Wind Girder Research Articles

Buckling behavior of floating-roof steel tanks under measured differential settlement

Large vertical cylindrical steel tanks constructed on soft foundations may bring forth various types of settlement, which is well known as the uniform settlement, the planar tilt and the differential settlement. Measured settlements of steel tanks in several practical projects are first summarized according to the in-site surveying data, and two kinds of settlement patterns are clearly defined, which are referred to as the global differential settlement and the localized differential settlement. Two practical floating-roof steel tanks are taken as the illustrative examples of large steel tanks, which are marked TK-2020 with the height-to-radius ratio of 0.35 as the representatives of large volume tanks and TK-2090 with the height-to-radius ratio of 0.7 as representatives of smaller volume tanks in this paper. Buckling behaviors of the two illustrative tanks under the global and localized differential settlement are investigated using the general-purpose finite element computer package ABAQUS by means of the geometrical nonlinearity algorithm. It is shown that for tanks under global differential settlement, local buckling occurs first at the eave wind girder, followed by a stable post-buckling behavior, so that the local buckling of the wind girder can be taken as the serviceability limit state and the post-buckling strength can be utilized in structural design of tanks. Moreover, the behavior of tanks under localized differential settlement is related to the degree of localization. The buckling behavior in the case of a large circumferential central angle for localized settlement is similar to that under global differential settlement, while the effect of the localized settlement with a relatively small central angle is more obvious than that of the global differential settlement, and the snap-through buckling induced by localized settlement would govern the design.

Experimental research on vibration reduction of high-rise petrochemical equipment

The wind-induced vibration of high-rise petrochemical equipment would do great harm to equipment operation and cause fatigue damage easily. Thus it is necessary to install some control device to reduce the vibration actively. Existing reinforcement methods include enlarging structural section, welding wind girder, adding braced frame system, fixing taut cable, etc. But each has some shortcomings. Therefore, the tuned mass damper (TMD), rarely used in high-rise petrochemical equipment, is studied by experiment to minimize wind-induced vibration, ensure safety operation and prolong service life. In the experiment, high-rise petrochemical equipment is properly simplified in order to verify the feasibility of the TMD. Parameters of the TMD are mainly researched, which include mass ratio and damping ratio. During the process, different mass ratios and damping ratios have been taken into account to understand the characteristics of the TMD under different conditions. By experiment, the changing tendencies of the natural frequency, damping ratio and top maximum displacement have been given after the simulator is implemented with the TMD. Experimental results show that the TMD is feasible for the wind-induced vibration control of high-rise petrochemical equipment, and that top maximum displacement of the simulator reduces by about 45% in the experimental condition. The experimental research has provided valuable preferences for practical application of the TMD in petrochemical field.

Buckling Analysis of a Super-Large Storage Tank

In this paper, buckling analysis was carried out on a super-large storage tank under uniform external pressure or wind pressure with finite element method. The critical pressures and buckling deformation modes are obtained and the effects of wind girders and reinforcing rings are investigated. It is found that the critical external pressure of the tank under uniformly applied external pressure obtained by the eigenvalue method is smaller than that obtained by the nonlinear method. Buckling only occurs on the windward side of the tank under the wind pressure. As strengthened by the wind girders and reinforcing rings at the upper par of the tank, buckling deformations here are much smaller than those at the lower part of the tank.

Floating-roof steel tanks under harmonic settlement: FE parametric study and design criterion

Large vertical steel tanks for fluid storage are usually constructed on soft foundations, so it is not surprising that the tank wall will settle unevenly with the settlement of the foundation, thus inducing deformations and stresses in the tank. This work investigates the linear static behavior of floating-roof tanks under harmonic settlement through finite element (FE) analyses. The influences of the radius-to-thickness ratio, the height-to-radius ratio and the wind girder stiffness on the structural behavior are first analyzed. Comparisons between the circumferential stresses in the wind girder and the vertical stresses in the tank bottom are then made. The displacement and the stress along the tank height are also discussed, and the concept of tank division along its height is presented. Finally, a design approximation for the radial displacement at the tank top is developed based on FE results, and a settlement criterion based on the top radial displacement is proposed which can be used in practical design.

Harmonic settlement effects on uniform and tapered tank shells

For economic reasons, foundations of large tanks for fluid storage tend to be shallow and may consequently suffer differential settlement under load. But these tanks are ductile and are able to tolerate limited settlement without distress. For an economic limitation of settlement, the structure should be analyzed rationally. In this paper, the effects of peripheral differential settlement on the shell are evaluated for the practical case of a tapering wall thickness in floating roof tanks which have a relatively flexible response to warping displacements. Previous research has centred on walls of uniform thickness, and is therefore of more limited relevance. Settlement of harmonic form is imposed at the base, and shell deformations and stresses determined in accurate finite element analysis. The significance of stresses in the primary wind girder, adjoining shell and at the bottom is assessed in relation to radial displacement at the top arising from the warping displacement. Results of recent laboratory tests particularly relevant to stress distribution are reported.

Stresses in Storage Tanks Caused by Differential Settlement

Differential settlement around the circumference of the foundation below the shell of a vertical cylindrical storage tank is a particularly severe form of settlement, and can cause distortion and stressing of the tank. The resulting deflections and stresses in the shell and primary wind girder of a tank with a floating roof can be analysed, assuming the shell to behave as a membrane. The analysis is reviewed and the results are applied to present a new design chart for predicting the maximum shell membrane stress caused by settlement. For unanchored tanks, the stiffness of a tank may be such that the shell can ‘bridge’ across localized soft spots in the foundation. A simplified analysis of bridging is presented and a criterion for predicting the onset of bridging is proposed, supported by model test results. Expressions for the associated shell membrane stresses are derived. For unanchored floating-roof tanks, it is concluded that the occurrence of bridging will always limit the maximum shell membrane stress to an acceptable value. However, the bending stresses in the shell-to-base joint of a bridging tank require separate assessment in all cases. The settlement criteria contained in the current British and American codes of practice for in-service inspection of tanks are reviewed in the light of these findings.

Displacements in Oil Storage Tanks Caused by Localized Differential Settlement

This paper presents design charts for predicting the maximum radial distortion of open-topped storage tanks caused by localized differential settlement of the tank foundations. It is well known that differential settlement can produce radial deflection of the tank shell sufficient to cause jamming of the floating roof. Predictions of shell deflections have often assumed the shell to be inextensional, an assumption which may not always be valid, particularly where the settlement is localized. Consequently, the authors have recently completed a more refined analysis of the deflections and stresses in the shell and the primary wind girder [1] in which the shell is considered to act as a membrane. They concluded that this membrane analysis is valid for all practical applications and proposed a procedure for predicting shell displacements caused by any general differential settlement profile using Fourier analysis. This paper firstly reviews the new membrane analysis and then illustrates its application to two specific localized settlement profiles commonly found in practice to produce easy-to-use design charts. Finally, the paper refers to experimental testing of a model tank, carried out to verify the validity of these design charts [2].

Analysis of Displacements and Stresses in Oil Storage Tanks Caused by Differential Settlement

Differential vertical settlement around the circumference of the foundations of large open-topped oil storage tanks can produce deformation of the tank including radial deflection of the tank shell. Excessive radial deflections may result in jamming of the floating roof. The results of an analysis by Malik et al. (1), based on the assumption that the behaviour of the shell is inextensional, are outlined. Two further analyses of the tank shell and the primary wind girder are presented. Both of these are simple, but use less restrictive assumptions than in reference (1). In the first analysis the shell is considered to act as a membrane. The second analysis makes use of a simplified version of the modified Donnell equation. The results of these analyses are compared with those of the analysis based on the inextensional behaviour of the shell. The limits of validity of the three different analyses are identified. It is proposed that the membrane solution is valid for all practical applications, and the results are presented in non-dimensional form in Fig. 6.

On the behaviour of open-topped oil storage tanks in high winds. part II. structural aspects

Evidence is presented and arguments advanced to support the proposition that vibration induced by turbulence in the air stream plays a significant role in initiating the collapse of open-topped oil storage tanks in high winds. On this basis a new criterion is suggested for calculating the size of the circumferential strengthening members of tanks (wind girders). It is pointed out that a new criterion for calculating the wind speed at which tanks fail can only be couched in probabilistic terms and while it is not yet possible to derive such a criterion, the necessary steps and research to do so are discussed. Some interesting results on flow-induced vibrations in circular cylindrical structures are derived and discussed in the light of other relevant research to gain a clearer understanding of such phenomena.

Tree Beam Continuum Element: Two Case Histories

The development of a unique lateral load resistant system for two tall and slender office towers is described. System design development is documented for a 52‐level downtown office tower with a frame aspect ratio (height/least width) in excess of 6.85 and a 45‐level suburban office tower with a frame aspect ratio in excess of 5.50. Due to limitations imposed by the buildings' configuration, conventional structural systems proved ineffective in resisting the applied hurricane loading. The tree beam continuum element was developed whereby a rigid girder with intermediate vertical cross arms above or below, or both, was connected between the braced core and the perimeter columns. The cross arms introduced a point of reverse bending in the wind girders, thus greatly augmenting their strength and stiffness. The tree beam system and a variation known as the staggered tree beam system provided a continuum element that elastically constrained the perimeter columns to resist overturning forces. The tree beam concept common to the two structures is explained in detail. Critical design aspects to be considered in the detailing of the “tree beam modules” are presented.