The radial stress induced by a bending moment in a member of constant cross section may be computed from
fr=3M/2Rbd
where
M= bending moment, in lb (N m)
R = radius of curvature at centerline of member, in (mm)
b =width of cross section, in (mm)
d =depth of cross section, in (mm)
When M is in the direction tending to decrease curvature
(increase the radius), tensile stresses occur across the grain. For this condition, the allowable tensile stress across the grain is limited to one-third the allowable unit stress in hori- zontal shear for southern pine for all load conditions and for Douglas fir and larch for wind or earthquake loadings. The limit is 15 lb/in2 (0.103 MPa) for Douglas fir and larch for other types of loading. These values are subject to modification for duration of load. If these values are exceeded, mechanical reinforcement sufficient to resist all radial tensile stresses is required.
When M is 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:
Cc=1-2000(t/R)2
where
t is the thickness of lamination, in (mm), and R is the radius of curvature of lamination, in (mm). Note that t/R should not exceed 1/ 100 for hardwoods and southern pine or
1/125 for softwoods other than southern pine. The curvature 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 Fc apply to bearing 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, Fc1 may be multiplied by the bearing area factor:
Cb=1+0.375/Lb
where Lb is the bearing length, in (mm) measured parallel to grain.
