3.2.2 Perform3D Model Description
The Perform3D model was constructed to replicate STEEL models as closely as possible.
All elements were given a fiber cross section with fiber areas matching those in STEEL as discussed in Section 1.5.5. Each fiber was designated with the same material model and the appropriate fiber area reductions were applied for fixed end connections and pinned connections. For brace elements an actual moment release element was applied to either end of the compound element to simulate the manner with which STEEL treats braces. For each Perform compound element a rigid end offset was applied to either end with the appropriate length matching that of STEEL. Furthermore, shear deformation in beams and columns was enabled using shear areas defined by,
𝐴!"= 𝑑𝑡!
𝐴!"= 2𝑏𝑡!
Where 𝐴!" is the shear area along the web and 𝐴!"is the shear area along the flanges. The shear modulus was found using,
𝐺 = 𝐸 2 1+𝑣
Where E is the Young’s Modulus and 𝑣 is the Poisson’s ratio taken to be 0.3.
As STEEL is a 2D analysis software, special restraints needed to be placed on the Perform3D model to ensure that out-‐of-‐plane behavior was eliminated. Therefore, all non-‐base nodes were given fixed conditions for the H2, RH1, RZ directions. All base nodes were given full fixed conditions.
3.2.3 Material Model Description
Due to limitations in both STEEL and Perform3D, it is not possible to get an exact match in the material model. As discussed previously, the STEEL material model is symmetric and consists of a linear elastic region, followed by a region of constant stress, which is then preceded by a strain hardening region represented by a cubic ellipse. Following this the curve will then drop to a defined residual value. In Perform3D, the nonlinear, non-‐buckling material model consists of a linear elastic region, followed by a secondary linear region, leading to a region of constant stress before reaching a region of negative slope before ultimately dropping to a residual value.
In an attempt to match these material models as closely as possible, the material used for the ETABS to STEEL comparison described in Section 3.1.3 was modified. The steel material model begins with a linear slope of 199.95 GPa (29000 ksi), yielding at 344.737 MPa (50 ksi).
The region of constant stress continues until a strain of 0.004 where a cubic ellipse with an intersection slope of 3467257 MPa (502883 ksi) and ultimate stress of 448.1 MPa (65 ksi) at a strain of 0.11. At a strain of 0.205 the STEEL material model drops to a residual stress of 0 MPa (0 ksi).
The Perform3D model also has a linear slope of 199.95 GPa (29000 ksi) with a yield stress of 344.747 MPa (50 ksi). The secondary linear region ends at a stress of 441.26 (64 ksi) and a strain of 0.05. The region of constant stress ends at a strain of 0.16 and then decreases to a stress of 344.747 MPa (50 ksi) at a strain of 0.207272. The Perform3D material will then remain at this stress until a strain of 0.218181 after which it drops to 0 stress. An image of this can be seen in Figure 3-‐28.
Figure 3-‐28 -‐ Material Model Description -‐ Perform3D vs. STEEL
3.2.4 Perform3D Analysis Limitations
While conducting several of the linear elastic time history analyses in Perform3D it was noticed that for the specific models, namely the two brace frame and twenty story moment frame, while STEEL and Perform3D yielded similar results for both the elastic stiffness, initial release point, mass, and period; following the removal of the horizontal acceleration the Perform3D model exhibited practically no damping. While the exact method is not perfectly clear it was revealed by CSI customer support that for steel fiber elements 0% of the axial stiffness for Rayleigh damping is used [20]. This was done by the Perform3D programmers to combat excessive energy dissipation found in their analyses when these axial fibers yield, resulting in an axial expansion. The issue is said to be caused by coupling between the bending and axial affects that is generally not present before yielding or cracking. Through their own analyses it was found that this affect resulted in excessive energy dissipation when using stiffness proportional Rayleigh damping [20]. The decision to remove axial stiffness from steel fiber elements was done to yield a more conservative answer in users’ analyses.
For most users this affect will not cause a large error in their simulation because, in general, fiber elements are only used in small, localized regions. However, in order to achieve a valid comparison between these two softwares the usage of fiber elements throughout the Perform3D model results in a practically no damping being applied in specific models. As a result, the free vibration analysis for both chevron brace frame models as well as the twenty story model resulted in a solution which could not be properly compared to the results of STEEL. However, for each of these models the static stiffness, initial release point from the analysis can still be compared as well as the results from the pushover analysis. For the
cantilever column, three story moment frame, and two bay three story moment frame models this approximation of no axial damping done by Perform3D is small enough that a relatively accurate comparison can still be made from the free vibration analysis as these models act primarily in bending.
Additionally, Perform3D does not include geometric updating. While for most typical analyses this will not result in a considerable difference, when calculating the ultimate capacity of the building as well as determine at what drift the structure experiences geometric instability the lack of geometric updating can begin to play a large difference. It is therefore expected that at very large strains the results of the STEEL and Perform analyses will diverge and it is expected for some of the more realistically weighted buildings that the STEEL analyses will become unstable at a lower drift. Furthermore, for extremely high drifts it was seen that the results from the STEEL pushover analysis can show a rapid increase in base shear following the collapse of the structure. It is believed this is caused by the manner in which STEEL conducts pushover analyses. Due to the monotonically increasing applied accelerations the amount of force being applied to the structure increases regardless of whether the structure is capable of resisting this force. However, since this force must be resolved in the system the base shear of the structure will continue to increase. Through examining the deformed shape of the structure it is clear that this increase in base shear is not indicative of an increase in structural capacity post-‐
collapse but rather an artifact of conducting a force controlled analysis.
3.2.5 Analysis Discussion
A total of six models were analyzed in both STEEL and Perform and their results compared. Each model was chosen to test a specific feature of STEEL to determine how the assumptions compare to those of Perform. The models begin with a simple three element cantilever column followed by a three story single bay moment frame and a three story single bay chevron brace frame. From here, the models increase in complexity to a two bay three story moment frame and then a two bay three story chevron brace frame. Lastly, a twenty story moment frame based on Hall’s U20 building [1] was analyzed.
For some of these models, properties such as the section sizes and masses may be considered nonrealistic, however, as the goal of this study was to compare the results of Perform and STEEL the actual specifics of the models are not as important as the comparative results from the two software systems. Often, particular masses or section sizes were chosen to encourage a specific type of nonlinear behavior or to simplify the model so as to reduce the number of variables for comparison.