Pushover Analysis of Reinforced Concrete Bridge Pier Designed as Per IRC-6 Codal Provision

Mohammad Farhan^* and Mohd Tasleem
^*Correspondence: Mohammad Farhan, Post Graduate Student, Department of Civil Engineering, Integral University, Lucknow, India, Tel: + 88840729682, Email:

Keywords

Bridges • Seismic • Concrete • Plastic hinges

Introduction

Majority of the Indian bridges were inadequately designed to resist seismic forces as per outdated building codes. The design shear capacities for short piers (having aspect ratio between 2 to 3) is found to be smaller than the corresponding shear demand under condition of flexural over strength. The lower transverse reinforcement as per previous codes resulted in lower displacement ductility and weaker post yield response. When seismic loading is applied to redundant RCC structure, as the members’ moment capacities are reached, discontinuities develop in structure. Plastic hinges develops and response of structure becomes inelastic. Due to smaller transverse reinforcement in the plastic hinge region at the ends of the piers, the longitudinal reinforcement lacks in developing required strength which results in spalling of the concrete, de-bonding and initiate slippage. Ultimately the pier base experiences either a brittle pull-out failure, or a brittle shear failure.

The bridge structure, in general, lacks in structural redundancy and hence suffers severe damage which leads to failure during ground motion. This paper conducts investigation at determining the adequacy of Strength of the reinforced concrete bridge designed as per the current seismic provisions of the Indian codes for bridge design, namely the IRC: 6-2011, IRC: 21–2010 and IRC: 78-2012. In this paper multi span RCC highway bridges with simply supported at ends are modelled and analyzed using IRC Class AA loading and structural response parameters such as Bending Moment, shear and deflection are obtained to obtain the serviceability. Further, pushover analysis if the bridge structure is performed on structural analysis software SAP 2000.

Literature Review

Target displacements and performance point

Target displacements and base shear are calculated for four different pushover analysis methods at performance point as per the procedures. Table 1 presents the base shear and target displacement values for bridge model. NWBR S30M calculated as per FEMA 356 displacement coefficient methods, capacity spectrum method (ATC 40), displacement modification method (FEMA 440) and equivalent linearization method (FEMA 440). These results are compared with Equivalent Static Method (ESM) as per IS Code [7].

Table 1. Target displacements for PA Methods for model NWBR S30M.

It is seen that base shear from all the methods is in similar range. DCM overestimates the shear demand slightly, but the deviation is small enough to be neglected. It is also noticeable that the differences in values of base shear and target displacement between the two basic methods (i.e., CSM and DCM) are reduced when obtained with their improved modification method (i.e., ELM and DMM).

Comparison of NSP with ESM shows that NSP demand is greater than two times the ESM demand for all the cases. Similar trends were seen in the results of the other bridge models also, that are discussed below.

Base shear and pier top displacement at performance point and the three performance levels, namely immediate occupancy (IO), life safety (LS) and collapse prevention (CO), for the two series of bridge models (series 1 varying pier height and series 2 varying span) are provided in Table 2 and Table 3 respectively.

Table 2. Base shear and displacement for series 1 (Varying height models).

Table 3. Base shear and displacement for series 2 (Varying span models).

In case of series 1 base shear at performance point is greatest for 5 m pier height and decreases suddenly as the height of pier is increased. Further the values remain similar for last three bridges of the series. Similar trend were also seen for base shear at various performance levels, the values of base shear for NWBR H5M are very high as compared to other bridges. At lower pier height the stiffness of bridge pier is very high and thus develop very high base shear at very low displacement. As for displacement at performance point and other performance levels, it is very small for the first bridge of series and goes on increasing. Last two bridges in series showing large displacements particularly at levels of LS and CP. Except for the first case, the performance point of all other bridges lies between IO and LS [8].

Base shear as well as displacement trends for series 2 is completely different from series 1. Base shear for the smallest span is lowest, increases with increase in span but shows decrement for last bridge. This trend is same for considered parameters (PP, IO, LS and CO). Displacement variations are similar at performance point with lowest values for smallest span and increases with increase in span of bridge. This trend is not true for displacement at other performance levels, showing random trends with increase in span. As expected the displacement values for LS and CP are on the higher side.

Pushover demand comparison with indian standard code

The inquiry of the Indian codal provisions for design of RC pier considering the international seismic design practices, and significance of implementing the performance based design approach in bridge design demands the comparison of performance based demand (NSP analysis) for piers with design demand as per the existing Indian standards. To facilitate the same the seismic analysis of the two series of model bridges is also performed with the approach stipulated by Indian Codes. The codes used for the analysis of bridges are IRC: 6-2016 (latest edition), IRC: 112-2011 (last edition) and IS1893-2016 Part I.

The results obtained from seismic analysis of bridges with two different approaches, i.e., Nonlinear Static Analysis and Indian Code base Linear Static analysis, are compared. The comparison is based on total base shear demand of bridge and max shear demand of critical pier as shown in Table 4 The shear demand values obtained for linear static method are factored 1.5 times to reach codal demand.

Table 4. Comparison of result of pushover analysis and linear static analysis.

The comparison of base shear bridges shows that pushover demand is very high against codal seismic demand for all the model bridges. The difference in the two demands is described by ratio Bp/Bi. Model with smallest pier height NWBR H5M has largest difference with ratio of 3.03 while model NWBR S60M with largest span shows smallest variation having ratio of 1.28. Similar trends are seen in case of max shear demand at critical pier also. The average values of the two ratios Bp/Bi and Vp/Vi for the ten model bridges are 2.21 and 2.27 respectively [9].

Conclusion

Only limited analysis is performed using only few analytical models and the following points can be drawn from this study.

1. For most cases performance point for pushover analysis lies between Immediate Occupancy and Life Safety level of performance. Thus Pushover methodology demands the structure to go beyond linear yielding.

2. The difference between the Pushover demand and Codal demand is very high and thus it is recommended to introduce non-linear static analysis approach in the Indian Codes.

3. The design procedure outlined in IRC codes does not account for the possibility of plastic hinge formation in an extreme seismic event. Non-linearity is completely neglected in seismic analysis.

4. Difference between base shear and target displacement for the two basic methods (i.e., CSM and DCM) are reduced when obtained with their improved modification method (i.e., ELM and DMM).

5. Bridge with small pier height shows very high values of base shear at very small deflection, thus failure of pier occurs before formation of plastic hinges. Further work is required to come up with plausible performance based analysis for smaller pier height bridges.

References

1. https://law.resource.org/pub/us/code/bsc.ca.gov/sibr/gov.fema.fema356.pdf
2. Federal Emergency Management Agency, FEMA 440:  Improvement of Nonlinear Static Seismic Analysis Procedures (2005).
3. https://www.atcouncil.org/pdfs/atc40toc.pdf
4. https: //iisee.kenken.go.jp/worldlist/24_India/24_India_Code.pdf
5. https://thelibraryofcivilengineer.files.wordpress.com/2015/09/irc-24-2001-standard-specifications-code-of-practice-for-road-bridges-steel-road-bridges.pdf
6. IRC: 21-2000. “Standard Specifications and Code of PSractice for Road Bridges, Section: III, Cement Concrete” The Indian Road Congress (2000).
7. SAP 2000. “Integrated Software for Structural Analysis and Design” (2016).
8. Manjula NK, Praveen Nagarajan and TM Madhavan Pillai. “A Comparison of Basic Pushover Methods” International Refereed Journal of Engineering and Science 2 (2013):  14-19.
9. Lande, PS and AD Yawale. “Seismic performance study of bridge using pushover analysis” International Journal of Mechanical and Production Engineering 2 (2014).