**2. Dynamic Loading Induced by Human Rhythmic Activities**

The description of the dynamic loads generated by human activities is not a simple task. The individual characteristics in which each individual perform the same activity and the existence of external excitation are key factors in defining the dynamic action charac‐ teristics. Numerous investigations were made aiming to establish parameters to describe such dynamic actions [1-6].

Several investigations have described the loading generated by human activities as a Fourier series, which consider a static part due to the individual weight and another part due to the dynamic load [1-6]. The dynamic analysis is performed equating one of the activity harmon‐ ics to the floor fundamental frequency, leading to resonance.

This study have considered the dynamic loads obtained by Faisca [7], based on the results achieved through a long series of experimental tests with individuals carrying out rhythmic and non-rhythmic activities. The dynamic loads generated by human rhythmic activities, such as jumps, aerobics and dancing were investigated by Faisca [7].

The loading modelling was able to simulate human activities like aerobics, dancing and free jumps. In this paper, the Hanning function was used to represent the human dynamic actions. The Hanning function was used since it was verified that this mathematical representation is very similar to the signal force obtained through experimental tests developed by Faisca [7].

The mathematical representation of the human dynamic loading using the Hanning func‐ tion is given by Equation (1) and illustrated in Figure 1. The required parameters for the use of Equation (1) are related to the activity period, T, contact period with the structure, Tc, pe‐ riod without contact with the model, Ts, impact coefficient, Kp, and phase coefficient, CD. Figure 2 and the Table 1 illustrate the phase coefficient variation, CD, for human activities studied by Faisca [7], considering a certain number of individuals and later extrapolated for large number of peoples. Table 2 presents the experimental parameters used for human rhythmic activities representation and Figure 3 presents examples of dynamic action related to human rhythmic activities investigated in this work.

$$\begin{aligned} F(t) &= CD \left\{ K\_{\rho} P \left[ 0.5 - 0.5 \cos \left( \frac{2\pi}{T\_c} t \right) \right] \right\} \\ F(t) &= 0 \end{aligned} \tag{1}$$

When *t* ≤*Tc*

When *Tc* ≤*t* ≤*T*

Where:

Considering all aspects mentioned before, the main objective of this paper is to investigate the beam-to-beam connections effect (rigid, semi-rigid and flexible) and the influence of steel-concrete interaction degree (from total to various levels of partial interaction) over the non-linear dynamic behaviour of composite floors when subjected to human rhythmic activ‐ ities [1,2]. This way, the dynamic loads were obtained through experimental tests with indi‐ viduals carrying out rhythmic and non-rhythmic activities such as stimulated and nonstimulated jumping and aerobic gymnastics [7]. Based on the experimental results, human

The investigated structural model was based on a steel-concrete composite floor spanning

site floor of a commercial building. The composite floor studied in this work is supported by steel columns and is currently submitted to human rhythmic loads. The structural system is

The proposed computational model adopted the usual mesh refinement techniques present in finite element method simulations, based on the ANSYS program [8]. This numerical model enabled a complete dynamic evaluation of the investigated steel-concrete composite floor es‐ pecially in terms of human comfort and its associated vibration serviceability limit states.

Initially, all the composite floor natural frequencies and vibration modes were obtained. In sequence, based on an extensive parametric study, the floor dynamic response in terms of peak accelerations was obtained and compared to the limiting values proposed by several authors and design codes [6,9]. An extensive parametric analysis was developed focusing in the evaluation of the beam-to-beam connections effect and the influence of steel-concrete in‐ teraction degree over the investigated composite floor non-linear dynamic response, when

The structural system peak accelerations were compared to the limiting values proposed by several authors and design standards [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, lead to a violation of the current human comfort cri‐

The description of the dynamic loads generated by human activities is not a simple task. The individual characteristics in which each individual perform the same activity and the existence of external excitation are key factors in defining the dynamic action charac‐ teristics. Numerous investigations were made aiming to establish parameters to describe

Several investigations have described the loading generated by human activities as a Fourier series, which consider a static part due to the individual weight and another part due to the

**2. Dynamic Loading Induced by Human Rhythmic Activities**

. The structural system consisted of a typical compo‐

load functions due to rhythmic and non-rhythmic activities are proposed [7].

constituted of composite girders and a 100mm thick concrete slab [1,2].

40m by 40m, with a total area of 1600m2

284 Advances in Vibration Engineering and Structural Dynamics

submitted to human rhythmic activities.

teria for these specific structures.

such dynamic actions [1-6].

F(t): dynamic loading (N);

t: time (s);

T: activity period (s);

Tc: activity contact period (s);

P: person's weight (N);

Kp: impact coefficient;

CD: phase coefficient

**Activity T (s) Tc (s) Kp** Free Jumps 0.44±0.15 0.32±0.09 3.17±0.58 Aerobics 0.44±0.09 0.34±0.09 2.78±0.60 Show 0.37±0.03 0.37±0.03 2.41±0.51

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

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

287

**Table 2.** Experimental parameters used for human rhythmic activities representation [7].

**Figure 3.** Dynamic loading induced by human rhythmic activities.

The investigated structural model was based on a steel-concrete composite floor spanning

site floor of a commercial building. The floor studied in this work is supported by steel col‐ umns and is currently submitted to human rhythmic loads. The model is constituted of

The steel sections used were welded wide flanges (WWF) made with a 345MPa yield stress

MPa Young's modulus was adopted for the steel beams. The concrete

composite girders and a 100mm thick concrete slab [1,2], see Figures 4 and 5.

. The structural system consisted of a typical compo‐

**3. Investigated Structural Model**

40m by 40m, with a total area of 1600m2

steel grade. A 2.05x105

**Figure 1.** Representation of the dynamic loading induced by human rhythmic activities.

**Figure 2.** Variation of the phase coefficient CD for human rhythmic activities [7].


**Table 1.** Numeric values adopted for the phase coefficient CD [7].

An Analysis of the Beam-to-Beam Connections Effect and Steel-Concrete Interaction Degree Over the Composite http://dx.doi.org/10.5772/51672 287


**Table 2.** Experimental parameters used for human rhythmic activities representation [7].

**Figure 3.** Dynamic loading induced by human rhythmic activities.

## **3. Investigated Structural Model**

**Figure 1.** Representation of the dynamic loading induced by human rhythmic activities.

286 Advances in Vibration Engineering and Structural Dynamics

**Figure 2.** Variation of the phase coefficient CD for human rhythmic activities [7].

**Table 1.** Numeric values adopted for the phase coefficient CD [7].

**People number Aerobics gymnastics Free Jumps** 1 1 1 3 1 0.88 0.97 0.74 0.96 0.70 0.95 0.67 0.94 0.64 0.93 0.62 0.92 0.60

The investigated structural model was based on a steel-concrete composite floor spanning 40m by 40m, with a total area of 1600m2 . The structural system consisted of a typical compo‐ site floor of a commercial building. The floor studied in this work is supported by steel col‐ umns and is currently submitted to human rhythmic loads. The model is constituted of composite girders and a 100mm thick concrete slab [1,2], see Figures 4 and 5.

The steel sections used were welded wide flanges (WWF) made with a 345MPa yield stress steel grade. A 2.05x105 MPa Young's modulus was adopted for the steel beams. The concrete slab has a 30MPa specified compression strength and a 2.6x104 MPa Young's Modulus. Ta‐ ble 3 depicted the geometric characteristics of the steel beams and columns.

The human-induced dynamic action was applied on the aerobics area, see Figure 6. The com‐ posite floor dynamic response, in terms of peak accelerations values, were obtained on the no‐ des A to H, in order to verify the influence of the dynamic loading on the adjacent slab floors, as illustrated in Figure 8. In this investigation, the dynamic loadings were applied to the structur‐

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

), according to reference [5]. The load distribution was considered symmetrically cen‐ tred on the slab panels, as depicted in Figure 8. It is also assumed that an individual person weight is equal to 800N (0.8kN) [5]. In this study, the damping ratio, ξ=1% (ξ = 0.01) was

(0.25 per‐

289

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

al model corresponding to the effect of thirty two individuals practising aerobics.

**Figure 6.** Dynamic loading: thirty two individuals practising aerobics on the investigated floor.

The proposed computational model, developed for the composite floor dynamic analysis, adopted the usual mesh refinement techniques present in finite element method simula‐ tions implemented in the ANSYS program [8]. The present investigation considered that both materials (steel and concrete) have an elastic behaviour. The finite element model is

In this computational model, all "I" steel sections, related to beams and columns, were repre‐ sented by three-dimensional beam elements (BEAM44 [8]) with tension, compression, torsion and bending capabilities. These elements have six degrees of freedom at each node: transla‐

On the other hand, the reinforced concrete slab was represented by shell finite elements (SHELL63 [8]). This finite element has both bending and membrane capabilities. Both inplane and normal loads are permitted. The element has six degrees of freedom at each node: translations in the nodal x, y, and z directions and rotations about the nodal x, y,

tions in the nodal x, y, and z directions and rotations about x, y, and z axes, see Figure 8.

son/m2

considered for all cases [5].

**4. Finite Element Modelling**

illustrated in Figure 7.

and z axes, see Figure 8.

The live load considered in this analysis corresponds to one person for each 4.0m2

**Figure 4.** Structural model: composite floor (steel-concrete). Dimensions in (mm).


**Figure 5.** Cross section of the generic models. Dimensions in (mm).


**Table 3.** Geometric characteristics of the building composite floor (mm).

The human-induced dynamic action was applied on the aerobics area, see Figure 6. The com‐ posite floor dynamic response, in terms of peak accelerations values, were obtained on the no‐ des A to H, in order to verify the influence of the dynamic loading on the adjacent slab floors, as illustrated in Figure 8. In this investigation, the dynamic loadings were applied to the structur‐ al model corresponding to the effect of thirty two individuals practising aerobics.

The live load considered in this analysis corresponds to one person for each 4.0m2 (0.25 per‐ son/m2 ), according to reference [5]. The load distribution was considered symmetrically cen‐ tred on the slab panels, as depicted in Figure 8. It is also assumed that an individual person weight is equal to 800N (0.8kN) [5]. In this study, the damping ratio, ξ=1% (ξ = 0.01) was considered for all cases [5].

**Figure 6.** Dynamic loading: thirty two individuals practising aerobics on the investigated floor.
