Operational load of the top, acting along the side wall of the furniture body, depending on its intensity, can cause a change in the shape which is the result of the loss of their stability. From a mechanical point of view, the side wall constitutes a board in which one longitudinal edge is free, the second one parallel to it and two transverse ones are supported in a discreet way. Therefore, the form of buckling of side walls depends on the number of horizontal partitions related to them (Figs. 7.50 and 7.51).
|
D @4w 2D @4w x dx4 ^ dx2dy2 |
|
d4w dy4 |
Critical loads of an orthotropic side wall can be determined by solving the equation:
where
Dt bending stiffness of the board (i = x, y, z,),
Ex linear elasticity module in the direction of x,
Ey linear elasticity module in the direction of y,
G shear modulus, h thickness of the board and
w function describing the surface of the board bending, substituting the following expression for the deflection of the board:
Hence, we obtain the equation describing the value of critical force for the side wall loaded longitudinally:
where
m = 1, 2, 3, …
