This agrees sufficiently with 74 lbs., the mean of two observed values.
402. Except in experiments Nos. 5 and 10, the differences are very small, and even in these two cases the differences are not sufficient to make us doubt that we have discovered the correct expression for the load generally sufficient to produce fracture.
403. We have already pointed out that a beam begins to sustain permanent injury when it is subjected to a load greater than half that which would break it ([Art. 368]), and we may infer that it is not in general prudent to load a beam which is part of a permanent structure with more than about a third or a fourth of the breaking weight. Hence if we wanted to calculate a fair working load in lbs. for a beam of pine, we might obtain it from the formula.
| area of section × depth | |
| 1500 × | —————————— |
| span |
Probably a smaller coefficient than 1500 would often be used by the cautious builder, especially when the beam was liable to sudden blows or shocks. The coefficient obtained from small selected rods such as we have used would also be greater than that found from large beams in which imperfections are inevitable.
404. Had we adopted any other kind of wood we should have found a similar formula for the breaking weight, but with a different numerical coefficient. For example, had the beams been made of oak the number 6080 must be replaced by a larger figure.
A BEAM UNIFORMLY LOADED.
405. We have up to the present only considered the case where the load is suspended from the centre of the beam. But in the actual employment of beams the load is not generally applied in this manner. See in the rafters which support a roof how every inch in the entire length has its burden of slates to bear. The beams which support a warehouse floor have to carry their load in whatever manner the goods are disposed: sometimes, as for example in a grain-store, the pressure will be tolerably uniform along the beams, while if the weights be irregularly scattered on the floor, there will be corresponding inequalities in the mode in which the loads are distributed over the beams. It will therefore be useful for us to examine the strength of a beam when its load is applied otherwise than at the centre.
406. We shall employ, in the first place, a beam 40" span, 0"·5 broad, and 1" deep; and we shall break it by applying a load simultaneously at two points, as may be most conveniently done by the contrivance shown in the diagram, [Fig. 53]. a b is the beam resting on two supports; c and d are the points of trisection of the span; from whence loops descend, which carry an iron bar p q; at the centre r of which a weight w is suspended. The load is thus divided equally between the two points c and d, and we may regard a b as a beam loaded at its two points of trisection. The tray and weights are employed which we have used in the apparatus represented in [Fig. 58].
