Stability of Board with Fixed Support on Perimeter

The method of completely attaching the rear walls of furniture in the body by gluing, due to the inability to disassemble, has never been used in industrial practice. From the cognitive point of view, to check the theoretical assumptions,
this example should be regarded as necessary. Timoshenko and Gere (1963), when presenting the approximate method for solving the case of a rectangular shield mounted on four sides, subject to shearing, introduced an approximate form of a curved sheet described by the function:

A 2nx 2py

w 1 — cos 1 — cos

4 a b

Huber (1922) suggests assuming a similar function of buckling for unidirectional boards loaded symmetrically. Further analysis of sheared boards, in solving cases of fixing around the whole perimeter, was developed by Skan and Southwell (1954) and also Budiansky and Connor (1948). Studies of critical states of rectangular boards freely supported on the perimeter, and applied to surface girders, were conducted by Girkmann (1957). Studies related to the stability of shields for various support conditions were also conducted by Cox (1933). A convenient and simple method for determining critical stresses for boards of various border conditions was also suggested by Wolmir (1956). He recommended calculating values of the coefficient k, according to the specified method of supporting a board. Therefore, the value of critical edge forces for the case of fixing edges can be expressed by the following equation:

where

5.5

k = 8.98 + у.

b2

For an orthotropic board, the critical values of contact forces are calculated according to the equation:

where

k coefficient dependent on the relation 1/n, determined on the basis of Table 7.8

Table 7.8 Value of the coefficient k for isotropic boards

1/p

0.0

0.2

0.5

1.0

2.0

3.0

5.0

TO

k

18.6

18.9

19.9

22.12

18.8

17.6

16.6

15.1