Elastic, Inelastic, and Plastic Analysis in Steel Structure Design

The design of steel structures is a complex process that requires a thorough evaluation of internal forces and displacements under various load combinations. Three primary design approaches are used: elastic analysis, inelastic analysis, and plastic analysis. Each method serves different purposes and is suitable for different structural requirements.

Elastic Analysis

As the simplest and most common approach, elastic analysis assumes that the structure behaves elastically, meaning it can return to its original shape after the load is removed. This approach is ideal for structures expected to experience only small deformations. Elastic analysis involves evaluating internal forces and deformations using linear elastic theory, which assumes a linear relationship between stress and strain.

The elastic analysis method provides a straightforward way to design steel structures, especially for lighter and simpler designs. It is extensively covered in Reference 2.

The following formula can be used for linear elastic analysis:

Stress E * Strain

Where E is the elastic modulus of the material and Strain is the deformation occurring under stress.

Inelastic Analysis

Inelastic analysis is applied when the structure is expected to undergo significant deformations or when the design load exceeds the elastic limit of the material. This method involves evaluating internal forces and deformations using nonlinear analysis, which accounts for the material's nonlinear behavior. Unlike elastic analysis, inelastic analysis can handle the structure's response beyond the elastic limit, but it does not consider the redistribution of moments after yielding.

Nonlinear analysis is necessary for structures subjected to dynamic loads or for those with complex geometries. The inelastic analysis is introduced in Reference 1.

The following formula can represent inelastic analysis:

Stress σ f(ε)

Where σ is the stress and ε is the strain, with a nonlinear relationship represented by f(ε).

Plastic Analysis

Plastic analysis is an advanced design method that considers the redistribution of moments after yielding, making it suitable for structures expected to undergo large deformations. This approach allows for the design of a preselected yield mechanism at the ultimate load level, leading to a known and predetermined response during extreme events.

Unlike elastic and inelastic analyses, plastic analysis provides a method to control the plastic behavior and design for more resilient structures. Detailed information on plastic analysis is provided in References 1 and 3.

The following formula can be used for plastic analysis:

ε ε_y α(σ - σ_y)

Where ε is the strain, ε_y is the yield strain, and α is the nonlinearity factor, with σ and σ_y representing the stress and yield stress, respectively.

By understanding the behavior of steel under different loading conditions, engineers can select the most appropriate design method to ensure the safety and durability of the structure.

Conclusion

In the design of steel structures, the choice between elastic, inelastic, and plastic analysis depends on the specific requirements and expected loading conditions. Each method has its unique advantages and limitations, but proper selection can significantly impact the safety, efficiency, and cost-effectiveness of the structure. For a comprehensive understanding, always refer to the latest design guidelines.