[Footnote 10: Only this form of beam is considered since it is the simplest. For cantilever and continuous beams, and beams rigidly fixed at one or both ends, as well as for different methods of loading, different forms of cross section, etc., other formulæ are required. See any book on mechanics.]
[Footnote 11: See Tiemann, Harry D.: Some results of dead load bending tests of timber by means of a recording deflectometer. Proc. Am. Soc. for Testing Materials. Phila. Vol. IX, 1909, pp. 534-548.]
[Footnote 12: A fourth might be added, namely, vibratory, or harmonic repetition, which is frequently serious in the case of bridges.]