Green roofs are considered to be one of the optimal tools for saving energy and protecting the environment in developed countries. In this paper, an analysis of the possible application of green roofs on existing residential buildings with flat roofs is presented. In the economic analysis, models of existing buildings in Belgrade, with two different types of green roofs, are studied. A key indicator of investment profitability in this investigation is the net present value (NPV) of the green roof project. Besides the private economic impact, other aspects of green roof applications, significant for sustainable development, have been highlighted. The values of the reductions in the annual energy needed for heating and cooling are compared for different scenarios. A maximum energy saving of 22% in the heating season is determined in the building energy simulation program for the model with an intensive green roof. Life cycle profit analysis was based on the probabilistic approach. The corresponding variance-based sensitivity analysis determined the impact of various parameters on the final result. In all models, the first order sensitivity index, which measures the impact of the number of residential units on the NPV, ranges from 12.2% to 63.6%. Sensitivity analysis showed that the benefit of property value increase has the highest influence on the calculated NPV in scenarios that account for this benefit. The obtained results in those scenarios indicate that the most probable NPV at the end of the life cycle is EUR 43/m² and EUR 82/m² for extensive and intensive green roofs, respectively.

A uniaxial material model for fatigue damage accumulation, established on the connection of unit elements, is presented in this paper. Although these units are regarded as micro-elements in the proposed model, they are based on a hysteretic operator that enables calculating hysteretic energy loss as an analytical expression. Further, this unit element represents a mechanical model with elastoplastic damage behavior in function of strain. The second level of modeling is defined by the connection of these units (micro-elements) with different values of total energy dissipated at failure. By changing the distribution of dissipated energy limit, various fatigue damage evolution laws are developed. Calculation of total and hysteretic energy loss in one loading cycle is also affected by fatigue damage as the varying number of unit elements are been eliminated when their maximum dissipation energy is reached. Material parameters for the model were defined based on the experimental monotonic and cyclic stress-strain tests, still, detailed comparison was not performed as the main advantage and aim of the paper was the development of the method for assessment of damage evolution in fatigue analysis. On the other hand, the number of cycles to failure ( N_f) and total heat dissipation are compared in both qualitative and quantitative aspects with experimental results. Finally, based on the proposed model, mean strain and load sequence effect diagrams were constructed. It is shown that the proposed model can provide a reliable estimation of fatigue life in the low-cycle regime of loading. The maximum error for the calculated N_f was 3% for constant strain loading for experiments with strain amplitude less than 5%. In load sequence fatigue life estimation, the proposed model demonstrated good accuracy, with a maximum error of 34%. Further, obtained results were achieved with different types of damage evolution that could be defined for the same material and fatigue life.

This paper considers the phenomenon of the instability of steel plane frame structures in the elastic–plastic domain. The numerical analysis uses finite element method, where the corresponding stiffness matrices are based upon the trigonometric and hyperbolic interpolation functions of normal forces. The tangent modulus concept is applied when buckling occurs in the plastic range. Thus, the stiffness matrices for nonlinear material behavior are also derived. The procedure for determining effective length factors of compressed columns, which implies a global stability analysis of entire frames, is established too. It means that the proposed approach is based on the assumption that the collapse of the structure occurs when the most loaded columns reach their stability limit. So, the presented procedure enables the calculation of the real critical load of plane frame structures in the elastic–plastic domain and determines the corresponding effective length factors.

This article delivers a new Preisach model representing the correlation between the elastoplastic behavior of structural mild steel under axial monotonic and cyclic loading with damage. The newly formed model is based on the experimentally defined correlation between axial monotonic and cyclic behavior of structural mild steel. To examine the monotonic and cyclic behavior of structural mild steel and find fitting material properties for the model, monotonic and cyclic axial tensile tests are performed. Tests are executed on coupons of the commonly used European structural steel S275. The model represents a mathematical description of modified single-crystal material behavior under monotonic loading. Two different approaches were used to describe damage in the multilinear mechanical model. The excellent agreement with experimental results is achieved by infinitely linking many single-crystal elements in parallel, forming the polycrystalline model. This model provides a good solution for everyday engineering practice due to its geometric representation in the form of the Preisach triangle and the lower costs of monotonic tests used to define material properties compared to cyclic tests.