In this paper, based on the free vortex theorem and the momentum equation, a theoretical model to predict the pressure head distribution, the pressure coefficient, the end depth ratio (EDR), and flow discharge at the brink of free overfalls in channels of different cross sections with sub-critical flow is presented. Using available experimental and theoretical results of other investigators for rectangular, triangular, exponential, trapezoidal, inverted triangular ( D-shaped), inverted semicircular and also circular channels, the proposed method has been examined. The presented theory agrees well with the experiments.

In the present study, free vibration behaviors of carbon nanotube (CNT) and boron nitride nanotube (BNNT) have been investigated via Eringen’ s nonlocal continuum theory. Size effect has been considered via nonlocal continuum theory. Nanotubes have become popular in the world of science thanks to their characteristic properties. In this study, free vibrations of Boron Nitride Nanotube (BNNT) and Carbon Nanotube (CNT) are calculated using the Nonlocal Elasticity Theory. Frequency values are found via both analytical and finite element method (FEM). Galerkin weighted residual method is used to obtain the finite element equations. BNNT and CNT are modeled as Euler-Bernoulli Beam and solutions are gained by using four different cross-section geometries with three boundary conditions. Selected geometries are circle, rectangle, triangle, and square. Frequency values are given in tables and graphs. The effect of cross-section, boundary conditions and length scale parameter on frequencies has been investigated in detail for BNNT.

In this paper, stress analyses in concrete sleeper has investigated by using results of the tests which have been done in main line of railway track. In these tests, special concrete sleeper (B70) installed in railway track. Five load cells fixed inside of the sleeper during constructing of that. After replacing this special sleeper with ordinary sleeper, and tamping in railway track, a train with certain axle load passed through that point of track. Forces on sleeper are analyzed (output of measurement). The results show that B70 concrete sleepers are designed well for tamped and no tamped cases. In the both cases, the stresses in sleeper cross sections are in allowed range. Also, the results show that the track without DTS operation (after replacing of the sleeper) decreases share of sleeper bearing and increases forces on adjacent sleepers. These forces together with dynamic effect of rail-sleeper interaction will accelerate sleeper's deterioration. This means that after replacing failured sleepers, the sufficient length of track must be operated by DTS and Tamping machines.

In this paper a method is presented for torsional analysis of non-homogeneous tubes with arbitrarily shaped cross-sections. A previously presented method based on Bredt’s theory is extended to achieve formulas for torsional analysis. Shear modulus varies through the thickness according to a power law distribution. To validate the accuracy of the presented formulas for angle of twist and shear stress, calculated results are compared with available analytical and numerical data. Moreover, the effects of thickness, bluntness of corners and cross-sectional shape are investigated. The presented formulas are relatively accurate, simple and applicable to thin to moderately thick cross-sections with constant wall thickness. Based on the method presented herein, one can achieve desirable maximum shear stress and angle of twist for a polygonal non-homogeneous tube using a proper bluntness. The presented formulas quickly converge and can be implemented in optimization programs.