CIB-W18 Timber Structures – A review of meeting 1-43 2 MATERIAL ...
CIB-W18 Timber Structures – A review of meeting 1-43 2 MATERIAL ...
CIB-W18 Timber Structures – A review of meeting 1-43 2 MATERIAL ...
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4 X(1 � X)<br />
Y �1� X �<br />
3s�1 accounts for quality and moisture effects by the value <strong>of</strong> s.<br />
For s = 1.67 this is:<br />
2<br />
Y �1� X<br />
The new criterion <strong>of</strong> the Eurocode, is applicable at constant m.c. except<br />
for the highest four grades above 15% m.c. Here s = 2.3 is safe giving: Y =<br />
1 - X/3 - 2X 2 /3.<br />
Because there will always be a linear cut <strong>of</strong>f <strong>of</strong> the failure criterion, a<br />
simple linear approach <strong>of</strong> the parabolic failure criterion is appropriate, and<br />
lines can be drawn through the Y values <strong>of</strong> point X = 0 and point X = 0.5<br />
and the Y values <strong>of</strong> the points X = 1 and X = 0.5 (avoiding too high estimates).<br />
Thus the failure criterion then becomes in general:<br />
1 1<br />
2 2<br />
� � � �<br />
� � � �<br />
Y � c X �1 when X � 0,5 with c � s �1 / 2 � 0,33<br />
c Y � X �1 when X � 0,5 with c � s � 0,33 / s � 0,33<br />
or when smaller: c2 � fm� d / fv,<br />
d�m, d where for rectangular cross sections:<br />
6M<br />
N<br />
Y � ; X �<br />
2 fmbh bhfc,0<br />
26-6-1 T A C M van der Put<br />
Discussion and proposal <strong>of</strong> a general failure criterion for wood<br />
Introduction<br />
Failure criteria, like the Norris, H<strong>of</strong>fmann, Tsai-Wu- criteria etc., can be<br />
seen as forms <strong>of</strong> a polynomial expansion <strong>of</strong> the real failure surface. This<br />
expansion <strong>of</strong> the failure surface in stress space into a polynomial, consisting<br />
<strong>of</strong> a linear combination <strong>of</strong> orthogonal polynomials, provides easily<br />
found constants (by the orthogonal property) when the expanded function<br />
is known, and the row can be extended, when necessary, without changing<br />
the already determined constants <strong>of</strong> the row. When choosing in advance a<br />
limited number <strong>of</strong> terms <strong>of</strong> the polynomial, up to some degree, the expansion<br />
procedure need not to be performed, because the result is in principle<br />
identical to a least square fit <strong>of</strong> the data to a polynomial <strong>of</strong> that chosen degree.<br />
This choice <strong>of</strong> the number <strong>of</strong> terms may depend on the wanted precision<br />
<strong>of</strong> the expansion and the practical use.<br />
Based on this principle <strong>of</strong> a polynomial expansion <strong>of</strong> the failure surface,<br />
the failure criterion is general, satisfying equilibrium in all directions.<br />
A general approach for anisotropic, not orthotropic, behaviour <strong>of</strong> joints,<br />
(as punched out metal plates), and the simplification <strong>of</strong> the transformations<br />
by 2 angles as variables, is given in a paper by Van der Put. A confirmation<br />
<strong>of</strong> the results <strong>of</strong> by means <strong>of</strong> coherent measurements (in the radiallongitudinal<br />
plane) and the generalization to an equivalent, quasi homogeneous,<br />
failure criterion for wood with small defects, showing, as will be<br />
discussed here, a determining influence <strong>of</strong> crack propagation on the equivalent<br />
main strengths, There thus is no reason to maintain the used invalid<br />
approximations and to not apply this consistent criterion, also for the<br />
Codes, for all cases <strong>of</strong> combined stresses. Thus far only this criterion gives<br />
the possibility <strong>of</strong> a definition <strong>of</strong> the <strong>of</strong>f-axis strength <strong>of</strong> anisotropic materials.<br />
<strong>CIB</strong>-<strong>W18</strong> <strong>Timber</strong> <strong>Structures</strong> <strong>–</strong> A <strong>review</strong> <strong>of</strong> <strong>meeting</strong> 1-<strong>43</strong> 2 <strong>MATERIAL</strong> PROPERTIES page 2.105