107. The strain upon a beam fixed at both ends has excited much attention, in consequence of a supposed difference between the results of theory and experiment. If it had been possible to fix a beam so that it should not have suffered extension beyond the point of fixing, the demonstrations of Emerson* and Professor Robinson† would have been perfectly correct; but it is evident that the beam will be extended beyond the point of support, and the quantity of extension must depend on the mode of fixing. According to the experiments of Belidor, the strength of a beam fixed at both ends is to the strength of a beam only supported at the ends as 3 is to 2.‡ M. Parent obtained nearly the same result. The stiffness will be nearly in the same proportion.

But we cannot in practice fix the ends of a beam into a wall without endangering its stability, therefore the determination of the stiffness of beams to suit such a case is not of much importance.

When, however, a long beam AB, is laid over several points of support, as in Fig. 42, a case of very common occurrence in building, the strength of the intermediate parts is nearly doubled, or twice as much as when the beams are cut into short lengths. Hence the carpenter will see the importance of using bridging and ceiling joists, and purlins, and rafters, in considerable lengths, so that a joist may extend over several binding joists, purlins over several trusses, and a rafter over several purlins; also, by contriving the joinings so that they shall not be opposite one another, a floor or roof may be made tolerably equal in strength. Hence, also, we see the importance of notching joists, purlins, and rafters over the supports, instead of framing them between.

Fig. 42.

When A Beam Is Fixed At Both Ends And Loaded In Th 52

* Emerson's ' Algebra,' prob. 182, p. 464. † 'Encyclopaedia Britannica,' art. Carpentry. ‡ ' Sciences des Ingenieurs,' liv. iv., chap. 3.