Liu et al 2020m - Revision history

Rimni at 09:04, 14 April 2021

2021-04-14T09:04:10Z

Rimni at 08:38, 14 April 2021

2021-04-14T08:38:05Z

Rimni: /* 4.2 Static pushover response of special-shaped column frame */

2021-04-14T08:34:24Z

‎4.2 Static pushover response of special-shaped column frame

Rimni at 08:33, 14 April 2021

2021-04-14T08:33:07Z

Rimni: /* 4.2 Static pushover response of special-shaped column frame */

2021-04-13T14:31:39Z

‎4.2 Static pushover response of special-shaped column frame

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Rimni: /* 4.1 Pushover analysis method */

2021-04-13T14:14:57Z

‎4.1 Pushover analysis method

Rimni at 13:57, 13 April 2021

2021-04-13T13:57:08Z

Rimni: /* 3. Finite element model of special-shaped column frame */

2021-04-13T13:53:43Z

‎3. Finite element model of special-shaped column frame

Rimni at 13:51, 13 April 2021

2021-04-13T13:51:26Z

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Rimni at 13:25, 13 April 2021

2021-04-13T13:25:27Z

@@ Line 14: / Line 14: @@
 (318 Liuhe Road, Xihu District, Hangzhou, Zhejiang, China)</div>
 -->
 ==Abstract==

@@ Line 338: / Line 338: @@
 It can be seen from [[#img-13|Figure 13]] that under the action of an earthquake of 7 degrees (0.1g), pink plastic hinges appear on the first to ninth storey beams of sheet 2. Under the action of an earthquake of 8 degrees (0.2g), dark blue hinges appear on the first to seventh storey beams of sheet 3, and pink hinges start to appear on the first storey columns. Under the action of 8 degree (0.3g) earthquake, red plastic hinges appear  on the second to fourth storey beams of sheet 2, and plastic hinges of varying degrees appear on the first to ninth storey columns.
-=5. Conclusion=
+==5. Conclusion==
 . The 12-storey special-shaped column structure with a height of 34.8m is basically intact under the action of a 7 degree (0.1g) earthquake. It is slightly damaged under the action of an 8 degree (0.2g) earthquake. Under the action of an 8 degree 0.3g earthquake, it collapses.
@@ Line 347: / Line 347: @@
 ==References==
 [1] Technical specification for concrete structures with specially shaped columns (JGJ149-2017). China Architecture & Building Press, Beijing, 2017.
@@ Line 354: / Line 356: @@
 [3] Tian W., Zhou M., Chen S. Design of concrete special-shaped column structure. China Architecture & Building Press, Beijing, 2007.
-[4] Shi G., Atluri S. N. Elasto-plastic large deformation analysis of space-frames: A plastic-hinge and stress-based explicit derivation of tangent stiffnesses. International Journal for Numerical Methods in Engineering, 26: 589-615, 1988.
+[4] Shi G., Atluri S.N. Elasto-plastic large deformation analysis of space-frames: A plastic-hinge and stress-based explicit derivation of tangent stiffnesses. International Journal for Numerical Methods in Engineering, 26:589-615, 1988.
-[5] Richard Liew J.Y., Chen H., Shanmugam N.E. Improved nonlinear plastic hinge analysis of space frame structures. Engineering Structures, 22: 1324-1338, 2000.
+[5] Richard Liew J.Y., Chen H., Shanmugam N.E. Improved nonlinear plastic hinge analysis of space frame structures. Engineering Structures, 22:1324-1338, 2000.
 [6] CSI Analysis Reference Manual for SAP2000, ETABS, and SAFE. Computer and Structures, Inc, Berkeley, 2007.
-[7] Scott M.H., Fenves G.L. Plastic Hinge Integration Methods for Force-Based Beam-Column Elements. Journal of Structural Engineering, 132: 244-252, 2006.
+[7] Scott M.H., Fenves G.L. Plastic Hinge Integration Methods for Force-Based Beam-Column Elements. Journal of Structural Engineering, 132:244-252, 2006.
 [8] FEMA 356. Prestandard and commentary for the Seismic Rehabilitation of Buildings. Federal Emergency Management Agency, 2000.
@@ Line 366: / Line 368: @@
 [9] Code for design of concrete structure (GB50010-2010). China Architecture & Building Press, Beijing, 2011.
-[10] Krawinkler H., Seneviratna G.D.P.K. Pros and cons of a pushover analysis of seismic performance evaluation[J]. Engineering Structures, 20(4-6):452-464, 1998.
+[10] Krawinkler H., Seneviratna G.D.P.K. Pros and cons of a pushover analysis of seismic performance evaluation. Engineering Structures, 20(4-6):452-464, 1998.
 [11] Einashai A.S. Advanced inelastic static (pushover) analysis for earthquake applications.  Structural Engineering & Mechanics, 12(1):51-69, 2001.
-[12] Hou S.，Ou J. A study of load pattern selection of pushover analysis and influence of higher modes. Earthquake Engineering & Engineering Vibration, 24(3): 89-97, 2004.
+[12] Hou S., Ou J. A study of load pattern selection of pushover analysis and influence of higher modes. Earthquake Engineering & Engineering Vibration, 24(3):89-97, 2004.
-[13] Zou X.K., Chan C.M. Optimal seismic performance-based design of reinforced concrete buildings using nonlinear pushover analysis. Engineering Structures, 27: 1289 - 1302, 2005.
+[13] Zou X.K., Chan C.M. Optimal seismic performance-based design of reinforced concrete buildings using nonlinear pushover analysis. Engineering Structures, 27:1289-1302, 2005.
 [14] ATC-40. Seismic Evaluation and Retrofit of Concrete Buildings: Volume 1.  Report No. SSC 96-01. Applied Technology Council, Redwood City, California, 1996.
@@ Line 379: / Line 381: @@
 [16] Beijing civil king software technology Co., Ltd. SAP2000 User Guide. China Communications Press, Beijing, 2012.

@@ Line 323: / Line 323: @@
 |-
 |style="padding:10px;"|  [[Image:Draft_Liu_754106674-image20.png|222px]]
 |-
 |  style="text-align: center;font-size: 75%;"|(a) 7 degree (0.1g) earthquake [sheet 2]
 |  style="text-align: center;font-size: 75%;"| (b) 8 degree (0.2g) earthquake [sheet 3]
 |-
-|style="padding:10px;"|  [[Image:Draft_Liu_754106674-image22.png|246px]]
+| colspan="2" style="padding:10px;"|  [[Image:Draft_Liu_754106674-image22.png|246px]]
 |-
-|  style="text-align: center;font-size: 75%;"|(c) 8degree (0.3g) earthquake [sheet 2]
+|  colspan="2" style="text-align: center;font-size: 75%;"|(c) 8degree (0.3g) earthquake [sheet 2]
 |- style="text-align: center; font-size: 75%;"
-| colspan="1" style="padding:10px;"| '''Figure 13'''. Plastic hinge distribution of the frame
+| colspan="2" style="padding:10px;"| '''Figure 13'''. Plastic hinge distribution of the frame
 |}

@@ Line 317: / Line 317: @@
-Take the two sheets (the sheet 2 and 3, see Figure 10) that deformed significantly under earthquakes of various intensity for analysis, and the plastic hinge distributions are shown in Figure 13.
+Take the two sheets (the sheet 2 and 3, see [[#img-10|Figure 10]]) that deformed significantly under earthquakes of various intensity for analysis, and the plastic hinge distributions are shown in [[#img-13|Figure 13]].
-<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
+<div id='img-13'></div>
-  [[Image:Draft_Liu_754106674-image20.png|222px]] </div>
+{| style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: auto;max-width: auto;"
-<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
+It can be seen from [[#img-13|Figure 13]] that under the action of an earthquake of 7 degrees (0.1g), pink plastic hinges appear on the first to ninth storey beams of sheet 2. Under the action of an earthquake of 8 degrees (0.2g), dark blue hinges appear on the first to seventh storey beams of sheet 3, and pink hinges start to appear on the first storey columns. Under the action of 8 degree (0.3g) earthquake, red plastic hinges appear  on the second to fourth storey beams of sheet 2, and plastic hinges of varying degrees appear on the first to ninth storey columns.
- [[Image:Draft_Liu_754106674-image21.png|216px]] </div>
-−
-<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
-(b) 8 degree (0.2g) earthquake [sheet 3]</div>
-−
-<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
- [[Image:Draft_Liu_754106674-image22.png|246px]] </div>
-−
-<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
-(c) 8degree (0.3g) earthquake [sheet 2]</div>
-−
-<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
-'''Figure 13'''. Plastic hinge distribution of the frame</div>
-−
 It can be seen from Figure 13 that under the action of an earthquake of 7 degrees (0.1g), pink plastic hinges appear on the first to ninth storey beams of sheet 2. Under the action of an earthquake of 8 degrees (0.2g), dark blue hinges appear on the first to seventh storey beams of sheet 3, and pink hinges start to appear on the first storey columns. Under the action of 8 degree (0.3g) earthquake, red plastic hinges appear  on the second to fourth storey beams of sheet 2, and plastic hinges of varying degrees appear on the first to ninth storey columns.
 =5. Conclusion=

@@ Line 189: / Line 189: @@
-Taking the density of reinforced concrete as 2402.77kg/m<sup>3</sup>. Calculate the mass of the model and estimate the horizontal force (ie, base shear) under the action of the basic seismic acceleration corresponding to each seismic intensity, as shown in Table 2.
+Taking the density of reinforced concrete as 2402.77kg/m<sup>3</sup>. Calculate the mass of the model and estimate the horizontal force (ie, base shear) under the action of the basic seismic acceleration corresponding to each seismic intensity, as shown in [[#tab-2|Table 2]].
-<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
+<div class="center" style="font-size: 75%;">'''Table 2'''. Model mass and horizontal force of the model under various earthquake accelerations</div>
-'''Table 2.''' Model mass and horizontal force of the model under various earthquake accelerations</div>
-{| style="width: 39%;margin: 1em auto 0.1em auto;border-collapse: collapse;"
+<div id='tab-1'></div>
-|-
+{| class="wikitable" style="margin: 1em auto 0.1em auto;border-collapse: collapse;font-size:85%;width:auto;"
-|  style="border-top: 2pt solid black;border-bottom: 2pt solid black;border-right: 1pt solid black;text-align: center;"|Mass
+|-style="text-align:center"
-|  style="border-top: 2pt solid black;border-left: 1pt solid black;border-bottom: 2pt solid black;text-align: center;"|4.90×10<sup>5</sup>kg
+! Mass !! 7degree (0.1g) !!8degree (0.2g) !! 8degree (0.3g)
 |-
-|  style="border-top: 2pt solid black;border-bottom: 2pt solid black;border-right: 1pt solid black;text-align: center;"|7degree (0.1g)
+|  style="text-align: center;"|4.90<math>\times 10^5</math>kg
-|  style="border-top: 2pt solid black;border-left: 1pt solid black;border-bottom: 2pt solid black;text-align: center;"|480.2KN
+|  style="text-align: center;"|480.2KN
-|-
+|  style="text-align: center;"|960.4KN
-|  style="border-top: 2pt solid black;border-bottom: 2pt solid black;border-right: 1pt solid black;text-align: center;"|8degree (0.2g)
+|  style="text-align: center;"|1440.6KN
-|  style="border-top: 2pt solid black;border-left: 1pt solid black;border-bottom: 2pt solid black;text-align: center;"|960.4KN
-|-
-|  style="border-top: 2pt solid black;border-bottom: 2pt solid black;border-right: 1pt solid black;text-align: center;"|8degree (0.3g)
-|  style="border-top: 2pt solid black;border-left: 1pt solid black;border-bottom: 2pt solid black;text-align: center;"|1440.6KN
 |}

@@ Line 166: / Line 166: @@
 The elastic modulus of C30 concrete selected in this paper is 30 000MPa, its Poisson's ratio is 0.2, the standard value of axial compressive strength is 20.1MPa, and the standard value of axial tensile strength is 2.01MPa. The selected HRB335 steel bar has an elastic modulus of 200 000 MPa, a Poisson's ratio of 0.27, a standard value of yield strength of 335 MPa, and a tangent modulus of 2 000 MPa after yielding. The selected HPB300 steel bar has an elastic modulus of 210 000 MPa, a Poisson's ratio of 0.27, a standard value of yield strength of 300 MPa, and a tangent modulus of 2 000 MPa after yielding [9].
-=4. Seismic performance Analysis of special-shaped column frame =
+==4. Seismic performance Analysis of special-shaped column frame==
-==4.1 Pushover analysis method==
+===4.1 Pushover analysis method===
 Pushover analysis is one of the main methods of elastoplastic analysis of seismic structures. This article mainly applies the Pushover analysis method of inverted triangular distribution horizontal loading mode to calculate the seismic response of the structural model [10-14].
-The seismic performance of the frame model under earthquakes with an intensity of 7, 8, and 9 degree is analyzed. According to "Code for Seismic Design of Buildings" (GB50011-2010), the corresponding relationship between seismic fortification intensity and design basic seismic acceleration is shown in Table 1 [15].
+The seismic performance of the frame model under earthquakes with an intensity of 7, 8, and 9 degree is analyzed. According to "Code for Seismic Design of Buildings" (GB50011-2010), the corresponding relationship between seismic fortification intensity and design basic seismic acceleration is shown in [[#tab-1|Table 1]] [15].
-<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
+<div class="center" style="font-size: 75%;">'''Table 1'''. Correspondence between seismic fortification intensity and design basic seismic acceleration</div>
-'''Table 1.''' Correspondence between seismic fortification intensity and design basic seismic acceleration</div>
-{| style="width: 61%;margin: 1em auto 0.1em auto;border-collapse: collapse;"
+<div id='tab-1'></div>
 |-
-|  style="border-top: 2pt solid black;border-bottom: 2pt solid black;border-right: 1pt solid black;text-align: center;"|Seismic fortification intensity
+|  style="text-align: center;"|7
-|  style="border-top: 2pt solid black;border-left: 1pt solid black;border-bottom: 2pt solid black;border-right: 1pt solid black;text-align: center;"|7
+|  style="text-align: center;"|0.10（0.15）g
-|  style="border-top: 2pt solid black;border-left: 1pt solid black;border-bottom: 2pt solid black;text-align: center;"|8
 |-
-|  style="border-top: 2pt solid black;border-bottom: 2pt solid black;border-right: 1pt solid black;text-align: center;"|Design basic seismic acceleration
+|  style="text-align: center;"|8
-|  style="border-top: 2pt solid black;border-left: 1pt solid black;border-bottom: 2pt solid black;border-right: 1pt solid black;text-align: center;"|0.10（0.15）g
+|  style="text-align: center;"|0.20（0.30）g
-|  style="border-top: 2pt solid black;border-left: 1pt solid black;border-bottom: 2pt solid black;text-align: center;"|0.20（0.30）g
 |}

@@ Line 142: / Line 142: @@
 |}
-=3. Finite element model of special-shaped column frame=
+==3. Finite element model of special-shaped column frame==
-A typical 12-storey special-shaped column frame is selected as the calculation model in this paper. There is no rectangular column in the structure. As shown in Figure 9 and Figure 10, it has 2 spans along the X direction and 2 spans along the Y direction, each span is 4.5m. The layouts of the 12 storeys are the same, and the height of each storey is 2.9m. The nonlinear elastoplastic analysis of the frame structure is realized on the basis of inserting PMM hinges at the beam and column ends of the frame.
+A typical 12-storey special-shaped column frame is selected as the calculation model in this paper. There is no rectangular column in the structure. As shown in [[#img-9|Figures 9]] and [[#img-10|10]], it has 2 spans along the X direction and 2 spans along the Y direction, each span is 4.5m. The layouts of the 12 storeys are the same, and the height of each storey is 2.9m. The nonlinear elastoplastic analysis of the frame structure is realized on the basis of inserting PMM hinges at the beam and column ends of the frame.
-<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
+<div id='img-9'></div>
- [[Image:Draft_Liu_754106674-image15.png|307x307px]] </div>
+{| style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: auto;max-width: auto;"
-<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
+<div id='img-10'></div>
- [[Image:Draft_Liu_754106674-image16.png|388x388px]] </div>
+{| style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: auto;max-width: auto;"
 The elastic modulus of C30 concrete selected in this paper is 30 000MPa, its Poisson's ratio is 0.2, the standard value of axial compressive strength is 20.1MPa, and the standard value of axial tensile strength is 2.01MPa. The selected HRB335 steel bar has an elastic modulus of 200 000 MPa, a Poisson's ratio of 0.27, a standard value of yield strength of 335 MPa, and a tangent modulus of 2 000 MPa after yielding. The selected HPB300 steel bar has an elastic modulus of 210 000 MPa, a Poisson's ratio of 0.27, a standard value of yield strength of 300 MPa, and a tangent modulus of 2 000 MPa after yielding [9].

@@ Line 50: / Line 50: @@
 Each plastic hinge is simulated by a discrete point hinge. All plastic deformation, whether it is translation or rotation, occurs in the point hinge. The hinge length is generally a fraction of the element length, and is often of the same order of magnitude as the section height [7].
-For each degree of freedom, a displacement-load curve can be defined to express the yield value and plastic deformation after yielding. This is achieved by a curve with five points <math>\bf A</math>-'''B'''-'''C'''-'''D'''-'''E''' [6]. In the nonlinear analysis of the frame in this paper, the deformation curve of the plastic hinge is defined as follows:
+For each degree of freedom, a displacement-load curve can be defined to express the yield value and plastic deformation after yielding. This is achieved by a curve with five points <math>\bf A</math>-<math>\bf B</math>-<math>\bf C</math>-<math>\bf D</math>-<math>\bf E</math> [6]. In the nonlinear analysis of the frame in this paper, the deformation curve of the plastic hinge is defined as follows:
 <div id='img-2'></div>
@@ Line 61: / Line 61: @@
-In [[#img-2|Figure 2]], the abscissa is the ratio of the frame element hinge rotation angle to the rotation angle scale factor ''SF''. This article takes ''SF''=1. The ordinate is the ratio of bending moment to yield bending moment. Point <math>\bf A</math> is the origin, and point B represents yield. There is no deformation in the hinge before ascending to point B, only plastic deformation beyond point <math>\bf B</math> will be revealed by the hinge. Point '''C''' represents the ultimate bearing capacity. Point '''D''' represents the residual strength. Point E represents complete failure .
+In [[#img-2|Figure 2]], the abscissa is the ratio of the frame element hinge rotation angle to the rotation angle scale factor ''SF''. This article takes ''SF''=1. The ordinate is the ratio of bending moment to yield bending moment. Point <math>\bf A</math> is the origin, and point B represents yield. There is no deformation in the hinge before ascending to point B, only plastic deformation beyond point <math>\bf B</math> will be revealed by the hinge. Point <math>\bf C</math> represents the ultimate bearing capacity. Point <math>\bf D</math> represents the residual strength. Point E represents complete failure .
-The points '''IO''' (immediate use), '''LS''' (life safety) and '''CP''' (collapse prevention) are specified in the plastic curve. They can be reflected in the analysis results and can be used for performance-based design.
+The points <math>{\bf IO}</math> (immediate use), <math>{\bf LS}</math> (life safety) and <math>{\bf CP}</math> (collapse prevention) are specified in the plastic curve. They can be reflected in the analysis results and can be used for performance-based design.
-With reference to the specification FEMA-356 of Federal Emergency Management Agency in the United States [8], the coordinates of each point in the figure selected in this article are as follows: '''B'''(1, 0), '''C'''(1.1, 0.015), '''D'''(0.2, 0.015), '''E'''(0.2, 0.025). The rotation angles (ie, plastic deformation radian) corresponding to IO, LS, and CP are 0.003, 0.012, and 0.015 respectively.
+With reference to the specification FEMA-356 of Federal Emergency Management Agency in the United States [8], the coordinates of each point in the figure selected in this article are as follows: <math>\bf B</math>(1, 0), <math>\bf C</math>(1.1, 0.015), <math>\bf D</math>(0.2, 0.015), <math>\bf E</math>(0.2, 0.025). The rotation angles (ie, plastic deformation radian) corresponding to IO, LS, and CP are 0.003, 0.012, and 0.015 respectively.
 The definition of plastic hinge rotation angle is shown in the [[#img-3|Figure 3]] [4].