feras temimi m.sc. presentation in structural engineering

Dynamic Analysis of Curved

Cellular Type Bridge DecksM.Sc. Thesis in Structural Engineering

By Feras Abdul Redha Abdul Razaq Al_Temimi

Supervisor Prof. Dr. Adnan Falih Ali

University of Baghdad

College of Engineering

Civil Engineering Department

Republic of Iraq

Ministry of Higher Education

&Scientific Research

Introductiono The continuing expansion of highway networks throughout the world is largely the result

of great increase in traffic, population and extensive growth of metropolitan urban areas.

This expansion has led to many changes in the use and development of various kinds

of bridges.

o This study presents a simplified procedure for developing an idealization of curved cellular type

bridge decks under free vibration and dynamic loads caused by earthquake base excitation.

o In the current study, the F.E.M analyses were carried out using (ANSYS) program, in addition to

the mathematical analysis using (MATLAB) program by based on the available procedure

by using the proposed algorithm of the new idealization technique. Comparison was made between

them to check the adequacy and suitability of the proposed element in analyzing the

cellular concrete bridge decks.

This new idealization technique should be doing through the following verifications:

o To study the effects of variation of several parameters on the dynamic behavior of curved cellular bridge

decks, these are: free vibration response analysis and earthquake response analysis.

o To carry out parametric studies showing the effect of varies configurations on the behavior of curved

cellular bridge decks, such as: (number of cells, web to flange thicknesses ratio, number of diaphragms

and live load).

o In addition to study the effects of some other parameters, such as: (element type, mesh size and

the cross-section area), on the behavior of curved cellular bridge decks.

Objective and Scope The primary objective of the present work is to develop a new simplified procedure and an alternative

reliable idealization technique for dynamic and earthquake response analysis of curved cellular bridge decks.

So, different configurations of cellular bridge decks will be studied to evaluate the dynamic behavior and

the maximum response.

Case Studies There are four primary case studies of cross-section area of curved box-girder bridges that are modeled in

the current study. The description of these case studies are as follows:

1. Case Study No. (1):

Rectangular single cellular curved box-girder bridge.


Rectangular double cellular curved box-girder bridge.

Case Studies3. Case Study No. (3):

Trapezoidal single cellular curved box-girder bridge.


Trapezoidal double cellular curved box-girder bridge.

Element Type: Two structural elements are modeled using finite element method (FEM). One is the main and other for verification. The description of these elements that are used for modeling are as follows:

1. SHELL63 (Elastic Shell) Element: (6 d.o.f / node) 2. Beam4 (3-D Elastic Beam) Element: (6 d.o.f / node)

Finite Element Modeling

Finite Element Modeling Meshing and Bridge Model:

The description of the curved box-girder bridge models that are studied, are as follows:

1. Curved Box Beam Model: Two main models that modeled by Beam4 element, as shown in figures below:

a- Typical Cantilever Curved Box Beam Model b- Typical Simply Supported Curved Box Beam Model

Finite Element Modeling2. Curved Box Shell Model:

There are four main models that modeled by SHELL63 element, once as cantilever and twice as simply supported (partially and fully restrained), as shown in figures below:

a- Typical Rectangular Single-Cellular Curved Box Shell Model b- Typical Rectangular Two-Cellular Curved Box Shell Model

i- Rectangular Cross-Section Curved Box Shell Model

Finite Element Modeling

c- Typical Trapezoidal Single-Cellular Curved Box Shell Model d- Typical Trapezoidal Two-Cellular Curved Box Shell Model

ii- Trapezoidal Cross-Section Curved Box Shell Model

Material Properties:The important material properties of concrete

models are (Linear, Elastic and Isotropic) that are used

in the studied cases which are shown in Table beside:

No. Material Properties Values

1 Elastic Modulus ( E ) 23.5 x 109 N/mm2

2 Weight Density ( γ ) 2500 Kg/m3

3 Poisson's Ratio ( υ ) 0.20

Development of the Panel Element (PE)

Panel Element Method

The new idealization technique is

based on a new element called "Panel Element

(PE)", which is capable of representing in -plane

and out-of-plane shear and flexural stiffness, in

two orthogonal directions, axial stiffness in

addition to the coupled torsional warping

stiffness through few local and global degrees-of-

freedom (d.o.f).

The description of the Panel Element (PE), and the Panel Element Method (PEM) that are proposed as

an idealization procedure for modeling the curved cellular type bridge decks, is as follows:

Span Length Mesh Size

Finite Element Method(FEM)

Panel Element Method(PEM)

No. of Elements No. of d.o.f No. of

Elements No. of d.o.f

20 mCoarse 16 120

16 55Fine 900 5520

30 mCoarse 24 168

24 77Fine 1320 8040

Several case studies concerning different bridge deck configurations were carried out to highlight the accuracy and reliability of the proposed idealization procedure (Panel Element Method (PEM)) in evaluating the behavior of cellular decks compared with Finite Element Method (FEM). The comparison of number of elements and d.o.f are as follows:

Program Verification

Length of Span

No. of Cells Mesh Size





Single CellCoarse 16 120

16 55Fine 900 5520

Double CellCoarse 28 180

28 80Fine 1728 10290

1. Effect of Number of Cells Variation: (NP = 4, ts=tw= 0.3 m, 20 m)

2. Effect of Span Length Variation: (NP = 4 and 6, ts=tw= 0.3 m, 20 and 30 m)

Program Verification

Length of Span

3. Effect of (Web Thickness : Slab Thickness) Ratio: (NP = 4, ts = 0.2 m, tw = 0.1, 0.2, 0.3 and 0.4 m, 20 m)

tw/tsRatio No. Of Cell





0.5Single 16 120 16 55Double 28 180 28 80

1Single 16 120 16 55Double 28 180 28 80

1.5Single 16 120 16 55Double 28 180 28 80

2Single 16 120 16 55Double 28 180 28 80

4. Effect of (No. of Diaphragms : Span) Ratio: (NP = 2, 4, 6 and 10, ts = tw = 0.3 m, 20 m)

No. of Panels No. Of Cell





2Single 8 72 8 33Double 14 108 14 48

4Single 16 120 16 55Double 28 180 28 80

6Single 24 168 24 77Double 42 252 42 112

10Single 40 264 40 121Double 70 396 70 176

Parametric Studies

1. Effect of Number of Cells:

No. of Cells(Rectangular)

AnalysisMethod

Type

Natural Frequency (ω) in ( Hz )

Mode No.

1 2 3 4 5

1FEM 2.915 3.671 14.724 18.718 21.250

PEM 2.97 3.71 15.44 17.82 22.32

2FEM 2.987 6.211 14.218 16.826 26.713

PEM 3.02 6.23 14.56 16.90 27.76

No. of Cells(Trapezoidal)

AnalysisMethod

Type

Natural Frequency (ω) in ( Hz )

Mode No.

1 2 3 4 5

1FEM 2.901 4.740 14.252 18.801 22.722

PEM 2.97 4.96 15.3 19.03 21.70

2FEM 2.969 7.048 13.509 15.623 28.564

PEM 2.99 7.08 13.72 16.52 29.97

I- Free Vibration Analysis: The proposed Panel Element idealization procedure (PE) is validated by

the free vibration response analysis of cellular bridge decks in different configurations, as follows:

To provide a better idea about the behavior of curved box girder bridge, some parametric studies are carried out

including four main factors, in addition to secondary factors, are as follows:

Applications To Free Vibration Analysis2. Effect of (Web Thickness : Slab Thickness) Ratio:

0 0.5 1 1.5 2 2.50

2

4

6

8

10

12

14

16

FEM

PEM

tw/ts ratio

Freq

uenc

y (H

z)

Mode No. 1

0 0.5 1 1.5 2 2.50

2

4

6

8

10

12

14

16

18

20

FEM

PEM

tw/ts ratio

Freq

uenc

y (H

z)

Mode No. 2

0 0.5 1 1.5 2 2.50

5

10

15

20

25

FEM

PEM

tw/ts ratio

Freq

uenc

y (H

z)

Mode No. 3

0 0.5 1 1.5 2 2.50

5

10

15

20

25

FEM

PEM

tw/ts ratio

Freq

uenc

y (H

z)

Mode No. 4

0 0.5 1 1.5 2 2.514

16

18

20

22

24

26

28

30

32

FEM

PEM

tw/ts ratio

Freq

uenc

y (H

z)

Mode No. 5

0 0.5 1 1.5 2 2.50

2

4

6

8

10

12

14

16

18

20

FEM

PEM

tw/ts ratio

Freq

uenc

y (H

z)

Mode No. 1

0 0.5 1 1.5 2 2.50

5

10

15

20

FEM

PEM

tw/ts ratio

Freq

uenc

y (H

z)

Mode No. 2

0 0.5 1 1.5 2 2.50

5

10

15

20

25

FEM

PEM

tw/ts ratio

Freq

uenc

y (H

z)

Mode No. 3

0 0.5 1 1.5 2 2.50

5

10

15

20

25

30

FEM

PEM

tw/ts ratio

Freq

uenc

y (H

z)

Mode No. 4

0 0.5 1 1.5 2 2.50

5

10

15

20

25

30

35

40

FEM

PEM

tw/ts ratio

Freq

uenc

y (H

z)

Mode No. 5

Single-Cell (Partially Restrained)

Single-Cell (Fully Restrained)

Applications To Free Vibration Analysis

0 0.5 1 1.5 2 2.50

5

10

15

20

25

FEM

PEM

tw/ts ratio

Freq

uenc

y (H

z)

Mode No. 4

0 0.5 1 1.5 2 2.50

5

10

15

20

25

30

35

40

FEM

PEM

tw/ts ratio

Freq

uenc

y (H

z)

Mode No. 5

0 0.5 1 1.5 2 2.50

2

4

6

8

10

12

14

16

18

20

FEM

PEM

tw/ts ratio

Freq

uenc

y (H

z)

Mode No. 2

0 0.5 1 1.5 2 2.50

5

10

15

20

25

FEM

PEM

tw/ts ratio

Freq

uenc

y (H

z)

Mode No. 3

0 0.5 1 1.5 2 2.510

10.5

11

11.5

12

12.5

13

FEM

PEM

tw/ts ratio

Freq

uenc

y (H

z)

Mode No. 1

0 0.5 1 1.5 2 2.50

2

4

6

8

10

12

14

16

18

20

FEM

PEM

tw/ts ratio

Freq

uenc

y (H

z)

Mode No. 1

0 0.5 1 1.5 2 2.50

2

4

6

8

10

12

14

16

18

20

FEM

PEM

tw/ts ratio

Freq

uenc

y (H

z)

Mode No. 2

0 0.5 1 1.5 2 2.50

5

10

15

20

25

30

FEM

PEM

tw/ts ratio

Freq

uenc

y (H

z)

Mode No. 3

0 0.5 1 1.5 2 2.50

5

10

15

20

25

30

FEM

PEM

tw/ts ratio

Freq

uenc

y (H

z)

Mode No. 4

0 0.5 1 1.5 2 2.50

5

10

15

20

25

30

35

40

FEM

PEM

tw/ts ratio

Freq

uenc

y (H

z)

Mode No. 5

Double-Cell (Partially Restrained)

Double-Cell (Fully Restrained)

Applications To Free Vibration Analysis3. Effect of Number of Diaphragms (Panels):

0 2 4 6 8 10 120

2

4

6

8

10

12

14

16

FEM

PEM

No. of Panels

Freq

uenc

y (H

z)

Mode No. 1

0 2 4 6 8 10 120

5

10

15

20

25

30

FEM

PEM

No. of Panels

Freq

uenc

y (H

z)

Mode No. 2

0 2 4 6 8 10 120

5

10

15

20

25

30

35

40

45

FEM

PEM

No. of Panels

Freq

uenc

y (H

z)

Mode No. 3

Single-Cell (Partially Restrained)

0 2 4 6 8 10 120

10

20

30

40

50

60

FEM

PEM

No. of Panels

Freq

uenc

y (H

z)

0 2 4 6 8 10 120

10

20

30

40

50

60

FEM

PEM

No. of Panels

Freq

uenc

y (H

z)

Mode No. 4 Mode No. 5

0 2 4 6 8 10 120

5

10

15

20

25

30

FEM

PEM

No. of Panels

Freq

uenc

y (H

z)

Single-Cell (Fully Restrained)

Mode No. 1

0 2 4 6 8 10 120

5

10

15

20

25

30

35

40

FEM

PEM

No. of Panels

Freq

uenc

y (H

z)

Mode No. 2

0 2 4 6 8 10 120

10

20

30

40

50

60

FEM

PEM

No. of Panels

Freq

uenc

y (H

z)

Mode No. 3

0 2 4 6 8 10 120

10

20

30

40

50

60

70

FEM

PEM

No. of Panels

Freq

uenc

y (H

z)

Mode No. 5

0 2 4 6 8 10 120

10

20

30

40

50

60

FEM

PEM

No. of Panels

Freq

uenc

y (H

z)

Mode No. 4


0 2 4 6 8 10 120

2

4

6

8

10

12

14

16

FEM

PEM

Panels No.

Freq

uenc

y (H

z)

0 2 4 6 8 10 120

5

10

15

20

25

30

FEM

PEM

No. of Panels

Freq

uenc

y (H

z)

Mode No. 2

Double-Cell (Partially Restrained)

Mode No. 1

0 2 4 6 8 10 120

5

10

15

20

25

30

35

40

45

FEM

PEM

No. of Panels

Freq

uenc

y (H

z)

Mode No. 3

0 2 4 6 8 10 120

5

10

15

20

25

30

35

40

45

50

FEM

PEM

No. of Panels

Freq

uenc

y (H

z)

Mode No. 4

0 2 4 6 8 10 120

5

10

15

20

25

30

35

40

45

50

FEM

PEM

No. of Panels

Freq

uenc

y (H

z)

Mode No. 5

0 2 4 6 8 10 120

5

10

15

20

25

30

FEM

PEM

Panels No.

Freq

uenc

y (H

z)

Double-Cell (Fully Restrained)

Mode No. 1

0 2 4 6 8 10 120

5

10

15

20

25

30

35

40

FEM

PEM

Panels No.

Freq

uenc

y (H

z)

Mode No. 2

0 2 4 6 8 10 120

5

10

15

20

25

30

35

40

45

50

FEM

PEM

Panels No.

Freq

uenc

y (H

z)

Mode No. 3

0 2 4 6 8 10 120

10

20

30

40

50

60

FEM

PEM

Panels No.

Freq

uenc

y (H

z)

Mode No. 4

0 2 4 6 8 10 120

10

20

30

40

50

60

FEM

PEM

Panels No.

Freq

uenc

y (H

z)

Mode No. 5

Applications To Free Vibration Analysis4. Effect of Live Load:

Load Case No.AnalysisMethod

Type

Natural Frequency (ω) in ( Hz )Mode No. (Single-Cell, Partially)

1 2 3 4 5

IFEM 10.800 18.910 20.339 20.616 21.231

PEM 10.85 18.96 20.87 22.91 26.04

IIFEM 10.609 18.576 19.980 20.252 20.856

PEM 10.58 18.62 21.21 22.12 22.99

IIIFEM 10.543 18.461 19.856 20.127 20.727

PEM 10.60 18.50 25.92 22.02 23.71


Type

Natural Frequency (ω) in ( Hz )Mode No. (Single-Cell, Fully)

1 2 3 4 5

IFEM 17.977 19.138 20.532 20.723 22.744

PEM 18.04 19.19 21.74 21.97 25.17

IIFEM 17.660 18.800 20.169 20.357 22.342

PEM 17.68 18.73 22.02 23.29 24.40

IIIFEM 17.551 18.684 20.044 20.231 22.204

PEM 17.59 18.73 23.15 22.20 25.61


Type

Natural Frequency (ω) in ( Hz )Mode No. (Double-Cell, Partially)

1 2 3 4 5

IFEM 11.302 17.762 19.677 19.968 20.756

PEM 11.32 17.71 20.95 22.45 25.90

IIFEM 11.206 17.612 19.511 19.799 20.581

PEM 11.23 17.58 20.60 21.51 22.76

IIIFEM 11.170 17.556 19.448 19.736 20.515

PEM 11.18 17.52 21.29 18.95 23.81


Type

Natural Frequency (ω) in ( Hz )Mode No. (Double-Cell, Fully)

1 2 3 4 5

IFEM 17.344 18.022 19.755 19.978 21.940

PEM 17.35 17.99 20.36 22.59 24.25

IIFEM 17.198 17.870 19.589 19.810 21.755

PEM 17.17 17.89 20.64 16.25 24.26

IIIFEM 17.142 17.813 19.526 19.746 21.685

PEM 17.17 17.78 21.54 21.49 25.48

Notes: I- Lane Loading. II- Military Loading C100 (Tracked). III- Military Loading C100 (Wheeled).


Mode Shapes of a Single-Cell Cantilever Curved Bridge Deck Model:

First Mode Third ModeSecond Mode Forth Mode Fifth Mode

Mode Shapes of a Double-Cell Cantilever Curved Bridge Deck Model:


Typical Mode Shapes of Models:


Mode Shapes of a Single-Cell Simply Supported Curved Bridge Deck Model (Fully Restrained):


Mode Shapes of a Double-Cell Simply Supported Curved Bridge Deck Model (Fully Restrained):


Applications To Seismic Analysis

1. Effect of Number of Cells:

2. Effect of (Web Thickness : Slab Thickness) Ratio:

No. of Cells

(X-dir.)

AnalysisMethod

(Cantilever)

Max. Bending Moment Max. Shear ForceMax.

Deflection (mm)Abs.

(kN.m)Nor. tom* (m)

Nor. tom* x L Abs. (kN) Nor. to

m*

1PEM 750.600 0.543 0.027 95.969 0.069 1.837

FEM 705.600 0.510 0.026 92.369 0.067 1.639

2PEM 691.992 0.275 0.014 91.152 0.036 1.312

FEM 614.742 0.244 0.012 75.672 0.030 1.273

No. of Cells

(Y-dir.)

AnalysisMethod

(Cantilever)

Max. Bending Moment Max. Shear ForceMax.

Deflection (mm)Abs.

(kN.m)Nor. tom* (m)


m*

1PEM 1056.912 0.764 0.038 407.235 0.295 5.700

FEM 1016.064 0.735 0.037 404.571 0.293 5.535

2PEM 1023.383 0.407 0.020 325.925 0.130 4.869

FEM 756.133 0.301 0.015 315.773 0.126 4.077

tw/ts(X-dir.)

AnalysisMethod(Fully)

Max. Bending Moment Max. Shear Force Max. Deflection

(mm)Abs.

(kN.m)Nor. tom* (m)


m*

0.5 PEM 1437.96 0.658 0.022 255.6 0.117 0.545FEM 1294.8 0.593 0.020 249 0.114 0.521

1 PEM 1720.8 0.661 0.022 333.6 0.128 0.561FEM 1572.6 0.604 0.020 320.4 0.123 0.485

1.5 PEM 2053.2 0.679 0.023 411.6 0.136 0.627FEM 1848.6 0.612 0.020 393.6 0.130 0.587

2 PEM 2413.56 0.701 0.023 493.2 0.143 0.700FEM 2124 0.617 0.021 464.4 0.135 0.637

tw/ts(Y-dir.)



(mm)Abs.

(kN.m)Nor. tom* (m)


m*

0.5 PEM 2313.6 1.059 0.035 784.8 0.359 3.548FEM 2106 0.964 0.032 669.6 0.307 3.311

1 PEM 2642.4 1.015 0.034 817.2 0.314 3.564FEM 2432.4 0.934 0.031 789.6 0.303 3.333

1.5 PEM 3154.8 1.044 0.035 1012.8 0.335 3.795FEM 2808 0.929 0.031 942 0.312 3.429

2 PEM 3624 1.053 0.035 1221.6 0.355 3.861FEM 3189.6 0.927 0.031 1108.8 0.322 3.590

II- Earthquake Response Analysis: Also, the proposed Panel Element idealization procedure (PE) is validated

by the earthquake response analysis of cellular bridge decks in different configurations. as follows:

Applications To Seismic Analysis3. Effect of Number of Diaphragms (Panels):

No. of Panels(X-dir.)

AnalysisMethod

(Partially)


(mm)Abs.

(kN.m)Nor. tom* (m)


m*

2 PEM 4209.6 1.116 0.037 1543.68 0.409 1.007FEM 3494.16 0.926 0.031 1157.76 0.307 0.931

4 PEM 3799.2 1.007 0.034 1607.04 0.426 0.957FEM 3229.2 0.856 0.029 1285.74 0.341 0.898

6 PEM 4022.4 1.066 0.036 1725.408 0.457 1.040FEM 3600 0.954 0.032 1449.36 0.384 0.980

10 PEM 4233.96 1.122 0.037 1778.544 0.471 1.092FEM 3895.2 1.032 0.034 1598.94 0.424 1.053

No. of Panels(X-dir.)



(mm)Abs.

(kN.m)Nor. tom* (m)


m*

2 PEM 2495.4 0.661 0.022 853.2 0.226 0.564FEM 2088.6 0.554 0.018 649.2 0.172 0.515

4 PEM 2401.92 0.637 0.021 866.16 0.230 0.591FEM 2082.24 0.552 0.018 689.04 0.183 0.558

6 PEM 2600.06 0.689 0.023 877.8 0.233 0.627FEM 2314.08 0.613 0.020 741.96 0.197 0.607

10 PEM 2720.4 0.721 0.024 918 0.243 0.653FEM 2498.4 0.662 0.022 787.8 0.209 0.650

No. of Panels(Y-dir.)

AnalysisMethod

(Partially)


(mm)Abs.

(kN.m)Nor. tom* (m)


m*

2 PEM 4500 1.193 0.040 1810.8 0.480 7.194FEM 3744 0.992 0.033 1379.556 0.366 6.402

4 PEM 4094.64 1.085 0.036 1829.232 0.485 6.930FEM 3542.04 0.939 0.031 1459.2 0.387 6.376

6 PEM 4572.18 1.212 0.040 1819.2 0.482 7.326FEM 4046.4 1.072 0.036 1568.34 0.416 7.029

10 PEM 4923.72 1.305 0.043 1954.08 0.518 7.755FEM 4432.8 1.175 0.039 1666.8 0.442 7.590

No. of Panels(Y-dir.)



(mm)Abs.

(kN.m)Nor. tom* (m)


m*

2 PEM 3226.8 0.855 0.029 1159.56 0.307 2.313FEM 2665.32 0.706 0.024 932.4 0.247 2.099

4 PEM 2966.04 0.786 0.026 1182.06 0.313 2.247FEM 2506.36 0.664 0.022 980.16 0.260 2.049

6 PEM 4423.4 1.172 0.039 1207.08 0.320 2.412FEM 2868.84 0.760 0.025 1055.7 0.280 2.300

10 PEM 3487.32 0.924 0.031 1234.8 0.327 2.534FEM 3145.68 0.834 0.028 1122 0.297 2.492

Applications To Seismic Analysis4. Effect of Live Load:

Notes: I- Lane Loading. II- Military Loading C100 (Tracked). III- Military Loading C100 (Wheeled).

Load Case No.(X-dir.)

AnalysisMethod

(Partially)


(mm)Abs. (kN.m)

Nor. tom* (m)


m*

IPEM 5731.8 1.519 0.051 1232.04 0.327 2.109FEM 5210.4 1.381 0.046 1207.44 0.320 1.888

IIPEM 6022.08 1.596 0.053 1030.224 0.273 1.700FEM 4938.12 1.309 0.044 958.2 0.254 1.630

IIIPEM 5915.16 1.568 0.052 1136.16 0.301 1.766FEM 4968.72 1.317 0.044 1068.12 0.283 1.729

Load Case No.(X-dir.)



(mm)Abs. (kN.m)

Nor. tom* (m)


m*

IPEM 4045.68 1.072 0.036 1037.64 0.275 1.234FEM 3277.32 0.869 0.029 1006.56 0.267 1.135

IIPEM 3027.96 0.802 0.027 764.604 0.203 0.825FEM 2685.6 0.712 0.024 703.44 0.186 0.749

IIIPEM 3566.88 0.945 0.032 924.84 0.245 1.095FEM 3192.48 0.846 0.028 884.76 0.234 1.013

Load Case No.(Y-dir.)

AnalysisMethod

(Partially)


(mm)Abs. (kN.m)

Nor. tom* (m)


m*

IPEM 5513.64 1.461 0.049 1920.24 0.509 10.655FEM 4907.16 1.301 0.043 1862.64 0.494 9.863

IIPEM 5549.76 1.471 0.049 1617.6 0.429 8.642FEM 4883.76 1.294 0.043 1486.44 0.394 7.850

IIIPEM 5487.24 1.454 0.048 1769.88 0.469 9.137FEM 4883.76 1.294 0.043 1633.68 0.433 8.642

Load Case No.(Y-dir.)



(mm)Abs. (kN.m)

Nor. tom* (m)


m*

IPEM 5316.3 1.409 0.047 1670.4 0.443 7.458FEM 4620 1.224 0.041 1656.6 0.439 7.029

IIPEM 5432.4 1.440 0.048 1383.48 0.367 7.029FEM 4666.8 1.237 0.041 1342.08 0.356 6.534

IIIPEM 5144.76 1.364 0.045 1542 0.409 7.117FEM 4665.6 1.237 0.041 1503.6 0.398 6.798

To According to the case studies considered in the present research, the major conclusions are as follows:

Conclusions

1) The Panel Element Method (PEM) of idealizing curved cellular type bridge decks is valid for the dynamic

analysis of free vibration and earthquake response of almost all-practical deck configurations, which are

considered.

2) The number of equations and iterations are largely reduced and hence less error is encountered since No. (d.o.f)

is limited.

3) Free vibration response can be evaluated accurately and through less computational efforts, because the (d.o.f)

are elimination.

4) The natural frequencies are more sensitive to the change in No. of diaphragms, that is, convergence of solution

is reached faster than finite element (FE) approach.

5) The Panel Element Method (PEM) has proved to be valid in estimating the earthquake response for both cells types.

6) The results obtained by the Panel Element Method (PEM) are acceptable for all the ranges of the aspect ratios.

It is recommended to investigate the efficiency of the proposed Panel Element Method (PEM)

idealization scheme in the following cases as future works:

Recommendations for Future Works

1) A parametric study on the effect of the number of the interior webs on the deflection, stresses developed

within the bridge.

2) Cases of continuous curved box-girder bridges, and torsional effect due to eccentricity of the loading.

3) Investigate the soil-structure interaction problem during strong earthquake motions.

4) It is recommended also to study the effect of geometric and material nonlinearities on the earthquake

response analysis of curved cellular box-girder bridges.

5) Finally, it is recommended that more different configuration of curved cellular box-girder bridge decks

are to be studied, such as, those with pre-stressed concrete.

Dynamic Analysis of Curved

Cellular Type Bridge DecksM.Sc. Thesis in Structural Engineering

By Feras Abdul Redha Abdul Razaq Al_Temimi

Supervisor Prof. Dr. Adnan Falih Ali

University of Baghdad

College of Engineering

Civil Engineering Department

Republic of Iraq

Ministry of Higher Education

&Scientific Research

feras temimi m.sc. presentation in structural engineering

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