TRANSVERSE STRENGTH OF MATERIALS.
When a beam, of any material, is loaded, the surface in contact with the load is compressed, and the opposite surface extended; and there is a line between these, which is neither compressed, nor extended, called the neutral line.
If the depth of a beam be doubled, the breadth, and length between supports remaining the same, its strength will be increased four times.
If its breadth be doubled, the other dimensions being as above, its strength will be doubled.
By increasing the distance between the supports of any beam, its strength is decreased in the same ratio; twice the distance between the supports will weaken the beam one-half; half the distance between the supports will enable it to bear twice the load.[48]
The same beam will bear twice the load, if, instead of being concentrated in the middle, it be equally distributed over the whole length of the beam.
If the load on a beam be placed near to one of the supports, instead of in the middle, its effect will decrease in the ratio of its proximity to the support.
Let S s represent the beam, W the load or weight in the middle, w the weight near s; then the load which the beam will carry at the point where w is placed will be found by the following proportion:—
As S w × w s : S W × W s :: W : w.
A beam, fixed at one end, and loaded at the other, will bear half the weight of one of the same length supported at each end.