412. When the beam gives way under these circumstances, there is not only a fracture in the centre, but each of the halves are also found to be broken across near the points of support; the necessity for three fractures instead of one explains the increase of strength obtained by restraining the ends to the horizontal direction.
413. In structures the beams are generally more or less secured at each end, and are therefore more capable of bearing resistance than would be indicated by [Table XXIV]. From the consideration of [Arts. 408] and [411], we can infer that a beam secured at each end and uniformly loaded would require three or four times as much load to break it as would be sufficient if the ends were free and if the load were applied at the centre.
BEAMS SECURED AT ONE END AND
LOADED AT THE OTHER.
414. A beam, one end of which is firmly imbedded in masonry or otherwise secured, is occasionally called upon to support a weight suspended from its extremity. Such a beam is shown in [Fig. 55].
In the case we shall examine, a b is a pine beam of dimensions 20" × 0"·5 × 0"·5, and we find that, when w reaches 10 lbs., the beam breaks. In experiment No. 8, [Table XXIV]., a similar beam required 36 lbs.; hence we see that the beam is broken in the manner of [Fig. 55], by about one-fourth of the load which would have been required if the beam had been supported at each end and laden in the centre.
Fig. 55.
We shall presently have occasion to apply some of the results obtained by the experiments made in the lecture now terminated.
LECTURE XIII.
THE PRINCIPLES OF FRAMEWORK.
Introduction.—Weight sustained by Tie and Strut.—Bridge with Two Struts.—Bridge with Four Struts.—Bridge with Two Ties.—Simple Form of Trussed Bridge.