Rudimentary Treatise on the Construction of Cranes, and Machinery for ... by Joseph Glynn

Author:Joseph Glynn
Language: eng
Format: epub
Publisher: J. Weale
Published: 1849-03-25T05:00:00+00:00

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the form of this beam on the end of a round tree, to be

sawn into a crane jib. It also shows the difference between it and the square beam. If the beam be not loaded in the middle, but have the weight laid upon it nearer to one support than the other, the stress will be as the product of .^ the two distances from the sup« ported ends. Thus, if a beam supported at both ends be 12 ft. long between the supports, and be loaded at 4 ft. from one end, the stress upon it compared with a similar beam loaded on the middle i^nll be as 4x8 = 32 is to 6x6 = 36, the stress decreasing in this proportion as the weight is brought nearer the end.

If the load be distributed equally over the whole length of the beam, the stress is equal to half that of a weight laid upon the middle of it.

If it were possible to fix the beam fast at both ends, instead of supporting it, as for instance, by building both ends into massive walls, the strength would be in«> creased in the proportion of 3 to 2, and the beam, if loaded until it broke, would break in three places instead of one. To fix a beam in this way is practically impossible; but it should be remembered that a long joist passing over several supports, and secured to them all, benefits by this law, and is stronger than if it were cut into short lengths.

If a beam be supported at both ends in a slanting direction, at an angle, its strength, as compared with that of a horizontal beam, is as the length of the beam is to the cosine of its elevation, so that, if the length of

60 OH THB OONST&VCTION OV CBANBS.

the beam be represented by the number 6, the elevation of its end by 4, and the cosine of elevation by 3, the strength of the slanting beam compared with that of a horizontal one is as 5 to 3, and it continues to increase as it is elevated from the horizontal position, where it is least, to the vertical position where it is greatest. When it has reached the perpendicular, there is no transverse stress, for the beam has become a pillar, and acts upon the thrust.

When horizontal rectangular beams are fixed at one end, and the load is suiq)ended from the other, the Strength is as the square of the depth multiplied by the breadth and divided by four times the lengUi.

Suppose one end of the beam to be built into a waU^ and a weight placed upon the other end, then suppose the beam to be lengthened and carried through the wall to an equal distance on the other side, and to be balanced by a weight at the other end, then the beam will be twice the length, loaded by twice the weight, tending to break it

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