Grillage analysis, a simplified method for modeling complex structures like bridge decks, presents certain limitations as outlined by E. C. Hambly:
Inconsistent Torques and Twists (Coarse Mesh): When using a coarse mesh in grillage analysis, the calculated torques (twisting moments) may not be equal in perpendicular directions. This discrepancy arises due to the simplified nature of the model, where the mesh resolution is insufficient to capture the intricate stress distribution accurately. Similarly, the twist (rotational deformation) may also differ in orthogonal directions. This inconsistency can lead to inaccurate predictions of the structural behavior, especially in cases with complex loading patterns or geometric irregularities.
Simplified Moment Calculation: In grillage analysis, the bending moment in a beam is primarily considered proportional to its curvature alone. However, in reality, the moment within an element is influenced by both the curvature in the beam’s direction and the curvature in the perpendicular direction. This simplification neglects the coupling effect between these curvatures, potentially leading to underestimation or overestimation of stresses and deformations.
These shortcomings highlight the need for careful consideration when applying grillage analysis. While it can be a valuable tool for preliminary design and quick assessments, its limitations should be acknowledged, and the results should be interpreted with caution, especially in situations where high accuracy is required. In such cases, more refined methods like finite element analysis may be necessary to capture the complex behavior of the structure accurately.