# Structural Non-Linear Models and Simulation Techniques: An Efficient Combination for Safety Evaluation of RC Structures

DOI: 10.4018/978-1-4666-8823-0.ch018
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## Abstract

Advances in computer technology allow nowadays the use of powerful computational models to describe the non-linear structural behavior of reinforced concrete (RC) structures. However their utilization for structural analysis and design is not so easy to be combined with the partial safety factors criteria presented in civil engineering international codes. Trying to minimize this type of difficulties, it is proposed a method for safety verification of RC structures based on a probabilistic approach. This method consists in the application of non-linear structural numerical models and simulation methods. In order to reduce computational time consuming the Latin Hypercube sampling method was adopted, providing a constrained sampling scheme instead of general random sampling like Monte Carlo method. The proposed methodology permits to calculate the probability of failure of RC structures, to evaluate the accuracy of any design criteria and, in particular, the accuracy of simplified structural design rules, like those proposed in civil engineering codes.
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## Fundamentals On Structural Safety Of Rc Structures

### Basic Safety Concepts

The structural safety requirements can be defined by using a limit state function, g(X), which is dependent on the basic variables governing the structural behavior, expressed by vector X, and can generally be defined by:

(1)

In this case, g(X) = 0 is the safety margin and the inequality, g(X) ≤ 0 represents the failure domain or, in other words, a violation of a limit state.

The basis of any rationally founded safety concept must be the probability of failure, pf. In a full probabilistic approach, this probability can be defined by:

(2) where fX(x) is the joint probability density function of X. The safety requirements can thus be expressed by condition pfp0, where p0 is the target probability of failure.

## Key Terms in this Chapter

Probability of Failure: Probability of an undesirable event occur causing a malfunctioning of the structure, when analysing the service performance, or causing the collapse, for an ultimate state.

Simulation Techniques: Methodologies that are used to analyse the behavior of the structures considering different possible values for the main parameters of the problem.

Design Codes: Definition of common practice rules to be applied in the structural design, ensuring a predefined safety level.

Structural Safety: Definition of the safety margins to assure that failure will occur or that specific criteria will be exceeded for very low probability levels.

Structural Analysis: Application of methods and techniques to determine the effect of loads applied on structures considering the resistance properties of the structural members.

Non-Linear Models: Numerical models to simulate the non-linear behavior of structures and materials, currently used in the analysis and design.

RC Structures: Structures made by a composite material constituted by concrete (material with a good performance for compressive stresses but relatively low tensile strength and ductility)and steel bars (having higher tensile strength and ductility), commonly named by reinforced concrete structures.

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