CIB-W18 Timber Structures – A review of meeting 1-43 2 MATERIAL ...

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Conclusion � All following conclusions apply for the normally used softwoods. � The tensor polynomial failure criterion can be regarded as a polynomial expansion of the real failure criterion. As a consequence, when a least square fitting procedure is used instead of the expansion procedure, a, in principle, complete polynomial up to the chosen degree is necessary (whereby terms of this compound polynomial may vanish by general symmetry conditions). Further this fit by a limited number of terms need not to show the precise right values of the expanded components and need not to pass all mean values of the measurements precisely and also p.e. the normality rule and convexity requirement need not to apply exactly. � In transverse direction a second order polynomial is sufficient to describe the strength. When for compression (perpendicular to the grain) the strength is defined as the value after flow and some strain hardening, a lower bound of the overall strength can be chosen that will be directional independent and the behaviour can be regarded to be quasi isotropic in the transverse direction. � There is a strong indication that for initial yield, or when the tangential plane is determining (as follows from direct measurements and the oblique-grain test), also for the longitudinal strengths a second order polynomial (with F12 = 0) is sufficient as yield criterion. When the test becomes unstable early, at initial crack extension, as for instance in the oblique-grain tension test or for compression in the "Shereisen" test (probably also in the radial plane), there are no higher order terms. Higher order terms thus are due to hardening effects (real hardening or equivalent hardening by crack arrest) depending on the type of test that may provide stable or unstable crack propagation after initial yield. � It is shown that, when the Hankinson parameter n = 2 for tension and compression, all higher order terms are zero. It is probable that this is a general property for timber, because when shear failure is free to occur the plane of minimum resistance, as usually in large timber beams and in glulam, it occurs in the tangential plane, showing no higher order terms. � For clear wood (and wood with small defects), in a stable test, the longitudinal shear strength in the radial plane increases parabolically with compression perpendicular to this plane depending on the coupling term F266 giving the Mohr equation or the Wu- equation, that can be explained by collinear micro-crack propagation in grain direction. This increase is an equivalent hardening effect, due to crack arrest by the strong layers, causing failure only to be possible by longitudinal crack propagation. It is shown that the increase of the shear strength is not due to Coulomb friction, being small for wood. � Because of the oriented crack-propagation, explaining the Wu-equation, F166 ≈ 0 for clear wood because of is in the same direction as the flat crack and thus not influenced by that crack. Except for small clear specimens at compression, (providing a high shear strength by the volume effect), there also is no indication of an influence of the normal coupling terms F12' F122 and F112 (due to hardening by confined dilatation). � For wood with (small) defects and local stress and grain deviations, an equivalent polynomial failure criterion is possible, showing therefore an influence of higher order terms. At least a fourth order polynomial is necessary for a reasonable description. A precise description by a third order polynomial is possible when 2 different criteria are regarded, one for longitudinal tension and for longitudinal compression (similar to the 2 Hankinson equations). � The general form of the criterion for the uni-axial off-axis strength for wood with defects, is at least determined by a fourth degree equation in σt) and can always be factorized as a product of two quadratic equations. This leads to extended Hankinson equations, for higher order terms, when n is different from n = 2. � Because of grain- and stress deviations, F166 will not be zero for timber, as for clear wood, because crack extension along the grain has components in longitudinal and transverse directions when there is a grain deviation and F166 and F266 are connected as components depending on the (local) structure. As crack extension component F166 will show a similar cut-off parabola as F266' indicating the common cause. � For the same reason, the uni-axial tensile strength in the main direction is determined by the shear strength of the oblique material planes and and F112 represents F266 the real material planes, showing the same Wu-parabola. Similar to F166, F122 may act as component in transverse direction of F112. � For wood with defects, when the principal strengths in the main planes (σc = 0) are determining, F112, F12 and F122 are zero, for longitudinal tension (due to early instability of the test). For combined shear failure (equivalent hardening), there are, for this case, small positve values of CIB-W18 Timber Structures – A review of meeting 1-43 2 MATERIAL PROPERTIES page 2.106
F112 and F122. It is however shown that for a practical criterion these terms can be neglected and only F166 and F266 remain for longitudinal tension. � For longitudinal compression at σc = 0, equivalent hardening by crack arrest, (high F112) as well as hardening by confined dilatation (showing a negative F122 and F12) may occur. This last type of hardening probably only occurs in the torsion tube test, because the negative F122 and F12 predict a compression peak that does not occur in the oblique grain test. For structural elements, this effect thus has to be neglected and the lower bound criterion with only F166 and F266 (and zero F12, F122 and F112) applies also for compression in the radial plane as follows from the good fit. � Because in the tangential plane, the higher order terms can be zero, the quadratic polynomial eq. 2 2 � 6 �1 �1 �1 � � � S X X XX 2 � 2 � YY � 2 � 2 � � � Y Y 2 , , , , 1 � should be used as lower bound for the Codes in all cases, for timber and clear wood, and because the equation represents initial yield as well it will apply for the lower 5th percentile of the strength. � For large sized timber and glulam, where shear failure (or longitudinal tensile failure) may pass radial as well as in tangential directions in the same failure plane, the following will apply: 2 � 6 � � 2 �1 � � �1 �� 1 � � � 2 �� 2 � 1 c 2 � � 266 � c , 166 1 1 1 1 1 , � � � � �� , � � � � �� , � S � Y X � � X �� X � � Y �� Y � � where c166 and c266 follows from oblique-grain tests based on the measured Cd and Ct values: F166 = Ct/X' + Cd/X; F266 = Ct/Y' + Cd/Y. � The Norris equations are not generally valid and only apply for uniaxial loading, identical to the Hankinson equation with n = 2, when the right (mostly) fictive shear-strength is used. These equations thus should not be used any more. � Therefore, for tapered beams and for all other cases with determining off-axis uni-axial strength, the general Hankinson equations for tension and compression (with n different from n = 2, depending on the measurements) should be used or the exact equations. 28-6-1 F Lam, H Yee, J D Barrett Shear strength of Canadian softwood structural lumber Abstract An experimental study has been conducted to evaluate the longitudinal shear strength of Canadian softwood structural lumber using a two span five point bending test procedure. Three species groups, Douglas fir, Hemfir and Spruce-Pine-Fir, have been considered. Approximately 40% of the failures can be attributed to shear failures. Two test configurations have been considered: test span to specimen depth ratios of 6 and 5. American Society for Testing and Materials (ASTM) shear block tests have been conducted to evaluate the shear strength of small clear specimens. Based on the ASTM shear block test results, finite element analyses coupled with Weibull weakest link theory have been used to predict the median shear failure loads. Good agreement between predicted and measured median failure loads has been observed. Conclusions An experimental study was undertaken to evaluate the longitudinal shear strength of three species groups of Canadian softwood structural lumber using a two span five point bending test procedure. Two test configurations were studied: span to depth ratios of 6:1 and 5:1. Longitudinal shear type failure was achieved in approximately 40% of the test cases. Based on the ASTM shear block test results, finite element analyses coupled with Weibull weakest link theory was used to predict the median shear failure loads. Predicted and measured median failure loads agreed well with an maximum under prediction error of 13%. CIB-W18 Timber Structures – A review of meeting 1-43 2 MATERIAL PROPERTIES page 2.107
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CONTENT 2.1 COMPRESSION PERPENDICUL
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23-12-4 H Riberholt, J Ehlbeck, A F
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30-17-1 F Rouger A new statistical
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CIB-W18 Timber Structures - A revie
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2.1 COMPRESSION PERPENDICULAR TO GR
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for solid sawn lumber and glulam ha
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The discussion is supplemented by t
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Figure 3. Load-deformation curves f
Page 17 and 18:
The results indicate a clear affini
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which has been already mentioned ab
Page 21 and 22:
served when testing whole CLT panel
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2) The mechano-sorptive effects in
Page 25 and 26:
and codified; optimised strategies
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36-11-1 R H Leicester, C H Wang, M
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For handling of moisture effects in
Page 31 and 32:
- The short-term tests had a mean m
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criteria, they may offer decisively
Page 35 and 36:
Conclusion The relation between the
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the laminations were determined and
Page 39 and 40:
27-12-3 E Serrano, H J Larsen Influ
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shear stress offered by competing s
Page 43 and 44:
e alarmed when a significant check
Page 45 and 46:
Measurement of shear deflections du
Page 47 and 48:
41-12-2 M Frese, H J Blass Bending
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tures". The Centre Technique du Boi
Page 51 and 52:
By setting γG = γQ1 = γQ2 = …
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ment. For instance, extreme distrib
Page 55 and 56: method which was commonly used in c
Page 57 and 58: 2.7 LOAD DURATION 6-9-3 T Feldborg,
Page 59 and 60: son curve", derived from small clea
Page 61 and 62: 19-9-4 U Korin Non-linear creep sup
Page 63 and 64: 24-9-1 T Toratti Long term bending
Page 65 and 66: Summary Based on the analysis of th
Page 67 and 68: when a dry period is followed by a
Page 69 and 70: - Jansson and Leijten both demonstr
Page 71 and 72: - The used methods and technologies
Page 73 and 74: ISO, generally through the technica
Page 75 and 76: ed. The significance of the choice
Page 77 and 78: However, there is another equally i
Page 79 and 80: 25-17-3 D W Green, J W Evans Moistu
Page 81 and 82: tion of settings. Since this proced
Page 83 and 84: posed approach is that the reliabil
Page 85 and 86: Conclusion It was concluded that th
Page 87 and 88: - The difference between E in edge
Page 89 and 90: On the basis of long-term experienc
Page 91 and 92: Conclusions The possibilities of vi
Page 93 and 94: Finland and Norway). Consequences w
Page 95 and 96: Fig. 1. A wind-induced compression
Page 97 and 98: emphasis on the modelling of the ef
Page 99 and 100: some trends are apparent. Based on
Page 101 and 102: - A higher COV of the raw material
Page 103 and 104: Visual grading of wood into strengt
Page 105: 4 X(1 � X) Y �1� X � 3s�1
Page 109 and 110: strength tends to increase with ris
Page 111 and 112: y assuming a normal distribution. E
Page 113 and 114: 19-12-3 F Colling Influence of volu
Page 115 and 116: - WF/Ww: 2:1 The single span three
Page 117 and 118: 40-6-2 M Poussa, P Tukiainen, A Ran
Page 119 and 120: 2.12 SIZE AND CONFIGURATION FACTORS
Page 121 and 122: While the estimates of the size eff
Page 123 and 124: ters for all grades and species. Si
Page 125 and 126: Modelling of length-wise distributi
Page 127 and 128: different things that affect the si
Page 129 and 130: sponds to the statistical approach
Page 131 and 132: fects. As a summary we may, for the
Page 133: More important than the volume effe
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