point, and in a beam uniformly loaded and
supported at either end is maximum at the points of support and
zero at the centre. In addition there is a shearing force
tending to move the fibres of the beam past each other in a
longitudinal direction. (See Fig. 12.) This longitudinal shear
is maximum at the neutral plane and decreases toward the upper
and lower surfaces.

[Illustration: FIG. 12.--Horizontal shear in a beam.]

Shearing across the grain is so closely related to compression
at right angles to the grain and to hardness that there is
little to be gained by making separate tests upon it. Knowledge
of shear parallel to the grain is important, since wood
frequently fails in that way. The value of shearing stress
parallel to the grain is found by dividing the maximum load in
pounds (P) by the area of the cross section in inches (A).

{ P }
{ Shear = --- }
{ A }

Oblique shearing stresses are developed in a bar when it is
subjected to direct tension or compression. The maximum shearing
stress occurs along a plane when it makes an angle of 45 degrees
P
with the axis of the specimen. In this case, shear = -----. When
2 A
the value of the angle [Greek: theta] is less than 45 degrees,
P
the shear along the plane = --- sin [Greek: theta] cos [Greek:
A
theta]. (See Fig. 13.) The effect of oblique shear is often
visible in the failures of short columns. (See Fig. 14.)

[Illustration: FIG. 13.--Oblique shear in a short column.]

[Illustration: FIG. 14.--Failure of short column by oblique
shear.]

|---------------------------------------------------------------------------|
| TABLE VIII |
|---------------------------------------------------------------------------|
| SHEARING STRENGTH ACROSS THE GRAIN OF VARIOUS AMERICAN WOODS |
| (J.C. Trautwine. Jour. Franklin Institute. Vol. 109, 1880, pp. 105-106) |
|---------------------------------------------------------------------------|
| KIND OF WOOD | Lbs. per | KIND OF WOOD | Lbs. per |
| | sq. inch | | sq. inch |
|-----------------------+----------+-----------------------------+----------|
| Ash | 6