Seismic analysis of steel liquid storage tanks by Endurance Time method

Thin-Walled Structures 50 (2012) 14–23

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Seismic analysis of steel liquid storage tanks by Endurance Time method H.E. Estekanchi n, M. Alembagheri Department of Civil Engineering, Sharif University of Technology (SUT), P.O. Box 11155-9313, Tehran, Iran

a r t i c l e i n f o

a b s t r a c t

Article history: Received 15 July 2010 Received in revised form 20 August 2011 Accepted 22 August 2011 Available online 18 October 2011

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 threedimensional 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. & 2011 Elsevier Ltd. All rights reserved.

Keywords: Endurance Time method Steel liquid storage tanks Seismic assessment Dynamic pushover Intensifying excitation

1. Introduction A main objective in seismic design of structures is to make sure that the structure has acceptable performance when subjected to earthquakes with various intensities and probability of occurrences during its service lifetime. Various well-known codes in the last two decades have been trying to lead their design criteria to follow performance-based design concepts [1]. A milestone of this trend can be considered SEAOC committee’s report. The performance level can be viewed as an acceptable damage state for the structure when it is subjected to an earthquake with specific intensity [2]. Design codes related to storage tanks have considered various performance levels, such as three earthquake risk levels in Iranian Oil Industry Seismic Design Guide (IOSG Code) [3]. Development of the performance-based design methods requires advancement of structural analysis methods to incorporate relatively complicated performance criteria. Time history dynamic analysis is a powerful and reliable method for seismic assessment of structures especially for those involving various sources of nonlinear behavior. In this method, dynamic behavior of tank is analyzed under earthquake accelerogram that is exerted to the base level of tank as a function of time, and response history of base shear, overturning moment, wall stresses and fluid wave height and other independent or derived response parameters are obtained. Selection of appropriate accelerograms and determination of tank

n

Corresponding author. Tel.: þ98 21 66164212; fax: þ98 21 66014828. E-mail address: [email protected] (H.E. Estekanchi).

0263-8231/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.tws.2011.08.015

responses under them considering nonlinear behavior of tank, result in accurate evaluation of tank performance. Many regulations were introduced in design codes for utilization of earthquake accelerograms, such as satisfaction of code’s design earthquake, considering soil profiles similar to construction site of tank, required minimum number of records, scaling of accelerograms, and specific procedure for their application to the tanks [3,4]. However, this method is the most time consuming method as compared with other analysis methods. In addition, in spite of good accuracy, complicated difficulties of this method have prevented its comprehensive utilization [5]. Consequently, researchers and engineers are looking for ways to improve analysis procedures by creating more effective methods with adequate accuracy, such as Pushover and IDA analyses that have their own advantages and disadvantages [6,7]. Endurance Time method (ET) is a new structural analysis method based on time history analysis utilizing predesigned intensifying dynamic excitation as a loading function. By subjecting the intended structure to a gradually intensifying excitation and monitoring its performance and response through the entire intensity measure of interest, considerable reduction in required computational demand as compared to conventional response history based analysis procedures can be achieved. In this paper, the basic principles of ET method as applicable to the analysis of storage tanks are reviewed; and afterward, practical application of ET method in seismic analysis of steel tanks using the proposed methodology is investigated. Application of ET method in the analysis of storage tanks and similar structures involving special structural forms such as shells interacting with fluids can pave the way for practical utilization of more reliable timehistory based methods in the analysis and design of these types of structures.

H.E. Estekanchi, M. Alembagheri / Thin-Walled Structures 50 (2012) 14–23

Nomenclature D E ET ETAF g GM H I IOSG mp mc mi ms mr mf

tank diameter modulus of elasticity of shell’s material Endurance Time method endurance time acceleration function ground acceleration ground motions maximum height of contained fluid importance factor Iranian Oil Industry Seismic Design Guide contained fluid total mass convective mass of fluid impulsive mass of fluid tank shell (wall) mass tank roof mass tank floor mass

2. A brief review of steel tanks seismic assessment Thin walled structures exhibit complicated dynamic behavior and their seismic assessment is a challenging problem in earthquake engineering. These complications are magnified in case of steel tanks where the fluid–structure interaction issues are involved. Westergaard’s researches in early 1930s could be considered as first studies about hydrodynamic pressures due to harmonic excitation [8]. He obtained hydrodynamic pressure on vertical rigid surface of a dam with infinite reservoir. First studies in the field of dynamic behavior of tanks were carried out assuming rigidity of wall and rigid connection of tank base to foundation. In 1934, Hoskins and Jacobsen studied vibration of rectangular tanks with rigid wall on nonflexible base that regarding to rigidity of wall and base they only obtained the dynamic response of contained fluid [9]. Housner in 1954 divided the fluid inside the tank into impulsive and convective parts [10]. The impulsive fluid could be assumed to move with the structure, and the convective fluid presents moving wave motion in the upper part. He showed that in most cases, major part of base shear and overturning moment is due to impulsive fluid. Based on convective fluid properties, sloshing motion of contained fluid free surface is determined. Edwards carried out research in the field of behavior and dynamic properties of tanks with flexible wall in 1969 [11]. He used Finite Element method in a computer analysis of tanks considering interaction of fluid and elastic wall of tank. In 1977, Veletsos and Yang showed that the assumption of rigid wall in tanks analysis leads to unreliable base shear and overturning moment [12]. Gupta and Hutchinson studied the effects of wall flexibility on the dynamic response of liquid storage tanks and indicated that for both shallow and deep tanks bulging frequencies decrease with reduction of wall thickness [13]. The dynamic pressure due to liquid sloshing has a maximum at the liquid surface level and a minimum at the bottom of the tank, and vice versa for the dynamic pressure due to bulging of the tank. They also showed that tank wall flexibility is an important parameter that considerably influences the dynamic pressure distribution in the bulging mode. Tedesco et al. in 1987 studied free vibration of cylindrical liquid storage tanks considering interaction of shell and liquid [14]. They indicated that the vibration of the convective fluid mass is unaffected by the vibration of the shell and stationary (impulsive) mass. In addition, it was observed that the vibration of the convective fluid mass is insensitive to shell flexibility. Gunawan et al. presented the free vibration characteristics of fluidfilled cylindrical shells on elastic foundations by a semi-analytical finite element method. They investigated the effect of fluid in a shell,

MDOF Ru Ruc R2 Sa SDS SDOF STDEV t te Ti Tc Y

r

15

multi-degree of freedom systems inherent overstrength and global ductility capacity of lateral resisting of impulsive mass inherent overstrength and global ductility capacity of lateral resisting of convective mass points scattering indicator in a diagram spectral acceleration spectral acceleration at period time of 0.2 s single degree of freedom system standard deviation wall (shell) thickness relative thickness of wall (shell) fundamental impulsive period fundamental convective period vertical distance from fluid surface to considered point fluid density

shell geometries, and foundation parameters on the dynamic behavior of fluid-containing shells [15]. Recently, ambient vibration tests and finite element modeling of tall liquid storage tanks performed by Amiri and Yazdi showed good agreement between the numerical and experimental values of dynamic parameters [16]. They also showed that the tanks roof has negligible effect on the natural frequencies of vibration but it has significant effect on the mode shapes of tanks. Barton and Parker used the Finite Element method for the evaluation of seismic behavior of unanchored tanks taking into account gap conditions for tank base uplifting [17]. Results of their research showed the importance of accurate attention to support conditions of tanks in seismic calculations. Because of impacts between base and tank floor due to uplifting, resultant forces and stresses are considerably greater than anchored state. Veletsos and Tang studied the soil–structure interaction effects on responses of laterally excited liquid storage tanks and showed that the effect of this interaction is negligible on sloshing of convective fluid [18]. Malhotra conducted researches on base uplifting of unanchored tanks. He indicated that base uplifting decreases the hydrodynamic forces on tank wall but increases the axial compressive stresses in the tank wall. In addition, the flexibility of base reduces the increasing rate of axial compressive stresses [19,20]. Tedesco et al. in 1989 appraised via the response spectrum technique the dynamic seismic response of flexible, liquid-filled cylindrical storage tanks and showed that impulsive and convective parts treat independently [21]. They presented a simple analytical procedure, applicable to both completely full and halffull tanks, which accurately predicts impulsive hydrodynamic wall pressures, shell stresses, base shear, and overturning moment. Their numerical comparisons illustrated the unconservativeness of the rigid tanks procedures that employed by many practicing engineers. Hamdan reviewed the behavior and design guidelines of cylindrical steel liquid storage tanks subjected to earthquake motions [22]. He presented field observations during past earthquakes together with Finite Element analyses and published experimental results to assess the accuracy of design guidelines, with special emphasis on Eurocode8 [23]. He emphasized the areas where design guidelines on that time required further development, such as more realistic consideration of the effects of sloshing, hydrodynamic pressures and tank base support on axial compressive stresses, overturning moment, base shear and hoop stresses. Haroun and Bhatia by Finite Element analyses showed that the hoop stresses are increased by uplift of the tank base [24]. Ozdemir et al. in 2010 analyzed the anchored and unanchored steel tanks by application of nonlinear methods for fluid–structure

H.E. Estekanchi, M. Alembagheri / Thin-Walled Structures 50 (2012) 14–23

3. Design methodology utilizing Endurance Time method Complications involved in the seismic response of thin walled structures in general and the added complexities of fluid–structure interaction effects in structures such as steel tanks makes dynamic analysis approaches the only practical way for reliable numerical simulation of their response. In ET method, the structure is subjected to artificial gradually intensifying dynamic excitation, and variations of relevant response parameters and damage indexes are monitored as the intensity is increased, and structural performance is assessed based on its response at various excitation levels [2,30,31]. By providing an estimate of the seismic response at various excitation intensities in a single time-history analysis, ET method considerably reduces the huge computational demand involved in standard dynamic analysis procedures. In this section, a brief introduction of the ET concept will be followed by proposed method as applicable to the analysis of steel tanks as a particular case of a thin walled structure involving fluid–structure interaction effects. A typical variation curve for a damage index in a structure, which is subjected to an intensifying accelerogram, is shown in Fig. 1. In this case, the structure can be considered to be a tank and the damage index can be considered to be the ratio of maximum existing Von-Mises stress in its wall to allowable stress. If acceptable value of damage index is limited to say one and the excitation is calibrated such that at a specific time, say 10th second, its intensity

1.6 1.4

Variation of Damage Index Endurance Limit

1.2 Damage Index

interaction in the Finite Element method and compared the results with the response parameters of tanks that are computed according to tank seismic design codes in current practice [25]. They concluded that all code provisions overestimate the maximum fluid free surface displacement and recommend conservative value to provide necessary freeboard. They showed that the response spectrum of selected input motion for the transient analysis should be consistent with code design spectrum for short and long period regions where the fundamental periods of impulsive and convective (sloshing) responses are dominant, respectively. The inconsistency of the design and input motion spectra in the long period region may breed significant difference in maximum free surface wave height and hydrodynamic pressure distribution along the tank wall near the free surface obtained from code provisions and those observed from transient analyses. In addition, they justified from compatible results of numerical and experimental studies that the Finite Element method is a reliable tool for the seismic analysis of not only anchored tanks but also unanchored tanks. Sloshing response, overturning moment, shell stresses and base uplift of tanks can be predicted with great accuracy by Finite Element method. Various mechanical models such as Housner’s two-mass model [10] and Haroun’s three-mass model [26] have been proposed for seismic analysis of storage tanks. In addition, various design charts were presented for determination of impulsive and convective frequencies, maximum base shear, overturning moment, and stress resultants in shell. Codes such as API650 (App. E) [27] and Eurocode8 (Part 4) [23] were formed based on researches of Wozniac and Mitchell [28] and Malhotra et al. [29], respectively. It should be noted that seismic analysis of storage tanks presents a very complicated structural engineering problem involving fluid–soil–structure interaction and complex phenomena such as nonlinear material behavior and buckling that does not yield to appreciable simplifications. Considering these complications on one hand and the new developments in the area of earthquake engineering including various seismic mitigation technologies such as application of fluid and metal dampers or base isolation, it is expected that more accurate response history based analysis procedures will become more popular in near future. As will be explained, ET method provides some potential advances in this direction.

1 0.8 0.6 0.4 0.2 0 0

2

4

6

8

10 12 Time (Sec)

14

16

18

20

Fig. 1. Assumed curve of damage index variation.

1.2 Ground Acceleration (g)

16

ETA20e03

0.8 0.4 0 -0.4 -0.8 -1.2 0

5

10 Time (Sec)

15

20

Fig. 2. ETA20e03 accelerogram.

matches with the specified design spectrum, then from Fig. 1, damage index for this tank at 10th second is about 0.79. Therefore, it can be concluded that assumed tank satisfies the specified design criterion [30]. While in this simplified example only a single response parameter (i.e. ratio of experienced to allowable Von-Mises stress) and a single intensity (corresponding to a particular target time) was considered, it should be clear that the concept can be readily extended to include various response parameters at different intensity levels in each analysis. Since the analysis is a dynamic one, it is applicable to various types of structures with different sources of complicated behavior. Estekanchi et al. introduced the basic concepts of ET method, providing some examples in SDOF and MDOF dynamic analyses [30]. Provision of a usable intensifying acceleration function is vital in the success of ET method. For ET acceleration functions to be useful, the results from applying them should correlate well with those from ground motions at different excitation levels. For this purpose, the concept of response spectrum was incorporated in the generation of ET acceleration functions [32]. The interesting property of ET acceleration functions is that each window of them from time 0 to time t produces a response spectrum that is proportional with the specified template spectrum with a scale factor of t/tTarget where tTarget is the time when spectra match the specified template spectrum with a scale factor of unity. These ET acceleration functions are produced using intensive numerical optimization procedures and are available through the website of Endurance Time method [33]. A sample intensifying accelerogram is shown in Fig. 2. ET acceleration functions of series ETA20e01-3 have been utilized in this article which are based on template response

H.E. Estekanchi, M. Alembagheri / Thin-Walled Structures 50 (2012) 14–23

17

Table 1 Basic characteristics of selected earthquakes. Record name

Earthquake

Station

Duration (s)

PGA (g)

Scaling factor

LADSP LPAND LPGIL LPLOB LPSTG MHG NRORR

Landers Loma Prieta Loma Prieta Loma Prieta Loma Prieta Morgan Hill Northridge

Yermo, Fire Station Anderson Dam, Downstream Gilroy, Gavilon College Phys. Sch. Bldg Santa Cruz, University of California Saratoga, Aloha Ave. Gilroy #6, San Ysidro Microwave Site Castaic, Old Ridge Route

50.0 39.6 39.9 39.9 39.9 29.9 40.0

0.171 0.244 0.356 0.441 0.504 0.286 0.514

3.17 2.26 1.18 1.10 1.36 1.78 1.15

spectrum obtained from seven actual ground motions selected from FEMA440 [34] records on soil class C. Properties of these earthquakes are listed in Table 1. Initial studies showed that ET records based on codified template spectrums, while producing good correlation with ground motions in predicting various damage indexes; do not have reasonable accuracy when nonlinear effects are significant [35]. However, later studies showed that ET acceleration functions that are directly matched with average spectrum of ground motions recorded on stiff soil conditions can produce a much improved and usable estimation of response parameters of ground motions scaled to different intensity levels [36]. Recent studies by various researchers have revealed the potential applicability of this procedure for tackling different seismic analysis and design problems [37–40]. Reliability and reasonable accuracy of estimates by ET method in seismic analysis of anchored and unanchored tanks using some different-shaped new-designed steel tanks in elastic and inelastic regions of response have been investigated in previous studies [41,42]. In this article, a general methodology for utilizing ET method in the analysis and design of steel liquid storage tanks is presented. A constructed steel tank has been considered as a simple example and the results are compared with the code regulations. The general methodology for the procedure is presented in Fig. 3. As shown in this diagram, the first step is to prepare a representative dynamic model of the tank. Dynamic models can be simplified or complicated based on the objectives of the design. Since ET method is based on time history analysis, there is virtually no limitation on the complexity of the model. In the next step, ET acceleration functions (called ETAFs here after) that are compatible with the specified design spectrum should be selected. A limited number of ETAFs are currently available [33] based on design spectrum for soil type II of Iranian Seismic Standard (ISS 2800) [4]. If compatible ETAFs are not available, a scaling procedure should be adopted to match the ETAF spectrum with the intended design spectrum in the vicinity of the fundamental period of the tank. It should be noted that in this study, ETAFs that are compatible with response spectra of actual ground motions, which have been scaled based on code’s regulations, are utilized for comparative purposes. In this case, the design and excitation spectra should be made to match at around fundamental period of vibration of the impulsive mass of the tank as recommended by the code. Considering the random nature of ETAFs, it is recommended to employ the average of the results from three ET analyses to achieve a more accurate estimation [32]. For initial design trials where a rough estimate is adequate, a single ET analysis at each cycle may suffice. After the ET analyses are completed, response history curves for various parameters such as maximum stresses and displacements and other effective parameters in tank design, are drawn as a function of time. ET diagrams are obtained as a maximum absolute value of the parameter up to intended time in order to find the maximum of each parameter at any time in ET analysis. Now the values of responses at target time in ET diagrams,

Prepare a dynamic model of the tank

Select ETAFs Compatible with specified design spectrum

Make design modifications

Run response history analysis using ETAFs

Draw ET curves corresponding to response parameters

Compare the values of response parameters with allowable ones at target time(s)

No

Performance acceptable? Yes

No

Design is Optimal? Yes Finalize design

Fig. 3. Design procedure using ET method.

as an estimation of maximum responses of actual scaled ground motions, are compared with their allowable values. It should be noted that ET analysis results by default includes the estimation of responses at different levels of excitation on a continuous scale with time. Consequently, it is possible for the designer to examine the response not only at the specified target intensity, but at its vicinity and other levels as well. As it will be shown, this provides a valuable insight for making reasonable design modifications. In addition, several target times corresponding to different performance levels can be utilized at the same time. For example, responses at service

18

H.E. Estekanchi, M. Alembagheri / Thin-Walled Structures 50 (2012) 14–23

and ultimate level earthquakes can be checked in each design cycle. The above mentioned procedure briefly explained considering an existing steel storage tank by utilizing a single analysis cycle.

4. Scaling of ground motions and ET functions IOSG Code [3] provisions that tanks should be designed based on design earthquake or risk earthquake level II. It is provisioned that design spectrum of ISS 2800 [4] soil type II, can be utilized as design spectrum in tanks design. In addition, it is provisioned that minimum three earthquake accelerograms that have been recorded on regions similar to the target region should be selected. Acceleration spectra of the longitudinal and transverse components of each earthquake should be determined with 5% damping and combined with SRSS method. Finally, the obtained spectrum is scaled so that in each period between 0.2Ti to 1.5Ti to be greater than 1.17 times design spectrum. Scaling factors obtained from this method (regarding to tank properties that has been modeled in Section 5) is seen in Table 1. According to general methodology, the target time in ET records should be set so that the average of acceleration spectra of ET records until that time becomes compatible with the average spectrum of ground motions (actual earthquakes) especially in the vicinity of impulsive and convective periods of considered tank. This time is readily calculated by considering the linear relation between acceleration response spectrum and record length in ET method. Seventh second is selected as target time in this article. The average spectrum of longitudinal components of scaled ground motions and first 7 s (target time) of ET records together with design spectrum of ISS 2800 [4] are shown in Fig. 4. It is expected that average of maximum responses of ET records until target time can estimate the average of maximum responses of ground motions in modeled tank because of the consistency between average spectrum of them in the vicinity of fundamental impulsive and convective periods of studied tank in Section 5.

Fig. 5. Illustration and general properties of modeled oil tank.

Fig. 6. Finite Element model of tank and contained fluid.

5. Practical case study For explanation and evaluation of ET general methodology, an anchored completely full oil tank constructed by Iranian Oil Building and Engineering Company has been modeled and studied as a typical practical case of a liquid storage tank. General specifications of this tank are shown in Fig. 5. Responses of this tank in unanchored state have also been investigated and will be presented in next sections. Finite Element model of tank together with contained fluid including 538 four-node shell elements with reduced integration 1.6

Tc ¼ Cc

1.4 Avg. of Scaled Ground Motions

1

rffiffiffiffi D 2

ð2Þ

in which coefficients Cc and Ci is determined from IOSG Code [3] regarding to ratio of maximum fluid height (H) to nominal diameter of tank (D). Geometric and material nonlinearities are considered in the analysis. Materials specifications are listed in Table 2. The model has been verified using simple static and hydrostatic concepts such as exerting weight to the model and applying constant horizontal and vertical acceleration to the tank. In all these verifications, responses at tank base, wall, and contained fluid were consistent with the theory [38].

Iranian Standard Design Spectrum

1.2 Sa (g)

formulation for shell, and 1064 eight-node cubic elements with reduced integration formulation for fluid is seen in Fig. 6. This tank has been analyzed using three-dimensional nonlinear time history analysis utilizing a general-purpose Finite Element analysis software [43]. Fundamental impulsive (Ti) and convective (Tc) periods of the tank are 0.065 and 3.440 s, respectively, according to code’s Eqs. (1) and (2)   rD 1=2 Ti ¼ CiH ð1Þ 2t e E

Avg. of ET Records until 7th Second

0.8 0.6 0.4 0.2 0 0

0.5

1

1.5

2 2.5 Period (Sec)

3

3.5

4

Fig. 4. Average spectrum of scaled ground motions and ET records until 7th second, together with code’s design spectrum.

5.1. Results and discussion Analysis results of aforementioned tank under longitudinal component of scaled ground motions and series ETA20e01-3 of ET

H.E. Estekanchi, M. Alembagheri / Thin-Walled Structures 50 (2012) 14–23

Dif f erence percentage ¼ ðRET REQ Þ=ðREQ Þ  100

ð3Þ

Table 2 Materials properties. Material

Parameter

Value

Steel

Density (kg/m3) Modulus of elasticity (GPa) Poisson’s ratio Yielding stress (MPa) Strain-hardening slope (%) Density (kg/m3) Viscosity (Pa s)

7800 204 0.27 240 3 700 0.002

Oil

0.9 0.8

Time Variation of Parameter ET Diagram of Parameter

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0

7

14

21

Time Fig. 7. Method of obtaining an arbitrary ET diagram.

4 3.5 Base Shear (MN)

in which RET is the average of values of ET diagrams at target time, and REQ is the average of maximum responses of scaled ground motions. Maximum absolute value of the response up to intended time is calculated in order to find the maximum of each parameter at any time in ET analysis as shown in Fig. 7. ET diagrams of base shear for three ET records (ETA20e01-3) are shown in Fig. 8. As it can be observed in Table 3, the hoop and axial stresses in tank wall are much smaller than yield stress, which shows that the design of tank shell is acceptable but it seems to be somewhat on the conservative side. Comparison of the standard deviations shows that except for compressive axial stress, in other cases, results of ground motions are more scattered. In addition, the difference percentages are generally below 10% which indicates reasonable estimation obtained from ET analysis. These difference percentages are resulted from random nature of earthquake records and difference between spectral accelerations at fundamental impulsive and convective periods of tank that are mentioned in Table 3. As noted earlier, in tank model, the base shear, shell stresses and relative deformations are strongly correlated to the impulsive state, and fluid wave height is more correlated to the convective state. Therefore, more accurate estimations of ET records for base shear and shell stresses are obtained by adjusting differences of spectral intensities in the vicinity of fundamental

impulsive period, and for wave height in the vicinity of fundamental convective period. Other researchers also report this issue [25]. It should be noted that responses of individual earthquakes can also be estimated using ET records. Target times of ET records for each earthquake in impulsive and convective states can be found as

Parameter

records; and difference percentages between averages of results of these two groups, which are computed according to Eq. (3), have been summarized in Table 3

19

3 2.5 2 ETA20e01 ETA20e02 ETA20e03 Avg. of Ground Motions

1.5 1 0.5 0 0

7

14

21

Time (Sec) Fig. 8. Base shear ET diagrams of three ET records.

Table 3 Summary of analysis results. Records

Base shear Vertical (MN) reaction (MN)

Relative horizontal deformation (mm)

Fluid wave height (m)

Shell hoop stress (MPa)

Shell axial stress (MPa)

Shell shear stress (MPa)

Shell Von-Mises stress (MPa)

Sa(Ti) (g)

Sa(Tc) (g)

Scaled ground motions LADSP 1.523 LPAND 1.745 LPGIL 1.408 LPLOB 1.848 LPSTG 2.331 MHG 1.523 NRORR 1.586 Avg. (REQ) 1.709 STDEV 0.312

3.959 4.141 4.178 3.875 4.337 3.735 3.808 4.005 0.220

0.765 0.780 0.765 0.843 0.993 0.698 0.772 0.802 0.094

0.343 0.329 0.167 0.071 0.513 0.259 0.387 0.296 0.146

54.260 60.480 58.920 60.450 67.540 52.480 52.860 58.141 5.397

11.620 11.690 12.650 12.890 14.620 11.770 9.756 12.142 1.487

14.050 16.240 13.930 17.170 23.810 14.080 15.330 16.373 3.504

57.600 63.870 61.250 64.030 72.020 55.360 56.560 61.527 5.774

0.665 0.656 0.798 0.647 0.895 0.645 0.629 0.705 0.101

0.076 0.078 0.041 0.019 0.110 0.056 0.082 0.066 0.030

ET records until target time ETA20e01 1.610 ETA20e02 1.630 ETA20e03 1.794 Avg. (RET) 1.678 STDEV 0.101

4.024 3.912 3.956 3.964 0.056

0.745 0.809 0.761 0.772 0.033

0.270 0.219 0.230 0.240 0.027

58.490 54.770 58.540 57.267 2.162

12.460 11.550 15.550 13.187 2.097

15.850 15.140 16.410 15.800 0.636

61.670 58.240 62.080 60.663 2.109

0.764 0.789 0.761 0.771 0.015

0.067 0.050 0.076 0.064 0.013

 1.017

 3.808

 18.895

 1.505

8.601

 3.499

 1.404

9.433

 2.646

Difference percentage (%)

 1.822

20

H.E. Estekanchi, M. Alembagheri / Thin-Walled Structures 50 (2012) 14–23

100 80 Stress (MPa)

follows: Supposing that earthquake X has spectral accelerations at fundamental impulsive and convective periods of the tank equal to A and B, respectively, while averages of these spectral accelerations until target time (7th second) of ET records equal to C and D, respectively. Therefore, target time of ET records for equating the average spectra of ground motions and ET records at impulsive period of considered tank (for estimating base shear and shell stresses) will be A/C  7, and at convective period (for estimating fluid wave height) will be B/D  7. Average of ET diagrams of shell stresses (that have been calculated in the middle surface of shell and are symbol of membrane stresses) and fluid wave height are shown in Fig. 9, along with maximum responses of individual earthquakes at target times that were determined based on the mentioned method. As can be seen from Fig. 9, the average of ET diagrams correlate well with the maximum responses of individual earthquakes at corresponding target times. This observation shows that ET records can be used in order to estimate the maximum results from various ground motions (that have various intensities) with reasonable accuracy.

Hoop Stress (ET) Axial Stress (ET) Shear stress (ET) Hoop Stress (GM) Axial Stress (GM) Shear Stress (GM)

60 40 20 0 0

7

14

21

Time (Sec)

Fluid Wave Height (m)

1.2 ETA20e01 ETA20e02 ETA20e03 Avg. of ET Records Ground Motions

1 0.8

5.2. Correlation of stresses In this section, correlation of middle surface stresses in tank’s shell resulted from the tank analyses is investigated. In some correlation diagrams, horizontal axis is average of maximum responses of considered stress resulted from ground motions in various elements of shell, and vertical axis is the same parameter resulted from ET diagrams at target time. These diagrams are used to study the correlation and compatibility of the results from ET analysis considering the results from ground motion analysis as basis. In some other correlation diagrams presented in this section, horizontal axis is average of maximum responses of considered stress in various elements of shell, and vertical axis is the individual maximum responses in various elements of shell.

0.6 0.4 0.2 0 0

7

14

21

Time (Sec)

60

Von-Mises Stress Y=X Linear (Von-Mises Stress)

60

Avg. of ET Records (MPa)

Avg. of ET Records (MPa)

Fig. 9. (a) Average of ET diagrams of middle surface stresses of shell and their maximum in ground motions. (b) ET diagrams of fluid wave height and its maximum in ground motions.

y = 0.9816x R = 0.9945

40

20

0

Hoop Stress Y=X Linear (Hoop Stress)

40

y = 0.985x R = 0.9947

20

0 0

60 20 40 Avg. of Ground Motions (MPa)

0

20 40 60 Avg. of Ground Motions (MPa)

y = 0.9993x R = 0.9876

Avg. of ET Records (MPa)

Avg. of ET Records (MPa)

16

12

8 Shear Stress

4

Y=X Linear (Shear Stress)

12

y = 1.0275x R = 0.9915

8

4

Axial Stress Y=X Linear (Axial Stress)

0

0 0

4 8 12 Avg. of Ground Motions (MPa)

16

0

4 12 8 Avg. of Ground Motions (MPa)

Fig. 10. Correlation diagrams together with their trend line, (a) Von-Mises stress, (b) hoop stress, (c) shear stress, and (d) axial stress.

H.E. Estekanchi, M. Alembagheri / Thin-Walled Structures 50 (2012) 14–23

These diagrams are used in order to study the level of scarring in various analysis procedures. The correlation diagrams for various stresses in tank’s shell together with their trend line are shown in Fig. 10. As can be seen, in all diagrams, stresses have an appropriate correlation and consistency, and scattering of points is so that calculated trend lines and Y ¼X line are nearly coherent. This indicates reasonable estimation of ET records from ground motions that are scaled based on the code regulations. The correlation diagrams for Von-Mises stress are shown in Fig. 11. As it can be seen and expected, results of ground motions are more scattered, and results of ET records have high correlation. Thus, it seems that instead of applying three ET records, even one record may be utilized for estimation of stresses in anchored steel tanks at least in initial design trials when analysis efficiency can overrule high accuracy. From Fig. 11(a), it is concluded that while the considered scaling factors regarding the code’s regulations are generally appropriate, for LPSTG record, it results in somewhat higher and for NRORR record, it results in somewhat lower than average response. 5.3. Comparison with code provisions In this section, responses of studied oil tank resulted from time history analyses using ground motions and ETAFs, are compared with the values resulted from equivalent static analysis method of IOSG Code [3].

Y=X LADSP LPAND LPGIL LPLOB LPSTG MHG NRORR

Ground Motions (MPa)

60

40

Impulsive and convective fluid masses are obtained from Eq. (4) for D/H44/3 mi ¼

tanhð0:866ðD=HÞÞ mp ¼ 215:10 ton 0:866ðD=HÞ

mc ¼ 0:230

ð4aÞ

  D 3:67H tanh mp ¼ 141:50 ton H D

ð4bÞ

In this model, total mass of contained fluid mp, is equal to 356.60 ton. Earthquake coefficients of impulsive mass, Ai, and convective mass, Ac, are obtained from Eq. (5) Ai ¼

Sa I ¼ 0:576 Ru

ð5aÞ

Ac ¼

1:5Sa I ¼ 0:302 Ruc

ð5bÞ

Eq. (6) proposes earthquake coefficient in vertical direction, Av, as follows: Av ¼ 0:2SDS I ¼ 0:219

ð6Þ

In Eqs. (5) and (6) I is 1.25, Sa for impulsive and convective periods are equal to 0.69125 and 0.2419, respectively, SDS is 0.875, and of Ru and Ruc are considered to be 1.5 [3]. Base shear and maximum fluid wave height obtained from Eqs. (7) and (8), and average of these parameters resulted from time history analyses (ground motions and ET records) are listed in Table 4. IOSG Code [3] provisions that tanks should be designed to resist the base shear obtained from Eq. (7) qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi V u ¼ V i2 þ V c2 ð7Þ in which the base shear corresponding to impulsive mass, Vi, and convective mass, Vc, are obtained as follows: V i ¼ Ai gðmi þ mr þ mf þ ms Þ ¼ 1:648MN

ð7aÞ

V c ¼ Ac gmc ¼ 0:420MN

ð7bÞ

In Eq. (7a), the parameters mf, ms, and mr are equal to 3.97 ton, 11.00 ton, and 4.08 ton, respectively. IOSG Code [3] estimates the maximum fluid wave height as in Eq. (8)

20

ds ¼ 0 0

60

20 40 60 Avg. of Ground Motions (MPa)

Y=X ETA20e01

ET Records (MPa)

21

ETA20e02 ETA20e03

40

Ruc Ac D 2

ð8Þ

As can be seen in Table 4 calculated base shear from IOSG Code’s [3] relationships is approximately equal to the base shear resulted from time history analyses, while the code proposes fluid wave height much greater than time history analyses. IOSG Code provisions 0.7ds as required freeboard, which seems very conservative regarding to obtained results. Other researchers also report this observation [25]. Hoop stresses at middle surface of shell are compared between time history and IOSG Code’s equivalent static analyses in eight levels of elements at various heights of tank which are shown in Fig. 6. The maximum obtained hoop stress at center of every level Table 4 Values of base shear and maximum fluid wave height.

20

0 0

20 40 60 Avg. of ET Records (MPa)

Fig. 11. Correlation diagrams, (a) ground motions and (b) ET records.

Parameter

Value

Base shear (MN) Vu Avg. of ground motions Avg. of ET records

1.700 1.709 1.687

Fluid wave height (m)

ds Avg. of ground motions Avg. of ET records

2.360 0.296 0.240

22

H.E. Estekanchi, M. Alembagheri / Thin-Walled Structures 50 (2012) 14–23

120

6

Avg. of Ground Motions Avg. of ET Records IOSG Code's Design Stress

5

100 Stress (MPa)

Distance from Tank Base (m)

7

4 3 2 1

80 60 40 20

0 0

10

20

30 40 Hoop Stress (MPa)

50

0

60

7

0

14

21

Time (Sec)

Fig. 12. Maximum hoop stresses along tank height in anchored state.

0.12

Nc ¼

0:189Ac rgD2 cosh½3:67ðHYÞ=D coshð3:67H=DÞ

ð9bÞ

and total hoop force in unit vertical length of wall, Ns, is obtained from Eq. (10) qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð10Þ Ns ¼ N 2i þN 2c þðAv Nh Þ2 Hoop stress due to earthquake,ss ¼ Ns =t, is algebraically added to hoop stress resulted from hydrostatic forces, sh ¼ N h =t, to form the design hoop stress. For calculation of IOSG Code’s design hoop stress, hydrostatic stresses have been computed based on no-wavy fluid surface. As it is evident in Fig. 12, hoop stresses proposed by IOSG Code (equivalent static analysis) in most levels are below the resulted hoop stresses from ground motions. This underestimation has been also reported by Tedesco et al. [21]. Their analytical procedure overestimates the hoop stresses due to hydrodynamic forces of impulsive mass in comparison with code. Hoop stresses in both ground motions and ET records are very close in most levels. Height levels which are close to the tank base undergo most stresses. These regions are prone to buckling and localized nonlinear behavior and a more refined Finite Element mesh should be utilized for them if detailed study of these phenomena is intended. 5.4. Estimation of responses in unanchored state ET analysis of unanchored steel tanks is studied in detail in Ref. [42]. One of the strengths of ET method is in versatility of comparing seismic response of two different design alternatives. This concept is demonstrated here by comparing the response of original tank with the one in unanchored state. The following assumptions are made for unanchored tank: friction coefficient of 0.4 between tank base and floor (see Bowles [44]), and Winkler springs’ vertical stiffness of 15.04 MN/cm (see FEMA440 [34] for a soil with density of 1600 kg/m3, shear modulus of 60 MPa, Poisson’s ratio of 0.25, and assumed foundation size of 10.5  10.5 m2). Some of ET diagrams resulted from ET analyses of studied tank in unanchored state in comparison with anchored state are shown in Fig. 13(a). As can be seen from this figure, the stresses in unanchored

0.09 Uplift (m)

is stated as hoop stress at that level. The results of Eqs. (9) and (10) (equivalent static analysis) and time history analyses are shown in Fig. 12. Hoop hydrodynamic forces in unit vertical length of wall due to impulsive mass, Ni, and convective mass, Nc, are determined from Eq. (9) for D/H44/3 "  2 #   Y Y D Ni ¼ 0:864Ai rgDH tanh 0:866 0:5 ð9aÞ H H H

0.06 ETA20e01 ETA20e02 ETA20e03 Avg. of ET Records

0.03

0 0

7

21

14 Time (Sec)

Fig. 13. ET diagrams of studied tank, (a) average of middle surface stresses of shell and (b) tank base uplifting in unanchored state.

Table 5 Comparison between values of ET responses in unanchored and anchored states. Parameter

Unanchored

Anchored

Hoop stress (MPa) Shear stress (MPa) Axial stress (MPa) von-Mises stress (MPa) Fluid wave height (cm) Uplift (mm)

66.59 25.58 54.31 82.61 25.50 39.86

57.27 15.80 13.19 60.66 24.00 –

state are generally greater than anchored state, especially axial compressive stress that is affected considerably by tank base uplifting in unanchored state. ET diagrams of uplift for three ET records and their average are shown in Fig. 13(b). ET method estimates the maximum shell stresses, fluid wave height, and tank base uplifting based on code’s design spectrum [4] as illustrated in Table 5. Based on this comparative study, it can be concluded that the studied tank produces a better seismic response in anchored state at most intensity levels. Obviously, this conclusion depends on the assumed parameters such as friction coefficient and soil stiffness.

6. Conclusions In this paper, the basic principles of ET method as applicable to the seismic assessment of steel liquid storage tanks are reviewed and its practical application using the proposed methodology is investigated. Endurance Time method (ET) is a new structural analysis method based on time history analysis utilizing

H.E. Estekanchi, M. Alembagheri / Thin-Walled Structures 50 (2012) 14–23

predesigned intensifying dynamic excitation as the loading function. In this method, considerable reduction in required computational demand as compared to conventional response history based analysis procedures can be achieved by subjecting the intended structure to a gradually intensifying excitation and monitoring its performance and response through the entire intensity measure of interest in each single response history analysis. This reduction of computational effort is important in analysis and design of storage tanks and similar thin walled structures where due to the inherently complicated structural response, the use of time-history based procedures are more appropriate. A code compatible procedure for utilizing this method was introduced and then applied in a practical example. Consistency and accuracy of estimations by ET method were investigated. Based on the analysis results, it can be concluded that ET acceleration functions used in this study can provide reasonably accurate estimate of seismic response of the studied storage tank. Consistency between spectra of ET acceleration functions and template spectrum at fundamental impulsive and convective periods of the tank can improve the accuracy of ET estimations. The comparison between responses from time history analyses using ground motions and ET acceleration functions with equivalent static analysis indicated accurate estimation of base shear, underestimation of hoop stresses and overestimation of fluid wave height by code’s relationships. Versatility of the application of ET method in comparative study of seismic response expected from different design alternatives was also demonstrated by an example involving the tank in anchored and unanchored states. It can be concluded that ET method, as a versatile dynamic pushover procedure, can be used in seismic assessment of steel liquid storage tanks and its application can pave the way for practical utilization of time-history based methods in seismic assessment of these types of structures.

Acknowledgment The authors acknowledge the support of Sharif University of Technology Research Council, and Iranian Oil Building and Engineering Co. (Contract NIOEC2/ER-CV/CON-EX05-00) for the support for this research. References [1] Bozorgnia Y, Bertero VV. Earthquake engineering: from engineering seismology to performance-based engineering. USA: CRC Press; 2004. [2] Mirzai A. Usage of ET method in performance-based design of steel frames. MSc thesis. Department of Civil Engineering, Sharif University of Technology, Tehran, Iran; 2007. [3] Iranian Oil Industry Seismic Design Guide (Publication No. 038), ISDCOI-08, Engineering and Internal Construction Center of Oil Ministry, Iran; 2007. [4] Iranian Code Of Practice For Seismic Resistant Design Of Buildings, INBC, Standard No. 2800-05, 3rd ed. Building and Housing research Center, Iran; 2005. [5] Moghaddam H. Earthquake engineering: theory and application. 2nd ed. Tehran, Iran: Farhang Publications; 2002. [6] Krawinkler H. Pushover analysis: why, how, when and when not to use it. In: Proceedings of the 1996 convention of the structural engineering association of California. Maui, Hawaii; 1996. p. 17–36. [7] Badri H, Daneshjoo F. Assessment of seismic performance of steel moment frames using static and dynamic IDA analyses. In: Proceedings of the fifth international earthquake engineering conference, Tehran, Iran; 2007. [8] Westergaard HM. Water pressure on dams during earthquakes. Transactions ASCE 1933;98:418–33. [9] Hoskins LM, Jacobsen LS. Water pressure in a tank cause by simulated earthquake. Bulletin of the Seismological Society of America 1934;24:1–32. [10] Housner GW. Earthquake pressures on fluid containers. Pasadena (CA): California Institute of Technology; 1954. [8th Technical report under Office of Naval Research]. [11] Edwards NW. A procedure for dynamic analysis of thin walled cylindrical liquid storage tanks subjected to lateral ground motion. PhD thesis. University of Michigan, Ann Arbor, Michigan; 1969.

23

[12] Veletsos AS, Yang JY. Earthquake response of liquid storage tanks. In: Advances in civil engineering through engineering mechanics. In: Proceedings of the engineering mechanics division specialty conferences. Raleigh (NC): ASCE; 1977. p. 1–24. [13] Gupta RK, Hutchinson GL. Effects of wall flexibility on the time response of liquid storage tanks. Engineering Structures 1991;13:253–67. [14] Tedesco JW, Kostem CN, Kalnins A. Free vibration analysis of cylindrical liquid storage tanks. Computers and Structures 1987;26:957–64. [15] Gunawan H, Mikami T, Kanie S, Sato M. Free vibrations of fluid-filled cylindrical shells on elastic foundations. Thin-Walled Structures 2005;43: 1746–62. [16] Amiri M, Sabbagh-Yazdi SR. Ambient vibration test and finite element modeling of tall liquid storage tanks. Thin-Walled Structures 2011;49:974–83. [17] Barton DC, Parker JV. Finite element analysis of the seismic response of anchored and unanchored liquid storage tanks. Earthquake Engineering and Structural Dynamics 1987;15:299–322. [18] Veletsos AS, Tang Y. Soil–structure interaction effects for laterally excited liquid-storage tanks. Earthquake Engineering and Structural Dynamics 1990;4:473–96. [19] Malhotra PK. Seismic response of soil-supported unanchored liquid-storage tanks. Engineering Structures 1997;123:440–50. [20] Malhotra PK. Base uplifting analysis of flexibly supported liquid storage tanks. Earthquake Engineering and Structural Dynamics 1995;2:1591–607. [21] Tedesco JW, Landis DW, Kostem CN. Seismic analysis of cylindrical liquid storage tanks. Computers and Structures 1989;32:1165–74. [22] Hamdan FH. Seismic behavior of cylindrical steel liquid storage tanks. Journal of Constructional Steel Research 2000;53:307–33. [23] Eurocode8. Design of structures for earthquake resistance, part 4: silos, tanks and pipelines. Brussels: European Committee for Standardization; 2006. BS EN 1998-4. 2006. [24] Haroun MA, Bhatia H. Analysis of tank damage during the 1994 Northridge Earthquake. In: Proceedings of the fourth US conference on lifeline earthquake engineering. ASCE: New York; 1995. p. 763–70. [25] Ozdemir Z, Souli M, Fahjan YM. Application of nonlinear fluid–structure interaction methods to seismic analysis of anchored and unanchored tanks. Engineering Structures 2010;32:409–23. [26] Haroun MA. Vibration studies and tests of liquid storage tanks. Earthquake Engineering and Structural Dynamics 1983;11:179–206. [27] API 650. Welded steel tanks for oil storage.10th ed. Washington, D.C: American Petroleum Institute; 2005. [28] Wozniac RC, Mitchell WW. Basis of design provisions for welded steel oil storage tanks. In: Proceedings of the Refining Department. API: Washington; 1978. p. 485–501. [29] Malhotra PK, Wenk T, Wieland M. Simple procedure for seismic analysis of liquid-storage tanks. Structural Engineering and International 2000;10: 197–201. [30] Estekanchi HE, Vafai A, Sadeghazar M. Endurance time method for seismic analysis and design of structures. Scientia Iranica 2004;11:361–70. [31] Razavi M. Evaluation of endurance time method compared to spectral dynamic analysis method in seismic analysis of steel frames. MSc thesis. Department of Civil Engineering, Sharif University of Technology, Tehran, Iran; 2007. [32] Estekanchi HE, Valamanesh V, Vafai A. Application of endurance time method in linear seismic analysis. Engineering Structures 2007;29:2551–62. [33] Estekanchi HE, Website of the endurance time method. [Online]. /http:// sharif.edu/  stkanchi/ETS, 24.04.2010. [34] FEMA 440. Improvement of nonlinear static seismic analysis procedures. Washington D.C: Federal Emergency Management Agency; 2005. [35] Estekanchi HE, Arjomandi K, Vafai A. Estimating structural damage of steel moment frames by Endurance Time method. Journal of Constructional Steel Research 2008;64:145–55. [36] Riahi HT, Estekanchi HE. Seismic assessment of steel frames with endurance time method. Journal of Constructional Steel Research 2010;66:780–92. [37] Samanipour K, Estekanchi HE, Vafai A, Keivani J. Performance of endurance time method in linear seismic analysis of steel tanks. Journal of Science and Technology 2009;46:59–72. [38] Alembagheri M. Assessment of seismic behavior of anchored and unanchored tanks using Endurance Time method. MSc thesis. Sharif University of Technology, Tehran, Iran; 2009. [39] Estekanchi HE, Basim MC. Optimal damper placement in steel frames by the Endurance Time method. The Structural Design of Tall and Special Buildings 2011;20:621–30. [40] Ahmadi M. Application of Endurance Time method in seismic assessment of irregular steel structures. MSc thesis. Sharif University of Technology, Tehran, Iran; 2010. [41] Alembagheri M, Estekanchi HE. Nonlinear analysis of aboveground anchored steel tanks using Endurance Time method. Asian Journal of Civil Engineering 2011;12:731–50. [42] Alembagheri M, Estekanchi HE. Seismic assessment of unanchored steel storage tanks by endurance time method. Earthquake Engineering and Engineering Vibration, accepted for publication. [43] Khoei AR, Gharehbaghi SA, Azami AR, Tabarraie AR. SUT-DAM: an integrated software environment for multi-disciplinary geotechnical engineering. Advances Engineering Software 2006;37:728–53. [44] Bowles JE. Foundation Analysis and Design.5th ed. Illinois: McGraw Hill; 1997.