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.
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.