Answer to Question #89444 in Mechanics | Relativity for Kavishka Dulanjana

Question

The wooden members A and B are to be joined by plywood splice plates which will be fully glued on the surfaces in contact.As part of the design of the joint and knowing that the clearance between the ends of the members is to be 8mm, determine the smallest allowable length L if the average shearing stress in the glue is not to exceed 800kPa.

Answer 1

The plywood splice plates will hold the either member A or B from two sides.

The area that will have to withstand the load $F$ thus should be doubled for the calculations:

$$A=2\cdot BH$$

The shear stress that the glue will experience is

$$\tau_0=\frac{F}{A}=\frac{F}{2BH},$$

solve this for $H$:

$$H=\frac{F}{2\tau_0 B},$$

$$L=2H+g=\frac{F}{\tau_0 B}+g=\frac{F}{8\cdot10^8 B}+0.008.$$