De-la-Colina 2022a - Revision history

Rimni: /* References */

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‎References

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 [30] Hernández H., Hernández A., Valdés G. Non-linear sloshing effect on storage tanks subjected to high earthquake ground motion. Rev. Int. Métodos Numer. Calc. Diseño Ing., 31(3):198–206, 2015. Spanish. [http://dx.doi.org/10.1016/j.rimni.2014.09.002 http://dx.doi.org/10.1016/j.rimni.2014.09.002].
-[31] Frandsen J.B,  Bortwick A.G. Simulation of sloshing motions in fixed and vertically excited containers using a  2-D inviscid &#x03c3;-transformed finite difference solver. J. Fluids Struct., 18:197–214, 2003.
+[31] Frandsen J.B,  Bortwick A.G. Simulation of sloshing motions in fixed and vertically excited containers using a  2-D inviscid <math>\sigma</math>-transformed finite difference solver. J. Fluids Struct., 18:197–214, 2003.
 [32] Cook R.D., Malkus D.S., Plesha M.E., Witt R.J. Concepts and applications of the finite element analysis. 4th ed. John Wiley and Sons: New York (NY), 2002.

@@ Line 694: / Line 694: @@
 [8] Veletsos A.,  Yang J. Earthquake response of liquid storage tanks. Proceedings 2nd Engineering Mechanics Specialty Conference, ASCE. Raleigh, (NC), 1977.
-[9] Malhotra, P.K., Wenk. T. ,Wieland, M. Simple procedure for seismic analysis of liquid-storage tanks. Struct. Eng. Int., 10(3):197-201, 2000.
+[9] Malhotra P.K., Wenk T., Wieland M. Simple procedure for seismic analysis of liquid-storage tanks. Struct. Eng. Int., 10(3):197-201, 2000.
 [10] European Committee for Standarization (CEN). Eurocode 8. Design of Structures for Earthquake Resistance. Part 4: Silos, tanks and pipelines. CEN: Brussels, 2006.
-[11] Epstein, H. Seismic design of liquid-storage tanks. J. Struct. Div., 102:1659-1673, 1976.
+[11] Epstein H. Seismic design of liquid-storage tanks. J. Struct. Div., 102:1659-1673, 1976.
-[12] Graham, E., Rodriguez, A. The characteristics of fuel motion which affect airplane dynamics. Report SM 14212. Douglas Aircraft Company, Santa Monica (CA). 1951.
+[12] Graham E., Rodriguez A. The characteristics of fuel motion which affect airplane dynamics. Report SM 14212, Douglas Aircraft Company, Santa Monica (CA), 1951.
-[13] Ibrahim, R. Liquid sloshing dynamics: Theory and applications. New York (NY): Cambridge University Press; 2005.
+[13] Ibrahim R. Liquid sloshing dynamics: Theory and applications. New York (NY): Cambridge University Press, 2005.
-[14] Langhaar, H. Energy Methods in Applied Mechanics. Krieger: Malabar (FL), 1962.
+[14] Langhaar H. Energy methods in applied mechanics. Krieger: Malabar (FL), 1962.
-[15] Minowa, C. Dynamic analysis for rectangular water tanks. Recent Adv. Lifeline Earthquake Engineering. Japan. 1980.
+[15] Minowa C. Dynamic analysis for rectangular water tanks. Recent Adv. Lifeline Earthquake Engineering, Japan, 1980.
-[16] Zhu, F. Rayleigh-Ritz method in coupled fluid-structure interacting systems and its applications. J. Sound Vib.,'' ''186:543-550, 1995.
+[16] Zhu F. Rayleigh-Ritz method in coupled fluid-structure interacting systems and its applications. J. Sound Vib., 186:543-550, 1995.
-[17] Moradi, R., Behnamfar, F., Hashem, S. Mechanical model for cylindrical flexible concrete tanks undergoing lateral excitation. Soil Dyn. Earthq. Eng.,'' ''106:148–162, 2018.
+[17] Moradi R., Behnamfar F., Hashem S. Mechanical model for cylindrical flexible concrete tanks undergoing lateral excitation. Soil Dyn. Earthq. Eng., 106:148–162, 2018.
-[18] Kim, J.K., Koh, H.M., Kwahk, I.J. Dynamic response of rectangular flexible fluid containers. J. Eng. Mech., 122(9): 807-817, 1996.
+[18] Kim J.K., Koh H.M., Kwahk I.J. Dynamic response of rectangular flexible fluid containers. J. Eng. Mech., 122(9):807-817, 1996.
-[19] Rashed, A.A., Iwan, W.D. Dynamic analysis of short-length gravity dams. J. Eng. Mech''.'','' ''111 (8):1067-1083, 1985.
+[19] Rashed A.A., Iwan W.D. Dynamic analysis of short-length gravity dams. J. Eng. Mech., 111(8):1067-1083, 1985.
-[20] Zhao, D., Hu, Z., Chen, G., et al. Nonlinear sloshing in rectangular tanks under forced excitation. In.t J. Nav Arch. Ocean Eng., 10:545-565, 2018.
+[20] Zhao D., Hu Z., Chen G., Lim S., Wang S. Nonlinear sloshing in rectangular tanks under forced excitation. In.t J. Nav Arch. Ocean Eng., 10:545-565, 2018.
-[21] Ning, D.Z., Song,. WH., Liu, Y., et al. A boundary element investigation of liquid sloshing in coupled horizontal and vertical excitation. J. Appl. Math., 2012:1-20. DOI:10.1155/2012/340640, 2012.
+[21] Ning D.Z., Song W.H., Liu Y., Teng B. A boundary element investigation of liquid sloshing in coupled horizontal and vertical excitation. J. Appl. Math., 2012:1-20, 2012. [https://www.hindawi.com/journals/jam/2012/340640/ DOI: 10.1155/2012/340640]
-[22] Hu, Z., Zhang, X., Li, X., et al. On natural frequencies of liquid sloshing in 2-D tanks using boundary element method. Ocean. Eng., 153:88–103, 2018. [https://doi.org/10.1016/j.oceaneng.2018.01.062 https://doi.org/10.1016/j.oceaneng.2018.01.062].
+[22] Hu Z., Zhang X., Li X., Li Y. On natural frequencies of liquid sloshing in 2-D tanks using boundary element method. Ocean. Eng., 153:88–103, 2018. [https://doi.org/10.1016/j.oceaneng.2018.01.062 https://doi.org/10.1016/j.oceaneng.2018.01.062].
-[23] Hwang, I.T., Ting, K. Boundary element method for fluid-structure interaction problems in liquid storage tanks.'' ''J. Press. Vessel. Technol., 111(4):435-440, 1989. [https://doi.org/10.1115/1.3265701 https://doi.org/10.1115/1.3265701].
+[23] Hwang I.T., Ting K. Boundary element method for fluid-structure interaction problems in liquid storage tanks. J. Press. Vessel. Technol., 111(4):435-440, 1989. [https://doi.org/10.1115/1.3265701 https://doi.org/10.1115/1.3265701].
-[24] Taylor, R.E., Wu, G.X., Bai, W., et al. Numerical wave tanks based on finite element and boundary element modeling. J. Offshore Mech. Arctic Eng., 130(3), 2008.
+[24] Taylor R.E., Wu G.X., Bai W., Hu Z.Z. Numerical wave tanks based on finite element and boundary element modeling. J. Offshore Mech. Arctic Eng., 130(3):031001, 2008.
-[25] Wu, G.X., Ma,.. QW, Taylor, R.E. Numerical simulation of sloshing waves in a 3D tank based on a finite element method.  Appl. Ocean Res., 20:337–355, 1998.
+[25] Wu G.X., Ma Q.W., Taylor R.E. Numerical simulation of sloshing waves in a 3D tank based on a finite element method.  Appl. Ocean Res., 20:337–355, 1998.
-[26] Aslam, M. Finite element analysis of earthquake-induced sloshing in axisymmetric tanks. Int. J. Numer. Methods Eng., 17:159-170, 1981.
+[26] Aslam M. Finite element analysis of earthquake-induced sloshing in axisymmetric tanks. Int. J. Numer. Methods Eng., 17:159-170, 1981.
-[27] Babu, S.S., Bhattacharyya, S. Finite element analysis of fluid-structure interaction effect on liquid retaining structures due to sloshing. Comput. Struc., 59(6):1165-1171, 1996.
+[27] Babu S.S., Bhattacharyya S. Finite element analysis of fluid-structure interaction effect on liquid retaining structures due to sloshing. Comput. Struc., 59(6):1165-1171, 1996.
-[28] Arafa,.. M. Finite Element Analysis of Sloshing in Rectangular Liquid-Filled Tanks.  J. Vib. Control, 13(7): 883–903, 2007. DOI: 10.1177/1077546307078833.
+[28] Arafa M. Finite element analysis of sloshing in rectangular liquid-filled tanks.  J. Vib. Control, 13(7):883–903, 2007. [https://journals.sagepub.com/doi/10.1177/1077546307078833 DOI: 10.1177/1077546307078833].
-[29] Cho, J.R., Lee, H.W. Non-linear finite element analysis of large amplitude sloshing flow in two-dimensional tank. Int. J. Numer. Methods Eng., 61:514–531, 2004. DOI: 10.1002/nme.1078.
+[29] Cho J.R., Lee H.W. Non-linear finite element analysis of large amplitude sloshing flow in two-dimensional tank. Int. J. Numer. Methods Eng., 61(4):514–531, 2004. [https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.1078 DOI: 10.1002/nme.1078].
-[30] Hernández, H., Hernández, A., Valdés, G. Non-linear sloshing effect on storage tanks subjected to high earthquake ground motion. Rev. Int. Métodos Numer. Calc. Diseño Ing., 31(3):198–206, 2015. Spanish. [http://dx.doi.org/10.1016/j.rimni.2014.09.002 http://dx.doi.org/10.1016/j.rimni.2014.09.002].
+[30] Hernández H., Hernández A., Valdés G. Non-linear sloshing effect on storage tanks subjected to high earthquake ground motion. Rev. Int. Métodos Numer. Calc. Diseño Ing., 31(3):198–206, 2015. Spanish. [http://dx.doi.org/10.1016/j.rimni.2014.09.002 http://dx.doi.org/10.1016/j.rimni.2014.09.002].
-[31] Frandsen, J.B,  Bortwick, A.G. Simulation of sloshing motions in fixed and vertically excited containers using a  2-D inviscid &#x03c3;-transformed finite difference solver. J. Fluids Struct., 18:197–214, 2003.
+[31] Frandsen J.B,  Bortwick A.G. Simulation of sloshing motions in fixed and vertically excited containers using a  2-D inviscid &#x03c3;-transformed finite difference solver. J. Fluids Struct., 18:197–214, 2003.
-[32] Cook. R.D., Malkus, D.S., Plesha,. ME., et al. Concepts and Applications of the Finite Element Analysis. 4th ed. John Wiley and Sons: New York (NY), 2002.
+[32] Cook R.D., Malkus D.S., Plesha M.E., Witt R.J. Concepts and applications of the finite element analysis. 4th ed. John Wiley and Sons: New York (NY), 2002.
-[33] Housner, G.W. Limit design of structures to resist earthquakes. ''Proc First World Conference on Earthquake Engineering'', Berkeley (CA), 1956.
+[33] Housner G.W. Limit design of structures to resist earthquakes. Proc First World Conference on Earthquake Engineering, Berkeley (CA), 1956.
-[34] Uang,. CM., Bertero, V.V. Evaluation of seismic energy in structures. Earthq. Eng. Struct. Dyn., 19:77-90, 1990.
+[34] Uang C.M., Bertero V.V. Evaluation of seismic energy in structures. Earthq. Eng. Struct. Dyn., 19(1):77-90, 1990.
-[35] Koh, H..M, Kim, J.K., Park, J.H. Fluid—structure interaction analysis of 3-d rectangular tanks by a variationally coupled BEM-FEM and comparison with test results. Earthq. Eng. Struct. Dyn., 27:109-124, 1998.
+[35] Koh H.M., Kim J.K., Park J.H. Fluid—structure interaction analysis of 3-d rectangular tanks by a variationally coupled BEM-FEM and comparison with test results. Earthq. Eng. Struct. Dyn., 27(2):109-124, 1998.
-[36] Dogangun, A., Livaoglu, R. Hydrodynamic pressures acting on the walls of rectangular fluid containers. Struct. Eng. Mech., 17(2):203-214, 2004.
+[36] Dogangun A., Livaoglu R. Hydrodynamic pressures acting on the walls of rectangular fluid containers. Struct. Eng. Mech., 17(2):203-214, 2004.
-[37] Flores, C. B. Comportamiento mecánico de tanques atmosféricos de almacenamiento. Tesis de maestría. Escuela Superior de Ingeniería y Arquitectura (ESIA), Instituto Politécnico Nacional (IPN), Ciudad de México, 2009.
+[37] Flores C.B. Comportamiento mecánico de tanques atmosféricos de almacenamiento. Tesis de maestría. Escuela Superior de Ingeniería y Arquitectura (ESIA), Instituto Politécnico Nacional (IPN), Ciudad de México, 2009.

@@ Line 675: / Line 675: @@
 ==References==
 [1] American Society of Civil Engineers. ASCE/SEI 07-16. Minimum design loads and associated criteria for buildings and other structures. ASCE: Reston, Virginia, 2017.
@@ Line 680: / Line 682: @@
 [2] Comisión Federal de Electricidad. Manual de diseño de obras civiles – Diseño por sismo. CFE: Ciudad de Mexico, 2009.  Spanish.
-[3] American Concrete Institute. ACI 350.3-06: Seismic Design of Liquid-Containing Concrete Structures and Commentary ACI: Farmington Hills, 2006.
+[3] American Concrete Institute. ACI 350.3-06: Seismic design of liquid-containing concrete structures and commentary ACI: Farmington Hills, 2006.
-[4] Housner, G.W. Dynamic pressures on accelerated fluid containers''. ''Bull. Seismol. Soc. Am., 47:15-35, 1957.
+[4] Housner G.W. Dynamic pressures on accelerated fluid containers. Bull. Seismol. Soc. Am., 47:15-35, 1957.
-[5] Housner, G.W. The dynamic behavior of water tanks. Bull. Seismol. Soc. Am., 53:381-387, 1963.
+[5] Housner G.W. The dynamic behavior of water tanks. Bull. Seismol. Soc. Am., 53:381-387, 1963.
-[6] Chen, W., Haroun, M, Liu, F. Large amplitude liquid sloshing in seismically excited tanks. Earthq. Eng. Struct. Dyn., 25:653-669, 1996.
+[6] Chen W., Haroun M, Liu F. Large amplitude liquid sloshing in seismically excited tanks. Earthq. Eng. Struct. Dyn., 25:653-669, 1996.
 [7] American Water Works Association. Welded carbon steel tanks for water storage. ANSI/AWWA D100-05 Standard. Denver, 2005.
-[8] Veletsos, A.,  Yang, J. Earthquake response of liquid storage tanks. Proceedings 2nd Engineering Mechanics Specialty Conference. ASCE. Raleigh, (NC). 1977.
+[8] Veletsos A.,  Yang J. Earthquake response of liquid storage tanks. Proceedings 2nd Engineering Mechanics Specialty Conference, ASCE. Raleigh, (NC), 1977.
 [9] Malhotra, P.K., Wenk. T. ,Wieland, M. Simple procedure for seismic analysis of liquid-storage tanks. Struct. Eng. Int., 10(3):197-201, 2000.

@@ Line 46: / Line 46: @@
 The seismic response of liquid-containing tanks has been also studied with numerical procedures. The main numerical methods include finite elements, boundary elements or finite differences. For example, Zhao ''et al''. [20] used the boundary-element method (BEM) to study the nonlinear sloshing in rectangular tanks under base excitations. In their study, the hydrodynamic pressures were validated with experimental tests. Ning ''et al''. [21] also used the BEM to study sloshing of liquids in tanks subjected to both horizontal and vertical excitations. Hu ''et al''. [22] studied the natural frequencies of 2D tanks using the BEM.
-The finite-element method (FEM) has also been used to study tanks subjected to ground motions. For instance, Hwang and Ting [23] combined the BEM and the FEM to study the dynamic response of liquid storage tanks subjected to earthquake ground motions. Taylor ''et al''. [24] also combined both finite and boundary elements to model the interaction of nonlinear waves in tanks. Wu ''et al''. [25] analyzed the sloshing waves in 3D tank using the FEM. Aslam [26] also studied sloshing in cylindrical tanks induced by ground motions. Babu and Bhattacharyya [27] studied the fluid-structure interaction effect on liquid-retaining structures due to sloshing using finite element analysis. Other studies using the FEM include references [28- 29].
+The finite-element method (FEM) has also been used to study tanks subjected to ground motions. For instance, Hwang and Ting [23] combined the BEM and the FEM to study the dynamic response of liquid storage tanks subjected to earthquake ground motions. Taylor ''et al''. [24] also combined both finite and boundary elements to model the interaction of nonlinear waves in tanks. Wu ''et al''. [25] analyzed the sloshing waves in 3D tank using the FEM. Aslam [26] also studied sloshing in cylindrical tanks induced by ground motions. Babu and Bhattacharyya [27] studied the fluid-structure interaction effect on liquid-retaining structures due to sloshing using finite element analysis. Other studies using the FEM include Arafa [28] and Cho and Lee [29].
 The finite-difference method (FDM) has been used, for instance, by Chen ''et al''. [6], by Hernandez ''et al''. [30] and by Frandsen and Bortwick [31] to study the nonlinear sloshing of a liquid contained in cylindrical and rectangular tanks subjected to ground motions.
@@ Line 488: / Line 488: @@
 ===3.2 Housner===
-In this subsection, the wall pressures are computed taking into account the references 4 and 5. The impulsive pressure is computed with the following formula, where <math display="inline">y</math> is measured from the liquid surface down (with <math display="inline">l = L/2</math> and <math display="inline">h = H</math>):
+In this subsection, the wall pressures are computed taking into account Housner [4,5]. The impulsive pressure is computed with the following formula, where <math display="inline">y</math> is measured from the liquid surface down (with <math display="inline">l = L/2</math> and <math display="inline">h = H</math>):
 {| class="formulaSCP" style="width: 100%; text-align: center;"
@@ Line 632: / Line 632: @@
 ====3.5.4 Total hydrodynamic pressures====
-As for the total pressures, the total wall pressures are shown in [[#img-7|Figure 7]]. The pressures computed in Ref [29] are also included in the figure. These values were computed with the finite element method (FEM) and are assumed here as the “exact” pressures.
+As for the total pressures, the total wall pressures are shown in [[#img-7|Figure 7]]. The pressures computed in Cho and Lee [29] are also included in the figure. These values were computed with the finite element method (FEM) and are assumed here as the “exact” pressures.
 <div id='img-7'></div>
@@ Line 647: / Line 647: @@
 For the wall design, an estimation of both the shear forces (<math display="inline">V</math>) and the bending moments (<math display="inline">M</math>) is required. An analysis of the walls can be carried out taking into account a theory of plates (either thin plate theory or thick plate theory). In the estimation of these forces (<math display="inline">V</math>) and the bending moments (<math display="inline">M</math>) a finite element analysis of the complete tank can also be considered, however given the accuracy involved in the estimations of pressures, this refinement is in many cases not justified. An isolated plate with adequate boundary conditions seems to be enough for the computation of forces. Since the length/height ratio of the tank of this example is larger than 2.0, a vertical strip of wall can be idealized as a contilever beam supported at the base with a width equal to 1.0 m. This simplification is used here as a simple way to compare these moments among the methods. In the case of reinforced-concrete tanks the bending moment referred here can be used to obtain the wall vertical reinforcement.
-The distributions of shear forces per unit width are shown in [[#img-8|Figure 8]]. It is clear that the distributions of these shear forces are similar among the methods. The shear forces computed with the proposed method resulted slightly larger than the finite element method (FEM) forces, given by Koh, Kim and Park [35]. The shear force at the wall base predicted by the proposed method resulted 13% larger than the value given by the FEM solution.
+The distributions of shear forces per unit width are shown in [[#img-8|Figure 8]]. It is clear that the distributions of these shear forces are similar among the methods. The shear forces computed with the proposed method resulted slightly larger than the finite element method (FEM) forces, given by Koh ''et al.'' [35]. The shear force at the wall base predicted by the proposed method resulted 13% larger than the value given by the FEM solution.
 <div id='img-8'></div>

@@ Line 604: / Line 604: @@
 <div class="center" style="width: auto; margin-left: auto; margin-right: auto;font-size:75%;">
-<math>{}^* t</math> is the thickness of the wall in the case of the study with flexible walls [35].</div>
+<math>{}^* t</math> is the thickness of the wall in the case of the study with flexible walls [35]</div>
 ====3.5.2 Convective pressures====

@@ Line 579: / Line 579: @@
 {| class="wikitable" style="margin: 1em auto 0.1em auto;border-collapse: collapse;font-size:85%;width:auto;"
 |-style="text-align:center"
-! Method !! D [m]
+! style="text-align: left;"| Method !! D [m]
 |-
 |  style="text-align: left;vertical-align: top;"|Housner

@@ Line 604: / Line 604: @@
 <div class="center" style="width: auto; margin-left: auto; margin-right: auto;font-size:85%;">
-* <math>t</math> is the thickness of the wall in the case of the study with flexible walls [35].</div>
+<math> * t</math> is the thickness of the wall in the case of the study with flexible walls [35].</div>
 ====3.5.2 Convective pressures====

@@ Line 581: / Line 581: @@
 ! Method !! D [m]
 |-
-|  style="text-align: center;vertical-align: top;"|Housner
+|  style="text-align: left;vertical-align: top;"|Housner
 |  style="text-align: center;vertical-align: top;"|0.71
 |-
-|  style="text-align: center;vertical-align: top;"|''Standard'' ASCE 7-16
+|  style="text-align: left;vertical-align: top;"|''Standard'' ASCE 7-16
 |  style="text-align: center;vertical-align: top;"|0.63
 |-
-|  style="text-align: center;vertical-align: top;"|ACI-350.3
+|  style="text-align: left;vertical-align: top;"|ACI-350.3
 |  style="text-align: center;vertical-align: top;"|0.75
 |-
-|  style="text-align: center;vertical-align: top;"|Method presented here
+|  style="text-align: left;vertical-align: top;"|Method presented here
 |  style="text-align: center;vertical-align: top;"|0.51
 |-
-|  style="text-align: center;vertical-align: top;"|CFE-2015
+|  style="text-align: left;vertical-align: top;"|CFE-2015
 |  style="text-align: center;vertical-align: top;"|0.71
 |-
-|  style="text-align: center;vertical-align: top;"|Ko, Kim and Park (<math display="inline">t = 0.5</math> m)*
+|  style="text-align: left;vertical-align: top;"|Ko, Kim and Park (<math display="inline">t = 0.5</math> m)*
 |  style="text-align: center;vertical-align: top;"|0.70
 |-
-|  style="text-align: center;vertical-align: top;"|Ko, Kim and Park (<math display="inline">t = 1.0</math> m and rigid)*
+|  style="text-align: left;vertical-align: top;"|Ko, Kim and Park (<math display="inline">t = 1.0</math> m and rigid)*
 |  style="text-align: center;vertical-align: top;"|0.30
 |}
-<div class="left" style="width: auto; margin-left: auto; margin-right: auto;font-size:85%;">
+<div class="center" style="width: auto; margin-left: auto; margin-right: auto;font-size:85%;">
 * <math>t</math> is the thickness of the wall in the case of the study with flexible walls [35].</div>