As a natural raw material, wood is characterised as both anisotropic, as well as volatile in its properties in the function of space; therefore, it is referred to as a nonhomogeneous material. Below are the physical theories of elasticity for an anisotropic body and understood as an equation binding the component of the stress tensor with the components of a strain tensor. The most general form of such equations in the linear theory of elasticity is the equation (Nowacki 1970): where
Oij stress tensor,
Aijkl tensor of elasticity and Eki strain tensor.
Botanical name 
Trade name 
Symptoms of illness 
Common use 
Inadvisable use 
Pericopsis elata v. Meeuwen 
Afrormosia, kokrodua, asamela 
Skin irritation 
To use inside and outside of buildings, furniture and veneers 

Afzelia africana Sm. 
Afzelia, doussi, lengue, ара 
Skin irritation, irritation of mucous membranes 
To use inside and outside of buildings 
Kitchens 
Gossweilerodendron balsamifentm Harms 
Agba, tola, tola branca 
Irritation of mucous membranes 
To use inside and outside of buildings, substitutes oak 

Antiaris africana Engl. 
Antiaris, bonkonko, oro, kirundu, andoum, upas 
Irritation of mucous membranes of the nose, throat and skin 
Furniture and veneers 

Turraeanthus africanus Pellegr. 
Avodire 
Irritation of mucous membranes, nosebleeds 
Luxurious finishing of building interiors, children’s furniture and veneers 

Distemonanthus benthamianus Baillon 
Ayan, movingui 
Mild allergies 
Doors, windows, office furniture 
Kitchens laundry rooms 
Castanospermum austraie A. Cunn. 
Black bean, moreton bay chestnut 
Contains isoflavones 
Finishing of building interiors, furniture and veneers 

Fagus sylvatica L. 
Beech 
Possibility of eczema caused by particulates and sawdust 
Furniture, food containers, tools, parts of musical instruments 

Betula papyracea Ait 
Birch 
Possibility of recurring skin irritation during sanding of wood 
Furniture and veneers 

Acacia melanoxylon R. Br. 
Blackwood 
Nosebleeds asthma, skin irritation 
Highquality furniture, finishing of building interiors, musical instruments 

Guibourtia tessmannii J. Leonard 
Bubinga, kevazingo 
Skin irritation 
Highquality furniture, finishing of building interiors, floors 
Table 4.2 Major species of wood showing toxic, irritant or sensitising properties (Hausen 1981) 
4.5 Materials Used in Furniture Design 205 
Botanical name 
Trade name 
Symptoms of illness 
Common use 
Inadvisable use 
Machaerium scleroxylon Tul. 
Caviuna vermelha, pao ferro, moradillo, jacaranda pardo, santos palisander 
Possible cases of skin irritation 
Highquality furniture, finishing of building interiors 

Cedrelci odorata L. 
Cedar, cedro 
Skin irritation 
Executive furniture, interior design 

Castanea sativa Mill. 
Chestnut, Spanish chestnut 
Possible cases of skin irritation 
Furniture, kitchen furniture, veneers 

Brya ebenus DC. 
Cocus, Jamaican ebony. 
Skin irritation 
Furniture, veneers 

Cordia miUenii Baker 
Cordia, canalete, freijo 
Skin irritation 
Furniture, finishing of building interiors 

Hymenaea courbaril L. 
Courbaril, locust 
Skin irritation 
Furniture 

Pseudotsuga menziesii (Mirb.) Franco 
Douglas fir, Oregon pine, douglasie 
Skin irritation and dermatitis, eczema 
Furniture, veneers 

Entandrophmgma angolense DC. 
Gedu nohor, tiama, edinam, kalungi 
Skin irritation 
Furniture 

Guarea thompsonii Sprague & Hutch. 
Guarea, bosse, obobo. 
Irritation of mucous membranes of the nose, throat and skin 
Furniture, finishing of building interiors 

Liquidambar styraciflua F. 
Gum, American sweetgum, red gum, bilsted, amberbaum 
Skin irritation 
Furniture, interior design 

TenninaHa ivorensis A. Chev. 
Idigbo, framire, emeri, black afara 
Skin irritation 
Furniture, finishing of building interiors 
Kitchen furniture 
(continued) 
206 4 Introduction to Engineering Design of Furniture 
Botanical name 
Trade name 
Symptoms of illness 
Common use 
Inadvisable use 
Chlorophorci excelsa Bentham and Hooker 
Iroko, kambala, mwule, odum 
Skin irritation 
Substitutes teak 

Larix decidua Miller 
Larch 
Skin irritation 
Furniture 

Shorea 
Lauan, red 
Skin irritation 
Furniture, interior design 

Terminalia superba Engler and Diels 
Limba, afara, korina 
Skin irritation, nosebleeds 
Chairs, interior design 

Diospyros celebica Bakh. 
Makassar Ebony, Coromandel 
Skin irritation and dermatitis, eczema 
Luxurious furniture, elements of musical instruments 

Khaya grandifoliola DC. 
African mahogany khaya, krala 
Skin irritation 
Furniture, executive offices, surfaces of worktops of office furniture 

Swietenia macrophyllci King 
American mahogany, tabasco, caoba 
Skin irritation 
Furniture, executive offices, interior design 

Tieghemella heckelii Pierre ex Chev. 
Makore, baku 
Irritation of mucous membranes of the nose and upper respiratory tract 
Furniture, veneers, highquality interior design, doors 

Man son ia altissima A. Chev. 
Mansonia, bete 
Skin irritation, cough, nosebleeds, headaches 
Telecommunications engineering, furnishings of building interiors 

Prosopis juliflora DC. 
Mesquite 
Skin irritation 
To use inside and outside of buildings, furniture and interior design 

Pterocarpus angolensis DC. 
Muninga, kejaat 
May cause allergies 
Furniture, veneers, highquality interior design 

Triplochiton scleroxylon K. Schum. 
Obeche, samba, wawa, abachi 
Asthma, skin irritation and rash 
Veneers, interior design 
4.5 Materials Used in Furniture Design 207 
Botanical name 
Trade name 
Symptoms of illness 
Common use 
Inadvisable use 
Nerium oleander L. 
Oleander, laurier rose 
Poisonings have toxic properties 
Haberdashery 
Kitchen, contact with food 
Olea europaea L. 
Olive wood 
Severe skin irritation and paralysis 
Interior design, jewelery, for turning 
Direct contact with body 
Aspidospenna peroba Fr. All 
Peroba rosa 
Skin irritation. Particulates and sawdust cause irritation of mucous membranes of the nose, irritation of larynx and eyes, weakness, drowsiness, sweating, fainting 
Outdoor furniture, hand tools 

Pinus radiata D. Don 
Radiata pine, Monterey pine 
Skin irritation caused by the presence of resin and turpentine 
Furniture 

Pinus silvestris F. 
Pine 
Skin irritation 
Furniture, stairs and many more 

Gonystylus ban can us Baillon 
Ramin, malawis 
Skin irritation 
Furniture and interior design 

Dalbergia nigra All 
Brazilian rosewood, Jacaranda, Rio palisandre 
Eczema of hands and face, skin irritation 
Furniture, interior design, veneers, musical instruments 

Dalbergia latifolia Roxb. 
East Indian rosewood, Indian palisandre 
Eczema, skin irritation 
Highquality furniture, interior design, elements of musical instruments 

Entandrophragma cylindricum Sprague 
Sapelli, sapele, sapeli 
Skin irritation 
Furniture, interior design, veneers 
(continued) 
208 4 Introduction to Engineering Design of Furniture 
By entering the engineering markings of components of the stress and strain
tensor – @11 @x, @22 @y, @33 @z, T12 Txy, T23 Tyz, T31 Tzx, £11 £x, £22 £y,
£33 = «z, Y12 = Yxy, Y23 = Yyz and 731 = Yzx, and entering the markings: An = Ann, …, A16 = A1131, …, A21 = A2211, …, A26 = A2231, …, we obtain the following form of generalised Hooke’s law (Litewka 1997):
@x 
‘A11 
A12 
A13 
A14 
A15 
A16 
_£x 

ry 
A21 
A22 
A23 
A24 
A25 
A26 
ey 

@z 
A31 
A32 
A33 
A34 
A35 
A36 
ez 

sxy 
A41 
A42 
A43 
A44 
A45 
A46 
Txy 

syz 
A51 
A52 
A53 
A54 
A55 
A56 
cyz 

szx _ 
_A61 
A62 
A63 
A64 
A65 
A66_ 
Jzx_ 
If the symmetry of stress and strain tensors is considered, the number of components is 36. But when we take into account the differentiating alternation of free energy function in relation to the tensor’s components:
dstjdski dSkidstj ’
where
V elastic energy,
then the number of the tensor A components will decrease to 21. In specific anisotropic cases, like for example an orthotropic body, tensor A has 9 components, and for a transversally isotropic body—5 components. By expressing the strains of an anisotropic body in the general form, the following equation can be written as follows:
eij aijkl ‘ rkl;
where
a compliance tensor and
aijki components of the compliance tensor determined by the measurement of the strains of planes of a three dimensional body, taking into account normal and shear strains (Fig. 4.9).
At the same time, the following dependencies apply: for the direction of Xaxis
_ ey ez ex ex
mxy — — ; V* — — ; Pzr. z — “ ; fizy, x — “ ;
ex ex czx Izy
for the direction of Yaxis

Thus, it is easy to write, e. g. an equation of normal strains in the direction of the Xaxis:
ex — E vyx£y vzxez + ^zyyX ■ czy ” 1ZX, X ■ yzx ” MryjX ■ Уху
By substituting the now wellknown dependencies e = a/E and у = т/G, we obtain, respectively:
e =X – v^ v ^ + и ^ + и —+ и – Xh С42П
ex E vyx E vzx E Hzy, x G ‘ игх, х g г их^,х g ’ ( )
Ex Ey Ez Gyz Gxz Gxy
or
ex E (rx vxyry vxzrz Г 1x, yzsyz Г 1x, xzsxz Г Ax^xy) –
Ex
For shear strains, e. g. ^ the equation of the sum of partial strains will have the form:
xy
yxy G ‘ 1y? x^ ■ ey ‘ Mx, xy ■ ex “г ■ ez "T” 1^,xy ■ yxz ""I” 1zy, xy ■ Tyz’
Gxy
hence finally
yxy — G i1xy, xrx + Mxyjry г Mxy^z г Mxyz^xz г 1xy, zyTyz г Txy) .
Gx
In the above equations, Ex, Ey and Ez are the linear elasticity modules at stretching, Gxy, Gxz and Gyz are shear elasticity modules in planes that are parallel to the lines of direction coordinates x, y, z, vxy, vyx, and vzx, vxz, vyz, vzy are Poisson’s
ratios characterising elongation in the direction of the first axis and shortening in the direction of the second axis of the plane. Coefficients, Mxzyz… ,Mxz>xy, called Chentsov coefficients (Ashkenazi 1958; Lekhnickij 1977), characterise shear strains in planes that are parallel to the coordinate system, caused by tangential stresses acting in the second planes parallel to the coordinate system. Coefficients, wyz>x… ,Mxy>z, according to Rabinowicz (1946) called the coefficients of mutual impact of first degree, they express elongation in the direction of the axis of the coordinate system, caused by tangential stresses acting in planes parallel to the coordinate system. Coefficients, Mxyz… ,Mz>xy, express shear strains in planes parallel to the global coordinate system, caused by normal stresses acting in the direction of the axis of the system. They can be called coefficients of mutual impact of the second degree (Ashkenazi 1958).
The equations above correspond only to the given Cartesian system of coordinates. Changing this system will automatically change the values of the coefficients,
although their number remains constant. However, if at any point of the anisotropic elastic body, three mutually perpendicular planes of its internal structure can be led, such material can be called orthotropic. Wood, as an orthotropic body, in a spatial state of stresses is subject to normal strains (Fig. 4.10) and changes in shape (Fig. 4.11).
By summing up the value of partial strains in particular anatomical directions, we obtain expressions for total strains in the form:
where
aL, aR, aT vector of normal stresses, respectively, in the direction:
longitudinal, radial and tangential;
El, Er, Et linear elasticity modules of wood, respectively, in the
direction: longitudinal, radial and tangential; and vLR, vLT, vRT, vTR, Poisson’s ratios, respectively, in anatomical directions: longi – vRL, vTL tudinalradial, longitudinaltangential, radialtangential, tan
gentialradial, radiallongitudinal and tangentiallongitudinal.
And expressions for shear strains are given as follows:
The generalised Hooke’s law in matrix convention has the form:
ri — Aijej; (434)
while for the discussed case, we will obtain:
_ 
ClEl 
CtlEl 
CrE,. 
0 
0 
0 

ffL 
Ct (vrt+v, t vrl) 
Ct (vrt+vltvrl) 
Ct 

Г7 
vlt (1—vlrvrl )Et Ct 
(1—vlrvrl )Et Ct 
(vrt+v, t vrl)Et Ct 
0 
0 
0 

ffR 
CrlEr 
(1—vlrvrl)(1—vlt vtl)Er 
(1—vlt vtl)Er 
0 
0 
0 

SLT 
— 
Ct (vrt+vlt vrl) 
Ct (vrt+vltvrl) 
Ct 

0 
0 
0 
glt 
0 
0 

SLR 
0 
0 
0 
0 
Glr 
0 

STR J 
0 
0 
0 
0 
0 
G7R 
e, eT 
X £R ;
Jlt
Ilk
Ttr
(4.35)
where:
Ct (1 – vLTvTL)(1 – VlrVrl) – (vTR + VlrVlt)(Vrt + TltTrlX
CL CT(vRT + vLTvRL) + vLTvTL(1 – vLTRvRL)(vRT + vLTvRL) + vRL(vL7(1 – vLTvRL)
(1 – vLTvTL) – ^LT^Th CR vTL(vRT + vltVrL) + vRL(1 – vLTvTLX
CTL vTL(1 – vlrVrl)(Vrt + VltVrL) + vRL((1 – vLRvRL)(1 – vLTvTL) – CtX
CRL FltC1 – vLTvRL)(1 – vLTvTL) – vLTCT
Table 4.3 shows a list of elastic properties of selected wood species, commonly used in the furniture industry.