𝗜𝗺𝗽𝗮𝗰𝘁 𝗼𝗳 𝗗𝗲𝗳𝗼𝗿𝗺𝗲𝗱 𝗚𝗲𝗼𝗺𝗲𝘁𝗿𝘆 𝗶𝗻 𝗦𝘁𝗿𝘂𝗰𝘁𝘂𝗿𝗮𝗹 𝗔𝗻𝗮𝗹𝘆𝘀𝗶𝘀 𝗼𝗳 𝗧𝘄𝗼-𝗛𝗶𝗻𝗴𝗲𝗱 𝗔𝗿𝗰𝗵
In structural engineering, different analysis methods are used in material linear elastic analysis. These methods can include the influence of imperfections and geometrically non-linear effects on structural behavior. Let’s summarize these methods and show how they impact the bending moment of a two-hinged arch.
👉 𝗟𝗶𝗻𝗲𝗮𝗿 𝗔𝗻𝗮𝗹𝘆𝘀𝗶𝘀 (𝗟𝗔):
Assumes small displacements and strains, using perfect geometry and linear stress-strain relationships. This method is ideal for evaluating elastic behavior in structures with minimal deformations but it cannot capture large deformations or second-order effects. As a result, imperfections and second-order effects need to be incorporated separately, typically through stability checks using buckling coefficients.
👉 𝗟𝗶𝗻𝗲𝗮𝗿 𝗕𝗶𝗳𝘂𝗿𝗰𝗮𝘁𝗶𝗼𝗻 𝗔𝗻𝗮𝗹𝘆𝘀𝗶𝘀 (𝗟𝗕𝗔):
Focuses on determining the critical load at which a structure may experience buckling, providing the buckling shape without accounting for imperfections. However, the results from LBA can be used to define imperfections, which are then used in subsequent GNIA calculations. Additionally, LBA can be applied to determine critical lengths for stability checks in LA.
👉 𝗚𝗲𝗼𝗺𝗲𝘁𝗿𝗶𝗰𝗮𝗹𝗹𝘆 𝗡𝗼𝗻-𝗟𝗶𝗻𝗲𝗮𝗿 𝗔𝗻𝗮𝗹𝘆𝘀𝗶𝘀 (𝗚𝗡𝗔):
Introduces geometric non-linearity. Global imperfections and stability checks based on system lengths for buckling may be considered. However, in the example below, simplified GNA is used to determine internal forces in an ideal, geometrically perfect structure, including just the effects of geometric changes under load.
👉 𝗚𝗲𝗼𝗺𝗲𝘁𝗿𝗶𝗰𝗮𝗹𝗹𝘆 𝗡𝗼𝗻-𝗟𝗶𝗻𝗲𝗮𝗿 𝗔𝗻𝗮𝗹𝘆𝘀𝗶𝘀 𝘄𝗶𝘁𝗵 𝗜𝗺𝗽𝗲𝗿𝗳𝗲𝗰𝘁𝗶𝗼𝗻𝘀 (𝗚𝗡𝗜𝗔):
Extends GNA by incorporating all imperfections, such as geometric deviations, residual stresses, and variations in boundary conditions. This method provides a more accurate representation of structural behavior by accounting for both geometric non-linearity and imperfections. Therefore, no individual stability checks are necessary.
📚 𝗘𝘅𝗮𝗺𝗽𝗹𝗲:
The two-hinged arch was first analyzed by #RFEM from #DlubalSoftware using Linear Analysis (LA), resulting in a bending moment of 140 kNm based on an ideal, geometrically linear model. GNA, including second-order effects, was then applied to a geometrically perfect model, producing a bending moment of 200 kNm. Next, Linear Bifurcation Analysis (LBA) identified the critical buckling mode, which helped define the imperfections for GNIA. Finally, GNIA, considering imperfections (shape from LBA and magnitude from EC3 guidelines), led to a final moment of 263 kNm, demonstrating the notable impact of imperfections and non-linearity on structural behavior.
