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A generalized microplane model, which was previously developed to describe tensile cracking and nonlinear triaxial response of brittle-plastic materials in compression and shear. is implemented in a finite element code. To limit localization instabilities due to strain softening and the consequent spurious meshsensitivity. the recently proposed concept of non local continuum with local strain (nonlocal damage) is adopted and combined with the microplane model. An effective numerical algorithm permitting large loading steps is developed by applying me idea of exponential algorithms previously used for creep. Problems due to nonsymmetry of the tangential stiffness matrix are avoided by using the initial elastic stiffness matrix in the incremental force-displacement relations. Numerical results demonstrate that the microplane model, which previously has allowed an excellent description of the test data on nonlinear triaxial behavior of concrete as well as unidirectional and multidirectional crack or crack shear, is endowed (in its nonlocal generalization) with the capability of also modeling tensile fracture. The model yields the correct transitional size effect observed in concrete and agrees with the recemly proposed size effect law. The formulation is applicable to brittle-plastic materials in general.

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This paper provides an overview of serviceability specifications given by the fib Model Code for Concrete Structures 2010 (fib MC2010 [1]). First, the reasons behind crack control and deflection control are discussed, then specific design rules are provided. Simple rules as well as detailed models are also presented. Numerical examples are provided in order to assist in the application of the design recommendations for crack control and deflection control (reinforced and prestressed concrete elements).Simple rules mean indirect control of cracking or deflections without calculations. Indirect crack control may include limitation of stresses and selection of maximum bar diameter or maximum bar spacing. Indirect deflection control normally means limiting the span‐to‐depth ratio.Detailed models are based on physical and mathematical approaches to cracking and deflections. The design crack width is expressed as the maximum bond transfer length multiplied by the mean strain between cracks. Deflection analysis can be provided by integrating curvatures or by using a simplified or refined method. Vibrations and numerical modelling of cracking are also briefly discussed.

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