Api 650 1988 Free Download Pdf

API 650's Annex E, which is an American Standard for designing aboveground steel storage tanks subjected to seismic loads, is reviewed by comparing the design provisions in Annex E with other well-known design documents around the world, including that of New Zealand and Japan. Several limit states such as hydrodynamic hoop stress, uplift, base plate stress, buckling, freeboard, and two stability mechanisms, shear and overturning are investigated. The design provisions for each of the documents were compared for identical tank geometries and seismic parameters for several different tank aspect ratios. The results show that API 650 is slightly under conservative in each of the material failure mechanisms compared to the New Zealand and Japanese design philosophies. The small disparity in results could be due to the fact that the approach in Annex E of API 650 is for tanks of rigid walls and a rigid foundation, whereas the New Zealand and Japanese documents consider tank and foundation flexibility. Despite some marginal differences, API 650 Annex E can be considered to adequately account for all the major failure states when compared to New Zealand and Japanese design documents for design purposes.

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... Housner's model also does not consider nonlinear material properties and nonlinear geometry deformations. Several researchers have investigated the effects of nonlinear uplifting tanks [14,[17][18][19][20][21][22][23][24][25][26][27][28][29][30]. One particular area of concern for nonlinear tanks subjected to seismic forces is elephant's foot buckling. ...

... On the reverse side of the tank to the elephant's foot buckle, base uplift tends to occur as the momentum of contained liquid acts on the shell wall, resulting in overturning forces. It has been shown that the recommended uplift for piping connections and attachments provided by API 650 at the base-to-shell connection for uplifting tanks does not compare well with analytical models under seismic loads [27]. In addition to elephant's foot buckling, tanks may buckle in the form of diamond-shaped buckles due to a seismic excitation. ...

... These new and improved methods for determining the behavior of nonlinear, uplifting, flexible tanks provide more accurate solutions for tanks under seismic loads. Despite this fact, it has been shown that provisions set by API 650 for seismic design provide suitable results using Housner's model which assumes rigid walls and a rigid base with elastic materials [27]. ...

A numerical analysis is conducted on several unanchored aboveground, open-top, steel, welded, liquid-containing storage tanks with imperfections subjected to seismic forces. Nonlinear material properties, nonlinear geometry deformations, and a flexible soil foundation idealized by a series of elastic springs are employed in order to simulate as-built field conditions of the tank at the time of the seismic event. A static pushover analysis was performed using impulsive and convective hydrodynamic effects of fluid contained in the tank subject to seismic motion modeled as an equivalent pressure distribution acting on the tank wall and base. Out-of-plumbness (OOP) imperfections, which is the deviation of the top of the tank shell with respect to the shell-to-base connection, and out-of-roundness (OOR) imperfections, which is a deviation in a given shell course with respect to the undeformed shell configuration, are implemented into the tanks to observe the comparative behavior when between perfect and imperfect tanks. The tolerances for construction prescribed by American Petroleum Institute (API) and recommended by the New Zealand Society of Earthquake Engineering (NZSEE) are used for the amplitude of the imperfections. In a worst case scenario, the OOP and OOR imperfections are combined. The analysis shows that the behavior of the tanks with imperfections using the API 650 tolerances show little deviation from the perfect tank conditions, and in some instances, even out-perform the perfect shell conditions, and thus shell imperfections when they are within the specified tolerances of relevant standard of construction pose little additional threat to the tank when experiencing a seismic event.

... These plates are selected according to the ASTM requirements, which state that they must have a thickness smaller than 50 mm. According to the API 650 standard, the maximum effort allowed by the product was 250 MPa, with a hydrostatic effort of 171 MPa [18]. ...

... A value for the diameter/height ratio of 1.2 was set and was consequently used to find the height and the diameter: the height of the tank was 15.2 m and the diameter of the tank that was calculated was 18.3 m. Following the API 650 standard [18],it would be necessary to anchor the tank to prevent potential disasters (A value of 1.66 of anchorage ratio was obtained). Tolima, much like the majority of Colombia, is a zone of high seismic activity, as well as of other geological phenomena like volcanoes. ...

... Adding anchors to the tank will diminish the probability of the tank falling over. Also, according to the appendix E of the API 650 Standard, the seismic load was calculated [18], which helped to define the geometrical characteristics of the tank (Table 1). ...

• Daniel Durán Aranguren
• Gabrielle Morantes
• Rocío Sierra

Biogas is a fuel that is generated through the anaerobic digestion of organic substances as they degrade biomass using a complex set of microbial biochemical reactions. Biogas is predominantly composed of flammable methane gas as well as carbon dioxide, providing a considerable value of energetic potential that, when adequately treated, can replace natural gas as a source of energy generation. In this work, a biogas production plant in Colombia was designed using experimental results from the co-digestion of mango residues and pig manure. In this scenario, the pig manure provides the ideal environment for the microbial population to conduct the anaerobic digestion process, which yields a required quantity of biofuel to generate electric power. Previous laboratory results proved that mango residues, in contrast with other tropical fruits, display an extremely favorable behavior in a bioreactor and yield an appreciable amount of biogas. With the help of mathematical models from the experimental data and, by dint of governmental regulations and geographical locations, a realistic quantitative study was carried out which hypothesized the construction of a biogas plant. A national and international analysis of the installed capacity of biogas production plants was performed to set up a framework in which it became possible to calculate the geometric and physical characteristics of the tanks and reactors involved in a biogas production plant. The tanks and reactors were consequently designed and a feasibility analysis proved that the Tolima region was the best to carry out this kind of project in Colombia.

... The buckling phenomenon of storage tanks can typically be categorised as: (i) elephant-foot buckling; (ii) diamond shape buckling. Elephant-foot buckling generally occurs in tanks that are mostly fully filled, is an elastic-plastic type of instability (NZSEE, 2009), (Sobhan, Rofooei and Attari, 2017), (Spritzer and Guzey, 2017), and can be described as an outward bulge of the tank shell. Due to the cyclic nature of seismic loading, elephant-foot buckling often extends around the full circumference of the tank wall. ...

... Due to the cyclic nature of seismic loading, elephant-foot buckling often extends around the full circumference of the tank wall. Diamond shaped buckling is a type of elastic instability (NZSEE, 2009), (Sobhan, Rofooei and Attari, 2017), (Spritzer and Guzey, 2017). Sobhan et al. (Sobhan, Rofooei and Attari, 2017) stated that elephant-foot buckling of the steel tank wall is caused by the interaction of both circumferential tensile stress close to the yield strength and by axial compressive stress exceeding the critical stress, whilst diamond shaped buckling is caused by severe axial compressive stresses. ...

It has been frequently observed that cylindrical wine storage tanks sustain varying levels of damage during earthquake induced shaking. Typical wine tank failure modes include elephant foot-buckling, diamond shaped buckling, and anchorage system failures. The seismic action loads and allowable structural response to prevent the possibility of such failure modes are suggested by the New Zealand Society of Earthquake Engineers (NZSEE) recommendations for seismic design of storage tanks. Using the collected damage data following the 2016 Kaikōura earthquake and the NZSEE recommendations, elephant-foot and diamond shaped buckling was investigated herein. Comparison of the obtained results and the allowable responses based on the NZSEE recommendations showed that the tank wall thickness and the behaviour of the anchorage system had the most dominant effects on these failure modes. Post-earthquake damage observations of the wine tanks showed that the occurrence of elephant-foot buckling was 1.8 times more frequent than the diamond shaped buckling failure mode.

... These dynamic hoop forces are sensitive to geometry and thickness of the tank wall shell, and if the exerted forces on the tank wall exceed the shell capacity, permanent deformation of the tank wall will be observed. Particularly, for the open top tank, the top of the tank walls can potentially undergo severe damage (Spritzer and Guzey 2017). Shell buckling is the main failure mode for groundsupported steel tanks. ...

Liquefied natural gas (LNG) is cleaner and cheaper for power generation than traditional energy sources. Many tanks that store LNG are located in coastal areas with less favorable geotechnical conditions and often in seismically active regions. The seismic loads acting on LNG tanks are highly affected by the soil–foundation–structure interaction (SFSI) and evaluating this effect is quite challenging as a result of the nonlinear response of the structure and foundation interacting with the soil. This paper presents the application of a three-dimensional (3D) numerical simulation technique to study the impacts of foundation type on the seismic behavior of a large LNG tank considering the SFSI effects. Fully nonlinear dynamic analysis under the influence of the 1994 Northridge and 1995 Kobe earthquakes are performed using finite-element analysis software ABAQUS version 2018 to assess the LNG tank seismic response under different foundation types, namely, end-bearing pile foundation and pile-raft foundation with two different frictional pile lengths. The results show the importance of the SFSI effect in evaluation of the seismic response of LNG tanks built on pile foundations. Indeed, choice of the deep foundation system and composition of the foundation in terms of raft effects and pile length can significantly change the dynamic response of an LNG tank and thus seismic forces in the foundation and superstructure

... Spritzer J.M. ve Guzey S. API 650 Annex E ile çelik tankların sismik analizini Yeni Zelanda ve Japon standartları ile karşılaştırmalı olarak yaptıkları araştırmaya göre; deprem sırasında, tank içindeki sıvı, yatay olarak hızlanır ve tank duvarında kuvvetler meydana getirir. Ayrıca karşılaştırdıkları standartlarda, hidrodinamik çember gerilimi (hoop stress), su yükselmesi, taban gerilmesi ve burkulma gibi hasar durumlarını gözlemlemişler [14]. ...

... In addition, in the standards, damage situations such as hydrodynamic hoop stress, uplift, base buckling, freeboard, stress and overturning were taken into consideration. According their to results, API 650 Annex E sufficiently considers all the major failures states unlike New Zealand and Japanese design documents [15]. ...

... unanchored) where stability against overturning is offered by the self-weight only. In that instance, the governing parameter is the aspect ratio of the structure, essentially guiding designers towards the anchored solution when slender systems are sought, and the unanchored for squat ones (Spritzer and Guzey 2017). The latter is usually more desirable as it eliminates the need for (costly) anchorage at the base, bearing in mind that it renders the system prone to uplift in the event of severe lateral loading. ...

Seismic base isolation is examined as a design alternative for supporting industrial facility liquid storage tanks against earthquake loading. A 160,000m 3 liquid storage tank is adopted as a case study, for which two designs are assessed, one with and one without base isolation. Using a nonlinear surrogate model and a set of ground motion records selected using the conditional spectrum approach for the average spectral acceleration intensity measure, Incremental Dynamic Analysis is employed to derive seismic fragility curves. Consequences of damage are evaluated in terms of downtime, considering the characteristics of petrochemical storage tanks, whereby any repair requires a lengthy list of actions dictated by health and safety requirements. The results reveal considerable benefits when base-isolation is employed, by drastically reducing downtime when sufficient displacement capacity is provided in the isolators.

... In addition, in the standards they are compared, damage situations such as hydrodynamic hoop stress, uplift, base buckling, freeboard, stress and overturning were taken into consideration. when compared to New Zealand and Japanese design documents, API 650 Annex E can be considered to take sufficient account of all major error situations [10]. ...

Cylindrical steel storage tanks are widely used for the storage of various liquids, industrial chemicals and firefighting waters. They have been used for cooling purposes in nuclear power plants in recent years. Liquid-storage tanks have many different configurations; however, in this study, cylindrical ground-supported liquid steel tanks were preferred due to their simplicity design and performance of resistances against seismic loads, when compared with other configurations. Earthquakes are a natural occurrence and are unpredictable and complex; thus, the steel storage liquid tanks are expected to withstand earthquake-related loads. These tanks may be exposed to some damages such as elephant-foot buckling, diamond-shape buckling, overturning and uplifting during earthquakes. They can also cause great financial and environmental damage with their hazardous chemical contents. Dimensions of cylindrical open-top, flat-closed and torispherical-closed-top tanks were determined for 3D-finite element method (FEM) models in an ANSYS workbench software. This article focuses on the seismic-activity-resistant ground-supported cylindrical (vertical) steel storage liquid tanks. Seismic analyses were conducted under El-Centro earthquake loads. Directional deformation, equivalent stress and acceleration results were presented for both impulsive and convective regions. In this study, directional deformations of the tanks with the same diameter and three different roofs (open-top, flat-closed and torispherical-closed) were compared after the seismic analysis. The results show that if the cylindrical steel water tank roof is closed in a torispherical dome shaped, the directional deformation will decrease. Hence, torispherial roof shape of tank is recommended.

... In addition, in the standards they are compared, damage situations such as hydrodynamic hoop stress, uplift, base buckling, freeboard, stress and overturning were taken into consideration. when compared to New Zealand and Japanese design documents, API 650 Annex E can be considered to take sufficient account of all major error situations [10]. ...

... The need for a thoughtful seismic design is highlighted by Brunesi et al. [36], Shih and Babcock [37], and many more. To address this safety need, Spritzer and Guzey [38,39] and Zui et al. [40] performed computational and experimental evaluations of tanks under seismic excitation. Similarly, wind loading can lead to catastrophic tank failures as reported by Godoy [41], Flores and Godoy [42], and Santella et al. [43]. ...

The American Petroleum Institute Specification 12D (API 12D) provides the oil and gas industry with ten tank designs with nominal capacities ranging from 500 bbl (79.5 m³) to 10,000 bbl (1590 m³). These tanks serve as a temporary product storage medium at the upstream segment of the industry, and are mass-produced to accommodate the demand. The structural performance of these ten 12D tanks is assessed in this study to verify that safe operation is maintained under various loading conditions. This study investigates the behavior and performance of the API 12D tank designs with a new rectangular cleanout with a semicircular top that is surrounded by a reinforcement pad. Various loading patterns were modeled in a finite element analysis approach including internal pressure, vacuum, hydrostatic pressure, and wind load. An elastic stress analysis, an elastic-plastic stress analysis, and an elastic buckling analysis were used in this work to compare the behavior of the tank designs against the failure criteria specified for each type of analyses. The stress level, plastic strain, buckling load, and tank uplift are reported for each of the ten API 12D tank designs and possible shell thickness variations are provided as insight into the performance expected with the new cleanout detail.

... Much research has been undertaken to investigate the dynamic behaviour of water and petroleum storage tanks that are typically composed of steel material that is different from the steel used to manufacture wine tanks, which in some cases have an open top or a floating roof, and that mostly have a low height to radius (H/R) aspect ratio and are either anchored or are unanchored to their foundation and rest on a concrete ring wall (e.g. see [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]). Currently limited research has been reported on damage data associated with wine storage tanks, with the most comparable earthquake damage data available being collected between 1933 and 1995 and reported by Cooper [26] based on an inventory of 424 water and petroleum storage tanks. ...

The 2013 Seddon earthquake (Mw 6.5), the 2013 Lake Grassmere earthquake (Mw 6.6), and the 2016 Kaikōura earthquake (Mw 7.8) provided an opportunity to assemble the most extensive damage database to wine storage tanks ever compiled worldwide. An overview of this damage database is presented herein based on the in-field post-earthquake damage data collected for 2058 wine storage tanks (1512 legged tanks and 546 flat-based tanks) following the 2013 earthquakes and 1401 wine storage tanks (599 legged tanks and 802 flat-based tanks) following the 2016 earthquake. Critique of the earthquake damage database revealed that in 2013, 39% and 47% of the flat-based wine tanks sustained damage to their base shells and anchors respectively, while due to resilience measures implemented following the 2013 earthquakes, in the 2016 earthquake the damage to tank base shells and tank anchors of flat-based wine tanks was reduced to 32% and 23% respectively and instead damage to tank barrels (54%) and tank cones (43%) was identified as the two most frequently occurring damage modes for this type of tank. Analysis of damage data for legged wine tanks revealed that the frame-legs of legged wine tanks sustained the greatest damage percentage among different parts of legged tanks in both the 2013 earthquakes (40%) and in the 2016 earthquake (44%). Analysis of damage data and socio-economic findings highlight the need for industry-wide standards, which may have socio-economic implications for wineries.

... unanchored) where stability against overturning is offered by the self-weight only. In that instance, the governing parameter is the aspect ratio of the tank (i.e. the ratio of fluid height over the tank radius), essentially guiding designers towards the anchored solution in slender tank configurations, and the unanchored for squat ones [10]. The latter is usually more desirable as it eliminates the need for (costly) anchorage at the base, yet, it renders the system prone to uplift in the event of severe lateral loading. ...

Motivated by the seismic response of unanchored liquid storage tanks, their uplift mechanism under strong lateral loading is examined. Using three-dimensional finite element models, nonlinear static analysis is conducted to define the moment-rotation relationship of uplifting tanks resting on rigid foundation and describe the evolution of critical response parameters with increasing level of lateral loading. Meridional and hoop stress, as well as their distribution and evolution with increased uplift are computed. Comparing the numerical results with the corresponding results from anchored tanks, striking differences are observed on the values of compressive meridional stresses and their distribution around the tank circumference. Cyclic analysis, associated with repeated uplift at both sides of the tank, is also performed, to obtain the corresponding hysteretic response and verify the assumption of nonlinear-elastic tank behaviour, used in several previous works. Finally, an analytical solution is developed, capable of describing tank uplift in an efficient manner. The analytical solution accounts for the special features of uplift, obtained from the finite element solution, and can be used for simple and reliable assessment of seismic performance in unanchored liquid storage tanks. KEY WORDS: liquid storage tank; seismic loading; nonlinear inelastic analysis; cyclic inelastic response; steel shell strength.

... A number of researchers have also analysed the influence of different base-isolation systems on the dynamic and seismic behaviour of cylindrical liquid storage tanks (see, for example, Shekari et al. 2010, Seleemah and El-Sharkawy 2011, Moeindarbari et al. 2014, Shahrjerdi and Bayat 2018, Sun et al. 2018. Moreover, some investigations have concerned seismic design of liquid tanks, including the aspects of soil flexibility (see, for example, Minoglou et al. 2013, Spritzer and Guzey 2017, Shekari 2018, Shekari et al. 2019. Other studies have been focused on the numerical evaluation of standard provisions. ...

In technical branches, such as chemical or petroleum industries, cylindrical steel tanks are essential structures used for storage of liquid products. Therefore, their safety and reliability is essential, because any failure might have dangerous consequences, in extreme cases may even lead to an environmental disaster. The aim of the presented paper is to show the results of the modal analysis concerning the cylindrical steel tank with self-supported roof which has been constructed in northern Poland. The investigation was carried out with the use of the FEM commercial computer program Abaqus. The values of natural frequencies, as well as the natural modes, for different levels of liquid filling (empty tank, partly filled and tank fully filled) were determined in the study. The results of the study clearly indicate that the increase in the liquid level leads to the substantial decrease in the natural frequencies of the structure.

... Spritzer and Guzey [16] compared the design provisions in Appendix E of API 650 with other wellknown design documents throughout the world, including those used in New Zealand and Japan. In comparative study, damage and states such as hydrodynamic hoop stress, elevation and floor tensioning, freeboard stress and tipping are taken into account. ...

... API 650 [41] is an American standard for seismic design of above-ground steel storage tanks. It was extensively reviewed by Spritzer and Guzey (2017) [42] and compared with other design codes and guidelines such as New Zealand [43] and Japan [44]. Failure mechanisms such as hydrodynamic hoop stress, uplift, base plate stress, and buckling were investigated. ...

• Iman Bahreini Toussi
• Reza Kianoush
• Abdolmajid Mohammadian

Liquid-containing structures are used for various municipal and industrial applications. The functionality of these structures in seismic regions is crucial. The main purpose of this study is to investigate the behavior of liquid under seismic excitations using numerical modelling. For this purpose, experimental and numerical studies are conducted. In the experimental tests, a ground-supported rectangular tank is excited on a shaking table. The tests are videotaped from two directions and subsequently analyzed frame-by-frame. Four different orientations are tested to investigate the effect of bilateral excitation. In the numerical simulations, the same tank is modeled in OpenFOAM—a computational fluid dynamics program—and the same excitations are applied. The results from the numerical and the experimental studies are compared, and reliability of the numerical model is discussed. Furthermore, using the numerical model, the pressure on the roof of the tank is obtained at various locations and examined for different excitations.

... refers to the sloshing of the free fluid-surface, and is tied to roof and upper-course damage on the tank. This so-called convective component seldom contributes noteworthy overturning actions on the tank and thus the decoupling among impulsive and convective may reasonably be taken for granted especially for squat tanks [14,15]. Evidently, from an assessment point of view, it appears that one is left with a single system influenced by two (largely uncorrelated) spectral acceleration ordinates [e.g. ...

A series of scalar and vector intensity measures is examined to determine their suitability within the seismic risk assessment of liquid storage tanks. Using a surrogate modelling approach on a squat tank that is examined under both anchored and unanchored support conditions, incremental dynamic analysis is adopted to generate the distributions of response parameters conditioned on each of the candidate intensity measures. Efficiency and sufficiency metrics are used in order to perform the intensity measure evaluation for individual failure modes, while a comparison in terms of mean annual frequency of exceedance is performed with respect to a damage state that is mutually governed by the impulsive and convective modes of the tank. The results reveal combinations of spectral acceleration ordinates as adequate predictors, among which the average spectral acceleration is singled out as the optimal solution. The sole exception is found for the sloshing‐controlled modes of failure, where mainly the convective period spectral acceleration is deemed adequate to represent the associated response due to their underlying linear relationship. A computationally efficient method in terms of site hazard analysis is finally proposed to serve in place of the vector‐valued intensity measures, providing a good match for the unanchored tank considered and a more conservative one for the corresponding anchored system.

... How to prevent foundation settlement and foundation design are organically combined to teach students. This part will carry out the following four topics: (1) the relationship between the compressibility of soil and the stability of tank foundation; (2) prediction method of tank foundation settlement; (3) safety evaluation method of storage tank under the condition of foundation settlement; (4) relevant measures to prevent foundation settlement [8] . Under the background of building large-scale oil storage in soft soil area, students can understand the design and safety evaluation of foundation settlement through the course of "Strength Design and Safety Management of Storage and Transportation Facilities", which is of positive practical significance for carrying out scientific research in related fields in the future. ...

• Chen Yanfei
• Ni Heng
• Zhang Hong
• Hou Fuheng

As one of the compulsory courses of oil and gas storage and transportation engineering, "Strength Design and Safety Management of Storage and Transportation Facilities" is a comprehensive course of both practicality and theory. In order to solve the unbalanced distribution of theoretical and applied content in the teaching process, the teaching team reformed the teaching mode of the structure design of large storage tanks in the course of "Strength Design and Safety Management of Storage and Transportation Facilities" and introduced case-based teaching. On the basis of the original course, practical engineering case analysis such as wind-induced buckling of large storage tank and uneven settlement of tank foundation was added, which increased the proportion of application content. It is a new type of discussion teaching integrating case collection, group discussion and after-class experience exchange. According to the recent three years of teaching practice, students' interest in this course has increased greatly and teaching quality has improved significantly, which fully verified the feasibility of engineering case-based teaching in teaching reform. The teaching team has gradually improved the teaching process according to the relevant experience and lessons in classroom practice and made a successful attempt in the teaching reform of storage and transportation structure safety courses, which is of positive significance for training application-oriented composite talents with the ability to solve practical problems in the new era.

... For upright cylindrical storage tanks, common seismic damage to the tank wall takes the form of diamond buckling or elephant's foot [7]. Diamond buckling occurs at a distance above the tank base or the connection between the tank wall and the base plate. ...

This research experimentally addresses the seismic response of a cylindrical liquid storage tank in terms of six factors, i.e., acceleration, displacement, hoop and axial stresses in the tank wall, sloshing and uplift. Both material and geometrical nonlinear interaction due to sloshing and uplift are considered. The simultaneous effects of the fixity condition, the supporting base flexibility and the aspect ratio on the response are presented in radar plots. The results reveal that, depending on the aspect ratio, the supporting base flexibility governs the overall response by activating uplift. A nonlinear elastic spring-mass model gives a good representation of the results.

... Broad tanks, in general, generate larger free surface waves and therefore have higher convective mass proportions compared to tall, slender tanks. For high aspect, ratios stability can control the design, where overturning and uplift of unanchored tanks are of great concern, while material limits are still critical (Spritzer et al, 2017). Tank design codes reflect the culmination of decades of work by many dedicated individuals. ...

stiffener that effect on the strutural behavior on liquid storage tank , there was used different steel shape profile and the tank seperate with courses that we have 1-6 courses , we are calculated the placed stiifener on the tank wall , thus we are using software finite element program that is called ANSYS then it is analyzed fundamental frequency, deformation, stress, buckling multiplier

... Moreover, corrosion of the tank [3] and welding process [4] may also affect the buckling behavior. Seismic effects on cylindrical storage tanks have been studied by many researchers [5][6][7][8][9] as dynamic buckling problems. However, other cases such as uniform external pressure or wind pressure are usually analyzed as quasi-static buckling problems [1]. ...

Aboveground vertical steel storage tanks use stiffener rings to prevent their shell wall from buckling under wind loading. The existing stiffener rings design rules from API 650 standard is known to be overly conservative. This study investigates the possibility of modifying the design rules by reducing the required size of the top stiffener ring to the same size as the intermediate stiffener ring. In this study, we used finite element analysis (FEA) to perform linear bifurcation analysis (LBA) and geometrically nonlinear analysis including imperfections (GNIA) to obtain failure load of modeled tanks. The buckling pressure load was obtained to ensure it is larger than the design pressure. Moreover, the effects of higher strength materials, different buckling modes, and various wind profiles were also studied to ensure the design suggested by this study is practical and universal to different situations. The results show that for cylindrical storage tanks, which only needs one intermediate stiffener ring, the size of the top stiffener ring can be set to the same size as the intermediate stiffener ring.

... In the recent past, the codes and standards have been regularly updated with the latest research contributions made thereupon [30,31]; whereas, the dynamic fluid-structure interaction (FSI) problem was further investigated in-depth for better understanding and improved response prediction [20], [4,57,65,74]. Furthermore, the dynamic behavior of the liquid storage tanks was studied by Moslemi and Kianoush [49], Ormeno et al. [51], Ruiz et al. [60], and Spritzer and Guzey [73]. ...

A numerical study of the base-isolated ground-supported cylindrical liquid storage tank is carried out using finite element method (FEM). The coupled acoustic-structural (CAS) approach in the FEM is used for the analysis of the base-isolated tanks with rigid and flexible walls with varying parameters. Base isolation systems used in the present study are laminated rubber bearing (LRB) and friction pendulum system (FPS). The effects of aspect ratio (liquid height to radius) of the tank, and the isolation time period on the seismic response of the base-isolated tank is considered for investigation. For this study, the broad and slender tanks with three different isolation time periods are considered, which exhibit their relative flexibility. The sloshing displacement, base shear, hydrodynamic pressure, and bearing displacement responses are evaluated for three-dimensional (3-D) rigid and flexible tanks subjected to bi-directional components of earthquake ground motions. Moreover, the FE results are compared with the commonly used mechanical lumped-mass model of the base-isolated tank. The results show that as the time period of the isolator increases, i.e. increased flexibility, the base shear response is considerably reduced in both the rigid and flexible, broad and slender tanks. The reduction in the impulsive component causing base shear is more as compared to the convective (sloshing) component in the base-isolated tanks. The sloshing displacement increases with increase in the time period of the base isolation systems in both the rigid and flexible tanks. The impulsive hydrodynamic pressure along the tank wall is reduced with introduction of the isolation systems and the reduction is significantly more in case of the flexible isolators. The bearing displacement increases with increase in the time period of the isolation system adopted.

A seismic analysis of ground-supported, three-dimensional (3-D) rigid-base steel cylindrical liquid storage tank is investigated, using a coupled acoustic-structural finite element (FE) method for fluid-structure interaction (FSI). In this method, the contained liquid in the tank is modelled using acoustic elements and the cylindrical tank is modelled using shell elements. The impulsive and convective terms are estimated separately by using the appropriate boundary conditions on the free surface of the liquid. The convergence and validation studies of the proposed FE model are conducted by comparing the results reported in the literature. The parametric studies are performed for rigid and flexible tanks for the varying slenderness of the open roof tanks. The sloshing displacement and base shear time history responses are evaluated for the 3-D tanks subjected to harmonic unidirectional ground motions. Further, the results are compared with the commonly used two and three lumped-mass models of the tank. Moreover, the seismic response quantities of the tank subjected simultaneously to the bi-directional horizontal components of earthquake ground motion are also investigated using the 3-D FE model, and the response quantities are compared with the lumped-mass models. The results obtained from the 3-D FE model and lumped-mass model are in close agreement. The average percentage difference in the 3-D FE and lumped-mass models for maximum sloshing displacement prediction is 15 percent to 20 percent and that for the base shear is about 4 to 10 percent, in the case of the uni-directional harmonic ground motions. It is concluded that the sloshing displacement is not affected by the tank flexibility, but the impulsive hydrodynamic pressure and the impulsive component of the base shear increases with the tank flexibility.

• Mohammad Reza Shekari

This study displays a coupled numerical process to scrutinize the sloshing response for multi baffled flexible cylindrical container subjected to lateral excitations. The developed algorithm is based on a coupled three-dimensional boundary element-finite element approach which allows computing sloshing natural frequencies, as well as seismic responses. The intricate liquid region is divided into several simple sub-regions so that in each liquid sector the Laplace equation is solved by introducing interface influence matrix and, finite element route is employed to model the tank shell. This process has a substantial influence on lessening computational cost and a good precision in evaluating the response of the whole system. The time variations of sloshing responses, base forces, the maximum hydrodynamic pressure and shell radial displacement in relation to various system parameters such as the liquid-fill depth, tank geometry and baffles arrangement are deliberated in detail. From these examinations, it may be concluded that with the installation of baffle rings inside the liquid tank, the dynamic response of such structures during severe earthquake ground shakings can be significantly diminished. Furthermore, in the exceptional case of long-period ground excitations, the seismic response of multi baffled containers may be controlled by the baffle rings only at particular statuses of shallow structures. For the case of slender containers, special considerations would be required to be assigned to the design of baffle plates believed to experience long-period seismic excitations. The proposed coupled numerical procedure can serve as a basis for future analysis of multi baffled cylindrical tanks in conjunction with fluid due to severe long-period earthquakes.

• Md Alimul Haque

The use of Learning Management Systems as a tool for designing, sharing, monitoring, and organizing various forms of teaching and training content marked a turning point in the development of E - Learning. Major technical advancements have converted the early LMS into a sophisticated program for organizing curriculum, giving rich-content course materials, assessment, and interactive collaboration since its beginnings. With numerous current research areas dealing with various technologies connected to the LMS, the structure, operations, and implementation of the LMS will undoubtedly alter in the future. The Internet of Things is the most crucial technology that is predicted to alter many parts of the future (IoT). We present a conceptual framework for a forthcoming E Learning with Intelligent automation in this article. We discuss how IoT will influence many aspects of the E - Learning, as well as the projected improvements and adjustments that IoT will bring to E- learning functionality. In this paper, we emphasize on the use of IoT services in the context of e-learning. We outline numerous services now provided by existing learning management systems in our framework, and show how these services will transform if they are merged with IoT services and connected to IoT modules and gadgets. We also suggest some additional services which will be achieved as a result of the integration of IoT into E-learning. We describe how each proposed E-learning. service will be implemented inside the E-learning., how it will be linked to other E-learning. services, and how it will be utilized to improve teaching and learning processes on the university campus

Base shear and sloshing response control in ground-supported circular cylindrical liquid storage tank is achieved by oblate spheroid base isolation (OSBI) system used along with floating surface diaphragm on the contained liquid. The new base isolation system, OSBI proposed herein is based on rolling-friction mechanism in ellipsoidal-shaped isolators in both the horizontal axes. The surface diaphragm is proposed to float on the free liquid surface to control the sloshing amplitude. The tank is analyzed using the coupled acoustic-structural (CAS) approach in finite element method (FEM). In order to have conformity of the present FE model, the FEM results are compared with the mechanical lumped-mass model of the tank (without surface diaphragm). The seismic response is investigated for the tank subjected to harmonic and real-earthquake excitations. The parameters considered for the analysis are the aspect ratio of the tank, eccentricity of the isolator, and thickness of the diaphragm. The seismic response quantities evaluated are base shear, sloshing displacement, and impulsive hydrodynamic pressure in the tank. Further, to study the effectiveness of the OSBI, the seismic responses of the tank subjected tri-directional components are compared with the two horizontal bi-directional components of the earthquakes. Also, the sloshing displacement with and without surface diaphragm in the non-isolated and base-isolated tanks are compared. From the results, it is observed that the OSBI system is efficient in mitigating the seismic responses in the tanks and the surface diaphragm is efficient in controlling the sloshing displacement. The superior performance of the proposed isolator depends on the design parameters, namely, eccentricity, and coefficient of rolling friction selected. The effectiveness of the surface diaphragm depends on the choice of material and thickness adopted.

• Md Alimul Haque

E-learning technology based on multimedia has had a tremendous impact on our daily teaching and learning activities. It has centred the learning process on the student. E-learning has become more fascinating than traditional education systems due to the usage of multimedia technologies. It began in the 1980s and has continued to develop since then. This innovative technology provides pupils with the benefit of studying in a fresh way. E-learning approaches make education more engaging and fascinating. It has also had a bigger influence on our culture and school system. It is now simple to study and teach without being fatigued. E-learning creates virtual learning environments on the internet via teacher-student interactions, online assessment, and interactive multimedia-based course material dissemination. Interactive multimedia delivers various kinds of media and suitable content delivery based on learners' learning styles, which improves learners' learning effectiveness. This article discusses the rapidly evolving technology of "Multimedia and e-education." Smart teaching approaches are increasingly being used in schools, as well as other institutions and organisations. E-textbooks are electronic textbooks that are used in a learner's actual class. The digital textbook makes advantage of the most recent smart gadget and technology. Keywords: Multimedia, Education, E- Learning, digital classroom

• Öznur özdinç
• CEM GÜNEŞOĞLU

Geçmişten günümüze kadar özellikle evlerimizde kullandığımız ve yaşam alanlarımızın vazgeçilmez ürünü olan halıların hem tasarım hem de üretim yönünden köklü bir geçmişi bulunmaktadır. Binlerce yıllık geçmişe sahip olan halı, dünyada giderek önem kazanmış ve dünya ticareti içerisinde kayda değer ürün gruplarından birisi haline gelmiştir. Günümüzde makine halıları ya dokuma tekniği kullanılarak ya da tufting metodu kullanılarak üretilmektedir. Üretilen bu makine halılarının kalitesi için ürünün yapısal özellikleri önem arz etmektedir. Müşterinin bir halıda bulunmasını istediği akustik yalıtım, konfor, termal yalıtım, görünüm, dayanıklılık ve güvenlik gibi özelliklerin arka planında yer alan halının yapısal özellikleri belirleyici niteliktedir. Makine halısının yapısal kalitesini belirleyen faktörlerin başında ise büyük oranda hav ipliğinin yapısı gelmektedir. Yapı içerisindeki hav ipliği incelendiğinde; sentetik liflerin sahip oldukları yüksek mukavemet ve aşınma direnci özelliği, kolay temizlenebilme özelliği, kimyasallara karşı yüksek direnç gösterme özelliği gibi avantajları sayesinde tekstil alanında yaygın olarak kullanıldıkları görülmektedir. Yapılan bu çalışmada aynı üretim parametrelerinden oluşmuş farklı kesit şekillerindeki polyester iplik kullanımının makine halıları üzerindeki etkisinin araştırılması amaçlanmıştır.

A numerical study is conducted using finite element models of large, circular, cylindrical, aboveground, steel, open-top, liquid storage tanks subjected to horizontal seismic forces. Nonlinearities of both material properties and geometry deformations are included. Soil-structure interactions are implemented into the finite element models by using a series of elastic springs representing a stiff soil foundation. Hydrodynamic hoop stresses, elephant's foot buckling, and uplift are measured for tanks with height to radius ratios, or aspect ratios, between 0.4 and 2.0. The finite element models are compared to the provisions of API 650 Annex E, with special attention to the anchorage ratio, J. The results show that, while the finite element models are much more complex than the theoretical and empirical equations provided in API 650, the total hoop and axial compressive stresses are comparable. Furthermore, the anchorage ratio limits set by API 650 seem to be in good agreement with the finite element models in terms of uplifting behavior.

Previous investigations have demonstrated that strong earthquakes can cause severe damage or collapse to storage tanks. Theoretical studies by other researchers have shown that allowing the tank to uplift generally reduces the base shear and the base moment. This paper provides the necessary experimental confirmation of some of the numerical finding by other researchers. This paper reports on a series of experiments of a model tank containing water using a shake table. A comparison of the seismic behaviour of a fixed base system (tank with anchorage) and a system free to uplift (tank without anchorage) is considered. The six ground motions are scaled to the design spectrum provided by New Zealand Standard 1170.5 (2004) and a range of aspect ratios (height/radius) is considered. Measurements were made of the impulsive acceleration, the horizontal displacement of the top of the tank and uplift of the base plate. A preliminary comparison between the experimental results and the recommendations provided by the liquid storage tank design recommendations of the New Zealand Society for Earthquake Engineering is included. The measurement of anchorage forces required to avoid uplift under varying conditions will be discussed.

• Assist Ersan Güray
• Ce
• Assist Gökhan
• Gokhan Yazici

Sloshing in medium sized tanks under earthquake load This paper presents results obtained by numerical study of sloshing effects in medium sized rectangular tanks subjected to a long-period seismic excitation. The Smoothed Particle Hydrodynamics (SPH) method is used, and the wave displacement and pressure are analysed. The intensity of sloshing effects depends not only on the peak ground acceleration but also on the dominant frequency of ground motion. Excessive sloshing displacements and pressures increase when the natural period of the contained liquid approaches the dominant period of ground excitation. Problem zapljuskivanja u spremnicima srednjeg kapaciteta pri potresnom opterećenju Ovaj rad prikazuje rezultate numeričkog ispitivanja utjecaja zapljuskivanja (eng. sloshing) u pravokutnim spremnicima srednjeg kapaciteta uslijed seizmičke pobude dugog perioda. Primijenjena je metoda hidrodinamike izglađenih čestica (eng. Smoothed Particle Hydrodynamics-SPH) te su analizirani valni pomaci i tlak. Intenzitet utjecaja zapljuskivanja ne ovisi samo o vršnom ubrzanju tla nego i o dominantnoj frekvenciji podrhtavanja tla. Prekomjerni pomaci i tlak uslijed zapljuskivanja rastu kada se prirodni period tekućine u spremniku približava dominantnom periodu podrhtavanja tla.

Material degradation due to corrosion significantly alters the seismic response of ground-based cylindrical steel storage tanks. A numerical study is conducted to investigate the effects of internal shell corrosion on the dynamic buckling of three cone roof ground-based, steel cylindrical tanks with height to diameter ratios (H/D) of 0.40, 0.63 and 0.95, subjected to horizontal seismic base excitations. Internal corrosion is considered as a time dependent uniform thinning of the wall at the upper and the lower parts of the tank being in contact with, respectively, atmospheric oxygen and acid gases and residual water. Detailed numerical models of the tank–liquid systems at different stages of corrosion degradation are subjected to two representing accelerograms and for each model the critical peak ground acceleration (PGA) for dynamic buckling of the shell and its associated mode of failure are evaluated. It is found that in all three tanks, the critical PGA is markedly reduced with thinning of the shell, irrespective of the type of ground input. The buckling mode of failure of the tanks also changed from an elastic diamond-shaped failure at the top of the shell to an elasto-plastic elephant foot type failure near the base, after 10 years for the shorter tanks (H/D=0.4 and 0.63) and after 15 years for the tallest tank. The effects of uniform corrosion degradation on the critical buckling load of the tanks were found to be such that after 20 years of thinning due to corrosion, the static loading alone was responsible for the elephant foot buckling of the shell.

• Praveen K. Malhotra

A systematic study is made of the effects of base uplifting on the seismic response of cylindrical liquid-storage tanks that are supported directly on flexible soil foundations. First, a detailed investigation is made of the effects of system parameters on the uplifting resistance and energy dissipation capacity of the partially uplifted base plate. It is shown that: (1) the hydrodynamic base pressures reduce the uplifting resistance as well as the energy dissipation capacity of the base plate; (2) the uplifting resistance increases with increase in the thicknesses of the base plate and the tank wall, and the stiffness of the foundation soil; and (3) the energy dissipation capacity increases with an increase in the base-plate thickness and the yield level of plate material, and reduces with increase in foundation stiffness and the thickness of the tank wall. Next, an efficient method is presented for the dynamic response analysis of flexibly supported unanchored tanks. It is shown that the flexibility of the foundation reduces the overturning base moment, and reduces significantly the axial compressive stresses in the tank wall, but these reductions are accompanied by increased values of plastic rotations and (in some cases) base uplifting and hoop compressive stresses.

• Mahmoud Reza Maheri
• R. T. Severn

The earthquake induced vibration of a ground-based cylindrical structure containing or surrounded by liquid produces hydrodynamic forces in the liquid which should be considered in aseismic design. In evaluating these pressures most current design codes assume the structure to be rigid and ignore the pressures due to its flexible response. In this paper the results of a number of experiments are presented which investigate the pattern and magnitude of the different types of impulsive hydrodynamic pressures in three steel cylindrical models. Extensive forced-vibration, simulated earthquake and impulse tests carried out on the models when water-filled, as well as when surrounded by water show high discrepancies between the overall hydrodynamic pressures and the pressures obtained when the cylinder is assumed rigid. Based on the experimental findings, a method is proposed which enables evaluation of the hydrodynamic pressures due to flexible response in the fundamental mode. Also, improvements are proposed on approximate design methods.

This paper reports results of the structural response of empty steel tanks under vertical ground motions. The tanks are modeled using a finite element discretization using shell elements, and the vertical motion is applied and analyzed using nonlinear dynamics. Several excitation frequencies are considered, with emphasis on those that may lead to resonance of the roof. The computational results illustrate that as the base motion frequency is tuned with the frequency of the first roof-mode of the tank, the system displays large-amplitude displacements. For frequencies away from such mode, small amplitude displacements are obtained. The effect of the height of the cylinder on the dynamic response of the tank to vertical ground motion has also been investigated. The vertical acceleration of the ground motion that induces significant changes in the stiffness of the tank was found to be almost constant regardless of the height of the cylinder.

This paper provides the theoretical background of a simplified seismic design procedure for cylindrical ground-supported tanks. The procedure takes into account impulsive and convective (sloshing) actions of the liquid in flexible steel or concrete tanks fixed to rigid foundations. Seismic responses - base shear, overturning moment, and sloshing wave height - are calculated by using the site response spectra and performing a few simple calculations. An example is presented to illustrate the procedure, and a comparison is made with the detailed modal analysis procedure. The simplified procedure has been adopted in Eurocode 8.

Ground-supported steel tanks experienced extensive damage in past earthquakes. The failure of tanks in earthquakes may cause severe environmental damage and economic losses. This study deals with the evaluation of the elastic buckling of above-ground steel tanks anchored to the foundation due to seismic shaking. The proposed nonlinear static procedure is based on the capacity spectrum method (CSM) utilized for the seismic evaluation of buildings. Different from the standard CSM, the results are not the base shear and the maximum displacement of a characteristic point of the structure but the minimum value of the horizontal peak ground acceleration (PGA) that produces buckling in the tank shell. Three detailed finite element models of tank-liquid systems with height to diameter ratios H/D of 0.40, 0.63, and 0.95 are used to verify the methodology. The 1997 UBC design spectrum and response spectra of records of the 1986 El Salvador and 1966 Parkfield earthquakes are used as seismic demand. The estimates of the PGA for the occurrence of first elastic buckling obtained with the proposed nonlinear static procedure were quite accurate compared with those calculated with more elaborate dynamic buckling studies. For all the cases considered, the proposed methodology yielded slightly smaller values of the critical PGA for the first elastic buckling compared to the dynamic buckling results.

• Praveen K. Malhotra

Seismic base isolation of ground supported cylindrical liquid-storage tanks is proposed by disconnecting the wall of the tank from the base plate and supporting it on a ring of horizontally flexible bearings; the base plate is supported directly on the ground. The gap between the wall and the base plate is closed with a flexible membrane, which prevents the loss of fluid from the tank and allows the tank wall to move freely in the horizontal direction. The effect of isolation on both the impulsive and the convective (sloshing) responses of the liquid is examined for two steel tanks–one broad and one slender. It is shown that isolation can reduce dramatically the hydrodynamic base shears, overturning moments, and axial compressive stresses in the tank wall without significantly increasing the vertical displacements of the liquid surface due to sloshing. Since the weight supported by the bearings is small compared to the total liquid weight, the bearings in slender tanks experience a net tensile force during strong shaking. © 1997 John Wiley & Sons, Ltd.

• J. Michael Rotter

Metal cylindrical bins, silos and tanks are thin shell structures subject to internal pressure from stored materials together with axial compression from the frictional drag of stored materials on the walls and horizontal loads. The governing failure mode is frequently buckling under axial compression. The internal pressure exerted by the stored fluids or solids can significantly enhance the buckling strength, but high internal pressures lead to severe local bending near the base. Local yielding then precipitates an early elastic-plastic buckling failure. This failure mode, commonly known as "elephant's foot buckling", has received relatively little attention to date and until recently was often ignored in tank and silo design.

• M Eeri
• Praveen K. Malhotra

Seismic ground motions excite long-period sloshing response in liquid-storage tanks. A minimum freeboard is needed to prevent the sloshing waves from impacting the roof of tanks. Since freeboard results in unused storage capacity, many tanks are not provided with the sufficient freeboard. As a result, sloshing waves impact the roof, generating additional forces on the roof and tank wall. This article presents a simple method of estimating these forces.

• Praveen K. Malhotra

An approximate method is presented for the analysis of earthquake induced uplifting in base plates of unanchored liquid-storage tanks that are supported directly on flexible soil foundations. The method takes due account of the non-linearities arising from the continuous variation of base contact area, membrane action and plastic yielding in the base plate. First, an 'exact' solution is presented for a uniformly loaded flexibly supported prismatic beam, uplifted by a concentrated force applied at one end. A series of such beams are later used in an approximate model of the base plate. The method is highly efficient and believed to be accurate for the level of uplifts encountered in practice. The results are presented for a range of foundation stiffness, representing loose sandy soils to rigid concrete mat. It is shown that, for the same overturning base moment, the flexibly supported tanks, in comparison with the rigidly supported tanks, experience significantly smaller axial compressive stress, but larger base uplift, foundation penetration, plastic rotation at plate boundary and hoop compressive stress in the tank wall.

• Mahmoud Reza Maheri
• R. T. Severn

Added-mass is an important parameter influencing the hydrodynamic interaction between liquid and a structure and consequently the hydrodynamic forces acting on that structure. For this purpose evaluation of the added-mass has been carried out by many investigators using the classical theory of hydrodynamics for rigid-body vibration. Using this concept, they have obtained accurate results for the fundamental frequency of vibration only. Recent theoretical studies have indicated that the added-mass in a flexible structure is different from that of the same structure when considered to be rigid. In the present paper the results of a number of experimental investigations are presented which examine the nature and magnitude of the added-mass in flexible vibration of three cylindrical models when containing water, as well as when surrounded by water. It is shown that the classical added-mass is only applicable to single-degree-of-freedom bodies, whether in rigid-body motion or flexible motion, and that the error in predicting the higher natural frequencies of the system is due to this discrepancy.

Steel conical tanks are widely used for liquid storage around the world and especially in North America. A number of those tanks collapsed in the last decades at different places as a result of instability of the steel shells. Despite being widely used, no specific design procedure is available for conical tanks under dynamic conditions. Most of the previous studies related to steel conical tanks focused on calculating the acting forces due to a seismic event. This study however, focuses on evaluating the capacity of conical tanks under hydrodynamic pressure resulting from horizontal ground excitation using non-linear static pushover analysis. The capacity is then compared to the seismic demand obtained using a previously developed mechanical model found in the literature for different seismic zones. This paper is a part of a larger study aiming to provide a simplified design procedure for steel conical tanks when subjected to earthquakes. The study is conducted numerically using a non-linear finite element model that accounts for the effects of large deformations and geometric imperfections on the stability of steel conical tanks.

• Medhat A. Haroun
• George W. Housner

A simple and sufficiently accurate method for estimating the seismic response of cylindrical liquid storage tanks is presented. A mechanical model, which takes into account the deformability of the tank wall is examined; it is based on the results of a finite element analysis of the liquid-shell system. The parameters of such a model are displayed in charts that facilitate the calculations of the effective masses, their centres of gravity, and the periods of vibrations. Detailed numerical examples are presented to illustrate the applicability of this model in predicting the maximum seismic response by means of response spectrum. Comparison with the exact solution of the problem conforms the validity of the method. (A)

Field evidence has established that strong earthquakes can cause severe damage or even collapse of liquid storage tanks. Many tanks worldwide are built near the coast on soft soils of marginal quality. Because of the difference in stiffness between the tank (rigid), foundation (rigid) and the soil (flexible), soil-foundation-structure interaction (SFSI) has an important effect on the seismic response, often causing an elongation of the period of the impulsive mode. This elongation is likely to produce a significant change in the seismic response of the tank and will affect the loading on the structure. An issue not well understood, in the case of unanchored tanks, is uplift of the tank base that usually occurs under anything more than moderate dynamic loading. This paper presents a comparison of the loads obtained using "Appendix E of API STANDARD 650" of the American Petroleum Institute and the "Seismic Design of Storage Tanks" produced by the New Zealand Society for Earthquake Engineering. The seismic response assessed using both codes is presented for a range of tanks incorporating a range of the most relevant parameters in design. The results obtained from the analyses showed that both standards provide similar base shear and overturning moment; however, the results given for the anchorage requirement and uplift are different.

• Nicola Buratti
• M. Tavano

Buckling plays a fundamental role in the design of steel tanks because of the small thicknesses of the walls of this class of structures. The first part of the paper presents a review of this phenomenon for liquid-containing circular cylindrical steel tanks that are fully anchored at the base, considering the different buckling modes and especially the secondary buckling occurring in the top part of the tank. A case study based on a cylindrical tank is then introduced in order to investigate various aspects of dynamic buckling. The finite element model of the case study tank is set-up using the added mass method for fluid modelling. The influence of pre-stress states caused by hydrostatic pressure and self-weight on the natural periods of the structure is first studied and it is found that this influence is very small as far as the global behaviour of the tanks is considered, while it is important for local, shell-type, vibration modes. In the following, the efficiency and sufficiency of different ground motion intensity measures is analysed by means of cloud analysis with a set of 40 recorded accelerograms. In particular, the peak ground displacement has been found being the most efficient and sufficient intensity measure so far as the maximum relative displacement of the tank walls is concerned. Finally, incremental nonlinear time-history analyses are performed considering the case study structure under recorded earthquake ground motions in order to identify the critical buckling loads and to derive fragility curves for the buckling limit state. Copyright

This paper presents a review of simplified seismic design procedures for elevated tanks and the applicability of general-purpose structural analyses programs to fluid–structure–soil interaction problems for these kinds of tanks. Ten models are evaluated by using mechanical and finite-element modelling techniques. An added mass approach for the fluid–structure interaction, and the massless foundation and substructure approaches for the soil–structure interactions are presented. The applicability of these ten models for the seismic design of the elevated tanks with four different subsoil classes are emphasized and illustrated. Designers may use the models presented in this study without using any fluid and/or special soil elements. From the models defined here, single lumped-mass models underestimate the base shear and the overturning moment. Because almost all the other assumptions for the fixed base give similar results, any method could be used, but the distributed added mass with the sloshing mass is more appropriate than the lumped mass assumptions for finite-element modelling, and is recommended in this study.

Endurance Time (ET) method is a time history based method for seismic evaluation of structures using intensifying dynamic excitation as the loading function. In this paper, application of this method in the analysis of steel tanks has been investigated. A methodology for practical application of ET method in seismic assessment of storage tanks has been presented. This methodology has been applied in three-dimensional nonlinear analysis of a particular anchored steel tank using Finite Element method, and results are compared with conventional codified design procedures. Results of the analyses indicate reasonable accuracy of the proposed method in estimation of seismic responses of steel tanks and its applicability in enhancing the design process of steel tanks considering various sources of complicated behavior. Comparative study of seismic response of the tank in anchored and unanchored states utilizing ground motions has been presented. Advantages and limitations of the procedure have also been discussed.

The influence of roof on the natural frequencies and the modes of fixed roof, ground supported, liquid storage tanks is presented in this paper. Attention is given to partially filled tanks with the same heights of 12.19 m and the aspect ratios (H/R) of 2, 1.52, and 1.33. The bottom of tanks is considered to be anchored to the foundation. The effect of the roof, along with the liquid height, on dynamic properties is investigated. For this purpose, each tank is modeled in 4 liquid levels, equal to 1.80, 4.80, 8.50, and 10.90 m and in two various roof conditions: with roof (WR) and open top (OT). The finite element package ANSYS is used to model the tank–liquid systems. Tank roof and wall are meshed by shell elements and the liquid is modeled using fluid finite elements. The fluid–structure interaction is taken into account by coupling the nodes at the interface of the fluid and the shell in the radial direction. Results of ambient vibration tests are used to verify the numerical procedure in which good agreement is observed between the numerical and the experimental modal parameters. It is found that the influence of roof on natural frequencies of axial and vertical modes is negligible whereas its effect on the natural frequencies of circumferential modes is significant. It is also concluded that at low liquid levels, equal to 1.80 and 4.80 m, the tank roof does affect the axial modes of the tallest and medium height tanks while, at all of the considered liquid heights and aspect ratios, the tank roof affects the circumferential mode shapes; this confirms the idea that the roof does restrain the tank top against radial deformations.

The present paper is concerned with the problem of modeling the fluid–structure interaction (FSI) in partially filled liquid containers. The study focuses on the sloshing phenomena and on the coupling computational fluid dynamics (CFD) analysis with the finite element stress analysis (FEA) used to predict the sloshing wave amplitude, convective mode frequency, pressure exerted on the walls and the effect of sloshing on the anchoring points forces. The interaction between fluids (water and air) and tank wall is modeled considering full and one-way coupling. Using the time history of an earthquake excitation, the results of the FSI model are compared with those obtained employing simplified mechanical models given in design codes. The coupling phenomenon was found to influence the sloshing effect, the impulsive pressure being amplified by the wall elasticity. The applied FSI methodology proves to be feasible in analyzing a 3D full coupled CFD/FEA storage tank subjected to a long time history excitation.

• S. Natsiavas
• C. D. Babcock

An explanation is provided for the earthquake-induced damage observed at the top of liquid storage tanks. An analysis is developed and the results are compared with experimental work. The basic steps of the analysis, which is developed for the general dynamic response of fluid-filled tanks under horizontal ground excitation, are first presented. In this analysis, the structural displacements are expanded in appropriate series forms which involve both rigid body and flexible components. The latter components are expressed as linear combinations of terms, each of which is a product of a function with assumed spatial dependence and an unknown time-dependent function. These time functions are then determined from the solution of the fluid/structure system equations, which are set up by employing Hamilton's principle. In the present work, results are obtained and compared with model tests carried out at Caltech, during which buckling was observed at the top of the tank under a known base excitation history.

• C. D. Babcock
• S. Natsiavas

An analysis developed for the response of liquid storage tanks under horizontal base excitation is employed and numerical results are obtained for unanchored tanks. These results are compared and found to be in good agreement with experimental data. Base uplift is shown to cause a dramatic reduction in the effective beam-type stiffness of a tank, which in turn reduces the tank response frequency and changes the developed hydrodynamic loads significantly. Based on these results, an explanation is provided for some great qualitative an quantitative differences in the behavior of a tank, resulting from its base fixity condition alone.

• S. Natsiavas

A set of equations is derived describing the dynamic response of cylindrical liquid storage tanks under horizontal ground excitation. The structure consists of a flexible cylindrical tank with a roof and a bottom plate and rests on a flexible ground through a rigid foundation. Portion of the base of the tank may separate from and lift off the foundation during ground motion. The solution of the hydrodynamic problem is first found in closed form. Then Hamilton's principle is applied and the equations governing the behavior of the coupled fluid/structure ground system are derived. During this procedure, the base uplifting is modeled by an appropriate rotational nonlinear spring placed between the base of the tank and the foundation.

• Andrew Whittaker
• Gary Hart
• Christopher Rojahn

The response modification factor plays a key role in the seismic design of new buildings in the United States. To date, the values assigned to this factor are based on engineering judgment and have little sound technical basis. Any improvement in the reliability of modern earthquake-resistant buildings in the United States will require the systematic evaluation of the building response characteristics that most affect the values assigned to the factor. To this end, a draft formulation that represents the response modification factor as the product of factors related to reserve strength, ductility, and redundancy is presented in the paper. Pertinent data from various analytical and experimental studies on reserve strength and ductility are also presented.

The work presented in this paper was motivated by the collapse of an elevated conical shaped water tower structure in Fredericton, Canada, in December of 1990. It is analytically based and involves nonlinear stability analysis of liquid-filled conical steel vessels possessing geometric imperfections and residual stresses. A finite-element formulation based on a newly developed consistent shell element that includes both geometric and material nonlinearities is used. Elastic stability analyses of conical shells with different geometric imperfection patterns are undertaken, and the results indicate that the presence of axisymmetric imperfections leads to the lowest limit load for the structure. The sensitivity of the hydrostatically loaded conical vessels to geometric imperfections and residual stresses is investigated by considering inelastic analyses of three cases: (1) perfect vessels; (2) same as case 1, but with axisymmetric geometric imperfections of the order of the thickness of the shell; and (3) same as case 2, but with the addition of residual stresses due to welding. Results of these analyses indicate that liquid-filled conical shells are quite sensitive to geometric imperfections and that yielding precedes elastic buckling for tanks having practical dimensions.

• Gonzalo S. Leon
• Eduardo A. M. Kausel

Refinements are presented on a model proposed originally by Wozniak for the seismic analysis of fluid storage tanks, which forms the basis of the provisions in the American Petroleum Institute design code API 650. It is found that use of the rules in API 650 may lead in some cases to underestimations of the maximum compressive stresses in the shell, and to overestimations of the tensile stresses in the straps of anchored tanks. The stiffness of these straps relative to that of the shell is shown to play an important role in the maximum compressive stresses that can be expected in the tank wall. In the case of unanchored tanks, the larger compressive shell forces result from the limited mass of fluid that can be mobilized before the buckling load in the shell is reached.

This study is motivated by the lack of information regarding seismic analysis and design of liquid-filled conical tanks. The main challenge in this type of fluid–structure interaction problem is the estimation of the forces associated with the hydrodynamic pressure resulting from the vibration of the structure. A simplified mechanical analog that can be used to estimate the forces associated with horizontal ground excitation is developed in this study. The proposed mechanical analog takes into account the flexibility of the tank walls and simulates both the impulsive and sloshing components of the hydrodynamic pressure. Parameters of this analog are displayed in chart form as functions of the geometrical parameters of the tanks including the angle of inclination of the tanks' walls. Finally, an example is provided to illustrate the application of the developed analog for evaluation of the response of liquid-filled conical tanks to horizontal ground excitation.

The influence of a fixed roof on the natural periods of vibrations of thin-walled aboveground steel tanks with clamped boundary conditions at the base is studied. Tanks with open-top, self-supported roofs, and roofs supported by rafters are considered, along with different tank aspect ratios. The self-supported roof geometries considered include dome, cone, shallow cone, and flat roofs; whereas the rafters supported roofs geometries study cone, shallow cone, and flat roofs. The effect of the aspect ratio, along with the roof configuration on the natural periods is discussed. It was found that the vibration of empty tanks with a fixed roof is dictated either by cylinder modes or roof modes of vibrations. For self-supported roofs predominant roof modes resulted, whereas for tanks with roofs supported by rafters, cylinder modes dominate the dynamic behavior of the tank. Roof dominant modes had natural periods that remain constant regardless of the aspect ratio considered. Cylinder modes, on the other hand, were characterized by natural periods that showed a linear dependence with the aspect ratio of the tank.

• Hyun Moo Koh
• Jae Kwan Kim
• Jang-Ho Park

A variationally coupled BEM-FEM is developed which can be used to analyse dynamic response, including free-surface sloshing motion, of 3-D rectangular liquid storage tanks subjected to horizontal ground excitation. The tank structure is modelled by the finite element method and the fluid region by the indirect boundary element method. By minimizing a single Lagrange function defined for the entire system, the governing equation with symmetric coefficient matrices is obtained. To verify the newly developed method, the analysis results are compared with the shaking-table test data of a 3-D rectangular tank model and with the solutions by the direct BEM-FEM. Analytical studies are conducted on the dynamic behaviour of 3-D rectangular tanks using the method developed. In particular, the characteristics of the sloshing response, the effect of the rigidity of adjacent walls on the dynamic response of the tanks and the orthogonal effects are investigated.

• George W. Housner
• Medhat A. Haroun

A method for analyzing the earthquake response of deformable, cylindrical liquid storage tanks is presented. The method is based on superposition of the free lateral vibrational modes obtained by a finite-element approach and a boundary solution technique. The accuracy of such modes has been confirmed by vibration tests of full-scale tanks. Special attention is given to the cos theta -type modes for which there is a single cosine wave of deflection in the circumferential direction. The response of deformable tanks to known ground motions is compared with that of similar rigid tanks to assess the influence of wall flexibility on their seismic behavior. Numerical examples are presented to illustrate the variation of the seismic response of two different classes of tanks, namely, ″tall″ and ″broad″ tanks. The significance of the cos n theta -type modes in the earthquake response analysis of irregular tanks is discussed.

• Anestis S. Veletsos
• Jong Y. Yang

After a brief review of the hydrodynamic forces induced in rigid tanks and a discussion of the accuracy of the G. W. Housner approach, this paper presents a brief account of a series of studies conducted recently with a view of assessing the influence of tank flexibility on the magnitude and distribution of impulsive and convective forces. The studies include the development of a simple approximate procedure for arriving at preliminary, order or magnitude estimates of the influence of tank flexibility; the formulation of a more refined analysis in which the tank is analyzed by use of a shell theory; the compilation and interpretation of numerical solutions over a range of the parameters involved; and studies of the natural frequencies and modes of vibration of both empty and liquid-filled tanks.

Conical steel vessels, having an upper cylindrical section and supported by a reinforced concrete shaft, are becoming widely used for water containment in elevated tanks. However, the current codes of practice for water structures in North America do not include any rational method for designing such vessels. In this study, a simple and rational design procedure that considers instability, yielding, large deformations, geometric imperfections, and residual stresses is developed for these hydrostatically loaded steel vessels. The procedure is based on a verified finite-element model and employs a multiple-regression analysis to develop formulas that relate the maximum stresses resulting from the hydrostatic pressure to geometric and thickness parameters. The approach uses these formulas to permit the design of variable thickness liquid-filled conical tanks that are subjected to both hydrostatic and snow load. Verification of the design procedure is carried out to prove that the procedure is accurate, economical, and conservative.

• A. S. Veletsos
• Yu Tang

A comprehensive analysis is made of the dynamic response of liquid containing, upright circular cylindrical tanks to a rocking base motion of arbitrary temporal variation. Both rigid and flexible tanks are examined. Critical response quantities for rigid tanks are evaluated over wide ranges of the parameters involved and the results presented in a form convenient for use in practical applications. The interrelationship of the responses of the system to rocking and lateral base motions of the same temporal variation is established, and it is shown that some of the effects of base rocking may be determined from available data concerning the response of laterally excited tanks. Additionally, the well-known mechanical model for a laterally excited tank is generalized to permit consideration of the effects of base rocking. The influence of tank flexibility is evaluated by an extension of a simple approximate technique proposed previously for laterally excited tanks.

• O.R. Jaiswal
• Durgesh C Rai
• Sudhir K. Jain

Liquid storage tanks generally possess lower energy-dissipating capacity than conventional buildings. During lateral seismic excitation, tanks are subjected to hydrodynamic forces. These two aspects are recognized by most seismic codes on liquid storage tanks and, accordingly, provisions specify higher seismic forces than buildings and require modeling of hydrodynamic forces in analysis. In this paper, provisions of ten seismic codes on tanks are reviewed and compared. This review has revealed that there are significant differences among these codes on design seismic forces for various types of tanks. Reasons for these differences are critically examined and the need for a unified approach for seismic design of tanks is highlighted.

We investigate dynamic buckling of aboveground steel tanks with conical roofs and anchored to the foundation, subjected to horizontal components of real earthquake records. The study attempts to estimate the critical horizontal peak ground acceleration (Critical PGA), which induces elastic buckling at the top of the cylindrical shell, for the impulsive hydrodynamic response of the tank–liquid system. Finite elements models of three cone roof tanks with height to diameter ratios (H/D) of 0.40, 0.63 and 0.95 and with a liquid level of 90% of the height of the cylinder were used in this study. The tank models were subjected to accelerograms recorded during the 1986 El Salvador and 1966 Parkfield earthquakes, and dynamic buckling computations (including material and geometric non-linearity) were carried out using the finite element package ABAQUS. For the El Salvador accelerogram, the critical PGA for buckling at the top of the cylindrical shell decreased with the H/D ratio of the tank, while similar critical PGAs regardless of the H/D ratio were obtained for the tanks subjected to the Parkfield accelerogram. The elastic buckling at the top occurred as a critical state for the medium height and tallest models regardless of the accelerogram considered, because plasticity was reached for a PGA larger than the critical PGA. For the shortest model (H/D=0.40), depending on the accelerogram considered, plasticity was reached at the shell before buckling at the top of the shell.

In this paper, the numerical model developed in the previous paper is used to study the seismic performance of elevated liquid-filled steel conical tanks. A number of conical tanks which are classified as tall or broad tanks according to the ratio of the tank radius to its height are considered. The consistent shell element is used to model the tank surfaces, while the coupled boundary-shell element formulation is employed to obtain the fluid added-mass which simulates the dynamic pressure resulting from a seismic motion. Linear springs are used to model the supporting towers. The natural frequencies of the liquid-filled tanks due to both horizontal and vertical excitations are evaluated. This is followed by a non-linear dynamic analysis, using an appropriately scaled real input ground motion, and which includes the effect of both geometric and material non-linearities. Thin-walled structures of this kind may exhibit inelastic behaviour and a tendency to develop localized buckles, thus diminishing stiffness. The consequence could lead to overall instability of the structure. In general, time-history analyses indicate that liquid-filled conical tanks, often possessing apparently adequate safety factors under hydrostatic loading, are shown to be very sensitive to seismic loading when ground motion frequencies contain those of the fundamental frequencies of the vessels themselves. © 1997 John Wiley & Sons, Ltd.

Conical steel shells are widely used as water containments for elevated tanks. However, the current codes for design of water structures do not specify any procedure for handling the seismic design of such structures. In this paper, a numerical model is developed for studying the stability of liquid-filled conical tanks subjected to seismic loading. The model involves a previously formulated consistent shell element with geometric and material non-linearities included. A boundary element formulation is derived to obtain the hydrodynamic pressure resulting from both the horizontal and the vertical components of seismic motion acting on a conical tank which is prevented from rocking. The boundary element formulation leads to a fluid added-mass matrix which is incorporated with the shell element formulation to perform non-linear dynamic stability analysis of such tanks subjected to both horizontal and vertical components of ground motion. Although, the formulation was developed for conical vessels, it is general and can be easily modified to study the stability of any liquid-filled shell of revolution subjected to seismic loading. The accuracy of fluid added-mass formulation was verified by performing the free vibration analysis of liquid-filled cylindrical tanks and comparing the results to those available in the literature. © 1997 John Wiley & Sons, Ltd.

• George C. Manos
• Ray W. Clough

The magnitude M = 6-5 Coalinga earthquake of 2 May 1983 caused intense ground shaking throughout the epicentral region. Unanchored cylindrical ground supported tanks located at six sites within this oil producing area were damaged; damages included elephant's foot buckling at the base of three moderate sized tanks, joint rupture and top shell buckling in one large old rivetted tank, bottom plate rupture of a relatively new welded tank and damage to the floating roofs of 11 tanks. Also oil spilled over the top of many tanks and secondary damages occurred in pipe connections, ladders, etc. In this paper an estimate is made of the intensity of ground motion at each of the tank sites, based on strong motion records made during the main shock and the strongest aftershock. Then response parameters specified by current codes are correlated with the damages observed at each tank site. Based on this comparison, it is concluded that current U.S. practice under-estimates the sloshing response of tanks with floating roofs and does not adequately address the uplifting mechanism of unanchored ground supported tanks.

• Visiting Scholar Hyun Moo Koh Professor
• Jae Kwan Kim
• Jang-Ho Park

A variationally coupled BEM–FEM is developed which can be used to analyse dynamic response, including free-surface sloshing motion, of 3-D rectangular liquid storage tanks subjected to horizontal ground excitation. The tank structure is modelled by the finite element method and the fluid region by the indirect boundary element method. By minimizing a single Lagrange function defined for the entire system, the governing equation with symmetric coefficient matrices is obtained. To verify the newly developed method, the analysis results are compared with the shaking-table test data of a 3-D rectangular tank model and with the solutions by the direct BEM–FEM. Analytical studies are conducted on the dynamic behaviour of 3-D rectangular tanks using the method developed. In particular, the characteristics of the sloshing response, the effect of the rigidity of adjacent walls on the dynamic response of the tanks and the orthogonal effects are investigated. © 1998 John Wiley & Sons, Ltd.

• Medhat A. Haroun

Theoretical and experimental investigations of the dynamic behaviour of ground-supported, deformable, cylindrical liquid storage tanks were conducted. The study was carried out in three phases: (I) a detailed theoretical treatment of the coupled liquid-shell system for tanks rigidly anchored to their foundations; (II) an experimental investigation of the dynamic characteristics of full-scale tanks; and (III) a development of an improved seismic design procedure.

Steel vessels in the form of combined conical-cylindrical shells are commonly used for liquid storage in elevated water tanks. A number of such tanks collapsed in different places around the globe due to instability of the steel shells. An essential cause of those collapses is the lack of adequate design procedures for such structures. In this study, a simplified design approach is developed to ensure safety of hydrostatically loaded combined steel conical tanks against buckling. The study is conducted numerically using a non-linear finite element model that accounts for the effects of large deformations and geometric imperfections on the stability of combined conical tanks. The finite element results together with a non-linear regression analysis are used to develop magnification functions that relate the overall shell stresses to the membrane stresses which can be evaluated analytically. Numerical examples are presented to explain application of the suggested design approach.

• Ralf Peek
• P. C. Jennings

Local uplift of the tank wall is perhaps the most important characteristic of the seismic behaviour of unanchored liquid storage tanks made out of steel. Such uplift is necessary, because unanchored tanks rely primarily on the weight of the liquid resting on an uplifted portion of the base plate to balance the overturning moments that occur during strong shaking. A simplified method of analysis for static lateral loads is developed, based on the assumption that the restraining action of the base plate can be modelled with equivalent, non-linear springs. This assumption, together with a Fourier decomposition of the displacements, simplifies the problem to the extent that it can be solved on a personal computer. The solutions are compared with those from experiments and those from current U.S. design analysis methods.

• George Gazetas

The paper reviews the state-of-the-art of analysing the dynamic response of foundations subjected to machine-type loadings. Following a brief outline of the historical developments in the field, the concepts associated with the definition, physical interpretation and use of the dynamic impedance functions of foundations are elucidated and the available analytical/numerical methods for their evaluation are discussed. Groups of crucial dimensionless problem parameters related to the soil profile and the foundation geometry are identified and their effects on the response are studied. Results are presented in the form of simple formulae and dimensionless graphs for both the static and dynamic parts of impedances, pertaining to surface and embedded foundations having circular, strip, rectangular or arbitrary plan shape and supported by three types of idealized soil profiles: the halfspace, the stratum-over-bedrock and the layer-over-halfspace. Consideration is given to the effects of inhomogeneity, anisotropy and non-linearity of soil. The various results are synthesized in a case study referring to the response of two rigid massive foundations, and practical recommendations are made on how to inexpensively predict the response of foundations supported by actual soil deposits.

• Fadi Hamdan

This paper presents a review on the behaviour and design guidelines of cylindrical steel liquid storage tanks subjected to earthquake motion. Field observations during past earthquakes are presented and then used together with finite element analyses and published experimental results to assess the accuracy of current design guidelines, with special emphasis on EUROCODE 8 (EC8), Earthquake Resistant Design of Structures, Part 4: Tanks, Silos and Pipelines (2nd draft, December 1993). The various phenomena addressed in this paper include sloshing and required free board, base shear and overturning moment applied at the base of the tank and the buckling strength of tanks. An important aim of this paper is to determine the areas where current design guidelines need further development.

The superior performance of the consistent shell element in the small deflection range has encouraged the authors to extend the formulation to large displacement static and dynamic analyses. The nonlinear extension is based on a total Lagrangian approach. A detailed derivation of the non-linear extension is based on a total Lagrangian approach. A detailed derivation of the non-linear stiffness matrix and the unbalanced load vector for the consistent shell element is presented in this study. Meanwhile, a simplified method for coding the nonlinear formulation is provided by relating the components for the nonlinear B-matrices to those of the linear B-matrix. The consistent mass matrix for the shell element is also derived and then incorporated with the stiffness matrix to perform large displacement dynamic and free vibration analyses of shell structures. Newmark's method is used for time integration and the Newton-Raphson method is employed for iterating within each increment until equilibrium is achieved. Numerical testing of the nonlinear model through static and dynamic analyses of different plate and shell problems indicates excellent performance of the consistent shell element in the nonlinear range.

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Source: https://www.researchgate.net/publication/312460584_Review_of_API_650_Annex_E_Design_of_large_steel_welded_aboveground_storage_tanks_excited_by_seismic_loads

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