Friedhelm Stangenberg

Reliability of reinforced concrete structures under fatigue

Abstract This paper focuses on time-variant reliability assessment of deteriorating reinforced concrete structures under fatigue conditions. A strategy combining two time scales, namely the micro-scale of instantaneous structural dynamics (or statics) and the macro-scale of structural lifetime, is proposed. Non-linear response of reinforced concrete structures is simulated by means of the finite element method with adequate material model. A phenomenological fatigue damage model of reinforced concrete is developed and calibrated against experimental results available in the literature. Reliability estimates are obtained within the response surface method using the importance/adaptive sampling techniques and the time-integrated approach. The proposed assessment strategy is illustrated by an example of a concrete arch under fatigue loading. The obtained results show a general inapplicability of local and linear fatigue models to system level of structures.

Measures of structural damage for global failure analysis

Abstract In building codes, the design of structures is generally based on their virgin state omitting most damage processes and disregarding future physical as well as chemical deterioration. Such concepts of disregard of structural stiffness degradation are in principle incapable of quantifying structural failure and thus of describing important aspects in modern structural engineering. The present paper supposes the modeling of local damage and deterioration phenomena on material point level and its mapping onto structural level. Here, it demonstrates that global damage measures, i.e. measures on structural level, can stringently be deduced from the reduction of the current structural stiffness, up to now an unsettled problem. Damage indicators are thus observable during incremental-iterative solutions of the tangent stiffness equation, where they estimate the distance from the actual structural state to failure varying from 0 to 1. Their applicability is finally demonstrated exemplarily on a reinforced concrete beam and a large shell.

Comparison of Building Collapse Simulation Results From Finite Element and Rigid Body Models

In case of planning a building demolition, the information about geometry, quality of building materials, the design of the load carrying system and documentation of the structural calculation is often incomplete and imprecise. Thus for the analysis of a collapse event, engineers are forced to consider the uncertainty of primary parameters influencing e. g. the resistance of structural elements of a building. This kind of uncertainty can be described using suitable data models such as fuzziness and fuzzy randomness [6]. Within such an ‘uncertain’ structural analysis the deterministic fundamental solution is applied repeatedly. A comprehensive overview over algorithms of fuzzy analysis and fuzzy stochastic analysis is given in [5]. First applications of uncertainty collapse analyses can be found in [7, 8]. However, considering several uncertain parameters in an analysis the problem dimension and the necessary effort can be quite high. To receive a good prediction for a complex building collapse, several hundred or even more deterministic solutions are needed. This requires an efficient and fast scheme to perform the analysis for highly nonlinear problems, concerning geometry, material and changing boundary conditions such as contact.

Nonlinear dynamic analysis of reinforced concrete structures

Abstract Dynamic ultimate load calculations mainly for reinforced concrete beams and plates, are discussed. Starting from the corresponding differential equations, the calculations also include the rotational inertia of single beam or plate elements as well as the shear deformations. With actual structural dynamic problems in nuclear power plants, the shear behaviour of reinforced concrete beams and plates is more important than it is usually, as is shown by examples. The finite propagation velocity of bending and shear waves are taken into account. Solution of the equations of motion is obtained by numerical intergration using finite time and space intervals. The calculations are performed using time dependent bending and shear laws for reinforced concrete up to the point of failure with realistic deformations. These latest scientific developments are of great significance for dynamic ultimate load analysis in practice. Elastic-plastic examples of application are compared with corresponding linear-elastic solutions. It is shown that the design of construction members based on elastic-plastic dynamic stress calculations in general is economically advantageous. This important conclusion is proven by numerical results. Also the relation to the approximation of a one-degree-of-freedom dynamic system, including or excluding the plastic ductility of the structural member, is demonstrated. Finally, lumped-mass multi-degree systems calculated by integrating numerically the corresponding equations of motion, are dealt with briefly. A nonlinear dynamic calculation of a foundation of a recently built reactor building is presented as an example for blast resistant analysis.

Optimized reinforcement of nuclear power plant structures for aircraft impact forces

Abstract Reactor buildings of nuclear power plants and, to some extent, also other buildings of the plant, according to the present safety requirements, have to be able to withstand aircraft impact forces. The building has to withstand this loading only once since afterwards it will be out of use. Accordingly, other criteria for design and the necessary safety measures are valid than in the case of service loads. Large deformations and the development of large cracks due to such loadings are insignificant from a construction point of view for reinforced concrete structures, i.e. the stresses can build up to the ultimate load carrying capacity. From the nuclear safety point of view, however, some restrictions are possible in this regard, e.g. to obstruct the penetration of fuel through the cracks. Basically all mild steels, with large ductility and without brittle fracture under sudden load increases, are suitable for this purpose. High stresses in the structure would, however, require uneconomical concentrations of mild steel. It is for this reason that the use of high strength steels, e.g. St 110/135, has been introduced in Germany for this kind of loading. Since the permissible deformations of reinforced concrete structures due to aircraft impact are large, a new kind of reinforcement is at hand. Through the use of wire strands or cables of high strength steel it is possible to reach a condition of cracks and large deformations due to ultimate loads in zones of point loading. The reinforcement takes on a distinctly curved shape and is able to carry the normal loads and shears through a suspension-structure action. The deformability of the structure for the analysed limit load state can be further increased through a bond-free net. This measure allows a more uniform stretching of the cables or strands over a larger zone. By making use of the higher allowable deformability of the structure and this type of reinforcement, savings in longitudinal reinforcement are possible. Reinforcement for shear is not relevant with this model and serves only a structural purpose. The structural thickness can be decreased as it depends only on the protection from penetration and is independent of the requirements for bending and shear.

Anchorages under tensile loading—A nonlinear numerical analysis

Abstract The behaviour of anchor bolts embedded in concrete and loaded in tension is investigated. Based on the state of the art of anchoring to concrete, a nonlinear finite-element model is developed, considering the influences on the behaviour and the maximum pull-out loads of anchorages. Special focus is given to the influences of concrete strength and of flexural reinforcement as well as of crack propagations in the concrete.

Lifetime-Oriented Design Concepts

Structures deteriorate during their lifetimes, e.g. their original quality decreases. In terms of structural safety, this reduces the original safety margin, a process, which also can be described as an increase of structural damage. If, in such deterioration, the safety parameter decreases below the admissible safety limit, or the structural damage parameter increases beyond the admissible damage limit, then the structural service life will be terminated. If the failure safety value or the structural damage parameter both reach unity, the structure (theoretically) will fail.

Deterioration of Materials and Structures: Phenomena, Experiments and Modelling

Reliable computational prognoses of the structural integrity and serviceability throughout the lifetime of structures require the realistic consideration of the damage behaviour of the construction materials for various loading scenrios including static and cyclic loading, environmental loading processes such as moisture and heat transport, corrosion processes, freeze-thaw actions and possible interactions between these long- and short-term processes. Both, load-induced damage mechanisms such as evolving microcracks and physically and chemically induced deterioration originate from mechanical, physical and chemical processes starting at lower scales of the microstructure of the materials. Investigating and understanding these processes acting at various scales is a prerequisite for the development of adequate and suitable material models suitable for life-time oriented simulations.

Damage-Oriented Actions and Environmental Impact on Materials and Structures

Mechanical loading and ambient actions on civil engineering structures and components cause lifetime-related deteriorations. Not the rare extreme loading events are in the first place responsible for the evolution of structural degradation but the ensemble of load effects during the life-time of the structure. It is of major importance to have models at hand which adequately reflect the experienced time histories of impacts, and which can include justified predictions of future trends. Leading types of loading and load-effects with relation to mechanical fatigue as well as damages due to hygro-thermal and chemical impacts are considered in this chapter. Selected contributions from wind and temperature effects with certain meteorological characteristics as well as from traffic loads on roads and railway lines are modeled as typical examples of contributions to mechanically induced degradations of structures. A specific aspect is the permanent settlement of soil due to high-cyclic, longterm loading, for which novel representations are developed. The attack of freeze-thaw circles in different environments and of chemical impacts leading to solving, swelling and leaching processes in concrete including principle interactions are discussed as examples for the main types of non-mechanically induced degradations.

A rational framework for damage analyses of concrete shells

Publisher Summary This chapter describes a numerical framework for nonlinear analyzes of concrete shells experiencing damage during their lifetime. Three major topics able to affect the accuracy of structural simulations are discussed—namely, the formulation of adequate finite elements that describe shell geometry, boundary, and load conditions—as well as deformations in presence of cracks with a high accuracy, the development of realistic material models, and the estimation of discretization errors. Among various factors affecting structural lifetime, mechanical damage associated with concrete cracking plays an essential role. The finite-element simulation is performed by use of a continuum-based and surface-oriented shell element. Such shell elements admit a realistic simulation of geometrical discontinuities as well as the definition of single loads and kinematic constraints. Furthermore, they allow an easy implementation of general three–dimensional constitutive laws.