In keeping with the general trend towards rationalisation, static calculations have of late also been programmed by electronic computers. The number of problems which can be advan tageously resolved in this way is, however, very limited as yet, partly on account of the relati vely high cost involved and partly due to the waiting time the statician must suffer after collect ing together his data and, finally, because the programming possibilities of the computer are limited. Nonetheless, if static calculations have to be rationalised, there is another way: all beam structures-whether they be continuous beams or frame constructions-are arithmetically based on individual spans which are freely supported or fixed at the ends. If the basic values for these can be ascertained quickly and accurately, then a considerable part of the arithmetical work is already done. It is the aim of this work to provide the statician with these values. An attempt has been made to deal as comprehensively as possible with all the cases of loading likely to arise in practice. Naturally, one case or another is bound to happen more frequently whilst others are seldom encountered. However, this allembracing programme is intended to make it possible for the user of this work, after a brief, familiarising period, always to use the same arithmetical pro cedure, the choice of the actual method being left to him.