Stress Concentrations in Elevated Steel Storage Tanks and Silos

Some problems of the stability of cylindrical and conical shells

Augmenting meting and solidification rates of latent heat storage unit (LHSU) is very much essential for its efficient operation. By the effective utilization of natural convection, rate of heat transfer can be enhanced and the conical shell is beneficent in this regard. Using fins further improves the charging and discharging rates. Hence, the current study is focused on analyzing melting and solidification characteristics of a conical shell and tube LHSU along with the effect of fin parameters viz., fin diameter and number of fins. Numerical analysis is chosen for this purpose and the performance is compared via melting/solidification times, energy stored, energy/exergy efficiencies. Initially, the performance of unfinned conical shell is compared with the cylindrical shell without fins and then the effect of fin parameters is presented. For melting process conical shell is found to be superior to cylindrical shell. 34.46% reduction in melting time is noted by using conical shell and rate of energy stored is also higher for conical shell. Increase in fin diameter caused an increase in melting time when 20 number of fins are used, whereas melting time got decreased with the increase in fin diameter when five number of fins are used. Hence, when a greater number of fins are used, lesser diameter is preferred for melting. For discharging process, conical shell took 60% more time than cylindrical shell. Even after using fins, solidification time is not drastically reduced in comparison with cylindrical shell.

This article presents a simple second-order theory for the determination of bending stresses which arise at the longitudinal welded joint of a pressurized, cylindrical shell subject to peaking, i.e., angular misalignment. Although this problem has been studied quite extensively over the years by a few authors and a few versions of simple formulas are available for the calculations of bending stresses at the welded joint, it is noted these formulas show considerable discrepancies when compared with the finite element solutions. As the additional bending stresses at the weld joint will lead to a shorter fatigue life of the joint, an improved theory to predict the peak stress at the weld joint, such as the one presented in this article, would be important and of interest to the design engineer and vessel inspector. The present theory has been validated against finite element results and shown to be extremely accurate.

Analytical solution for vibration of generally laminated conical and cylindrical shells

A comparative analysis of the dynamic stability of cylindrical and conical shells with the same geometric and mechanical characteristics under periodic uniformly distributed axial compression was presented. The study of the stability of steady periodic vibrations of thin elastic shells was based on the joint use of the method of curvilinear grids, the projection method and the parameter continuation method combined with the Newton–Kantorovich method. Geometrically nonlinear relations of the thin elastic shells theory are formulated on the basis of the vector approximation of the displacements function in the general curvilinear coordinate system in tensor form and satisfy the Kirchhoff-Love hypothesis. The discretization of the differential equations of the steady forced vibrations in the direction of the generating shells using the method of curvilinear grids was carried out. The components of the elements displacement vectors of the shells middle surface in the circular directionare approximated by trigonometric series. Reduction of the number of generalized coordinates of the discrete dynamic model of shells steady forced vibrations was performed by the Bubnov-Galerkin basis reduction method. A transition from vector ordinary differential equations to a nonlinear system of algebraic equations was made. The construction of a mathematical model of the dynamic stability of steady forced nonlinear vibrations of thin elastic shells was performed according to Floquet's theory using the projection method. The criterion for the loss of stability was the equality to zero of the determinant of the matrix of linearized equations of steady forced nonlinear vibrations of shells according to the Lyapunov theorem. A comparative analysis of frequencies and modes of natural vibrations of cylindrical and conical shells with the same geometric and mechanical characteristics and boundary conditions was performed. Nonlinear steady vibrations of the shells due to periodic axial compression were studied. The critical values of the dynamic load and the corresponding forms of loss of shell stability in the range of lower frequencies of their natural vibrations were obtained.

The membrane forces discussed in the last two chapters are sufficient to resist many commonly encountered loading conditions. At locations where the deflection is restricted or there is a change in geometry such as cylindrical-to-spherical shell junction, the membrane theory is inadequate to maintain deflection and rotation compatibility between the shells as illustrated in Example 7–3. At these locations discontinuity forces are developed which result in bending and shear stresses in the shell. These discontinuity forces are localized over a small area of the shell and dissipate rapidly along the shell. Many structures such as missiles (Fig. 8-1), pressure vessels, and storage tanks are designed per the membrane theory and the total stress at discontinuities is determined from the membrane and bending theories. In this chapter the bending theory of cylindrical shells is developed and in Chapter 9 the bending theory of spherical and conical shells is discussed.

Nonlinear thermal elastic buckling of conical shells

A unified Fourier series solution for vibration analysis of FG-CNTRC cylindrical, conical shells and annular plates with arbitrary boundary conditions

In Algeria, the seismic design of elevated concrete storage tanks is carried out in accordance with seismic standard, involving a behavior coefficient of the structure. This behaviour coefficient is used to determine the internal forces and to estimate the inelastic deformations undergone by the structure. For the elevated water tank, considered as reverse pendulum structure, this coefficient assumes a constant value (R=2) in the Algerian seismic code. Taking into account a single value, whatever the seismic zone, the site of implantation and the geometric characteristics of the structure, can lead to design errors leading to oversizing, hence an additional cost of the structure. Thus, faced with the need to design resistant structures while minimizing construction costs, it is important to precisely determine the value of this behaviour coefficient to introduce into the evaluation of the structure's response. In this research, the seismic performance of an RC elevated tank is analyzed, using a nonlinear approach based on the Pushover method, initially using the behavior coefficient prescribed by the Algerian seismic code, then secondly using the behavior coefficient approximated by a power-type law, taking into account the seismic zone, the type of soil, the height of the structure and the storage capacity. The results of this study highlight the influence of the value of the behavior coefficient on the seismic performance and the level of damage to an elevated tank.

An axial crack in a cylindrical shell is investigated by use of a 10th order shell theory, which accounts for transverse shear deformations as well as a special kind of orthotropy. The symmetric problem is formulated in terms of two coupled singular integral equations, which are solved numerically. The asymptotic membrane and bending stress fields ahead of the crack are found to be self similar. Stress intensity factors are given as a function of the shell parameter for various values of the ratio shell radius to shell thickness. Considerable differences from 8th order shell theory results are found for the bending stresses, while the membrane stresses of the 8th order theory seems to be a lower limit reached for very thin shells.

Natural frequency analysis of imperfect GNPRN conical shell, cylindrical shell, and annular plate structures resting on Winkler-Pasternak Foundations under arbitrary boundary conditions

D E L I P R Results of an extensive experimental program on the stability of cylindrical and conical shells under axial compression are presented and discussed. The experimental data indicate that the buckling coefficient varies with radius-thickness ratio. A study of other data in the literature showed that most of the experimental results fell within or near the scatterband obtained in the present evaluation. A lower bound design curve is also contained in the paper.

A layerwise-differential quadrature method (LW-DQM) is developed for the vibration analysis of a stiffened laminated conical shell. The circumferential stiffeners (rings) and meridional stiffeners (stringers) are treated as discrete elements. The motion equations are derived by applying the Hamilton’s principle. In order to accurately account for the thickness effects and the displacement field of stiffeners, the layerwise theory is used to discretize the equations of motion and the related boundary conditions through the thickness. Then, the equations of motion as well as the boundary condition equations are transformed into a set of algebraic equations applying the DQM in the meridional direction. The advantage of the proposed model is its applicability to thin and thick unstiffened and stiffened shells with arbitrary boundary conditions. In addition, the axial load and external pressure is applied to the shell as a ratio of the global buckling load and pressure. This study demonstrates the accuracy, stability, and the fast rate of convergence of the present method, for the buckling and vibration analyses of stiffened conical shells. The presented results are compared with those of other shell theories and a special case where the angle of conical shell approaches zero, i.e. a cylindrical shell, and excellent agreements are achieved.

The problem of a cylindrical shallow shell with axial cracks on both sides of a hole is investigated by use of the expressions in the context of Muskhelishvili's complex potentials by means of comformal mapping. The values of bending stresses and displacements around a hole for the shell are shown in Tables and variation of moment and stress intensity factors at the tip of the cracks are also illustrated.

The current investigation delved into the seismic analysis, design intricacies, and assessment of the response of elevated steel containment tanks when supported by concentrically braced frames. The primary focus was placed on comprehending the behavior of the supporting structure, recognizing its heightened vulnerability to damage under horizontal excitation—insights gleaned from reconnaissance teams studying earthquake aftermaths worldwide. A specific case study unfolded featuring a steel concentrically braced frame as the supporting structure, aligning with prevalent industry norms. Throughout the entire process, spanning design phases, seismic vulnerability assessments, and response evaluations, special emphasis was placed on the internal fluid sloshing phenomena. This nuanced consideration plays a pivotal role in shaping the dynamic response of the system. The study introduces two distinct design methods: the first method aligns with relevant international codes, while the second method innovatively incorporates the compressive strength of the braces into its approach. To evaluate the dynamic response of the elevated tank, both linear and nonlinear advanced analyses were employed. The comparative analysis of various strategies underscores the impact of the chosen design methodology on the overall system response. This multifaceted exploration aims to contribute valuable insights to the seismic resilience and design optimization of elevated steel containment tanks, furthering the understanding of their performance under seismic forces.