Distributed Plasticity Modeling for Frame Elements in CSI Software

Distributed plasticity modeling in frame elements can be essential for capturing a more realistic structural response. In programs like SAP2000, ETABS, and CSiBridge, it is possible to assign Fiber Hinges (P-M2-M3) that capture the nonlinear behavior along the frame element’s length, addressing both flexural and axial interactions as well as different materials (e.g., concrete and steel). 

In the latest versions of CSI software, this modeling can be set up more conveniently, thanks to automated hinge discretization methods. In earlier versions, the approach was similar but required manual creation of each hinge segment, subdividing the frame element into multiple elements. The current approach, relying on different distribution methods (including Equal Spacing), makes material nonlinearity in frame elements substantially more intuitive. 

1. Fundamental Concepts

In most global structural analyses, assuming linear material behavior is generally sufficient. In steel members, for example, yielding may only occur under specific ultimate limit states. In reinforced concrete members, there may be nonlinear phenomena linked to cracking even at service loads. Nevertheless, one can often reduce elastic stiffness or apply force redistribution rules while still assuming overall linear-elastic behavior. 

However, there are certain advanced applications where capturing the effective stiffness variation along the element becomes critical. In such cases, it may be indispensable to model material nonlinearity directly, incorporating concrete cracking, steel yielding, or even failure. Two main approaches exist: 

• Concentrated Plasticity: Plasticity occurs only at the frame ends (plastic hinges), idealizing the yield mechanism in a simplified manner. 
• Distributed Plasticity: Nonlinearity develops progressively over several cross sections along the member’s entire length, using multiple fiber hinges. 

Among the available techniques, fiber hinges (Fiber P-M2-M3) are frequently the most comprehensive for representing distributed plasticity. The software generates a fiber mesh for each cross section, integrating forces (P, M2, M3) and corresponding deformations (U1, R2, R3) based on each material’s stress-strain relationship. 

2. Fiber Hinges 

Fiber hinges allow for combining various materials (e.g., concrete and reinforcing steel) and offer the following advantages: 

• Coupled axial and flexural response: Each fiber can be independently compressed or tensioned, ensuring that material nonlinearity is captured at any location. 
• Versatile section definition: The software can automatically generate fibers for parametric sections, or the user can employ Section Designer for custom geometry and refined control. 
• Progressive modeling: Yielding develops progressively in regions where stresses reach the yield limit, avoiding the assumption of a single lumped point of failure. 

3. New Automated Hinge Distribution Methods

Recent versions of CSI software have introduced automated procedures that simplify distributing fiber hinges along frame elements. Two main approaches stand out: 

• Equal Spacing: The user defines the number of hinges, and the software subdivides the member into equal segments. 

• Distributed Plasticity: Other methods, such as Gauss-Lobatto or Gauss-Legendre (with five or seven integration points), provide finer control over hinge distribution.

In previous software releases, it was necessary to manually subdivide the frame element into multiple segments, assigning a fiber hinge to each segment and carefully defining hinge lengths. Now, simply indicate how many hinges you need or choose the desired distribution method to cover the entire member, and the software can automatically generate finite elements centered around those hinges. 

4. Practical Example: Analysis of a Slender Reinforced Concrete Column 

This example focuses on a slender reinforced concrete column in SAP2000, comparing two different levels of reinforcement to see how varying reinforcement affects second-order moments. 

Step by Step: 

1. Define Materials and Section

• Set up stress-strain curves for both concrete and reinforcement steel.
• Establish the cross-sectional geometry and reinforcement details.

2. Create and Assign the Fiber Hinge

• Use Fiber P-M2-M3 of type “Default from Section.” 
• The hinge length can be any value; each hinge automatically takes the corresponding tributary length (input only relevant for assigning discrete hinges). 
• Assign 10 equally spaced hinges along the column.

3. Nonlinear Analysis

• Convert the load combination into a nonlinear load case, including P-Delta effects.

4. Compare Results

• Evaluate moment demands for each reinforcement scenario. 
• Note that reduced stiffness leads to higher second-order moments.

This example highlights how quickly you can modify section properties and immediately analyze corresponding nonlinear behavior in detail. 

Additional example: Exercise 14 in the Geometric Nonlinearity course provides another application of distributed plasticity in nonlinear buckling analyses. 

5. Notes on Older Program Versions

Beginning with SAP2000 and CSiBridge version 25 (and ETABS version 21.2), assigning distributed hinges became much simpler: the user can select from multiple discretization methods, and the software adjusts hinge lengths automatically. Older versions could achieve the same outcome but required either subdividing the frame object or manually assigning multiple hinges along the frame, paying special attention to each hinge length. 

Section 3.5 of the SAP2000 Advanced course describes two strategies for pre-v25 models: 

Exercise 37: Assign multiple hinges along a reinforced concrete beam, using Section Designer and User-Defined Fiber Hinges. (*) 
Exercise 38: Subdivide a concrete column into multiple segments, each with a hinge length equal to that segment’s actual length. 

In Exercise 37, the fiber table generated by Section Designer is copied to build a User-Defined Fiber Hinge. This approach can be helpful for importing fibers from external software (e.g., via Excel). Still, simply using “Default from Section” would be sufficient for the program to automatically read the defined cross-sectional fibers. 

Conclusion 

Using fiber hinges to model distributed plasticity in frame elements is a valuable tool for incorporating material nonlinearity into SAP2000, ETABS, and CSiBridge. The automated longitudinal and transverse discretization features streamline analysis, reduce errors, and simplify the modeling process. 

Overall, distributed plasticity modeling with fiber hinges—together with the automatic discretization resources (available in SAP2000 and CSiBridge v25+ and ETABS v21.2+)—enhances the software’s nonlinear analysis capabilities for reinforced concrete, steel, composite, or any material with a defined stress-strain curve. This approach delivers deeper insights into ultimate capacity, enabling a realistic evaluation of buildings and bridges, especially for advanced design or retrofit projects. 

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