Risk and Reliability Analysis: Theory and Applications by Paolo Gardoni

Author:Paolo Gardoni
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

The A-limit state (steel elongation) bounds the lower part of the safety domain in the above diagram. The B-limit state (extreme concrete fiber crushing) bounds the middle part and the C-limit state (general concrete crushing) bounds the upper part. A simultaneous positive sign of all three functions characterizes the safety domain.

7 Aerodynamic and Seismic Forces

Aerodynamic and seismic actions are time dependent and are generally considered to be very random phenomena. If these actions were known as functions of time, a dynamic structural analysis could be performed leading to a time dependent force vector within a given section (N(t), My(t), Mz(t)) which, if the section had been properly designed, would remain constantly within the safety domain bounded by the interaction curves. It is clear that this approach is only conventional since it does not take into account the loading history and inelastic behavior of materials which have a significant impact on the response and capacity of the structure.

Moreover, the load time history is very rarely known in detail. However, it is possible in practice, through a probabilistic or stochastic analysis, to define a curve or a surface boundary (typically an ellipse or an ellipsoid) within which the section forces will remain or, at least, outside of which the section forces will go with a known and very small probability (see Capra and Davidovici 1984).

Take, for example, the bending moment and axial force in a beam section resulting from static forces, yielding the static response and , and seismic forces in one horizontal direction, yielding the dynamic responses and . Assume that and are the response spectrum values of and for the ith mode.

If the dynamic response were governed by a sole mode, then the maximum dynamic responses and would be reached simultaneously.

Because of the multiplicity of vibration modes and partial correlation between modes, maximum axial force and maximum bending moment will not be reached simultaneously.

However, an elliptic envelope of combined bending moment and axial load can be defined as:

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