Page 229 - Civil Engineering Formulas

TIMBER ENGINEERING FORMULAS 163

d smaller dimension of rectangular section
E modulus of elasticity
f allowable compressive stress parallel to grain in short column of given
c
species
f allowable compressive stress parallel to grain in given column

COMPRESSION ON OBLIQUE PLANE

Consider that a timber member sustains a compressive force with an action line
that makes an oblique angle with the grain. Let

P allowable compressive stress parallel to grain
Q allowable compressive stress normal to grain
N allowable compressive stress inclined to grain
angle between direction of stress N and direction of grain

By Hankinson’s equation,
PQ
N (6.16)
2
2
P sin Q cos
In Fig. 6.1, member M must be notched at the joint to avoid removing an
1
excessive area from member M . If the member is cut in such a manner that AC
2
and BC make an angle of /2 with vertical and horizontal planes, respectively,
the allowable bearing pressures at these faces are identical for the two mem-
bers. Let
A sectional area of member M 1
f pressure at AC
1
f pressure at BC
2
It may be readily shown that

sin ( /2) cos ( /2)
AC b BC b (6.17)
sin sin
F sin F sin tan ( /2)
f 1 f 2 (6.18)
A tan ( /2) A
This type of joint is often used in wood trusses.