# Stiffness of Socle

An open body of a case furniture piece can be stiffened to torsion by increasing the thickness of one or a few of its boards. The use of thick boards for all elements of the furniture piece improves the efficiency of the construction, but at the same time increases its weight, material consumption and the total cost of the product. The low effectiveness of this solution causes that designing works should be concentrated more on focusing the material in one board (Fig. 7.29). The stiffness of a wardrobe made from the same boards of the thickness d amounts to

whereas the stiffness of the body, in which the thickness of the bottom has been increased and the thickness of remaining elements have been decreased, has the value

fe5d = I^Gd3 0.8441 + 62.71 + 0.211 , (7.77)

3bc a c b

Assuming the dimensional proportions c = 2a = 4b, we obtain that

k5d = 13kd. (7.78)

The stiffness of the body of a furniture piece with one horizontal board thickened is thirteen times greater, while 12.5 units of stiffness comes from a board with a thickness 5d, and the remaining 1/2 units from boards with the thickness 3/4d. Stiffening the body of the furniture piece with a thick-walled board is expensive due to the high content of material. This cost can be significantly reduced by using reinforcement in the form of plinths and socles with fins (Dzi^gielewski and Smardzewski 1995).

Let us consider the deformation of a single-chamber wardrobe with a socle (Fig. 7.30). Like other boards, the socle is also subject to torsional deformation. Its stiffness can be determined, similarly to the stiffness of a five-element body of a furniture piece, by placing the socle in a local Cartesian system of coordinates X, Y and Z (Fig. 7.31). The value of the coefficient of stiffness for this furniture element is expressed by the equation:

For the socle of a furniture piece of rack structure, the stiffness coefficient kc is

(7.80)

while for the flange structure

stiffness of the socle, thickness of the ith element, appropriate overall dimensions, shear modulus of the element and

the number of elements corresponding to the dimensions of the frontal socle skirt, S = 2 for a four-element socle, S = 1 for a three-element socle (no skirt from the side of the rear wall).

In the considered case, the stiffness of the body depends on the torsional stiffness of the socle and that on the torsional stiffness of components. It is already known, however, that the torsional stiffness of boards depends, among others, on the module of figural deformations G, which value in relation to the module of linear deformations for isotropic materials remains in the familiar equation:

E

2(1 + v) ’

where

и Poisson’s ratio (for particle boards v = 0.28).

By taking advantage of the bending work of wood or wood-based materials, the stiffness of the socle, thus the entire body, can be easily increased. This can be achieved by applying fins in socle boards (Fig. 7.32). A finned board subjected to clean torsion deforms similarly to a board without fins. The diagonal of the board is bent according to the parabola, and the fin is in a state of clear bending (Dzi^gielewski and Smardzewski 1995). This kind of deformation can be written, according to the indications in Fig. 7.32, as follows:

. A

A = baZy

where

Because the work of external forces performed over the system must be equal to the sum of internal forces, then in the case of fin bending, we shall obtain

1 Pi Ac = -^ I W2 dg,

2 2EJJ h

g

where

 @2f (g)- 2EJ Ac 9g2 a2 + b2 (7:88) jgh3 12 (7:89)
 W = EJ

which gives

The stiffness of a fin can, therefore, be written by the equations:

By determining the stiffness of a single-chamber wardrobe, we demonstrated that the doors, if they are not inserted into the case, only constitute additional mass load

and do not improve the stiffness of the furniture piece. By inserting them into the body, it makes the furniture a coherent closed profile, which stiffness increases by dozens. Closing a socle with a thin board from the side of the socle (Fig. 7.33) makes it a stiff, six-sided box torsionally loaded, similarly to the entire construction of the furniture piece.

The presented ways of stiffening the furniture body refer to one element, which is the bottom in the form of a thick, single board or socle constituting a subas­semblage. By inserting this element into the furniture body, the stiffness of other components of the furniture piece should be established, disregarding the bottom (or socle) excluded in thought. In this case, the stiffness of the body is expressed by the equation:

. ПА Gid3 2

k = § 5(Щ + k"

 Fig. 7.34 Construction of furniture with top in the form of: a socle, b crown

where

n_1 Gd3 2 the stiffness of all elements of the furniture body with a socle excluded

^ 3Щ – ai in thought and

kn stiffness of the socle as the nth element of the furniture piece.

The stiffness of the complex socle constitutes the sum of the stiffness of com­ponents, which is why for the n-element socle with a fin, we can write as

kn = kc + kz. (7.94)

The previously presented methods of designing stiffening of the construction of case furniture concern mainly the bottom and the socle. However, the same rea­soning can be applied to the top boards, especially since furniture having decorative masking skirts over the top board in the shape of a socle or crown is becoming increasingly common on the market (Fig. 7.34). These decorative elements are perfect for hiding the designed reinforcements, also on the top surface. Cooperation of fins and skirts with the board, however, requires the constructional insurance of a fixed angle between the board and the fin. In the case of a skirt with a free end (Fig. 7.35a), this end should be connected with the board using an extra element, e. g. a block. Using two intersecting fins (Fig. 7.35b) requires a constructional solution of the middle node. Another solution to this problem is to mount one fin under the board of the bottom, and the other over the surface top of the furniture (Fig. 5.35c).

Updated: October 8, 2015 — 10:38 pm