivalent means of using Castigliano's Principle. As the degree of indeterminacy of the structure increases, the solution of the equations becomes more laborious. Most of the methods aim at reducing such labor by a suitable choice of unknowns. This paper is an attempt in that direction. 2. Consider a structure whose degree of statical indeterminacy is N. Denote by M the true moment profile in the structure under a given load, and by Mo the moment profile under the same load when the structure has been made statically determinate by removing N constraints (the so-called basic structure). The effect of the removed constraints may be replaced by the combined effect of N unknown generalized forces (couples and forces) X\, X2l • • • , Xn■ The generalized displacements of the loaded structure at the points of application and in the directions of X\, X2, • • • , Xn, are assumed to be known and will be denoted by 5i, 52, ■ • • , 8n(If Xi is a couple, S; is a rotation; if Xi is an ordinary force, 8, is an ordinary displacement.) Let be the moment profile obtained when the force corresponding to X,; = 1, Xj = 0 for j^i, acts on the (unloaded) basic structure. Then the moment profile XiMi represents the effect of the ith constraint. Superposing the moment profiles due to the load and the constraints yields the true moment profile M:

An application of orthogonal moments to problems in statically indeterminate structures