SHEAR PROBLEMS IN TIMBER ENGINEERING ANALYSIS AND SOLUTIONS

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1 SHEAR PROBLEMS IN TIMBER ENGINEERING ANALYSIS AND SOLUTIONS Ernst Gehri ABSTRACT: Actual knowledge in shear behaviour has not been enough considered in engineering practice, resulting in avoidable failures. Reason for that is an inadequate basis of actual shear values in the Codes, without consideration of real design situations. In the paper are presented factors which have major influence on the shear behaviour: test configuration, size or volume, moisture content and temperature. Proposals are made for a more realistic approach. KEYWORDS: Shear failure, size effect, test configuration, moisture content, temperature 1 INTRODUCTION Wood like all layered materials shows in shear, compared to the lengthwise properties (parallel to the grain), a very weak and brittle behaviour. Due to this brittle behaviour the size effect on the characteristic shear strength is strong. This is not enough considered in actual design procedures. As a result lot of failures in timber structures are initiated by shear. Shear problems may be reduced by: - more appropriate and realist design values - use of wood species with higher shear capacity - use of engineered products with cross-linked composite configuration. 2 PRINCIPLES FOR THE DESIGN 2.1 GENERAL Principles for the design of timber structures are laid down e.g. in the Eurocodes. There is written, that the design models shall take in account: - material properties (e.g. modulus of elasticity, strength and failure mode) - time dependent behaviour of the materials - climatic conditions for the materials (temperature, moisture and variations) - design situations. 2.2 MATERIAL PROPERTIES Material properties like strength and stiffness parameters to be used in the design shall be determined: - on the basis of tests - for the types of action effects which the material will be subjected in the structure. The last requirement a very important one has in the past often been overlooked. Inadequate material properties may lead to unsafe design and construction. Ernst Gehri: Im Lindengut 13, 8803 Rüschlikon, Switzerland, gehri@emeritus.ethz.ch 2.3 EXAMPLE FOR DESIGN SITUATION In Figure 1 are shown two similar design situations. The beam elements are the same, the only difference consists in the way of load introduction: in case (a) are acting compression forces, in case (b) tensile forces. In any case the equilibrium is fulfilled and the resulting shear force in the beam is the same. Figure 1: Design situations for a beam (same shear force and diagram); load introduction by glued-in bars Questions: Do we have the same shear capacity? Do we have for these two design situations the correct strength and stiffness parameter for the action shear? Can we use the same materials properties? For which test situations or test configurations are the properties determined? 3 MATERIAL PROPERTY: SHEAR 3.1 GENERAL Frequent design situations are beams subjected to shear forces (see Figure 1). Shear failure occurs longitudinal (longitudinal shear or shear parallel to the grain). The shear values to introduce are given in EN338 for sawntimber or EN1194 for glulam. In both cases possible cracking may be considered, by the introduction of a crack factor. The values are based on dry material (normal climate: 20 C and 65% relative humidity) Remark: Background of an elementary (and not new) property like shear seems not to be so clear!

2 3.2 SHEAR STRENGTH AND TIMBER SPECIES In older structures most connections were based on the shearing strength of the timber. Experience had shown the better behaviour of hardwoods in relation to shear strength and stiffness compared to softwoods. For keys and dowels higher performing hardwood like oak was commonly used. It is therefore astonishing to see that meanwhile and based on erroneous research the shear capacity and stiffness of softwoods has increased and on the other side of hardwoods decreased (see EN338). Note: Shear tests according to EN408 are done on a defect free material called wood and not on lumber or timber available for structural use. According to EN338 the shear strength and stiffness of softwood boards C40 and ash boards D50 are the same: - shear strength: f v,k = 4,0 N/mm 2 - shear modulus: G mean = 0,88 kn/mm 2. Own tests made on glued-laminated timber using spruce laminations C40 and ash laminations D50 showed striking differences. 3.3 SHEAR AND CRACKS In sawn timber of larger section cracks due to drying are unavoidable. Only by splitting up the log into smaller sections like boards and using an adequate drying procedure cracks may be reduced or avoided. The reason for that is that the piece can more easily deform without cracking; unequal shrinkage causes warp. In glued-laminated timber and adequate grading of the laminations only minor cracks, which can be disregarded, may appear. The introduction of a crack factor for glulam is therefore not justified. The problem is here, that the characteristic values fixed in EN1194 are too high, and can not be reproduced by tests. Instead of correcting the shear values an artificial crack factor was than introduced. After years of service more intense cracks and in glulam also delaminations are appearing (see Figure 4). This is on one side a matter for quality assurance and on the other side of material aging. Table 1: Shear properties of spruce and ash (mean not characteristic values) Glulam laminations Shear strength N/mm 2 Shear modulus kn/mm 2 Spruce: C40 Ash: D50 3,6 6,7 0,65 1,10 Factor: ash/spruce 1,9 1,7 The shear strength is based on tests with beams of 120/480 mm and a shear area A shear = mm 2. The load configuration can be seen from Figures 2 and 3. The shear modulus is directly determined from the measurement of the shear deformation in each panel. Figure 2: Shear-beam test configuration; dimensions Figure 3: Test at neue Holzbau Figure 4: A near 100 years old glued-laminated arch with large zones of open glue-lines The residual shear strength of such an element was experimentally evaluated. About 1/3 of the nowadays required material property was achieved, still enough for an arch type structure. A similar reduction was found on the shear modulus. To have a better insight in the influence of cracks, a series of artificial cracked beams has been tested. Only the inner 1/3 of the lamination with was glued (the outer 2/3 s of the beam section 120/480 mm remained unglued or open). The mean shear strength was about 2 N/mm 2 or more than 50% of an uncracked similar girder.

3 Figure 5: Artificial cracked beams 3.4 SHEAR AND MOISTURE CONTENT Shear properties are based on tests made at normal climate, e.g. 20 C and 65% relative humidity, which lead to about a moisture content of 12%. In service class 2 the average moisture content can vary between 12 and 20%, but it is accepted that it may exceed 20% a few weeks per year. With increasing moisture content the resistance against internal slipping of one part upon another along the grain decreases. The shear strength for moisture content between 12 and 20% decreases by 2.5% per 1% increase of moisture content. f v,w% = f v,12% [ (w 12%)] (1) The same reduction can be applied on the shear modulus. The relationship is based on tests with clear wood [1]. Since the shear properties are quit not influenced by the timber quality (knots may even have a positive effect) the relationship is generally valid. The effect of moisture content on shear has been confirmed on shear block tests [2] and on finger-joints tested in tension [3]. In both cases shear is a determinant property for the load transmission. Since shear is affected by moisture content, higher moisture in the finger-joint decreases the tensile strength of the joint. The result is also a decrease of bending strength of the glued-laminated timber: in service class 2 a reduction of about 20% should therefore be considered. 3.5 SHEAR AND TEMPERATURE Higher temperature leads to a softening of the wood structure, resulting in a reduction of strength and stiffness. A good approximation (for the range 20 C to 100 C) is given by equation (2). f v,t = f v,20 [1 0,0038 (T -20 )] (2) It is practice to accept, that no reduction is needed up to 50 C, even though the difference is more than 10%. This must therefore be covered by the partial factor for material properties γ M. The reason for this practice is the small influence on the bending strength, material propriety which is only used for the timber strength classification. 3.5 TO SUM UP Moisture and temperature have on the shear properties major influence. For service class 2 where higher moisture and temperature (than occurring in the test values based on climate 20 C and 65% r.h.) may occur and are admitted, a reduction on shear strength and stiffness should be provided for. It is recommended to reduce the values by 20%. Cracks reduce strength and stiffness. The degree of cracking is not assessable to a direct measurement. An indirect way would be to measure the shear stiffness and based in a similar relationship between modulus of elasticity and tensile strength to obtain indications about the level of cracking and about the shear strength. Naturally as for tensile strength other factors additionally affect the shear strength. 4 TEST CONFIGURATION 4.1 TEST CONFIGURATION IN EN408 The actual test configuration in EN408 can only be applied with defect material and small size. Effectively the material tested is wood and not timber. The results may not be used directly, only the relationship. Furthermore the test results not to real shear, but to a combination of shear and compressive stress perpendicular to the grain (see Figure 6). Figure 6: Combination of shear parallel to the grain and compressive strength perpendicular to the grain 4.2 SHEAR-BEAM TESTS Bending test configuration was created to obtain bending failures and eliminate as possible other failure modes like shear: for sawn timber normally with span to depth of 18, for glulam often with reduced side spans (4.5 h instead of 6h). Through better grading higher bending strength is achieved, but not higher shear strength (in the contrary the defect free material shows lower shear strength). As a result increasing number of shear failures are occurring in bending tests. This may be frustrating for establishing bending values, but very interesting in regard to shear. We obtain here representative shear values (lower values of the shear distribution).

4 In the same way as for bending, where shear failures may be avoided by a correct relationship shear to bending, we may avoid bending failures by fixing another relationship. As a result we will obtain a beam with the following geometry: 4.3 SIZE OR VOLUME EFFECT Knowing the very brittle behaviour at failure state, an important size effect must be expected. One of the most extensive research data was done in Canada by Longworth in 1977 [4]. As reference were proposed shear area and shear volume. Reanalysing the test data and taking in consideration the moisture content of the specimens, the following relationship can be used: f v, mean = 100 A shear -0,28 (3) where f v, mean = shear strength in N/mm 2 and A shear = shear span area, as defined in Figure 9, in mm 2. Figure 7: Specimens geometry: (a) for bending with a = 4.5 to 6 h; (b) for shear with possible bending; (c) for shear with a about 1.5 to 2h Knowing (see 4.3) the great influence of size on the shear strength (much greater than for bending) there is an imperative requirement to declare the size of the test specimens or refer the value to a so-called reference size or reference shear-beam (in analogy to the reference bending beam). Figure 9: Definition of shear span area 7 Longworth (equ.3) and own results shear strength in N/mm^ Figure 8: Reference shear-beam (dimensions) Test configuration has to be as near as possible to the problem envisaged: from point of view of material (similar as possible in the structure) as for the way the forces are acting. The load introduction has been done usually by compression perpendicular to grain. This results in very large (long) plates; the effective shear field (with high constant stress) is much smaller than the geometric one. The shear strength is only valid for the smaller shear area or volume (see 4.3). Such long supports are in practice unrealistic. The loads are introduced more concentrated using large screws or glued-in rods. This should therefore also be considered in the test configuration. In the test procedure easily the measurement of the shear stiffness may be included (shear modulus can also be obtained in normal bending tests) shear area in *10^3 mm^2 Figure 10: Influence of shear span area on the shear strength Note that the tests were made on new beams (without drying cracks). For the reference size (see Figure 8) mean shear strength of about 3.5 N/mm 2 is obtained. 4.4 INFLUENCE OF LOAD INTRODUCTION By the use of glued-in rods it is easily possible to examine the effect of different cases of load introduction (see Figure 11). A series of 4 beams with the configuration (a) and (c) were tested. The beam depth was 480 mm; the shear panel quadratic. The test configuration (c) or ZZ-configuration showed lower shear strength of about 15% compared to the test configuration (a), usual test condition. The result was expected and confirmed the formulation given in Swiss Code SIA 265:2003 for shear combined with normal stresses perpendicular to the grain.

5 Figure 11: Cases of load introduction 4.5 CONTINUOUS BEAMS Earlier statements Based on the commonly simplified design of beams the following will be found when going from the singlespan with central concentrated load F to the double span beam (see Figure 12): - if bending determinant: 1/3 more load - if shear determinant: about ¼ less load. - Leicester/Young (1991) [6] Shear strength tends to be more important in the design of continuous rather than single span beams. Because of this, there has been a proposal in Australia, that double span test specimens should be used for ingrade shear strength measurements. However, in some recent studies using LVL (laminated veneer lumber), some anomalies were noted in short-span shear tests, including the fact that shear failures appeared to be inhibited in double-span tests. These findings let the Authors a little perplex and they concluded: However, it is already obvious from the test results, that some modification to conventional structural theory needs to be made in the case of design for the shear strength of continuous beams. - Sanders (1996) [7] Sanders (1996) and Rammer et al (1997) proposed to change the common shear test on single span (3-point test configuration) to a double-span configuration (or 5-point test). Only by such a test configuration realistic shear values (higher values without possible influence of end cracks) could be obtained point-configuration versus 3-point Fortunately the findings of Egner were never introduced in the Codes; about the modification of the conventional structural theory nothing was more heard about from by Leicester/Young; only the 5-point test configuration is still alive. Therefore only this point will be discussed. The protagonists showed that the shear strength obtained is higher and therefore should better correspond with the true shear value. Figure 12: Single versus double-span beam The following are the load carrying capacities: on shear: F v,single = 1,33 (b h f v ) F v,double = 0,97 (b h f v ) on bending: F m,single = 0,111 (b h f m ) F m,double = 0,148 (b h f m ) These findings seem not to be covered by test results. Therefore many researchers conclude that the continuity over the middle support might be the reason. Three researchers and their statements are cited below. - Egner (1958) [5] It seems justifiable to allow over the continuous support higher shear design values, e.g. the double of those admissible for end supports. Figure 13: Test configuration according to [7] The test were made as usually by introduction of the loads on compression perpendicular to the grain, resulting in large or long plates to reduce possible crushing. Comparing directly the failure loads F single to F double it was found that F single F double, as can bee seen in Figure 14 (which is not in accordance to the classical approach as presented in Figure 12). In Figure 14 are given the loads in function of a relative shear volume; this is possible since the dimensions of plates for load introduction were chosen proportional to beam size. The differences in shear strength between 5-point to 3-point are justified by the absence of drying checks (end splits) in the central part

6 of the beam. Unfortunately the same relationship can be found for wet beams, as can be seen from Figure 14. relative shear capacity relative shear volume Figure 14: Analysis of [7] based on failure loads: upper curves for dry beams; lower curves for wet beams (blue for 5-point and red for 3-point test configuration) A look on Figure 14, were the dimensions are drawn true to scale, show the unrealistic small volume of the beam subjected to shear and the much smaller volume tested in the 5-point configuration compared to the 3- point configuration. In view of the large size effect as presented in 4.3 and the incorrect calculation of the central reaction (without taking in consideration for the analysis the shear deformation) no justification for the 5-point configuration is found Own tests It may be disappointing that 2 single-span beams have higher shear capacity than a double-span beam. By connecting rigidly over the support the two single-span beams the shear capacity will decrease, whereas the bending capacity and the stiffness will increase. beam showed clearly, that 3-point testing is still an adequate test configuration for shear. Furthermore it could be shown that the shear strength by relating to the same shear span area is independent of the system used (single-span or double-span), if the same load introduction direction is applied (see 4.4). 5 CONCLUSIONS It is amazing (for not to saying unbelievable) that such a fundamental timber property like shear is not proper defined. - Need for a test configuration which takes in consideration the predominate type of action and the material to be applied. Use structural timber instead of wood and a shear-beam configuration. - Need for a reference size (or reference sizes for sawn timber and glulam). Shear values are strongly size dependent; therefore relationships for other sizes needed. - Need for a better defined shear field for testing using glued-in bars (or large screws) for the introduction of the loads. - Need for modification factors for other climate conditions than 20 and 65% relative humidity: for other moisture contents and for higher temperatures up to 60 C. - Show the way to measure directly the shear or angular deformation and from that the easy and simple determination of the shear modulus. - Use the shear stiffness as indicator of the extent of the cracking; this using a similar relationship as between modulus of elasticity and strength parallel to the grain. - Need for corrective indications for other load applications. Proposals where made to establish reliable strength and stiffness values on shear. ACKNOWLEGMENT Thanks goes to the neue Holzbau AG, Lungern for all the support and to my friend Peter Haas for preparing and testing most of the specimens. Figure 15: Tests on continuous beams at neue Holzbau Own tests with measurement of the shear deformation (which is linear correlated through the shear modulus to the shear stress and shear force) made on the same beam once as single-span and once as continues REFERENCES [1] Wood Handbook. Forest Product Laboratory.1987 [2] Gehri E.: Einfluss der Feuchte auf die Druckscherfestigkeit verklebter Proben. Interner Versuchsbericht [3] Gehri E.: Feuchteinfluss auf Festigkeit Zugfestigkeit von Keilzinkenverbindungen. Interner Versuchsbericht [4] Longworth J.: Longitudinal shear strength of timber beams. Forest Prod. J. 27(8), p [5] Egner K.: Belastungsversuche mit durchlaufenden geleimten Holzbalken in I-Form. Bauen mit Holz 18, S [6] Leicester R.H. and Young F.G.: Shear strength of continuous beams. CIB-W18/ Oxford 1991 [7] Sanders C.L.: The effects of testing conditions on the measured shear strength of wood beams. Washington State University, Pullman