Page 232 - 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-grade test data, accounts for differences in F , F , and F related to width and in
c
t
b
F and F related to length (test span).
b
t
For visually graded timbers [5 5 in (127 127 mm) or larger], when the
depth d of a stringer beam, post, or timber exceeds 12 in (304.8 mm), the design
value for bending should be adjusted by the size factor
C F (12 / d) 1/9 (6.26)
Design values for bending F for glued-laminated beams should be adjusted for the
b
effects of volume by multiplying by
C V K L 5.125 1/x (6.27)
12
21
L d b
where L length of beam between inflection points, ft (m)
d depth, in (mm), of beam
b width, in (mm), of beam
width, in (mm), of widest piece in multiple-piece layups with various
widths; thus, b ) 10.75 in (273 mm)
x 20 for southern pine
10 for other species
K loading condition coefficient
L
For glulam beams, the smaller of C and the beam stability factor C should be
L
V
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
3M
f r (6.28)
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
horizontal shear for southern pine for all load conditions and for Douglas fir and
2
larch for wind or earthquake loadings. The limit is 15 lb/in (0.103 MPa) for
Douglas fir and larch for other types of loading. These values are subject to