Beam Modeling in ETABS and SAP2000: What Changes in Modal Analysis? 

 

In the world of structural engineering, ETABS and SAP2000 are two of the most reputable and widely used software for analysis and design. Although they share the same calculation engine from Computers and Structures, Inc., there are subtle differences in their modeling philosophy that can lead to unexpected results. One of these differences, which has a profound impact on dynamic analysis, lies in how mass is accumulated at the internal nodes of frame finite elements. 

 

The Problem: The Difference in Nodal Mass Accumulation  

The central issue is how masses from the frame elements themselves are accumulated at the nodes for modal analysis, especially at the internal nodes generated by the mesh of Shell finite elements that connect to frame elements. 

  • In SAP2000: When a beam (modeled as a single frame object) is intersected by the slab mesh, SAP2000 lumps the masses applied to the beam at the connection nodes along the beam's span. This results in a dynamic model where the effect of nodal masses is applied at multiple points along the beam, even if it is not physically divided. 
  • In ETABS: The default behavior is different. ETABS accumulates the total masses applied to frame objects only at the nodes that define the start and end of these objects. The intermediate nodes of the frames, generated by the slab's automesh along the beam's length, do not receive their portion of tributary mass for the modal analysis. 

This difference is particularly critical in structures with long-span beams carrying significant loads. The correct distribution of mass is fundamental for the accurate determination of vertical vibration modes.

 

Practical Demonstration: Three Models, Two Results  

To illustrate the impact of this difference, let's analyze a simple structure: a slab-beam system with a cantilevered balcony, where the edge beams are modeled as single objects. The expected behavior is that the first vibration modes will be dominated by the vertical movement of the cantilever's corner. 

 

Model in SAP2000  

  • Modeling: The structure is modeled in SAP2000 with the edge beams represented by single frame objects of 26.5m and 21.5m. The slab is modeled with an automesh. 
  • Modal Analysis: The program distributes the masses applied to the object to all nodes, including the intermediate nodes along the beams generated by the intersection with the slab. 
  • Result: The first vertical vibration mode has a period of 0.269 seconds. 

 

Model in ETABS  

  • Modeling: The same structure is replicated in ETABS, with the beams also modeled as single frame objects. 
  • Modal Analysis: ETABS concentrates the frame object's masses at the end nodes, ignoring the actual distribution of these masses along the object. 
  • Result: The first vertical vibration mode has a period of 0.501 seconds. 

Single Frame Object SAP2000 vs ETABS

 

The difference is significant. The period in ETABS is 85% longer than in SAP2000, representing a "virtually" more flexible structure that does not correspond to physical reality. This discrepancy can lead to an incorrect assessment of the structure's vertical vibrations.

 

Forcing Mass Distribution in ETABS  

Fortunately, the solution to match the results is conceptually simple and easy to implement, ensuring the correct consideration of mass in the modal analysis. 

The strategy involves physically dividing the frame objects (beams) at the points where the slab mesh generates intermediate nodes. By transforming a single frame object into a set of smaller frame segments, we force ETABS to create "real" nodes at these locations. Consequently, the program will assign the tributary mass from the self-weight and applied loads on the beam to each of these nodes. 

 

Model in ETABS (With the Solution Applied)  

  • Modeling: In the ETABS model, the beams are divided into multiple frame objects whose nodes coincide with the slab's automesh nodes. 
  • Modal Analysis: With physical nodes present along its length, ETABS now correctly assigns the tributary mass to each of them. 
  • Result: The first vertical vibration mode has a period of 0.269 seconds, precisely matching the result obtained in SAP2000. 

Frames Divided into Multiple Objects - ETABS

 

This approach ensures that the structure's mass matrix is assembled correctly, reflecting the actual mass distribution and producing more realistic vertical modal results.

 

Conclusion and Recommendations  

Modal analysis is the foundation for any rigorous dynamic study. The difference in the treatment of nodal masses between ETABS and SAP2000 is not a software error, but rather an intrinsic characteristic of their modeling philosophy that engineers must be aware of and know how to address. 

To accurately analyze the dynamic behavior in the vertical direction in ETABS models, it is recommended to divide the frame objects (beams) in the specific areas where precision in obtaining vertical modes is required.