Next, the results of the two bay, three story moment frame structure will be discussed. The goal of this model was to test the capability of the two softwares to deal with the pass-‐ through forces generated by the moment frames separated by a pinned connected beam. This model will also help evaluate STEELs ability to conduct nonlinear analyses on more complex moment frame structures.
3.1.8.1 Model Description
This model consists of two bays of moment frame, three stories tall, connected by pinned beams. An image showing the section assignments for this model can be seen in Figure 3-‐12. This model used a Rayleigh damping model with a mass proportional coefficient of 0 and a stiffness proportional coefficient of 0.00196.
Figure 3-‐12 -‐ Two Bay Three Story Moment Frame -‐ Section Assignments
For this model more realistic sizes of W24x94’s and W21x111’s were chosen for the beams in the moment frames and pass-‐through frame respectively while W12x136’s were chosen for the columns. As before the floors are 3.6576 m (12 ft) tall, yielding a total structure height of 10.9728 m (36 ft), with a bay width of 7.3152 m (24 ft).
Weight and force assignments for this model can be seen in Figure 3-‐13. This figure shows weight assignments of 0.94 kN (0.212 kip) for all nodes on the top floor and 1.89 kN (0.424 kip) for all other nodes. Additionally, the top nodes were given a horizontal force of 22.241 kN (5 kip) for the linear stiffness comparison.
Figure 3-‐13 -‐ Two Bay Three Story Moment Frame -‐ Force Assignments
3.1.8.2 Free Vibration Analysis
The results from the free vibration analysis can be seen in Figure 3-‐14. The free vibration analysis shows an initial elastic deformation of 5.3 mm and 5.5 mm for STEEL and ETABS respectively, or a difference of 0.84%. The application of the horizontal acceleration resulted in a pre-‐release amplitude of -‐6.55 mm and -‐6.46 mm for STEEL and ETABS respectively, or a baseline difference of 1.815%. Following the removal of the horizontal acceleration, the first peak for the two softwares was 6.158 mm and 6.179 mm, or a difference of 0.351% and after 30 oscillations it was found that STEEL had an amplitude of 0.581 mm while ETABS had an amplitude of 0.591 mm, a difference of 1.67%. Finally, averaging the peak-‐to-‐peak oscillation
time for STEEL and ETABS resulted in an approximate period of 0.0474 s and 0.0462 s respectively.
Again, the results from this analysis demonstrate agreement between the two softwares. The majority of the difference is found in the initial elastic displacement. Shifting the ETABS results down so the two results share a common static equilibrium displacement helps demonstrate this point. An image of this can be seen in Figure 3-‐15. This plot shows that the period of oscillation and damping between the two softwares is nearly identical. The marginal difference in elastic stiffness can be explained by the difference in pinned connections used by the two softwares. While ETABS assumes a perfect pinned connection, meaning zero moment capacity; STEEL assumes a small, but non-‐zero, capacity. As discussed in Section 1.5.5, STEEL assumes the middle two fibers of the web are given an area modifier such that the total area of the section is roughly preserved, this results in a small, but not insignificant, moment capacity resulting in an increase in stiffness. As these results show, the STEEL results are consistently stiffer than the ETABS results which, in part, is due to the extra capacity in the pass through elements. As true pinned connections actually contain a small amount of moment capacity, it is expected that the true result would be somewhere in-‐between these two results.
Figure 3-‐14 -‐ Two Bay Three Story Moment Frame -‐ Free Vibration Analysis
3.1.8.3 Pushover Analysis
The results from the pushover analysis can be seen in Figure 3-‐16. This plot again shows an overall agreement in the elastic stiffness of the model, the small difference is due to the assumptions that pinned connections have a non-‐zero moment capacity. However, the yield paths of the two models is nearly identical. In fact, if the ETABS curve is scaled back by the 5.191% elastic stiffness differential the similarity between the two curves becomes apparent. An image of this can be seen in Figure 3-‐17. This plot shows that the two softwares produce nearly identical initial yield paths when the difference in stiffness is taken into account. This plot also shows the difference in convergence characteristics between the two softwares. While ETABS fails to converge after a drift of roughly 1%, the STEEL model is capable of converging through p-‐delta instability.
Figure 3-‐17 -‐ Two Bay Three Story Moment Frame -‐ Pushover Analysis -‐ Scaled
3.1.8.4 Discussion
These models demonstrated the ability of STEEL to analyze pass-‐through forces in beams as well as properly determine the interaction between a moment frame and pinned connections. The differences found in the elastic stiffness between the two softwares is due largely in part to the assumptions made in STEEL. Allowing pinned connections to have a non-‐ zero moment capacity results in additional stiffness that is not modeled in ETABS. While neither software is incorrect, a limited moment capacity in pinned connections is more realistic. Additionally, the similarities in the pushover curves between the two models, especially after the adjustment for discrepancies in elastic stiffness, demonstrates the ability of STEEL to