Comparison Between ETABS and Manual Calculations: Differences and Acceptable Ranges

ETABS and manual calculations are both fundamental tools in the field of structural analysis and design. While ETABS leverages sophisticated algorithms and advanced modeling techniques, manual calculations rely on traditional engineering principles and methods. Ideally, the values derived from both approaches should align closely, especially in simpler cases. However, various factors can lead to discrepancies. This article explores the reasons for these differences and the acceptable ranges for variations.

Factors Contributing to Differences

The discrepancies between ETABS and manual calculations can arise from several sources:

Modeling Assumptions

ETABS offers a more versatile platform, allowing for detailed and complex modeling, including nonlinear behavior and dynamic analysis. These capabilities may not be fully replicated in manual calculations, leading to differences in results.

Load Combinations

ETABS and manual calculations may use different load combinations and factors, which can result in variations in the outcomes.

Boundary Conditions

The way supports and constraints are modeled in ETABS may differ from those assumed in manual calculations, contributing to discrepancies.

Material Properties

Variations in material properties and their representation can also lead to distinct results.

Quantifying the Difference

To measure the extent of the difference between ETABS and manual calculations, the following formula can be used:

Percentage Difference (ETABS Value - Manual Value) / Manual Value × 100%

Acceptable Ranges

In practice, a percentage difference within 5-10% may be considered acceptable, especially for less complex structures. For critical and precise applications, a closer alignment within 1-3% is typically desirable.

However, it's important to recognize that the range considered acceptable can vary depending on the specific application and the complexity of the structure.

Case Study Analysis

In a case study, I compared the stresses and deflections on various beams using multiple manual calculation methods and ETABS. The results showed that the differences were within 3% maximum, even when considering the Timoshenko Shear Deformation model.

Two key aspects need clarification:

Approach for Manual Calculations

The method used for manual calculations significantly impacts the results. There are various techniques, such as the classical method, stiffness method, and flexibility method. In my study, the stiffness method produced the closest results.

Mesh Size and Number of Elements in ETABS

The number of elements or the mesh size in ETABS can affect the discrepancies between the results. For instance, modeling a beam with 1, 2, and 4 elements resulted in the 4-element model providing the closest match.

As shown in the figure, convergence to the exact solution as the number of elements increases in a finite element solution highlights the importance of precise meshing.

Exact Solution Clarification

It is crucial to define the exact solution in the context of manual calculations. Which method are we using for manual calculations? This can help in determining the acceptable range of differences.

Conclusion

It's not accurate to declare that the results of ETABS should be within a 3% range. What is significant is the recognition that the term 'manual calculation' is too broad and that different methods can yield varying results. Thus, ETABS and other FEM-based software must adopt similar rules to produce comparable outcomes.