Introduction

Finite Element Analysis (FEA) has become a cornerstone of modern engineering practice. Its widespread adoption has transformed the design workflows across numerous disciplines—from automotive to aerospace and especially in structural engineering. In fact, it’s nearly impossible to imagine contemporary engineering without it. The primary reason for its popularity lies in its ability to simulate complex geometries, materials, and loadings with impressive accuracy. As structures evolve to become more intricate and performance-driven, FEA offers an indispensable means of validating their performance before construction or manufacturing.

While the structural steel industry has embraced FEA wholeheartedly and integrated it seamlessly into design standards and best practices, the adoption and effectiveness of FEA in the realm of structural concrete remain a more nuanced topic. Concrete is inherently complex: it is non-homogeneous, exhibits nonlinear behavior even at relatively low stress levels, and undergoes cracking, creep, and shrinkage over time. These characteristics make concrete a far more challenging material to model accurately using finite elements compared to steel.

Despite these challenges, there are several software packages—such as Prokon’s SUMO—that aim to bring FEA into the realm of practical structural concrete design. As someone who has worked extensively with SUMO, I’ve been intrigued by how well it simulates concrete structures and how its output compares to more traditional hand-calculation methods. This blog explores some of these simulations, their outcomes, and the questions they raise about how FEA should be used in reinforced concrete design.

Successful Applications of FEA in SUMO

In my exploration of SUMO, I’ve conducted multiple simulations involving concrete elements. In many of these, the results from the FEA closely matched those obtained from manual calculations. One notable case involved the use of plane shell elements to model a reinforced concrete beam (see Designing a Concrete Beam Using SUMO FEA Only). The comparison between the program’s steel reinforcement recommendations and those derived from conventional hand calculations yielded minimal variance. In most cases, the reinforcement areas suggested by SUMO were slightly more conservative, primarily because of its more sophisticated treatment of bending and torsional moments.

In a separate webinar earlier this year, I modeled various concrete elements including flat slabs and pad footings (see Investigating Slab Moments Calculated using FEA versus Code-Based Values – Part 01). I then compared the moment distributions generated by SUMO with those predicted by hand calculations, which were based on simplified code-based methods. The outcomes varied: in some instances, the differences were negligible, while in others, they were quite significant. These inconsistencies suggest that while certain components—such as beams and specific footing configurations—can be confidently designed using FEA, the same cannot yet be said universally, particularly for slabs.

FEA versus Moment Coefficients

The investigation that prompted this blog began with a recurring discussion I’ve had with colleagues: can raft foundations be designed effectively using FEA? Rafts are complex systems that distribute loads through slab-like action, and they are often analyzed using moment coefficient methods similar to those used for two-way spanning slabs. This led me to first take a closer look at how FEA handles two-way slabs before diving into the even more intricate domain of raft foundations.

The traditional method for two-way slab design, particularly when supports are regular and boundary conditions are well-defined, often relies on moment coefficients. These coefficients, found in standards such as SANS 10100, offer a simple and effective way to determine design moments without resorting to full numerical simulations. They’re especially useful for hand calculations, where speed and simplicity are essential.

In my test, I created a simple slab model in SUMO using a 200 mm thick, 25 MPa concrete slab with pinned linear supports along all four sides. The applied load was a uniform distributed load (UDL) of 11.6 kN/m², excluding self-weight to simplify the analysis. I used an average finite element mesh size of 100 mm, which provides a good balance between accuracy and computational efficiency. Importantly, I maintained a constant span length in the x-direction (Lx), while varying the span in the y-direction (Ly) to explore different Ly/Lx ratios, as referenced in Table 15 of SANS 10100.

Using 1-meter-wide integration strips (see Prokon Know-How: SUMO Integration Strips) in both directions, I extracted the moment results (Mx and My) from the FEA model and compared them to those calculated using the moment coefficients. These comparisons were logged in Excel and plotted for clarity. What I observed was rather interesting—and perplexing. The variation between Msx (moment in the x-direction) and Msy (moment in the y-direction) values from SUMO and those derived via hand calculations fluctuated unpredictably. In some cases, a small change in Ly would produce a large discrepancy; in others, the results would align surprisingly well.

In an effort to reconcile these differences, I began to explore whether manipulating the flexural rigidity of the slab in the x-direction (Dxx) could bring the FEA results closer to the hand-calculated moments. In SUMO, Dxx is a bending stiffness modifier, and the idea was simple: adjust Dxx until the Msx value from the FEA matched the one derived using moment coefficients.

Initially, the results were promising. For a given Ly/Lx ratio, I could easily find a Dxx value that would make the Msx values identical. However, problems quickly emerged. Firstly, there was no apparent formula or mathematical relationship that consistently described how Dxx should be adjusted across different Ly/Lx ratios. Even within a narrow range of Ly/Lx values, the relationship was inconsistent. Sometimes a pattern seemed to emerge, but applying it to a new test case would often lead to unsatisfactory results.

Moreover, modifying Dxx to better align Msx values inevitably impacted Msy. As stiffness in the x-direction increased, the slab began to attract more moment in that direction, reducing moment in the y-direction. This trade-off suggested that even if I could match one moment direction, the overall system behavior would change in a non-trivial way, making the results less reliable or realistic.

While I did not succeed in developing a single formula to calculate Dxx for any given Ly/Lx ratio, I did discover something potentially valuable. When the variation in Msx values (between hand calculations and SUMO results) was similar across two different Ly/Lx ratios, the corresponding Dxx values were also similar. This suggests that there may be a path forward in categorizing Dxx values based on ranges or groupings of Ly/Lx rather than a single, continuous function.

This observation is preliminary, and much more data and testing are needed to confirm its validity. However, it opens up the possibility of developing lookup tables or design aids for engineers using FEA to model two-way slabs—tools that could help bridge the gap between traditional coefficient-based methods and modern numerical analysis.

These findings did, however, raise a critical question: should we even try to match FEA results with moment coefficient values? If the coefficients already offer a reliable approximation, then what is the added value of forcing an FEA model to replicate those numbers, especially if it distorts the global behavior of the slab?

Conclusion

The journey of applying Finite Element Analysis to structural concrete design is still ongoing. While the technology is mature and widely used in structural steel applications, concrete—because of its complex, nonlinear, and non-homogeneous nature—presents unique challenges. My work with Prokon’s SUMO software has shown that FEA can be very effective for designing concrete beams and certain types of footings. In these applications, the correlation with traditional hand calculations is strong, and the models provide valuable insight into behavior under load.

Slab design, however, remains a gray area. Using moment coefficients from standards like SANS 10100 to validate FEA outputs is useful, but matching those values through adjustments to slab stiffness (Dxx) has proven to be an unreliable and potentially misleading endeavor. Modifying Dxx affects the entire structural response, and the pursuit of numerical agreement can lead to less realistic modeling outcomes.

Nonetheless, there is value in the patterns observed. The similarity of Dxx values across slabs with similar Msx variation suggests that we may one day categorize Dxx modifiers based on grouped Ly/Lx ratios, providing a practical bridge between FEA and traditional design methods.

Until then, engineers must approach FEA of concrete with a careful balance of confidence and skepticism. Used appropriately, it is a powerful tool that can enhance understanding, refine designs, and push the boundaries of what we can model. But it should be used in conjunction with sound engineering judgment and not as a replacement for code-based checks, especially when those codes are based on decades of empirical data and proven practice.