Add the ability to assign nonlinear axial force-deformation behavior to individual frame and truss members, allowing RAM Elements to automatically redistribute internal forces when a member reaches a specified tensile or compressive strength.
Currently, RAM Elements primarily relies on elastic member stiffness when determining internal force distribution. This makes it difficult to evaluate structural systems in which yielding or buckling of individual members limits the forces that can develop elsewhere in the structure.
Proposed Functionality
Allow users to specify axial force limits and post-yield stiffness independently for tension and compression.
The feature should include:
User-defined tensile and compressive yield limits: Specify maximum axial forces, including expected material strengths such as R_yF_yA_g, or other user-defined capacities.
Nonlinear axial stiffness: Automatically transition from elastic axial stiffness to a user-defined post-yield tangent stiffness when the specified force limit is reached.
Plastic force redistribution: Continue the analysis beyond initial yielding, maintaining the previously developed axial force while redistributing additional loads to other structural members.
Incremental load application: Apply loading in increments to identify the sequence of member yielding and subsequent redistribution.
Independent tension and compression behavior: Allow different force-deformation relationships for tensile yielding, compressive yielding, and compression buckling.
Analysis results: Report the sequence of yielding, maximum member forces, accumulated plastic deformation, and resulting connection forces.
Optional strain hardening: Allow users to specify post-yield stiffness to approximate material strain hardening.
Example Application: Steel Truss Moment Frames
In steel truss moment frames, the chords are frequently different sizes, with larger chords proportioned for compression buckling and smaller chords proportioned for tensile resistance.
Under seismic loading, a smaller chord may reach its expected tensile yield strength before a larger chord can develop its full tensile capacity.
Once the smaller chord yields, its axial stiffness decreases, potentially redistributing additional forces to other members and connections.
Currently, evaluating this behavior requires multiple analyses with manually modified member stiffnesses and external calculations to superimpose incremental forces.
The proposed feature would allow RAM Elements to perform this analysis directly, providing a more efficient means of evaluating system-level yielding mechanisms and the corresponding maximum connection demands.
Benefits
Reduce the need for multiple manually modified structural models.
Improve evaluation of structural force redistribution after initial yielding.
Support performance-based and capacity-design investigations.
Allow engineers to identify governing yielding mechanisms and connection demands.
Reduce the need for specialized nonlinear analysis software for relatively simple structural systems.
Provide additional functionality for trusses, braced frames, tension-only systems, and other structures with nonlinear axial behavior.
Suggested Implementation
A practical initial implementation could use an elastic-perfectly-plastic axial material model with optional bilinear strain hardening.
Users would define:
Initial axial stiffness, EA.
Tensile yield force, P_{yt}.
Compressive yield force, P_{yc}.
Post-yield tangent stiffness ratio, E_t/E.
Optional maximum plastic deformation limits.
RAM Elements would incrementally apply loads, update member tangent stiffnesses as yielding occurs, and continue solving for equilibrium until the specified load or displacement target is reached.
The feature should also support unloading and load reversal for seismic applications, with appropriate hysteretic behavior.
Requested Outcome: Enable engineers to evaluate nonlinear axial yielding and subsequent structural force redistribution within RAM Elements without manually modifying member stiffnesses or performing separate incremental analyses.