Behaviour of beam depends on its depth. A beam is considered as deep, if the depth span ratio is 0.5 or more. In the available beam theories, we have to apply correction in case of deep beams. In the present work, method of initial functions (MIF) is used to study the effect of depth on the behaviour of concrete beam. The MIF is an analytical method of elasticity theory. It gives exact solutions of different types of problems without the use of assumptions about the character of stress and strain. In this method, no correction factor is required for beams having larger depth. Results are obtained for three different cases of depth span ratios and compared with available theory and finite element method-based software ANSYS. It is observed that deep beam action starts at depth span ratio equal to 0.25.

The paper predicts the shear strength of high-strength steel fiber-reinforced concrete deep beams. It studies the effect of clear span-to-overall depth ratio on shear capacity of steel fiber high-strength deep beams using artificial neural network (ANN8). The three-layered model has eight input nodes which represent width, effective depth, volume fraction, fiber aspect ratio and shear span-to-depth ratio, longitudinal steel, compressive strength of concrete, and clear span-to-overall depth ratio. The model predicts the shear strength of high-strength steel fiber deep beams to be reasonably good when compared with the results of proposed equations by researchers as well as the results obtained by neural network (ANN7) which is developed for seven inputs excluding span-to-depth ratio. The developed neural network ANN8 proves the versatility of artificial neural networks to establish the relations between various parameters affecting complex behavior of steel fiber-reinforced concrete deep beams and costly experimental processes.

Recently, soil-steel bridges have become more commonly used as railway-highway crossings because of their economical advantages and short construction period compared with traditional bridges. The currently developed formula for determining the minimum depth of covers by existing codes is typically based on vehicle loads and non-stiffened panels and takes into consideration the geometrical shape of the metal structure to avoid the failure of soil cover above a soil-steel bridge. The effects of spans larger than 8 m or more stiffened panels due to railway loads that maintain a safe railway track have not been accounted for in the minimum cover formulas and are the subject of this paper. For this study, two-dimensional finite element (FE) analyses of four low-profile arches and four box culverts with spans larger than 8 m were performed to develop new patterns for the minimum depth of soil cover by considering the serviceability criterion of the railway track. Using the least-squares method, new formulas were then developed for low-profile arches and box culverts and were compared with Canadian Highway Bridge Design Code formulas. Finally, a series of three-dimensional (3D) finite element FE analyses were carried out to control the out-of-plane buckling in the steel plates due to the 3D pattern of train loads. The results show that the out-of-plane bending does not control the buckling behavior of the steel plates, so the proposed equations for minimum depth of cover can be appropriately used for practical purposes.

This paper is concerned with the economical comparison between two commonly used configurations for double layer grids and determining their optimum span-depth ratio. Two ranges of spans as small and big sizes with certain bays of equal length in two directions and various types of element grouping are considered for each type of square grids. In order to carry out a precise comparison between different systems, optimum design procedure based on the Cuckoo Search (CS) algorithm is developed. The CS is a meta-heuristic algorithm recently developed that is inspired by the behavior of some Cuckoo species in combination with the Levy flight behavior of some birds and insects. The design algorithm obtains minimum weight grid through appropriate selection of tube sections available in AISC Load and Resistance Factor Design (LRFD). Strength constraints of AISC-LRFD specification and displacement constraints are imposed on grids. The comparison is aimed at finding the depth at which each of the different configurations shows its advantages. The results are graphically presented from which the optimum depth can easily be estimated for each type, while the influence of element grouping can also be realized at the same time.

In space domes, geometrical changes are the main factors that determine the forces in the structural members. This paper has addressed the effects of the height-to-span ratio variations on the reliability of space domes. Applied loads, nodes coordinates, member’s cross-section, modulus of elasticity, and yield stress are the random variables, and FORM (first-order reliability method), SORM (second-order reliability method), MCS (Monte Carlo sampling) and IS (importance sampling) were the methods used to evaluate the reliability of such structures. Results showed that FORM yielded better solutions; reliability increased with an increase in the height-to-span ratio, and a change in the performance function changed the reliability index and sensitivity coefficient. Hence, for domes with height-to-span ratios less than 0.3, the displacement performance function is the effective function and for ratios greater than 0.3, the stress performance function should be considered as the critical function.