The simplified method of analysis (“truss” analysis) was developed about 30 years ago when computers were slow and mostly unavailable and the industry needed a method of analysis simple enough to compute by hand. When using the pure simplified analysis, all loads are applied to the truss joints only and members are to be pin-connected at their ends (a pinned or hinged joint is a joint between structural members that allows an unlimited angle of rotation between them), which means no bending forces are transfer through the joints and all of the forces transferred are axial. It is a procedure to determine all the axial forces, tensile or compressive, for each truss member. Chord members are also subject to bending forces. The simplified method used in previous editions of ANSI/TPI 1 uses tables of factors to determine chord moments. Bending moments are checked at panel points and at mid-panel points and these two moments are used to determine the critical combined stress of the chord.
In reality, truss joints do not exhibit purely pinned behavior. With a metal plate located at each joint, the joint does have a capacity to resist rotation. And since in the simplified method moments transmitted through the joints are ignored plate sizes are based only on axial forces and generally smaller plates are required. But, the decreased cost from the smaller plate sizes may result in an increased cost of lumber needed. Also, in order for a truss with pin-connected members to be stable, it must be entirely composed of triangles.
A Matrix method of structural analysis is an example of what is called an exact method. Bending force calculations are included as part of the analysis to determine the internal forces in the truss. As part of a matrix analysis, joint rigidity is one of the design considerations. A perimeter break (where chords change slope, such as at a peak) may be considered as pinned, as rigid (a rigid or fixed joint is connection between structural members that does not permit relative motion between them), or as somewhere in between. As the joint rigidity is increased, the bending forces in the adjacent members will generally increase at the joint but decrease in the middle of the adjacent panels. This affects both member and plate design. Larger plates are sometimes required because they are designed for more bending moment, but at the same time, the member’s lumber grade adjacent to the joint will often be lower. Generally smaller size and/or lower grades of lumber are required when rigidity is added to a perimeter break. Any type of truss can be readily designed using a matrix method.
While the simplified method of analysis was the predominant method for many years, it has noteworthy limitations and does not accurately model the true behavior of the joints in a metal plate connected wood truss.
To bring design models closer to the true structural performance ANSI/TPI 1-2002 moved the Simplified Design procedure from the mandatory portion of the Standard to the non-mandatory Commentary, which is not, considered part of the code. In ANSI/TPI 1-2007, the Simplified Design procedure has been completely removed. Only structural analysis methods in which the truss members are designed to resist axial forces and bending moments, such as the matrix stiffness method, are recognized by ANSI/TPI 1-2002 and ANSI/TPI 1-2007.
When using the matrix method of structural analysis we typically assume that joints are either fully pinned or fully rigid. This type of assumption greatly simplifies the truss analysis and design process but may not accurately reflect the true deflection and distribution of internal forces. In a real metal plate connected wood truss, the actual joint behavior is complicated, as joints are not fully rigid or fully pinned. The rigidity of the joints is somewhere in between or what we call semi-rigid, which means the joint transfers some bending force due to partial rigidity. The degree of rigidity at a perimeter break may vary with applied load, panel length, lumber size and grade, and plate size. Even though, computer technology may make it is possible to model semi-rigid joints, completely accurate models are not possible due to complexity and variability in the stiffness of the real joints.