COMPRESSION ON
AN OBLIQUE PLANE
Determine whether the joint in Fig. 3 is satisfactory with respect to bearing if the allow-
able compressive stresses are 1400 and 400 lb/in^2 (9653 and 2758 kPa) parallel and nor-
mal to the grain, respectively.
Calculation Procedure:- Compute the compressive stress
Thus, / = PIA = 9000/3.625^2 = 685 lb/in^2
(4723.1 kPa). - Compute the allowable
compression stress In the main
member
Apply Hankinson's equation: N = PQI(P sin^2 6
- Q cos^2 0), where P = allowable compressive
stress parallel to grain, lb/in^2 (kPa); Q = allow-
FIGURE 3 able compressive stress normal to grain; lb/in^2
(kPa); N = allowable compressive stress in-
clined to the grain, lb/in^2 (IdPa); 6 = angle be-
tween action line of N and direction of grain.
Thus, sin^2 0-0.36, cos^2 0 = (4/5)^2 = 0.64; then N= 1400(400)/(1400 x 0.36 + 400 x 0.64)
= 737 lb/in^2 (5081.6 kPa) > 685 lb/in^2 (4723.1 kPa). Therefore, the joint is satisfactory.
- Alternatively, solve Hankinson's equation by using
the nomogram in the Wood Handbook
DESIGN OF A NOTCHED JOINT
In Fig. 4, Ml is a 4 x 4, F = 5500 Ib (24,464 N), and
stresses are P = 1200 lb/in^2 (8274 kPa) and Q = 390 lb/in^2 (2689.1 kPa). The projection of
Ml into M2 is restricted to a vertical dis-
tance of 2.5 in (63.5 mm). Design a suit-
able notch.
Calculation Procedure:- Record the values of the
trigonometric functions of
and ^/2
The most feasible type of notch is the
one shown in Fig. 4, in which AC and BC
bisect the angles between the intersect-
ing edges. The allowable bearing pres-
sures on these faces are therefore identi-
FIGURE 4 cal for the two members.