CIVIL ENGINEERING FORMULAS

166 CHAPTER SIX

values for southern pine are based on the adjustment equation given in Ameri-
can Society for Testing and Materials(ASTM) D1990. This equation, based on
in-gradetestdata, accounts for differences in Fb,Ft, and Fcrelated to widthand in
FbandFtrelated to length (test span).
For visually graded timbers [55 in (127127 mm) orlarger], when the
depthdof a stringer beam, post, or timberexceeds 12 in (304.8 mm), the design
value for bending should be adjusted by the size factor

(6.26)

Design values for bending Fbfor glued-laminated beams should be adjusted for the
effects of volume by multiplying by

(6.27)

where Llength of beam between inflection points, ft (m)
ddepth, in (mm), of beam
bwidth, in (mm), of beam
width, in (mm), of widest piece in multiple-piecelayups with various
widths; thus, b)10.75 in (273 mm)
x20 for southern pine
10 for other species
KLloading condition coefficient

For glulam beams, the smaller of CVand the beam stability factor CLshould be
used, not both.

Radial Stresses and Curvature Factor

The radial stress induced by a bending moment in a member of constant cross
section may be computed from

(6.28)

whereMbending moment, inlb (Nm)
Rradius of curvature at centerline of member, in (mm)
bwidth of cross section, in (mm)
ddepth of cross section, in (mm)

WhenMis 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
horizontal shear for southern pine for all load conditions and for Douglas fir and
larch for wind or earthquake loadings. The limit is 15 lb/in^2 (0.103 MPa) for
Douglas fir and larch for other types of loading. These values are subject to

fr

3 M

2 Rbd

CVKL

21

L

12

d

5.125

b 

1/x

CF(12 / d)1/9