ECONOMIC DESIGN OF RCC BOX CULVERT THROUGH COMPARATIVE STUDY OF CONVENTIONAL AND FINITE ELEMENT METHOD

There are several researches already have been done on behavior of reinforced concrete (RC) box culverts in past with different conditions of loads. The design and analysis of box culverts is a complex task. The present era offers the finite element analysis of 3D model of structures, making it easier through software. The conventional methods have been used extensively for design but the use of finite element method (FEM) has not been so popular yet. Finite element analysis of box culvert for parametric studies has been carried out, even for different aspect ratio. Here an effort has been made to show the economic and effective design can be achieved by doing finite element analysis of a box culvert whose concept can be used for large structural design as well. This paper shows the comparative study of analysis of conventional method using STAAD software and of FEM using ANSYS software.

The chosen fixed dimension of box culvert is firstly analyzed in STAADPro software that follows the conventional method to analyze the structure. The same culvert is analyzed in ANSYS 14.0 to get the results for finite element method with the same load conditions. Foremost objective of the paper is to compare the results of analysis through conventional methods by STAAD software with FEM done by ANSYS software for developing economic design with same safety. II.

REQUIREMENT OF FINITE ELEMENT METHOD
The FEM is a numerical technique that has been used for various design and analysis purposes not only by the means of computer aided software but also manually. The complex systems dealing with real life problems, dynamic loads, impact loads, time and space dependent loads and the combinations of these can be dealt using this technique. The FEM provides detailed calculations of each part of the member under consideration for the critical system subjected to fixed or random loading. This method can be employed using different software in present world such as SAP, ANSYS, ABAQUS FEA etc. The design and calculation of results due to complex loading have been made easier through the software. One such software is used in this paper to apply the FEM for the best results.
III. LOADS ON THE CULVERT There are various types of loads acting on culvert during its service period. These loads may or may not remain constant as the time passes. While calculating the load on culverts, there are several factors to be kept in mind such as design parameters involving angle of dispersion of live load, coefficient of earth pressure, depth of cushion etc for critical loads. [5,6]. Single type of load considered at a time will sometimes give worst case. But it is required to take the critical combination of all the loads acting on a structure. Any structure subjected to multiple types of loads must be analyzed as per the critical combination of the loads [3]. A box culvert during service period is subjected to the following loads:  Live Loads  Impact loads  Dead load of top and side slabs  Water pressure from inside  Earth pressure from outside  Earth's up-thrust A critical combination of the above mentioned loads that has been considered in the analysis is - When the culvert is full that is when the water inside the culvert is to the height of internal side slab till the bottom of the haunch [3,14] The random set of loads are considered as per the range specified [3]: Live Load = 4 kN/m Dead load of top slab = 9.5 kN/m Side Slab weight = 27 kN Water Pressure (linearly varying load) = 3.5 kN/m to 36.5 kN/m Earth Pressure (linearly varying load) = 3 kN/m to 24.6 kN/m Up-thrust from soil under bottom slab = 30 kN/m The modeling is done according to the properties of M20 grade concrete with the following properties. Modulus of elasticity = 22360 N/mm 2 Poisson's ratio = 0.17 Figure 1 shows the line diagrams of the loads that have been applied on the culvert in STAAD software. The two ends of the bottom slab are fixed so that the up-thrust can also be taken into consideration. Water pressure is linearly varying inside and earth pressure linearly varying outside the culvert. Live loads and dead loads are taken uniformly distributed load. A load case consisting of the critical combination of the applied loads has been taken into consideration.

V. FINITE ELEMENT ANALYSIS IN ANSYS
In the modern era, the FEM analysis can be performed to a large extent and with higher accuracy. There are several software available that can minimize the risk and give accurate results. Abolmaali A. and Garg A. k. [12] have also developed finite element models and performed experimental analysis designed as per ASTM C1433-05 to show the shear transfer device is unsupported across the joint. Software like SAP and ABAQUS have already been implemented for the analysis of box culvert for wheel load and other complex real life loads. It has been seen that the solution to such loads are not easy and sometimes impossible by the means of conventional methods [11,13]. FEM can be applied where the loads are dynamic in nature or where the varying loads are experienced [8]. The ANSYS software can make its mark in the field of analysis and design with accurate results and least effort and can solve these complex loads and simulate it to get critical case and effective and economic design. Fig 4 shows the dimension of the culvert used in ANSYS which is same as in STAAD. 4m x 4m internally and with the wall thickness of 0.3m, its outer dimension is 4.6m. The 3-D model is in isometric view. The first step in the software is to correctly model the structure, then to apply the loads in the right directions so that accurate results can be obtained.  Fig. 5 shows the meshing of the box culvert into an integral structure. The most important part in the analysis of a structure by finite element method is breaking the overall the structure into different small elements before analyzing. The element taken here is solid65 which is capable of cracking in tension and crushing in compression. The solid65 element is generally used for 3D modeling of solid without reinforcement bars which is the case in this paper. They are also capable of plastic deformation and creep.  VI.  Table 1 shows the comparison of the two methods, conventional method in STAAD and FEM in ANSYS with respect to maximum bending moments, area of steel reinforcement required and the cost of steel. It can be seen clearly that there is significant reduction in moments and consequently cost of project is reduced by 11.5%. The cost difference can be remarkable in large projects and effective design can be achieved through FEM.

VII. CONCLUSION
The study results clearly infer that the culvert if designed through finite element method rather than conventional method would not only save the material and money but also make the design safer. Hence following points are concluded from the study  Results show the difference of 16.46% in positive bending moment.  A difference of 27.4% is seen in negative bending moment in FEM from conventional method  Area of steel for maximum positive bending moment is decreased by 8.6% and for maximum negative bending moment it is decreased by 14.8%  Distribution steel is decreased by 8.8% for maximum positive bending and 14.6% for maximum negative moment.  Difference in the cost is 11.5% which is huge for large projects.  Modeling and design in ANSYS is easier than any other software and gives more economic design.
The application of FEM through ANSYS software can save large amount of money and effort in design and implementation of box culvert and other structures.