PROJECT NO. 5410P001

FORESTRY CANADA NO. 12

COMPUTER ANALYSIS OF PARALLEL CHORD TRUSS SYSTEMS

Progress Report

by

C. Lum

Wood Engineering S c i e n t i s t

March, 1991 This project was financially supported by Forestry Canada

under the Contribution Agreement existing between the iovernment orCanada and Forintek Canada Corp.

NOTICE

This report i s an i n t e r n a l Forintek Canada Corp. ("Forintek") docximent, f o r release only by permission of Forintek. This d i s t r i b u t i o n does not co n s t i t u t e p u b l i c a t i o n . The report i s not t o be copied f o r , or c i r c u l a t e d to, persons or parties other than those agreed to by Forint e k . A l s o , t h i s report i s not to be c i t e d , i n whole or i n part, unless p r i o r permission i s secured from Forintek.

Neither Forintek, nor i t s members, nor any other persons a c t i n g on i t s behalf, make any warranty, express or implied, or assume any l e g a l r e s p o n s i b i l i t y or l i a b i l i t y f o r the completeness of any information, apparatus, product or process disclosed, or represent t h a t the use of the d i s c l o s e d information would not i n f r i n g e upon p r i v a t e l y owned r i g h t s . Any reference i n t h i s report to any s p e c i f i c commercial product, process or service by tradename, trademark, manufacturer or otherwise does not nec e s s a r i l y constitute or imply i t s endorsement by Fo r i n t e k or any of i t s members.

7 -t '

SUMMARY

Truss t e s t data c o l l e c t e d from f u l l scale t e s t s of 40-ft. p a r a l l e l chord trusses and 28xl6-ft. p a r a l l e l chord truss systems are being analyzed. Two computer models - NSAT and TBEAM - are being v a l i d a t e d against the t e s t data. To extend these models to system a n a l y s i s models, t h e i r output i s being used as data f o r the Floor Analysis Program, FAP. A n a l y t i c a l r e s u l t s f o r 40- and 28-ft. p a r a l l e l chord trusses from one t r u s s p l a t e manufacturer are presented.

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TABLE OF CONTENTS

Page

SUMMARY i

LIST OF TABLES i i i

LIST OF FIGURES i i i

1.0 OBJECTIVE 1

2.0 INTRODUCTION 1

2.1 BACKGROUND 1

2.2 WORK PLAN FOR 1990-91 1

3.0 METHOD 2

3.1 COMPUTER MODELS: NSAT, TBEAM, FRAME AND FAP 2 3.2 SINGLE TRUSS ANALOGS: NSAT AND TBEAM 4 3.3 TRUSS SYSTEM ANALOGS: FAP 6 3.4 USING FAP TO DETERMINE THE EFFECTIVE WIDTH , 14

4.0 RESULTS AND DISCUSSION 15

4.1 SENSITIVITY STUDY 15 4.2 ASSESSMENT OF THE EFFECTIVE FLANGE WIDTH 16 4.3 TRUSS MODEL VERIFICATION 16

5.0 CONCLUSIONS 22

6.0 REFERENCES 23

APPENDIX I CALCULATING EQUIVALENT JOIST PROPERTIES FOR A PARALLEL CHORD TRUSS

APPENDIX II PROPERTIES OF THE FLOOR SYSTEM USED IN THE EFFECTIVE WIDTH STUDY

LIST OF TABLES

Table 1. Equivalent J o i s t Dimensions (A) and Mechanical Properties (B)

Table 2. Results of the E f f e c t i v e Width Study Using FAP With (A) and Without Sheathing Gaps (B) E:G Ratio = 100

Table 3. Results of the E f f e c t i v e Width Study Using FAP With (A) and Without Sheathing Caps (B) E:G Ratio = 17

Table 4. Predicted and Measured Mid-Span Deflections at Design Load

Table 5. Comparison of L a t e r a l Load D i s t r i b u t i o n Using FAP with Methods A and B

LIST OF FIGURES

Figure 1. TBEAM analog of a sheathed top chord

Figure 2. 40-ft. p a r a l l e l chord trusses supported by bottom chord

Figure 3. 28-ft. p a r a l l e l chord trusses supported by top and bottom chord

Figure 4. T y p i c a l TBEAM j o i n t analog

Figure 5. T y p i c a l NSAT j o i n t analog

Figure 6. Truss loading on a p a r a l l e l chord truss to determine equivalent s o l i d wood j o i s t modulus of e l a s t i c i t y

Figure 7. Truss loading on a p a r a l l e l chord t r u s s to determine equivalent s o l i d wood j o i s t shear modulus

1.0 OBJECTIVE

The objective of t h i s project i s to v e r i f y the s t r u c t u r a l a n a l y s i s computer model developed, using the p a r a l l e l chord t r u s s and t r u s s system t e s t database; and to present the r e s u l t s from t e s t i n g and a n a l y s i s i n a t e c h n i c a l paper.

2.0 INTRODUCTION

2 .1 BACKGROUND

In the f i e l d , s t r u c t u r a l systems are judged according t o how well they perform as a system, not by how well the i n d i v i d u a l members or components perform. Designers are responsible f o r ensuring that a system made of a p a r t i c u l a r material meets the minimum requirements of the end user or the b u i l d i n g codes.

Unfortunately, p r e d i c t i n g the performance of a system i s considerably more d i f f i c u l t than p r e d i c t i n g the performance of a s i n g l e component. As a r e s u l t , wood trus s system designers need to make s i m p l i f y i n g assumptions so that t h e i r structure can be analyzed with e x i s t i n g design t o o l s . Such s i m p l i f y i n g assumptions may or may not r e s u l t i n s a t i s f a c t o r y systems. This uncertainty becomes c r i t i c a l when systems are being designed f o r s t r u c t u r a l l y more demanding app l i c a t i o n s such as i n long span non­r e s i d e n t i a l b u i l d i n g s . By understanding system behavior, we can develop e f f i c i e n t and r e l i a b l e design procedures.

To obtain t h i s understanding, s p e c i a l i z e d s t r u c t u r a l a n a l y s i s models for wood must be developed and v a l i d a t e d with f u l l scale s t r u c t u r a l t e s t s . Once t h i s phase i s completed, one can evaluate the r e l i a b i l i t y and develop appropriate design procedures for buildings constructed of various wood products. The emphasis i n t h i s p r o j e c t i s on systems whose primary s t r u c t u r a l members are p a r a l l e l chord trusses.

To date, f u l l scale t e s t s on 40-ft. p a r a l l e l chord tru s s e s and 28-ft. long by 16-ft. wide p a r a l l e l chord truss systems have been completed. A p a r a l l e l chord t r u s s model, TBEAM, has also been developed.

2.2 WORK PLAN FOR 1990-91

The work plan for the 1990-91 f i s c a l year i s to complete the p a r a l l e l chord t r u s s analysis, and to compare the experimental r e s u l t s to p r e d i c t i o n s from three computer models developed f o r analyzing p a r a l l e l chord t r u s s . A f l o o r system analysis program, FAP, w i l l be used i n combination with e i t h e r NSAT or TBEAM to model the complete t r u s s system performance.

Most of the changes introduced i n the current wood design code CAN/CSA 086.1-M89 are rela t e d to work by Foschi et a l . (1989) on s i n g l e member r e l i a b i l i t y . In si n g l e member r e l i a b i l i t y studies, s i n g l e member design equations are used i n the r e l i a b i l i t y analysis to determine the most appropriate material performance fa c t o r .

Because of the complexity of systems such as f l o o r s b u i l t with p a r a l l e l chord trusses, computer-based s t r u c t u r a l a nalysis models are used. These models, along with the design assumptions made by the design, have an e f f e c t on the s t r u c t u r a l r e l i a b i l i t y of the system being considered. Therefore, to develop r e l i a b i l i t y - b a s e d design procedures f o r complex systems, analysis models used by both researchers and designers must be val i d a t e d and compared. Furthermore, design procedures associated with a p a r t i c u l a r design model must be assessed as w e l l .

In t h i s report, three t r u s s models are evaluated. One i s cu r r e n t l y used extensively by designers f o r s t e e l , concrete and wood str u c t u r e s . The second was developed as part of t h i s research program s p e c i f i c a l l y f o r l i g h t metal plated wooden trusses. The t h i r d model i s the most advanced wooden t r u s s analysis model a v a i l a b l e and has been used e x c l u s i v e l y f o r research purposes. This report focuses on these three t r u s s a n a l y s i s models and a f l o o r analysis model developed f o r s o l i d lumber j o i s t f l o o r s . Two design concepts that may be considered i n a f l o o r or roof system design — e f f e c t i v e flange width and l a t e r a l load sharing — are also discussed. While not part of t h i s research program, the long-term objective i s to make these t o o l s and design concepts a v a i l a b l e f o r the development of re l i a J a i l i t y - b a s e d design procedures f o r complex systems.

3.0 METHOD

3.1 COMPUTER MODELS: NSAT, TBEAM, FRAME AND FAP

The performance of sing l e 40-ft. p a r a l l e l chord trusses subjected to a uniformly d i s t r i b u t e d g r a v i t y load on the top chord are compared with the performance predicted from two analysis computer programs f o r l i g h t metal-plate connected trusses: NSAT and TBEAM. The progrsim NSAT i s a modified version of SAT, the "Structural Analysis of Trusses" program (Foschi 1977), Like SAT, NSAT i s capable of modelling the non-linear l o a d - s l i p response between the l i g h t metal connector p l a t e s and the underlying wood member. The differe n c e between SAT and NSAT i s that NSAT can model a truss having more than one connector p l a t e type, while SAT i s l i m i t e d to trusses having only one type of connector p l a t e . Both models have been validated f or p i t c h and p a r a l l e l chord trusses (Lum and Varoglu 1988; Karacabeyli et a l , 1990). Because of the complexity of the input required, both SAT and NSAT have remained e s s e n t i a l l y a n a l y t i c a l t o o l s f o r research purposes.

The TBEAM program was written during the fourth year of t h i s p r o j e c t . What distinguishes t h i s model from SAT and standard plane frame analysis programs i s that any member i n the tru s s can be modelled as a T- or I-beam with incomplete composite action, between the flanges and the main member. Incomplete composite action occurs when there i s r e l a t i v e s l i p between the plywood sheathing or flange, and the j o i s t or s t i f f e n e r . For example, a n a i l e d connection would provide incomplete composite a c t i o n , while a connection glued with a s t r u c t u r a l adhesive such as phenol r e s o r c i n o l formaldehyde would provide f u l l composite action.

Gaps i n the sheathing are also considered by the TBEAM model. The e f f e c t of gaps i s modelled by i n s e r t i n g a d i s c o n t i n u i t y i n the a x i a l s t i f f n e s s of the sheathing. This approach i s s i m i l a r to how pin-ended members are modelled i n frame analysis programs. The advantage of t h i s approach i s that gaps can be inserted and removed from the analog with very l i t t l e e f f o r t .

A s e c t i o n of a sheathed top chord i s shown i n Figure 1. In TBEAM, the top chord or the s t i f f e n e r layer i s separated into segments (Ml to M3). I f sheathing i s attached, a "flange" member ( F l to F3) must be s p e c i f i e d f o r each chord segment. Gaps i n the sheathing can only be located at j o i n t s connecting flange members. In Figure 1, a gap i s shown at j o i n t J3.

There are two ways of i n s e r t i n g a gap i n the sheathing analog. One i s that gaps can be s p e c i f i e d as two j o i n t s placed at the gap l o c a t i o n with, fo r example, member F2 attached to one j o i n t and member F3 attached to the other j o i n t . A l t e r n a t i v e l y , a s i n g l e j o i n t can be placed at the gap. Member F2 may be attached to j o i n t J3 and member F3 l e f t unattached to J3. Therefore, a gap can be inserted and removed by simply unlocking or locking member F3 from J3. An anomaly of t h i s approach and the formulation of the model i s that the sheathing on e i t h e r side of the gap i s forced to rotate the same amount as the s t i f f e n e r . Consequently, bending stresses appear on the sheathing edges adjacent to the gap, when i n f a c t these edges should be free of any normal stresses. This model anomaly has not been found to a f f e c t the TBEAM model's a b i l i t y to p r e d i c t the d e f l e c t i o n of composite beams with gaps.

As a tru s s analysis t o o l , the TBEAM model considers the s e m i - r i g i d a x i a l and r o t a t i o n a l behaviour of the truss-plated j o i n t s . The j o i n t e c c e n t r i c i t y e f f e c t s which may influence the o v e r a l l t r u s s behavior i s also included. Local stresses i n the truss members r e s u l t i n g from j o i n t e c c e n t r i c i t y , however, are not determined. I t was assumed that l o c a l stresses would be analyzed with a s p e c i a l i z e d j o i n t model. Unlike NSAT, TBEAM uses a l i n e a r approximation of the plate connector's l o a d - s l i p

response. In TBEAM, the truss p l a t e connections's l o a d - s l i p response i s approximated by a l i n e connecting the o r i g i n and a point on the l o a d - s l i p curve at the design load l e v e l .

FRAME, a standard plane frame s t r u c t u r a l analysis model generally used by the design community, i s a subset of the TBEAM program. The FR7VME analog contains only continuous or pinned j o i n t s . Using pinned j o i n t s to represent the connector plates provides reasonable estimates of the o v e r a l l truss s t i f f n e s s up to curr e n t l y accepted design load l e v e l s (Lum and Varoglu 1988). However, the member forces are misleading, e s p e c i a l l y the bending moment induced by r o t a t i o n of the web members r e l a t i v e to the chords.

To compare the sing l e truss analysis r e s u l t s to the f u l l system performance, FAP or the "Floor Analysis Program" (Foschi 1982) w i l l be used. This program was developed to analyze s o l i d lumber j o i s t f l o o r s , not p a r a l l e l chord truss systems. Therefore, some preliminary a n a l y s i s i s required to determine equivalent s o l i d lumber properties f o r trusses, which w i l l then allow FAP to be used. The procedure used to derive equivalent s o l i d lumber j o i s t properties for trusses i s discussed i n t h i s report.

These models provide estimates of trus s d e f l e c t i o n s and t r u s s member forces under s p e c i f i e d loading conditions. Closed form so l u t i o n s do not e x i s t for the trusses tested i n the study. Instead, d e f l e c t i o n s from the truss computer models w i l l be compared with the t e s t r e s u l t s . Because member stresses are not a v a i l a b l e from the t e s t r e s u l t s , predicted stresses must be compared among the computer models being evaluated. Member str e s s r e s u l t s w i l l not be presented at t h i s time.

3.2 SINGLE TRUSS ANALOGS: NSAT AND TBEAM

To date, data f i l e s f o r NSAT and TBEAM have been prepared f o r a l l trusses tested e a r l i e r on i n the study. Twelve d i f f e r e n t t r u s s configurations w i l l be analyzed. These are shown i n Figures 2 and 3- This report covers only the analysis of the 40-ft. p a r a l l e l chord tr u s s boxed i n Figure 2 and the 28-ft. t r u s s and truss system boxed i n Figure 3. These trusses a l l use t r u s s p l a t e s from a common p l a t e manufacturer. A d d i t i o n a l d e t a i l s of the 40- and 28-ft. trusses may be found i n Lum (1987) and Lum (1989), respect ive l y .

The TBEAM model w i l l be used to analyze the system trusses with and without sheathing attached. This w i l l give an estimate of the b e n e f i t s of composite ac t i o n . Where the analysis includes sheathing, the sheathing w i l l be modelled with and without gaps. A t y p i c a l TBEAM t r u s s j o i n t analog i s shown i n Figure 4. The j o i n t at the centre of the connector p l a t e i s placed by TBEAM and hidden from the user by s t a t i c condensation.

A t y p i c a l NSAT j o i n t analog i s shown i n Figure 5. The same procedure was used f o r preparing NSAT analogs for every j o i n t i n the trusses analyzed. Although some j o i n t s analogs may be optimized to minimize the computational requirements, t h i s was not done. Using a consistent procedure to develop j o i n t analogs f a c i l i t a t e s the development of a pre-processor or automatic j o i n t analog generator. B a s i c a l l y , l i n k zones were used to d i v i d e the connector p l a t e i n t o connector areas and l i n k zone lengths were defined by the l i m i t s of the plate rather than of the connector areas. Gap control was only enforced at a s i n g l e point at the end of each compression member. Gap closure r e s u l t i n g from r e l a t i v e member r o t a t i o n was therefore ignored i n the NSAT analog.

3.3 TRUSS SYSTEM ANALOGS: FAP

The SAT and TBEAM models are capable of modelling only a s i n g l e t r u s s . To extend the s i n g l e truss analysis models to multi-truss assemblies, FAP, w i l l be used. I t accounts f o r the l a t e r a l load sharing when the sheathing i s continuous across several trusses or j o i s t s . Unlike TBEAM, FAP also models the shearlag causing non-uniform s t r e s s d i s t r i b u t i o n i n the sheathing perpendicular to the length of the j o i s t s . This feature of FAP makes i t useful f or determining the e f f e c t i v e flange width f o r the TBEAM model. However, because the FAP computer program was written f o r s o l i d j o i s t f l o o r s , a procedure to develop equivalent s o l i d wood j o i s t p roperties from i n d i v i d u a l trusses had to be developed.

Sheathing properties for t r u s s systems are s i m i l a r to those i n s o l i d j o i s t systems. Therefore, only equivalent j o i s t properties f o r the p a r a l l e l chord trusses i n a system need to be defined. Two approaches to c a l c u l a t i n g equivalent j o i s t properties for trusses w i l l be discussed: Method A and Method B, For both methods, the equivalent j o i s t dimensions assumed f o r the truss are shown i n Table 1. The moment of i n e r t i a and cross-section area were calculated using the dimensions given i n the ta b l e , and the shear area was assumed to be 0.83 times the c r o s s - s e c t i o n area.

Method A i s as follows: With the section properties c a l c u l a t e d , the equivalent j o i s t modulus of e l a s t i c i t y , E, and the shear modulus, G, are determined according to Table 1.

Figure 2. 40-ft. p a r a l l e l chord trusses supported by bottom chord

Figure 3. 28-ft. p a r a l l e l chord trusses supported by top and bottom chord

Table 1

Equivalent J o i s t Dimension for FAP Truss Dimension

J o i s t length Distance between the support centres (same).

J o i s t thickness Actual truss or lumber thickness (same).

J o i s t depth Depth of truss between the centre-line of the chords.

This distance was selected rather than the overall

depth of the truss because the chord centre-lines

coincide with the theoretical line of action (e.g.

bending joist stress = axial tensile stress).

B

Equivalent J o i s t Mechanical Property f o r FAP

Procedure t o Obtain Property

J o i s t Modulus of E l a s t i c i t y E of a solid joist with the depth defined as above which

would allow the joist to deflect the same amount as the truss

subjected to end moments (tension chord in tension and

compression chord in compression) as shown in Figure 6.

J o i s t Shear Modulus G of a solid joist with the E calculated as above which would

deflect the same amount as the truss subjected to centre-point

loading. The centre-point loading is shown in Figure 7. FAP

uses a common E:G ratio for all joists in the'system;

therefore, an average E:G ratio will need to be determined

from all the trusses in a given assembly.

Both Method A and B ignore a number of items which may l i m i t the usefulness of the r e s u l t s . When composite action occurs between the sheathing and a j o i s t , an a x i a l tension force as well as the bending forces are applied to the j o i s t . The procedure o u t l i n e d above does not determine the a x i a l s t i f f n e s s of an equivalent j o i s t . Consequently, FAP may not be able to predict the amount of composite a c t i o n created by n a i l i n g sheathing onto the t r u s s . This then implies t h a t the stresses determined by FAP may not be correct.

Second, both methods only consider the d e f l e c t i o n at a s i n g l e point, such as at the mid-span d e f l e c t i o n of the bottom chord, to determine the trus s s t i f f n e s s . I t may not always be possible to match the j o i s t and trus s d e f l e c t i o n s at a l l points i n a t r u s s .

c c -—1 • •

L QJ 03

JD 0 E

.—1 QJ •_

• m

E i t h e r NSAT or TBEAM (without sheathing attached) may be used to derive the equivalent E and G. An excunple of the procedure and a comparison between a truss and a s o l i d wood j o i s t are given i n Appendix I for the bottom chord supported roof truss analyzed and presented i n t h i s report. With Method A, the average E:G r a t i o f o r t h i s t r u s s c o n f i g u r a t i o n was about 100 using TBEAM analogs and 120 using NSAT analogs.

The TBEAM model should provide a more accurate assessment of E and G than NSAT at design load l e v e l s . The reason i s that NSAT models the non-linear connector p l a t e response. With NSAT i t would be d i f f i c u l t t o assess the equivalent E and G and s t i l l ensure that a l l connector p l a t e j o i n t s are not stressed at l e v e l s higher than what would be normally reached at design load l e v e l s . The E:G r a t i o obtained with e i t h e r t r u s s model i s r e l a t i v e l y high compared with an E:G r a t i o of 17 normally assumed f o r s o l i d wood. One should note that the equivalent E:G r a t i o f o r a t r u s s i s not only a material property, but also a geometric property which depends on the type of truss being analyzed.

In Method B, shear d e f l e c t i o n i s not assumed to occur. Instead, the bending s t i f f n e s s encompasses both shear and bending d e f l e c t i o n s . A standard beam ec[uation, appropriate for the loading to be applied to the system, i s f o r example, then used to c a l c u l a t e E. The equation f o r a si n g l e concentrated load on a beam w i l l be used i f the system i s subjected to a l i n e load placed along a l i n e perpendicular to the j o i s t s . When Method B r e s u l t s are used with FAP, the E:G r a t i o should be assigned a low value, such as 0.1, to ensure that no shear d e f l e c t i o n s are computed.

At t h i s time, i t may not be prudent to r e l y on FAP to p r e d i c t the amount of composite action occurring between the t r u s s and the sheathing. I t may also not be reasonable to r e l y on FAP to determine the s t r e s s state i n the t r u s s . However, assuming that the a x i a l and bending s t i f f n e s s of a truss i s constant, the FAP analysis using equivalent j o i s t p r operties f o r the trusses should provide accurate estimates of the load d i s t r i b u t i o n within a system subject to uniform loading. To obtain the l a t e r a l load d i s t r i b u t i o n , a c h a r a c t e r i s t i c stress can be examined, f o r example the bending s t r e s s at mid-span. The load applied to each t r u s s can then be proportioned by the r a t i o of the c h a r a c t e r i s t i c stress to the sum of c h a r a c t e r i s t i c stress across a l l trusses. This i s permissible because FAP i s a l i n e a r model. An example of t h i s i s given i n Appendix I.

When a sheathed j o i s t i s loaded, the sheathing stresses p a r a l l e l to the length of the j o i s t are non-uniform. For a system under uniform load, the stresses are maximum d i r e c t l y over the j o i s t and minimum mid-way between the j o i s t s . The diffe r e n c e between the maximum and minimum str e s s depends on the r e l a t i v e a x i a l s t i f f n e s s of the j o i s t and sheathing, and the bending s t i f f n e s s of the j o i s t . Generally, the designer w i l l not have the resources to determine t h i s non-uniform st r e s s state. E i t h e r the designer ignores the contribution of the sheathing (which i s c u r r e n t l y done f o r wood design), or the designer assumes a uniform s t r e s s over an " e f f e c t i v e flange width." This width i s generally taken to be equal to the spacing of the beam elements. However, for widely spaced beam elements ( i . e . , a tr u s s or j o i s t ) , t h i s assumption may not be reasonable. For t h i s l a t t e r case, two e f f e c t i v e widths can be defined: one that allows the corr e c t stresses to be calculated i n the beam element, and another that allows the correct d e f l e c t i o n to be cal c u l a t e d .

Composite action i s cu r r e n t l y considered i n concrete and s t e e l design, and these design codes provide equations to determine the e f f e c t i v e width. Such information i s not e x p l i c i t l y a v a i l a b l e i n the Canadian Wood Design Code but i s contained i n "system f a c t o r s " used for designing f l o o r j o i s t s .

For t h i s study, an e f f e c t i v e width equal t o the t r u s s spacing (610 mm) i s assumed i n the TBEAM an a l y s i s . Is t h i s a reasonable assumption? In assessing the e f f e c t i v e width, we are intere s t e d i n the width at which any increase i n the flange width would r e s u l t i n l i t t l e or no decrease i n the stresses and d e f l e c t i o n s .

The FAP model may be used to check the e f f e c t i v e width assumed i n the TBEAM an a l y s i s . However, s e n s i t i v i t y studies using FAP suggest that the a x i a l s t i f f n e s s of the beam should be accurately modelled to determine the e f f e c t i v e flange width. Because a procedure to e s t a b l i s h the a x i a l s t i f f n e s s of a truss has not yet been established, the question of whether the e f f e c t i v e width used i s reasonable must be l e f t unanswered. However, some preliminary r e s u l t s using FAP to assess the e f f e c t i v e width, assuming the a x i a l s t i f f n e s s i s known, are presented below.

4.0 RESULTS AND DISCUSSION

At the time of t h i s report, one 40 f t . p a r a l l e l chord t r u s s design and trusses f o r one 28 f t . f l a t roof assembly have been analyzed. Before conducting the analysis of the t e s t systems, a conducted a study t o determine the s e n s i t i v i t y of a structure's performance to the model parameters. S e n s i t i v i t y analysis using a bottom chord supported roof t r u s s system with 12.5 mm t h i c k sheathing attached revealed the following: (the model used i n the s e n s i t i v i t y analysis are given i n brackets)

. Composite action i n a t r u s s system i s not as great as i n a s o l i d j o i s t system f o r t y p i c a l n a i l e d connections [TBEAM, FAP]. This suggests some di f f e r e n c e i n how a truss and a j o i s t behave i n bending and i n t e r a c t with the sheathing. The d i f f e r e n c e may be due to the low a x i a l s t i f f n e s s of trusses, compared with s o l i d wood j o i s t s .

. Composite ac t i o n i s not s e n s i t i v e to v a r i a t i o n s i n the connector s t i f f n e s s [TBEAM, FAP]. Therefore, the s t i f f n e s s of the n a i l e d connection does not have to be accurately determined.

. compared to a s o l i d wood j o i s t , the "beam shear" s t i f f n e s s of a p a r a l l e l chord t r u s s i s low. Consequently, the truss bending s t i f f n e s s c a l c u l a t e d using beam equations w i l l vary according t o how the load i s applied, unless shear deformations are also c a l c u l a t e d .

. Gaps i n the sheathing have a noticeable e f f e c t on the o v e r a l l t r u s s s t i f f n e s s . This, however, depends on the amount of composite a c t i o n provided by the connector layer and the thickness of the sheathing. The TBEAM analogs are more s e n s i t i v e to the presence of gaps i n the sheathing than are the FAP analogs [TBEAM, FAP].

. Although FAP may be used to determine the l a t e r a l load sharing i n multiple t r u s s systems, i t assumes that the sheathing i s continuous across a l l j o i s t s i n a system. For widely spaced systems and long spans, the l a t e r a l load sharing may be lower not only because of the longer sheathing span, but also because the sheathing i s not continuous over as many spans [FAP].

In summary, j o i s t and truss systems appear to behave d i f f e r e n t l y . This i s p r i m a r i l y due to the low beam shear s t i f f n e s s of trusses as compared to that of s o l i d wood j o i s t s . Differences i n the a x i a l s t i f f n e s s of trusses and j o i s t s of the same s i z e w i l l also a f f e c t how well FAP models a p a r a l l e l chord tr u s s system. Gaps, i f present i n a system, w i l l also a f f e c t the s t r e s s and deformation state of the system and must be considered i n the a n a l y s i s .

4.2 ASSESSMENT OF THE EFFECTIVE FLANGE WIDTH

To study the e f f e c t i v e width, we recorded j o i s t mid-span d e f l e c t i o n and extreme f i b r e stress from FAP analysis f or j o i s t spacing from 300 to 1,000 mm. Although each FAP analysis used a d i f f e r e n t j o i s t spacing, the product of the j o i s t spacing and the uniform load was kept constant so that the t o t a l load applied to a j o i s t was equal f o r each FAP a n a l y s i s . Table 2 summarizes the e f f e c t i v e width study and shows the changes i n maximum stre s s and j o i s t d e f l e c t i o n with j o i s t spacing.

In Table 2A and 2B - r e s u l t s are presented for j o i s t s with low shear s t i f f n e s s . Tables 3A and 3B present r e s u l t s f or j o i s t s with average shear s t i f f n e s s f o r wood beams. These figures suggest that f o r the beam properties used, shear deformation i n the beam and gaps i n the sheathing do not influence the point at which an increase i n the flange width ceases to decrease the j o i s t stress or d e f l e c t i o n . As i n d i c a t e d i n the t a b l e , the e f f e c t i v e width f o r t h i s beam i s approximately 600-700 mm at t h i s j o i s t spacing. We can use FAP to develop e f f e c t i v e width f a c t o r s , provided we can determine the a x i a l s t i f f n e s s of the j o i s t or t r u s s .

4.3 TRUSS MODEL VERIFICATION

V e r i f i c a t i o n of TBEAM f o r trusses i n f l o o r or f l a t roof systems can only be done by comparing the predicted d e f l e c t i o n s with the measured d e f l e c t i o n s . Member stresses, p a r t i c u l a r l y the maximum stre s s and the l o c a t i o n of maximum str e s s , can only be compared between models. Table 4 provides a comparison of the mid-span d e f l e c t i o n s as predicted by TBEAM, FRAME and NSAT with the experimental r e s u l t s .

The experimental r e s u l t s are given with the e f f e c t of compression s p l i c e buckling present and then removed. Compression s p l i c e buckling was monitored during the system t e s t i n a l l trusses. To determine the c o r r e c t i o n to the mid-span d e f l e c t i o n , TBEAM analogs were analyzed to f i n d the mid-span d e f l e c t i o n caused by a unit gap closure at each compression s p l i c e . This r e s u l t was then proportioned by the amount of gap closure measured during the f u l l scale t e s t to determine the c o r r e c t i o n to the mid-span d e f l e c t i o n .

A l l system r e s u l t s shown i n Table 4, in c l u d i n g computed r e s u l t s from FAP, have been adjusted so that each truss i s ca r r y i n g i t s design load. A l t e r n a t i v e l y , the d e f l e c t i o n s may be given for each t r u s s when the uniform design load i s applied to the system. In t h i s case, trusses may be subjected to a higher or lower load than the design load, depending on the r e l a t i v e s t i f f n e s s of the truss and adjacent trusses, and the s t i f f n e s s of the sheathing i n bending. S t i f f trusses w i l l tend to carry more of the applied load, and limber trusses w i l l tend to carry l e s s .

E x t e r i o r trusses, because they are only loaded to one side, w i l l d e f l e c t l e s s than the adjacent t r u s s . Consecjuently, the e x t e r i o r trusses may end up car r y i n g more load than indicated by t h e i r load t r i b u t a r y area. An ex t e r i o r t r u s s with high t o r s i o n a l r i g i d i t y w i l l also tend to carry more load.

Table 2

Results of the E f f e c t i v e Width Study Using FAP With (A) and Sheathing Gaps (B), E:G = 100

A

J o i s t Spacing (mm)

Uniform Load (kPa)

Mid-Span Stress (MPa)

Mid-Span D e f l e c t i o n

(mm)

300 9.60 27.7 123.2

400 7.20 26.9 119.0

500 5.76 26.1 114.9

600 4.80 25.4 111.5

700 4.11 24.9 109.0

800 3.60 24.6 107.4

900 3.20 24.4 106.1

1,000 2.88 24.2 105.1

Unsheathed Joist 2.88 N/mm 30.9 142.9

Input properties for FAP analysis are listed in Appendix II. Plywood is 12.5 ram with gaps spaced

1200 mm along the span. Ratio E:G set at 100.

Uniform load and joist spacing combination results in the same total load applied to a single joist.

Table 2 Results of the E f f e c t i v e Width Study Using

FAP With (A) and Sheathing Gaps (B), E:G = 100 B

J o i s t Spacing (mm)

Uniform Load (kPa)

Mid-Span Stress (MPa)

Mid-Span De f l e c t i o n

(mm)

300 9.60 27.4 121.5

400 7.20 26.6 117.2

500 5.76 25.8 113.1

600 4.80 25.1 109.8

700 4.11' 24.6 107.3

800 3.60 24.3 105.7

900 3.20 24.1 104.5

1,000 2.88 24.0 103.6

1 Unsheathed Joist 2.88 N/mm 30.9 142.9

' Input properties for FAP analysis listed in Appendix 0. 12.5 mm plywood with no gaps.

RaUo of E to G set at 100.

^ Uniform load and joist spacing combination results in the same total load applied to a single joist.

Table 3 Results of the E f f e c t i v e Width Study Using

FAP With (A) and Sheathing Gaps (B), E:G = 17 A

J o i s t Spacing (mm)

Uniform Load (kPa)

Mid-Span Stress (MPa)

Mid-Span De f l e c t i o n

(mm)

300 9.60 27.3 102.3

400 7.20 26.5 98.5

500 5.76 25.7 95.0

600 4.80 25.1 92.0

700 4.11 24.6 89.7

800 3.60 24.3 88.2

900 3.20 24.1 86.9

1,000 2.88 24.0 86.0

Unsheathed Joist 2.88 N/mm 30.9 124.2

Input properties for FAP analysis listed in Appendix H. 12.5 mm plywood with no gaps. Ratio of E to G set at 17.

Uniform load and joist spacing combination results in the same total load applied to a single joist.

Table 3

J o i s t Spacing (mm)

Uniform Load (kPa)

Mid-Span Stress (MPa)

Mid-Span D e f l e c t i o n

(mm)

300 9.60 27.5 103.9

400 7.20 26.8 100.3

500 5.76 26.1 96.7

600 4.80 25.4 93.7

700 4.11 24.9 91.4

800 3.60 24.6 89.8

900 3.20 24.4 88.5

1,000 2.88 24.2 87.5

Unsheathed Joist 2.88 N/mm 30.9 124.2

' Input propeities for FAP analysis listed in Appendix II. 12.5 mm plywood with gaps spaced 1200 mm along the span.

Ratio of E to G set at 17.

^ Uniform load and joist spacing combination results in the same total load applied to a single joist.

For the FAP/TBEAM r e s u l t s given i n Table 4, TBEAM was used to c a l c u l a t e equivalent j o i s t properties f o r use i n FAP, according to Method A. Each truss tested i n the roof system was analyzed and the average E:G r a t i o was cal c u l a t e d . Equivalent j o i s t properties were also c a l c u l a t e d f o r the same trusses following Method B. The TBEAM analysis was done on trusses without sheathing attached t o the top chord. Table 5 compares the displacements c a l c u l a t e d by FAP when equivalent j o i s t p r o p e r t i e s f o r trusses are cal c u l a t e d according to Method A and Method B. While Method A causes FAP to predict higher d e f l e c t i o n s than when Method B i s used, the load d i s t r i b u t i o n across the eight trusses i s v i r t u a l l y i d e n t i c a l . Note that GNB9-P3 i s the s t i f f e s t t r u s s i n the system and thus c a r r i e d the lar g e s t proportion of the t o t a l load applied to the system.

Table 4

Truss TBEAM FRAME NSAT FAP Test Test Number TBEAM I3a] [3b]

(mm) (mm) (mm) (mm) (mm) (mm)

GN5-40 47.3 45.9 45.2 44.8 41.7

GN6-40 47.2 45.9 46.2 48.3 44.1

GN7-40 47.4 46.0 46.3 52.0 50.6

GNB8-P1 17.3 16.8 17.0 15.6 18.6 18.6

GNB6-P2 38.9 38.0 38.8 34.4 33.4 33.4

GNB9-P3 29.9 28.6 30.2 26.0 32.8 29.8

GNB7-P4 40.0 39.0 40.5 35.2 42.9 36.5

GNB1-P5 32.2 31.0 33.4 28.3 36.9 31.5

GNB4-P6 35.2 34.1 36.1 30.9 41.2 33.3

GNB2-P7 33.8 32.7 34.0 29.8 38.2 32.9

GNB3-P8 33.8 32.7 34.1 29.6 35.3 30.6

GNB5-P9 17.8 17.2 17.6 16.2 21.0 20.3

' Outer trusses GNB5-P9 and GNB8-P1 are only loaded to half design load and only have half the effective flange width.

^ Total applied load for each truss GN5-40 to GN7-40 is 24.9 kN. Total applied load for each truss

GNBl-28 to GNB9-28 is 11.7 kN.

^ Deflection adjusted (b) and unadjusted (a) for compression splice buckling.

As shown i n Table 4, TBEAM, FRAME and NSAT a l l gave comparable estimates of the mid-span d e f l e c t i o n . FRAME does not include connector s l i p and therefore would be expected to underestimate t r u s s d e f l e c t i o n s . Because TBEAM uses the secant modulus (defined by a l i n e i n t e r c e p t i n g the connector l o a d - s l i p curve at the design load l e v e l ) , t h i s model w i l l tend to underestimate the connector s t i f f n e s s at load l e v e l s below the design load l e v e l . This assumes that the truss designer w i l l optimize the s i z e of a l l connector areas i n a truss so that a l l connections are equally stressed when the f u l l design load i s applied to the t r u s s .

tJa.

Comparison of L a t e r a l Load D i s t r i b u t i o n Using FAP with Method A and B Equivalent J o i s t Properties when a

Uniform Design Load Is Applied to the System

Method A Method B

Defle c t i o n (mm) [1]

% T o t a l Applied Load [2]

D e f l e c t i o n (mm) [3]

% T o t a l Applied Load

[2]

GNB8-P1 16.4 6.6 16.1 6.7

GNB6-P2 29.7 10.8 27.9 10.7

GNB9-P3 30.4 14.6 29.0 14.5

GNB7-P4 31.3 11.1 29.6 11.2

GNB1-P5 30.1 13.3 28.8 13.3

GNB4-P6 30.4 12.3 29.0 12.3

GNB2-P7 30.8 12.9 29.3 13.0

GNB3-P8 28.5 12.0 27.0 11.9

GNB5-P9 16.2 6.3 15.7 6.4

SUM = 99.9 100

Mid-span deflection includes shear deflections.

PercenUge of total load applied to the system that will be carried by each truss. This is calculated from the ratio of the joist

stress to the sum of the stress across all eight joists.

Mid-span deflection does not include shear deflection.

Except f o r truss GNB6-P2, the NSAT/FAP d e f l e c t i o n r e s u l t s were smaller than those observed during the roof system t e s t . The s t i f f e r r e s u l t s may be due t o the method used t o obtain equivalent j o i s t p r o p e r t i e s f o r trusses, p a r t i c u l a r l y when c a l c u l a t i n g the a x i a l s t i f f n e s s .

Although FRAME, TBEAM and NSAT provide d e f l e c t i o n data with s i m i l a r accuracy, there are s t i l l features of these models that need to be evaluated. What would then d i s t i n g u i s h the models would be t h e i r a b i l i t y

to determine member forces. Member force information i s not presented here. However, because FRAME i s only capable of modelling the j o i n t as a pin, and w i l l obviously underestimate any member moments at the connection.

The a v a i l a b i l i t y of accurate truss d e f l e c t i o n s makes i t p o s s i b l e to use FAP to estimate the l a t e r a l load sharing i n a p a r a l l e l chord t r u s s system. This i s necessary f o r studies on developing load-sharing factors f o r wood design codes.

5.0 CONCLUSIONS

Displacement r e s u l t s demonstrate that TBEAM i s able to model the performance of p a r a l l e l chord trusses with accuracy comparable to NSAT. Comparisons s t i l l need t o be made between member forces as predicted by the models. This a b i l i t y would have a more s i g n i f i c a n t impact on system design as s i n g l e member design information becomes more p r e c i s e and designers are required to obtain more accurate assessments of members i n a structure.

The FAP model may be used to determine the degree of l a t e r a l load sharing i n a p a r a l l e l chord truss system. I f a d d i t i o n a l information on the a x i a l s t i f f n e s s of the t r u s s can be obtained, then i t can a l s o be used t o determine the degree of composite act i o n . S i m i l a r l y , studies on the e f f e c t i v e flange width can be conducted.

6.0 REFERENCES

Foschi, R.O. 1977. Analysis of wood diaphragms and trusses. Part I I : Truss-plate connections. Can. J . Civ. Eng. 4(3):353-362.

Foschi, R.O. 1982. S t r u c t u r a l analysis of wood f l o o r systems. J . of the S t r u c t u r a l Div., ASCE, Vol. 108, No. ST7, 1557-1574.

Foschi, R.O., B.R. Folz, and F.Z. Yao. 1989. R e l i a b i l i t y - b a s e d design of wood structures. Structures Research Series. Report No. 34, Civ. Eng. Dept., Uni v e r s i t y of B r i t i s h Columbia, Vancouver, B.C. 282 p.

Karacabeyli, E., E. Varoglu, C. Lum and L. Olson. 1990. S t r u c t u r a l Performance of Punched Metal Plated Glulam Trusses. Proc. 1990 International Timber Engineering Conf., Tokyo, Japan. FPRS. V o l . 3. 693-700.

Lum, C. 1987. Testing and analysis of p a r a l l e l chord trusses. Report to the Canadian Forestry Service. Forintek Canada Corp., Vancouver, B.C. 24 p. with appendices.

Lum, C. and E. Varoglu. 1988. Testing and a n a l y s i s of p a r a l l e l chord trusses. Proc. 1988 International Conf. on Timber Engineering, Seat t l e , Washington, U.S.A. FPRS. Vol. 1, 460-466.

Lum, C. 1989. Testing and analysis of p a r a l l e l chord trusses and f l a t r o o f / f l o o r systems. Report to Forestry Canada. Forintek Canada Corp., Vancouver, B.C. 43 p.

APPENDIX I

CALCXniATING EQUIVALENT JOIST PROPERTIES FOR A PARALLEL CHORD TRUSS

C a l c u l a t i n g Equivalent J o i s t Properties f o r a P a r a l l e l Chord Truss

Method A - Ca l c u l a t i n g Apparent E and G

A shear-free modulus of e l a s t i c i t y for an equivalent j o i s t can be obtained by applying a constant end moment to the t r u s s . Using the mid-span d e f l e c t i o n c a l culated by the truss analysis program and equation [1], an apparent E for the equivalent j o i s t can be ca l c u l a t e d . Because l a t e r a l loads on a truss also causes the truss to d e f l e c t i n shear, an apparent G for the j o i s t should also be determined. The e a s i e s t method i s to load the t r u s s under a centre-point. Given the apparent E c a l c u l a t e d from [1] and the mid-span d e f l e c t i o n under a known centre-point load, the apparent G can then be calculated using equation [2].

ML̂ E = [1]

8d„I

E = modulus of e l a s t i c i t y of the equivalent j o i s t M = constant bending moment applied to the trus s L = span or distance between supports ( j o i s t or truss) d„ = mid-span d e f l e c t i o n of the truss due to end moment M I = moment of i n e r t i a of the equivalent j o i s t

PL r G =

4A, L dp - PL^ / 48EI J [2]

where

G = shear modulus of the equivalent j o i s t P = concentrated load applied at the mid-span of the tr u s s Av = shear area of the equivalent j o i s t dp = mid-span d e f l e c t i o n of the truss due to a concentrated load P

Method B - Ca l c u l a t i n g Apparent E

When using method B, the truss should be analyzed using the same type of loading as when i t i s i n a system. In t h i s case, the tru s s i s subjected to a uniformly d i s t r i b u t e d load. From the truss a n a l y s i s , the c a l c u l a t e d mid-span d e f l e c t i o n can be then used with equation [3] (mid-span d e f l e c t i o n of a beam subjected to uniformly d i s t r i b u t e d loading) to ca l c u l a t e an apparent E for the equivalent j o i s t . This E, unlike the E calculated using method A, includes the e f f e c t of shear d e f l e c t i o n s . Therefore, any analysis performed with t h i s E value should be done with the shear modulus set to a high value.

BwL" E = [3]

384d^I

where

E = modulus of e l a s t i c i t y of the equivalent j o i s t w = uniformly d i s t r i b u t e d load applied to the truss L = span or distance between supports d^ = mid-span d e f l e c t i o n of the truss due to a uniform load of w I = moment of i n e r t i a of the equivalent j o i s t

C a l c u l a t i n g L a t e r a l Load D i s t r i b u t i o n

Once the equivalent j o i s t E (and G) are cal c u l a t e d f o r each tr u s s , the equivalent j o i s t properties can be used i n FAP to determine the l a t e r a l load d i s t r i b u t i o n . That i s , what proportion of the t o t a l load applied to the system i s c a r r i e d by each tr u s s . The bending stresses c a l c u l a t e d by FAP does not indic a t e the actual stress l e v e l i n a t r u s s . But provided a l l the trusses i n the system are of the same configuration and equally spaced, the FAP stress can be used to determine how the load i s d i s t r i b u t e d among the trusses i n the system. The basic assumption i s that the s t r e s s c a l c u l a t e d by FAP i s d i r e c t l y proportional to the load c a r r i e d by the t r u s s .

If the FAP stresses f o r a p a r a l l e l chord f l o o r system subjected to a uniform load are known, then we can assume that the load c a r r i e d by each truss can be ca l c u l a t e d according to equation [4].

Wi = — — W [4]

where

Wj = uniform load to be applied to truss i S; = bending stress f o r j o i s t i as determined by FAP W = uniform load applied to the surface of the p a r a l l e l chord truss system S = summation over a l l the trusses i n the system (j = 1, n)

The value of W; can then be used i n a si n g l e truss a n a l y s i s to determine the member stresses. This approach only estimates the l a t e r a l load d i s t r i b u t i o n ; i t does not determine the e f f e c t of composite a c t i o n between the t r u s s and the sheathing on the truss member forces.

PROPERTIES OF THE FLOOR SYSTEM USED IN THE EFFECTIVE WIDTH STUDY

J o i s t properties Span Thickness Depth E

8,400 mm 38.1 mm 360 mm 10.3 MPa

Plywood properties Thickness Dx

Dx

Dxy

Ky

12.5 mm 52,500 N-mm' 3,152 N-mm' 64,800 N-mm"' 371,000 N-mm' 373,000 N-mm 2.46(10*) N-mm 203,000 N-mm 67,800 N-mm

N a i l properties K = 1.0 kN/mm per n a i l