Influence of mechanical properties material on ...

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characteristics of a reinforced concrete bridge with was presented. The numerical model of the bridge was. The two-coefficient Mooney-Rivlin constitutive model.
Influence of mechanical properties of concrete and elastomeric material on dynamic characteristics of RC bridge Joanna M. Dulińska1, Radosław Szczerba2 1

2

Cracow University of Technology, Technology Warszawska 24, 31-155 Cracow, Poland Rzeszow University of Technology,, al. Powstancow Warszawy 12, 35-959, Poland emails: [email protected] .edu.pl,[email protected]

Słowa kluczowe: reinforced concrete bridge, bridge dynamic characteristics, elastomeric bearings, Poisson’s ratio, ABAQUS

1. Introduction In the paper the analysis of dynamic characteristics of a reinforced concrete bridge with steel-laminated elastomeric bearings was presented. The numerical model of the bridge was created with the Abaqus software. The two-coefficient two Mooney-Rivlin constitutive model for hyperelastic non-linear linear elastomeric material was replaced with equivalent linear model. A comparative analysis of the natural frequencies obtained for different mechanical properties of concrete and elastomeric materials was carried out. It was proved that the natural frequencies of the bridge strongly depended depend on the Poisson’s ratio of elastomeric bearings.

2. FE model of bridge with steel--laminated elastomeric bearings For calculations of dynamic characteristics of RC bridge with steel-laminated elastomeric bearings the ABAQUS program was used [1]. [ The FE model of the bridge was based on the geometry of an existing structure erected in a region of mining activity in Poland. The length of the central bridge span was 26.1 26 m. The three piers of 2.95 m high with a diameter of 1.1 m were located regularly at a distance of 3.75 m. The abutments were situated 7.05 m away from the extreme piers. The fixed boundary conditions reflected the high rigidity of the foundation rock. The reinforced concrete was assumed to be homogeneous and linear-elastic elastic material. The 3D numerical model of the bridge was discretized by 58843 tetrahedral 10-node node finite elements [2]. Fig. 1 shows the model of the bridge.

tric view and the location of elastomeric bearings at the tops Fig. 1. Model of the bridge: the axonometric of the columns

The length and the width of the elastomeric bearing were assumed 0.6 m. It was composed of two steel cover plates, each 20 mm thick, between which elastomeric laminae reinforced with steel shims were placed. The thickness of one elastomeric layer was assumed 8 mm, the thickness of one steel reinforcement was 3 mm. Fig. 2 presents the elastomeric bearing.

Fig. 2. Model of steel-laminated elastomeric bearing [mm]

3. Dependence of dynamic characteristics of the bridge on mechanical properties of materials Firstly, the dependence of the natural frequencies on the modulus of elasticity of the concrete material was analyzed. The Poisson's ratio was assumed as 0.17. The mass density of the concrete material was chosen as 2400 kg/m3. The following data were introduced: modulus of elasticity E = 27 GPa (concrete C25/30), modulus of elasticity E = 34 GPa (concrete C35/45), modulus of elasticity E = 44 GPa (concrete C90/105). The influence of the elasticity modulus on the natural frequencies is shown in Table 1. Tab. 1. The influence of the elasticity modulus on the natural frequencies. Frequency [Hz]

Frequency no.

E = 27 GPa

E = 34 GPa

E = 44 GPa

1

3.6

4.0

4.3

2

5.7

6.5

7.1

3

8.0

8.7

9.3

4

10.4

11.6

12.6

5

12.4

14.2

15.7

Secondly, the dependence of the natural frequencies on the Poisson’s ratio of elastomeric bearings was examined. The Mooney-Rivlin constitutive model for hyperelastic non-linear elastomeric material was replaced with the equivalent linear model. The values of Poisson’s ratio varied from 0.452 to 0.49995 [3]. Table 2 presents the influence of Poisson’s ratio of bearings on the natural frequencies of the bridge. Tab. 2. The influence of the Poisson’s ratio of elastomeric bearings on the natural frequencies. Frequency [Hz]

Frequency no.

ν = 0.452

ν = 0.475

ν = 0.490

ν = 0.495

v0.4995

ν = 0.49995

1

3.2

3.5

4.0

4.3

4.7

4.8

2

5.9

6.1

6.5

6.848

7.5

7.7

3

6.7

7.4

8.7

9.787

11.3

11.6

4

10.4

10.8

11.6

12.563

14.7

14.8

5

12.5

13.2

14.2

14.456

14.8

15.3

The modes of vibrations (from the first to the fourth) are presented in Fig. 3.

Fig. 3. Subsequent modes of vibrations of the bridge.

4. Conclusions On the basis of the comparative analysis concerning the influence of different properties of concrete and elastomeric materials the following conclusions could be formulated: 1. The usage of the alternative modulus of elasticity of concrete material resulted in some minor changes in the natural frequencies. The increase in the elasticity modulus of the concrete material caused the increase in natural frequencies up to 20%. For the highest values of Poisson’s ratio even the increase of 50% in the natural frequencies occurred in comparison with the lowest values of Poisson’s ratio. 2. Neither the elasticity modulus of the concrete material nor the Poisson’s ratio of the elastomeric bearings affected the modes of vibrations very much. The shape of particular modes remained nearly the same.

References 1. 2.

3.

ABAQUS, (2010), Users Manual V. 6.10-1, Dassault Systemes Simulia Corp., Providence, RI. Dulinska J.M. and Szczerba R.: Simulation of dynamic behaviour of RC bridge with steellaminated elastomeric bearings under high-energy mining tremors, Key Engineering Materials, Trans Tech Publications, Switzerland, Vol. 531–532, 2013, pp. 662-668, doi:10.4028/ www.scientific.net/KEM.531-532.662. Buckle I., Nagarajaiah S., Ferrell K., Stability of Elastomeric Isolation Bearings: Experimental Study, Journal of Structural Engineering, Vol. 128, no. 1, 2002, p. 3-11.