Computational & Technology Resources
an online resource for computational,
engineering & technology publications 

Computational Science, Engineering & Technology Series
ISSN 17593158 CSETS: 7
COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: B.H.V. Topping, Z. Bittnar
Chapter 14
Structural Damage: Simulation and Assessment Y.S. Petryna+, W.B. Krätzig* and F. Stangenberg+
+Institute for Reinforced and Prestressed Concrete Structures Y.S. Petryna, W.B. Krätzig, F. Stangenberg, "Structural Damage: Simulation and Assessment", in B.H.V. Topping, Z. Bittnar, (Editors), "Computational Structures Technology", SaxeCoburg Publications, Stirlingshire, UK, Chapter 14, pp 351377, 2002. doi:10.4203/csets.7.14
Keywords: material damage, simulation, reinforced concrete structures, damage measure, statistical uncertainties.
Summary
This paper deals with two actual issues of computational
structures technology  simulation and assessment of structural
damage. The paper shows how the understanding of damage processes
helps to define, quantify and even to measure the damage degree of
structures.
Damage simulation begins usually with a proper nonlinear material modeling able to describe deformation processes with damage constituents. Among a wide variety of damage phenomena the present work concentrates on mechanical damage of reinforced concrete under monotonic and cyclic loading. From the simulation viewpoint the socalled instantaneous (timeindependent) and essentially longterm damage effects are distinguished. The plasticity and microcracking of concrete under compression, the fracture of concrete under tension, the yielding of reinforcement and the damage of the bond between concrete and steel under static loading belong to the first group. The paper discuss main features of a uniform material model of reinforced concrete able to simulate these processes and refer to such a model recently developed in [1]. The model is based on elastoplastic continuum damage theory and implemented in the finite element software FEMAS [2]. This material model is further extended to account for such longterm damage effects as highcycle fatigue and creep, relevant to many practical problems of civil engineering structures. In contrast to existing models the new fatigue damage model proposed in [3] accounts for damage evolution, for impact of fatigue on system behavior as well as its feedback. Therefore, it is able to realistically predict intermediate material states during fatigue life. The damage evolution law for concrete is adopted in accordance to the history of plastic strain accumulation observed experimentally and then calibrated on the fatigue life predictions resulting from the SN (Wöhler) curves. For damage accumulation in steel, acceptable estimates are obtained using the PalmgrenMiner hypothesis. The concrete creep is described by the ratetype law and the nonaging rheologic model according to the solidification theory [4]. As only longterm consequences of creep are of interest, the relevant creep strain is reduced to the socalled viscoelastic strain. The creep law is integrated over time by the unconditionally stable exponential algorithm using the middle point of each time interval in the logarithmic scale. The interaction of timeindependent and longterm damage mechanisms takes place during the equilibrium iterations of the finite element structural model. Several approaches have been developed in the last decades to evaluate structural damage through changes in dynamic response. However, they are typically limited to damage detection and localization. A basic concept of structural damage assessment with respect to carrying capacity, a challenging task of any assessment, has been recently proposed by the first two authors [5]. The present contribution completes this approach with a new virtualenergybased (VEB) structural damage measure estimating reduction of the strain energy attributed to vibration modes. The VEB damage indicator has been shown to be closely related to the Mode Assurance Criterion (MAC) widely used in vibration monitoring. This fact opens the perspective of its successfully application both in numerical and experimental assessment techniques. The inherent uncertainties of material, geometrical and structural parameters are taken into account statistically. The finite element structural analysis is combined with MonteCarlo simulations to solve the eigenvalue problem with respect to randomly generated stiffness and mass matrices and determine the output statistics of the damage measure. For illustration purposes the approach has been applied first to simulate and then to estimate the damage evolution of a reinforced concrete beam. The results obtained numerically are compared to experimental ones available in the literature. The sensitivity of modal parameters and damage measures to uncertainties are statistically studied in the second example of a 3span slab concrete bridge. References
purchase the fulltext of this chapter (price £20)
go to the previous chapter 
