Safety of Reinforced Concrete Framed Structures


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Title: Safety of Reinforced Concrete Framed Structures

Author(s): Milik Tichy and Milos Vorlicek

Publication: Special Publication

Volume: 12


Appears on pages(s): 53-84


Date: 1/1/1965

With discussion by Theodore Zsutty, Jack R. Benjamin, C. Allen Cornell, and Milik Tichy and Milos Vorlicek. Because the ultimate strength and deformation ability of critical sections are random variables, the ultimate strength of a structure must likewise be a random variable. If the structure is subjected to load from one source and there is only one possible collapse mechanism, the determination of the ultimate strength ZU of the structure is simple. If the structure is subjected to load from one source but there are m possible collapse mechanisms, it becomes necessary to analyze the structure with the aid of equations of the type given herein. The ultimate strengthZUj, for j = 1, 2, . . . , m of the structure is determined by means of each of these equations assuming the occurrence of the j-th collapse mechanism. The probability pUj that the structure will change into the jth mechanism may be ascertained for a definite value of the load for each random variable ZUj But the actual probability of failure must be expressed with the aid of the so-called conditional probabilities since the individual mechanisms are not always statistically independent. If the structure is subjected to load from v sources and there are m possible collapse mechanisms an equation for the jth mechanism will graphically be represented by an interaction diagram. For a given population of structures, identical according to the design, there exists a number of possible combinations of load with a corresponding probability of failure pU. Geometrically speaking, they are points in the v - dimensional space. Their locus is the so called boundary of the safe domain IImin. When the deformation ability of a structure is considered, the system of equations forms the starting point. In this instance the random variable Zuj is a linear combination of ultimate moments MUi and the ultimate plastic rotation 0U of the section. The statistical solution is analogous with the previous one. It may be demonstrated that the variability in ultimate strength of a redundant structure is lower than that of a statically determinate one in all cases. Consequently, the application of the statistical method must result in savings of material in redundant structures.