The Hidden Costs of Optimization, Part I

Optimizing truss jobs is intended to lead to a reduction in lineal feet of lumber used in a project, but that reduction in lumber may make the trusses’ ability to distribute forces through connections more critical. It’s important to understand how the computer software performs optimization. Without that knowledge, there can be unintended consequences to optimization, which can result in hidden costs on a project.

Question

How can a Truss Designer avoid system design errors such as when bearings are undersized?

Answer

The Truss Designer needs to understand the assumptions and analysis methods of the software and the loading requirements of ASCE-07: Minimum Design Loads for Buildings and Other Structures. The following example shows issues that can arise from relying too heavily on computer analysis without taking into account ASCE-07 in the context of the automated loading and applied load assumptions that computer programs use when designing and optimizing trusses.

Example: Reactions of Truss Exceed Capacity of Bearing

Girder trusses generally consume the heaviest applied loads, which are then distributed to bearing locations. These types of trusses are frequently made into two- or three-ply trusses to help withstand the member forces generated. When analyzing a girder truss, the Truss Designer needs to keep in mind the assumptions the computer program makes, in order to ensure that the truss and its bearing conditions are adequate. On a Truss Design Drawing, the required bearing width indicates the minimum bearing width required for the truss, based on the lumber used in the truss per the truss manufacturer’s inventoried species, grades and sizes of the truss lumber. The Truss Designer does not have the same control over the lumber that is used for the bearing condition (e.g., wall top plate, steel beam, etc.). There are instances where the bearing area of the truss is sufficient, given the size of the bearing, but insufficient based on the bearing capacity of the actual bearing surface that the truss will rest on in the finished building.

The minimum required bearing width is calculated by dividing the maximum reaction force at the bearing by the adjusted compression stress of the lumber. For trusses bearing on the narrow or wide face of a truss chord, the compression perpendicular to grain (Fc⊥) is used. The Technical Q&A in the April 2007 issue of SBC addressed minimum required bearing and provided the following example problem:

The end of a bottom chord bearing, three-ply roof girder truss bears on top of a 2x4 exterior wood wall in a single-family residence. The bottom chords of the girder consist of 2400f – 1.8E 2x10 Southern Pine Lumber, and the top wall plate is No 2 SPF. The maximum reaction force is 12,000 lbs. What is the minimum required bearing for this truss and the wall plate?

The example indicates that the 2x4 wall provides adequate bearing length for the truss, but it is insufficient in terms of the bearing capacity of the top plate. Since the truss design only evaluates the materials in the truss, the Truss Design Drawing for this girder would indicate that 3.5" of bearing is sufficient. However, crushing in the top plate of the wall will most likely occur, unless the wall is increased to 2x6 and a lumber species with a higher Fc⊥ is used.

The table below provides the maximum truss reaction load based on the allowable perpendicular to grain bearing capacities of selected species of lumber commonly used in wall top plates. The reaction forces are derived for both 2x4 and 2x6 wall widths, as well as with and without the Cb, and Cplate factors. The reaction values are based on Cm, Ct, and Ci = 1.0, and assumes that the truss bears on the full width of the lumber plate.

While it is the Building Designer’s responsibility to verify the capacity of the bearing surface, the Truss Designer must ensure that the truss-to-bearing surface connection can be made without crushing. For instance, while a two-ply girder can be analyzed without failure on the computer screen, the reactions at the bearings may be so great that the required bearing capacity cannot feasibly be achieved.

A common setting that Truss Designers can specify in the software is to automatically upgrade the material of the bearing to the material of the bottom chord of the truss. While this can be helpful when designing with specific grades of lumber, the setting needs to be used cautiously when designing with machine stress rated (MSR) lumber, due to its higher Fc⊥ design values. Likewise, it’s important to remember that MSR is not typically used for top plates of wall assemblies and related bearing members in actual building construction. If trusses are designed prior to knowing the bearing material, or if the bearing material is unknown, using a table similar to the one above can help Truss Designers verify that the resulting reaction is feasible. With the aid and availability of a wide variety of bearing enhancers, an engineered steel fixture designed to increase the effective width of the truss to reduce the required Fc⊥ of the top plate, higher reactions can be achieved than with the truss alone.

If any truss (girders typically are the greatest concern) is designed without verifying that the capacity of the bearing surface is feasible given the materials used, the analysis using the flowchart below needs to be completed for the truss.

While a two-ply girder may pass analysis, it may still need to become a three-ply in order to obtain the reactions needed for connections, or it may need to be designed using bearing enhancers. While a third ply adds cost to a project because an extra truss will need to be built and shipped, it is more affordable than trying to fix the issue after the fact. It is critical that the Truss Designer understand his or her scope of responsibility and how the trusses interact with the rest of the structure. This will ensure a safe structural system that resists loads as designed without unanticipated crushing.

See an upcoming issue for another optimization example that examines when loads are missing from structural fascia.