CIVIL ENGINEERING FORMULAS

TIMBER ENGINEERING FORMULAS 167

modification for duration of load. If these values are exceeded, mechanical rein-
forcement sufficient to resist all radial tensile stresses is required.
When Mis in the direction tending to increase curvature (decrease the
radius), the stress is compressive across the grain.For this condition, the design
value is limited to that for compression perpendicular to grain for all species.
For the curved portion of members, the design value for wood in bending
should be modified by multiplication by the following curvature factor:

(6.29)

wheretis the thickness of lamination, in (mm); and Ris the radius of curvature
of lamination, in (mm). Note that t/Rshould not exceed 1/100 for hardwoods
and southern pine or 1/125 for softwoods other than southern pine. The curva-
ture factor should not be applied to stress in the straight portion of an assembly,
regardless of curvature elsewhere.

Bearing Area Factor

Design values for compression perpendicular to the grain Fcapply to bear-
ing surfaces of any length at the ends of a member and to all bearings 6 in
(152.4 mm) or more long at other locations. For bearings less than 6 in
(152.4 mm) long and at least 3 in (76.2 mm) from the end of a member, Fc
may be multiplied by the bearing area factor:

(6.30)

whereLbis the bearing length, in (mm) measured parallel to grain. Equation
(6.30) yields the values of Cbfor elements with small areas, such as plates and
washers, listed in reference data. For round bearing areas, such as washers, Lb
should be taken as the diameter.

Column Stability and Buckling Stiffness Factors

Design values for compression parallel to the grain Ftshould be multiplied by
the column stability factor Cpgiven by Eq. (6.31):

(6.31)

where design value for compression parallel to the grain multiplied by all
applicable adjustment factors except Cp
FcE

E modulus of elasticity multiplied by adjustment factors

KcEE/(Le/d)^2

F*c

CP

1 (FcE/Fc*)

2 c



B

1 (FcE/Fc*)

2 c 

2



(FcE/Fc*)

c

Cb

Lb0.375

Lb

Cc 1  (^2000) 
t
R
2