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STRUCTURAL RELIABILITY AND RISK ANALYSIS – 4 Year FILS

1. INTRODUCTION TO RANDOM VARIABLES THEORY

Reliability – the ability of a system or component to perform its required functions under
stated conditions under a specified period of time.

Structural reliability objective – to develop criteria and methods aiming at ensuring that
buildings (structures) built according to specifications will not fail to preserve the functions
for a specified period of time.

Uncertainty
- Random (aleatory) uncertainties – that are related to the built in reliability
phenomena and informations that cannot be reduced through better knowledge.
- Epistemic uncertainties – that are related to our inability to predict the future
behavior of systems. It can be reduced through better understanding and modeling.

Example: Analysis of a frame structure

Live load + dead loads
Lateral load
(wind, A s
earthquake)
N M Bending
moment

A A s
Steel area Compressive
force
Steps: Model (1) – Imposed Loads (2) – Structural Analysis (3) – Sectional Analysis (4) –
Design for some limits states (5).

Model (1) - Epistemic uncertainty
Loads (2) – dead, wind, live loads are evaluated using the codes.
Random uncertainty (in the codes) - one way to take care, is the use of the safety factors (5%
less than or 5% greater than – see the class of concrete)
Structural Analysis (3) - Epistemic uncertainty (linear elastic materials – strains proportional
to stresses)
Sectional Analysis (4) - Random + Epistemic uncertainty
Design for some limits states (5) – ultimate limit states (safety), serviceability limit states.
For power plants – LOCA – local lose of cooling agent

Uncertainties can be reduced to physical models:
- random variable (RV) – dead load, material strength
- random process – wind velocity, ground acceleration.

The random variable (RV) – is a quantity whose value cannot be predicted with sufficient
accuracy before performing the experiment.

In engineering statistics one is concerned with methods for designing and evaluating
experiments to obtain information about practical problems, for example, the inspection of
quality of materials and products. The reason for the differences in the quality of products is

UTCB, Technical University of Civil Engineering, Bucharest 6