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Claudio Davey
Grillage Analysis by Surana PDF: A Comprehensive Guide to Bridge Deck Analysis
Bridge deck analysis is a crucial step in the design and construction of bridges. It involves determining the stresses, deflections, and forces in the bridge deck due to various loads and conditions. Bridge deck analysis can be performed using different methods, such as finite element method, plate theory, or grillage analogy.
Grillage analogy is a well-established computer-aided method of bridge deck analysis that simplifies the complex bridge deck into an equivalent grid of beams. The method can handle various types of bridge decks, such as slab bridges, T-beam bridges, and box-girder bridges. It can also account for rigid or flexible support conditions, and right, skew, or curved plan layouts.
Grillage analogy is based on the stiffness method, which relates the nodal deformations and forces by corresponding stiffness matrices. The procedure and recommendations for idealizing the actual bridge deck and loadings into mathematical models are discussed in detail in the book Grillage Analogy in Bridge Deck Analysis by C. S. Surana and Ramji Agrawal[^1^]. The book also provides two ready-to-use programs, GRID and GRID2D, along with descriptions of various subroutines, that can analyze a variety of bridge decks accurately and obtain all the responses required in the design.
If you are looking for a comprehensive guide to bridge deck analysis using grillage analogy, you can download the PDF version of Grillage Analogy in Bridge Deck Analysis by C. S. Surana and Ramji Agrawal from this link[^2^]. You will also get access to the input-data and output results of all the worked-out examples in the book. This will help you understand the concepts and applications of grillage analogy better and save you time and effort.
Grillage analogy is a powerful and versatile method of bridge deck analysis that can help you design safe and efficient bridges. Download Grillage Analogy by Surana PDF today and learn how to use it effectively.
In this article, we will explain the basics of grillage analogy and how to use it for bridge deck analysis. We will also show you some examples of bridge decks that can be analyzed using grillage analogy and the results obtained from the programs GRID and GRID2D.
What is Grillage Analogy?
Grillage analogy is a method of bridge deck analysis that simplifies the complex bridge deck into an equivalent grid of beams. The grid consists of longitudinal and transverse beams that are connected at discrete nodes. The nodes represent the points where the actual bridge deck is supported by girders or piers. The beams represent the stiffness and mass properties of the bridge deck segments between the nodes.
The advantage of grillage analogy is that it reduces the number of degrees of freedom and equations to be solved compared to other methods, such as finite element method or plate theory. It also allows for easy application of loads and boundary conditions. Moreover, it can handle various types of bridge decks, such as slab bridges, T-beam bridges, and box-girder bridges. It can also account for rigid or flexible support conditions, and right, skew, or curved plan layouts.
Grillage analogy is based on the stiffness method, which relates the nodal deformations and forces by corresponding stiffness matrices. The stiffness matrix of each beam element is derived from the basic beam theory, assuming small deflections and linear elastic behavior. The stiffness matrix of the entire grillage is obtained by assembling the stiffness matrices of all the beam elements using appropriate transformation matrices. The nodal deformations and forces are then calculated by solving a system of linear equations.
How to Use Grillage Analogy for Bridge Deck Analysis?
To use grillage analogy for bridge deck analysis, the following steps are required:
- Transform the actual bridge deck into an equivalent grillage model by selecting appropriate grid size, beam properties, and support conditions.
- Apply the loads and boundary conditions to the grillage model.
- Use a computer program, such as GRID or GRID2D, to analyze the grillage model and obtain the nodal deformations and forces.
- Interpret the results and compare them with the design criteria and specifications.
The first step is the most important and critical one, as it involves idealizing the actual bridge deck into a mathematical model. The accuracy and efficiency of grillage analogy depend largely on how well the grillage model represents the actual bridge deck. The procedure and recommendations for idealizing the actual bridge deck and loadings into mathematical models are discussed in detail in the book Grillage Analogy in Bridge Deck Analysis by C. S. Surana and Ramji Agrawal.
Examples of Bridge Decks Analyzed Using Grillage Analogy
In this section, we will show you some examples of bridge decks that can be analyzed using grillage analogy and the results obtained from the programs GRID and GRID2D. These examples are taken from the book Grillage Analogy in Bridge Deck Analysis by C. S. Surana and Ramji Agrawal, where you can find more details and explanations.
Example 1: Slab Bridge with Right Plan Layout
A slab bridge with a right plan layout is shown in Figure 1. The bridge has a span of 20 m and a width of 10 m. The slab thickness is 0.3 m. The bridge is supported by two rigid piers at each end. The bridge is subjected to a uniformly distributed dead load of 25 kN/m and a live load of Class 70R as per IRC:6-2014.
The equivalent grillage model for this bridge is shown in Figure 2. The grid size is selected as 1 m x 1 m. The beam properties are calculated from the slab properties using equivalent width concept. The support conditions are modeled as fixed joints at each pier location.