Page 227 - Civil Engineering Formulas

TIMBER ENGINEERING FORMULAS 161

For columns of circular cross section, the formula becomes
P 0.22E
(6.8)
A (l/d) 2
The allowable unit stress, P/A, may not exceed the allowable compressive stress,
c. The ratio, l/d, must not exceed 50. Values of P/A are subject to the duration of
loading adjustment given previously.
Nomenclature for Eqs. (6.6) to (6.8) follows:
P total allowable load, lb (N)
2
2
A area of column cross section, in (mm )
2
c allowable unit stress in compression parallel to grain, lb/in (MPa)
d dimension of least side of column, in (mm)
l unsupported length of column between points of lateral support, in (mm)
2
E modulus of elasticity, lb/in (MPa)
r least radius of gyration of column, in (mm)
For members loaded as columns, the allowable unit stresses for bearing on
end grain (parallel to grain) are given in data published by lumber associations.
These allowable stresses apply provided there is adequate lateral support and end
cuts are accurately squared and parallel. When stresses exceed 75 percent of
values given, bearing must be on a snug-fitting metal plate. These stresses apply
under conditions continuously dry, and must be reduced by 27 percent for
glued-laminated lumber and lumber 4 in (102 mm) or less in thickness and by
9 percent for sawn lumber more than 4 in (102 mm) in thickness, for lumber
exposed to weather.

COMBINED BENDING AND AXIAL LOAD

Members under combined bending and axial load should be so proportioned
that the quantity
P a /P M a /M 1 (6.9)

where P total axial load on member, lb (N)
a
P total allowable axial load, lb (N)
M total bending moment on member, lb . in (Nm)
a
M total allowable bending moment, lb . in (Nm)

COMPRESSION AT ANGLE TO GRAIN

The allowable unit compressive stress when the load is at an angle to the grain is
2
2
c c (c )/[c (sin ) (c ) (cos ) ] (6.10)