r rectangular prismatic
beams of the same material, mode of support, and loading, the
load which a given beam can support varies as follows:

(1) It is directly proportional to the breadth for beams of the
same length and depth, as is the case with stiffness.

(2) It is directly proportional to the square of the height for
beams of the same length and breadth, instead of as the cube of
this dimension as in stiffness.

(3) It is inversely proportional to the span for beams of the
same breadth and depth and not to the cube of this dimension as
in stiffness.

The fact that the strength varies as the _square_ of the height
and the stiffness as the _cube_ explains the relationship of
bending to thickness. Were the law the same for strength and
stiffness a thin piece of material such as a sheet of paper
could not be bent any further without breaking than a thick
piece, say an inch board.
|-------------------------------------------------------------------------------------|
| TABLE IX |
|-------------------------------------------------------------------------------------|
| RESULTS OF STATIC BENDING TESTS ON SMALL CLEAR BEAMS OF 49 WOODS IN GREEN CONDITION |
| (Forest Service Cir. 213) |
|-------------------------------------------------------------------------------------|
| | Fibre | | | Work in Bending |
| COMMON NAME | stress at | Modulus | Modulus |-------------------------------|
| OF SPECIES | elastic | of | of | To | To | |
| | limit | rupture | elasticity | elastic | maximum | Total |
| | | | | limit | load | |
|-----------------+-----------+----------+------------+----------+----------+---------|
| | | | | In.-lbs. | In.-lbs. | In.-lb. |
| | Lbs. per | Lbs. per | Lbs. per | per cu. | per cu. | per |
| | sq. in. | sq. in. | sq. in. | inch | inch | inch |
| | | | | | | |
| Hardwoods | | | | | | |
| | | | | |