Page 225 - Civil Engineering Formulas

TIMBER ENGINEERING FORMULAS 159

BEARING

The allowable unit stresses given for compression perpendicular to the grain
apply to bearings of any length at the ends of beams and to all bearings 6 in
(152.4 mm) or more in length at other locations. When calculating the required
bearing area at the ends of beams, no allowance should be made for the fact that,
as the beam bends, the pressure upon the inner edge of the bearing is greater than
at the end of the beam. For bearings of less than 6 in (152.4 mm) in length and
not nearer than 3 in (76.2 mm) to the end of the member, the allowable stress for
compression perpendicular to the grain should be modified by multiplying by the
3
factor (l 8 )/l , where l is the length of the bearing in inches (mm) measured
along the grain of the wood.

BEAMS

The extreme fiber stress in bending for a rectangular timber beam is

f 6M/bh 2 (6.1)
M/S
A beam of circular cross section is assumed to have the same strength in bend-
ing as a square beam having the same cross-sectional area.
The horizontal shearing stress in a rectangular timber beam is

H 3V/2bh (6.2)
For a rectangular timber beam with a notch in the lower face at the end, the
horizontal shearing stress is
H (3V/2bd ) (h/d ) (6.3)
1 1
A gradual change in cross section, instead of a square notch, decreases the
shearing stress nearly to that computed for the actual depth above the notch.
Nomenclature for the preceding equations follows:
2
f maximum fiber stress, lb/in (MPa)
M bending moment, lb in (Nm)
h depth of beam, in (mm)
b width of beam, in (mm)
3
3
2
S section modulus ( bh /6 for rectangular section), in (mm )
2
H horizontal shearing stress, lb/in (MPa)
V total shear, lb (N)
d depth of beam above notch, in (mm)
1
l span of beam, in (mm)
P concentrated load, lb (N)