Fig. 53.
407. We proceed to break this beam. Adding weights to the tray, we see that it yields with 117 lbs., and cracks across between c and d. On reference to [Table XXIV]. we find from experiment No. 2 that a similar bar was broken by 77 lbs. at the centre; now ³/₂ × 77 = 115·5; hence we may state with sufficient approximation that the bar is half as strong again when the load is suspended from the two points of trisection as it is when suspended from the centre. It is remarkable that in breaking the beam in this manner the fracture is equally likely to occur at any point between c and d.
408. A beam uniformly loaded requires twice as much load to break it as would be sufficient if the load were merely suspended from the centre. The mode of applying a load uniformly is shown in [Fig. 54].
Fig. 54.
In an experiment actually tried, a beam 40" × 0"·5 × 1" placed edgewise was found to support ten 14 lb. weights ranged as in the figure; one or two stone more would, however, doubtless produce fracture.
409. We infer from these considerations that beams loaded in the manner in which they are usually employed are considerably stronger than would be indicated by the results in [Table XXIV].
EFFECT OF SECURING THE ENDS OF A BEAM
UPON ITS STRENGTH.
410. It has been noticed during the experiments that when the weights are suspended from a beam and the beam begins to deflect, the ends curve upwards from the supports. This bending of the ends is for example shown in [Fig. 54]. If we restrain the ends of the beam from bending up in this manner, we shall add very considerably to its strength. This we can do by clamping them down to the supports.
411. Let us experiment upon a beam 40" × 1" × 1". We clamp each of the ends and then break the beam by a weight suspended from the centre. It requires 238 lbs. to accomplish fracture. This is a little more than half as much again as 152 lbs., which we find from [Table XXIV]. was the weight required to break this bar when its ends were free. Calculation shows that the strength of a beam may be even doubled when the ends are kept horizontal by more perfect methods than we have used.