MODELLING AND VIBRATION ANALYSIS OF REINFORCED …

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MODELLING AND VIBRATION ANALYSIS OF REINFORCED

CONCRETE BRIDGE

Shivanandan T N*1, Meghashree M*2

*1PG Student, Department Of Civil Engineering, Dayananda Sagar College Depart Of Engineering,

Bengaluru, Karnataka, India.

*2Assistant Professor, Department Of Civil Engineering Dayananda Sagar College Of Engineering,

Bengaluru, Karnataka, India.

ABSTRACT

As catastrophic bridge collapse accidents not only cause significant loss of property, but also have a severe

social impact. Therefore, the structural health monitoring of bridges for damage detection by vibration analysis

gets more attention. Reinforced concrete bridges are the most common and extended structures present in the

worldwide. These structures are often characterized by Piers, Abutments, deck slabs. This paper looks on the

work of modelling and analysis of bridge in STAAD.Pro software, and the specific bridge model is taken of a

particular span. It is subjected to vary Young’s modulus (E) in the mid span of bridge deck slab to induce

damage in order to obtain maximum bending moment, as the structural strength reduces. From the analysis

Mu/bd2 values from SP 16 code is used to identify the damage on the bridge deck slab, then natural frequency of

the bridge, mode shapes, variation of the deflection and node displacements of bridge deck slab under the

action of static and dynamic load at different aspect ratios with original design parameters and at failure is

carried out in this project.

Keywords: Natural Frequency, Mode Shapes, Maximum Bending Moment, Deflection, Node Displacement.

I. INTRODUCTION

Roads are the lifelines of contemporary transport and bridges are the foremost vital elements of transportation

systems. They are prone to failure if their structural deficiencies are remain unidentified. Due to aging of

existing bridges and the increasing traffic loads, monitoring of bridge deck slab during service time has become

more important than ever. The structural health monitoring of bridge refers to the process of implementing a

damage detection and characterization strategy. There is a need for Structural health monitoring techniques to

supplement visual inspections as more bridges are in need of in-depth assessments and ongoing monitoring to

ensure they are still fit for purpose. Vibration monitoring is a useful evaluation tool in the development of a

non-destructive damage identification technique, and relies on the fact that occurrence of damage in a

structural system leads to changes in its dynamic properties. The dynamic response of bridges subjected to

moving loads has long been an interesting topic in the field of civil engineering. The load-bearing capacity of a

bridge and its structural behavior under traffic can be evaluated using well-established modelling. Among the

tools available today for structural investigation, dynamic techniques play an important role from several

points of view. Particularly, by measuring the structural response, they allow us to identify the main

parameters governing the dynamic behavior of a bridge, namely natural frequencies, mode shapes and

damping factors. Modal analysis, usually based on finite element method, is commonly used to determine the

vibration characteristics, such as natural frequencies and associated mode shapes of a structure

II. METHODOLOGY

Modeling methodology:

First Assessment of Load on the bridge as per IRC-6-2017 section Ⅱ specifications.

Creating model of the bridge using STAAD.pro software.

Material Properties and Load Modelling:

Properties for Deck slab concrete is taken as E= 25 x 10 6 kN/m2; µ= 0.17; ρ= 25 kN/m3. The dead load contains

of self-weight of the whole structure. This is accounted through geometrical properties of sections and unit

weight of materials used. The primary live load on Highway Bridge is of the cars moving on it. Indian Roads

Congress (IRC) recommends different kinds of widespread hypothetical vehicular loading systems in IRC





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6:2017, for which a bridge is to be designed. The vehicular live load consists of a set wheel loads which can be

distributed over small areas of contacts of wheels and form patch loads and dealt with as concentrated loads

acting at centres of contact areas. This will acquire the maximum response resultants for the layout, different

positions of every type of loading system as per IRC 6:2017 is tried at the bridge deck. The load is moved

longitudinally and transversely in small steps to occupy a large number of various positions on the deck. The

largest force reaction is obtained at each node. As per IRC 6:2017 , 2 lane of class A or one lane of class 70R

should be considered to get most response under hypothetical vehicular loading systems.

Analysis methodology:

Analyzing the model for static and dynamic loading (vibration analysis) for different aspect ratios.

STATIC ANALYSIS

Typical simply supported two- lane bridge study cases are considered in this study. Aspect ratios of 0.50,

1.01, 1.52, and 2.03 are considered as parameters of deck slab of 0.7m thickness. The aspect ratios

considered for analysis are shown in Table.

Table 1: Shows the Aspect Ratios along the bridge.

Length in m (L) Breadth in m (B) Aspect ratio (L/B)

0 8.45 0

4.3 8.45 0.50

8.6 8.45 1.01

12.9 8.45 1.52

17.2 8.45 2.03

By varying the material property of the structure such as young’s modulus of concrete (E) in percentages

of 5, 10, 15, 20, 25in the bridge deck slab imposing/inducing damage to the structure and locating it.

Using maximum bending moment getting from the bridge model in the Mu/bd2 value from SP 16 code

analyzing the model for damage.

Variation of mode shapes, fundamental frequencies, node displacements are to be found out.

III. MODELING AND ANALYSIS

Modelling using STAAD.pro V8i SS6 Software

STAAD pro is a robust program that can profoundly intensify analytical and design abilities of engineer’s for

structures. Functioning of simple or complex structures under stationary or dynamic states can be checked

using STAAD pro. Instinctive and unified traits make implementations of any complicated practical problem to

implement. For this bridge, plate modelling has been considered and STAAD.Pro has been used for further

process.

Structural details

Parameters

1. RCC Deck Slab of Span 8.6m(Each slab)

2. Length of abutment/ width of the bridge 8.45m

3. Height of the bridge above nala bed projection 4.0m

4. Thickness of the abutment 0.5m

5. Thickness of the deck slab 0.7m

6. Live load considered for design is as per IRC 70R, and Class A-2 lane

Dead load=636.70 KN (from SP 20 2002 Plate No- 7.10 Page No 162)

Live load=635.00 KN

7. Grade of concrete M-30

8. Grade of steel Fe 500





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Load estimation

Dead load

It includes self-weight, weights of finishes. A self-weight multiplier of one which means to add the entire self-

weight of the building in the load case.

Self-weight of the structural members will be considered as given in the below Table 1.2 on the basis of IS: 875

(Part 1)-1987 code.

Table 2: Density of materials

Self-weight of plain concrete 24kN/m3

Density of RCC 25kN/m3

Self-weight of un compacted soil 20kN/m3

Density of steel 78.50kN/m3

Live load

Live load comprises of those loads whose position or magnitude or both may change, the live load on deck slab

is taken as vehicular load. Live load includes 70R Wheeled, 70R Tracked, 40T Bogie loads, out of which Class A-

2 lane loads are placed on carriageway for analysis. These live loads are placed on carriageway for the analysis,

based on carriageway width and number of lanes.

Live load considered for design is as per IRC Class A-2 lane. This loading is normally adopted on all roads on

which permanent bridges and culverts are constructed. This type of loadings are considered for bridges having

Carriageway width 5.3m and above but less than 9.6m.

Figure 1: shows the vehicular load considered as per IRC 6 2017

Frequency calculation load

For frequency calculation, self-weight in X, Y, Z directions is assigned.

Pressure on full plate is calculated and assigned on the deck slab as plate load in Global X, Y, and Z Directions.

Pressure on the full plate=total axle load on the deck slab/cross sectional area of the deck slab

Pressure on the full plate= (27+27+114+114+68+68+68)/ (17.2x8.45)

Pressure on the full plate=486/145.34

Pressure on the full plate=3.34kN/m2

Structural frame models

The plan and the 3D view of the model developed using STAAD.Pro software is shown in Fig.

Figure 2: Reinforced concrete bridge grid model





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Figure 3: 3D view of Reinforced Concrete Bridge

Figure 4: Bridge under the action of static load/ self-weight.

Bridge model under the dynamic loading. i.e., under the action of vehicular load at different aspect

ratios.

Figure 5: Bridge model under the dynamic loading at the aspect ratio of 0

Figure 6: Bridge model under the dynamic loading at the aspect ratio 0.50

Figure 7: Bridge model under the dynamic loading at the aspect ratio of 1.01





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Figure 10: Bridge model under the natural frequency calculation load

ANALYSIS

Pre analysis checks Before analysing the model, it should be checked to know whether there is any error. Then

the model should be rectified until no errors come.

Post analysis checks After a model is analysed by STAAD.Pro it is very important to check the basic

characteristics of the model.

The Maximum Bending moment in the deck slab under original design properties is noted and Mu/bd2 from SP

16 code provision for percentage of steel in tension and compression is considered.

The associated mode shapes, frequencies, and node displacement in the deck slab with the original design

properties are noted/considered for analysis.

For inducing damage/failure on the bridge deck slab, the Young’s modulus of concrete (E is reduced in

percentages of 5, 10, 15, 20, 25,.etc. ) is changed in the mid span section of the bridge deck slab.

Under reduced Young’s modulus of concrete (E is reduced in percentages of 5, 10, 15, 20, 25,.etc. ) in the deck

slab of the bridge and due to change in strength property of concrete, the change in the maximum bending

moment in the deck slab at each percentage of reduction of young’s modulus of concrete(E) is noted and

considered for analysis.

The failure occurring in the deck slab of the bridge at particular percentage of reduced young’s modulus of

concrete (E) is identified by comparing Mu/bd2 value of the deck slab under original design properties with that

of the Mu/bd2 value of the deck slab under reduced Young’s modulus of concrete (E is reduced in percentages of

5, 10, 15, 20, 25,.etc. ) in the deck slab of the bridge.

Then, the associated mode shapes, frequencies, and node displacement in the deck slab with the reduced

Young’s modulus of concrete (E is reduced in percentages of 5, 10, 15, 20, 25,.etc. ) in the deck slab of the bridge





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is compared with that of the associated mode shapes, frequencies, and node displacement in the deck slab with

the original design properties.

For analysis part only part of the bridge deck slab of dimensions, length (L) 17.2m and breadth (B) 8.45m is

considered under 2 lane class A type of loading.

The maximum bending moment, mode shapes and their associated frequencies of the bridge deck slab

under the original properties

Table 3: shows the maximum bending moment in the bridge at original design properties.

Plate number MX kNm/m

559 307.495

223 302.67

604 -301.0799

585 279.291

239 277.415

607 -264.874

249 -264.345

240 257.426

596 256.923

258 253.946

252 236.601

276 236.558

Maximum bending moment in the bridge is 307.495kN-m/m.

Mu =307.495x8.6=2644.457 kN-m

Mu/bd2obtained=( 2644.457x106) / (1000x6502)

=6.26 N/mm2

From SP 16 for M 25 grade concrete and Fe 415 grade steel, for 2 way reinforced deck slab

For d1/d=(50/650)=0.0769 say 0.10

Where,

d1=cover=50mm

d= effective depth=700-50=650mm

For Pt=2.102 and Pc=0.961,

Mu/bd2=6.4 N/mm2> Mu/bd2obtained , hence safe.





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Figures 11: shows the modeshapes of the bridge under the action of dynamic load.

Table 4: shows the frequency of the mode shapes associated with it.

Frequency(Hz) Period (seconds)

13.510 0.074

18.265 0.055

19.938 0.050

23.351 0.043

42.434 0.024

Figure 12: shows the variation of the frequency v/s time graph at 0% 0f E reduction

0

5

10

15

20

25

30

35

40

45

0.07402 0.05475 0.05015 0.04282 0.02357

Fre

qu

en

cy(H

ert

z)

Time(Sec)

Frequency





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Analysis of the bridge under varied/ reduced young’s modulus (E) of the concrete

Checking for Mu/bd2 value under 25% of E reduced in the deck slab of bridge.

Table 5: shows the maximum bending moment in the bridge at 25% of E reduction

Plate MX kNm/m

240 -316.295

565 308.078

561 303.441

563 279.967

258 -279.106

545 -273.792

587 258.097

567 257.414

588 254.525

Maximum bending moment in the bridge is 316.295kN-m/m.

Mu =316.295x8.6=2720.137 kN-m

Mu/bd2obtained=( 2720.137x106) / (1000x6502)

=6.4382 N/mm2

From SP 16 for M 25 grade concrete and Fe 415 grade steel, for 2 way reinforced deck slab

For d1/d=(50/650)=0.0769 say 0.10

Where,

d1=cover=50mm

d= effective depth=700-50=650mm

For Pt=2.102 and Pc=0.961,

Mu/bd2=6.4 N/mm2< Mu/bd2obtained , hence the bridge is failing at 25% of E reduction

Table 6: shows the frequency associated with the mode shapes at the 25% 0f E reduction

Frequency (Hz) Period (Seconds)

12.929 0.07735

17.772 0.05627

19.592 0.05104

23.03 0.04342

41.169 0.02429

Figure 13: shows the variation of the frequency v/s time graph at 25% 0f E reduction

0

10

20

30

40

50

Frequency (Hz) vs Period (sec)

Frequency(Hz)vs Period(sec)





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Table 7: Deflection in the bridge deck slab before and after failing

Deflection values in the bridge under 0% and 25% E reduction

Node Y-Trans mm Absolute mm Node Y-Trans mm Absolute mm

496 -2.613 2.613 496 -2.623 2.623

498 -2.586 2.586 498 -2.595 2.595

494 -2.505 2.505 494 -2.516 2.516

500 -2.469 2.469 500 -2.477 2.477

497 -2.289 2.289 193 -2.476 2.476

492 -2.276 2.276 191 -2.471 2.471

499 -2.274 2.274 195 -2.34 2.34

193 -2.209 2.209 189 -2.329 2.329

495 -2.201 2.201 497 -2.299 2.299

191 -2.198 2.198 492 -2.286 2.286

502 -2.179 2.179 499 -2.283 2.283

501 -2.151 2.151 495 -2.211 2.211

195 -2.098 2.098 502 -2.187 2.187

189 -2.071 2.071 501 -2.159 2.159

493 -2.023 2.023 192 -2.154 2.154

521 -2.003 2.003 194 -2.146 2.146

490 -1.995 1.995 197 -2.119 2.119

522 -1.988 1.988 187 -2.118 2.118

520 -1.932 1.932 190 -2.06 2.06

Variation of Node displacement of plate node number 240 in the bridge at 0% and 25% E reduction

under the action of loads.

At 0% of E reduction (Table 8)

Table 8: shows the node displacement values under static and dynamic loads at different aspect ratios

LOAD CASE Horizontal x Vertical y Horizontal z Resultant

1 SELF WEIGHT 0 -0.329 -0.002 0.329

2 LOAD GENERATION, LOAD #2 -0.001 -0.567 -0.011 0.567

3 LOAD GENERATION, LOAD #3 0.004 -0.041 -0.013 0.043

4 LOAD GENERATION, LOAD #4 0.006 0.278 -0.007 0.278


6 LOAD GENERATION, LOAD #6 0 0 0 0

7 FREQUENCY CALCULATION

LOAD 0.052 0.35 0.123 0.375

At 25% of E reduction (Table 9)





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Table 9: shows the node displacement values under static load and dynamic loads at different aspect ratios

Table 10: Variation of the node displacement due to static load and dynamic loads at different aspect ratios

LOAD CASE Resultant at 0% Resultant at 25% difference in %

1 SELF WEIGHT 0.329 0.372 13.06

2 LOAD GENERATION, LOAD #2 0.567 0.625 10.23




6 LOAD GENERATION, LOAD #6 0 0 0

7 FREQUENCY CALCULATION LOAD 0.375 0.418 11.46

IV. RESULTS AND DISCUSSION 1. The model of the solid slab bridge is done using STAAD.pro V8i (select series 6) software as per the design

details are available. The bridge in this project is analysed under the live load of class A 2-lane load. These

live loads are placed on carriageway for the analysis, based on carriageway width and number of lanes.

2. After the model is checked for the error free, the Mu/bd2 value= 6.4 N/mm2 is considered as reference, for

two way reinforced deck slab from SP 16 code for the percentage of steel in the deck slab in tension and

compression.(i.e., for Pt=2.102 and Pc=0.961)

3. A trial and error method is applied to induce damage/failure on the bridge deck slab by changing/reducing

the young’s modulus of the concrete (E) in percentages of 5, 10, 15, 20, 25 in the mid-span section of the

deck slab. Then, the obtained Mu/bd2 value of 6.261 N/mm2, 6.263 N/mm2, 6.3 N/mm2,6.4382 N/mm2 at

5,10,15,20,25 percentage of E reduction respectively are compared to Mu/bd2 reference value obtained

from SP 16 code.

4. It is noticed that the bridge deck slab fails at the 25% of E reduction in the deck slab of bridge. The Mu/bd2

obtained at 25% of E reduction is greater than the reference value of the Mu/bd2.

i.e. (Mu/bd2 obtained =6.4382 N/mm2) > (reference value of the Mu/bd2=6.4 N/mm2)

5. At the failure it is observed that there is slight reduction in the frequency of vibration with respect to the

time period and there is significant increase in the deflection and node displacement values.

6. The maximum deflection in the bridge under original design parameters is 2.613mm, 2.586mm, 2.505mm…,

at the nodes 496, 498, 494 .., respectively. And the change in deflection values at the 25% of E reduction in

the bridge deck slab is 2.623, 2.595, 2.516.., respectively.

7. After the failure occurs at the node number 240, the difference in the node displacement value of the node

number 240 before and after failing under the action of static load is 13.06%. While, the difference in node

displacement value under the dynamic/live load at the aspect ratios 0, 0.50, 1.01, 1.52, 2.03 is 10.23, 16.27,

5.035, 4.6875, 0 percentages(%) respectively.

8. The frequency of vibration associated with the mode shapes of the bridge under original design parameters

is 13.510, 18.265, 19.938, 23.351, 42.434 Hz respectively. While, the frequency associated with the mode

LOAD CASE Horizontal x Vertical y Horizontal z Resultant

1 SELF WEIGHT 0 -0.372 -0.002 0.372

2 LOAD GENERATION, LOAD #2 -0.002 -0.625 -0.011 0.625

3 LOAD GENERATION, LOAD #3 0.004 -0.048 -0.013 0.05



6 LOAD GENERATION, LOAD #6 0 0 0 0

7 FREQUENCY CALCULATION LOAD 0.055 0.395 0.123 0.418





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shapes of the bridge under failure or at 25% of E reduction in the bridge deck slab is 12.929, 17.772, 19.592,

23.03, 41.169 Hz respectively. It is noticed that there is a slight variation in the frequency of vibration at

failure.

V. CONCLUSION 1. In the present study the bridge investigated is solid slab bridge with abutment type piers, under the self-

weight and live load considered of class A 2-lane type of vehicular load as per IRC: 6-2017 section Ⅱ, this

code book mainly deals with loads and load combinations for bridges. It specifies the different types of loads

and their combinations to be considered in the design of a bridge.

2. In this project damage/ failure identification in the bridge deck slab is done by Mu/bd2 values getting for

maximum bending moment in the deck slab from SP 16 code.

3. The difference in the node displacement value of the node number 240 before and after failing under the

action of static load is 13.06%. While, the difference in node displacement value under the dynamic/live

load at the aspect ratios 0, 0.50, 1.01, 1.52, 2.03 is 10.23, 16.27, 5.035, 4.6875, 0 percentages(%)

respectively.

4. The study can be extended to other types of RCC and PSC bridges with different live loads, and with other

combination of loads such as braking loads, impact loads, temperature loads and earth pressure as per IRC:

6-2017 section Ⅱ code.

5. The study can also be done on bridge piers and abutments by formulating appropriate methodology.

VI. REFERENCES [1] D. H. K. B. K. Han, “Simple Method of Vibration Analysis of Three Span Continuous Reinforced Concrete

Bridge with Elastic Intermediate Support.pdf,” pp. 23–28, 2004.

[2] N. H. Hamid, M. S. Jaafar, and N. S. U. Othman, “Analysis of Multi-column Pier of Bridge Using STAAD.Pro

Under Static and Dynamic Loading,” InCIEC 2015, pp. 169–182, 2016, doi: 10.1007/978-981-10-0155-

0.

[3] P. K. C. T. K. D. C. S. Surana, “Vibration of continuous bridges under moving vehicles,” J. Sound Vib., pp.

619–632, 1994.

[4] T. J. Memory, D. P. Thambiratnam, and G. H. Brameld, “Free vibration analysis of bridges,” Eng. Struct.,

vol. 17, no. 10, pp. 705–713, 1995, doi: 10.1016/0141-0296(95)00037-8.

[5] F. T. K. Au, Y. S. Cheng, and Y. K. Cheung, “Vibration analysis of bridges under moving vehicles and

trains: an overview,” Prog. Struct. Eng. Mater., vol. 3, no. 3, pp. 299–304, 2001, doi: 10.1002/pse.89.

[6] J. Maeck and G. De Roeck, “Damage assessment using vibration analysis on the Z24-bridge,” Mech. Syst.

Signal Process., vol. 17, no. 1, pp. 133–142, 2003, doi: 10.1006/mssp.2002.1550.

[7] M. Roopa, H. Venugopal, and T. G. Nischay, “Static and Vibration Analysis of Bridge Deck Slabs.”

[8] P. S. Bhil, “Vibration Analysis of Deck Slab Bridge,” Int. Res. J. Eng. Technol., vol. 6, no. 8, pp. 667–670,

2015.

[9] Y. S. Cheng, F. T. K. Au, and Y. K. Cheung, “Vibration of railway bridges under a moving train by using

bridge-track-vehicle element,” Eng. Struct., vol. 23, no. 12, pp. 1597–1606, 2001, doi: 10.1016/S0141-

0296(01)00058-X.

[10] Z. Zhu, L. Wang, Z. Yu, W. Gong, and Y. Bai, “Non-Stationary Random Vibration Analysis of Railway

Bridges under Moving Heavy-Haul Trains,” Int. J. Struct. Stab. Dyn., vol. 18, no. 3, pp. 1–21, 2018, doi:

10.1142/S0219455418500359.

IRC CODES

[11] IRC 6-2017 - Section Ⅱ loads and load combinations

[12] IRC 112-2019 – Code of practice for concrete road bridges.

[13] SP 16 – Design aids for Reinforced concrete to IS456.

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