The exceedingly large top drift and bottom bending moment due to the weakening of shear walls in tall buildings by door, window and corridor openings is one of the most frequently encountered problems of structural engineering. An elegant way of tackling the foregoing problem is to employ stiffening beams. Authors who tried to find closed form solutions could handle only cases with up to two stiffening beams. With the approach used in the present study, a computer program which can find analytical expressions for the design of coupled shear walls with many stiffening beams has been prepared making use of the MATHEMATICA computer algebra system, rendering possible an optimization with respect to different parameters. In all of the previous works, all properties of the shear walls and the connecting beams have to be kept constant along the height of the building. The present work can treat a coupled shear wall with any number of stiffening beams and flexible connections, having any number of occasional changes in the properties of the shear walls and the connecting beams. A perfect agreement has been observed between the results of the present study and those of (SAP90) Structural Analysis Program in the examples used for the verification of the present method. Thus, the present method proves to be a perfect mean of predesign, since it gives results in an extremely short time.

Determining the bearing capacity of the soil and its subsidence is one of the most important parameters that must be carefully evaluated when designing a safe foundation. In the present study, using a physical model, the behavior of the foundation located on sandy soil under static loading and the effect of various factors on soil behavior have been investigated. In this laboratory study, the effect of foundation width, sandy soil density and amount of overhead on strip foundation subsidence has been investigated. The soil material used in this study is poorly grained medium sand (SP). The foundation model has a width of 5, 7.5 and 10 cm and its length is 34 cm. The sand raining technique has been selected to obtain a homogeneous sample with a definite relative density and repeatability of laboratory conditions. The loading system is compressed air that has the ability to apply a uniform and static load. The relationship between the final relative settlement and the width of the foundations located on medium-density sandy soils is linear, and as the foundation width increases, the final relative settlement reaches less than its final ultimate bearing capacity. At the same pressure, the settlement of the foundation located on medium-density sandy soils is about 10 % higher than the foundation located on dense sandy soils. Soil behavior up to a pressure of about 50% of the final bearing capacity is linearly elastic. The pressure- settlement relationship of the strip foundation is linear up to about 5% of the foundation width. General shear failure occurs at a relative settlement of about 12 to 14%. For this reason, it is suggested to determine the ultimate bearing capacity of the strip foundation located on sandy soil, the amount of pressure such as 12% .

Esthetics is one of the prosthetic treatment goals. Correct selection of anterior teeth, regarding size and appearance, results in a successful treatment. The goal of the present research was to investigate the relationship between interzygomatic width and maxillary anterior teeth width in order to find a better determinant for artificial anterior teeth selection. In this study, the interzygomatic width and maxillary central incisors width and also the width of six maxillary anterior- teeth, in 71 subjects (29females and 42 males) were measured. The results showed a significant difference in maxillary anterior teeth width, comparing men and women, (P<0.05). These measurement in people under study, are less than Europeans. The interzygomatic width was also more in men than women (P<0.05), which is, less than of European race. The ratio between interzygomatic and central maxillary incisor width was 15:1 which is less than 16:1 that is used in clinic. Thus, it is recommended to pay more attention to anterior teeth selection, especially in young patients.

Background and Aim: Esthetics is one of the prosthetic treatment goals. Correct selection of anterior teeth, regarding size and appearance, results in a successful treatment. Using the extra oral indicators is a common method to determine the size of the tooth. In this study, the correlation between the facial widths (in bizygomatic and intercondylar areas) and the mesiodistal width of maxillary central incisors was analyzed.Materials and Methods: A cross-sectional study was conducted on 100 qualified students, 50 females and 50 males. Two facial widths comprising Intercondylar width -distance between two approximately Beyron hinge axis- and bizygomatic width -two most convex points of zygomatic arch- were marked and measured by a facebow and a digital caliper. Mesiodistal maxillary central incisors’ widths were measured by a digital caliper. The collected data were analyzed via Pearson correlation coefficient.Results: The mesiodistal width of right central incisor was 8.47±0.56. The mesiodistal width of left central incisor was 8.54±0.64.The bizygomatic width was 126.15±6.74. The intercondylar width was 131.43±5.41. There was no correlation between bizygomatic width and central incisors (P>0.05) and a weak correlation between intercondylar width and central incisors in Iranian community.Conclusion: Facial width is not recommended as a suitable landmark for estimating the mesiodistal width of maxillary central incisors.

There are many cases in which the foundation, in addition to static load, is exposed to cyclic loading, such as earthquakes, traffic loads, and machine vibrations. In this laboratory study, the effect of foundation width, sandy soil density, number of loading cycles, static and cyclic overhead intensity on cyclic strip foundation settlement has been investigated. The soil material used in this research is poorly graded medium sand (SP). The foundation model has a width of 5, 7.5 and 10 cm and its length is 34 cm. In medium and dense sandy soils, the average amount of foundation settlement in the first loading cycle is about 46 and 51% of the total cyclic settlement, respectively. Medium-density sandy soils below the foundation have failed at a settlement of 22 to 27% of the foundation width. The dense sandy soil beneath the foundation has failed at a settlement of 33 to 43% of the width of the foundation. The lower the total overhead entering the soil, the more loading cycles the soil can withstand to fail; That is, with increasing static and cyclic overhead, the soil is failed in a smaller number of cycles. Due to the creation of permanent settlements under the effect of cyclic loads, in the design of foundations under the effect of this type of load, the amount of predicted settlement must be less than the allowable amount.

In this paper, we consider the width invariant trapezoidal and triangular approximations of fuzzy numbers. The presented methods avoid the effortful computation of Karush-Kuhn-Tucker Theorem. Some properties of the new approximation methods are presented and the applicability of the methods is illustrated by examples. In addition, we show that the proposed approximations of fuzzy numbers preserve the expected value too.