INTERNATIONAL JOURNAL OF CIVIL AND STRUCTURAL ENGINEERING Volume 3, No 3, 2013

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1 INTERNATIONAL JOURNAL OF CIVIL AND STRUCTURAL ENGINEERING Volume 3, No 3, 2013 Copyright by the authors - Licensee IPA- Under Creative Commons license 3.0 Research article ISSN Dynamic analysis of T-Beam bridge Supriya Madda 1, Kalyanshetti M.G 2 1- Post graduate student, Walchand Institute of Technology,Solapur, India. 2- Assistant Professor, Civil Engineering Department, Walchand Institute of Technology, Solapur, India. supriya.madda@gmail.com doi: /ijcser ABSTRACT Generally, structures are subjected to two types of load: static and dynamic. However, the majority of civil engineering structures are designed with the assumption that all applied loads are static. The effect of dynamic load is not considered because the structure is rarely subjected to dynamic loads; more so, its consideration in analysis makes the solution more complicated and time consuming. This feature of neglecting the dynamic forces may sometimes become the cause of disaster, particularly in the case of earthquake. Nowadays, there is a growing interest in the process of designing structures capable to withstand dynamic loads, particularly, earthquake-induced load. This is needed to be done, because, in present scenario where earthquakes are occurring frequently, dynamic force cannot be neglected. Therefore it is proposed to do dynamic analysis of bridge deck for various span of bridge by varying no. of longitudinal girders. The detailed study is carried out for T- Beam Bridge, for two lane and four lane of spans 15m, 20m, 25m, 30m, 35m using IRC class A loading. For analysis SAP2000 software is used. Finally, to envelope the serviceability, the bridge responses are obtained. Keyword: Longitudinal girder, dynamic analysis, T-beam bridge, SAP2000, IRC class A. 1. Introduction For ordinary structures, static analysis is sufficient but for important structures particularly for bridges, dynamic analysis needs to be carried out. Because, it provides an accurate measure of expected structural response for a given earthquake or any kind vibrations and also it ensures a simple and direct load path is provided for each frame. One of the aspects to be considered while assessing the dynamic response of bridges subjected to live loads is the problem of vibration. The passage of any load over a bridge causes the span to deflect from the equilibrium position, causing a series of oscillations. This phenomenon continues till either the structure comes back to its equilibrium position or is again activated by the passage of another load. Therefore, dynamic behaviour of bridge deck needs to be studied. Using IRC Class A loading bridge responses such as Bending Moment (BM) and deflection are obtained to assess the serviceability. Further, with the help of SAP2000 software dynamic analysis is done by Response Spectrum Method to obtain dynamic parameters such as natural frequency and time period. This study aims at interpreting the output from the dynamic analysis of the computer model of the bridge in order to check the resonance criteria. 1.1 Indian Road Congress The Indian Road Congress (IRC) has formulated standard specifications and codes of practice for road bridges with a view to establish a common procedure for the design and construction of road bridges in India. The specifications are collectively known as the Bridge code. Prior Received on January 2013 Published on March

2 to the formation of the IRC bridge code, there was no uniform code for the whole country. Each state (or province) had its own rules about the standard loading and stresses. The Indian Roads Congress (IRC) Bridge code as available now consists of eight sections as below: 1. Section-I : General features of design 2. Section-II : Loads and stresses 3. Section-III : Cement concrete (Plain and reinforced) 4. Section-IV : Brick, stone and block masonry 5. Section-V : Steel road bridges 6. Section-VI : Composite construction 7. Section-VII : Foundations and Substructures 8. Section-VIII: Bearings 1.2 Dynamic behaviour of bridge deck The dynamic characteristics of bridges are frequency, mode shapes and damping ratio of its normal mode of vibration. These can be determined by the excitation of bridge, measure of response, analysis of data. Determination of natural frequency is important since their relation to frequency content of forcing function has major influence on the bridge response. The natural period of vibration T (sec) of the structure is the time required for one cycle of free vibration. It is related to the natural circular frequency of vibration ω (rad/sec) and the natural cyclic frequency of vibration f (Hz) as follows: T = f = = These frequencies are natural properties of the structure when it is allowed to vibrate freely without any external excitation. In addition, the circular frequency ω is defined as: Thus, the natural frequency of simply supported beam or bridge of uniform section depends only on the mass (m) and stiffness of the structure (k). Vibration of bridges is a nuisance to users because of associated physiological and psychological effects. The other reason to control vibration is the structural one. The effect of vibration is to cause additional stresses in the structure over and above the static effects. Certain thumb rule provisions incorporated in the codes of practices such as limiting the ratio of deflection to span and restricting the spandepth ratios, tend to make the structure more rigid and thus less prone to vibrations. But these provisions are not based on evaluations of frequency and the amplitude of vibrations likely to occur and hence cannot be taken as a guarantee against occurrence of undue vibrations even under normal loads. Hence, dynamic analysis need to perform to obtain dynamic parameters. Some of the methods are as follows 1. Time History Analysis International Journal of Civil and Structural Engineering 496

3 2. Response Spectrum Analysis 3. Rayleigh Ritz Method 4. Finite Element Method Dynamic analysis of T-Beam bridge In this proposed study, bridge model is analyzed by Response Spectrum Analysis. 2. Response Spectrum Analysis A plot of the peak value of a result of response quantity as a function of the natural vibration period Tn of the system, or a related parameter such as circular frequency, or cyclic frequency fn, is called the response spectrum for that quantity. Now, a central concept in earthquake engg., the response spectrum provides a convinient means to summerize the peak response of all possible linear Single Degree of Freedom (SDF) systems to perticular component of ground motion. It has been adopted as a standard way of representation of effect of ground acceleration on structures. It also provides a practical approach to apply the knowledge of structural dynamics to the design of structures and development of lateral force requirements in the building codes. 2.1 Parametric study Dynamic analysis of T-beam bridge deck is done by Response Spectrum Analysis with the help of SAP2000 software. A complete schedule of parametric study is given in table 1. Table 1: List of studied parameters Type of Bridge T-Beam Bridge Span 15,20,25,30,35m Lane of Bridge Two lane Four lane Carriageway width 7.5 m 14 m No. of longitudinal girders 3 3,4,5,6 Thickness of longitudinal girders 300mm 500mm No. of cross girders 5 5 Thickness of cross girders 250mm 250mm Depth of deck slab 215mm 215mm International Journal of Civil and Structural Engineering 497

4 Thickness of wearing coat 75mm 75mm IRC standard live load Class A-2 trains Class A- 4 trains Depth of longitudinal girder and cross girder is kept same for each bridge model. For 15 m span, it is m and for all the remaining spans it is 2 m. And this pattern is same for all the considered cases in the present work. Parametric study is carried out as per following cases Table 2: list of cases of parametric study Case No Lane Longitudinal girders Cross girders Span IRC Live load Case-I Two lane ,20,25,30,35 Class Loading A Case-II Four lane ,20,25,30,35 Class Loading A Case-III Four lane ,20,25,30,35 Class Loading A Case-IV Four lane ,20,25,30,35 Class Loading A Case-V Four lane ,20,25,30,35 Class Loading A All bridge models are prepared and analyzed using SAP2000. Bending moments, deflection and deflection/span ratio of all the spans are determined. On the basis of which the serviceability criteria is checked. This is followed by dynamic analysis of bridge to obtain natural frequency and time period. With the help of these dynamic parameters, possibility of resonance is checked. This is studied by parametric investigation and are presented in the form of graph as follows 1. Variation of maximum total bending moment with respect to Span for 2 Lane bridge with 3 longitudinal girders 2. Variation of maximum deflection with respect to with respect to Span for 2 Lane bridge with 3 longitudinal girders 3. Variation of frequency with respect to Span for 2 Lane bridge with 3 longitudinal girders International Journal of Civil and Structural Engineering 498

5 4. Variation of time period with respect to Span for 2 Lane bridge with 3 longitudinal girders 5. Variation of maximum total bending moment with respect to Span for 4 Lane bridge 6. Variation of maximum deflection with respect to Span for 4 Lane bridge 7. Variation of frequency with respect to Span for 4 Lane bridge 8. Variation of time period with respect to Span for 4 Lane bridge Figure 1: Variation of Maximum total bending moment with respect to span for 2 lane bridge Figure 2: Variation of Maximum deflection with respect to span for 2 lane bridge International Journal of Civil and Structural Engineering 499

6 Figure 3: Variation of frequency with respect to span for 2 lane bridge Figure 4: Variation of time period with respect to span for 2 lane bridge International Journal of Civil and Structural Engineering 500

7 Figure 5: Variation of Maximum total bending moment with respect to span for 4 lane bridge Figure 6: Variation of Maximum deflection with respect to span for 4 lane bridge International Journal of Civil and Structural Engineering 501

8 Figure 7: Variation of frequency with respect to span for 4 lane bridge Figure 8: Variation of time period with respect to span for 4 lane bridge International Journal of Civil and Structural Engineering 502

9 3. Observations Following observations are obtained from detailed parametric study and above graphs: 1. Bending Moment in longitudinal girders: For two lane bridges, with the increase in span, selfweight of bridge increases and hence maximum bending moment increases. Rate of increase in BM is mild up to 25m, beyond that, rate increases. Thus for higher span i.e. greater than 25m, BM in longitudinal girder increases with higher rate. This trend is same for Four Lane Bridges also. But as the no. of longitudinal girders increases, total BM decreases. 3 longitudinal girders case gives maximum total BM, while 6 longitudinal girders case gives minimum value. 2. Deflection: Cross beams equalizes the deflections of the girders carrying heavy loading with those of the girders with less loading. Hence in all girders deflection is almost same. With the increase in span, deflection increases. In the case of Four Lane Bridges, as the no. of longitudinal girder increases, deflection decreases. Deflection is maximum for 3 longitudinal girders case and minimum for 6 longitudinal girders case. For both the case, rate of increase in deflection is more up to 25 to 35m comparing with span range 15 to Frequency and time period: For each span first mode shape gives least frequency and max. time period. For shorter span frequency is on higher side which goes in reducing with the increase in span and with the increase in span, time period goes on increasing. For four lane case, as the no. of longitudinal girders increases, frequency increases and time period decreases. Limiting Value for deflection/span ratio is = 2.66x10-3 as specified by IRC. From this value, serviceability criteria can be checked. Frequency of vehicle (passing over bridge) is considered between 3 5 Hz. This frequency need to be avoided to prevent resonance. 4. Conclusions This proposed study is carried out for two lane and four lane bridges of spans 15m, 20m, 35m, 30m and 35m using IRC class A loading by varying a number of longitudinal girders. SAP2000 software is used for this work. Following conclusions may be drawn from the graphs (figure 1 to figure 8 ) and observations 1. For two lane bridges, all the bridge spans except 35 m, give reasonable results of deflection/span ratio, which are acceptable. But for span 35m (2.51x10-3 ), it is very close to permissible limit (2.66x10-3 ) which may lead to serviceability problems in future. Same will be situation for similar kind of bridge beyond a span of 35 m. 2. For four lane bridges, Deflection/span ratio values for shorter spans i.e. up to 30 m are within permissible limit for all the combinations of longitudinal girders. But for 35 m span, of 3 LG (2.665x10-3 ) and 5 LG (2.19x10-3 ) systems, there is no marginal difference between actual and permissible value (2.66x10-3 ). Hence, it is quite possible that, they may lead to serviceability problems. 3. Vehicle frequency is considered between 3 5 Hz. Hence, frequency of bridge should not fall in the vehicle frequency band to avoid resonance. However, the frequency for span 25m and 30m of two lane bridges fall in the vehicle frequency band of 3 5 Hz. Hence, there may arise issues related with vibration. It may be safe to state that, all other spans will not pose any vibration related problems. International Journal of Civil and Structural Engineering 503

10 4. For Four lane bridges, similar to Two Lane Bridge case, the frequency of bridge for span 25m and 30m fall in the vehicle frequency band of 3 5 Hz. Hence, there may arise issues related with vibration. 5. It may be safe to state that, all other spans will not pose any vibration related problems as they do not fall in the vehicle frequency band. It may be said that, medium range span bridge i.e. 25 to 30 m will be subject to vibration problems. However, too short or long span bridges may not create vibration related problems. 5. References 1. Azad A.K and El-Boghdadi M.H, Static Analysis of Multibeam Bridge deck, 4th Saudi Engg. Conference, Nov Ayman M. Elmahdy, Hisham A. Elarobaty, El Mostafa M. Higazy & Mohammad N. Fayed, Dynamic Behaviour of Bridge/Vehicle Interactive Systems, 12th International Colloquium on Structural & Geotech Engg. at Cairo-Egypt, Dec Melcer., (2006), Vehicle - Road interaction, Analysis in a frequency domain, Slovak Journal of Civil Engineering, 3(4), pp Munirudrappa and Dhruvaraja Iyengar, Dynamic Analysis of Continuous Span Highway Bridge, ISET Journal of Earthquake Technology, Paper No. 392, Vol. 392, March Mohamad Najim Mahmood and Ayad Thabit Saeed Al-Ghabsha., (2006), Dynamic analysis of bridges subjected to moving vehicles, Al-Rafidain Engineering, 14(4). 5. IRC: 1984, Special report: State of the Art Dynamic Behaviour of Highway Bridges. 6. Johnson Victor, Essentials of Bridge Engineering, Oxford & IBH Publishing Company Pvt, Ltd. New Delhi. 7. IRC: 1984, Special report : State of the Art Dynamic Behaviour of Highway Bridges. 8. IRC: Standard Specifications and Code of Practice for Road Bridges, Section I General Features of Design (Seventh Revision) 9. Pankaj Agarwal & Manish Shrikhande, Earthquake Resistant Design of Structures, Pentice hall of India private Limited, New Delhi. International Journal of Civil and Structural Engineering 504