Span tables are a useful tool for many applications, but they do not accurately account for all the complexities of fiber-reinforced polymer (FRP) loading.

In this article, we will discuss the six items that need consideration when evaluating structural loading and are not often included in span tables. For these reasons, it is best to use finite element analysis (FEA) on a project-by-project basis to properly analyze structural loading in FRP Z sub-framing applications.

1. Eccentric loading

   • Eccentric loading occurs when the load does not apply directly in the same plane where the Z sub-framing attaches to the substrate. This type of loading creates a bending moment in the member that the analysis must account for.

2. Cantilevered loading

   • Cantilevered loading happens when the load applies away from where the Z sub-framing attaches to the substrate, creating a moment and shear force in the member.

3. Combined eccentric and cantilevered loading

   • Combined eccentric and cantilevered loading occurs when a load applies away from the attachment to the substrate of a member that experiences eccentric loading, creating a moment and shear force in the member.

4. Different reactions of positive and negative loading on asymmetrical FRP shapes

   • Asymmetrical FRP shapes react differently to positive (into the member) and negative (away from the member) loading. For example, the positive loading will cause the shape to deflect in the opposite direction of the negative loading.

5. Force concentrations due to point loading

   • Force concentrations due to point loading can cause a significant increase in stress on the member, as opposed to using uniform or distributed loading.

6. Fastener stress concentrations

   • Fastener stress concentrations are a significant factor to consider when analyzing the structural loading of FRP Z-girts. These concentrations can significantly increase stress on the member, which the analysis must account for.

Z-Shaped Sub-Framing Girts

However, the structural analysis of Z-shaped girts can be challenging. The difficulty arises from the Z-shape’s double asymmetry and the eccentricity of the applied loads. The load path goes through the flanges of the Z-shapes, specifically at the fastener locations. The asymmetry of the section and the eccentricity of the applied loads create additional torsional and warping stresses and deformations in the Z-shaped girts.

Consequently, the analysis of Z-shaped girts is significantly complex. To properly account for the complexities of structural loading in FRP Z-girt sub-framing applications, it is best to use FEA on a project-by-project basis. This ensures that the member is designed correctly and can safely support the applied loads.

5 Best Practices for Structural Loading Analysis of Z-Shaped Sub-Framing:

Below are best practices for structural stress analysis of Z-shaped sub-framing for cladding support and exterior wall applications:

1. Load approximation using uniform loading will underestimate both stresses and deflections of the girts. Using accurate modeling of loads as point loads at the fastener locations is the best practice to provide accurate stress and deflection results.
2. Consider both directions of loading for the stress analysis of the Z-shaped girts. The direction of the loading, whether toward or away from the wall (positive or negative), makes a significant difference in the results due to the asymmetry of the section.
3. A 3D FEA modeling and analysis computer software capable of using the exact geometry of the sub-framing girt and accurately modeling the loading must be used. Any calculations that do not use accurate mechanics formulas specific to the Z-sections and do not explicitly consider the eccentricity of the loading will give inaccurate results and underestimate stresses and deformations.
4. Consider both deflection and stress analysis.  If a girt has a safety factor of 4 in stress in all directions but fails in deflection—or vice versa—consider it an overall failure and unsuitable for the design.
5. Model the end condition of individual girts correctly. Account for all design conditions in the structural analysis, particularly the effect cantilevers can have on torsional loading.

Figure 1: Left, a butt joint cantilever is shown at the end of an FRP Z-shaped subframe. In the middle, the deflection torsional effects appear after applying wind and dead loads. On the right, the stress torsional effects appear after applying wind and dead loads.

Guidelines for Accurate Finite Element Analysis (FEA):

Although you can use both steel and FRP structurally within the building envelope, analyze them differently when it comes to finite element analysis. Consider complexities such as orthotropic analysis, point loading, stress concentrations, and cantilevers when performing a structural analysis on FRP.

The following general guidelines are necessary to accurately model structural components or systems:

1. Orthotropic Analysis

   • Because FRP properties vary greatly in different directions, perform an orthotropic analysis. This type of analysis is more complex than a usual isotropic analysis and considers the different directional properties of the material.

Figure 2: Property Directions for Orthotropic Materials

2. Point Loading

   • Cladding options like stucco may result in uniform loading, but most claddings used with FRP sub-structures must utilize point loading to get the most accurate structural results. Place point loads at the worst-case location, which is most likely midway between the attachments of the FRP sub-structure to the substrate. This will result in worst-case stress concentrations, providing a more realistic model for what is occurring on the actual wall.

Figure 3: FEA with Point Loading

3. Non-Bonded Contacts

   • It is important to use non-bonded contact sets when modeling FRP components. This will prevent the model from being too rigid and will more accurately reflect the behavior of the material.

4. Mesh

   • When creating a mesh for an FRP model, it is important to use a curvature-based mesh. This will result in the largest number of nodes and elements, which will provide more accurate results. By following these guidelines, you can be sure that your structural analysis of FRP components is accurate and reflective of the material’s behavior.

5. Cantilevers

   • When modeling a cantilever, it is important to use a worst-case scenario. Use the maximum cantilever between spans. For example, if the span is 16″, use a cantilever of 15″. This approach provides a realistic design for the FRP substructure when used on the wall.

6. Fastener Placement

   • In general, space fasteners and edge distances in FRP as follows: 1) Center-to-center spacing should be at least 5 times the fastener diameter, 2) Fasteners should be no closer than 2.5 times the fastener diameter from the edge of the profile, 3) Fasteners should be no closer than 3 times the fastener diameter from the end of the profile. This will help avoid fastener stress concentrations.

By following these guidelines, you can be sure that your structural analysis of FRP components is accurate and reflective of the material’s behavior.

Final Checks

• A professional engineer should review or perform any FEA or set of calculations for the cladding assembly. Only a Professional Engineer with knowledge of FRP should sign off on the settings and results provided by the FEA. The FEA analysis must include the following items: validation of mesh size, loading model, and boundary support model.
• Provide FEA to replicate and evaluate areas of the longest FRP girt cantilever span possible between intermediate framing members/attachment.
• Install butt joints on a minimum surface width of 3″ or a double stud condition to ensure proper fastener margins to FRP.

Conclusion

When designing with FRP, it is important to consider all aspects of the material to create a safe and effective structure. This includes understanding how to properly analyze the structural loading of FRP Z-shaped sub-framing. By following best practices, like FEA, accounting for point loads, etc., and consulting with a professional engineer, you can ensure that your FRP structure will be able to withstand the specified loads for each project.

Footnotes:

• While most projects cannot use uniform loading, there are specific situations where it can be used. Best practices should be used for this decision.
• Cantilevers are less of a concern when a splice joint is used to connect adjacent Z-shapes.

*The information listed is based upon the material samples available in the marketplace and datasheets from materials available at the current time of testing. The data listed does not cover all materials from other markets or applications.

Download the full Engineering Study on Structural Loading of FRP Z-Girt Sub-Framing below.

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