RACKING STRENGTH OF PAPERBOARD BASED SHEATHING MATERIALS

Transcription

1 ABSTRACT RACKING STRENGTH OF PAPERBOARD BASED SHEATHING MATERIALS by Wu Bi A small-scale racking test was developed to evaluate paperboard sheathing materials used for framed-wall construction and provided an economic alternative to standard wall tests. Both 16in and 32in sample sizes were investigated. The load-deformation response of three commercial sheathing boards was investigated, and initial racking stiffness and racking strength were proposed as parameters for characterizing the board. The racking test results showed that the initial paperboard racking stiffness correlated to elastic modulus and caliper, but the response was insensitive to paperboard orientation or test dimensions. Observations and results showed that both panel buckling and paperboard cutting at the staples affected the racking response. The results presented in this thesis indicated that the dominate factor influencing the racking response was load transfer to the frame through the staples as shown by the much stiffer response of samples where the sheathing was attached to the frame with glue.

2 RACKING STRENGTH OF PAPERBOARD BASED SHEATHING MATERIALS A Thesis Submitted to the Faculty of Miami University in partial fulfillment of the requirements for the degree of Master of Science Department of Paper Science and Engineering by Wu Bi Miami University Oxford, Ohio 2004 Advisor Dr. Douglas Coffin Reader Dr. Amit Shukla Reader Prof. Michael Waller

3 TABLE OF CONTENTS 1.0 Introduction Racking Strength and Stiffness of Paperboard Shearing Literature Review Racking Test Standards Lateral Nail Resistance Test Small-scale Racking Test Problem Analysis Standard Racking Tests Analysis The Designed Racking Test Analysis & Correlation with Standard Racking Test Problem Statement Proposed Hypotheses Experimental Design Experiments Materials, Characterization and Instruments Simplified Small-scale Racking Tester and Testing Design in & 16in Racking Testers General Racking Testing Procedures Paperboard Buckling Measurement Data Analysis Methods (Slope Method) Paperboard Staple Resistance Tests Testing Program Results and Discussion Paperboard Characterization 47 ii

4 4.2 Effects of Paperboard Orientation on Racking Strength Effects of Paperboard Properties on Racking Strength in Racking Tests in Racking Tests Effects of Middle Stud in 32in Racking Tests in & 16in Racking Tests Comparison Paperboard Staple Resistance Study Paperboard Staple Cutting and Buckling in Racking Tests Gluing for Sheathing Application Conclusions and Summary Main Features of Designed Small-scale Racking Tester Mechanics of Racking Test Effects of Paperboard Properties on Racking Strength Recommendations for Future Work References Appendix..92 iii

5 LIST OF TABLES Table 1: Table 2: Table 3: Table 4: Table 5: Table 6: Table 7: Table 8: Table 9: Table 10: Table 11: Characterization data of three grades of paperboards Two types of slope values of 32in racking tests with three grades of paperboards without middle stud Slope values of three grades of paperboards using the same 32in racking tester setup (setup 16)..54 Two types of slope ratios of 32in racking tests and paperboard modulus (kpli) ratios comparison within three paperboard grades (H: highesttype; V: average-type) in racking tests slope values of three grades of paperboards (setup S12-14).58 Slope ratios of 16in racking tests and paperboard modulus (kpli) ratio comparison within three paperboard grades. 58 Buckling extent (in) of 16in racking tests measured at the net racking extension of 0.12in and 0.18in.59 Paperboard staple cutting forces (lb) in staple resistance tests...74 Comparison of actual maximum racking load to the calculated values by staple resistance test Slope data (average-type and highest-type) for 16in racking tests with glue method, and compared to average slopes of 16in tests using staple methods...80 Slope ratios of 16in racking tests by glue and paperboard modulus (kpli) ratio comparison within three paperboard grades.. 83 iv

6 LIST OF FIGURES Figure 1: Racking test wall configuration for ASTM E 72 [2] (Reprinted with permission from ASTM International)...3 Figure 2: Racking test assembly for ASTM E564 [3] (Reprinted with permission from ASTM International) Figure 3: Measurement of wall-diagonal elongation [3] (Reprinted with permission from ASTM International)...4 Figure 4: Standard wood frame for racking test (ASTM E72 [2]) (Reprinted with permission from ASTM International)... 6 Figure 5: Test assembly for lateral nail resistance measurement [10] (Reprinted with permission from ASTM International)...8 Figure 6: Experimental vs. predicted racking performance for wall sheathed gypsum board in McCutcheon s research work [9] (Reprinted with permission from ASCE) Figure 7: Small-scale loading apparatus by USDA Forest Service FPL [4] 10 Figure 8: Experimental vs. predicted racking performance for wall sheathed lowdensity ½ in. orientated flakeboard (left) and ½ in. pine flakeboard (right) in McCutcheon s research work [9] (Reprinted with permission from ASCE)..11 Figure 9: Small-scale racking test frame in Patton-Mallory s work [11] (Reprinted with permission from ASCE).11 Figure 10: Racking load vs. wall aspect ratio for gypsum walls sheathed on one side (redrawn based on the Patton-Mallory s data from [11]).12 Figure 11: Racking load vs. wall aspect ratio for small walls double or single sheathed (redrawn based on the Patton-Mallory s data from [11])..13 Figure 12: Set-up for simple racking test system [12] Figure 13: Direct shear.. 14 Figure 14: Shear buckling of infinite panel [12] Figure 15: Standard racking loading and resulting first order stress state. 20 Figure 16: New racking test loading and resulting first order stress state.20 Figure 17: Horizontal racking displacement ( ) in standard racking test condition v

7 Figure 18: Diagonal racking displacement (δ) in the designed racking test condition...22 Figure 19: Setup of the designed simplified small-scale racking tester system (left) and 32 by 32in racking test frame (right) Figure 20: Corner connection design of two metal frame sides Figure 21: Two metal frame sides connected by a hatch pin. 27 Figure 22: U-shaped small-scale (32by32in) racking test frame connected on the MTS tensile tester without inserted edge woods..28 Figure 23: Paperboard orientation test using a middle wood stud in 32by32in racking tester 29 Figure 24: Edge wood used in the 16in racking test Figure 25: Edge wood inserted in the metal frame of 16in racking test 30 Figure 26: Stapler and staple used for paperboards sheathing applying 32 Figure 27: Effect of loose screw connection on the load-extension curve (16by16in racking test Setup S12)...33 Figure 28: Effect of four not-centered staples in one side on the racking load-extension curve (16by16in racking test Setup S13). 34 Figure 29: Ruler and holder for racking test buckling measurements Figure 30: 16in racking tester frame with attached holder for buckling measurement Figure 31: Ruler for buckling measurement in 16in racking test..36 Figure 32: Examples of raw load-extension curves tested by the designed 16in racking tests with structural (B) paperboards Figure 33: Examples of calculated slope (lb/in) curves vs. raw diagonal extension (in) in 16in racking test with structural (B) paperboards Figure 34: Slack deformation removal by slope method Figure 35: Illustration of slope average...41 Figure 36: Comparison of paperboard edge alignment before and after racking test...42 Figure 37: Setup of the staple resistance test with one perpendicular staple Figure 38: Illustration figure of staple resistance test (using 2 staples).43 Figure 39: One example of staple resistance test load-strain curve vi

8 Figure 40: Structural (B) paperboards CD/MD orientation comparison...48 Figure 41: Super structural (C) paperboards CD/MD orientation comparison..49 Figure 42: Super structural (C) paperboards CD/MD orientation comparison (only data from second wood surface)...50 Figure 43: Racking shear strength-shear strain curves of 32in racking tests with three grades of paperboards Figure 44: Different shapes of three grades of paperboards..53 Figure 45: Load-strain curves of three grades paperboards on the same setup S16 of 32in racking tester without middle stud.. 54 Figure 46: 16in racking tests load-shear strain curves (setup S12-S14)...57 Figure 47: Comparison of 32in racking tests with and without middle stud for standard (A) paperboards Figure 48: Comparison of 32in racking tests with and without middle stud for structural (B) paperboards...61 Figure 49: Comparison of 32in racking tests with and without middle stud for super structural (C) paperboards Figure 50: Initial highest-type slope (average values) comparison between 32in/16in racking tests...63 Figure 51: Initial average-type slope (average values) comparison between 32in/16in racking tests...63 Figure 52: Racking load-strain curves of 32in and 16in test for paperboard A 65 Figure 53: Racking load-strain curves of 32in and 16in test for paperboard B 66 Figure 54: Racking load-strain curves of 32in and 16in test for paperboard C.66 Figure 55: Paperboard staple resistance test with different net tension length using one, two and three parallel staples (Board A, MD samples) Figure 56: Comparison of tensile test and staple resistance test with two parallel staples (MD samples of board A) Figure 57: Effects of parallel staple numbers using MD samples of paperboard B...70 Figure 58: Effects of parallel staple numbers using MD samples of paperboard C...71 Figure 59: Effects of parallel staple numbers using CD samples of paperboard C...72 vii

9 Figure 60: Figure 61: Figure 62: Figure 63: Figure 64: Figure 65: Figure 66: Figure 67: Staple resistance Load-stain curves for three grades of paperboard CD samples with one staple perpendicular to loading direction.73 Staple maximum cutting force in resistance test vs. paperboard caliper with best-fit linear lines (one staple perpendicular to loading direction). 74 Illustrations of staple leg cutting fibers in paperboard slips.75 Racking load-strain curves of 32in tests with paperboard C using different number of staples in racking tests load-shear curves using glue as sheathing method in racking tests of standard (A) paperboards using glue and staples in racking tests of structural (B) paperboards using glue and staples in racking tests of super structural (C) paperboards using glue and staples...82 viii

10 LIST OF SYMBOLS a Height of shear wall b Length of shear wall Stud span in racking tests B.W. Basis weight of paperboard as sheathing materials C Restraint coefficient at shear wall edges E Elastic modulus of paperboard (lb/in 2 ) E 1, E 2 Paperboard elastic modulus (lb/in 2 ) at the specified direction of 1 or 2 E MD, E CD Elastic modulus (lb/in 2 ) at paperboard MD or CD direction F Racking strength from the basic frame (lb) in eq. (1-2) G In-plane shear stiffness (lb/ft 2 ) H Height of racking frame or racking wall K Racking coefficient (dimensionless) in eq. (1-2) Racking coefficient for frame contribution (lb/in) in eq. (1-8) L Length of racking frame or racking wall N Number of sheathing sheets on the frame in eq. (1-2) p Racking load per unit length (lb/ft) P Racking load (lb) P 1, P 2 Racking load (lb) for racking condition 1 or 2 p cr P F P S Critical buckling load per unit length (lb/ft) Racking load (lb) from racking frame contribution Racking load (lb) from sheathing material contribution R Ultimate racking strength (lb) in eq. (1-2) S Lateral nail resistance of a single fastener at ultimate load (lb) in eq. (1-2) t Paperboard thickness or caliper (in) t p δ γ Sheathing material thickness in points Diagonal deformation of racking test Shear stain in racking test γ 1 γ 2 Shear stain for racking test condition 1 or 2, int Horizontal racking deformation 1, 2, 3, 4 Horizontal or vertical deformation at the position 1, 2,3 or 4 in the standard racking test according to ASTM E564 ix

11 τ Shear stress in racking test τ 1, τ 2 Shear stress at racking test condition 1 or 2 x

12 ACKNOWLEDGEMENTS This thesis work definitely couldn t be finished without the suggestions and help from faculty, staff and students of Miami University (Oxford, Ohio). First of all, I would like to thank my research advisor, Dr. Douglas Coffin, for his consistent support, guidance and patience throughout this project. Mr. Rodney Kolb, the research staff of paper science department, also contributed a lot to this project in designing and making the racking testers and preparing testing materials. Dr. Amit Shukla and Prof. Michael Waller as the thesis committee members, gave many valuable suggestions for both research and the final thesis edition. Also, I would like to thank all the other faculty, staff and graduate students in paper science department for their suggestions and help. Also special thanks to the company of Fibre Converters (Constantine, MI) providing testing paperboards and to Dr. Chris Peterson for contributing some testing woods. Finally, to my parents in China and my cousin in Cincinnati (Ohio), love and thanks. Without their great support the project would never have been possible. xi

13 1.0 Introduction The walls of buildings must have adequate strength and rigidity to resist wind and seismic forces. Sheathing materials are normally applied to one or both faces of wall framing to limit in-plane wall distortion, called racking, and prevent collapse. Common sheathing materials used in home construction include plywood, gypsum board and flakeboard, which have thickness on the order of one half-inch. Paper based sheathing materials are now being produced for prefabricated homes. The caliper of these materials is less than one eighth of an inch. Currently, the racking strength of these materials is inadequate for general home construction, but if the racking strength could be improved these paperboard sheathing materials could be applied to other building applications. Wall-racking tests are used to evaluate sheathing materials racking stiffness and strength and actual wall performance. For shear wall applications, the HUD Minimum Property Standards (U.S. Department of Housing and Urban Development 1979) [1] required that an 8-by-8ft-wall must carry a minimum ultimate load of 5200lbs, as determined from ASTM (American Standard for Testing and Materials) E72 [2]. Also, maximum deformation and maximum residual deformation at 1200lbs and 2400lbs were specified [1]. Standard racking test according to ASTM E72 tests an 8 by 8ft wall racking performances, which is time-consuming and expensive. An alternative test, the lateral nail resistance test, was found to be an unreliable prediction of the full-scale (8 by 8ft) wall racking strength because nail behavior is not same in the lateral nail resistance test and standard wall racking test. It is desirable to design a small-scale racking test to evaluate sheathing material properties. A small-scale racking test would be less expensive and timesaving. The scope of this thesis work was to design a simplified small-scale racking tester and investigate the mechanics of the racking test. Two picture-frame shear testers were developed for use in a Universal tester. Using commercial paperboard based materials a series of tests were conducted to determine how the test results were affected by conditions, such as number of staples, and paper properties such as 1

14 orientation. In the following, the literature on racking testing is reviewed, the design and set-up for the new small-scale racking testers is described, and results of testing are presented and analyzed. 1.1 Racking Strength and Stiffness of Paperboard Shearing Paperboard sheathing materials are used in the construction of homes providing both in-plane shear stiffness and insulation. HUD specifies minimum racking strength values for home construction [1]. Racking load is the load in the plane of a framed wall required to shear the wall a certain deflection. Standard procedures such as ASTM E72 [2], HUD [1] and TAPPI T1005 cm-83 [14] have already been fairy well established to measure racking strength of the framed and sheathed walls (8 by 8ft, or 2.4 by 2.4m). A general wall racking test configuration without sheathing materials is shown in Figure 1 [2]. The bottom of the test panel is attached to a timber or steel plate that is fixed to the base of the loading frame. Horizontal loading is applied to the top of the loading frame and is measured by the testing machine. According to American Standard for Testing and Materials (ASTM) E 72 [2], the shear displacement can be expressed by the calculated horizontal deflection based on measurements using a three-gage method (Figure 1). Three indicating dials are located in the lower left, lower right and upper right corners of the testing assembly. The lower left dial and lower right dial measure the rotation of the panel and slippage of the panel, respectively. And the upper right dial measures total of rotation and slippage plus the panel deformation. The horizontal deflection ( ) can be calculated by subtracting the sum of the two lower dials readings from the upper right dial reading. 2

15 Figure 1: Racking test wall configuration for ASTM E 72 [2] (Reprinted with permission from ASTM International) Figure 2: Racking test assembly for ASTM E564 [3] (Reprinted with permission from ASTM International) 3

16 For the racking test according to ASTM E 564, which is used to simulate the actual complete wall performance (Figure 2 [3]), the shear displacement can be expressed either by the measured wall-diagonal elongation δ (Figure 3 [3]), or the calculated horizontal internal shear displacement int. The diagonal elongation can be easily and directly measured, while the internal shear displacement can be calculated by measuring the vertical and horizontal displacements at the bottom and top of the wall (Figure 2 [3]). The relationship between diagonal elongation (δ) and internal shear displacement ( int or ) is shown by the calculation formula in Figure 3 [3]. Figure 3:Measurement of wall-diagonal elongation [3] (Reprinted with permission from ASTM International) The internal shear displacement ( int) can be calculated by the following Equation (1-1) [3]. a int= ( 2-4) (1-1) b Where, a: height of the shear wall in Figure 2 (m or ft) b: length of the shear wall in Figure 2 (m or ft) 1: horizontal slip of the base point 1 in Figure 2 (m or ft) 4

17 2: vertical displacement of the base point 2 in Figure 2 (m or ft) 3: horizontal displacement of the top point 3 in Figure 2 (m or ft) 4: vertical displacement of the base point 4 in Figure 2 (m or ft) Comparisons were made by Tuomi and Gromala [4] between the three-gage method and the diagonal method. They found that the three-gage method had slightly larger deflections at the same loading forces. It was put forth that this discrepancy was caused by the incorrect assumption in the three-gage method that the panel rotates as a rigid body. The measurement of the wall-diagonal elongation facilitates the analysis of panel racking deformation and evaluation of the sheathing materials without the need of accounting for wall rotation and translation. 1.2 Literature Review Racking Testing Standards When the use of wallboard sheathing first arose, a general guidance was developed in 1949 for racking tests, and was contained in the Federal Housing Administration (FHA) Technical Circular No. 12 (6). It was only to function as an interim standard pending establishment by a nationally recognized permanent standard. Now the ASTM (American Standard for Testing and Materials) standard test E 72 [2] and Test E564 [3] are commonly applied for racking tests. As for the ASTM standard test E72, a standard frame (8 by 8ft, or 2.4 by 2.4m) is used with sheathing materials such as plywood, gypsum board, structural insulating board, etc. The standard wood frame and the racking load assembly are shown in Figure 4 and Figure 1, respectively. Although the sheathing materials are the main contributor to racking strength and stiffness, the frame also adds to the strength and stiffness. Therefore, for the case where ASTM E 72 is applied to evaluate the stiffening effect of the sheathing materials, new identical frames built by the specified wood species with the same average density should be used for each racking test. The test frame should not only have the same structure as that in Figure 4, but also be conditioned to have the similar moisture content 12-15%. In addition, the attachment of sheathing to the test frame is very important. Fasteners should be appropriately driven perpendicular to the 5

18 sheathing surface with recommended spacing and pattern. Slight differences of fastener penetration, angle of fasteners or edge clearance can result in appreciable variations on testing results. Figure 4: Standard wood frame for racking test (ASTM E72 [2]) (Reprinted with permission from ASTM International) As for the ASTM E 564 [3] that is used to simulate the actual complete wall performance, no standard wood frame or boundary conditions are recommended. During a racking tests complying with ASTM E 564, the boundary conditions are to be selected so that they are similar to the actual wall conditions used in practice. According to ASTM E 72 and E564, at least 2 or 3 runs with new testing arrangements should be done for each test. Both kinds of the full-scale wall racking 6

19 tests are expensive and time-consuming to run for research and factory quality control purposes. So there is a need for a more convenient and less expensive tests that can predict the racking resistance of the sheathing and sheathed wall Lateral Nail Resistance Test One simplified test used to help evaluate sheathing materials is the lateral nail resistance test. The relationship between the racking strength and lateral nail resistance has been investigated [4-9] for applications with fiberboard having a thickness of about one-half-inch thickness wood fiberboards. The lateral nail resistance test measures the resistance of a nail to lateral movement through a board. The standard test assembly for ASTM D 1037 is shown in Figure 5 [10]. Before the test, nails are appropriately driven into the board at the center of the board width and are located ¼, 3/8, ½ or ¾ in. (6, 9, 12 or 18 mm) from the board end. Both Neisel s [5-6] research work on ¾ in. fiberboard sheathings during the 1950 s and Welsch s [7] study on 1/2 in. fiberboard sheathings during the 1960 s showed that there were linear relationships between the ultimate racking strength (R: lb) and ½ inch lateral nail resistance (L: lb). Each study found different constants for the linear relationships. To best fit the experimental data in the plots of the ultimate racking strength (lb) vs. the lateral nail resistance (lb), the different slopes (all positive) and interceptors (negative or positive) were yielded in the different models. All the racking tests and the lateral nail resistance tests were conducted in accordance with ASTM E 72 and ASTM D 1037, respectively. The differences were believed to be related with different nails used and the different loading rate for both racking test and lateral nail resistance test. 7

20 Figure 5: Test assembly for lateral nail resistance measurement [10] (Reprinted with permission from ASTM International) In 1977, an equation for calculating ultimate racking load was developed by Tuomi and Gromala [4] as show in Equation (1-2). This expression is based on an energy balance that specifies the work done by the externally applied load resisted by the internal energy offered by the fasteners. The equation assumes that the frame distorts like a parallelogram while the sheathing material stays rectangular. R= N S K + F (1-2) Where, R: the ultimate racking strength (lb) S: the lateral nail resistance of a single fastener at ultimate load (lb) N: number of sheathing sheets on the frame F: the racking strength from the basic frame (lb) K: racking coefficient Although Tuomi and Gromala s [4] results from ½ and 25/32in regular-density fiberboard sheathings showed good agreement between the actual ultimate racking strength and the predicted value calculated by the linear equation, further research work by Price and Gromala [8] shows the linear equation is not applicable for sheathing materials (1/2 and 5/8 in. flakeboard) with high racking strengths. More recently, a general nonlinear model based on the energy approach was developed by McCutcheon [9]. A simple power curve was used to define the nonlinear 8

21 relationship between nail loading and nail slip. But the racking strength prediction by this analytical model was not excellent as shown in Figure 6. Figure 6: Experimental vs. predicted racking performance for wall sheathed gypsum board in McCutcheon s research work [9] (Reprinted with permission from ASCE) Small-scale Racking Test In addition to predicting racking strength using the lateral nail resistance test, smallscale wall racking tests have been utilized to evaluate sheathing materials and predict full-scale wall racking behaviors [4, 8, 9, 11]. The small-scale racking test is more convenient and less expensive than the full-scale racking test. It also has been found to yield a more reliable prediction of racking strength than the nail resistance test [9]. However there is little research work investigating small-scale tests. Currently no small-scale racking test standard is available. ASTM E 72 and ASTM E 564 can function as the reference before new standard for small-scale racking test is developed. Back in 1970 s, a small-scale loading apparatus, as shown in Figure 7, was developed by Forest Products Laboratory (FPL) [4]. Both small-scale (2 by 2ft) and full-scale (8 by 8ft) racking tests were done to study the relationships between racking strength and lateral nail resistance [4, 8]. However the research group did not further 9

22 investigate and study the relationship between full-scale and small-scale racking strength. Figure 7: Small-scale loading apparatus by USDA Forest Service FPL [4] More recently, McCutcheon [9] replaced the lateral nail tests with small-scale racking tests to infer the nail behaviors during racking test, which was further used to calculate full-scale wall racking behaviors. This kind of small-scale=>nail load-slip=>full-scale method was applied on the considerations of that the nail behaviors during lateral nail resistance test was not exactly the same as that during in racking test. Accurate predictions could be made on full-scale wall racking behaviors up to moderate load levels. The comparisons of actual racking behavior and predicted one were shown in Figure 8. In 1985, Patton-Mallory et. al [11] studied the effect of the wall length on the racking strength for both small-scale (Height=2 ft, Length=2-8ft) and full-scale (Height=8 ft, Length=8-24ft) tests. The small-scale racking test frame used in this study [11] is shown in Figure 9. The racking load is applied at the lower right corner of the frame. The steel test frame forces the wall to deform as a parallelogram. The horizontal wall displacement can be simply calculated by measuring the upper right corner and lower 10

23 left corner displacements. The ultimate racking load is measured as the load when the load no longer increased with increasing wall deformation. Figure 8: Experimental vs. predicted racking performance for wall sheathed lowdensity ½ in. orientated flakeboard (left) and ½ in. pine flakeboard (right) in McCutcheon s work [9] (Reprinted with permission from ASCE) Figure 9: Small-scale racking test frame in Patton-Mallory s work [11] (Reprinted with permission from ASCE) Ultimate racking loads were plotted against wall aspect ratio (Length/Height) for both full-scale and small-scale single-sheathed gypsum walls as shown in Figure 10. For both types of walls, the ultimate racking load was proportional to wall length for 11

24 aspect ratios ranging from 1 to 3. The stiffness (racking load per unit length) for full-scale wall did not exhibit similar behavior and longer walls had larger stiffness values. For the small-scale walls that are double or single sheathed with plywood and/or gypsum, the ultimate racking strengths are similarly proportional to aspect ratio except for the double-sheathed gypsum walls. The detailed results are shown in Figure 11. For the tests using double-sheathed gypsum boards, the ultimate racking stiffness decrease with increasing the small-scale wall aspect ratio. McCutcheon [9] and Patton-Mallory s [11] research work suggest that it is possible to predict full-scale wall racking behavior by small-scale racking tests. McCutcheon [9] concluded small-scale racking tests were more reliable than the lateral nail resistance tests. For paper-based products, no information on racking behavior can be found in the literature. In addition, staples are used instead of nails, and again no information on the resistance of the staples can be found in the literature. The need for alternative testing methods to evaluate the racking strength of walls sheathed with paper-based materials does exist. Figure 10: Racking load vs. wall aspect ratio for gypsum walls sheathed on one side (redrawn based on Patton-Mallory s data from [11]). 12

25 Figure 11: Racking load vs. wall aspect ratio for small walls double or single sheathed (redrawn based on Patton-Mallory s data from [11]). 1.3 Problem Analysis Standard Racking Tests Analysis Previous research works focus mainly on the ultimate racking strength to check wall racking properties or evaluate sheathing materials that are either gypsum board or wood based. Many of these materials are much thicker than the paper-based sheathing boards. In addition to maximum racking strength, the standards specify a minimum racking load at a deflection of inch for an 8by8 ft wall. Thus, for the paper-based sheathing we are mainly interested in small deflections and the pertinent structural properties, may be quite different than in previous studies. We hypothesize that instead of nail or staple pullout dominating the load deformation behavior it will be the in-plane shear stiffness and panel shear buckling characteristics of the sheathing material itself. Thus, changes to the material could have a significant impact on the racking stiffness. An equation for estimating the racking load at small racking deflection (0.125 in.) was developed by Coffin and Hsieh [12]. A simple picture of the racking testing system is shown in Figure 12. The bottom of the testing frame is fixed to a base. During the test, 13

26 the racking load (P) is applied at the top of the frame and the horizontal deflection ( ) is measured. Although the frame also contributes to the racking strength, the sheathing material is the main contributor. The relevant test to evaluate the behavior of sheathing is believed to be a direct shear test as illustrated in Figure 13. Figure 12: Set-up for simple racking test system [12] Figure 13: Direct shear 14

27 For small deformation ( =0.125in. over 8 ft) conditions, the assumption can be made that shear stress (τ: lb/ft 2 or N/m 2 ) is proportional to the engineering shear strain (γ: dimensionless). τ = Gγ (1-3) G is the in-plane shear stiffness with the unit lb/ft 2 or N/m 2 and can be estimated by the empirical relationship with MD and CD direction modulus (E MD and E CD ) that are determined by tensile tests [15]. G= 0.39 EMDE CD (1-4) As for the racking load (P), it can be viewed as the sum of two parts from frame (P F ) and sheathing materials (P S ). The shear stress (τ) on the sheathing materials can be calculated by dividing the load P S by the wall length (L) and the sheathing thickness (t). PS τ = (1-5) Lt And the shear strain (γ) can be estimated by dividing the racking deflection ( ) by wall height (H). γ = (1-6) H So Equation (1-3) can be rewritten as the Equation (1-7). PS Lt L = G or PS = Gt (1-7) H H And the racking load for frame (P F ) can also be estimated using a similar expression with K as frame stiffness (lb/ft). 15

28 L = (1-8) PF K H So the total racking load (P) can be expressed as the sum of the above two equations. L P= Ps+ PF = ( Gt+ K) (1-9) H The expression derived above is based on small shear strain (γ). For an 8 by 8 ft wall, γ= /H=0.125 in./8ft=0.125/(8*12)= , which is fairy small and the Equation (1-9) is justifiable. It is believed that Equation (1-9) will overestimate the actual racking strength because the stress-strain curve of paper is not linear and more importantly buckling of the panel is likely to occur. If we assume (1) K=0, (2) L=H, (3) Equation (1-4) is reasonable, and (4) scaling the racking load with thickness of the board to a common laminated thickness of 100 points, the Equation (1-9) can be rewritten as the Equation (1-10). 100 P= 0.39( EMDECD t) ( ) (1-10) tp Where, t p is the thickness of the board in points. If we use p=p/l (load per foot of wall length) as the predicted load, the Equation (1-10) is changed to be Equation (1-11). P 100 p= = 0.39( EMDECD t) ( ) (1-11) L L tp The predicted p values might be higher than actual values due to several reasons explained by Coffin and Hsieh [12]. The most important reason would be the initial waviness or panel buckling of the sheathing materials before inch deflection, which greatly reduces the shear stiffness and racking load at a certain deflection. 16

29 Critical buckling of a shear panel was investigated by Coffin and Hsieh [12]. For a racking test with stud span (b=16 in.) and height (H=96 in.) which gives H/b=6, the solution of buckling of an infinite strip subjected to shear as given by Lekhnitskii [13] can be applied. The described problem is shown in Figure 14. In Equation (1-12), p cr represents the critical shear load per unit length on the panel, b is the spacing between studs, x (or 1) and y (or 2) represent the vertical direction and horizontal direction of the wall, respectively. Figure 14: Shear buckling of infinite panel [12] E t p = 0.36C E E (13.2 C 22.2) (1-12) cr E1 b Where, C depends on the restraint at the edges. From the Equation (1-12), we can see that the critical buckling load depends on the orientation of the board. The ratio of the critical buckling load to the racking load at in. deflection can be expressed as the Equation (1-13). 2 pcr E2 tl = 0.92C 4 2 p E1 b (1-13) It was found by Coffin and Hsieh [12] that estimated load ratios using Equation (1-13) for 100-point board was less than 1, for most cases. If MD is oriented horizontally and the MD-CD ratio, E MD /E CD, is quite large (7 for full restraint at the studs C=22.2, or 17

30 54 for least restraint C=13.2), the ratio given by Equation (1-13) might be larger than 1. We expect that in most cases buckling of the sheathing materials will reduce the ultimate racking strength and the load at the 0.125in deflection. In this thesis research, racking tests were done with two small-scale racking testers. For the case of small deflections of paperbased sheathing materials, Equation (1-9) can be used to determine variables that affect the racking strength. These are discussed below. (1) Elastic modulus From the Equation (1-9), we see the racking load (P) has a linear relationship to in-plane shear stiffness (G). We expect that MD and CD modulii (E MD and E CD ) will influence racking load and correlate to racking strength. Such relationship agrees with field experience, although no published work on this point was found. Orientation of the sheathing materials may also influence racking strength. Orienting the MD direction (higher modulus) of the sheathing at wall s horizontal direction may help to reduce the buckling effect on the wall racking performance. (2) Paperboard thickness According to Equation (1-9), if all other constants are held fixed, increasing the thickness of the paperboard should increase racking resistance. The research work by Price and Gromala [8] supports the relationship that walls sheathed with thicker same kind of materials have higher average maximum racking strength and a smaller racking deflection at 1600 lb loading force. If buckling occurs, sheathing thickness will play a more important role because critical buckling load (p cr ) is proportional to thickness (t) cubed, t 3. (3) Wall geometry Equation (1-9) suggests that the racking strength is proportional to wall length/height ratio (L/H). From the limited research data (shown in Figure 11) by Patton-Mallory [11] and the coworkers, the linear relationships (almost 18

31 proportional) between racking strength and aspect ratio (L/H) for small-scale (2 by 2ft) racking tests is found except for the double-sheathed gypsum board, although the ultimate racking strength is tested. More investigation on this aspect will be done in this thesis work. (4) Moisture content Moisture content can influence the MD and CD modulii (E MD and E CD ). High moisture content will reduce E MD and E CD and in-plane shear stiffness (G). Price and Gromala s [8] research work shows that the higher the moisture content, the greater loss in racking strength. (5) Basis Weight It is not fair to compare racking strength or stiffness at the different basis weights. We might take it for granted that higher basis weight of sheathing will give the higher racking strength. But Coffin and Hsieh s [12] research data show that some lower basis weight sheathings have higher specific geometric mean stiffness ( EMDE CD /B.W.). This phenomenon suggests that paperboard laminated with more lightweight layers might have higher overall shear stiffness and racking strength. When sheathing materials with the same basis weight are produced using different number of layers, their racking strengths are affected by the number and strength of the ply bonds The Designed Racking Test Analysis & Correlation with Standard Racking Test The small-scale racking test apparatus discussed in chapter 3.2, consists of a metal frame hinged at the corners. The designed small-scale racking test system is similar to the standard racking test system in that main load imparted to the sheathing is a shear stress, but the manner of loading is different. The shear stress directions and quantities calculated according to shear stress definition are shown in the Figure 15 and Figure 16 for two systems. 19

32 Figure 15: Standard racking loading and resulting first order stress state Figure 16: New racking test loading and resulting first order stress state If we equate the shear stresses (τ 1 =τ 2 ) for two systems (L=H), the racking strengths from sheathing contribution (P 1S, P 2S ) for the two cases are related as expressed in Equation (1-14) 2 2 τ1lt = P1S = P2S = ( 2 τ2lt ) (1-14) 2 2 In the standard racking test, one usually measures horizontal racking displacement ( : Figure 17) and the designed racking test measures diagonal racking displacement (δ: Figure 18), the relationship between and δ must be determined before rewriting Equation (1-9) for the designed racking test system. 20

33 Figure 17: Horizontal racking displacement ( ) in standard racking test condition For the small deformation standard racking test ( =0.125in. over 8 ft), the shear strain (γ1) can be calculated by dividing the racking deflection ( ) by wall height (H) according to Equation (1-6). If the same shear strain occurs in the designed racking test condition which means γ1= 2γ2 (Figure 17-18), the diagonal racking displacement (δ) can be calculated according to the geometric analysis shown in Figure 18. δ = (1-15) 2 21

34 Figure 18: Diagonal racking displacement (δ) in designed racking test condition Now we can use Equation (1-14) and Equation (1-15) to rewrite Equation (1-9) to predict racking strength for the designed racking test conditions where we have no contribution from the testing frame. L L = 2( ) δ = 0.78 E E δ ( ) (1-16) H H P2 Gt MD CD t Equation (1-16) shows that the theoretical racking load is proportional to thickness (t), geometric mean modulus ( EMDE CD ), diagonal racking displacement (δ ) and aspect ratio (L/H). This is of course for the case of no buckling. The actual racking strength will be reduced if buckling occurs. 22

35 2.0 Problem Statement Standard full-scale racking tests are expensive and time-consuming to run. But there are no alternative methods to evaluate sheathing materials. Several previous research works suggest small-scale racking test might prove to be a good alternative which is less expensive and timesaving for factory quality control and future research work focused on the sheathing material. The effects of paperboard properties on racking strength have not been previously investigated. Investigation on these paperboard variables is needed so that one can develop strategies to improve the racking strength. The objectives of this thesis research work are: 1. Design, build, and evaluate a simplified small-scale racking tester. 2. Evaluate differences in racking response of different commercial paperboards. 2.1 Proposed Hypotheses Based on previous problem analysis and discussion, the thesis work will test the following three variables effects on paperboards racking strength: (a) the EMDECD t values of three kinds of paperboard (type A, B and C) with different thickness, (b) geometries of paperboards (16 by 16in, 32 by 32in), and (c) orientation (MD/CD) of paperboards (using 32in racking tester with middle stud). So the three hypotheses are listed as below. (a) If buckling occurs, paperboard CD oriented along the middle stud (or longer side of rectangular tester) will have higher racking strengths than when MD is oriented along the middle stud (or longer tester side). (b) Without buckling, increased paperboard elastic modulus and caliper ( EMDECD t : kpli) will increase paperboard racking strength for the same dimension of racking test. (c) Without buckling, increased dimensions of paperboards will not affect the racking strength per foot of paperboard length (lb/ft), if using the same type of paperboards (same thickness and elastic modulus). 23

36 3.0 Experimental Design 3.1 Experiments Materials, Characterization and Instruments (1) Materials Commercial sheathing materials labeled as type A (standard grade), B (structural grade) and C (super structural grade) produced by Fibre Converters (Constantine, MI) (delivered as 48 by 48 inch panel) with increased thickness from grade A to C was cut into either a 16 by 16 inch panel, or a 32 by 32 inch panel. Then the paperboards were conditioned at the constant relative humidity (RH=50%) and temperature (23 C) in a paper testing room for at least one week. (2) Paperboard Characterization and Instruments (a) Caliper (inch) Paperboard caliper for each specimen was measured with a Mitutoyo Dial Caliper gage. A total of 12 measurements taken around the edges with three readings per edge were recorded and the average was computed. (b) Basis Weight (lb/1000ft 2 ) To determine basis weight, 5 samples with the dimensions of 5.0 by 10.0 inch were cut. The mass of each sample was determined using an Analytic Balance and the B.W. was calculated as: B.W. (lb/1000ft 2 ) = Weight (g) * ( lb/1000g) * (144in 2 /ft 2 ) * 1000/(50in 2 ) (c) Moisture Content (%) To determine moisture content, five samples with dimensions of 5.0 by 8.0 inch were obtained. Both the initial mass and the oven-dry mass (board at 103 C for 3 days) were determined. The oven-dried samples were cooled in a desiccator. Continue drying until reaching a constant dried weight. The moisture content of boards was calculated by the following formula: Moisture Content % = (Initial W. Dried W.)/Dried W. * 100% (d) Elastic Modulus (measured as Elastic modulus thickness: klb/in) 24

37 Cut MD and CD strips (width 0.5in and length 8.0in) for three paperboard grades for tensile modulus test. The tensile tests were done by Instron 3344 series EM Test Instrument with clamp length of 6 inches. The Merlin software calculated the Elastic Modulus automatically. Results were averaged from measurements for each paperboard grade and direction condition. 3.2 Simplified Small-scale Racking Tester and Testing Design in & 16in racking testers The small-scale racking tester was designed to induce shear in the panel. This is similar to the standard racking tester. The tester records the racking load and deformation. It also provides a testing frame to which the sheathing materials are fastened, but the frame is designed to contribute minimal resistance to the racking deformation. Thus, the racking load can be considered the load carried by the sheathing. Figure 19 shows the setup of the simplified small-scale racking tester. The tensile tester MTS model 1122 functions as the racking load instrument, and its software (TestWorks Version 3.07) helps control the tester and record the racking load deformation automatically. The stated limit to the loading force for the MTS 1122 is 1000 lbs, but in several tests we used a maximum load closer to 1300 lbs. The racking test frame connects to the racking load instrument. The testing frame is shown in Figure 19 and has the following important features: (1) free rotation of the metal frame, (2) replicable edge woods inserted in the metal frame for multiple sheathing applications, (3) allowing a middle wood stud installed on 32in racking tester, (4) shared connection pins in two testers and different edge wood shapes in 16in tester, (5) four metal bars on front sides for force balance, and (6) paperboard corner cutting before sheathing application. These aspects are described and discussed as following. 25

38 Figure 19 : Setup of the designed simplified small-scale racking tester system (left) and 32 by 32in racking test frame (right) a) Free rotation of the frame. The frame is hinged at all four corners. This is different than the standard racking tester uses a wood frame nailed at the corners providing rigid connections (Figure 4). The rigid framing would contribute to the racking strength. Here we are interested in evaluating the effects of sheathing materials properties on racking strength. The only contribution to racking strength from the frame would be through friction in the hinged corners. The free rotation of the hinges is produced by connecting the metal frames at the corner with hatch pins, which are shown in Figure 20 and Figure 21. A blank test without sheathing materials showed a negligible racking load of 3lbs at a diagonal elongation of 0.5inch. The testing frame can be easily connected on the MTS tensile tester through top and bottom hatch pins (Figure 22). 26

39 Figure 20: Corner connection design of two metal frame sides Figure 21: Two metal frame sides connected by a hatch pin b) The frame uses replaceable wood inserts to fasten the sheathing to the frame. The designed metal framing is U-shaped (Figure 22). Wood inserts fit into the frame opening and secured to the metal frame with screws. The open side provides a face where the sheathing is attached to the board. Using this 27

40 method for the framing allows for a rigid frame, and replaceable bases for attaching the sheathing. c) The larger frame has the option of installing a middle stud as shown in Figure 23. The middle wood stud is installed on the backside of the tester frame using 2 very long dry-wall screws (3in length) connected directly into the inserted edge framing. The middle stud does not prevent test frame free rotation during the racking tests. A blank test without sheathing also showed a negligible racking load 0.5lb at a diagonal extension of 0.5inch depending on friction conditions. Figure 22: U-shaped small-scale (32by32in) racking test frame connected on the MTS tensile tester without inserted edge woods 28

41 Figure 23: Paperboard orientation test using a middle wood stud in 32by32in racking tester d) For the 16in racking tester, the same connecting pins as used in the 32inch racking tester frame are fastened on the four short hollow metal fames. To provide enough length of edge wood for sheathing stapling in multiple tests on the same edge woods, the woods are cut into the shape shown in the Figure 24 and inserted in the metal frame as shown in Figure 25. The longer side (12inches) is used for paperboard stapling, while the shorter side (about 7.5inches) is inserted in the metal frames. Three wood dry-wall screws (2.25in length) longer than those used in 32in racking test (1.25in length) are applied on each side for firm connection between the wood inserts and the metal frames. Also longer hatch pins (4.75in length instead of 4in hatch pins in 32in racking test) are used to accommodate the change of wood dimensions. 29

42 e) At the front side of the tester, four metal bars connects through the four hatch pins to balance the force on both sides of the middle paperboard, which avoids bending the frame towards the opposite side. Figure 24: Edge wood used in the 16inch racking tests Figure 25: Edge wood inserted in the metal frame of 16inch racking test f) Because of the hatch pins connection features on the corners, the applied paperboard corners must be cut away for sheathing application onto the edge woods. This is one of the differences between the standard racking tester and the designed small-scale racking tester. So no staples can be applied on the corner, which results in the relative weaker sheathing connection. 30

43 3.2.2 General racking testing procedures For the simplified small-scale racking test, the following general racking test procedures were followed. a) Sheathing materials and testing frame wood were cut to correct dimensions and conditioned for at least one week. b) The racking load cell (1000lb capacity) was calibrated according to the suggested procedures by the testing software (TestWorks). Once calibrated, there was no need to repeat calibration before each test. c) The four sides of the metal framing (16 by 16in or 32 by 32in) were connected by four hatch pins and attached to the MTS tensile tester through top and bottom hatch pins. Once this is done, keep it connected until switching to different dimension racking tests. d) Then screws were driven into wood inserts through holes on the backside of the metal frames for connection onto tester frames. e) The paperboard was clamped to the frame. An angle was used to make sure the frame was square and the alignment of paperboard edges to the testing frame was verified before clamping. f) Mark the desired staple positions on paperboard. Staples should be centered at the wood inserts width. The staple is 1by1in (16 gage, almost square cross section of staple legs) and a mark of 1in length was drawn for each staple. g) Then a staple gun was utilized to staple the paperboard on the four wood inserts (Figure 26). Staples were placed 3 inches apart along the edges and if utilized 6 inches apart for the middle stud. This gives 8 staples/side and 4 staples/side are applied in 32in and 16in racking tests, respectively. The staple length direction is perpendicular to shear stress direction on four sides. 31

44 h) Start the TestWorks and select appropriate testing parameters such as the limiting racking load and extension, loading speed and etc. Loading speed was kept as 0.1in/min for all tests in this thesis work. Then Zero the displacement meter and loading force. Figure 26: Stapler and staple used for paperboards sheathing applying i) Run the racking test until stopped by the preset parameter or the system safety requirement. Use handset controller to pause and resume the test, if buckling is measured in the middle of the test. j) Removing the racking load by handset controller. Removes all the staples and return the TestWorks to the zero position. k) For the next run, a new paperboard will be used. Conduct the same step (e) through step (j). Edge woods can be used for 3 to 6 runs by shifting the stapling positions clockwise or count-clockwise at least half inch. Replace edge wood inserts if necessary as step (d). Besides above general procedures, following aspects are important and will affect the test results. 1) Screws connection between the edge woods and metal frame must be tight. Screws should be perpendicularly driven into edge woods. After one or two tests, the screws 32

45 connection might be loose especially for 16inch tests. Before a new test, connection check is strongly suggested. Slight loose connections of several screws will result in racking load-extension curve change at the initial racking load region (Figure 27). Figure 27: Effect of loose screw connection on the load-extension curve (16by16in racking test Setup S12) 2) Staples should be applied on the center of edge wood width. Staple length is 1inch, and the width of edge woods is 1.5 inches. Paperboards surface is very smooth, so careful stapling is very necessary to make sure the staples are at the expected penmarked places. Sometimes one staple leg can be too near one wood edge, which results in weak sheathing application. Sometimes, marking mistakes also results in staples applied at that side away from the edge wood center. All such tests with bad stapling will result in the load-extension curve shape change, and the testing results should be excluded. One example is shown in Figure 28. Un-centered staple during sheathing application reduced paperboard racking strength. 33

46 Figure 28: Effect of four not-centered staples in one side on the racking loadextension curve (16by16in racking test Setup S13) 3) Loading speed is also an important factor influencing the load-extension curve. The faster the loading speed, the higher the paperboard racking strength. The ASTM E72 suggests the loading speed not higher than 790lbs in 2 minutes [2]. In this thesis work, all tests select the speed 0.1in/min, which is near the ASTM suggested speed in the initial region, for the case of using paperboards as sheathing here Paperboard buckling measurement To evaluate the buckling extent, out-of-plane displacement was measured. The motion of the frame is defined by the movement of the crosshead on the tensile tester. If the board cannot conform to this deformation by in-plane deformation, buckling of the panel will result. A simple device was constructed to measure the out-of-plane displacement of the paperboard. It consisted of a holder and ruler as shown in Figure 29. The holder is attached on the backside of the tester frame (Figure 30) and the ruler can be adjusted until it is touching the paperboard back (Figure 31). The initial distance from paperboard surface before the racking test was also measured. The difference between these two measurements gives the out-of-plane displacement at the measurement location. To compare samples, the measurements were made a prescribed extension 34

47 of the crosshead. When the extension was reached, the test was paused to hold the racking deformation constant. The decrease of racking loads shown in Figure 28 is caused by relaxation during buckling measurement. The measurement was taken at the center of the buckling region where paperboard usually buckles most. Figure 29: Ruler and holder for racking test buckling measurements Figure 30: 16in racking tester frame with attached holder for buckling measurement 35

48 Figure 31: Ruler for buckling measurement in 16in racking test During the measurement, care was taken not to push the paperboard especially for the thinnest paperboard (Grade A). The determination of net extension where the loading process pauses was difficult because of initial slack in the sample. The method used to accomplish this involved monitoring the racking load values shown on the computer screen. Once the slack is pulled out, the load rate will increase. At this moment, the corresponding extension value was recorded, which should be near (usually smaller than) the calculated slack extension value determined by the slope method discussed later. Adding the desired board extension to this estimated slack extension gave the total extension where buckling was measured. Overall, this technique might not be very accurate. The tip of ruler contacting the paperboard surface is not small as a point. So the measured buckling is actually the lowest buckling extent in the ruler-paperboard contact region. Also the real extension or shear strain where buckling measured might not be exactly same. However this simple tool can give us a rough estimate of the extent of buckling for three different paperboard grades. 36

49 3.3 Data Analysis Methods (slope method) Because there is slack in the system when loading starts, a method to account for this slack and calculate an initial slope was needed. The slack deformation is caused by the slack connection of the designed racking tester frame to the MTS tensile tester. It is difficult to completely zero out the weight of the frame and sample. Part of this weight is carried by the bottom of the tensile tester. When the frame starts moving the initial deformation is the entire movement of the frame. When the load is removed from the bottom of the tensile tester, a region of constant force versus displacement is encountered where any more slack in the frame connections is pulled out. At some point, the frame is fully loaded and the paperboard begins to resist the movement. At this point the load increases. Figure 32 shows some examples of the raw loadextension curves tested by the 16in racking tester. All racking tests in this thesis have similar slack deformation as shown in Figure 32. Figure 32: Examples of raw load-extension curves tested by the designed 16in racking tests with structural (B) paperboards The extent of this slack deformation and the corresponding racking load depends on the total weight of tester frame and the individual tester connection condition. The tester total weight, including tester metal frames, edge woods, and paperboard, is about 23 lbs and 32lbs for 16in and 32in racking testers, respectively. The typical 37

50 lifting load (dead load) to remove the slack deformation is 15-20lbs and 10-20lbs for 16in and 32in (without middle stud) racking tests respectively. But some test runs can be far away from these ranges depending on the individual setup connection condition. To compare racking strength at a certain racking deflection or strain, the slack deformation must be removed. A simple way is to select a starting point on the raw load-extension curve, draw a linear line back towards zero racking load, remove dead load and finally shift the curve back to origin. To do this, the starting point and the slope of the linear line must be determined. For this work, the reference point was taken as the point with the maximum slope of the load deformation curve. Average local slope values are calculated over a small range of extension (20 data pairs corresponding to about 0.004in diagonal extension). Figure 33 shows some examples of the calculated slope curves against raw diagonal extension. Figure 33: Examples of calculated slope (lb/in) curves vs. raw diagonal extension (in) in 16in racking test with structural (B) paperboards The initial lifting load (dead load) was determined from the raw data in Microsoft Excel. Usually a constant load region as shown in Figure 32 was observed. Beyond that region, load starts increase. At this point, the load was determined to be dead load. To estimate the position of zero displacement, the tangent of the curve at the location 38

51 of the maximum slope is extended. The displacement corresponding to the dead load is taken as zero deformation of the board. This is illustrated in Figure 34. After the displacement is shifted by subtracting the reference deformation for zero shear strain, dead load is subtracted from the load values. This results in the load versus diagonal displacement curve shown in Figure 34 as the line that passes through the origin. All load-extension curves in this thesis were modified using the scheme described above. Figure 34: Slack deformation removal by slope method Based on the modified racking load (lb) and extension (in) data, diagonal racking strain or racking shear strain can be calculated. The modified diagonal racking extension (δ: in) divided by the diagonal distance of the square tester ( 2H ), gives the diagonal racking strain. Based on Equation (1-15) in the previous problem analysis, racking shear strain equals = 2δ. So racking shear strain is double of the diagonal strain. H H In order to compare racking results for the two test dimensions, the results were converted to load divided by diagonal length, and shear strain. The distributed load value is the product of the shear stress (τ: lb/ft 2 ) and paperboard thickness (t: ft), and in this thesis work it is called the racking shear load (lb/ft). All the racking curves in the chapter 4 (Results and Discussion) are plots of racking shear load against shear strain, unless otherwise specified. 39

52 The highest slope value is used to compare paperboard initial racking stiffness. In the designed small-scale racking system, length (L) equals height (H). So Equation (1-16) can be expressed as Equation (3-1). P/ δ = 0.78 EMDECD t (3-1) The term (P/δ) (lb/in) corresponds to the calculated slope value of the modified racking load (lb) extension (in) curve. The geometric mean modulus ( EMDE CD ) has a unit of lb/in 2 and caliper (t) has the unit of inch. The constant 0.78 is a dimensionless coefficient. So the slope value (P/δ: lb/in) is positively proportional to paperboard thickness and geometric mean modulus in the designed racking system. The highest slope positions mostly are in the range of small-deformation (around racking shear strain, similar as 0.125in small horizontal deformation in standard 8 by 8ft racking tests). The easiest way is to use the highest slope value as an index to evaluate paperboard initial racking shear stiffness, as shown by Equation (3-1). Figure 33 shows the three slope curves of 16in racking tests using structural (B) paperboards. The slope peak values are quite different ranging from below 6000 to above 7000 lb/in. The shapes of the slope peaks are different in different racking test runs. Some peaks are quite sharp with relatively high peak values, while others are broad with relatively low peak values. This suggests the some shortcoming of using the highest slope value to evaluate paperboard initial racking strength. In fact, the highest slope only represents a local condition on load-extension curve. Another better way is to average the slope values around the highest slope position in an appropriate range. Because three grades of paperboards are tested using both 16in and 32in racking testers. To avoid dimension difference, slope values are plotted against the racking shear strain, as shown in Figure 35. In the designed racking system tested with the selected three grades of paperboards, racking shear strain of is arbitrary selected to be the range for slope average. The highest slope position is not necessary to be the center of the slope average range, due to the non-symmetric shape 40

53 of slope peak. To find the slope average region on the slope-shear strain curve, several trials are necessary to find the largest average-slope value. This is done by shifting slope average region (fixed shear strain range: ) around the slope peak and averaging slope values until find the largest one. Figure 35 shows two slope average examples. Although the highest-slopes are quite different, slope-average yields quite the same average values. In the following discussion, we will call these two types of slope as highest-type (H-type) slope and average-type (V-type) slope. Figure 35: Illustration of slope average 3.4 Paperboard Staple Resistance Test Besides shearing and buckling of the paperboard during the racking test, the staples also were observed to cut through the paperboard. At the region especially near the ultimate racking load, the loads being carried though the staples to the frame are sufficiently high to start cutting the board. The thicker the paperboard, the stronger the resistance to both buckling and cutting by staples. The result of this cutting is that the edges of board are no longer aligned with the frame as shown in Figure

54 Figure 36: Comparison of paperboard edge alignment before and after racking test To evaluate the staple-cutting resistance of the paperboard, staple resistance tests were developed and conducted. The nature of this test is similar to the nail resistance test introduced in the chapter of Introduction (Literature Review). Two paperboard strips with the same width of the wood (1.5in) used in the frame are aligned with specimen of wood and stapled on wood at opposite ends. The free ends of the paperboard are clamped to the jaws of an Instron 3344 series EM Test Instrument (Figure 37). Different number staples (1 to 3 staples in this thesis) were used with either parallel or perpendicular staple orientation to tension direction. Paperboard MD and CD samples were tested for all three grades. An illustration figure of staple resistance test using two staples (both parallel and perpendicular staple orientations) is shown as Figure 38. The net paperboard length under tension (net gage length) is the difference of total gage length and staple distance in middle. Three different net gage lengths were tested (5.5in, 8.5in and 10.5in). A typical staple resistance load-strain curve is shown in Figure 39. During the later half of the test, paperboard cutting was clearly observed. This cutting corresponds with region of the curve where the load is fairly constant near lbs. Finally, a point is reached where the paperboard at one of the staple points is broken. 42

55 Figure 37: Setup of the staple resistance test with one perpendicular staple Figure 38: Illustration figure of staple resistance test (using 2 staples) 43

56 Figure 39: One example of staple resistance test load-strain curve 3.5 Testing Program Three hypotheses were proposed (in Problem statement), which were the main focus of this thesis work. But paperboard staple resistance tests and racking tests with gluing were also conducted to explore the racking mechanics. All conducted tests are listed at the end of this chapter. For the testing of three hypotheses, the testing program was as following. Hypothesis (a) Testing Orientation of paperboards may affect racking performance. For this thesis work using the designed simplified small-scale racking tester, paperboard orientation makes difference only for rectangular panels in the paperboard. To test the orientation effect, a middle wood stud was placed in the 32x32 frame as shown in Figure 23. This gives the rectangular panel and we can assess the role of MD-CD orientation with respect to racking stiffness. Racking stiffness and strength values of paperboards with MD and CD oriented parallel to middle stud were conducted for three grades of paperboards. Five samples of both MD and CD aligned with the stud were conducted. Hypothesis (b) and (c) Testing 44

57 A series of tests were conducted to determine the racking response of the three board types in regards to hypotheses (b) and (c). Tests for the three boards at both the 16in and the 32in frames were conducted. No stud was used in the 32in frame. For each board type, 4-7 tests were conducted for each sample type (not including tests with bad sheathing). The initial racking stiffness was determined from the load elongation data and compared to the estimated shear stiffness of the board. For example, using 32 by 32in paperboards, three types of paperboards (A, B and C) will be characterized to calculate the EMDECD t values and be conducted the racking tests. If buckling is not a big contributor, a linear relationship between the EMDECD t values and racking strength should be observed. However if buckling is important, paperboard racking stiffness should be reduced and paperboard A should undergo the largest reduction. If buckling is not important, the same racking stiffness and strength (lb/ft) should be observed for the two different dimensions of the same type of paperboards. On the other hand, if buckling is important, samples tested with the 16 inch frame will have higher racking strength (lb/ft), because smaller span spacing (b) gives higher critical buckling load (p cr ) according to Equation (1-12). List of conducted tests 1. Paperboard characterization of A, B, and C 1. Grammage, 5 measurements 2. Moisture content, 5 measurements 3. Caliper, 12 measurements for each board, all boards tested 4. Elastic modulus, measurements 2. Paperboard MD/CD orientation 32in racking tests with middle stud (5 MD and 5 CD tests for board B & C, only 1 MD and 2 CD tests for board A) 3. 32in racking tests without middle stud (total 5+2=7 tests for each board grade: A, B & C) 4. 16in racking tests (4 tests for each board grade: A, B & C) 45

58 5. Paperboard staple cutting tests 1. Net gage length tests (one test each condition, total 9 tests) 5.5in, 8.5in and 10.5in MD sample of board A One, two and three parallel staples 2. Staple number tests (one test each condition, total 18 tests) One, two and three parallel staples Three board grades: A, B & C MD & CD samples 10.5in net gage length 3. Paperboard grade and staple orientation tests (one test each condition, total 24 tests) One and two staples Parallel and perpendicular staple orientations Three board grades: A, B & C MD & CD samples 10.5in net gage length 6. Staple number 32in racking tests without middle stud (Board C) 7. 16in racking tests with gluing (three grades) The results of all tests outlined above are presented, analyzed, and discussed in the next chapter. 46

59 4.0 Results and Discussion 4.1 Paperboard characterization Table 1 provides the mean and standard deviations (S.D.) of the measured properties of three paperboard grades. (The raw data are given in Appendix A.) Table 1: Characterization data of three grades of paperboards Paperboard Properties Standard (A) Structural (B) Super Structural (C) Avg. S.D. Avg. S.D. Avg. S.D. Basis Weight (lb/1000ft 2 ) Caliper (t: in) Moisture Content (%) Elastic Modulus (kpli) (Et) MD (Et) CD EMDECD t The above data clearly show that both caliper and basis weight increase from grades of standard A through super structural C. The moisture contents of three paperboards are quite similar, in the range of 8-9%. The measured elastic modulii (kpli) are given as stiffness per unit width, in contrast to the traditional materials definition of stiffness per unit area. For paperboard MD direction, elastic modulus of standard A grade is about 25% lower than those of structural B and super structural C grades. Super Structural C grade is almost same as structural B. For paperboard CD direction, there is only a slight increase from grade A to C. If the racking strength prediction given in Equation (1-16) is correct, the racking behavior should not be that different between the boards B and C. On the other hand, if buckling is important, board C should perform better than B because of the greater magnitude of caliper of C. 47

60 4.2 Effects of paperboard orientation on racking strength Based on the buckling analysis, paperboard with the CD aligned with the middle stud in the 32 inch racking tester will have higher racking strength than a sample with the MD aligned with the middle stud. Because of the limited number of paperboards supplied and some early trials with the standard grade paperboards, only structural and super structural paperboards have enough test runs for the orientation comparison purpose. For both paperboards, five runs of each orientation condition were tested. The curves of racking shear load (lb/ft) vs. shear strain processed by the maximum slope method are shown in Figure 40 and Figure 41 for boards B and C, respectively. For both board types, there were only small differences between CD and MD orientation. Paperboards with CD aligned along the middle stud seem to have slightly higher racking strengths than MD orientation at higher racking loads. Figure 40: Structural (B) paperboards CD/MD orientation comparison 48

61 Figure 41: Super structural (C) paperboards CD/MD orientation comparison To better check the orientation effect, statistical t test is applied to compare the average racking strengths of CD and MD orientations at some selected racking strain levels. The results are listed in the Appendix B. With increasing strain level, P values of statistical t test decrease from % to 10-30%. Smaller P values in t test means more chance of correctly stating that two group means are significantly different. If setting the confidence level to be 95%, we conclude that MD/CD orientation effects on racking strength are not significantly different even at the high shear strain level, based on the comparison results. For board C, Figure 41 shows a separation into two series (big variations) at small to medium racking strain range. The most likely reason is the different racking tester setup conditions caused by a change in wood surfaces and replacement of the middle stud for the last 5 racking tests. If only picking the tests using the second wood surface (upper curves), the load-strain curves shown in Figure 42 are obtained. Once again, paperboards with CD aligned with the middle stud are on average slightly higher than MD orientation at the high racking load range. Statistical t test once again told us that MD/CD orientation was not significantly different at 95% confidence level. 49

62 Figure 42: Super structural (C) paperboards CD/MD orientation comparison (only data from second wood surface) Based on the above orientation comparison results using two grades of paperboards, we conclude the orientation effect on racking strength in our designed system is not significant. The possible reasons are: 1) the middle stud divides the square tester into two 32 by 16 inch rectangular areas. The orientation effect from buckling analysis is based on the infinite panel (See Figure 14), which is not the same condition as our designed system. 2) Racking load level (1000lb) was still lower than the ultimate racking strengths of board B and C. Unfortunately, there were not enough paperboards A left for the tests. Only three runs were done with the results presented in the chapter 4.4 to study middle stud effects. With the lowest bending stiffness, paperboards A might show some differences between MD and CD orientations at racking load level near the ultimate racking strength. 3) Also during the tests, buckling was found to pass through middle stud. This might be caused by the big staple spacing (6in) on middle stud. In future work, it might be helpful to try 3in staple spacing to observe MD/CD orientation difference. When the orientation tests were conducted, the method to measure buckling had not yet been developed. The lack of differences in the MD and CD orientations was 50

63 partly the reason for developing the methods. In future work, the methods developed in this thesis project could help improve the understanding of these differences. 4.3 Effects of paperboard properties on racking strength in racking tests Each five tests paperboard C and A were conducted on two sides of edge wood inserts, followed by 5 tests of paperboard B on the another set of wood inserts. The quality of edge woods is similar, but there might have some variation of wood density. The wood density effect is not evaluated in this thesis work. The final load strain curves are shown in Figure 43 and the slope values (both highest-type and average-type) of all three grades of paperboards are listed in Table 2. Figure 43: Racking shear strength-shear strain curves of 32in racking tests with three grades of paperboards 51

64 Table 2: Two types of slope values of 32in racking tests with three grades of paperboards without middle stud Board Grades Test # Average S.D. Highest 5359* Standard A Type Average 4666* Type Highest _ Structural B Type Average _ Type Highest Super Structural C Type Average Type *: Low value, but still in ±2(S.D.), not outliers. : Low slope values possible due to loose screw connection. The Figure 43 generally shows the racking strength increases with increasing paperboard elastic modulus and caliper from standard grade through super structural grade. This is also confirmed by the initial slope data in Table 2. Table 2 also shows that one test with the largest highest-type slope value does not always have the largest average-type slope value. This means slope average method in the selected strain range (0.0016) might be appropriate. For the tests of structural (B) paperboards, something happens after the first run which results quite low stiffness in Figure 43 and low slope values (both highest-type and average-type slope) underlined in Table 2. The most possible cause was that screws connecting edge woods and metal frames loosened after the first run. By experience, screws often slightly loosen after one or two tests, which can result in significant initial slope reduction and shape changes of load-extension curves. It s important to check connecting screws and tighten them before each racking test. Another suspicion that may lead to large variation is paperboard curls in different ways during conditioning depending on the paperboard grades. By experience, the structural (B) paperboards are most difficult to be flat during sheathing application (stapling) and standard (A) paperboards are the easiest to be flat because of smallest caliper. Figure 44 shows the different shapes of three types paperboards viewed from 52

65 topside. Structural (B) paperboards and super structural (C) paperboards have more complicated shape than diagonal curl. The shape change of load-extension curves of structural paperboards after the first run might be caused by the change of paperboard orientations with respect to paperboard buckling direction. Figure 44: Different shapes of three grades of paperboards Because of the failure of testing structural paperboards, another 32in racking test setup is prepared. All three grades of paperboards are tested with 2 runs for each grade. The load-strain curves are shown in Figure 45 and the slope data are listed in Table 3. The reversed peaks in the middle of the curves are caused by relaxation during buckling measurements. 53

66 Figure 45: Load-strain curves of three grades paperboards on the same setup S16 of 32in racking tester without middle stud Table 3: Slope values of three grades of paperboards using the same 32in racking tester setup (setup 16) Board Grades Test # 1 2 Average Standard Highest-Slope A Average-Slope Structural Highest-Slope B Average-Slope Super Highest-Slope Structural C Average-Slope : High values of tests without any testing error, possibly due to paperboard property variations. Once again, the load-strain curves show the increase of racking strength with increasing paperboard modulus (kpli) from standard (A) paperboards through super structural (C) paperboards, which is also confirmed by slope data. For standard (A) paperboards, the two types of slope values in Table 3 are very close to the results of the previous five runs (average value of highest-type slope: about 6000; average value 54

67 of highest-type slope: about 5000). But for the second test of structural (B) and two tests of super structural (C) paperboards, the slopes are much higher than those of previous tests. Because of run out of 32in paperboards, no more replicates could be done. Connecting screws were checked and tightened before each test. Also there was no error of sheathing application. Two paperboards (one board B and one board C) were stored vertically against the wall, while the rest of paperboards were piled together under a heavy box. These two high slope values might be caused by the strength variation of individual paperboard. So data of these two tests were not excluded. Using the average values of two type slopes in Table 2 and Table 3 and paperboard modulus (kpli) data in Table 1, slopes and modulus ratios within three paperboard grades are compared, which are shown in Table 4. Table 4: Two types of slope ratios of 32in racking tests and paperboard modulus (kpli) ratios comparison within three paperboard grades (H: highest-type; V: average-type) Ratios between Paperboard Modulus Slope ratios (Five runs) Slope ratios (Setup 16) Slope ratios (All runs) two types of ( Et) MD( Et) CD H-type V-type H-type V-type H-type V-type Paperboards Ratio Super/Stand (C/A) Stru./Stand (B/A) Super/Stru. (C/B) The slope ratio data in Table 4 are all around paperboard modulus ratio. For the data of five run average, the ratios calculated by average-type slope are closer to the paperboard modulus ratio values than those using the highest-type slope. For the data of setup 16, all slope ratios are higher than the modulus ratios due to high slope values of paperboard B and C. But the average results of all 32in-racking runs for each type paperboard give the very good agreement between slope ratios and modulus ratios, especially using average-type slope. As for the last check, the highest slopes usually occur in the range of lbs depending on paperboard grades in 32in racking tests, which are mostly in the 55

68 presumed small-deformation range of racking shear strain (similar as 0.125in small horizontal deformation in standard 8 by 8ft racking tests). So using initial slope values is appropriate to evaluate paperboard racking strength without buckling. Based on the previous results using the designed 32in racking tester, we confirmed the hypothesis that paperboard racking strength is proportional to elastic modulus and caliper if without the significant buckling effect. Once buckling is significant at the high racking strain, paperboard thickness will play more important role as predicted by theoretical buckling analysis. Although the quite similar modulus (kpli) of structural (B) and super structural (C) paperboards, Figure 43 and Figure 45 show significant difference of racking strengths between them at the region of relative large shear strain. This is due to the significant higher caliper and bending stiffness of super structural (C) paperboards. Buckling extents at 0.24in net diagonal extension (after removing the estimated slack extension) are measured at the place of maximum out-of-plane deformation during the setup 16 tests for these two paperboards. The raw data are listed in Appendix C. The average buckling of two racking test runs are 0.63in and 0.56in for paperboard B and C, respectively. As what expected, the super structural (C) paperboards with higher bending stiffness buckle less than the structural (B) paperboards. So both racking strength and buckling data confirm the hypothesis that thicker paperboards have higher racking strength with less buckling due to larger caliper and higher bending stiffness in racking tests To block any effect of different racking tester setup (the same dimension) on paperboard racking performances, each 16in racking tester setup was used to test all three grades of paperboards. The Figure 46 shows racking test load-strain curves of three 16in racking tester setup (Setup 12, 13 and 14: total 12 tests). Results of several tests with bad sheathing application are not reported. Proper staple positions (centered at the edge wood width and the correct staple spacing) are very important especially in 16in racking tests with only 4 staples on each side. Connecting screws were checked and tightened before each run. And during the test, buckling was measured at the net extension of 0.12in or 0.18in (0.12in deformation in 16in racking test has the 56

69 same racking shear strain of 0.24in deformation in 32in racking tests). Paperboards after sheathing application were usually more flat than those in 32in tests especially at paperboard center. All raw load-extension curves have good shapes (smooth with proper direction) in the small to mediate racking strain range. Two types of slopes are listed in Table 5. Figure 46: 16in racking tests load-shear strain curves (setup S12-S14) Figure 46 shows that only slight difference between the structural (B) and super structural (C) paperboards until near the end of test. Because of smaller dimension of 16in racking tests compared to 32in tests, buckling is quite limited in 16in racking tests. As what the previous analysis predicts, without significant buckling super structural (C) and structural (B) paperboards are very similar due to their close modulus (kpli) values. This is also supported by the slight larger slope values of super structural (C) paperboards than those of structural (B) paperboards. 57

70 Table 5: 16in racking tests slope values of three grades of paperboards (setup S12-14) Board Grades Standard A Structural B Super Structural C Test # Average S.D. Highest- Slope Average- Slope Highest- Slope Average- Slope Highest- Slope Average- Slope The slope data once again show that slope average method is appropriate with smaller standard deviations than those of using the highest-type slope. The test with the largest highest-type slope value does not always have the largest average-type slope value. Table 6 lists the slope ratios within these three paperboards grades, which are compared to the paperboards modulus ratios. The slope ratios calculated by both two types of slope values agree quite well with the paperboard modulus ratios. Table 6: Slope ratios of 16in racking tests and paperboard modulus (kpli) ratio comparison within three paperboard grades Ratios between Paperboard Slope Type Two types of Modulus Highest-Type Average-Type Paperboards EMDECD t Ratio Super/Stand (C/A) Struct./Stand (B/A) Super/Struct. (C/B) As also for the last check, the highest slope occurs in the range of lb depending on the paperboard grades during the 16in racking tests, which are also in the presumed small deformation range ( racking shear strain: similar as 0.125in horizontal deflection in 8by8ft standard racking test). So the slope average near the highest slope position is appropriate to study the relationship between paperboard 58

71 initial racking stiffness and paperboard elastic modulus (kpli) without the significant buckling effect. Buckling extents were also measured at the net extension of 0.12in or 0.18in shown in Table 7. The raw data are listed in the Appendix C. The variation within different runs of the same grade paperboards was quite big. Besides the variation from paperboard strength, paperboard cutting by staple legs can happen at the measured racking strain, which affects the extent of paperboard buckling. The relationship between staple cutting and buckling will be discussed in detail later. Because at the four corners of the testing frame there is no enough place to place the paperboards and to insert edge wood, paperboard corners must be cut without stapling. The staple spacing at the edge wood is 3in and staple positions shift half inch in the next run. So the differences of staple positions both at the edge wood width direction and the direction along the edge wood will also contribute the racking strength variations. Table 7: Buckling extent (in) of 16in racking tests measured at the net racking extension of 0.12in and 0.18in Net Extension 0.12in 0.18in Test # Average 1 Standard A Structural B Super Structural C The buckling data in Table 7 show the standard (A) paperboards have the biggest outof-plane deformation which is more than 6 times of the other two types of paperboards. Structural (B) and super structural (C) paperboards undergo the almost same buckling extensions comparing to the big standard deviation. Also it is not very surprising that these two kinds of paperboards have smaller buckling at 0.18in racking deformation than those measured at the 0.12in racking extension. From Figure 46, it is not expected to observe the difference between these two grades of paperboards until racking shear load is above 450lb/ft in 16in tests. 59

72 Based on racking test results of the 16in and 32in without middle stud, we confirmed the hypothesis about the effects of paperboard properties on racking strength. 4.4 Effects of middle stud in 32in racking tests Besides the effects of paperboard orientation tested with one middle stud in 32in racking tests, we are interested in explore the effect of middle stud on racking strength. The middle stud separates the square metal frame into two rectangular areas. It also provides additional restrains at middle, although the staple spacing is double of that at edges. Comparing the 32in racking test results with and without middle stud, we would expect to see some differences of racking behaviors. The racking shear load-shear stain curves of with and without middle stud are superimposed for each paperboard grade, as shown in Figure 47, 48 and 49. The only significant difference between stud and without stud is at the region of significant buckling for standard (A) paperboards. In Figure 47, both MD and CD stud orientation result in higher racking strength than the test condition without middle stud. Less difference is observed for structural (B) grade as shown in Figure 48, but from the trend of curves the significant difference might show if up to higher loading level. Due to the highest bending stiffness of paperboard C, no difference is shown when loaded to 1000lb in Figure 49. We conclude that one middle stud with 4 staples applied on in our designed 32in tester improves racking strength only at the region of large buckling. The comparison of initial slopes shows that tests without middle stud are slightly larger than those with middle studs (average of both MD and CD orientation conditions). This is most likely caused by the slight screw loose during the tests with middle studs when we did not realize the screw would become slightly loose after one or two test runs. As we stated previously, loose screw will result in significant decrease of initial slopes. In future, better results of MD and CD orientation tests should further explore the effects of middle stud. Also double number of staples on middle stud (the same staple spacing as edge) is recommended. Different sheathing application methods (such as glue discussed in later) can also be used for this testing purpose. 60

73 Figure 47: Comparison of 32in racking tests with and without middle stud for standard (A) paperboards Figure 48: Comparison of 32in racking tests with and without middle stud for structural (B) paperboards 61

74 Figure 49: Comparison of 32in racking tests with and without middle stud for super structural (C) paperboards in & 16in racking tests comparison Based on Equation (3-1), initial slopes are not affected by racking test dimension change due to the square shapes of two racking testers. The final average values of the initial slope (both highest-type and average-type) are compared between the two dimensions racking tests, shown in Figure 50 and Figure 51. As expected, the two dimensions result in almost the same initial slopes if calculated by average-type slope. If comparison by the highest-type slopes, 32in-racking tests have larger slope values than 16in racking tests. It once again suggests the average-type slope is better than highest-type slope to evaluate paperboard initial racking strength. 62

75 Figure 50: Initial highest-type slope (average values) comparison between 32in/16in racking tests Figure 51: Initial average-type slope (average values) comparison between 32in/16in racking tests Some aspects of racking tests are slightly different in 16in and 32in racking test. First, the inserted edge woods in 16in racking tester have a different shape (Figure 24 and Figure 25) from the straight rectangular shape used in 32in racking test. The wood thickness is about 7cm at the center for 16in racking test, which are much thicker than 63

76 those for 32in racking tests. Longer screws are used in 16in racking tests to have the firm connection between edge woods and racking tester metal frames. The racking load or shear stress transfer from metal frame through connecting screws, edge woods, staples and finally to paperboards. Any force transfer loss will results in lower paperboard racking strength. So above slope results comparison suggests the connecting screws are not loose and the edge wood thickness does not affect the force transfer. Another difference between 16in and 32in racking tests are paperboard corner cut. A 3by3in straight triangle is cut from 32in paperboard, while the dimension of corner cut in 16in paperboard is 2.5by2.5in. Staple number of sheathing application on each side is 4 or 8 in 16in or 32in racking test, respectively. So the effective loading length (loading area/paperboard caliper) is relatively smaller in 16in test than that in 32in test. A rough estimation of effective loading length is 11in (16-2*2.5=11) or 26in (32-2*3=26) for 16in or 32in tests, respectively. So at the same racking shear load (lb/ft), paperboards in 16in racking test undergo higher stress than those in 32in tests. The stress ratio of 16in to 32in is 26/2/11=1.18. This 18% higher stress puts the same grade paperboards in 16in racking test at the disadvantage place if comparing their slopes with 32in paperboards, which might explain the higher slopes (the highest-type slope) of 32in tests in Figure 50. In the range of buckling is significant, the 16in racking tests should have the higher racking strength than 32in racking tests due to the smaller stud span (b) in Equation (1-12) and Equation (1-13). At the same racking shear load (lb/ft), paperboard in 32in tests should have larger buckling than those in 16in tests. This is confirmed by comparing the structural (B) and super structural (C) paperboards buckling data in both 16in and 32in tests. The average buckling in 32in racking tests is 0.63in and 0.56in at the net extension of 0.24in for structural (B) or super structural (C) paperboards, respectively. This is much bigger than the average buckling data in 16in tests measured at the same shear strain (or net extension 0.12in), only 0.04in for both paperboards B and C. The superimposed load-strain curves of both 32in and 16in-racking test for each kind of paperboard are shown in Figure There is no difference of initial racking 64

77 stiffness for three grades of paperboards. Here we are interested in the medium-tolarge racking deformation region where buckling is significant. All three Figures show the racking strengths in 16in tests are higher than those in 32in tests at significant buckling regions. Also with increased paperboards thickness, buckling extents are reduced because of the increased bending stiffness. So for standard (A) paperboards, some differences occur between 16in and 32in curves in the range of racking shear load 150lb/ft, while the differences show until 200lb/ft and 300lb/ft for structural (B) and super structural (C) paperboards, respectively. Figure 52: Racking load-strain curves of 32in and 16in test for paperboard A 65

78 Figure 53: Racking load-strain curves of 32in and 16in test for paperboard B Figure 54: Racking load-strain curves of 32in and 16in test for paperboard C Based on the comparisons of racking load-strain curves, slope and buckling data of 16in and 32in tests, we successfully tested the hypothesis that racking test dimension 66

79 does not affect paperboard initial racking stiffness without buckling. And when buckling is significant, we also proved the reduced span (b) in 16in tests results in much smaller buckling extent and higher racking strength. 4.6 Paperboard staple resistance study Using Equation (1-17), theoretical initial slopes of racking load-strain curves can be calculated from tested paperboard elastic modulus data (kpli). The theoretical slopes of three grades of paperboards are 13100lb/in, 15700lb/in and 16600lb/in for standard (A), structural (B) and super structural (C) paperboards, respectively. These values are more than double of the tested slopes in the range of lb/in. As previously mentioned, the racking load or shear stress transfers from the metal frame, through the connecting screws to the wood and finally through staples to the paperboard. The wood inserts are much stiffer than the paperboards, and should not exhibit significant deformation if the screws are tightened. But when shear stress transfers through staples, it is only over very small bearing surfaces of the paperboard around the staple legs. Staples actually cut the paperboard as shown in Figure 36. The cutting deformation contributes to the total racking extension, which reduces paperboard racking strength and stiffness. Staple resistance tests as described previously were carried out using three grades of paperboards, both CD and MD samples. Variables of the staple resistance test were studied and are discussed in the following. 1. Paperboard net tension length As shown in Figure 38, the total paperboard net gage length includes the top and bottom parts. The two paperboard samples have the same length. The middle position of staples is 1in away from the paperboard ends. The actual tension length of each paperboard sample might have slight differences due to paperboard clamping position shift. To test the effect of total net tension length change, MD samples of standard (A) paperboard were used for all this part of testing. Staples were oriented parallel to the loading direction. The length between clamps is 12in for the net gage length of

80 and 8.5in, while the clamps distance is 13in in the case of 10.5in net gage length. One, two and three staples were tested for each net tension length condition. A total of 9 tests were done and resulted in the loading-strain curves shown in Figure 55. Figure 55: Paperboard staple resistance test with different net tension length using one, two and three parallel staples (Board A, MD samples) Figure 55 shows that at initial loading regions, tests with longer net gage length have higher resistance strengths at the same total strain due to less staple cutting effects involved. If we picking resistance tests using two staples, compare the curves with tensile test curve of MD sample of paperboard A, as shown in Figure 56. Paperboard resistance strengths approach the tensile strength with increasing the net gage length. Tensile tests were conducted at the same loading speed (1in/min) and the paperboard strips width was 0.5in width that was 1/3 of those samples in resistance tests. So loading force in tensile test is tripled before comparison. Tests with one staple and triple staples have the same approaching trend with increasing net gage length. 68

81 Figure 56: Comparison of tensile test and staple resistance test with two parallel staples (MD samples of board A) Also Figure 55 shows that the maximum staple cutting forces are not dependent on net gage lengths, for each staple number condition. The final cutting force is 70-80lb, lb, or lb for one staple, two or three staples respectively. These maximum cutting forces are much lower that the maximum load in the tensile test (3*166lb, about 500lb). So this suggests the staple cutting is a very important limitation of paperboard strength in the staple resistance test, and likely in the racking tests. Because paperboard net gage length significantly affects the paperboard behaviors in staple resistance tests at initial loading region, the following resistance tests were conducted with the fixed clamp distance of 15in and net gage length of 10.5in. 2. Staple number If back to results in Figure 55, we found that the maximum cutting force double or triple if using two or three staples. This suggests that each staple evenly sustains part of loading tension. 69

82 Other grades of paperboards MD or CD samples were also tested to check staple number effects. For easy stapling, staples were parallel to loading direction for this testing purpose. Resistance tests curves of structural (B) and super structural (C) paperboards MD samples are shown in Figure 57 and 58. Both grades of MD samples tests show paperboard resistance strengths increase and approach tensile strengths with increasing staple numbers. Once again, we see that the maximum cutting forces are double and triple if using two and three staples, except that triple staple test of super structural (C) paperboard. This is caused by slight paperboard-clamp slip due to very smooth surface of paperboards (like plastic) at high loading force level. Figure 57: Effects of parallel staple numbers using MD samples of paperboard B 70

83 Figure 58: Effects of parallel staple numbers using MD samples of paperboard C CD samples of three paperboard grades were also tested with parallel staples. Because of much weaker strengths of CD samples than MD samples, the maximum cutting forces using three staples are near the breaking strength in the tensile test. As an example, Figure 59 shows the resistance tests curves using super structural (C) paperboards with one, two and three staples. In this case, the paperboard staple cutting is not the extreme limiting factor like in MD sample tests, because both CD sample of paperboard elastic deformation and deformation by staple cutting are both important. Paperboard samples break before reaching the maximum cutting forces for two and three staples tests. Tests with two other paperboard grades had similar behaviors with the curves listed in Appendix D. Although it was not successful to test staple effect on maximum cutting force using CD samples, at initial loading region increased paperboard resistance strengths were all observed with increasing staple numbers. Based on above test results, we conclude that staples evenly sustain part of total loading tension in staple resistance tests. The maximum staple cutting forces are double or triple using two or three staples, if paperboard tensile strength is not a limiting factor (such as using MD samples). 71

84 Figure 59: Effects of parallel staple numbers using CD samples of paperboard C It is surprising that the tensile curves of MD samples are almost overlapped on the staple resistance curves at the initial region, especially for tests using paperboard B as shown in Figure 57. Passing the initial region, the slopes of tensile curves almost double for both tests using paperboard B and C (shown in Figure 57-58). Previously reported elastic modulii are corresponding to the large values in the middle region. But for CD samples, the tensile curves of are quite linear as shown in Figure 59. Unfortunately it is impossible to check the all the tensile curves, because the curve data of the last run was only kept by Instron 3344 EM testing system. If paperboard behaviors at initial region in tensile test correspond to the real paperboard elastic modulus for MD samples, the real modulii EMDECD t will be about 30% lower than the reported ones previously. In future, cares should be taken to check the modulus curve shape. 3. Paperboard grades To test paperboard grade effects, new resistance tests of three paperboard grades were done on the same middle wood for each testing condition. Eight test conditions were MD or CD samples with one or two staples either parallel or perpendicular to loading direction. One example of load-strain curves of staple resistance tests is shown in 72

85 Figure 60 using CD samples with one perpendicular staple. All tests under those eight test conditions give the similar results that overall paperboard strengths in staple resistance tests increase from standard (A) through super structural (C) paperboards, with the other curves listed in Appendix E. Figure 60: Staple resistance Load-stain curves for three grades of paperboard CD samples with one staple perpendicular to loading direction Here we are more interested in the maximum staple cutting forces, which are listed in Table 8 for all 24 tests. If the fibers in three types paperboards are uniformly the same quality, the staple cutting force should linearly increase with increasing paperboard thickness. In fact, no good linear relationships are observed for all testing conditions. One example of the plot of cutting force vs. paperboard thickness is shown in Figure 61. It suggests the qualities of fiber are not same in different paperboard grades. Previous discussion based on the caliper and elastic modulus data also suggests that more amount of weak fiber or other materials are used in super structural paperboards. So instead of plotting against paperboard thickness, product of elastic modulus and thickness is used which yields better linear relationships. Such plots are listed in Appendix F. 73

86 Table 8: Paperboard maximum staple cutting forces (lb) in staple resistance tests Staple Cutting Force CD Samples MD Samples (lb) A B C A B C One Parallel Staple Perpendicular Double Parallel Staples Perpendicular Figure 61: Staple maximum cutting force in resistance test vs. paperboard caliper with best-fit linear lines (one staple perpendicular to loading direction) Based on above testing data, we conclude during paperboard staple cutting the resistance comes from the section areas around staple legs on paperboard thickness direction. The staple cutting force linearly increases with increasing paperboard elastic modulus (kpli). 4. Staple orientation Different staple orientation with respect to loading direction and fiber direction in paperboard results in different staple leg cutting conditions. All four staple cutting conditions are illustrated in Figure 62. Fibers in CD samples will be subjected to 74

87 staple cutting across fiber length direction for both parallel (PARA) and perpendicular (PERPEND) staple orientation cases. This might have larger resistance from fiberfiber bonding and possible fibers than resistance in MD samples. But MD samples are much stronger than CD samples if without staple cutting. And total tested extension or strain includes both staple-cutting deformation and paperboard itself elastic deformation. Figure 62: Illustrations of staple leg cutting fibers in paperboard slips The 24 staple resistance tests results have been presented in above paperboard grade effects discussions. The maximum staple cutting force data listed in Table 8 show that there are no large differences between MD and CD sample. This suggests staple resistance by fiber bonding and paperboard tensile strength are both important in our testing system. In fact, the significant differences of maximum staple cutting force are from staple orientation. Perpendicular staple orientation gives significant higher resistance forces than parallel staple orientation in each same kind of test condition. For example, tests with one staple using MD samples, tests with perpendicular staple give 20-50lb higher cutting forces than those with parallel staple. This difference can only originate from staple related behaviors. Careful check of staple leg dimensions found that cross- 75

88 section of staple leg is almost square. A possible reason is staples are likely to be pushed against the paperboard surface during staple resistance tests if in the perpendicular orientation condition. The reinforced connection might result in higher paperboard resistance strengths. In summary, staple resistance study found that staples evenly sustain part of the total loading tension. The staple cutting force linearly increases with increasing paperboard thickness and elastic modulus. Staple in perpendicular to loading direction gives higher resistance strength than parallel staple orientation. At the region of staple cutting, paperboard strength and fiber-staple orientation are both important. The average effects result in no significant difference between MD and CD samples. 4.7 Paperboard staple cutting and buckling in racking tests In racking tests, staples are always perpendicular to shear stress direction on all sides. Two sides are like MD samples in staple resistance tests, and the other two sides are CD samples. If staple behaviors are similar in racking tests as staple resistance tests, perpendicular staple orientation should results in higher paperboard cutting resistance strength and less racking strength loss. In future work, parallel staple orientation can be also carried out to further explore staple behaviors in racking tests. Racking tests with double and five-times of normal numbers of staples (8 staples/side) were done using 32in racking tests with super structural (C) paperboards. The testing procedure was not same as the normal one. At first, one test with 8 staple/side are carried out, then remove the racking load and apply another 8 staples/side, reload after waiting 10 minutes, then repeat above procedure using 24 more staples/side. The racking strengths are significantly improved which is shown in Figure 63. The initial slope (Highest type) at normal number of staple is 6973lb/in, which increases to 7998lb/in and 10272lb/in if using double and five-times number of staples, respectively. 76

89 Figure 63: Racking load-strain curves of 32in tests with paperboard C using different number of staples So if using more staples, each staple leg will sustain less shear stress that should reduce the extent of staple cutting and shear stress can be more evenly transferred between paperboard and racking metal frames. Also using more staples increases the edge restraints that expressed as the value of C in Equation (1-12) and Equation (1-13), which increases critical buckling load or reduces the extent of actual buckling during racking tests. So racking strength increase with more staples can originate from reduced buckling or reduced staple cutting or both of them. Unfortunately buckling extents were not measured in these tests. The average cutting force of MD/CD tests with one perpendicular staple in resistance tests can be used to estimate the ultimate racking strength when paperboard staple cutting is significant. A simple calculation of the maximum racking load is to multiple the average cutting forces in resistance tests by staple number on each side of racking tester, and a coefficient 2 to convert the force to diagonal direction in racking tests. The calculated ultimate racking strengths for both 16 and 32in tests are compared to the actual values in Table 9. 77

90 Table 9: Comparison of actual maximum racking load to the calculated values by staple resistance test Paperboard Grades Actual Ultimate Racking Strength Calculated Ultimate Racking Strength 32in 16in 32in 16in Standard lb lb 1143lb 571lb A Structural 1060lb lb 1697lb 848lb B Super Structural C >1200lb >1000lb 1799lb 899lb For 16in racking tests, the calculated values are quite close to the actual ultimate racking strengths, while the calculated values are much higher than actual ones for 32in racking test. The previous buckling data show the extents of buckling in 32in racking tests are about 15 times larger than those in 16in tests for structural (B) and super structural (C) paperboards. As we know the racking tester is not square during the loading, so paperboard must buckle or to be cut by staple to accommodate the forced large shape change. By experience, the larger the extent of buckling, the less paperboard cutting by staple, or vise versa. This observation is reasonable and the two ways of paperboard responses (besides shear deformation) to racking tester shape change both exist and compete to each other. Another thing needing notice is that extreme buckling results in paperboard out-ofplane pulling away from staples, which the direction of force is not the same as that in staple resistance tests. So in the case of large buckling like the 32in racking tests, the extent of staple cutting is reduced and not the same nature as the staple resistance test. So the calculated ultimate racking strength from the maximum staple cutting force is not the good estimation for 32in racking test without the middle stud. So at the region near ultimate racking strength, buckling has a major impact on strength for the 32in test without middle stud, while paperboard staple cutting is the racking strength limit-controlling factor in 16in racking test. If this is true, improved racking stiffness and strength using more staples in 32in racking tests originates mainly from the reduced buckling. 78

91 In future work, individual racking test with increased number of staples can be done instead of reloading procedures, with buckling measurement. Both 16in and 32in racking tests are recommended to confirm and further explore the relationship of paperboard staple cutting and buckling. 4.8 Gluing for sheathing application As discussed previously, the actual slopes of three grades paperboards are less than half of the theoretical values. Even with five times more staples with paperboard C in 32in racking test without middle stud, the initial slope (Highest-type) is only lb/in, which is about 38% lower than the calculated value (16600lb/in) if the elastic modulus data are correct. The suspicion that real modulus EMDECD t is 30% lower than the reported value was previously discussed in section 4.6 (staple number effects). In future work, elastic modulus testing is strongly recommended with the same loading speed (0.1in/min instead of 1in/min) as racking tests. Paperboard corner cutting in our designed racking test and not possible infinite strong sheathing edge connection presumed in model prediction (either gluing or stapling) can also account for the lower measured initial slopes. In practical situations, using so many staples will significantly increase material and labor costs. Another approach is to try different sheathing method. Here we tried gluing as paperboard sheathing method. It has the advantages of uniform connection between paperboards and edge wood inserts in our racking system or racking walls in practical application conditions. This is closer to the ideal sheathing conditions presumed in the theoretical racking strength analysis. There is no paperboard staple cutting involved during the racking test using glue. The weakening effects will mostly originate from the buckling. But glue gives an image of relative weak connection comparing to using staples. Here liquid nail type of glue was tried for sheathing application. Liquid nail is relative strong in glue products, which is appropriate for application on wood and for other construction purposes. A uniform layer of liquid nail glue was applied on the paperboard edges, which covers the whole edge wood surfaces. Then the glued paperboard was clamped on the metal frames to make sure the paperboard contacts 79

92 the edge wood surfaces due to the paperboard curl problem. One 16in racking test of each kind paperboard is performed after 24 hours drying in constant temperature and relative humidity paper testing room. Buckling extent was also measured at the net extension of 0.12in. The load-strain curves of racking tests are shown in Figure 65 and the slope data are listed in Table 10 and compared to the 16in tests with staple as sheathing method. Figure 64: 16in racking tests load-shear curves using glue as sheathing method Table 10: Slope data (average-type and highest-type) for 16in racking tests with glue method, and compared to average slopes of 16in tests using staple methods Paperboard Grade Highest-type Slope Average-type Slope Glue Staple Glue Staple Standard A Structural B Super Structural C Because glue test of structural (B) paperboard (as shown in Figure 64) failed quite early due to the weak glue at one corner, buckling data was not available. This might also slightly reduce the initial slope. Figure 64 shows that the load-strain curves are 80

93 very linear. Both types of slopes are much higher than those of tests using staples. The differences between two types of slope values are relatively small due to the large linear range of the load-strain curves. The highest-type slope of gluing test (9142lb/in) using paperboard C is between the slope values of double staples (7998lb/in) and fivetimes staples (10272lb/in) 32in tests using the same grade paperboard. Clearly shown in Figure 65-67, gluing method gives much stronger paperboard racking stiffness and strength than staple method (16in tests). Glue method is especially superior than the common staple method at the medium to large racking deformation region. This is caused by avoiding staple cutting that might be the racking strength limit-controlling factor in 16in racking test. For future work, gluing method can be used in 32in racking tests. The racking strength increase using glue over staple can be compared between two dimensions of racking tests. Because gluing method does not eliminate buckling happening, it is expected to see less racking strength (percentage) increase in 32in tests using glue over staple, if buckling is strength limit-control factor in 32in tests. Figure 65: 16in racking tests of standard (A) paperboards using glue and staples 81

94 Figure 66: 16in racking tests of structural (B) paperboards using glue and staples Figure 67: 16in racking tests of super structural (C) paperboards using glue and staples The slope ratios between paperboard grades are listed in Table 11, which are compared to the modulus ratios. Because there is only one test of each grade of paperboard and possible lower initial slope of paperboard B due to weak gluing at one 82

95 corner, the slope ratios are not perfectly agreeable to the modulus ratios. More replicates of glue tests are suggested in future work, which needs more time due to glue drying. Table 11: Slope ratios of 16in racking tests by glue and paperboard modulus (kpli) ratios comparison within three paperboard grades Ratios between Paperboard Slope Type Two types of Modulus Highest Average Paperboards EMDECD tratio Type Slope Type Slope Super/Stand (C/A) Struct./Stand (B/A) Super/Struct. (C/B) The buckling data measured at the same net extension (0.12in) are 0.28in and 0.04in for standard (A) and super structural (C) paperboard using glue. The buckling extent is slightly higher than the average values using staples for paperboard A (0.21in), and the same for paperboards C (0.04in). Without staple cutting in gluing tests, bigger buckling extent should be expected for paperboard s response to the same certain of racking test frame shape change. Buckling data for paperboard B in gluing test was not available due to the opposite buckling direction towards wood inserts instead of metal bars. At a certain extent, further buckling was prevented by metal frames. For future work, one sheathing method using combination of glue with as many staples as possible can be tried to test the limiting slope and paperboard strength in our designed racking test system, which should approach the theoretical values. Another way is to redesign the racking tester which provide super strong edge restrains and without the need of paperboard corner cutting. The strong edge restrain might be achieved using some kind of clamping uniformly applied on the whole length of paperboard edges. So there is no need of glue or staple, and the test will be even more convenient to run than the current designed system. And the racking strength variations between different runs will be reduced by avoiding the sheathing application quality variations. Racking strength using this kind of tester will be more predictable by sheathing materials modulus data. 83

96 5.0 Conclusions and Summary In this thesis work, two small-scale racking testers (16in and 32in) were designed for evaluating the racking performance of paperboards (about 0.1in thickness). The smallscale racking testers were evaluated for three paperboard grades. Based on the results of this work, we draw the following conclusions. 5.1 Main features of designed small-scale racking tester Like the standard racking tester, the small-scale tester loads the sheathing material in shear. Unlike the standard racking tester, the small-scale testers were designed to be more convenient for evaluating the sheathing materials. (1) The core of the designed tester is the small-scale racking tester frame, which can be easily connected on the loading apparatus (MTS 1122 tensile tester in our lab). (2) The apparatus consists of a metal frame hinged at the corners by hatch pins. This design gives free rotation of tester frame. So the resistance to deformation should come from the paperboard and the fasteners. (3) Replaceable wood studs are inserted in the U-shaped metal frames for paperboard sheathing application (stapling or glue). Multiple tests can be done on each setup by shifting staple positions. (4) A wooden middle stud can be connected to the metal frame to mimic 16 inch spacing of studs. (5) No sheathing connection was possible at the corners due to the hatch pin connection design. Paperboard corners were cut to fit the space. (6) Total more than 200 tests were done on two dimensions of testers. The 32inracking tester gave consistent performance. For the 16in tester, racking results appeared to be more dependent of initial setup. 5.2 Mechanics of the racking test 5.2.1: Effects of middle wood stud in 32in racking test The initial slopes of tests with middle stud were slightly lower than those in the 32in racking tests without middle stud. Possibly this was due to the loose screw connections that were not realized when the testing was done. Improved 84

97 racking strengths using the middle stud were observed only in tests of standard (A) paperboard, where large buckling existed. For grades B and C, the buckling was not so large and appeared not to influence the response up to the load limit of the tester (1000lb). No buckling data were taken for tests with middle stud. So we conclude that the middle stud with 6in staple spacing in our 32in tests improves racking strength when large buckling is present : Effects of racking test dimensions Based on the test results of three grades paperboards in 16in and 32in (without middle stud), we found initial slopes (average-type) were almost same for the two different dimensions. So dimension change of square racking tests does not affect racking stiffness and strength when there is no significant buckling. The magnitudes of buckling measured at same shear strain in 32in tests were about 15 times larger than those in 16in tests. The superimposed load-strain curves also showed higher racking strengths of 16in tests than those in 32in test for all three grades. So we conclude that panel buckling lowers racking strength but has little effect on racking stiffness : Staple resistance study The phenomenon of the increased racking stiffness and strength by using gluing or more staples suggests weakening effects of non-uniform shear stress transfer and paperboard staple cutting. Staple paperboard resistance tests were done to further explore the staple behaviors in racking test. Based on previous results and discussion, we conclude the following. In tests of MD samples with staples parallel to the tension direction, the maximum cutting force was proportional to the number of staples, and therefore we can determine a staple cutting force. No significant differences of the maximum cutting force between MD and CD samples were observed. Maximum cutting force was positively correlated with paperboard caliper and elastic modulus for all fiber-staple orientation conditions (MD-Parallel, MD- Perpendicular, CD-Parallel and CD-Perpendicular). We conclude that stress transfer takes place at the staple leg and paperboard contacting area, which is proportional to paperboard thickness. The correlation to elastic modulus is 85

98 probably due to the different paperboard structure and materials in the different paperboard grades affect both modulus and intrinsic resistance to cutting. We conclude both paperboard strengths and staple-fiber orientations are important. However, tests with staple perpendicularly oriented to tension direction always gave higher maximum cutting force than parallel staple orientation. This might be caused by the reinforced sheathing connection (staple pushed against the paperboard) if staple is perpendicularly oriented : Paperboard staple cutting vs. buckling The large deformations that are imposed on the frame during the tests can not be accommodated by in-plane shear deformation of the sheathing alone. The paperboard buckles and/or is cut by the staples. In racking tests, fiber-staple orientations are MD-Perpendicular on two sides, and CD-Perpendicular on the other two sides. Using measured maximum cutting force from the staple resistance study, the calculated ultimate racking strengths were agreeable to measured values only for 16in racking tests. For 32in racking test without the middle stud, buckling was about 15 times larger than that in 16in test. Also large buckling might result in the different nature of staple cutting. So we conclude staple cutting is the strength-controlling factor in 16in racking test, while buckling has a major impact on strength for the 32in test without middle stud : Glue as sheathing method Sheathing application using liquid nail glue greatly improved paperboard racking stiffness and strength especially at the medium to large deformation in 16in racking test. Paperboard initial stiffness using liquid nail is comparable to those racking tests using double and five-times staples in 32in racking tests. We conclude it is caused by uniform shear stress transfer without staple cutting. Buckling extents were slightly larger than those using staple for sheathing application due to the removed staple cutting. 86

99 5.3 Effects of paperboard properties on racking strength 5.3.1: Paperboard Orientation Effects Testing results on 32in racking tests with middle stud showed insignificant difference between MD and CD orientations, compared at 95% confidence level. The possible reasons might be that the analysis was for an infinite panel and our designed test is finite and the lack of restraint, due to the large staple spacing, allows the buckling to pass across the middle stud : Paperboard Elastic Modulus and Caliper Effects As expected, both 16in and 32in racking tests showed good agreement between initial slope ratios and paperboard EMDECD t ratios within three paperboard grades. Superimposed load-strain curves clearly confirmed the expected racking stiffness and strength increase with increasing paperboard stiffness ( EMDECD t ), and less racking strength loss using thicker paperboards. Also buckling measurements confirmed the much larger buckling of paperboard A than the other two paperboards. The predicted racking stiffness was about 50% greater than the measured stiffness. Although this is partly due to uniformity of load transfer, and different time-scales in testing, we suspect that the MD stress-strain behavior of this paperboard has peculiar behavior with initial internal slack in the response. This merits further investigation before conclusions can be drawn. 87

100 6.0 Recommendations for future work 1. Paperboard curl should try to be prevented under conditioning or long time storage due to the suspected effects on racking strength. 2. Influence of wood density for inserts should be evaluated. 3. The unstable performance of 16in racking tests might be caused by the shared metal frame connection pins. It is recommended to make a new set of connecters for the 16in racking tester, to save switch time and initial setup adjustments. 4. Racking load speed effects are suggested for future evaluation. Or to be simple, paperboard elastic modulus can be retested under the same loading speed as in racking tests. 5. Paperboard orientation effects should be re-tested with buckling measurements, due to the possible loose screw problem not realized at the first stage of testing. Test with smaller staple spacing on middle stud are also recommended to further explore the orientation effects on racking strength. These new results can be compared to 32in racking tests without middle stud to further study middle stud effects. 6. Racking tests by glue method are suggested to test the effects of paperboard properties, orientation and middle stud on racking strength and to further understand the mechanics of the racking test. 7. Paperboard corner cutting effects can be confirmed by tests with varied staple patterns (the distance between staple and corner, staple spacing). 8. Staple number tests (both 16 and 32in, not loading-reloading procedure) are suggested with buckling measurement, which will help to further understand staple cutting effects. 88

101 9. Staple oriented parallel to shear direction can also be tried for future comparison with the current results (all perpendicular staple orientation), to further evaluate the staple behaviors in racking tests. 10. A new small-scale racking tester design might be possible with some kind of edge clamping, which provides both strong and uniform edge restrains without needs of staples or gluing. Paperboard corner cutting might also be minimized in this new design. 89

102 7.0 References [1] Sherwood, G. and Moody, R. C., Light frame wall and floor system: analysis and performance, General Technical Report FPL-GTR-59, Madison, WI: U.S. Department of Agriculture, Forest Service, Forest Products Laboratory, [2] Standard Test Methods of Conducting Strength Tests of Panels for Building Construction, ASTM E72, American Society for Testing and Materials, Philadelphia, PA, [3] Standard Practice for Static Load Test for Shear Resistance of Framed Walls for Buildings, ASTM E564, American Society for Testing and Materials, Philadelphia, PA, [4] Tuomi, Roger L. and Gromala, David S., Racking Strength of Walls Let-in Corner Bracing, Sheet Materials, and the Effect of Loading Rate, U.S. Department of Agriculture, Forest Service, FPL301, 20ps, (1977). [5] Neisel, R. H. and Guerrera, J. F., Racking Strength of Fiberboard Sheathing, Tappi, 39:9, (1956). [6] Neisel, R. H., Racking Strength and Lateral Nail Resistance of Fiberboard Sheathing, Tappi, 41:12, (1958). [7] Welsch, G. J., Racking Strength of Half-Inch Fiberboard Sheathings, Tappi, 46:8, (1963). [8] Price, Eddie W. and Gromala, David S., Racking Strength of Walls Sheathed with Structural Flakeboards Made from Southern Species, Forest Products Journal, 30:12, (1980). [9] McCutcheon, William J., Racking Deformations in Wood Shear Walls, Journal of Structural Engineering, 111:2, (1985). [10] Test Methods for Evaluating Properties of Wood-Based Fiber and Particle Panel Materials, ASTM D1037, American Society for Testing and Materials, Philadelphia, PA, [11] Patton-Mallory, Marcia and Wolfe, Ronald W., Soltis, Lawrence A. and Gutkowski, Richard M., Light-Frame Shear Wall Length and Opening Effects, Journal of Structural Engineering, 111:10, (1985). [12] Coffin, Douglas W. and Hsieh, Jeff, Racking Strength of Paperboard Based Sheathing Materials (Report to Caraustar), Paper Science and Engineering Department, Miami University, Oxford, OH (513)

103 [13] Lekhnitskii, Anisotropic Plates, Gordon and breach Science Publishers, New York, NY, [14] Racking Strength of Structural Insulating Board, T1005 cm-83, TAPPI, Atlanta, GA, [15] Baum, G. A., Brennan, D. G., and Habeger, C.C., Orthotropic Elastic Constants of Paper, Tappi, 64:8, (1981). 91

104 8.0 Appendix Appendix A1: Caliper (inch) data of the standard (A) paperboards Board# A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A

105 Appendix A2: Caliper (inch) data of the structural (B) paperboards Board# B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B

106 Appendix A3: Caliper (inch) data of the super structural (C) paperboards Board# C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C

107 Appendix A3: Caliper (inch) data of the super structural (C) paperboards (continued) Board# C C C C C C C C

108 Appendix A4: Paperboard elastic modulus data ( EMDECD t: kpli) (sample 0.50in width, 6.0 in tension length and loading speed 1in/min) Paperboard Super Super Grade & Direction Standard A-MD Standard A-CD Structural B-MD Structural B-CD Structural C-MD Structural C-CD Average S.D EMDECD t

109 Appendix A5: Paperboard basis weight (lb/1000ft 2 ) tested by 5.0*10.0in sample area Standard Paperboard A Sample # Weight (g) B.W. (lb/1000ft 2 ) Average 280 S.D. 10 Structural Paperboard B Sample # Weight (g) B.W. (lb/1000ft 2 ) Average 370 S.D. 10 Super Structural Paperboard C Sample # Weight (g) B.W. (lb/1000ft 2 ) Average 470 S.D

110 Appendix A6: Paperboard moisture content (MC%) tested by 4.0*6.0in sample area Standard Paperboard A Drying Time 3days 3days 4days 4days 6days 6days Sample # Initial WT. (g) Dried WT. (g) MC % Dried WT. (g) MC% Dried WT. (g) MC% Average S.D Structural Paperboard B Sample # Initial WT. (g) Dried WT. (g) MC % Dried WT. (g) MC% Dried WT. (g) MC% 1* Average (8.2)* 0.5 S.D (0.2)* *: The average data in ( ) does not include sample 1 due to extreme big variation Super Structural Paperboard C Sample # Initial WT. (g) Dried WT. (g) MC % Dried WT. (g) MC% Dried WT. (g) MC% Average S.D

111 Appendix B.1: Statistical t test of comparison of racking strength of two orientation conditions for structural (B) paperboards Appendix B.2: Statistical t test of comparison of racking strength of two orientation conditions for Super Structural C grade paperboards 99

112 Appendix B.3: Statistical t test of comparison of racking strength of two orientation conditions for Super Structural C grade paperboards (only Data from second wood surface) 100