CIVIL ENGINEERING FORMULAS

TIMBER ENGINEERING FORMULAS 163

dsmaller dimension of rectangular section

Emodulus of elasticity

fcallowable compressive stress parallel to grain in short column of given

species

fallowable 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

Pallowable compressive stress parallel to grain

Qallowable compressive stress normal to grain

Nallowable compressive stress inclined to grain

angle between direction of stress Nand direction of grain

By Hankinson’s equation,

(6.16)

In Fig. 6.1, member M 1 must be notched at the joint to avoid removing an
excessive area from member M 2. If the member is cut in such a manner that AC
andBCmake 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

Asectional area of member M 1

f 1 pressure at AC

f 2 pressure at BC

It may be readily shown that

(6.17)

(6.18)

This type of joint is often used in wood trusses.

f 1 

F sin 

A tan (/2)

f 2 

F sin  tan (/2)

A

ACb

sin (/2)

sin

BCb

cos (/2)

sin

N

PQ

P sin^2 Q cos^2