FEM-analysis

A FEM-analysis has been done in ANSYS to obtain the natural frequencies and the mode shapes of the floor. These are then compared to the actual modes of vibration obtained from the analysis done with experimental data. By doing some iterations, the model has been tuned such that its natural frequencies match with the measured ones as well as possible.

The bearing walls will be assumed to be fixed: the motion of the exterior walls is expected to be mainly in x- and y-direction, while the measurements have only been carried out in z-direction.

Model of the floor

As the floor is symmetrical, it can be modelled by mirroring a CAD-geometry that consists of:

• Half a concrete hollow-core slab.

• Two parts of concrete hollow-core slabs.

• Part of the wall

This geometry is shown in figure 3.28.

Fig. 3.28. CAD-geometry

By including the two parts of concrete hollow-core slabs instead of just the half slab, information about the connections between the slabs can be added to the modell.

From the CAD-geometry, three components were built:

• The layer of concrete hollow-core slabs, consisting of 16 slabs + part of a slab, with a total width of 19.8 meters (figure 3.29).

• The concrete top floor (figure 3.30).

• The wall (figure 3.31).

Fig. 3.30. Bottom view of the concrete top floor

Fig. 3.31. The wall

The model of the connection between the wall and the long sides of the floor has been based on figure 3.3 (page 15), and figure 3.32, which shows a bottom view of this connection.

Fig. 3.32. Bottom view of the connection between the floor and the wall

Figure 3.33 shows how this connection was modelled.

Fig. 3.33. Connection between the floor and the wall in the FEM-model

Next, the internal connections were modelled:

1. A rigid connection between hollow-core slabs and the top floor: the floor is ’one’ part.

2. A bridge bearing support between the wall and the hollow-core slabs along the long sides of the floor.

3. A bonded connection between the wall and the shorter sides of the wall. The stiffness of connections 2 and 3, which are highlighted in figure 3.34, are tuned on the modal measurement results.

Fig. 3.34. The connections of which the stiffness was tuned

Results

The first nine modes of vibration as obtained from the FEM-analysis will be shown in figures 3.35 - 3.43. Their natural frequencies can be found in the captions of the figures.

Fig. 3.35. Mode 1: 6.89 Hz

Fig. 3.36. Mode 2: 12.38 Hz

Fig. 3.38. Mode 4: 21.06 Hz

Fig. 3.40. Mode 6: 31.36 Hz

Fig. 3.42. Mode 8: 40.91 Hz

Fig. 3.43. Mode 9: 42.95 Hz

Comparison with the measurements

The modal results of the FEM-analysis have been tuned on the first three measured natural frequencies. Figures 3.44 and 3.45 show the mode shapes found from the measurements with their corresponding modes found with FEM, the natural frequencies at which they occur, and the percentage show- ing the (mis)match between FEM and measurements, as defined in Eq. 3.10.

percentage= fF EM fmeasured

×100% (3.10)

Fig. 3.45. Comparison of the third to sixth mode

The first natural frequency of the model matches well with the actual first natural frequency. This is not surprising nor conclusive, as the floor’s mass and stiffness were tuned to match the first natural frequency. The second and third calculated natural frequency, however, deviate significantly from the measured ones.

The fourth, and especially the sixth mode of vibration show a good match between simulation and reality in terms of the frequency. However, the simu- lated shape of the sixth mode differs from the measured one: along the short direction of the floor the deflection has a similar shape (note that the colors red and blue are interchangeable, as the direction in which an anti-node is plotted is arbitrary), but the measured mode also has nodes and anti-nodes along the long direction. This may also be the effect of a different mode being superimposed on the shape calculated from the finite element model. The fifth mode of vibration does not show up in FEM: the finite element model is entirely symmetrical, so the simulation will never be capable of pre- dicting this asymetrical mode.

The second and third mode have a (near-) constant deflection along the x- direction (i.e., the vertical direction in the contour plots) and a sinusoid-like deflection along the y-direction, whereas the fourth and sixth mode have an

almost constant deflection along the y-direction, and a sine-shaped deflection along the x-direction. Since the fourth and sixth mode match significantly better than the second and third one, it appears that the model can describe the gradient of the stiffness rather well over the x-direction well, but not over the y-direction.

The concrete hollow-core slabs are positioned along the x-direction, so the individual bending stiffness of the slabs has been modelled pretty well. The stiffness gradient in y-direction depends highly on how the parallel slabs are connected to each other: when the (stiffness-) properties of these connections not properly defined in the model, the second and third mode will show in- accuracies, even if the fourth and sixth one match. Modelling the connection between two adjacent slabs is a very important (but unfortunately also very difficult) matter: along the length of the floor, 16 of them occur. Therefore, the connections will determine a large part of the dynamics. In x-direction, the floor consists almost entirely out of concrete hollow-core slab; the two connections with the outer walls at the ends will only have a small effect on the bending stiffness as a function of the x-coordinate.

This hypothesis, however, could not have been verified so far. The contrast between the mismatch of the second and third mode, and the match of fourth and sixth mode, could just as well be explained by some other phenomenon.

Chapter 4

Conclusion

A modal analysis was to be performed on the floor of a building and use the results to make more accurate finite element models. A tenantless floor of Capitool 15, an office building, was used for the analysis.

Some tests were done to develop a measuring technique with the right mea- surement parameters that were sure to yield usable data for the rest of the analysis, after which the measurements were carried out and data was col- lected.

A method to extract and visualize mode shapes was developed, and this method proved to work outstandingly well: it could effortlessly be applied on other structures as well (see appendix D).

The mode shapes visualized from the data can very well be compared to pictures of mode shapes a generated by FEM-simulations. Being able to evaluate simulation results by comparing them to the actual mode shapes is very useful as it provides insight on how accurate a model is and how the model can be improved. This evaluation also made clear that it is difficult to make an accurate FEM model of (a part of) a building. This is not surprising: when an attempt is made to model a building, many parameters – especially boundary conditions – are unknown. However, now that a method to visualize mode shapes from measured data is available, buildings may be modelled more accurate in the future, as more insight can be gained in how and why a model deviates from reality.

Chapter 5

Recommendations

Based on the findings gained, a number of recommendations have been made. Hopefully these will contribute to a better insight in modal building analysis in the future.

5.1

Including measuring points along the floor’s

edges or supports

It is important to know and how a floor is supported along its edges or at other points where it is connected to the rest of the building, while most of the uncertainties in creating a finite element model of a floor are in these boundary conditions. During the analysis of the floor in Capitool 15 no measurements directly along the walls were done, so this information was missing.