Elastic Bending Strength Research Articles

Cross-Section Optimization of Sandwich-Type Cylindrical Wind Turbine Towers

As wind energy is aggressively expanding within the alternative sources' part of modern world's energy pie, the need of addressing various obstacles that limit further wind utilization becomes all the more urgent. From a structural engineering point of view, surmounting the tower-base diameter limitation, dictated by the current transportation capabilities, is one of the industry's primary issues. The concept presented in this study, as a means to address this issue, is the implementation of a composite, sandwich-type tower section instead of today's predominant, conventional steel-only tubular section. The proposed section consists of two steel faces and a core of some lightweight material, binding and keeping them at a specified distance, thus providing significantly improved mechanical properties with minimal additional weight and cost. As an initial step towards a feasibility investigation of the proposed section, the analytical expressions that govern its behavior under either axial or bending loads are formulated in the current study. The results are verified by comparison with those obtained from a specialized composite section software, as well as a general purpose finite element software. The analytical solution is then employed to carry out extensive parametric analyses, involving a wide range of material qualities and layer thicknesses, leading to the optimization of the section, in terms of either elastic bending strength or initial stiffness. Finally, the determination of the optimal section-properties, which provide the most efficient solution regarding both criteria, is addressed, resulting in a preliminary design tool for sandwich-type, wind-turbine-tower sections.

A closed-form solution for elastic buckling of thin-walled unstiffened circular cylinders in pure flexure

To date, despite the significant development in the field of structural mechanics, there still remains a paradox in the solutions available for a classical shell buckling problem. The difference in strength between a cylindrical shell under uniform axial compression and that under pure bending is not quite well investigated. This lack of research is reflected in the wide variations in the elastic bending strength and the slenderness limits given in current international design standards. The discrepancies in the available classical solutions and hence the design rules have initiated the current research. The main aim of this paper is to present a closed-form solution for the elastic buckling strength of unstiffened circular cylinders under pure bending using a new simplified energy approach employing the well-known Ritz method. Two types of analyses are presented for cylinders with large (D/t>200) and medium (100<D/t<200) diameter-to-thickness ratios. A unique testing rig was used to experimentally verify the new theory using a Moiré fringe film. The theoretical results are compared against the available and present test results and the existing classical solutions. The current design rules for thin-cylinders in international steel specifications are also compared, and the newly derived design curve is proposed which was found in a good agreement with the available test results.

Geometric Properties of Shipbuilding Structural Profiles in Probabilistic Terms to Be Used in Elastic Bending Strength Calculations

As a result of the corrosion wear, which is treated as a random phenomenon, the geometric properties of shipbuilding structural profiles (bulb plates, inverted angles/L-profiles, channels, symmetric or asymmetric Fundia T-bulbs, symmetric or asymmetric builtup T-bars, and flat bars) are presented as random functions of the ship’s age. Evenly distributed corrosion wear along each cross section’s dimension is assumed (different corrosion wear may be considered along each of the cross section’s dimensions). Taylor series approximation method is applied to present the geometric properties used for assessment of elastic bending strength in probabilistic terms. The proposed method allows for comparison between different structural profiles using as a criterion the probability that these structural profiles will meet given Renewal Criteria requirements throughout the ship’s lifetime. Based on its calculation, one can select the most reliable structural profile. The method also allows for better planning of ship repair and maintenance work. The method can also be used to reveal the already implemented risk in the existing empirical Renewal Criteria through analysis of the structural components, their location, ship’s type and size. This is one of the first steps towards development of Reliability-based Rules for building and classing of steel ships.

A numerical model for predicting the bending strength of Larssen steel sheet piles

Larssen piles are U-shaped in cross-section and are connected together by sliding joints to form quay walls, cofferdams and other types of retaining walls. Since the sliding joints are located along the centreline of the pile wall, slippage of one pile relative to another can lead to a 70% reduction in elastic bending strength. This slippage can be partially prevented by installing the piles in pairs, with the interlocks ‘crimped’ to prevent inter-pile movement. However, like non-crimped piles, the bending strength is difficult to predict since slip still can occur between the crimped pile pairs. This paper presents a numerical model for predicting the bending stresses and crimp forces in crimped pairs of Larssen piles. Tests are also reported on one-sixth scale pile walls constructed from extruded aluminium Larssen piles, with the results compared with those from the numerical model. Stress predictions from the numerical model are shown to be in close agreement with the experimental results, and can be used to economise on the crimping necessary to achieve the full composite bending strength.