The current procedure for designing many types of light frame structures is based on the design of individual components that make up the system, without much consideration of the components influence on each other, i.e. load redistribution. In most cases, the forces in these components are obtained by the analysis of an individual planar system, e.g. a truss or a frame, assumed to carry loads from its tributary area. This tributary area is defined as the area with a width equal to the spacing of the planar systems. In addition, the sizing of the components (for timber structures and steel structure under allowable stress design) assumes that the acting forces do not exceed code specified values.

The above procedure ignores the following:

a)There is significant load redistribution taking place across planar systems (e.g trusses), thus a challenge to the tributary area approach.

b)The in-situ performance of a component may be very different from the laboratory based code specified values, i.e. there is need to include strength variability and load sharing.

In recent times, however, design specifications are slowly and indirectly recognizing the system influence on component performance. For example the National Design Specification (NDS) for wood construction (NFPA, 1991) allows an increase of the allowable bending stresses by a repetitive use factor Cr (clause 4.3.4 of NDS (NFPA, 1991)) of 1.15 for bending members whose pacing does not exceed 24 inches on center. Both the ACI Specifications and the AISC Specifications allow some moment redistribution under certain circumstances. All this is an indirect attempt to acknowledge structural system effect. In this paper we will concentrate on system effect in light-frame constructions, mainly metal-plated truss roof systems.

Background

A number of studies on system performance have been reported in the literature. For wood structural systems these have been mainly in the area of floors and walls with relatively few studies on roof systems . Examples of such studies include those reported by Foschi (1985), Gromala and Wheat (1986), Folz and Foschi (1986), just to mentioned a few. In a study of floor systems, Folz and Foschi (1986) proposed the use of a system factor to be applied in the resistance side of an LRFD format equation (ANSI, 1982) during the design of single members. The argument for this approach was: a) there is a reduced chance of having weaker member being placed at the most stressed position in the system, and b) there is load sharing which is influenced by the action of the sheathing and the semi-rigid nature of the connections. Recently, Rosowsky and Ellingwood (1991) conducted some studies on the reliability of floor systems in which the influence of decking thickness as well as the mechanisms of load distribution and redistribution after initial member failure were examined. In this study, system factors were found to be insensitive to decking thickness, to assumed load distribution and redistribution following member failure, and to system size.

In other related studies, Cohen (1991) points out the fact that the influence of cladding on the response of structures has, in general , been ignored. She went further to quote studies in which large differences in lateral displacements, natural frequency, member force distribution, and forces in panel-to-frame connections between clad and unclad frames were found. These lead to the conclusion that the cladding has significant contribution to the structural performance of the system which for the time being is largely ignored.

As far as roof systems performance is concerned, there have been a number of studies in that area. These include studies by Mayo (1978), Price (1982), Wolfe et al (1986), Cramer and Wolfe (1989), Lafave (1990), Mtenga (1991) just to mention a few. In the studies by Cramer and Wolfe (1989), the roof system was modeled as pin jointed trusses with the sheathing accounted for in the top-chord T-beam action and as two distributor beams, one each at the middle of the slope of a pitched truss roof system. These distributor beams were treated as continuos beams spanning across the trusses. One of the major observations of this study was that there was considerable distribution of loads away from a single loaded truss in the system, with the loaded truss carrying around 50 percent of the load directly applied to it. The distribution effects were observed to be contained within three of four trusses on each side of the loaded truss. These model based observations were very close to experimental observation for similar system configuration as were reported by Wolfe et al (1986). In a related study, Mayo (1978) reported test results showing significant load sharing in a roof system made up of fink trusses braced together by purlins. It was these roof performance observations that motivated the author to be involved in system performance and reliability, as reported by Mtenga (1991). Briefly, the model developed for the purpose of this study will be discussed followed by observations from this study which was confined to metal-plated wood trusses roof systems.

The System Modeling and Strength Simulation

The strength of both the individual trusses and the roof system were determined using a computer program specifically developed for this purpose. In this program code named NARSYS, an acronym for Non-linear Analysis of Roof SYStems, the structure is modeled with two main types of elements, namely the wood elements and the connector elements. The connector elements are assumed to behave in a nonlinear manner, in which the load-deformation follows an exponential function relationship, similar to that developed by Foschi (1977). However, unlike Foschi's model, the connector was modeled as two translational springs and one rotational spring acting at the center of gravity of any particular wood-plate contact area. With this kind of modeling we were able to simplify the connector model considerably, which was necessary for the modeling of the entire system. In addition this connector modeling allowed the inclusion of connection eccentricities, which has been found to be a factor in the performance of metal plated trusses (Poutanen 1986, 1988). In analyzing the system, the top-chord elements were modeled as two layer components consisting of the 2 by 4 wood members and the sheathing. This modeling was based on a study by Warner and Wheat (1986). Furthermore the trusses were connected together by a series of beams, running across the trusses, each corresponding to the width of plywood sheathing panel. The details of the truss and system modeling used in this study are well documented by Mtenga (1991) and Shrestha et al (199_).

In order to verify the accuracy of the model, an identical truss was analyzed by several other models and for comparison purposes, the results are presented in Table 1. Presented in this table are the axial forces, bending moments and combined stress index (CSI) as defined by the National Design Specification (NDS) (NFPA, 1986) for the design of members with combined loading, i.e. this factor should not exceed 1.0. The location numbers in a fink truss are as shown in Fig. 1. Model 1 is based on Truss Plate Institute (TPI) (1985) Design Specification for Metal Plate Connected Wood Trusses. Model 2 consists of modeling the truss as a rigid frame with slope continuity enforced at all joints. Model 3 consists of rigid frame model with the rigidity in bending reduced to 75 percent of complete rigidity at the peak of the truss only. Model 4 and 5 is a model developed by Foschi (1977) for the analysis of metal plated wood trusses, and is a popular model in industry especially in research circles. The difference between 4 and 5 is the way truss is supported. In model 4 the supported node is on the top-chord, while model 5 the supported node is on the bottom chord. Model 6 is the model developed for this study. Model 1,2 and 3 do not take into consideration eccentricities, which may be one of the possible explanations for their different results from those of models 5 and 6. Poutanen (1986,1988) has found eccentricities to have significant effect on truss performance. From these results we can make the

Fig.1 Outline of a 28 ft. 6/12 Fink Truss Showing Locations Monitored for the Values of Table 1

Table 1. Forces and Moments Comparison for Different Modeling Assumptions

(originally presented by Cramer, Peyrot and Wolfe (1991)).

Location          1        2        3        4        5       6     

TPI - Model 1                                                       

Moment,           0        0      -3742      0        0       0     
in.-lb                                                              

Axial Force,    -1423     1216    -1210     425     -1042    425    
lb                                                                  

CSI              0.28     0.28     0.98     0.10    0.20     0.10   

Rigid Frame -  Model 2                                              

Moment,          1059    -1059    -3021      28     -2605     22    
in.-lb                                                              

Axial Force,    -1415     1200    -1195     375     -1027    375    
lb                                                                  

CSI              0.49     0.49     0.83     0.09    0.72     0.09   

Semi-rigid -Model 3                                                 

Moment,          1057    -1057    -3039     -21     -1772    -18    
in.-lb                                                              

Axial Force,    -1415     1200    -1195     375     -1027    375    
lb                                                                  

CSI              0.49     0.49     0.83     0.09    0.55     0.09   

SAT Top Chord -Model 4                                              

Moment,          1139    -1062    -3040     -167    -1756    -61    
in.-lb                                                              

Axial Force,    -1317     1187    -1084     374     -1084    374    
lb                                                                  

CSI              0.48     0.48     0.81     0.12    0.56     0.10   

SAT Bottom Chord -Model 5                                           

Moment,          3428     537     -2324     -270    -1940    -60    
in.-lb                                                              

Axial Force,    -1208     1075     -990     315     -990     315    
lb                                                                  

CSI              0.91     0.35     0.65     0.13    0.58     0.08   

NARSYS -Model 6                                                     

Moment,          3079     447     -2409     -218    -1668    -81    
in.-lb                                                              

Axial Force,    -1293     1079    -1074     319     -992     319    
lb                                                                  

CSI              0.86     0.34     0.69     0.12    0.52     0.09   

observations can that, the NARSYS model produces forces consistent with the results of industry tested SAT model, and thus is a good predictor of truss and roof system strengths as intended in this study.

For strength simulation purposes, the properties of the components that were used in program NARSYS, to determine the strengths, were randomly generated. In all cases, the parameters were assumed to have a lognormal distribution. With this assumption we were able to avoid the possibility of generating negative values. A computer code separate from NARSYS was developed for this purpose. The data so generated was used repeatedly for various system configuration parameters i.e. three different slopes, three different spans, two different wood-metal plate contact area and three plywood sheathing sizes. This allowed the investigation of the influence of these system configurations given the same material properties. The details of the simulation procedure and simulation results are presented by Mtenga (1991) and Mtenga et al (199_). Presented in Fig.2 are the configurations of the trusses whose strengths were simulated.

Fig. 2 Configuration of Simulated Systems

Summary of Results

Presented in Table 2 are examples of results obtained in this study, i.e. results for 28 ft. span system with standard ("small") plate sizes. In Table 2, Rdt stands for strength of "designers' truss" which is a truss with all its components having properties equal to their 5 percent exclusion value., Rms is the average system strength value, and R5w is the 5-percent exclusion value for the distribution of the strength of weakest truss in a system.

Table 2. Strength Ratios for a 28 ft. Span System with Standard Plate Sizes

                                                                               

                  in.    in.  1 in.    in.    in.  1 in.    in.    in.  1 in.  
System Slope                                                                   

                1.39   1.41   1.45   1.19   1.18   1.25   1.59   1.57   1.67   

                1.42   1.44   1.47   1.25   1.29   1.33   1.80   1.80   1.91   

                1.43   1.46   1.52   1.21   1.28   1.36   1.78   1.89   2.00   

Presented in Table 3 are the coefficients of variation of simulated strengths for a 28 ft. span configuration with standard plate size. It should be pointed out that the coefficient of variation of the properties of the components that were used to simulate these results were ranging from 25 percent, for the connector parameters and compression strength of the wood members, to 52 percent for the tension strength of the wood members. These component parameter variations were in accordance to component studies such as those by Gerhards (1983).

Table 3 . Coefficient of Variation (in %) of the Strength for a 28 ft. Span System with Standard Plate Sizes

             Single       Weakest                   System                    

             Truss        in System      in. ply      in. ply    1 in.  ply   
System                                                                        
Slope                                                                         

                               16.6         7.2            7.5         6.7    
             14.8                                                             

                               18.1         5.7             5.3        5.0    
             13.8                                                             

                    13.3       17.8         8.3             7.6         6.6   

Observations

>From these results and the detailed results as presented in Mtenga(1991), the following observations can be made:

1. There is considerable strength variability reduction, as measured by the coefficient of variability, as one moves from the individual components to the individual truss to the system. Thus strength reduction factors derived according to ANSI recommendations for LRFD format (ANSI, 1982) at component level may lead to some conservative results.

2. There is a significant difference between our "designers' truss", Rdt, and the 5 percent exclusion strength value, R5s, of the system. Thus we can afford to overstress our designer truss by a factor of , without exceeding any set margin of safety.

3. Since the strength system is always greater than the weakest truss in that particular system, as measure by the ratio in Table 2, we can say that the roof system is not a weak link model (series model).

4. Examination of the failure patterns revealed some critical areas, which when detailed properly or reinforced, lead to significant improvement on the system performance.

Conclusions and Recommendations

1.We need to include system effect in the design of structural components. Work is under way to develop a more rational procedures of including this system effect in the design of wood structural systems (Folz and Foschi (1989), Mtenga et al (199_) etc)

2. Proper and careful detailing of critical areas in the system is a very critical area. Thus, we should emphasize this area from the early stages in our engineering training.

3. With the coming of powerful computing abilities, maybe it is time to get away from the log table/slide rule based analysis and design procedures, and thus look more at the entire system performance in our daily engineering practice.

4. Further system performance studies are necessary , as way of assessing the global reliability of the entire structure, and not just that of a component as we are currently doing.

References

ANSI (American National Standard Institute) 1982. American National Standard minimum design loads for buildings and other structures, ANSI A58 1 -1982".

ASCE Task Committee on LRFD for Engineered Wood Construction, 1988. "Load resistance factor design for engineered wood construction : A Pre-standard Report". ASCE 345 E. 47 th St., NY 10017.

Cohen J. M. 1991. "Cladding Design: Whose Responsibility?". ASCE Journal of Performance of Constructed Facilities, Vol. 5 No. 3 , Aug. 1991

Cramer S. M. and Wolfe R. W. 1989. "Load distribution model for light-frame wood roof assemblies". ASCE Journal of Structural Engineering, Vol.115, No. 10.

Folz B. and Foschi R. O. 1089. "Reliability_based design of wood structural systems". ASCE Journal of Structural Engineering Vol. 115, No. 7.

Foschi R. O. 1977. "Analysis of wood diaphragms and trusses. Part II: Truss-plate connections". Canadian Journal of Civil Engineers. Vol 4.

Gerhards C. C. 1983. "Characterization of physical and mechanical properties of 2 by 4 truss lumber". Research paper FPL-431, USDA, Forest Products Laboratory, Madison WI 53705.

Gromala D.S and Wheat D.L 1986. " Structural Analysis of Light-Frame subassemblies". Proceedings of a ASCE sponsored Workshop on Wood Research, held in Milwaukee Wisconsin, Oct. 1983.

Lafave K. D. 1990. "Experimental and analytical study of load sharing in wood truss roof systems". M.S. thesis, Civil Engr. Dept., Washington State University, Pullman, WA.

Mayo A. P. 1978. "Trussed rafter roofs: Load distribution and lateral stability". Building Research Establishment (BRE), Inf. paper No. IS 24/78, Prince Risborough Laboratory, Aylesbury, Buckinghamshire, UK.

Mtenga, P. V. 1991. "Reliability performance of light-Frame wood roof Systems". a Ph.D. dissertation submitted at the University of Wisconsin-Madison, May 1991.

Mtenga, P. V. , Cramer S.M. ,Peyrot A.H. and R.W. Wolfe 199_. "System Factors for Light-Frame Wood Roof Structures". A tentative tittle of a paper under preparation possibly for ASCE Structural Journal.

NFPA (National Forest Products Association) 1986. National Design Specification (NDS) for wood construction, Washington D.C.

Pierce C. B. 1982. "Load sharing between rafters in a traditional roof structure". Building Res. Establishment (BRE), Inf. paper No. IP 5/82, Prince Risborough Laboratory, Aylesbury, Buckinghamshire, UK.

Poutanen T. T. 1986. "Joint eccentricity in trussed rafters". CIB-W18/19-14-2, Florence, Italy

Poutanen T. T. 1988. "Eccentricity in a nail plate joint". Proceedings of the 1988 International Conference on Timber Engineering, held in Seattle, Washington, pp 266-272.

Rosowsky D. and Ellingwood B. 1991. "System reliability and load sharing effects in light-frame wood construction". ASCE Journal of Structural Engineering, Vol. 117, No.4.

Shrestha D., Cramer S.M. and Mtenga P.V. 199_. "Computation of forces in metal-plate connected wood trusses". Submitted to ASCE Structural Journal.

Warner J. H. and Wheat D.L. 1986. "Analysis of structures containing layered beam-columns with interlayer slip". Technical report, Civil Engr. Dept. Univ. of Texas at Austin.

Zahn J. J. 1986. "Design of wood members under combined load". ASCE Journal of Structural Engineering, Vol. 112, No. 9.

Acknowledgements

The author gratefully acknowledge supporting contributions to this work by Prof. A.H. Peyrot, Prof. S.M.Cramer of the University of Wisconsin-Madison and R.W.Wolfe of the Forest Products Laboratory. In addition, will like to acknowledge positive critique from many fellow graduate students at the Univ. of Wisconsin-Madison during 1987/91 period.

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