sin αst

LIST OF ATTACHMENTSSTRUCTURAL ANALYSIS OF BLADES
150
E.2 Mechanical properties
Characteristic values for key mechanical properties of pinus taeda are listed in table E.1
[30, p. 5-2 to p. 5-26]. The stated strengths are ultimate, except for the compressive
strength perpendicular to the grain, which is reported as stress at the proportional limit,
since there is no clearly defined ultimate stress for this property.
Density
[kg/m 3]
Modulus of
elasticity
(EL)
[MPa]
Compressionparallel
to grain
[kPa]
Compression
perpendicular
to grain
[kPa]
Shear
parallel to
grain
[kPa]
Shear
perpendicular
to
grain
[kPa]
Tension
perpendicular
to grain
[kPa]
Tension
parallel
to grain
[kPa]
571 a 13530 b 49200 5400 c 9600 2688 d 3200 c 90400 e
a) The density is calculated from the specific gravity of the wood (Gx = 0.51), based on volume at the
moisture content of 12%: �12 = 1000 kg/m 3 Gx (1 + 0.12) [30, p. 4-10]
b) The modulus of elasticity is determined from beam bending tests, where the deflection is assumed to
be only flexural, i.e. due to compression and stretching of fibres parallel to the axis of the beam.
However shear stresses also contribute to the deflection and to correct for this, the modulus of elasticity
is increased by 10% [30, p. 5-2]
c) Values presented are average of radial and tangential strength
d) Calculated as 28% of the shear strength parallel to grain [30, p. 5-15]
e) Strength is increased by 13% to achieve a value that is valid for 12% moisture content [30, p. 5-26]
Table E.1: Mechanical properties for pinus taeda
Being an orthotropic material twelve constants are needed to describe the elastic behav-
iour of wood: three moduli of elasticity E, three moduli of rigidity G, and six Poisson’s ra-
tios μ. The modulus of elasticity of table E.1 is parallel to the grain and therefore denoted
EL. From this the additional moduli of elasticity and moduli of rigidity, tabulated in table
E.2, are determined [30, p. 5-2].
ET
[MPa]
ER
[MPa]
GLR
[MPa]
GLT
[MPa]
GRT
[MPa]
1055 1529 1109 1096 176
Table E.2: Moduli of elasticity and moduli of rigidity
The three moduli of rigidity denoted by GLR, GLT, and GRT are the elastic constants in the LR,
LT, and RT planes, respectively.
The Poisson's ratios of an orthotropic material are different in each direction. They are
denoted by μLR, μLT, μRL, μTL, μRT, and μTR. The first letter of the subscript refers to direction of
applied stress and the second letter to direction of lateral deformation. Only three of the