Civil Engineering Reference
In-Depth Information
This formula is applicable only when the results of its use do not
indicate a higher stress than the maximum allowable unit stresses (as
defined by the stress grade of the timber used). The ratio
l
d
in this
equation is sometimes called the
slenderness ratio
.Asanexample
of the use of this formula, consider the following problem.
How much of a load may safely be imposed on a 6-inch
/
×
6-inch
dressed yellow pine column that is 12 feet long?
The slenderness ratio, or
l
/
d
,of6-inch
×
6-inch columns 12 feet
long is
144
24, and the modulus of elasticity of almost all good
yellow pine is 1,760,000 pounds per square inch. This is the calcu-
lation:
=
/
6
0
.
3
×
1
,
760
,
000
=
917 pounds per square inch
24
×
24
The cross-sectional area of standard 6-inch
6-inch timbers is
30.25 square inches. Therefore, the total load allowable on the col-
umn will then be:
×
917
×
30
.
25
=
27
,
739 pounds
An important point with respect to timber in compression is that
the ends should be cut exactly square so that there will be a full
bearing surface. Otherwise the timber will be subjected at the ends
to more than the working stress (see Figure 4-3).
Shearing Stresses
Shearing stresses in wood are dangerous only in the direction parallel
to the grain. It is almost impossible to shear the material across the
grain until the specimen has been
crushed
. The crushing strength,
then, and not the shearing resistance of the wood, will govern the
maximum stress that can be applied to the wood.
The standard shearing test for woods with the grain was devel-
oped by the American Society for Testing Materials (ASTM), and
the procedure is standardized. The specimens are standard dimen-
sions, shaped as shown in Figure 4-4 in pairs, one with the notch
at right angles to that in the other. The results of the tests on the
two specimens are averaged, but usually they vary only slightly. The
blocks are tested in a special shear tool that is loaded in a universal
testing machine, with the load applied at a rate of .024 inch per
minute.
The results of testing different types of woods vary widely. To pro-
vide for this lack of uniformity, the shear allowances in stress-rated
timbers may contain a reduction factor (safety factor) of as much as
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