The Compressive Stress-strain Relationship of Timber

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1 The Compressive Stress-strain Relationship of Timber Jin-Ky Song,a, Sn-Yong Kim 2,b, and Sang-Won Oh 3,c Department of Architectral Engineering, Chonnam National University, Gwangj , Soth Korea 2 Korea Engineering&Consltant, Gwangj, Soth Korea 3 Department of Architectral Engineering, Chonnam National University, Gwangj , Soth Korea a jgsong@chonnam.ac.kr, b sny90@hanmail.net, c xing2@hanmail.net ABSTRACT The prpose of this stdy is to analyze the compressive behavior of timber and to model the compressive stress-strain relationship of timber mathematically. In the Ultimate Strength Design Method or the Limit State Design Method, stress-strain relationship has a big effect on design vale. Therefore it is very important above all things to discover compressive stress-strain relationship of timber. The strength and Yong's modls of timber is affected by species of trees, degree of growth, moistre content, specific gravity and so on and the deviation is large. For that reason when compressive load work on timber parallel to grain, maximm strength, Yong's modls, and ltimate strain in the maximm load can show differently according to grade and varios factors. Bt this stdy limits coniferos machine grade to E7, and ses moistre content and specific gravity for parameter. The compressive stress-strain relationship shows differently according to destrction type, and general destrction type is Wedge-Splitting destrction. The nmerical formla is proposed in Ascending Part and Descending Part by sing bilinear line. KEYWORDS: stress-strain relationship, moistre content, specific gravity. INTRODUCTION. Prpose and Scope of Stdy Since environmental isses have become the center of the world, researches on eco-friendly architectre materials to sbstitte for concrete have lively condcted. Wood is a typical eco-friendly material and shold be sed for a member design after definitely defining material properties. The allowable stress design method which is crrently sed for wood in Korea has a non-economic problem de to its relatively high safety of maximm stress. However, becase it is cased by wood's own properties sch as nevenness and water vlnerability nlike iron, maximm stress and maximm strain, as well as correlation between stress and strain in the state of compression shold be definitely defined. Once correlation between stress and strain is definitely defined, accrate and economic design is possible. Accordingly, the prpose of this stdy was to examine correlation between compressive stress and strain in wood and model mathematically. Althogh correlation between stress and strain in wood may vary with a variety of factors, this stdy tested by placing moistre content and specific gravity that can have a great effect as variables, and limited wood to machine grade E7 of a coniferos tree. Then, a compressive test method for wood was considered, and behavioral characteristics in elastic and plastic areas associated with failre patterns were examined. 977

2 2. A THEORITICAL APPROACH 2. Relationship between Compressive Strength, Specific Gravity, and Moistre Content in Wood Fiber satration point(fsp) refers to the state that althogh the cell walls of wood are fll of bond water, there is no free water in the cell lmen. The specific gravity, weight, and strength of wood greatly vary with moistre content condition based on FSP. The specific gravity of wood is indicated as actal weight of wood against wood volme on condition of any moistre content, that is, the rate of oven dry weight of wood. Below FSP, while volme decreases as moistre content becomes lower, over dry weight is constant, so the specific gravity of wood becomes higher with a decline in moistre content. Also, as wood becomes higher in specific gravity, actal amont of wood against certain volme increases and its textre becomes tight, so strength increases with the increase in specific gravity in general. 2.2 Stress- Relation Models In the compressive area, one of the simplest stress-strain relation models is the bilinear elastic-plastic model. This model was first proposed by Neely and nonlinear stress-strain behavior was observed(fig. (a)). Bazan sggested revised bilinear elastic-plastic stress-strain relation. He sggested the model that stress-strain relation is linear p to the proportional limit, bt stress redces to the linear with the increase in strain(fig. (b)). Fig. (c) and (d) show stress-strain relation models sggested by Malhotra and Mazr and Glos. f c f c me α E r = tanα f s me (a) Neely (b) Bazan (c) Malhotra (d) Glos Figre. Stress-strain relationship models β E = tanβ tan E 3. COMPRESSIVE TEST 3. Specimen Making The size of specimen was 50mm 50mm in cross section according to ASTM D43 and the length of fiber was 200mm. To indce reliable compression failre in ASTM, failre shold occr in the test section. To achieve this, it is indicated that it is more favorable that the moistre content of specimen end is lower than that of the center. However, since, in reality, it is very difficlt to lower moistre content only in the end, as shown in Fig. 2, we reinforced the end with a carbon fiber to indce failre within the test section. (b) Measring and the (a) Ctting a carbon (c) Adhesion of a carbon mixtre of main fiber fiber materials and admixtre Figre 2. Reinforcement of a carbon fiber to the specimen (d) Cre 978

3 Table. Specimen scheme Name Section Length Specific Gravity (g/cm 3 ) Moistre Content (%) Name Section Length Specific Gravity (g/cm 3 ) Moistre Content (%) SR SR SR SR SR SR SR SR SR SR SR SR SR SR SR SR SR SR SR SR Test Method As shown in Fig. 3, a moistre content meter was sed to measre moistre content, and an atomatic balance which can measre p to max. 500g was sed to measre specific gravity. For actation and measrement, althogh it is prescribed in ASTM that strain shold be 0.003mm/mm per minte, this test selected the drift control method and was condcted in the way of atomatic save sing UTM of 500kN and data logo. (a) Measrement of (b) Measrement of (c) Actation and measrement moistre content specimen weight Figre 3. Measrement of specimen and actation and measrement 4. TEST RESULTS 4. According to ASTM, fiber-directed compression failre patterns of wood were classified according to its shape as shown in Fig.4. The test reslts sggest that there were classified failre modes. Table 2 shows the analysis of test reslts. (a) Crshing (b) Wedgesplitting Figre 4. Compression failre patterns (c) Shearing (d) Splitting (e) Compression & Shearing (f) Brooming or End-Rolling 979

Table 2. Test reslts Name ( 0-6 ) p ( 0-6 ) ( 0-6 ) p (MPa) E (GPa) Failre Type SR 0 4887 379 0 0.75 42.2 6.47 Splitting+Shearing SR2 0 3335 9848 0 0.7 45.72 9.76 Wedge-Split SR3 0 3776 2574 0 0.

4 Table 2. Test reslts Name ( 0-6 ) p ( 0-6 ) ( 0-6 ) p (MPa) E (GPa) Failre Type SR Splitting+Shearing SR Wedge-Split SR Wedge-Split SR Shearing+Splitting SR Wedge-Split SR Shearing SR Wedge-Split SR Shearing SR Wedge-Split SR Wedge-Split SR Crshing SR Shearing+Splitting SR Splitting+Shearing SR Shearing SR Compression & Sheaing SR Wedge-Split SR Shearing+Splitting SR Shearing+Splitting SR Shearing SR Wedge-Split Notes) : initial strain, ltimate stress p : proportional limit strain, : ltimate strain, 4.2 Stress- Relation Associated with Failre Patterns : initial stress, p : proportional limit stress, : As a reslt of the test, crve patterns of stress-strain varied with failre patterns. Fig. 5(a) shows wedge-splitting failre, Fig. 5(b), shearing failre, Fig. 5(c), crshing failre, and finally Fig. 5(d), splitting-shearing failre. (a) Wedge-splitting (b) Shearing 980

5 (c) Crshing (d) Splitting-shearing Figre 5. Stress-strain relation associated with failre patterns 5. SUGGESTION OF STRESS-STRAIN EQATION In this stdy, the Bazan model eqation was sed becase it is the most common and easy to indce. As seen in the Figre, the wedge-splitting failre pattern which is the most common of several failre patterns was sed as a basic model. Ascending Part STRESS = β X () Y Descending Part = β 2 X + α Y (2) STRAIN Figre 6. Proposed stress-strain model In Fig. 6, ascending and descending parts can be expressed as straight lines as shown in Eqation () and (2) respectively. If we sbstitte ltimate strain( ) into Eqation () and (2), Eqation (3) is given, and finally we can find ltimate strain( ) and ltimate strength( ) throgh Eqation (4) and (5). β = β2 + α (3) α = (4) ( β β 2) αβ = (5) m ( β β 2) If we sbstitte data shown in Table,2 into Eqation (4) and (5) and express each coefficient as parameter abot moistre content and specific gravity, the following eqation can be given. Ascending Part = β ( ) (6) 2 3 ( β = 360( mc) ( mc) ) (7) 98

6 Descending Part = α + β 2 ( ) (8) ( α =.5( mc) + 250( sg) 60) (9) 3 3 ( β 2 = 20( mc) ( sg) ) (0) Notes) mc : moistre content, sg : specific gravity 6. CONCLUSION The analysis of transfer characteristic by compression test sggests that wood with compression load had very dctile behavior. Also, compression failre patterns were similar to those defined in ASTM D43, and stress-strain crves varied with the failre patterns. Wedge-splitting failre was the most common. Since model eqations proposed in consideration of moistre content and specific gravity generally predicted test reslts well, they can be flly sed as basic materials for strctre interpretation. ACKNOWLEDGMENTS This work was spported by the Korea Research Fondation Grant fnded by the Korean Government(MOEHRD)" (The Regional Research Universities Program/Biohosing Research Institte) REFERENCES Architectral Institte of Korea, Korean Bilding Code 2005 Timber constrction manal, fifth edition, American Institte of Timber Constrction Korean Indstrial Standard (KS F 2206, KS F 2208),2004 ASTM Designation : D43-94 Andrew H. Bchanan, Bending Strength of Lmber. Jornal of strctral Engineering, Vol. 6, No.5, May, 990 T. E. Conners, Appleton WI, Segmented models for stress-strain diagrams. Wood Science and Technology.23,pp Bostroem L, The stress-displacement relation of wood perpendiclar to the grain. Wood science and technology,v.28 no.5,994,pp.39- Wilson wal shingla, Strength model and finite element analysis of wood beam colmns in trss applications 982

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