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STRUCTURAL DESIGN - PART 18

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28. Results of the seismic analysis


The following table lists the steps and the sub-steps used in the non-linear analysis for each seismic load combination.

Prevailing earthquake along Z

Prevailing earthquake along X

Prevailing earthquake along Y

%

load step

Sub

Step

%

load step

Sub

Step

%

load step

Sub

Step

100% Gravity

 

1

 

1

100% Gravity

 

1

 

1

100% Gravity

 

1

 

1

10%

Earthq.

 

2

 

1

10%

Earthq.

 

2

 

1

10%

Earthq.

 

2

 

1

20%

Earthq.

 

3

 

1

20%

Earthq.

 

3

 

1

20%

Earthq.

 

3

 

1

30%

Earthq.

 

4

 

1

30%

Earthq.

 

4

 

1

30%

Earthq.

 

4

 

1

40%

Earthq.

 

5

 

4

40%

Earthq.

 

5

 

5

40%

Earthq.

 

5

 

2

50%

Earthq.

 

6

 

10

50%

Earthq.

 

6

 

5

50%

Earthq.

 

6

 

2

60%

Earthq.

 

7

 

10

60%

Earthq.

 

7

 

10

60%

Earthq.

 

7

 

5

70%

Earthq.

 

8

 

20

70%

Earthq.

 

8

 

10

70%

Earthq.

 

8

 

5

80%

Earthq.

 

9

 

20

80%

Earthq.

 

9

 

15

80%

Earthq.

 

9

 

10

90%

Earthq.

 

10

 

25

90%

Earthq.

 

10

 

15

90%

Earthq.

 

10

 

10

100%

Earthq.

 

11*

 

*

100%

Earthq.

 

11

 

20

100%

Earthq.

 

11

 

10

110%

Earthq.

 

12*

 

*

110%

Earthq.

 

12

 

20

110%

Earthq.

 

12

 

15

120%

Earthq.

 

13*

 

*

120%

Earthq.

 

13

 

30

120%

Earthq.

 

13

 

15

130%

Earthq.

 

14*

 

*

130%

Earthq.

 

14

 

30

130%

Earthq.

 

14

 

20

140%

Earthq.

 

15*

 

*

140%

Earthq.

 

15

 

30

140%

Earthq.

 

15

 

20

* Load steps not performed because the structure collapsed in the preceding steps.

At the Load Step no. 15 the 140 % of the seismic load is reached (corresponding to the importance factor g I = 1.4).

 


29. Results for the load combination with prevailing earthquake along Z


In this load combination the bridge is loaded in its weakest direction.

The bridge collapses before reaching the total design seismic load, at the load step no. 10 and sub-step no. 24, reaching the 89.6% of the total seismic load (without the importance factor). The bridge can resist against an horizontal acceleration of 0.314 g, as the spectral ordinate of the main mode of vibration is 0.35 g.

Load-displacement diagram for the crown section (displacements in cm)

The structure behaves linearly up to the load step no. 7, after the overall stiffness reduces. The following figures show the principal stresses S3, S2 and S1.

 

S3 Assonometric view at the load step no. 10 and sub-step no. 24

S3 Extrados and intradox at load Step no. 10 and sub-step no. 24

S2 Extrados and intradox at load Step no. 10 and sub-step no. 24

S1 Extrados and intradox at load Step no. 10 and sub-step no. 24

 


29. Results for the load combination with prevailing earthquake along X


In this load combination the bridge is loaded in its longitudinal direction. The bridge can support the whole design seismic load in this direction (included the importance factor).

The analysis reaches the load step no. 15 and the sub-step no. 30.

The bridge can resist an horizontal acceleration of 0.49 g, as the spectrum ordinate of the mode of vibration considered is equal to 0.35 g.

Load-displacement diagram of the cross section (displacements in 10-1 cm)

The bridge behaves linearly up to the load step no. 10, later at the load step no. 11 the yield load is reached, with a reduction of the overall stiffness.

The following figures show the principal stresses S3, S2 and S1.

 

S3 Assonometric view at load step no. 15 e sub-step no. 30

Under this load combination the bridge assumes the typical anti-symmetrical configuration.

 

S3 Extrados and intradox at the load step no. 15 and sub-step no. 30

In the previous figures it appears clearly how the tractions induced by the dead loads in the intradox of the bridge are increased by this seismic load combination.

 

S2 Extrados and intradox at the load step no. 15 and sub-step no. 30

S1 Extrados and intradox at the load step no. 15 and sub-step no. 30

 


30. Results for the load combination with prevailing earthquake along Y


The bridge can support the whole design seismic load in this direction (included the importance factor).

The arch tends to be unloaded and loses partly its capacity of "redistribution and confining" of the tractions due to the seismic components in the X and Z directions (present with a factor of 0.3).

The analysis stops at the load step no. 15 and sub-step no. 20, reaching the total design load.

The bridge can resist a vertical deceleration of 0.294 g, as the maximum spectrum ordinate of the considered mode of vibration is 0.21 g.

Load-displacement diagram of the crown (displacements in cm)

The bridge behaves linearly up to the load step no. 11, later at the load step no. 12 the yield load is reached and the overall stiffness decreases.

The following figures show the principal stresses S3, S2 and S1.

 

S3 Assonometric view at the load step no. 15 and sub-step no. 20

S3 Extrados (top) and intradox (below) at the load step no. 15 and sub-step no. 20

 

S2 Extrados (top) and intradox (below) at the load step no. 15 and sub-step no. 20

S1 Extrados (top) and intradox (below) at the load step no. 15 and sub-step no. 20


CREDITS:

Intellectual property of this report and of the design drawings is owned by the University of Florence - Department of Civil Engineering

author of the text: Prof.Eng. Andrea Vignoli other contributes have been mentioned in related paragraphs

- General Engineering Workgroup -

SOURCE:

Final Design Report

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