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Time and size effects for tension perpendicular to grain in wood Mau, Tak Jee 1976

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TIME AND SIZE EFFECTS FOR TENSION PERPENDICULAR TO GRAIN IN WOOD by TAK JEE MAU B. Sc. i n C i v i l Engineering Washington State University, 1973 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in the Department of CIVIL ENGINEERING We accept t h i s thesis as conforming to the required standard The University of B r i t i s h Columbia April, 1976 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y available f o r reference and study. I further agree that permission f o r extensive copying of t h i s thesis f o r scholarly purposes may be granted by the Head of my Department or by his representatives. It i s understood that copying or publication of t h i s thesis f o r f i n a n c i a l gain s h a l l not be allowed without my written permission. Mau, Tak Jee Department of C i v i l Engineering The University of B r i t i s h Columbia 2075 Wesbrook Place, Vancouver, Canada V6T 1W5 A p r i l , 1976 i ABSTRACT F a i l u r e of pitched-tapered glulam beams i n t e n s i o n perpendicular to g r a i n has been a t t r i b u t e d to the inadequacy of the present method of c a l c u l a t i n g s t r e s s e s . In t h i s t h e s i s , the f a c t o r s of time and s i z e f o r t e n s i o n perpendicular to g r a i n were i n v e s t i g a t e d to determine how they would a f f e c t the allowable s t r e s s e s . A t o t a l of 229 Douglas F i r glulam blocks of two s i z e s were loaded f o r ?0 days i n uniform t e n s i o n perpendicular t o g r a i n to i n v e s t i g a t e time e f f e c t . Test data were analyzed by developing estimates f o r the s t r e n g t h r a t i o s . R e sults i n d i c a t e that s t r e n g t h reductions increase at an i n c r e a s i n g r a t e w i t h the log a r i t h m of time. The p r e s e n t l y used time f a c t o r s were shown to be conservative and could be increased f o r the 2-month, the 7-day and the 1-day d u r a t i o n s . Experimental data a l s o i n d i c a t e that the present time f a c t o r s may be non-conservative f o r load dur a t i o n s l e s s than 5 minutes and more than ?0 days. In a d d i t i o n , short-term t e s t i n g of 24-0 Southern Pine glulam blocks of three s i z e s was performed to i n v e s t i g a t e s i z e e f f e c t . R e sults show that the r e l a t i o n s h i p between specimen strength and volume i s a s t r a i g h t l i n e i n a l o g . - l o g . p l o t , thus v e r i f y i n g the weakest-link model f o r Southern Pine. Comparison w i t h Douglas F i r data taken from l i t e r a t u r e was a l s o made. I t was found that Southern Pine i s d e f i n i t e l y 11 stronger than Douglas F i r In tension perpendicular to grain. Size e f f e c t , however, i s almost i d e n t i c a l f o r the two species. S i g n i f i c a n t difference was observed i n the long-term test r e s u l t s between the two specimen volumes. This may be due to the e f f e c t of siz e , but i t could also be caused by the d i f f e r e n t stress l e v e l s used f o r the two volumes. i i i TABLE OF CONTENTS Page A b s t r a c t i Table of Contents i i i L i s t of F i g u r e s v L i s t of Tables v i i Acknowledgment v i i i Chapter One : I n t r o d u c t i o n 1 1. 1. The Problem 1 1. 2. O b j e c t i v e s 2 1. 3. Scope 3 Chapter Two : Background and The o r i e s 4 2. 1. ^  E f f e c t of Load D u r a t i o n - Madison Test ... 4 2. 2, Recent Research 5 2. 3. E f f e c t of S i z e - Weakest-Link Model ...... 6 Chapter Three : Planning and P r e p a r a t i o n 9 3. 1. O u t l i n e of T e s t i n g Approach 9 3. 2. Other C o n s i d e r a t i o n s 10 3. 3. P r e p a r a t i o n of Test M a t e r i a l 12 Chapter Four J Method of T e s t i n g 15 4. 1. Mounting Devices 15 4-. 2. Short-term Test Method 16 4. 3. Long-term Test Setups 17 4. 4. Long-term Test Method 17 Chapter F i v e : Test Data f o r Time E f f e c t 20 5. 1. Method of Ranking 20 5. 2. C o n t r o l Data 21 5. 3. S u r v i v a l Rate 22 5. 4. Str e n g t h R a t i o - C o n t r o l Curve Method .... 23 5. 5. St r e n g t h Reduction wi t h Time 26 5. 6. S i z e E f f e c t 27 5. 7. Comments on C o n t r o l Curve Method 27 5. 8. Str e n g t h R a t i o - S t r a i g h t Line Method .... 28 5. 9. Comparison between the Two Methods 30 5.10. Average St r e n g t h R a t i o v s . Time Curves.... 30 5.11. Conclusions 32 i v Page Chapter S i x J T e s t Data f o r S i z e E f f e c t 34 6. 1. Short-term S t r e n g t h Data 34 6. 2. Log. Str e n g t h v s . Log. Volume 35 6. 3. Douglas F i r Data 3& 6. 4. Conclusions 38 Chapter Seven s M i s c e l l a n e o u s Observations 39 7. 1. Modulus of E l a s t i c i t y 39 7. 2. Moisture Content 40 7. 3. Mode of F a i l u r e 40 7. 4. Creep 43 Chapter E i g h t t D i s c u s s i o n and Summary „ 46 8. 1. Time E f f e c t 46 8. 2. R e l a t i o n of Southern Pine R e s u l t s to ASTM ( S i z e E f f e c t ) 47 8. 3. Allowable S t r e s s e s - Southern Pine 49 8. 4. Summary 52 L i s t of References 103 v LIST OF FIGURES Page 1. Pitched-tapered Glulam Beam 53 2. Madison Test 54 3. Specimen Configuration 55 4. Specimen Mounting Devices 56 5. Test Setup f o r Large Specimens 57 6. Test Setup f o r Small Specimens 58 7. Short-term Strength - Douglas F i r 59 8a. Survival Rate f o r Large Specimens 60 8b. Survival Rate f o r Small Specimens 6 l 9. Strength Ratio - Control Curve Method 62 10a. Strength Ratio vs. Time (large) - Control Curve Method 63 10b. Strength Ratio vs. Time (small) - Control Curve Method ... o 64 11a. Ranked Data at 168 p s i (large) 65 l i b . Ranked Data at 138 p s i (large) 66 11c. Ranked Data at 125 p s i (large) 67 12a. Ranked Data at 358 psi (small) 68 12b. Ranked Data at 277 p s i (small) 69 12c. Ranked Data at 226 p s i (small) 70 13. Strength Ratio - Straight Line Method 71 14a. Strength Ratio vs. Time (large) - Straight Line Method .. 0 72 14b. Strength Ratio vs. Time (small) - Straight Line Method 73 15. Average Strength Ratio vs. Time 74 16a. Short-term Strength - Southern Pine (large) 75 v i Page 16b. Short-term Strength - Southern Pine (medium) 76 16c. Short-term Strength - Southern Pine (small) 77 17. Short-term Strength - Southern Pine Combined Samples 78 18. Volume-Strength Relationship 79 19a. Typical Load-Deflection Plots - Douglas P i r 80 19b. Typical Load-Deflection Plots - Southern Pine 81 20a. Stress-Strain Plots - Douglas F i r 82 20b. Stress-Strain Plots - Southern Pine .............. 83 21. Typical Failures 84 22a. Long-term Deflection at 168 psi (large) 85 22b. Long-term Deflection at 138 psi (large) 86 22c. Long-term Deflection at 125 p s i (large) 87 22d. Long-term Deflection f o r Small Specimens 88 23a. "Creep" at 168 psi (large) 89 23b. "Creep" at 138 psi (large) 90 2 3 c "Creep" at 125 psi (large) 91 23d. "Creep" f o r Small Specimens 92 24. Time Factors 93 v i i LIST OF TABLES Page 1. S u r v i v a l Counts - Douglas F i r 9^ 2a. Strength Data - Short-term t e s t s 95 2b. S t r e n g t h Data - Southern Pine combined samples .. 96 3. C o e f f i c i e n t s of Regression Equation 97 4. Parameters f o r W e i b u l l D i s t r i b u t i o n s 97 5. Modulus of E l a s t i c i t y 98 6a. Moisture Content - short-term t e s t samples 99 6b. Moisture Content - Douglas F i r long-term t e s t samples ... 100 7a. F a i l u r e Type Counts - short-term t e s t samples ... 101 7b. F a i l u r e Type Counts - Douglas F i r long-term t e s t samples ... 102 ACKNOWLEDGMENT The author wishes to thank his supervisor, Professor Borg Madsen, f o r h i s many suggestions and encouragement i n the development of t h i s thesis. Valuable ideas and remarks from Dr. J.D. Barrett i n the writing of the thesis are very much appreciated. Special thanks also go to the technical s t a f f of the Structures Laboratory, University of B r i t i s h Columbia, f o r the i r assistance i n building the test apparatus. A p r i l 1976 Vancouver, B.C. 1 CHAPTER ONE  INTRODUCTION Pitched-tapered, glulam beams ( F i g . 1), when subjected to v e r t i c a l l o a d s , develop s i g n i f i c a n t t e n s i o n p e r p e n d i c u l a r - t o -g r a i n s t r e s s e s a t the m i d - s e c t i o n of the beam. These s t r e s s e s have caused f a i l u r e s i n beams made of Douglas F i r . However, no such f a i l u r e s have been r e p o r t e d i n beams made of Southern Pine. These f a i l u r e s have caused the method of p i t c h e d - t a p e r e d beam d e s i g n t o be que s t i o n e d . 1.1. The Problem When the f a i l u r e s f i r s t occurred i n 1965t two aspe c t s were questi o n e d . The f i r s t was a l a c k of an a c c u r a t e s t r e s s a n a l y s i s method. In t h i s r e s p e c t , F o s c h i ( l ) employed the concept of c y l i n d r i c a l a n i s o t r o p y and v e r i f i e d the r a d i a l s t r e s s formula f o r curved beams of constant depth. For pitc h e d - t a p e r e d beams, he developed an exact a n a l y s i s method to determine the change i n r a d i a l s t r e s s d i s t r i b u t i o n caused by the v a r y i n g beam depth. The method was v e r i f i e d e x p e r i m e n t a l l y by Fox (2) and was adopted f o r d e s i g n purposes i n Canada i n 1970(3). The second aspect of the problem concerns the d e t e r m i n a t i o n of a l l o w a b l e s t r e s s e s i n t e n s i o n p e r p e n d i c u l a r 2 to grain. The present method i s described i n (4) as follows! The allowable stress In tension perpendicular to grain i s one-third of the allowable stress in horizontal shear. The allowable stress i n horizontal shear i s i n turn obtained as follows: Allowable stress i n horizontal shear = s b * F m c * Ffe * l/Fs& where s^ , = the 5th percentile l e v e l f o r small clear specimens i n shear with 95$ confidence, assuming normal d i s t r i b u t i o n F J J J Q = factor f o r moisture content F = fac t o r f o r load duration F S A = factor of safety Thus, according to the formula, the allowable stress in shear i s obtained by multiplying the basic stress s^ by a series of factors. These factors are assumed to be independent of each other. As noted i n the formula, size e f f e c t i s not accounted for and time e f f e c t i s assumed to be independent of strength. 1.2. Objectives The s p e c i f i c aim of t h i s research i s : 1. to study the e f f e c t of load duration on the tension perpendicular-to-grain strength of Douglas F i r , 2. to study the short-term strength of Southern Pine subjected to tension perpendicular to grain and compare with the re s u l t s f o r Douglas F i r specimens, 3 3. to study the e f f e c t of size on specimen strength, 4. to study the inte r a c t i o n of duration of load and size e f f e c t . 1.3. Scope 1. Load duration or time e f f e c t w i l l be investigated by subjecting Douglas F i r specimens to t e n s i l e loads at d i f f e r e n t stress l e v e l s f o r a period of about 70 days. Observation of deformation behavior and f a i l u r e mode w i l l be made. 2. Southern Pine specimens of d i f f e r e n t sizes w i l l be subjected to a standard rapid loading to detect i f a size e f f e c t e x i s t s . 3. Results from the aforementioned two sets of tests w i l l be compared wherever possible. 4 CHAPTER TWO  BACKGROUND AND THEORIES 2 .1 . E f f e c t of Load Duration - Madison Test The presently used time-strength relationship ( 3 . 4 ) i s derived from the widely accepted Madison curve(Pig . 2 ) . In 1943. long-term bending tests were commenced at the Forest Products Laboratory, Madison, Wisconsin (5). A t o t a l of 126 -1" x 1" x 14" clear bending Douglas F i r specimens were subjected to constant loads ranging from 60 to 95$ of the loads that caused f a i l u r e of matched control specimens i n a standard s t a t i c bending test of about 5-minute duration. The r e s u l t i n g data were plotted as percent stress r a t i o s versus logarithm of time to f a i l u r e . A hyperbolic curve was then f i t t e d empirically to accommodate the long-term data and other information obtained from impact t e s t i n g . The curve was represented by the following equatloni Y = 108.4 / x ° ' 0 4 6 3 5 + 18.3 where Y = stress expressed as a percentage of the standard-test strength X = duration of stress i n seconds. According to the curve, the 50-year strength i s 9/ l6 of the standard-test strength. Factors for other load 5 durations were also derived from the curve. Though only-bending tests were performed, the use of these factors was extended to a l l other strength properties f o r wood except modulus of e l a s t i c i t y . The allowable t e n s i l e stress perpendicular to grain f o r Douglas P i r was set at 65 p s i . This value i s to be used f o r normal load duration and dry service condition. Subsequent to the mentioned beam f a i l u r e s , the value was a r b i t r a r i l y changed to 15 psi i n the United States. No change was made i n Canada. 2.2. Recent Research Tests carried out recently indicate that the allowable stress of 65 p s i i s non-conservative while the value of 15 psi may be overly conservative. In load duration tests carried out by Madsen(6), glulam blocks were tested using d i f f e r e n t step-wise ramp loading rates. His test r e s u l t s indicated that the tension perpendicular-to-grain strength of Douglas F i r decreased with increasing load duration at a l l stress l e v e l s , contrary to his observation with bending specimens. Furthermore, the strength reductions were more serious than si m i l a r test r e s u l t s i n shear and bending(7,8,9)• As a conclusion, he suggested that the present allowable stress of 65 psi used in Canada i s too high. Peterson(10), i n his t e s t s , loaded glulam blocks at constant stresses. His yet unpublished r e s u l t s , however, f a i l e d to support the need f o r 6 an allowable stress as low as 15 p s i . The two sets of data seem to suggest that the allowable stress should be between 15 p s i and 65 p s i . The limited amount of available data makes i t d i f f i c u l t to determine the appropriate value. Thus, more te s t i n g of the tension perpendicular-to-graln property seems to be j u s t i f i e d . 2.3. E f f e c t of Size - Weakest-Link Model Barrett(11), in 19?4, presented a t h e o r e t i c a l model that relates short-term tension perpendicular-to-grain strength to volume. According to the model, the logarithm of strength decreases l i n e a r l y with the logarithm of specimen volume f o r geometrically s i m i l a r specimens;,, s i m i l a r l y loaded. The model i s based on two premises: 1. Flaw d i s t r i b u t i o n i s a material c h a r a c t e r i s t i c . The strength of material i s considered to be controlled by the size of the c r i t i c a l flaw i n the loaded volume. This i s a basic reason f o r the s t a t i s t i c a l v a r i a t i o n i n the strength properties of material. 2. A specimen i s considered to be made up of elements analogous to the l i n k s of a chain. The strength of the chain i s controlled by the strengths of i n d i v i d u a l l i n k s i n the chain. For p e r f e c t l y b r i t t l e materials, t o t a l f a i l u r e occurs when fracture occurs at the weakest l i n k . The strength of the material i s represented by a 7 cumulative d i s t r i b u t i o n function, denoted by: F (x) = P (X«x) where P = a pro b a b i l i t y function X = a strength component x = generalized stress. For a given volume of V, the sur v i v a l p r o b a b i l i t y S i s : S = 1 - F (x) (1) It was shown that F (x) could be expressed as: F (x) = 1 - exp (B) In his presentation, Barrett used a two-parameter Weibull d i s t r i b u t i o n f o r F (x) which has the lower l i m i t of strength equal to zero. For a uniform stress d i s t r i b u t i o n , B becomes: B - -< *max / » ) k V where x m a x = a stress value m = scale parameter of the Weibull d i s t r i b u t i o n k = shape parameter of the Weibull d i s t r i b u t i o n . On substitution into Equation (1), the following equation i s obtained: log x m a x = a - (1/k) log V (2) where a = a constant f o r a given s u r v i v a l p r o b a b i l i t y S (a = (1/k) log (In U/S)) + log m) Thus, according to Equation (2), a l i n e a r r e l a t i o n s h i p 8 i s predicted between the logarithm of strength and the logarithm of volume f o r geometrically s i m i l a r specimens subjected to uniform stresses. Available tension perpendicular-to-grain data f o r Douglas F i r seem to support the hypothesis(11). In t h i s thesis, size e f f e c t s on the short-term strengths of Douglas F i r and Southern Pine w i l l be Investigated on the basis of Equation (2). In addition, comparison between the strengths of the two species w i l l be made. 9 CHAPTER THREE  PLANNING MD PREPARATION The p r o j e c t was conducted i n the S t r u c t u r e s Laboratory of the Department of C i v i l E n g i n e e r i n g , U n i v e r s i t y of B r i t i s h Columbia. Long-term t e s t s were c a r r i e d out i n the basement of the l a b o r a t o r y . The temperature was kept a t about 20°C throughout the t e s t p e r i o d . Although the humidity was not c o n t r o l l e d , i t was reasonably s t a b l e due to the nature of the room. 3 • 1 • O u t l i n e of T e s t i n g Approach  Time e f f e c t : 1. S t r e s s l e v e l s to be used f o r long-term l o a d i n g were e s t a b l i s h e d from a c o n t r o l sample broken i n a standard t e s t i n g machine. 2 . Matching samples of specimens were then s u b j e c t e d to dead loads a t the s e l e c t e d s t r e s s l e v e l s f o r a p e r i o d of about 70 days. 3 . The time to f a i l u r e of the specimens was observed and deformation measured. 4 . A f t e r 70 days, s u r v i v i n g specimens were loaded t o f a i l u r e u s i n g the c o n t r o l t e s t procedure. S i z e e f f e c t : 1. Southern Pine specimens of three d i f f e r e n t volumes 10 were tested to destruction i n the standard t e s t i n g machine. 2. Moisture content was measured. 3. S p e c i f i c gravity was calculated. 3.2, Other Considerations a. Sample size In order to obtain acceptable s t a t i s t i c a l information, Mad sen(12) recommended a minimum sample size of 80 from his simulation t e s t s . However, due to the l i m i t a t i o n s of time and specimen material, a sample size of 40 was used i n t h i s research. It was r e a l i z e d that t h i s compromise would make the test r e s u l t s less conclusive. b. Specimen size Glulam blocks with square loading surfaces(Pig. 3) were used as test specimens. Two sizes were used f o r Douglas P l r specimens and three sizes for Southern Pine. These sizes were selected to be s u f f i c i e n t l y d i f f e r e n t to detect size e f f e c t s . c. Rate of loading f o r short-term tests Loading rates were selected to cause f a i l u r e i n approximately 2 minutes for the Douglas F i r controls. Thus, the 2-minute strength was used as the standard strength. For Southern Pine, one loading rate was chosen to be 100 psi/min.. A second rate of 11 20 psi/min. was selected to investigate i f t h i s slower rate would s i g n i f i c a n t l y vary the test r e s u l t s . d. Long-term load duration A test period of 70 days was chosen i n order to span about 10^ minutes (5 decades i n log. time sca l e ) . e. Selection of stress l e v e l s The stress l e v e l s f o r the long-term loading were selected to be the 10th, 25th and 50th percentile l e v e l s of the control sample. The above considerations resulted i n the following s p e c i f i c s f o r the testing programme: Time E f f e c t  Sample size - Douglas F i r Control Long-term!70 days) Size (inches) 10th 25th 50th 5-1/8x5-1/8x12(large) 40 at 100 psi/min. 34* 35* 40 1 x 1 x 6 (small) 40 at 200 psi/min. 40 40 40 Size (Inches) Size E f f e c t  Sample size - Southern Pine rate of loading 100 psi/min. 200 psi/min, 5 x 5 x 22 (large) 2-3/8 :x 2-3/8 x 10 (medium) 1 x 1 x 6 (small) 40 40 42** 40 40 38** •Deviation from the sample size of 40 due to shortage of test material. **Deviation due to loss of specimens with defective glue-lines and subsequent replacement. 12 3.3. Preparation of Test Material Some researchers(6, 10) studying tension perpendicular to grain cut their specimens serially from a limited number of glulam beams. This source of material has an inherent disadvantage. If the glulam beam contains one exceptionally weak board, specimens cut from the beam would likely f a i l in the same plane at about the same stress values. Thus, the resulting strength distribution may contain an element of bias. To avoid this shortcoming, 5f"x 5i"x l i " pieces were cut from a large number of different 2" x 6 " Douglas Fir boards. A gluing jig which could contain 27 specimens at one time was borrowed from a local glulam manufacturer. Sixteen pieces, picked at random, were glued together with a caesin adhesive. The grain orientation was the same as in glulam beams. After 24 hours of cure, the blocks were trimmed to a size of 5-1/8" x 5-1/8" x 24". However, t r i a l tests showed some of the glue-lines were defective. This was probably caused by the boards being warped and insufficient pressure applied in the gluing process. It was decided that this material had to be discarded. Instead, glulam blocks that had undergone previous load duration tests were used as replacement material. These blocks were originally cut from two 5%" x 24" Douglas Fir glulam beams glued with phenol resorcinol, and had two coats of polyurethane varnish applied on their surfaces. One of the 13 beams was made of clear boards while the other of commercial material. The replacement blocks were trimmed to a size of 5-1/8" x 5-1/8" x 12". Examination showed the number of blocks made of clea r and commercial material was about the same. The 1" x 1" x 6" specimens were cut from the above mentioned replacement blocks. Only 4 specimens were made from each large block so as broad a sampling as possible was obtained. Two coats of varathane varnish were applied to reduce fluctuations of moisture content i n the wood. The fin i s h e d specimens were grouped at random into samples of 4-0 and t h e i r dimensions measured. To make the Southern Pine specimens, 1,200 l i n e a l feet of 2" x 6" x 4' boards were purchased from a l o c a l supplier. After storage i n the laboratory f o r a month, they were planed, cut and glued In the same manner as the Douglas F i r . The finished specimens were 5" x 5" x 22" i n siz e from which blocks of 2-3/8" x 2-3/8" x 10" and 1" x 1" x 6" were cut. They were then varnished and grouped i n the same way as the Douglas F i r . T r i a l tests showed the glue-lines of these blocks to be sound and i t was decided to use the specimens. The configuration and dimensions of the d i f f e r e n t specimens are shown i n F i g . 3« 14 It should be noted that the replacement Douglas F i r blocks had been broken once before. Their strengths could therefore be s l i g h t l y greater than the population values. As f a r as studying the long-term behavior, they were considered adequate specimens. 15 CHAPTER FOUR  METHOD OF TESTING 4.1. Mounting Devices In order to transfer only a t e n s i l e load to the specimen, any e c c e n t r i c i t y causing moments had to be avoided. To achieve t h i s , the specimens were checked to ensure t h e i r end surfaces were f l a t and perpendicular to t h e i r lengths. An accurate load transfer bracket was developed. For the large Douglas F i r specimen, a 3/4" x 6 " x 6 " s t e e l plate was mounted onto each end surface with sixteen 2f" Robertson screws(Fig. 4(a)). A st e e l l i n k was welded i n the exact centre of the plate to which a chain was fastened by means of a chain shackle. However, the same method could not be used f o r the 1" x 1" specimens due to t h e i r small end surfaces. Instead, 1"-thick blocks were cut from a 2"-diameter aluminum rod. The blocks were d r i l l e d and machined as shown in F i g . 4(c). The specimen was then accurately placed and glued to the 1.42"-diameter trough with a r e s i n type epoxy. A chain was then placed in the s l o t provided and a pin was inserted through the chain l i n k . The mounting devices f o r the Southern Pine specimens 16 followed the same arrangement as the Douglas F i r . F i g . 4(b) shows the device f o r the 2-3/8" x 2-3/8" specimens. T r i a l tests showed the mounting devices were adequate f o r strength and did minimize e c c e n t r i c i t i e s . 4.2. Short-term Test Method A 200-kip Tinlus Olsen machine with a d i a l type loading speed selector was used f o r the large specimens. The small and medium specimens were tested i n a Satec Universal System. Loading speeds were as shown in the table on page 11. A displacement transducer was mounted on each specimen and connected to a Mosely X-Y Plotter to give a load-deformation pl o t . After the specimen f a i l e d , i t s moisture content was measured by means of a resistance type moisture meter. The following information was obtained f o r each specimen: 1. Dimensions 2. Load at f a i l u r e 3. Time to f a i l u r e 4. Load-deformation plot 5. Mode of f a i l u r e 6. Moisture content - three readings f o r every large specimen - two readings f o r every medium specimen - one reading f o r every small specimen 17 4.3- Long-term Test Setups The apparatus shown In Pig. 5 was used f o r the large Douglas F i r specimens. The mechanical advantage was 15»1. Test benches were provided for simultaneous te s t i n g of 42 specimens. The apparatus f o r the small specimens i s shown i n F i g . 6. The mechanical advantage was 5«1• A t o t a l of 60 benches were b u i l t . The weights of the lever beams and t h e i r accessories were accounted f o r i n the stress c a l c u l a t i o n . 4.4. Long-term Test Method The percentile stress l e v e l s to be used f o r the long-term tests were determined from the short-term control test data. This topic would be treated i n d e t a i l i n the next chapter. The amount of lead required was calculated to obtain the desired stress l e v e l . Displacement gauges were i n s t a l l e d on 5 to 10 specimens of each test sample to determine the long-term deformation behavior. Before loading, the gauge length was measured and the gauge zeroed. Lead ingots, each weighing about 25 l b s . , were applied one by one. When the prescribed stress l e v e l was reached, a new gauge reading and the time to the nearest minute were recorded. The process of loading one speoimen took about 5 to 10 minutes depending on the stress 18 l e v e l used. Most specimens emitted a cracking sound when loaded which would either die off or increase i n frequency. The l a t t e r was usually a warning of Impending f a i l u r e . In one case, the author observed a large specimen emitting cracking noise f o r 4 minutes before f i n a l f a i l u r e occurred. Since the load duration e f f e c t would be analyzed on a logarithmic time scale, frequent observations of the loaded specimens were p a r t i c u l a r l y important at the early stage. Thus, observation was made once every 3 hours i n the f i r s t 24 hours. From then on t i l the 7th day, observation was made once every 8 hours, a f t e r that, once or twice a day. Whenever a specimen was found broken, the time was recorded and i t s moisture content was measured. The following information was obtained f o r each broken specimeni 1. Dimensions 2. Time when the prescribed stress l e v e l was reached 3. Time at f a i l u r e (discovery of f a i l u r e ) 4. Load at f a i l u r e 5 . Mode of f a i l u r e 6. Moisture content 7. Deformation readings and corresponding times. After a period of 70 days, the surviving specimens 19 were taken down and loaded to f a i l u r e i n the same manner as the control t e s t s . This was done to determine the strengths of the specimens and to test i f they had been damaged by the long-term loading. 20 CHAPTER FIVE  TEST DATA FOR TIME EFFECT 5.1. Method of Ranking The method of ranking described by Madsen(12) was used to present the short-term strength data, as i l l u s t r a t e d i n F i g . 7. The abscissa represents ranked order and the ordinate the strength. The points are plotted i n ascending order. A two-parameter Weibull d i s t r i b u t i o n curve was f i t t e d to the ranked data by means of a computer program provided by the Western Forest Products Laboratory, Vancouver, B.C.. The curve can be expressed by the following equationi F = 1 - e - ( x / m ) k (3) where F .= pr o b a b i l i t y of f a i l u r e x = a stress value m = scale parameter k = shape parameter Transferring x to the l e f t side, Equation (3) becomest x = m ( - l n ( l - F ) ) 1 / k (3a) which i s the form of the curve i n F i g . 7. The method of f i t t i n g c a l l s for* F = (R-0.3)/(N + 0.4) 21 where R = rank N = sample size This gives a s l i g h t l y d i f f e r e n t curve from Equation (3»). But the discrepancy decreases with larger sample size and i s i n s i g n i f i c a n t f o r the chosen sample size of 40 i n t h i s research. 5.2. Control Data Fig . 7 shows the ranked data and f i t t e d Weibull d i s t r i b u t i o n curves f o r the large and small Douglas F i r specimens. The average time to f a i l u r e was about 2 minutes f o r the large specimens and 1.7 minutes f o r the small specimens. The two-parameter Weibull curves give f a i r l y good f i t to the ranked data. The e f f e c t of size on strength i s c l e a r l y demonstrated. For example, the median strengths are 180 p s i and 350 p s i for the large and small specimens respectively. The long-term test stress l e v e l s (the 10th, 25th and 50th percentiles) were selected from F i g . 7. For example, to obtain the 50th percentile f o r the large specimens, a v e r t i c a l l i n e was drawn upward from X = 0.50. At the inters e c t i o n with the ranked data, a horizontal l i n e was drawn and the ordinate read. The following table shows the stress l e v e l s used in the long-term t e s t s : 22 Percentile Level (psi) Size (inches) 10th 25th 50th 5-1/8 x 5-1/8 x 12 (large) 125 138 168 1 x 1 x 6 (small) 226 277 358 These stress values w i l l be quoted d i r e c t l y in the following analysis of long-term data to avoid confusion between the two specimen s i z e s . 5.3. Survival Rate Prom the time to f a i l u r e data, the number of f a i l u r e s 2 3 f o r each stress l e v e l which had occurred at 1, 10, 10 , IO-', 4 c 10 and 10^ minutes were counted. Table 1 l i s t s these numbers fo r the two specimen s i z e s . As expected, some f a i l u r e s occurred during the ap p l i c a t i o n of the lead ingots. For s i m p l i c i t y i n quoting, these f a i l u r e s were denoted as f a i l u r e s on loading. In Table 1, the numbers In brackets represent the s u r v i v a l percentages expressed r e l a t i v e to the number of specimens stronger than the selected stress l e v e l . The s u r v i v a l percentage a f t e r each f a i l u r e i s plotted against the logarithm of time to f a i l u r e i n Fig . 8a and F i g . 8b ( l e t t e r notations of the same figure number r e f e r r i n g to the same subject but f o r d i f f e r e n t specimen sizes or stress l e v e l s ) f o r the large and small specimens respectively. Each step i n the plot indicates a specimen f a i l u r e . 23 For a l l samples, the s u r v i v a l percentages decrease at an increasing rate with logarithmic time at a l l stress l e v e l s . (On a l i n e a r time scale, the decrease w i l l be at a decreasing rate.) On the average, the decrease seems to be more serious i n the small specimens. At a time of 10-* minutes (approx. 70 days), the e f f e c t of stress l e v e l on s u r v i v a l percentages i s c l e a r l y shown. Apparently both the specimen size and stress l e v e l affected the test r e s u l t s but i t i s d i f f i c u l t to separate the two e f f e c t s . 5 . 4 . Strength Ratio - Control Curve Method The long-term data were also analyzed using the strength-ratio format of the Madison t e s t . Strength r a t i o i n t h i s case was defined as described below. However, before proceeding further, two assumptions were made: 1. The long-term test sample was assumed to have a strength d i s t r i b u t i o n s i m i l a r to the control sample, in both magnitude and shape of d i s t r i b u t i o n . This could be j u s t i f i e d by the fa c t that the samples had been grouped at random. 2. The short-term strength of a specimen was indicated by the length of time i t could survive a prescribed stress l e v e l . Thus, the specimen that had the shortest time to f a i l u r e was assumed to be the weakest specimen. The specimen that had the second shortest time to f a i l u r e was the second weakest 24 specimen and so on. Based on these two assumptions, the data could now be investigated. The process involved the following steps i 1. The two-parameter Weibull curve from the control data was plotted, as shown i n Pig. 9 . This would be considered as the control strength d i s t r i b u t i o n . 2. A horizontal l i n e was then drawn at the desired stress l e v e l . That portion of the l i n e , denoted by m, was divided into equal inte r v a l s according to the number of specimens i n the test sample that survived f a i l u r e on loading. 3 . A v e r t i c a l l i n e was then drawn bise c t i n g the f i r s t i n t e r v a l . That portion of the l i n e below the f i t t e d curve, indicated by p^, represents the estimate of the short-term strength of the weakest specimen. The magnitude of the stress l e v e l , denoted by q, i s the strength of the specimen at f a i l u r e . Thus, the strength r a t i o of the f i r s t failed, specimen could be obtained by d i v i d i n g q by p^. In the same manner, strength r a t i o s f o r other specimens could be estimated, as shown i n Fig . 9» 4. When p l o t t i n g strength r a t i o as a function of the logarithm of time f o r one specimen size at a prescribed stress l e v e l , the f i r s t point represents the strength r a t i o f o r the specimen with the shortest time to f a i l u r e . The second point indicates the 25 strength r a t i o f o r the specimen with the second shortest time to f a i l u r e and so on. 5. Steps 1 to 4 were repeated f o r the other stress l e v e l s . F i g . 10a shows the completed plot f o r the large specimens at the three stress l e v e l s . F i g . 10b shows the plot f o r the small specimens. Data points at the same stress l e v e l were connected by straight l i n e s to emphasize the trend of the data. The Madison curve was also plotted, adjusted to a 2-minute time to f a i l u r e which was the average time to f a i l u r e f o r the controls. (The adjusting was done by f i r s t obtaining the strength r a t i o s at selected load durations from the presently used Madison curve. These strength r a t i o s were then used to construct the 2-minute curve. For example, the "new" strength r a t i o f o r the 10-mlnute duration was obtained by d i v i d i n g the "old" strength r a t i o f o r 10-minute duration by that f o r 2-minute duration.) The a p p l i c a t i o n of load to a prescribed stress l e v e l took about 5 to 10 minutes to complete, as mentioned, e a r l i e r . A question could therefore be raised about the data points that l i e within the period of 1 to 10 minutes. If the loading time was included, the f i r s t few data points should have been shifted further to the r i g h t . The Madison test report(5) did not mention the method of loading or i f the loading time had been included. While f a i l u r e s on loading were excluded in the present analysis, i t seemed j u s t i f i e d to ignore the loading 26 time i n Pig. 10a and Pig. 10b. 5.5. Strength Reduction with Time As shown i n Pig. 10a, almost a l l of the data points f o r the large specimens l i e above the Madison curve. Strength r a t i o s at the three stress l e v e l s decrease slowly u n t i l a load duration of about 5t000 minutes, (approx. 3 days), but from then on, decrease i n strength r a t i o becomes steeper. However, towards 10^ minutes (approx. 70 days), the data at 138 p s i become almost p a r a l l e l to the Madison curve. On the whole, strength r a t i o decreases, at an increasing rate with the logarithm of time. The trend could be represented by a convex curve. In contrast, the Madison curve i s s l i g h t l y concave. While data at one stress l e v e l are c l e a r l y separated from data at another l e v e l , the e f f e c t of stress l e v e l on strength does not show a consistent pattern. Data at 168 p s i (the highest stress l e v e l ) l i e in between data at the other two l e v e l s . This may be due to a sampling problem. If the same tests were repeated many times, the e f f e c t of stress l e v e l might be more d i s t i n c t . The data points f o r the small specimens (Fig. 10b) are scattered above and below the Madison curve. Decrease i n strength r a t i o with time i s more pronounced than the large specimens. After a period of 10** minutes (approx. 7 days), most of the data points l i e below the Madison curve. Again, 27 the e f f e c t of stress l e v e l i s not well defined. Data f o r the three stress l e v e l s are mixed together, showing no d i s t i n c t trend. 5.6. Size E f f e c t On the whole, i t seems that strength reductions are greater in the small specimens than i n the large specimens. This may be caused by the d i f f e r e n t sizes of the specimens. The small specimen has a volume of 6 In.3, compared to the 315 3 i n . of the large specimen. However, the e f f e c t of stress l e v e l could also be the cause. The large specimens were subjected to stresses ranging from 125 psi to 168 p s i while the small ones from 226 p s i to 358 p s i . It i s unfortunate that size e f f e c t on long-term behavior has been complicated by stress l e v e l . Had the stress l e v e l s used f o r the two specimen sizes overlapped, the e f f e c t of size might have been shown independent of stress l e v e l . 5.7 Comments on the Control Curve Method The f i r s t assumption made in the control method was that the strength d i s t r i b u t i o n of the long-term test sample i s si m i l a r to that of the control sample i n both magnitude and shape of d i s t r i b u t i o n . To test the v a l i d i t y of t h i s assumption, the long-term test r e s u l t s and the post-70-day test strengths were ranked f o r each sample. Pigs. 11a, l i b , 11c and Figs. 28 12a, 12b, 12c show such plots f o r the large and small specimens respectively. Each stress l e v e l i s shown separately. Also shown i s the Weibull d i s t r i b u t i o n curve f o r the appropriate specimen size obtained from the control sample. As indicated in the figures, only a few of the post-70-day data show low values r e l a t i v e to the stress l e v e l used (Pigs, l i b , 11c). This suggests that reduction i n strength due to the long-term loading i s small. In the figures, the square symbols designate the strength values f o r specimens that broke during loading. Because the load was applied at increments of 25 l b s . , most of these points are probably higher than the actual strengths of the broken specimens. Nevertheless, the v a l i d i t y of the assumption can be tested by observing how close the Weibull curve f i t s the post-70-day data and the number of f a i l u r e s on loading. While F i g . 11c shows a good f i t , the other figures do show some discrepancies. In most cases, the Weibull curves predict more f a i l u r e s on loading than occurred. A better analysis method would therefore be desirable. 5.8. Strength Ratio - Straight Line Method The assumption that the strength of a specimen i s indicated by the time to f a i l u r e was retained i n t h i s method. Fig. 13 explains the method. The test r e s u l t s f o r the whole sample were ranked. Then, based on these data, the o r i g i n a l 2 9 strength d i s t r i b u t i o n was reconstructed f o r the missing portion, i . e . the f a i l u r e s within 70 days. The point b was chosen as the s t a r t i n g point f o r the missing portion of the d i s t r i b u t i o n f o r the reason that i t separates the long-term f a i l u r e s from the specimens weaker than the selected stress l e v e l . The post-70-day data were considered v a l i d as part of the strength d i s t r i b u t i o n , i . e . no strength loss due to the 70-day loading. Only exceptionally low values were disregarded. These were considered to be specimens that had been damaged during the 70-day loading. In F i g . 13, the rectangle a-b-c-d i s the area within which the missing portion of the strength d i s t r i b u t i o n can be expected to occupy. While impossible to reconstruct the exact d i s t r i b u t i o n , an estimate could be made by observing the general shape of the two Weibull curves i n F i g . 7. The diagonal b-d i n F i g . 13 was chosen to be the "best" estimate of the strength d i s t r i b u t i o n f o r the missing portion. This method was then applied to a l l the long-term data. Following a s i m i l a r process as outlined i n the control curve method, the strength r a t i o f o r the f i r s t f a i l u r e was obtained by d i v i d i n g q by p^ t as shown in F i g . 13. The strength r a t i o f o r the second f a i l u r e i s q/P2 a n d s o o n « T n e r e s u l t s from the above c a l c u l a t i o n are shown i n F i g . 14a and F i g . 14b f o r the large and small specimens respectively. These figures show the same general tendency as the data in F i g . 10a and F i g . 10b. The curves for a l l the stress 30 l e v e l s are convex even though the 1" x 1" x 6" curve at 358 p s i may be close to a straight l i n e . The position of a l l data i s raised in general, indicating less strength reductions than res u l t s obtained by using the control curve method. The e f f e c t of stress l e v e l i s more d i s t i n c t f o r the small specimens. On the whole, a conclusion as to the e f f e c t of stress l e v e l on long-term strength, cannot be drawn. 5«9« Comparison between the Two Methods As observed, the number of f a i l u r e s on loading predicted by the Weibull curve did not match well with the test r e s u l t s . In such cases, the control curve method involved s h i f t i n g the long-term data on the normalized rank. This may d i s t o r t the actual strength d i s t r i b u t i o n . The straight l i n e method does not have t h i s shortcoming. Furthermore, i t u t i l i z e s the observed data both i n the low end and the high end of the d i s t r i b u t i o n . For t h i s reason, i t i s considered superior to the control curve method. In a l l subsequent analyses, r e s u l t s by the straight l i n e method w i l l be used. 5.10. Average Strength Ratio-time Curves In order to obtain a better understanding of the general time-strength re l a t i o n s h i p , the average strength r a t i o versus logarithmic time curve was constructed for each specimen s i z e . The average strength r a t i o s were calculated at selected load durations and a curve was drawn through the points. The 31 r e s u l t i n g plot i s shown in F i g . 15 f o r both methods of ca l c u l a t i n g strength r a t i o s . The Madison curve based on a 2-minute time to f a i l u r e was also plotted. No extrapolation beyond the test period was attempted. Fi g . 15 c l e a r l y demonstrates that the straight l i n e method gives a lower estimate of strength reductions than the control curve method. In addition, strength reductions are less serious i n the large specimens than i n the small ones. A l l curves indicate that strength r a t i o s decrease at an increasing rate with the logarithm of time. In contrast, the Madison curve predicts strength r a t i o s to decrease with the logarithm of time but at a decreasing rate. In addition the figure shows that the Madison curve i s non-conservative f o r load durations le s s than about 5 minutes and possibly i n the decade beyond 10^ minutes (approx. 70 days) i f the tendency of the curves continues. The Madison test report(5) states that t h e i r curve was obtained by f i t t i n g three sets of data. The f i r s t set was from impact loading tests with an average strength r a t i o of 175$ and an average time to f a i l u r e of 0.01 second. The second set was from rapid loading tests and the third from long-term constant load tests. The upswing of the curve at the upper l e f t corner of the p l o t ( F i g . 2) i s apparently due to the e f f o r t to f i t the impact data as c l o s e l y as possible. It i s questionable whether data from these impact tests should have 32 been included f o r the purpose of curve f i t t i n g because d i f f e r e n t t e s t i n g methods may produce d i f f e r e n t r e s u l t s even f o r the same type of specimens. Another point to be noted i s that the Madison curve was obtained from bending-test data. Whether i t can be applied to tension perpendicular to grain i s highly questionable. The research reported here contained twice as many specimens as the Madison load duration tests and deals d i r e c t l y with the strength property i n question, i . e . tension perpendicular to grain. Therefore, test r e s u l t s from t h i s research are more conclusive than the Madison test which dealt primarily with bending. 5.11. Conclusions 1. The tension perpendicular-to-grain strength of Douglas F i r decreases at an increasing rate with the logarithm of time. This i s opposite to the Madison curve which predicts strength reductions to increase with the logarithm of time but at a decreasing rate. 2. Test results indicated that the present design method i s non-conservative at load durations l e s s than 5 minutes and possibly beyond 70 days f o r tension perpendicular to grain, but conservative for times in between. 33 There i s a s i g n i f i c a n t difference i n long-term test r e s u l t s between the large and small specimens. This may be caused by the d i f f e r e n t specimen sizes, but the e f f e c t of stress l e v e l could also be the cause. 34 CHAPTER SIX  TEST DATA FOR SIZE EFFECT 6.1. Short-term Strength Data Southern Pine of three d i f f e r e n t sizes were tested to f a i l u r e at loading rates of 100 psl/min. and 20 psi/min. i n order to determine strength-size r e l a t i o n s h i p . Some of the 1" x 1" x 6" specimens did f a i l in the g l u e - l i n e s . They were discarded and replacement specimens were added to the sample. The test r e s u l t s f o r each of the three specimen sizes f o r both loading rates were ranked and Weibull d i s t r i b u t i o n curves f i t t e d . F i g . 16a, F i g . 16b?and. Fig. 16c show the plots fo r the large, medium and small specimens respectively. S t a t i s t i c a l information i s l i s t e d i n Table 2a, as well as r e s u l t s f o r the two Douglas F i r control t e s t s . As shown i n F i g . l6a. F i g . l6b and F i g . l6c, differences i n test r e s u l t s due to the d i f f e r e n t loading rates are small and appear to be i n s i g n i f i c a n t . Average times to f a i l u r e range from 2.5 to 21.4 minutes (Table 2a). For that range of f a i l u r e times, the Madison curve predicts a difference i n strength r a t i o of about 8% while present Douglas F i r long-term test r e s u l t s predict a difference of 2% (Fig. 15). Thus, the Southern Pine data seem to t i e i n with the present test r e s u l t s rather than with the Madison duration of load concept. 35 Since differences due to d i f f e r e n t loading rates can be considered i n s i g n i f i c a n t , the r e s u l t s from the two loading rates were combined as shown i n Fig. 17. These combined res u l t s w i l l be used i n subsequent analyses. Weibull curves were f i t t e d , which give a good: f i t throughout the whole range. Fig . 17 indicates c l e a r l y the e f f e c t of s i z e . Short-term strength increases with decreasing specimen volume. For example, the median strengths are 250 p s i , 360 p s i and 510 p s i f o r the large, medium and small specimens respectively. Additional s t a t i s t i c s are l i s t e d i n Table 2b. It i s noted that the c o e f f i c i e n t of v a r i a t i o n i n strength has the tendency to become greater with smaller specimen s i z e . The same tendency i s observed i n Douglas Fir(Table 2a). 6.2. Log Strength vs. Log Volume The r e l a t i o n s h i p between strength and specimen volume was also studied using the model suggested by Barrett(11). The method was discussed, previously i n Chapter Two. In F i g . 18, the abscissa represents the logarithm of volume while the ordinate the logarithm of strength. The mean strengths for the three volumes were plotted, as well as the 10th and 90th percentile values obtained from the f i t t e d curves. The same information f o r Douglas F i r i s also shown i n F i g . 18. Linear regression analysis was performed with the mean strengths of the Southern Pine samples according to 36 Equation (2). Results are shown as a broken l i n e i n Pig. 18. It can be seen that the Southern Pine test r e s u l t s are consistent with a l i n e a r r e l a t i o n s h i p between the logarithm of strength and the logarithm of volume, as predicted by Equation (2). For the purpose of comparison, Barrett's regression l i n e f o r a l l his Douglas F i r d a t a ( l l ) i s shown as a s o l i d l i n e . The two regression l i n e s show that Southern Pine i s stronger than Douglas F i r i n tension perpendicular to grain. For example, f o r a volume of 1,000 i n . ^ , the strength of Southern Pine i s 210 p s i as compared to the 105 psi f o r Douglas F i r . For a volume of 6 in.'*, the values are 500 psi and 300 p s i respectively. The slopes of the two regression l i n e s do not d i f f e r s i g n i f i c a n t l y . The c o e f f i c i e n t s of the two regression l i n e s are l i s t e d i n Table 3. The parameters f o r the Weibull d i s t r i b u t i o n curves are l i s t e d i n Table 4- f o r both Douglas F i r and Southern Pine. The average k-value f o r Southern Pine by curve f i t t i n g i s 3.812 and the k-value by regression i s 5.74?. Theore t i c a l l y , these two values should be equal. The kind of v a r i a t i o n as noted i s not uncommon as k-value i s usually sensitive to sample si z e . 6.3. Douglas F i r Data The mean strengths of the two Douglas F i r samples (Fig. 18), while showing a decrease with increasing volume, are somewhat higher than the Douglas F i r regression l i n e . 37 This may be due to the fact that the test material have undergone previous tests. The o r i g i n a l specimens had a volume of 630 i n . 3 which i s twice the large specimen volume used i n t h i s research. It i s possible to use Equation (2) to compare the strength differences between previous values and those obtained i n t h i s t e s t . At a given su r v i v a l p r o b a b i l i t y f o r two d i f f e r e n t volumes V1 and V,, Equation (2) becomes: respectively. With = 630 i n . ^ , the o r i g i n a l specimen volume, V"2 = 315 i n . , the specimen volume i n t h i s t e s t , k = 4.902, the slope parameter f o r the Douglas F i r regression l i n e i n Fig. 18, the above equation becomes: x 2 = 1.152 x 1 Using t h i s equation, the average strength of specimens with a volume of 315 in.-' i s obtained, as shown i n the following table: where x and x_ are the strength values f o r and V 2 Time to f a i l u r e N Average Strength (psi) V 1 = 630 i n . 3 V 2 = 315 i n . 10 min. only 28 150.6* 173.5 1 min. & 10 min. 54 156.2* 179.9 * Madsen(6) 38 Comparing the values i n the r i g h t column with the present average strength of 180.7 p s i , It i s observed that the second f a i l u r e plane of the Douglas F i r material is@only 0.5% to 3.8$ stronger than the f i r s t f a i l u r e plane. This difference in strength i s considered i n s i g n i f i c a n t . Thus, i t i s confirmed that the replacement specimens are adequate f o r tes t i n g purposes. 6.4. Conclusions 1. Southern Pine i s stronger than Douglas F i r i n tension perpendicular to grain. This may p a r t i a l l y explain why f a i l u r e s have not been found i n pitched-tapered glulam beams made of Southern Pine. 2. Southern Pine exhibits size e f f e c t i n tension perpendicular to grain. Logarithm of strength decreases l i n e a r l y with the logarithm of volume, as predicted by the weakest-link model. 3. The short-term test r e s u l t s f o r the two Douglas F i r samples were found to be consistent with the weakest-link hypothesis. 4. It appears that the size e f f e c t i n tension perpendicular to grain f o r Southern Pine i s the same as f o r Douglas F i r . 39 CHAPTER SEVEN  MISCELLANEOUS OBSERVATIONS 7.1. Modulus of E l a s t i c i t y Load-deformation plots were obtained f o r a l l short-term test specimens. Modulus of e l a s t i c i t y was calculated as follows: Modulus of e l a s t i c i t y , E = s t r e s s / s t r a i n = P/A D7L = (P/DML/A) where P = load at f a i l u r e A ~ cross-sectional area of specimen D = deformation L = gauge length The slope of the load-deformation plot , P/D, was measured from the plot. By multiplying t h i s value by L/A, the E-value was obtained. Table 5 l i s t s the s t a t i s t i c s of the E-values f o r both Douglas F i r and Southern Pine. The average E-values are about 93x10"* p s i and 109x10 psi f o r Douglas F i r and Southern Pine respectively. As indicated i n Table 5, there i s a tendency f o r the E-value to increase with increasing specimen s i z e . Some t y p i c a l load-deflection plots are shown i n F i g . 40 19a and F i g . 19b f o r Douglas F i r and Southern Pine respectively. The same plots are converted to a s t r e s s - s t r a i n presentation In F i g . 20a and Fig . 20b. In general, the plots are straight l i n e s though a few are s l i g h t l y curved. 7.2. Moisture Content Table 6a l i s t s the s t a t i s t i c s of moisture content values f o r a l l short-term test samples. Overall average moisture content values are about 7.4$ and 8,6% f o r Douglas F i r and Southern Pine respectively. Table 6b l i s t s the moisture content values for Douglas F i r long-term test samples. Each sample includes f a i l u r e s on loading, f a i l u r e s within 70 days and post-70-day f a i l u r e s . Overall average i s about 8.2%, somewhat higher than the 7.4$ f o r the short-term t e s t samples. The difference may be due to the exposure of the long-term specimens to the Influence of the environment. 7.3. Mode of Failur e Each specimen was c l a s s i f i e d into one of the following four categories i Type I - f a i l u r e s involving wood defects such as pi t h s , knots, pitch pickets and r a d i a l cracks that occur i n the f a i l u r e plane. These defects are considered to have strength reducing e f f e c t s i n the wood i t s e l f . 41 Type II - f a i l u r e s occurring close to the load transfer device at the end of the specimen,, without any apparent wood defect present. For the large and medium specimens, any f a i l u r e plane that shows screw holes i s included i n t h i s category. For the small specimens, any f a i l u r e occurring at a plane less than i " from the aluminum block Is also considered a Type II f a i l u r e . Type III - f a i l u r e s occurring close to a glue-line (glue f a i l u r e s excluded), without any apparent wood defect present. This type of f a i l u r e may be due to stress concentrations developed because of d i s c o n t i n u i t y i n wood grain between adjacent laminations. It may also be due to the nonuniformity of the spring wood and summer wood at the gl u e - l i n e . Type IV - f a i l u r e s that do not f a l l into the above three categories. Specimens with defective glue-lines were excluded i n the analysis and they had been replaced. F i g . 21 shows photographs that exemplify the four types of f a i l u r e . The wood species, specimen size and f a i l u r e type designation are i n d i c a t e * in the photographs. In F i g . 21(a), among the Type I f a i l u r e s , the f i r s t from the l e f t shows a r a d i a l crack and a knot i n the f a i l u r e plane; the second shows 42 the presence of a p i t h while the third a f a i l u r e along a r a d i a l crack. In the same photograph, the f i r s t from the right shows screw holes, a Type II f a i l u r e ; the second from the right indicates f a i l u r e across the gl u e - l i n e , a Type III f a i l u r e . The other Type III f a i l u r e shows ripped f i b r e s and exposed adhesive which i s denoted by the dark colour on the f a i l u r e plane. In F i g . 21(b), a pitch pocket occurs i n the f i r s t specimen from l e f t and a knot i n the second from l e f t . In F i g . 21(c), the f i r s t two Southern Pine f a i l u r e s from l e f t involve exposed adhesive over most of the f a i l u r e plane where no ripped f i b r e s are present. In f a c t , these two specimens are considered to have defective glue-lines and were excluded from data analysis. Table 7a and Table 7b l i s t the number of f a i l u r e types i n each test sample. Table 7a i s f o r short-term tests while Table 7b f o r Douglas F i r long-term samples. As shown i n Table 7b, more than half (55%) of the f a i l u r e s on loading were caused by wood defects. This r a t i o i s higher than that f o r the subsequent test period which i s "}!%, Failure Type II and Type III account f o r about 68% of a l l the post-70-day f a i l u r e s . Hence, It appears that stress concentrations due to knots etc. are most severe and cause early f a i l u r e s at low stresses. On the other hand, stress concentrations at the growth rings cause f a i l u r e s at higher 43 stresses. 7.4. Creep Long-term deformation was plotted as a function of time i n Figs. 22a, 22b, 22c and 22d f o r d i f f e r e n t specimen sizes and stress l e v e l s . Each l i n e represents the deformation behavior of a single specimen. Recordings for specimens that survived only a few days were excluded from the pl o t s . Deformations at zero time represent the e l a s t i c deformations of specimens when they were loaded to the prescribed stress l e v e l . In general, deformations increased rapidly during the f i r s t three to seven days with the small specimens showing a considerably steeper climb. After t h i s , they appeared to l e v e l off but fluctuations were observed. In one case(Fig. 22c), the specimens a c t u a l l y recovered a l l the e l a s t i c deformations on the 70th day. The maximum r a t i o of long-term deformation to e l a s t i c deformation i s about f i v e . Some specimens f a i l e d within the 70-day loading but no c h a r a c t e r i s t i c of the deformation curves seems to suggest impending f a i l u r e . Since recordings were taken only once a day, t e r t i a r y creep was not detected. It i s also noticed that specimens loaded on the same day show sim i l a r f l u c t u a t i o n patterns. This seems to suggest that the environment did a f f e c t deformation behavior. A temperature recorder was placed in the basement of the 44 laboratory f o r 24 hours. Results showed that temperature was stable at about 20°C, However, no recordings of temperature and humidity were made during the test period. Thus, the ef f e c t s of the environment on deformation behavior could not be quantified. The above presentation of deformation as a function of time involved the parameters of stress l e v e l and specimen s i z e , making d i r e c t comparison d i f f i c u l t . To avoid t h i s shortcoming, an alt e r n a t i v e presentation was made: E = s/(D/L) = s(L/D) or 1/E = (D/L)/s where s i s stress l e v e l ; E, D and L are defined as before. Thus, the l/E-value of a specimen at a certa i n time could be obtained by d i v i d i n g i t s t o t a l deformation at that time by Its gauge length and the stress l e v e l concerned. This l/E-value involves an element of creep. In the same manner as before, the l/E-value was plotted as a function of time, as shown in Pigs. 23a, 23b, 23c and 23d. The thick l i n e represents the average l/E-value or "creep". For the large specimens, the average 1/E-values for specimens at 168 p s i and 138 psi are approximately of the same magnitude. The average l/E-value at 125 p s i shows less creep f o r the entire test period. This suggests that a higher stress l e v e l w i l l cause greater creep with time. However, the r e s u l t s f o r the small specimens do not seem to support the suggestion. 45 As shown i n F i g . 23d, "creep" at 226 p s i i s s i g n i f i c a n t l y higher than "creep"...at 277 p s i . However, displacement gauges were i n s t a l l e d on only 10 specimens of each test sample and most of these happened to f a i l i n a short time. Thus only a few specimens were observed throughout the test period. 46 CHAPTER EIGHT  DISCUSSION AND SUMMARY 8.1. Time E f f e c t The strength reductions obtained from t h i s research are less than predicted by our present concept f o r load durations from about 5 minutes to 70 days. The test period of 70 days covers design load durations f o r snow (2 months), falsework (7 days), and. wind and earthquake (1 day). Pig. 24 indicates the time factors f o r these design load durations from the average curves obtained by using the straight l i n e method of estimating strength r a t i o s . Two Madison curves were plotted,:one based on a 5-minute test and the other on a 2-minute t e s t . As shown in the figu r e , the 5-minute curve gives somewhat higher time factors than the 2-minute curve. The following table l i s t s the time factors f o r the three design load conditions mentioned: Time Factors {%) Madison Tests Load duration (5-min.) 5-1/8"x5-l/8 , ,xl2" l " x l " x 6 " 2-month 7-day 1-day 71 77 82 79 89 94 70 79 86 47 Numbers i n the second column correspond to the present load duration factors. For the small specimens, test r e s u l t s are not appreciably d i f f e r e n t from the present factors. For the large specimens, the time factors f o r the 7-day and the 1-day durations are greater than the present values by as much as 15$. This suggests that f o r p r a c t i c a l design s i t u a t i o n s , the present load duration factors could be increased f o r tension perpendicular to grain f o r loading periods up to at lea s t 2 months. Moreover, the general trend of the test r e s u l t s indicates that strength reductions may become greater than predicted by the present method i n the decade beyond 10-* minutes (approx. 70 days), as shown by the broken l i n e s i n F i g . 24. Also the trend of the test r e s u l t s at 1-mlnute duration does not seem to support the present time factor of 124$ (twice normal load duration factor) f o r impact loads. It i s recommended that add i t i o n a l tests be carried out f o r time periods not covered by t h i s research. 8.2. Relation of Southern Pine Results to ASTM (Size E f f e c t ) In his investigation of size e f f e c t on tension perpendicular-to-graln strength of Douglas F i r , Barrett(11) expressed the strength of an equivalent uniformly loaded unit volume as: 48 where s = strength of equivalent uniformly loaded unit volume x = nominal stress at f a i l u r e f o r ASTM max specimen b = factor used to correct f o r ef f e c t s of volume and stress d i s t r i b u t i o n i n the ASTM specimen, dependent on the shape parameter The s^-value Barrett found f o r Douglas F i r ASTM specimens agreed cl o s e l y with the unit volume strength predicted by his regression analysis of glulam block data. The same method was employed i n t h i s thesis to rel a t e ASTM strength to the regression analysis r e s u l t s f o r Southern Pine. For s i m p l i c i t y i n c a l c u l a t i o n , a shape parameter of 4.63 was used. This i s also the value suggested by Barrett f o r commercial Douglas F i r . The choice of 4.63 can be j u s t i f i e d by the f a c t that the slope of the Southern Pine regression l i n e i s not s i g n i f i c a n t l y d i f f e r e n t from that of the Douglas F i r ( F i g . 18). As l i s t e d i n the Wood Handbook(13), Southern Pine ASTM strength in.tension perpendicular to grain at 12% moisture content i s 470 p s i . Using Equation (4) with k = 4.63s b = 1.0854 and s t = 470(1.0854) = 510 psi Using the correction formula f o r moisture content as described 49 In (13). S 4 . = 601 psi at 8.6$ m.c. which i s the average moisture content of the Southern Pine used i n t h i s research. The average s p e c i f i c gravity obtained from 80 pieces cut from tested specimens and oven dried i s O.56. This value i s close to the published value of 0.54(13). Hence, no correction f o r s p e c i f i c gravity i s made. This unit volume strength of 601 p s i i s somewhat lower than the 720 p s i predicted by the regression a n a l y s i s ( P i g . 18). Apparently, the regression analysis based on only three values i s weak. Hence, more tests are required using other specimen sizes than the ones used i n t h i s research so that a better regression l i n e can be obtained. 8.3. Allowable Stresses - Southern Pine In a recently published paper, Barrett, Foschi and Fox(14) presented a method to calculate the allowable stress f o r uniformly stressed blocks where size e f f e c t s are accounted f o r . This method i s to be adopted by the Canadian Standards Association. The method can be expressed i n the formulai Allowable stress, s f t = s1 v~1/*/Z ^ (5) where = unit volume strength at a s u r v i v a l p r o b a b i l i t y of .95 V = volume of block 50 k = shape parameter Z Qc ~ capacity factor, r a t i o between the load f o r a s u r v i v a l probability of .95 and the design load The value of s^ can be calculated by the equation* s x = m ( -In S ) 1 / k where m = scale parameter from the two-parameter Weibull equation S = .95, the survival p r o b a b i l i t y selected k = 4.63, the shape parameter selected The value of m can be calculated by using Equation (3) with P = .50 and k = 4.63» x = 601 p s i for ASTM and x = 720 p s i f o r test strength from t h i s research. The r e s u l t i n g allowable stresses by using Equation (5) are shown in the following table f o r the three specimen volumes used. Allowable stresses f o r Douglas F i r are also l i s t e d . Allowable Stresses i n Tension Perpendicular to Grain - p s i a l l k = 4.63 Southern Pine Douglas F i r ASTM Test Volume-ln.3 s-^343 s-^410 s-,=267* 550 (5x5x22) 55 66 43 56 (2-3/8x2-3/8x10) 89 108 70 6 (1x1x6) 146 175 113 * Barrett (14) 51 These allowable values were obtained by using a capacity factor of 1.6 f o r normal load duration. Allowable stresses could also be calculated from test data by d i v i d i n g the stress at a s u r v i v a l p r o b a b i l i t y of .95 by the capacity f a c t o r of 1.6. Results are shown in the following table J Southern Pine Strength - p s i Volume - in.3 k Stress at S = .95 Allowable Stress 550 4.49 135* 84 56 3.39 170* 106 6 3.56 245* 153 * obtained from Pig. 17. The above two tables show that the allowable stresses in tension perpendicular to grain f o r Southern Pine can d e f i n i t e l y be higher than f o r Douglas F i r . The published allowable value of 67 psi(4) f o r Southern Pine seems to be good 3 only f o r a uniformly stressed volume of about 200 i n . , i f the ASTM strength (s^) i s used in Equation (5). Test r e s u l t s however suggest that the allowable values could be higher due to a higher s^-value. This i s inconclusive due to the limited experiment. It i s suggested that more testing with d i f f e r e n t Southern Pine specimen volumes Is necessary to establish an appropriate unit volume strength s^ to be used i n Equation (5). 52 8 . 4 . Summary Load duration tests were performed with tension perpendicular to grain f o r Douglas F i r f o r a period of 70 days. Glulam block specimens of two sizes, each loaded at three d i f f e r e n t stress l e v e l s , were used. Test r e s u l t s showed strength reductions to increase with time i n a trend d i f f e r e n t from the Madison load duration curve. For p r a c t i c a l design situations, i t i s suggested that the present 2-month, 7-day and 1-day load duration factors could be increased. Short-term tension perpendicular-to-grain tests were also carried out f o r Southern Pine of three d i f f e r e n t volumes. Results showed that Southern Pine i s stronger than Douglas F i r in tension perpendicular to grain. This may p a r t i a l l y explain why no f a i l u r e s in Southern Pine pitched-tapered beams have been found. Size e f f e c t was observed, which agrees cl o s e l y with the prediction of the weakest-link model. However, the size e f f e c t f o r Southern Pine i s almost i d e n t i c a l to that observed in Douglas F i r . Long-term test data were shown to be s i g n i f i c a n t l y d i f f e r e n t between the two specimen volumes. This could be due either to the e f f e c t of size or to the d i f f e r e n t stress l e v e l s used but the r e a l cause could not be established from t h i s limited experiment. 53 10 !00 1,000 10,000 DURATION OF STRESS TO FAILURE (HOURS) F i n ? M A D I S O N T E S T 55 DOUGLAS FIR 5 5>8" (large) Fig. 3 SPECIMEN CONFIGURATION (a) (c) 6" 2.4" Fig. 4 Specimen Mounting Devices Fig. 5 TEST SETUP FOR LARGE SPECIMENS Fig. 6 TEST SETUP FOR SMALL SPECIMENS NORMALIZED RANK Fig. 7 SHORT-TERM STRENGTH -• DOUGLAS FIR TIME - minutes Fig. 8a SURVIVAL RATE FOR LARGE SPEC!f*1EMS 80 N O Z> 00 60 40 20 0 0.1 L i l t 358 PSI 1 J . 1 1 J H I i , l 2 2 6 PSI «—| 277 PSI DOUGLAS FIR • "xl^xG" TENSION PERP. I i i i n n r i 11 i H 226 PSI 277 PSI j 35 8 PSI I J I I I H I I L-, i T J | | M i l l I 226 PSI 1 , JJ. 277 PSI 358 PSI 10 100 1,000 TIME - minutes 10,000 100,000 ON Fig. 8b SURVIVAL RATE FOR S^ALL SPECIMENS NORMALIZED RANK Fig. 9 STRENGTH RATIO - CONTROL CURVE METHOD LOAD DURATION-minutes ON Fig. IOa STRENGTH RATIO vs. TIME (LARGE) CONTROL CURVE METHOD TENSION PERP. © specimen at 358 psi o specimen at 277 psi A specimen at 226 psi M i l l I I I I I HI 10 1 0 0 1 , 0 0 0 LOAD DURATION -minutes 1 0 , 0 0 0 100,0 ( STRENGTH RATIO vs.TIME (SMALL) CONTROL CURVE METHOD DOUGLAS FIR 5!/8" x5^8 "x 12" TENSION PERP. NORMALIZED RANK Fig. Ha RAMKED DATA AT 168 PSI (LARGE) NORMAL IZED RANK Fig. 12a RANKED DATA AT 358 PSi ( SMALL) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 N O R M A L I Z E D R A N K F!g.S2b RANKED DATA AT 277 PSI (SMALL) 600 0.4 0.5 0.6 0.7 NORMALIZED RANK Fid. !2c RACKED DATA AT 226 PSI (SMALL) o S.R. for 1st failure « q/pi S.R. for 2nd failure = q/p2 S.R. for 3rd failure = q/p3 ASSUMED STRENGTH d U A A specimens considered damaged • o ^ o^b c STRESS LEVEL 1 2 3 4 5 6 7 8 9 ranked in order of time to failure P 3 P 2 P I • failure during loading o failure within 70 days A failure on machine after 70 days l l : I J L_ 0.0 0.2 0.3 0.7 0.8 0.4 0.5 0.6 NORMALIZED RANK Fig. 13 STRENGTH RATIO - STAIGHT LINE METHOD 0.9 .C DURATION OF LOAD TO FAILURE - minutes ^ IV) Fig. 14a STRENGTH RATIO vs. TIME (LARGE) STRAIGHT LINE METHOD DURATION OF LOAD TO FAILURE - minutes Fig. 14b STRENGTH RATIO vs.TIME (SMALL) STRAIGHT LINE METHOD 100 90 I I I I 0 s O 80 < or UJ 60 I x I x 6 I I I I II I I I 1 I 1111 5 ,/8"x5'/8"xl2 B I I 111 llli 50 0.1 DOUGLAS FIR TENSION PERR Madison straight line method -control curve method IJLJJUWL i i l i i i n , 1 U J±LU 1 JJ1JJ, ' 1 1 ' " " I 1 111 I I 11 10 100 1,000 10,000 LOAD DURATION - minutes 100,000 1,000,000 Fig. 15 AVERAGE STRENGTH RATIO vs. TIME 1000 800 vt CL 600 (!) SOUTHERN PINE 5" x 5"x 22" TENSION PERP. Loading rate 100 psi/min. 20 psi/min. Weibull N 40 40 0.0 0.1 0-2 0-3 0.4 05 0.6 NORMALIZED RANK 0.7 1.0 Fig. 16a SHORT-TERM STRENGTH - SOUTH. PINE (LARGE) lOOOf 0.0 0.4 0.5 0.6 NORMALIZED RANK Fig. I6b SHORT-TERM STRENGTH - SOUTH. PINE (MEDIUM) NORMALIZED RANK Fig. 16c SHORT-TERM STRENGTH - SOUTH. PINE (SMALL) NORMALIZED RANK Fig. 17 SHORT-TERM STRENGTH - SOUTH. PINE (COMBINED) VOLUME - in.3 DEFLECTION - inches Fig.!9a TYPICAL LOAD-DEFL. PLOTS DOUGLAS FIR Fig.SSt* TYPICAL LOAD-DEFL PLOTS SOUTHERN PINE STRAIN - in./ln. Fig.20a STRESS-STRAIN PLOTS - DOUG. FIR 600 jp Fig. 20b STRESS-STRAIN PLOTS - SOUTH. PINE a Southern P,„e g.4.x*4xio I3ZL IE Failure. Typm /xlx6 HcugUs F i r 1 I M Southern M Pinm. JZ m TIME " days a Fig. 22a LONG-TERM DEFL. AT 168 PSI (LARGE) 98 .10 .08 -C CJ c - .06 A denotes failure D O U G L A S FIR 5 ^ x 5 ' / 8 " x 12" T E N S I O N PERR S T R E S S L E V E L « 125 PSI 10 20 30 40 50 TIME - days 60 70 GO Fig.22c LONG-TERM DEFL. AT 125 PSI (LARGE) x: u c O I-o LJ _J LL LU Q 30 40 50 TIME - days 00 00 Fig.22d LONG-TERM DEFL. FOR SMALL SPECIMENS 6.o r DOUGLAS FIR 5 V x 5 'Vx 12" TENSION PERP. 30 40 50 TIME - days Fig. 23a " CREEP" AT 168 PSI (LARGE) 6.01 5.0 DOUGLAS FIR 5^8" x 5Venx\2n TENSION PERP. no recordings here STRESS LEVEL • 138 PSI 30 40 50 TIME - days 60 70 80 ° Fig. 23b "CREEP" AT 138 PSI (LARGE) TIME - d a y s Fig. 23c "CREEP" AT 125 PSI (LARGE) NO 0 10 20 30 40 50 60 70 80 TIME - days Fig. 23d "CREEP" FOR SMALL SPECIMENS 94 Table 1 : Survival Counts — Douglas F i r 5-1/8" x 5-1/8 (large) " x 12" 1" X 1" X (small) 6" stress l e v e l - p s i 168 138 125 358 277 226 Load Durations (minutes) 40 i 35 sample 34 size 40 40 40 0 28 30 30 25 34 35 1 28 29 (100.0)(96.7) 30 (100.0)* 23 (92.0) 34 35 (100.0X100.0)* 10 28 28 (100.0)(93.3) 30 (100.0) 22 (88.0) 33 (97.1) 34 (97.1) 10 2(1.7 hr.) 27 (96.4) 27 (90.0) 30 (100.0) 14 (56.0) 31 (91.2) 30 (85.7) 10 3(l6.7 hr.) 26 (92.9) 24 (80.0) 29 (96.7) 11 (44.0) 27 (79.4) 29 (82.9) 10^(7 days) 18 (64.3) 18 (60.0) 28 (93.3) 7 (28.0) 16 (47.1) 26 (74.3) 10 5(70 days) 6 (21.4) 12 (40.0) 22 (73.3) 1 (4.0) 9 (26.5) 18 (51.4) * Numbers i n brackets r e f e r r i n g to s u r v i v a l i n percentages expressed r e l a t i v e to the number of specimens i n the test sample that survived f a i l u r e on loading. 95 Table 2a s Strength Data — short-term tests Southern Pine 5"x5"x22" 2-3/8"x2-3/8"xl0 l M x l " x 6 " (large) (medium) (small) loading rate — psi/min. 100 20 100 20 100 20 average time to f a i l u r e - minutes 2.5 12.5 3.8 15.2 5.1 21.4 N 40 40 40 40 42 38 x-psi 230.9 243.2 378.0 357.3 507.3 519.0 s.d.-psi 63.7 54.1 123.5 113.8 146.8 170.0 c.v.-# 27.6 22.2 32.7 31.8 28.9 32.8 Douglas F i r 5-1/8 "x5-l/8"xl2" (large) l " x l " x 6 " (small) loading rate 100 - psi/min. 200 average time to 2.0 failure-minutes 1.7 N 40 40 x-psi 180.7 3^7.7 s.d.-psi 48.3 103.2 c.v.-# 26.7 29.7 96 Table 2b « Strength Data — Southern Pine combined samples Southern Pine 5"x5"x22" 2-3/8 , ,x2-3/8"xl0" l n x l " x 6 M (large) (medium) (small) N 80 80 80 x - p s i 237.0 367.6 512.8 s.d. - psi 59.8 119.9 159.9 c v . - % 25.2 32.6 31.1 97 Table 3 : Coeff i c i e n t s of Regression Equation* shape coeff. of degree parameter determina- of ti o n freedom a** k R 2 DF Southern Pine combined(means) 2.860 5.747 0.99 1 Douglas F i r a l l data(means, weighting by sample s i z e ) * * * 2.654 4.902 0.87 11 * log. x m a x = a - (1/k) log. V (2) ** Logarithm of unit volume strength. *** Barrett(11). Table 4 : Parameters of Welbull D i s t r i b u t i o n * Southern Pine specimen size sample size N scale parameter m (psi) shape parameter k 5"x5"x22" (large) 80 259.8 4.491 2-3/8"x2-3/8"xl0" (medium) 80 409.2 3.390 l M x l " x 6 " (small) 80 569.4 3.555 average = 3.812 Douglas F i r specimen size sample size N scale parameter m (psi) shape parameter k 5-1/8"x5-l/8Hx-12" (large) 40 198.9 4.162 l"x l " x 6 " (small) 40 385.2 3.710 -(x/m) k * F = 1 - e v ' ' . (3) 98 Table 5$ Modulus of E l a s t i c i t y Southern Pine 5"x5,,x22" 2-3/8 "x2-3/8"xl0" l " x l M x 6 " (large) (medium) (small) N 82 33 74 x - 10 3 p s i 126.2 106.3 94.7 s.d.-10 3 p s i 46.6 49.8 43.5 c v . - % 36.9 ^6.8 45.9 Overall average E-value f o r Southern Pine = 109.1x10-* p s i (no weighting) Douglas F i r 5-l/8"x5-l/8"xl2" l " x l " x 6 " (large) (small) N 36 37 x - 10 3 p s i 118.3 67.8 s.d.- 10 3 p s i 61.8 22.8 c v . - % 52.2 33.6 Overall average E-value f o r Douglas F i r = 93.1 x 103 p s i (no weighting) 99 Table 6a s Moisture Content — short-term test samples Southern Pine 5"x5"x22M 2-J/Q"x2-J/QnxlO" l " x l " x 6 " (large) (medium) (small) N* 240 160 80 x - % 8.2 8.9 8.7 s.d.- % 1.1 0.54 0.46 o.v.- % 12.8 6.0 5.3 Overall average m.c. f o r Southern Pine = 8.6$ (no weighting) Douglas F i r 5-1/8 "x5-l/8 "x l2" l " x l M x 6 " (large) (small) N* 80 40 x - % 7.28 7.46 s.d.- % 0.46 0.34 c v . - % 6.3 4.5 Overall average m.c. f o r Douglas F i r = 7.4$ (no weighting) * Total number of mvc. recordings f o r the test sample. 100 Table 6b : Moisture Content — long-term test samples 5-1/8 "x5-l/8' (large) •xl2" stress l e v e l - psi l" x l " x 6 " (small) 168 138 125 358 277 226 N* 80 70 68 37 39 40 X - % 7.80 7.96 8.56 8.55 8.17 8.15 s .d, - % 0.67 0.65 0.66 0.79 0.62 0.60 c v . - % 8.6 8.2 7.7 9.2 7.5 7.4 Overall average m.c. = 8.2% (no weighting) * Total number of m.c. recordings f o r the test sample. 101 Table 7a : Failure Type Counts — short-term tests Southern Pine 5"x5"x22" 2-3/8"X2-3/8"xlO" l " x l " x 6 " (large) (medium) (small) Fa i l u r e Type* 80 sample size N 80 80 I 18 10 4 II 14 20 21 III 27 35 22 IV 21 15 33 Douglas F i r 5- 1/8"X5T1/8 mX12" 1"X1"X6" (large) (small) Fa i l u r e Type* sample size N 40 40 I 10 15 II 8 9 III 15 9 IV 7 7 * F a i l u r e types as defined i n Section 7.3. of the text. 102 Table 7b s Failure Type Counts — long-term tests Douglas F i r 5-1/8"x5-l/8"xl2 M l " x l " x 6 " (large) (small) sample size N* 109 1 2 0 load duration Failu r e Type** f a i l on load. within 70 days post-70-day t o t a l f a l l on load within 70 . days post-70-day t o t a l I 12 18 10 40 14 17 3 34 II, 1 10 11 22 4 15 7 26 III 1 17 17 35 3 30 16 49 IV 7 3 2 12 5 4 2 11 Total 21 48 40 109 26 66 28 120 * Combining the samples f o r the three stress l e v e l s . ** Failure types as defined i n Section 7.3. of the text. 103 LIST OF REFERENCES 1 . FOSCHI, R.O. 1 9 6 8 . P l a n e - s t r e s s problem i n a body w i t h c y l i n d r i c a l a n i s o t r o p y , with s p e c i a l r e f e r e n c e t o curved Douglas F i r beams. Department of F o r e s t r y and Ru r a l Development, Departmental P u b l i c a t i o n No. 1244, Ottawa, O n t a r i o . 2 . FOX, S.P. 1 9 7 0 . Experimental v e r i f i c a t i o n of a s t r e s s a n a l y s i s method f o r the double-tapered p i t c h e d g l u e d -laminated beam. Department of F i s h e r i e s and F o r e s t r y , P u b l i c a t i o n No. 1277, Ottawa, O n t a r i o . 3. CODE OF RECOMMENDED PRACTICE FOR ENGINEERING DESIGN IN IN TIMBER. C.S.A. 0 8 6 , Canadian Standards A s s o c i a t i o n , Ottawa, 1 9 7 0 . 4. TIMBER CONSTRUCTION MANUAL, second e d i t i o n , American I n s t i t u t e of Timber C o n s t r u c t i o n , John Wiley, New York, 1 9 7 4 . 5. WOOD, L.W. 1951. R e l a t i o n of s t r e n g t h of wood to d u r a t i o n of l o a d . U.S. Department of A g r i c u l t u r e , F o r e s t Products Laboratory, Report No. 1 9 1 6 . 6 . MADSEN, B. 1 9 7 2 . D u r a t i o n of loa d t e s t s f o r wood i n t e n s i o n p e r p e n d i c u l a r to g r a i n . U n i v e r s i t y of B r i t i s h Columbia, Department of C i v i l E n g i n e e r i n g , S t r u c t u r a l Research S e r i e s No. 7 t Vancouver, B.C. 104 7. MADSEN, B. 1971. Duration of load tests f o r dry lumber i n bending. University of B r i t i s h Columbia, Department of C i v i l Engineering, Structural Research Series No. 3, Vancouver, B.C. 8. MADSEN, B. 1972. Duration of load tests f o r wet lumber in bending. University of B r i t i s h Columbia, Department of C i v i l Engineering, Structural Research Series No. 4, Vancouver, B.C. 9. MADSEN, B. 1972. Duration of load tests f o r dry lumber subjected to shear. University of B r i t i s h Columbia, Department of C i v i l Engineering, Structural Research Series No. 6, Vancouver, B.C. 10. PETERSON, J. 1973. Oregon State University, C o r v a l l i s . Personal communication. 11. BARRETT, J.D. 1974. Effect of size on tension perpendicular-to-grain strength of Douglas-fir, Wood and Fiber 6{Z)i 126-143. 12. MADSEN, B. 1972. An engineering approach to estimating the 5th percentile l e v e l s f o r s t r u c t u r a l properties of wood. University of B r i t i s h Columbia, Department of C i v i l Engineering, Structural Research Series No. 8, Vancouver, B.C. 105 13. WOOD HANDBOOK, revised e d i t i o n , Handbook No. 72, U.S. Department of Agriculture, 1974. 14. BARRETT, J.D., R.O. FOSCHI and S.P. FOX. 1975. Perpendicular-to-grain strength of Douglas-fir. Canadian Journal of C i v i l Engineering 2 ( 1 ) s 50-57. 

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