Applying two definitions of the union of IF-events, P. Grzegorzewski gave two generalizations of the inclusion-exclusion principle for IF-events. In this paper we prove an inclusion-exclusion principle for IF-states based on a method which can also be used to prove Grzegorzewski's inclusion-exclusion principle for probabilities on IF-events. Finally, we give some applications of this principle by extending some results regarding the classical probabilities to the case of the IF-states.

Despite the definition of failure being almost thoroughly studied in other theories such as elasto-plasticity, this paper studies the possibility of capturing or defining some limit states in hypoelastic materials. It is shown that for many hypoelastic materials the limit state, as a notion of failure, can take the place of the yield or failure in classical plasticity. The procedure is general, and all equations are rational, i.e. they are not dependent on a particular form of a constitutive equation. Constitutive equations cover those applied to both metallic and non-metallic materials. Some practical results were obtained for a particular form of a hypoelastic equation which resembles the Drucker-Prager criterion for the form of the limit state. Results were also examined against a set of experimental data.

Fragility curve, based on the Performance-based earthquake engineering (PBEE), is a fundamental tool in assessing the probabilistic seismic Performance of concrete gravity dams. Determination of the dam limit-states (LSs) is necessary for estimation of fragility curve. In this research, four LSs in seismic Performance of massive structure have been utilized for Pine Flat dam. To address this, the Incremental Dynamic Analysis (IDA) method has been applied to the integrated dam-reservoir finite-element model. Evaluation of seismic behavior, demand and capacity of the tallest monolith has been investigated by implementing IDA. A new comprehensive method in terms of IDA and statistical analysis has been used for determination of each defined LS based on the certain value of the engineering demand parameter (EDP). To assess probabilistic Performance of the dam, the exceeding probability of the LSs curves has been developed at various intensity measures based on the tree EDPs. It was found that the defined LSs have the capability indeed to be used in probabilistic framework.

Forming limit Diagrams are useful tools for evaluation of formability in the sheet metals. In this paper the effects of yield criteria on predictions of the right and left-hand sides of forming limit diagrams (FLDs) are investigated. In prediction of FLD, Hosford 1979, “Karafillis-Boyce” (K-B) and BBC2000 anisotropy yield functions have been applied. Whereas the prediction of FLD is based on the “Marciniak and Kuczynski” model, thus a numerical approach using the Newton-Raphson method has been used. Forming limit Diagrams have been obtained for Al 6111-T4 and AA5XXX alloys and results have been compared with published experimental data. Results indicate that predictions of FLD are very sensitive to selection of yield criterion. Also it was found that the FLD of K - B yield function has a better agreement than that by other yield criteria.

There are several sources of uncertainty in the analysis and design of steel moment resisting frames, the random assumption of each of which can have a significant effect on the satisfaction of Performance requirements of the structure. Among these factors, structural parameters can be mentioned, the most important of which are yield stress, modulus of elasticity, sections geometry and structural mass. Evaluating the impact of these factors depends on how the parameters are distributed and modeled. In this study, three common types of uniform, normal and log normal distributions for the parameters of mass structures, yield stress, modulus of elasticity and sections geometry that are random in nature are considered and using Monte Carlo method, the effect of uncertainty of these parameters is considered. The seismic Performance of steel structures is investigated. Studies are performed on 4 structures of 3, 5, 10 and 15 floors of steel moment resisting frames with medium ductility, which are designed according to Iranian regulations. In order to model the structures and perform incremental dynamic analysis, Open Sees software was used. In order to evaluate the seismic Performance of the structures, fragility curves were used. The results show that the type of distribution does not have a significant effect on the results of applying uncertainties. It is also observed that considering the mass uncertainty, increases the acceleration range in the Collapse Prevention (CP) and life safety (LS), which shows the significant effect of mass uncertainty compared to other parameters.

This study designed to examine and test the constructs of reversal theory.The main purpose of this study was to examine the effect of metamotivational dominance on motor Performance, arousal, pleasantness and telic and paratelic states reversal in dart throwing beginner while performing under easy and difficult tasks. For this purpose, the Paratelic Dominance Scale distributed among 140 male students and at the result, 32 participants were randomly selected into two groups (16 in a telic group and 16 in a paratelic group). The study contained three blocks of eight trials, which each trail contained 4 throws. Participants were asked to complete the Affect Grid and the Telic State Scale in pretest and after trials 8, 16, 24.Dates analyzed with repeated measure, Ancova test, paired t test and LSD Post Hock test statistical methods. The results showed that there was significant difference between the telic and paratelic participant in telic and paratelic states reversal (in easy task, p=0.002, in difficult task, p=0.001), arousal (in difficult task, p=0.006) and pleasantness (in easy task, p=0.04, in difficult task, p=0.01). Overall, the study only partially confirmed the reversal theory postulations.

Forming limit diagram (FLD) shows the formability of metal sheets under different loading conditions before that necking is taken place. In this paper, the application of plastic instability criterion for prediction of necking and also FLD have been investigated. Using Balart’s anisotropic yield function and plastic instability criterion in different strain ratios, limit strains have been calculated, and then the limit strains have been converted to limit stresses. To verify the analytical results, a free bulge setup with the ability of applying the axial feeding has been fabricated. Tubes have been undergone different loading paths and different plane strain conditions have been induced to obtain FLD. FLDs which have been obtained using plastic instability criterion have been compared with experimental results. The results show that swift instability criterion for tubes have the best prediction of FLD in tube hydroforming process.