**5. Dynamic Analysis**

For practical purposes, a non-linear time-domain analysis was performed throughout this study. This section presents the evaluation of the composite floor vibration levels when submitted to human rhythmic activities. The composite floor dynamic response was deter‐ mined through an analysis of its natural frequencies and peak accelerations. The results of the dynamic analysis were obtained from an extensive parametric analysis, based on the fi‐ nite element method using the ANSYS program [8].

fact that the structural system becomes more susceptible to excessive vibrations induced by

An Analysis of the Beam-to-Beam Connections Effect and Steel-Concrete Interaction Degree Over the Composite

f01 6.63 6.18 6.06 6.39 5.98 5.84 f02 6.75 6.46 6.36 6.52 6.26 6.13 f03 7.10 6.58 6.43 6.84 6.35 6.19 f04 7.11 6.77 6.65 6.85 6.54 6.40 f05 7.17 7.02 6.91 6.94 6.79 6.67 f06 7.35 7.16 7.05 7.08 6.91 6.78

**Table 5.** Composite floor natural frequencies (Beam-to-beam semi-rigid connections: Sj

**Figure 11.** Steel-concrete composite floor fundamental frequency (f01) variation.

**Total Interaction Partial Interaction (50%) Rigid Semi-rigid Flexible Rigid Semi-rigid Flexible**

= 12kNmm/rad. Stud 19mm:

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human rhythmic activities.

Sj

= 200kN/mm).

**Frequencies (Hz)**

In order to evaluate quantitative and qualitatively the obtained results according to the pro‐ posed methodology, the composite floor peak accelerations were calculated and compared to design recommendations limiting values [6,9]. This comparison was made to access a pos‐ sible occurrence of unwanted excessive vibration levels and human discomfort.

## **5.1. Natural Frequencies and Vibration Modes**

The steel-concrete composite floor natural frequencies were determined with the aid of the numeric simulations, see Tables 4 and 5. The structural behaviour of the beam-to-beam con‐ nections (rigid, semi-rigid and flexible joints) and the stud connectors (from total to various levels of partial interaction cases) present in the investigated structural model were simulat‐ ed objectifying to verify the influence of these connections and the steel-concrete interaction degree on the composite floor dynamic response.


**Table 4.** Composite floor natural frequencies (Beam-to-beam semi-rigid connections: Sj = 12kNmm/rad. Stud 13mm: Sj = 65kN/mm).

Considering the investigated composite floor natural frequencies, a small difference be‐ tween the numeric results obtained with the use of total interaction or partial interaction (50%) can be observed. The largest difference between the natural frequencies was approxi‐ mately equal to 5% to 7%, as presented in Tables 4 and 5 and illustrated in Figure 11.

Another interesting fact concerned that when the joints flexibility (rigid to flexible) and steel-concrete interaction degree (from total to partial) decreases the composite floor natural frequencies become smaller, see Tables 4 and 5. This conclusion is very important due to the fact that the structural system becomes more susceptible to excessive vibrations induced by human rhythmic activities.

**5. Dynamic Analysis**

292 Advances in Vibration Engineering and Structural Dynamics

nite element method using the ANSYS program [8].

**5.1. Natural Frequencies and Vibration Modes**

degree on the composite floor dynamic response.

**Table 4.** Composite floor natural frequencies (Beam-to-beam semi-rigid connections: Sj

**Frequencies (Hz)**

Sj

= 65kN/mm).

For practical purposes, a non-linear time-domain analysis was performed throughout this study. This section presents the evaluation of the composite floor vibration levels when submitted to human rhythmic activities. The composite floor dynamic response was deter‐ mined through an analysis of its natural frequencies and peak accelerations. The results of the dynamic analysis were obtained from an extensive parametric analysis, based on the fi‐

In order to evaluate quantitative and qualitatively the obtained results according to the pro‐ posed methodology, the composite floor peak accelerations were calculated and compared to design recommendations limiting values [6,9]. This comparison was made to access a pos‐

The steel-concrete composite floor natural frequencies were determined with the aid of the numeric simulations, see Tables 4 and 5. The structural behaviour of the beam-to-beam con‐ nections (rigid, semi-rigid and flexible joints) and the stud connectors (from total to various levels of partial interaction cases) present in the investigated structural model were simulat‐ ed objectifying to verify the influence of these connections and the steel-concrete interaction

> f01 6.57 6.14 6.00 6.32 5.91 5.76 f02 6.69 6.41 6.30 6.45 6.19 6.05 f03 7.03 6.52 6.37 6.76 6.27 6.31 f04 7.04 6.71 6.58 6.77 6.46 6.31 f05 7.11 6.97 6.85 6.87 6.72 6.58 f06 7.28 7.10 6.98 7.01 6.83 6.68

Considering the investigated composite floor natural frequencies, a small difference be‐ tween the numeric results obtained with the use of total interaction or partial interaction (50%) can be observed. The largest difference between the natural frequencies was approxi‐

Another interesting fact concerned that when the joints flexibility (rigid to flexible) and steel-concrete interaction degree (from total to partial) decreases the composite floor natural frequencies become smaller, see Tables 4 and 5. This conclusion is very important due to the

mately equal to 5% to 7%, as presented in Tables 4 and 5 and illustrated in Figure 11.

**Total Interaction Partial Interaction (50%) Rigid Semi-rigid Flexible Rigid Semi-rigid Flexible**

= 12kNmm/rad. Stud 13mm:

sible occurrence of unwanted excessive vibration levels and human discomfort.


**Table 5.** Composite floor natural frequencies (Beam-to-beam semi-rigid connections: Sj = 12kNmm/rad. Stud 19mm: Sj = 200kN/mm).

**Figure 11.** Steel-concrete composite floor fundamental frequency (f01) variation.

In sequence, Figure 12 presents the composite floor vibration modes when total and parti‐ al interaction situations were considered in the numerical analysis. It must be emphasized that the composite floor vibration modes didn't present significant modifications when the connections flexibility and steel-concrete interaction was changed. It must be empha‐ sized that the structural model presented vibration modes with predominance of flexural effects, as illustrated in Figure 12.

and Figure 6), have generated peak accelerations higher than 0.5%g [6,9]. This trend was confirmed in several other situations [1,2], where the human comfort criterion was violated.

An Analysis of the Beam-to-Beam Connections Effect and Steel-Concrete Interaction Degree Over the Composite

**Figure 13.** Composite floor dynamic response. Semi-rigid connections and partial interaction): Node A.

**Figure 14.** Composite floor dynamic response (Semi-rigid connections and partial interaction): Node B.

In sequence of the study, Tables 6 and 7 show the peak accelerations, ap (m/s2

**Node A**

practising aerobics were applied on the composite floor.

**Interaction Model ap (m/s2)**

Limiting Acceleration: alim = 0.50m/s2 (5%g - g: gravity) [6,9]

**Table 6.** Composite floor peak accelerations: Nodes A, B, C and D (see Figure 6).

Complete

Partial (50%)

ing to nodes A to H (Figure 6), when thirty two dynamic loadings, simulating individual

**ap (m/s2) Node B**

Rigid 0.26 0.17 0.17 0.26 Semi-rigid 0.28 0.20 0.20 0.28 Flexible 0.30 0.44 0.43 0.30

Rigid **0.53** 0.36 0.36 **0.53** Semi rigid **0.62 0.63 0.63 0.62** flexible **0.60 0.80 0.80 0.60**

**ap (m/s2) Node C**

**ap (m/s2) Node D**

), correspond‐

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295

**Figure 12.** Investigated structural model vibration modes (total and partial interaction).

#### **5.2. Maximum accelerations (peak accelerations) analysis**

The present study proceeded with the evaluation of the structural model performance in terms of human comfort and vibration serviceability limit states. The peak acceleration anal‐ ysis was focused in aerobics and considered a contact period carefully chosen to simulate this human rhythmic activity on the analysed composite floor.

The present work considered a contact period, simulating aerobics on the composite floor, Tc, equal to 0.34s (Tc = 0.34s) and the period without contact with the structure, Ts, of 0.10s (Ts = 0.10s). Based on the experimental results [7], the floor dynamic behaviour was evaluat‐ ed keeping the impact coefficient value, Kp, equal to 2.78 (Kp = 2.78). Figures 13 and 14 illus‐ trate the dynamic response (displacements and accelerations) related to nodes A and B (see Figure 6) when thirty two people are practising aerobics on the composite floor.

Based on the results presented in Figures 13and 14, it is possible to verify that the dynamic actions coming from aerobics, represented by the dynamic loading model (see Equation (1) and Figure 6), have generated peak accelerations higher than 0.5%g [6,9]. This trend was confirmed in several other situations [1,2], where the human comfort criterion was violated.

In sequence, Figure 12 presents the composite floor vibration modes when total and parti‐ al interaction situations were considered in the numerical analysis. It must be emphasized that the composite floor vibration modes didn't present significant modifications when the connections flexibility and steel-concrete interaction was changed. It must be empha‐ sized that the structural model presented vibration modes with predominance of flexural

**Figure 12.** Investigated structural model vibration modes (total and partial interaction).

The present study proceeded with the evaluation of the structural model performance in terms of human comfort and vibration serviceability limit states. The peak acceleration anal‐ ysis was focused in aerobics and considered a contact period carefully chosen to simulate

The present work considered a contact period, simulating aerobics on the composite floor, Tc, equal to 0.34s (Tc = 0.34s) and the period without contact with the structure, Ts, of 0.10s (Ts = 0.10s). Based on the experimental results [7], the floor dynamic behaviour was evaluat‐ ed keeping the impact coefficient value, Kp, equal to 2.78 (Kp = 2.78). Figures 13 and 14 illus‐ trate the dynamic response (displacements and accelerations) related to nodes A and B (see

Based on the results presented in Figures 13and 14, it is possible to verify that the dynamic actions coming from aerobics, represented by the dynamic loading model (see Equation (1)

Figure 6) when thirty two people are practising aerobics on the composite floor.

**5.2. Maximum accelerations (peak accelerations) analysis**

this human rhythmic activity on the analysed composite floor.

effects, as illustrated in Figure 12.

294 Advances in Vibration Engineering and Structural Dynamics

**Figure 13.** Composite floor dynamic response. Semi-rigid connections and partial interaction): Node A.

**Figure 14.** Composite floor dynamic response (Semi-rigid connections and partial interaction): Node B.

In sequence of the study, Tables 6 and 7 show the peak accelerations, ap (m/s2 ), correspond‐ ing to nodes A to H (Figure 6), when thirty two dynamic loadings, simulating individual practising aerobics were applied on the composite floor.


**Table 6.** Composite floor peak accelerations: Nodes A, B, C and D (see Figure 6).


enabled a complete dynamic evaluation of the investigated steel-concrete composite floor especially in terms of human comfort and its associated vibration serviceability limit states.

An Analysis of the Beam-to-Beam Connections Effect and Steel-Concrete Interaction Degree Over the Composite

The influence of the investigated connectors (Stud Bolts: 13mm and 19mm) on the compo‐ site floor natural frequencies was very small, when the steel-concrete interaction degree (from total to partial) was considered in the analysis. The largest difference was approxi‐

On the other hand, when the joints flexibility (rigid to flexible) and steel-concrete interac‐ tion degree (from total to partial) decreases the composite floor natural frequencies be‐ come smaller. This fact is very relevant because the system becomes more susceptible to

The composite floor vibration modes didn't present significant modifications when the con‐ nections flexibility and steel-concrete interaction was changed. The investigated structure presented vibration modes with predominance of flexural effects. The results have indicated that when the joints flexibility (rigid to flexible) and steel-concrete interaction degree (total

(alim = 0.50m/s2

lead to a violation of the current human comfort criteria for these specific structures.

Pedro Colmar Gonçalves da Silva Vellasco, Luciano Rodrigues Ornelas de Lima,

ations were compared to the limiting values proposed by several authors and design standard [6,9]. The current investigation indicated that human rhythmic activities could induce the steel-concrete composite floors to reach unacceptable vibration levels and, in these situations,

The authors gratefully acknowledge the support for this work provided by the Brazilian Sci‐

, Sebastião Arthur Lopes de Andrade,

(ap = 0.80 m/s2

http://dx.doi.org/10.5772/51672

297

: semi-rigid model), while the maximum accepted peak

) [6,9]. The structural system peak acceler‐

: flexi‐

to partial) decreases the composite floor peak accelerations become larger.

The maximum acceleration value found in this work was equal to 0.80m/s2

(ap = 0.63 m/s2

mately equal to 5% to 7%.

excessive vibrations.

ble model) and 0.63m/s2

**Acknowledgements**

**Author details**

José Guilherme Santos da Silva\*

acceleration value is equal to 0.50m/s2

ence Foundation CAPES, CNPq and FAPERJ.

\*Address all correspondence to: jgss@uerj.br

Elvis Dinati Chantre Lopes and Sidclei Gomes Gonçalves

State University of Rio de Janeiro (UERJ), Rio de Janeiro-RJ, Brazil

**Table 7.** Composite floor peak accelerations: Nodes E, F, G and H (see Figure 6).

The results presented in Tables 6 and 7 have indicated that when the joints flexibility (rigid to flexible) and steel-concrete interaction degree (total to partial) decreases the composite floor peak accelerations become larger. These variations (joints flexibility and steel-concrete interaction) were very relevant to the composite floor non-linear dynamic response when the human comfort analysis was considered.

It must be emphasized that individuals practising aerobics on the structural model led to peak acceleration values higher than 5%g [6,9], when the composite floor was submitted to thirty two people practising aerobics, violating the human comfort criteria (amax = 0.50m/s2 > alim = 0.50m/s2 ), see Tables 6 and 7. However, these peak acceleration values tend to decrease when the floor dynamic response obtained on the nodes E to H (see Figure 6) was compared to the response of nodes A to D (see Figure 6), see Tables 6 and 7.
