Non-Linear modeling of the heel joint of metal plate connected roof trusses

Traditional truss design and analysis assumes pinned joints at the connections. Other design provisions recommend that the trusses be designed and analyzed as frame structures, with careful consideration of the stress, timber behavior, and joint response. A large body of knowledge has been compiled detailing truss behavior as it relates to member properties and responses. However, the modeling of the actual metal plate connections is still the least developed. The semi-rigid behavior of the joints must be accounted for to accurately model the behavior of the joints and the truss. This paper details a procedure used to develop a semi-rigid non-linear heel joint model using the software package SAP 2000. The results of the modeling are very encouraging. A good agreement exists between experimental data gathered by Guinther (1998) and the heel joint model developed. INTRODUCTION The basis for the design of metal plate connected wooden trusses in the United States is governed by two trade associations. The associations are the Truss Plate Institute (TPI) and the Wood Truss Council of America (WCTA). TPI represents the manufacturers of the metal plate connectors. TPI is responsible for developing and publishing the design and testing methodology for metal plate connected trusses. Both of these associations are recognized by the building code agencies, and as a result most building codes reference the design procedures set forth by TPI and WCTA. Truss design by the TPI simplified method relies on empirical data to produce the most economical wood truss. The simplified method resembles traditional truss design that a majority of computer software programs utilize. Under the simplified method, all truss loads, both applied and reaction, must occur at a joint and all joints are pinned. With loads occurring solely at the joints, the truss members only experience axial forces. To account for bending in truss members an additional series of equations was added to approximate these stresses. In traditional truss design the bending stresses are considered to be a secondary stress in most applications. Traditional truss design and analysis assumes pinned joints at the connections as well. Other design provisions recommend that the trusses be designed and analyzed as frame structures, with careful consideration of the bending stress, timber behavior, and joint response (Aasheim 1991). The analysis of the truss as a frame member forces all joint to be fixed and produces bending stress in the truss members. A large body of knowledge has been compiled detailing truss behavior as it relates to member properties and responses. However, the modeling of the actual metal plate connection is still the least developed. A technique for modeling the semi-rigid non-linear behavior of the heel joint will be discussed in this paper. The semi-rigid behavior of the joints must be accounted for to accurately model the behavior of the joints and the truss. PREVIOUS RESEARCH Most of the current research details the attempt to produce an empirical formula for predicting wood truss behavior and the effects of the variable wood properties. Only two facilities, Forest Products Laboratories and Bucknell University, have conducted a series of full-scale tests on heel joints and trusses. The main difficulty in researching wood trusses arises from the large variability in the properties affecting wood behavior. Previous researchers note the difficulty in modeling and predicting their behavior due to the large amount of variables involved. A list of some of the variables that affect the joint behavior are listed below: 1 Technical Staff, D’Huy Engineering Inc., Bethlehem, PA 2 Department Chairman, Dep. of Civil and Environmental Engineering, Bucknell University, Lewisbirg, PA Size and number of teeth Plate thickness and orientation Grain orientation and direction of loading Lumber species Specific gravity (SPG) of the lumber Moisture content (MC) of the lumber The joint pressing force used to seat the plate The time between fabrication and testing Several researchers have been able to correlate general trends among the lumber properties. McCarthy and Wolf (1987) noted that the specific gravity (SPG), moisture content (MC) and the modulus of elasticity parallel to the grain (MOE) have significant effects on the parameters needed to define truss joint behavior. King and Wheat (1987) concur with McCarthy’s conclusion that SPG is highly correlated to lumber strength and stiffness, especially within lumber species. Poutanen (1988b) notes however, that when the influence of the plate eccentricity is considered, changing the MOE or SPG has little if any effect on the eccentric movement of the plate. Researchers agree that contact forces occurring at the intersection of members during loading alters the response of the joints. Since the fabrication of the truss joints is not set to standard tolerances, gaps occur between the two lumber members joined by the metal plate connector. Under load the gap tends to close. When the gap closes, contact occurs between the connected members, creating a new path to transfer load. The new load path alters the joint characteristics and the response changes. In general, the presence of the contact transfer point or points tends to increase the strength and stiffness of the joint. It is also generally agreed upon that the area of plate contact with the wood affects the behavior of the joint. According to Maragechi, K. and Itani R.Y. (1984), the rotational stiffness of the joints is directly proportional to the area of contact between the plate and the connected wood members. Therefore, it can be inferred that in order to create a stiffer joint with regards to rotation, a larger metal plate should be used. King and Wheat (1988) reported that the bending moments in the members are sensitive to the connection stiffness. Therefore, larger metal plate connectors increase the joint stiffness producing larger member bending moments. King and Wheat also reported that axial forces in truss members are relatively independent of connection stiffness, but are greatly influenced by overall truss geometry. The basic empirical equation used to predict load-displacement response was developed by R.O. Foschi (1979). The equation, shown below, relates joint performance to plate orientation with respect to grain direction of the lumber and the orientation of the applied load.