# Stability of Case Furniture

Due to the safety of the user, the stability of furniture is probably the most important characteristic. As far as fractures of elements or cracks in the joints cause a gradual loss of stiffness in the construction, depending on the size of these defects, the loss of stability of the furniture, especially of a large weight, may suddenly and immediately endanger the health or life of the user. This especially concerns fur­niture for children and infants, who cannot respond to states of imminent danger. Current methods for assessing construction stability come down to laboratory measurements of horizontal or vertical load values, for which the furniture is subject to displacement. Below are solutions that enable to closely assess, through analysis, the stability of the designed piece of furniture.

In furniture of a case construction, first the coordinates of the centre of gravity of the construction in a state of operational load must be determined. To this end, the transverse cross section of a furniture piece in a side view should be considered (Fig. 7.57), taking into account both the mass loads and operational loads. An interesting value of the x coordinate of the centre of gravity is determined from the equation:

(7.183)

in which

n m к p

Eo* = E ^ ^ AiqAixi^ ^ ^ VsiqVixi~b ^ ^ Aqiqqixi; (7-l84)

i=1 i=1 i=1 i=1

n m к m

E& = E

i=1 i=1 i=1 i=1

where

V; volume of element,

Pi density of element,

A, area of shelves, horizontal partitions, bottom and top,

qAi surface load of shelves, horizontal partitions of the bottom,

Vsi volume of the drawer, qVi volume load of the drawer,

Api area of the door of horizontal rotation axis, qpi surface load of the door of horizontal rotation axis and x; abscissa of coordinates of location of the centre of gravity of element or load, in relation to the beginning of the system.

Knowing the location of the centre of gravity x of the furniture block, the balance state of the body based on known dependencies can be established, and when

• x > a the body loses balance on its own (falls over without the use of external force),

• x = a the body maintains in shaky balance, that is in a state when any small horizontal force P causes a loss of its stability,

• x < a the body maintains fixed balance and a certain horizontal force is needed to throw the furniture piece off this state. The value of this load can be written in the form

where

a and h dimensions of the side cross section of the body and Pkr acceptable critical load.

Dressers composed of a bottom part and an upper part set on top pose a par­ticular danger to the user (Fig. 7.58). No connection of both parts and a change in the location of the centre of gravity of the body by opening a door cause the risk of the upper part tipping over. In order to answer the question of whether a piece of furniture can lose stability on its own and/or what minimum force can lead to a loss

 Fig. 7.58 Calculation scheme of the loss of stability of a dresser’s top part before and after opening the doors

 Fig. 7.59 The calculation scheme of the strength of the screw joint connecting the top part with the base

of stability, the static schemes set out in Fig. 7.58 should be used. This drawing shows the construction of a furniture piece filled with operational load, in which the doors of the extension are closed. The same drawing, on a scheme next to it, illustrates an identically loaded construction, in which the doors of the extension are open. Fig. 7.59 shows the solution of the structural node, which is to prevent the extension from tipping over as a result of external loads. For all calculation schemes, the following indicators have been adopted:

aj width of the side wall of top extension,

c spacing of screw connectors,

dg thread diameter of screw connector,

h2 height of the side wall of top part,

hj total height of the segment (with the top part),

k’W shearing strength of the wood-based material (particle board),

MPkr moment of force Pkr,

MQw moment of force Qw,

Ms moment of force Ps,

Pkr external critical force causing loss of stability of the furniture top part,

Ps force pulling out the screw connector from the body of the top part or bottom

cabinet,

Qm resultant mass load of the top part,

Qs resultant of central load of the door wing,

Qu resultant operational load of the top part,

Qw resultant force deriving from the sum of all mass and operational forces,

Qz resultant of external load of the door wing,

xm location of the resultant vector of the mass load of top part Qm,

xs location of the resultant vector of the central load of the door wing Qs,

xu location of the resultant vector of the operational load of top part Qu,

xw location of the vector of the resultant force Qw and

xz location of the resultant vector of the external load of the door wing Qz

The calculation methodology presented below allows to establish the following:

• whether the furniture piece is stable without any external load at the most favourable and least favourable scheme of usage,

• when the furniture piece will lose its stability under the influence of external load and

• what the minimum value of an external critical load is, when a self-stable furniture piece can lose stability and tip over.

For the provided constructions, the location of the vector of resultant force and the value of the resultant force should be calculated according to the following formulas:

The furniture loses its stability under the influence of external load if the value of the external force is greater than that determined on the basis of the following formula of critical force values:

Pkr = Qw (a1 ~ Xw) . (7.189)

h2

In securing the top part against tipping over, by additionally fixed screws, the value of external force causing the loss of stability of the top part can be increased; thus, the safety of the structure can be increased. After fastening a metal connector, the value of external critical force can be calculated from the equation:

Pkr = a* + . (7.190)

h2