One of the important aspects of structural engineering is whether a building or a bridge would stand up to the forces acting upon it. The methods of analysis and modeling that were used to predict this particular behavior have grown in sophistication over the years.
One of the sophisticated methods that has been popularized in recent times is called Geometrically and Materially Nonlinear Analysis (GMNA). This analysis is used to model and calculate the real-world behavior of structural elements with specific accuracy, particularly when the geometrical changes and material softening are significant. This article investigates everything about GMNA.
Introduction to GMNA
GMNA, or Geometrically and Materially Nonlinear Analysis, is a method of structural analysis that takes into account mathematical and geometrical considerations and is developed with regard to the analysis of deformation of a structure under load.
GMNA, or material non-linearity, which is the elastoplastic and plastic non-linear behavior of a material, is the response of materials to stress. To incorporate all these variables, GMNA accounts for a structure’s performance under different loads.
Thus, GMNA compliments traditional linear analysis methods. Considering that small deformations are proportional to the loads placed on a structure, linear analysis often struggles to contain accurate results.
Linear analysis is well suited for structures under small loads, but components such as steel hollow sections undergo extreme changes in shape when subjected to thick compression or bending. GMNA was designed with these issues in mind by applying more accurate definitions to material behavior and geometry.
The Evolution of Analysis Methods
In the past, structural engineers used linear analysis to model the behavior of building components. Linear analysis is inherently based on the assumption that the material behaves elastically and the deformations do not exceed the elastic range.
In extreme loads, this premise is highly problematic for certain components. With the advent of nonlinear analysis techniques such as Materially Nonlinear Analysis (MNA), everything changed. Plastic deformation is continually dependent on geometry.
In other words, geometric assumptions rely on the absence of plastic deformation in some scenarios. To address these limitations, GMNA was developed to simulate material and geometric nonlinearities more accurately. GMNA is able to better capture structural behavior because it accounts for the severe deformations.
How GMNA Works
GMNA is the amalgamation of two features: geometrically nonlinear analysis and materially nonlinear analysis. Each section contributes to the whole in the following manner:
Geometrically Nonlinear Analysis
This method simulates how the structure performs under load by analyzing what happens to the shape of the structure during the loading. Any load that acts on a structure will tend to change its shape.
These deformations, when significant, will tend to affect the performance of the structure. It is also the case that linear analysis neglects the impact of these geometric changes. GMNA does, however, incorporate these geometric changes to create a more accurate model for structures that experience large displacements.
Materially Nonlinear Analysis
This section focuses solely on the performance of various materials when they are stressed beyond their plastic limit. In general, materials such as steel and concrete are elastic with small loads; however, they are known to plastically deform or fracture with larger loads of stress. Such behaviors can be modeled due to material nonlinearity, which is important in anticipating the performance of structural elements with large loads on them.
Impact on Design and Results
Analytical results when using GMNA will almost always differ from what is obtained using more traditional means and methods. Indeed, it is fair to say, GMNA results for tensioned members exceed expectations for less conservative estimates and are more restrictive for compressive members.
Such alterations of the parameters or change of results can have a dire impact on the end cost of design, especially for members considering the extreme value of checking code perimeter. Remember that any pre-existing projects created using the IDEA Statica version 10.0 will yield different results if recalculated in version 10.1 with GMNA active.
This is because the introduction of GMNA accounted for the effects of large deformations for recalculation purposes where earlier versions did not. Engineers should make an effort to double check previous versions of the designs to see what differences, if any, exist in the calculations.
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Conclusion
Geometrically and Materially Nonlinear Analysis (GMNA) is best described as a feature in software that allows for greater efficiency in structural analysis of the most intricate of structures.
By adding geometric and material non-linearities, GMNA enables more plausible structural responses to be estimated. This method is particularly advantageous for thin-walled members, which are prone to large deformations that many methods fail to analyze.