Campbell 2019a - Revision history

Rimni at 12:48, 9 December 2020

2020-12-09T12:48:09Z

Rimni: /* 3.1.2 Tests of confined masonry walls with openings */

2020-12-09T12:15:04Z

‎3.1.2 Tests of confined masonry walls with openings

Jaime Campbell at 14:53, 29 January 2020

2020-01-29T14:53:49Z

Jaime Campbell at 14:52, 29 January 2020

2020-01-29T14:52:25Z

Rimni at 14:53, 22 January 2020

2020-01-22T14:53:33Z

Rimni at 14:51, 22 January 2020

2020-01-22T14:51:46Z

Rimni at 14:49, 22 January 2020

2020-01-22T14:49:47Z

Rimni at 14:48, 22 January 2020

2020-01-22T14:48:48Z

Rimni at 14:30, 22 January 2020

2020-01-22T14:30:11Z

Rimni at 14:19, 22 January 2020

2020-01-22T14:19:07Z

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 As described in Campbell and Durán's contribution, the non-linear behavior of masonry walls is greatly explained by the bond between bricks and mortar [13]. For this reason, the most relevant part of the model is the representation of the mortar and the union between this and the masonry units through special elements.
-In general, this simplified micro-model considers finite elements for masonry units, and a model for joints defined by two parallel non-linear springs (one longitudinal and one transversal to the joint) that define the axial and transverse behavior of the mortar. In addition, a contact element, which joins these springs in series, defines the behavior of the interface between the mortar and the unit, considering the friction and the adherence limit between these two elements. This set is connected to the nodes of each finite element, as shown in Figure 1.
+In general, this simplified micro-model considers finite elements for masonry units, and a model for joints defined by two parallel non-linear springs (one longitudinal and one transversal to the joint) that define the axial and transverse behavior of the mortar. In addition, a contact element, which joins these springs in series, defines the behavior of the interface between the mortar and the unit, considering the friction and the adherence limit between these two elements. This set is connected to the nodes of each finite element, as shown in [[#img-1|Figure 1]].
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 The mechanical properties and thickness of the mortar were used for the definition of the non-linear springs to represent the longitudinal and transverse structural behavior of the mortar.
-In this case, the force-displacement curve of these elements was defined taking into account the stress-strain curve of the mortar, the tributary area of the unit over the node and the thickness of the joint. The force at each point of the force-displacement curve was defined by considering the stress multiplied by the tributary area (Figure 2), and the displacement was defined by taking into account the unit deformation multiplied by the length of the spring. This length was taken as 9/10 of the thickness of the joint, considering that the length of the contact element is 1/10 of the thickness of the joint. This idea was valid for longitudinal and transverse springs.
+In this case, the force-displacement curve of these elements was defined taking into account the stress-strain curve of the mortar, the tributary area of the unit over the node and the thickness of the joint. The force at each point of the force-displacement curve was defined by considering the stress multiplied by the tributary area ([[#img-2|Figure 2]]), and the displacement was defined by taking into account the unit deformation multiplied by the length of the spring. This length was taken as 9/10 of the thickness of the joint, considering that the length of the contact element is 1/10 of the thickness of the joint. This idea was valid for longitudinal and transverse springs.
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 - The size of the opening is 0,64 m wide and 0,54 m high.
-The geometry information is shown in Figure 3.
+The geometry information is shown in [[#img-3|Figure 3]].
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 ===3.2 Tests of masonry walls without openings===
-This section shows a full wall with reinforced masonry tested at Universidad de La Serena [19] and a full wall with confined masonry tested at Universidad de Chile [17]. The materials and geometry characteristics, as well as those used for the tests, were the same of the previous tests shown for Universidad de La Serena and Universidad de Chile. The geometric characteristics of the walls are shown in Figures 6 and 7. The walls tested at University of La Serena were three of the same characteristics (Walls 01, 02 and 03). The walls tested at University of Chile were two of the same characteristics (MLC-T1-01 and MLC-T1-02).
+This section shows a full wall with reinforced masonry tested at Universidad de La Serena [19] and a full wall with confined masonry tested at Universidad de Chile [17]. The materials and geometry characteristics, as well as those used for the tests, were the same of the previous tests shown for Universidad de La Serena and Universidad de Chile. The geometric characteristics of the walls are shown in Figures [[#img-6|6]] and [[#img-7|7]]. The walls tested at University of La Serena were three of the same characteristics (Walls 01, 02 and 03). The walls tested at University of Chile were two of the same characteristics (MLC-T1-01 and MLC-T1-02).
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 ===4.1 Comparison between tests and models===
-This section presents the comparison between the capacity curves obtained from the models and those obtained through the tests for each of the walls described in section 3.1.1 (Figure 8), section 3.1.2 (Figures 9 to 14) and section 3.2 (Figures 15 and 16). More details regarding these results can be found in the work of Balboa and Silva [15]. In all these graphs, the drift was calculated considering the horizontal displacement divided by 2,1 m, which is the height of the walls from the bottom to the center of the bond beam.
+This section presents the comparison between the capacity curves obtained from the models and those obtained through the tests for each of the walls described in section 3.1.1 ([[#img-8|Figure 8]]), section 3.1.2 (Figures [[#img-9|9]] to [[#img-14|14]]) and section 3.2 (Figures [[#img-15|15]] and [[#img-16|16]]). More details regarding these results can be found in the work of Balboa and Silva [15]. In all these graphs, the drift was calculated considering the horizontal displacement divided by 2,1 m, which is the height of the walls from the bottom to the center of the bond beam.
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 ==4.2 Comparison of models with different openings==
-Additionally, in Figure 17 a full reinforced masonry wall (the same of Figure 6 of section 3.2) is compared with the behaviour, according to the proposed model, of a reinforced masonry wall with a door opening (at the center, b=0,56 m and h=1,98 m) and with a window opening (at the center, b=1,11 m and h=1,32 m). Finally, Figure 18 shows a comparison between a full confined masonry wall (the same of Figure 7 of section 3.2) and confined masonry walls with different openings (MLC-T2, MLC-T3 and MLC-T6 in positive cycle).
+Additionally, in [[#img-17|Figure 17]] a full reinforced masonry wall (the same of [[#img-6|Figure 6]] of section 3.2) is compared with the behaviour, according to the proposed model, of a reinforced masonry wall with a door opening (at the center, b=0,56 m and h=1,98 m) and with a window opening (at the center, b=1,11 m and h=1,32 m). Finally, [[#img-18|Figure 18]] shows a comparison between a full confined masonry wall (the same of [[#img-7|Figure 7]] of section 3.2) and confined masonry walls with different openings (MLC-T2, MLC-T3 and MLC-T6 in positive cycle).
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 At Universidad de Chile, four different types of walls with openings were constructed (testing two walls for each type), achieving a total of eight tests related to confined masonry walls with openings, maintaining the same general dimensions and properties characteristics to compare their subsequent behavior. All of these types of walls were compared to the proposed model. These tests were executed through the use of a reaction frame equipped with a hydraulic double action cylinder. The walls were subjected to alternating cycles of lateral loading, applied in the plane of the wall, stopping the test when a maximum displacement of 28 mm was reached. All the tests were controlled by the lateral displacement of the wall, measuring in the middle of the wall at half the height of the bond beam, applying two load cycles for each level of displacement. In the case of walls with non-symmetrical openings(MLC-T4 and MLC-T6), the tests and models were defined considering the two directions of the horizontal load and response (positive and negative cycles).
-The tested walls had different shape, size and location of the opening. They were classified as indicated in Table 1. The geometry for each wall is presented in Figures 4 and 5.
+The tested walls had different shape, size and location of the opening. They were classified as indicated in [[#tab-1|Table 1]]. The geometry for each wall is presented in Figures [[#img-4|4]] and [[#img-5|5]].
 <div class="center" style="font-size: 75%;">'''Table 1'''. Type of walls tested at Universidad de Chile [17]
 </div>
-{| style="width: 80%;margin: 1em auto 0.1em auto;border-collapse: collapse;font-size:85%;"
+<div id='tab-1'></div>
 |-
-|  style="border: 1pt solid black;text-align: center;vertical-align: bottom;"|'''Type of wall'''
+|  style="text-align: center;vertical-align: bottom;"|Wall with large centered window
-|  style="border-top: 1pt solid black;border-bottom: 1pt solid black;border-right: 1pt solid black;text-align: center;vertical-align: bottom;"|'''Denomination'''
+|  style="text-align: center;vertical-align: bottom;"|Type 2
-|  style="border-top: 1pt solid black;border-bottom: 1pt solid black;border-right: 1pt solid black;text-align: center;vertical-align: bottom;"|'''Identification of wall'''
+|  style="text-align: center;vertical-align: bottom;"|MLC-T2-01; MLC-T2-02
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|'''Size of the opening'''
+|  style="text-align: center;vertical-align: top;"|b=2,005 m; h=1,125 m
 |-
-|  style="border-left: 1pt solid black;border-bottom: 1pt solid black;border-right: 1pt solid black;text-align: center;vertical-align: bottom;"|Wall with large centered window
+|  style="text-align: center;vertical-align: bottom;"|Wall with small centered window
-|  style="border-bottom: 1pt solid black;border-right: 1pt solid black;text-align: center;vertical-align: bottom;"|Type 2
+|  style="text-align: center;vertical-align: bottom;"|Type 3
-|  style="border-top: 1pt solid black;border-bottom: 1pt solid black;border-right: 1pt solid black;text-align: center;vertical-align: bottom;"|MLC-T2-01; MLC-T2-02
+|  style="text-align: center;vertical-align: bottom;"|MLC-T3-01; MLC-T3-02
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|b=2,005 m; h=1,125 m
+|  style="text-align: center;vertical-align: top;"|b=0,785 m; h=1,125 m
 |-
-|  style="border-left: 1pt solid black;border-bottom: 1pt solid black;border-right: 1pt solid black;text-align: center;vertical-align: bottom;"|Wall with small centered window
+|  style="text-align: center;vertical-align: bottom;"|Wall with door – centered window
-|  style="border-bottom: 1pt solid black;border-right: 1pt solid black;text-align: center;vertical-align: bottom;"|Type 3
+|  style="text-align: center;vertical-align: bottom;"|Type 4
-|  style="border-top: 1pt solid black;border-bottom: 1pt solid black;border-right: 1pt solid black;text-align: center;vertical-align: bottom;"|MLC-T3-01; MLC-T3-02
+|  style="text-align: center;vertical-align: bottom;"|MLC-T4-01; MLC-T4-02
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|b=0,785 m; h=1,125 m
+|  style="text-align: center;vertical-align: top;"|b=1,090 m; h=1,000 m
 |-
-|  style="border-left: 1pt solid black;border-bottom: 1pt solid black;border-right: 1pt solid black;text-align: center;vertical-align: bottom;"|Wall with door – centered window
+|  style="text-align: center;vertical-align: bottom;"|Wall with centered door
-|  style="border-bottom: 1pt solid black;border-right: 1pt solid black;text-align: center;vertical-align: bottom;"|Type 4
+|  style="text-align: center;vertical-align: bottom;"|Type 6
-|  style="border-top: 1pt solid black;border-bottom: 1pt solid black;border-right: 1pt solid black;text-align: center;vertical-align: bottom;"|MLC-T4-01; MLC-T4-02
+|  style="text-align: center;vertical-align: bottom;"|MLC-T6-01; MLC-T6-02
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|b=1,090 m; h=1,000 m
+|  style="text-align: center;vertical-align: top;"|b=0,480 m; h=2,000 m
-|-
-|  style="border-left: 1pt solid black;border-bottom: 1pt solid black;border-right: 1pt solid black;text-align: center;vertical-align: bottom;"|Wall with centered door
-|  style="border-bottom: 1pt solid black;border-right: 1pt solid black;text-align: center;vertical-align: bottom;"|Type 6
-|  style="border-top: 1pt solid black;border-bottom: 1pt solid black;border-right: 1pt solid black;text-align: center;vertical-align: bottom;"|MLC-T6-01; MLC-T6-02
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|b=0,480 m; h=2,000 m
 |}
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 - Beam height 0,20 m with longitudinal reinforcement 4<math>\varphi</math>10 and stirrups <math>\varphi</math>6 [mailto:@ @] 15.
-- The size of the openings is presented on Table 1.
+- The size of the openings is presented on [[#tab-1|Table 1]].
 ===3.2 Tests of masonry walls without openings===

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-|style="padding:10px;"| [[Image:Review_149504853691-chart10.svg|510px]]
+|style="padding:10px;"| [[Image:Campbell_2019a_7850_test-image19.png|510px]]
 |- style="text-align: center; font-size: 75%;"
 | colspan="1" style="padding:10px;"| '''Figure 17'''. Comparison of capacity curves for reinforced masonry walls without and with openings (models)
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 {| style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: auto;max-width: auto;"
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-|style="padding:10px;"| [[Image:Review_149504853691-chart11.svg|510px]]
+|style="padding:10px;"| [[Image:Campbell_2019a_5456_test-image20.png|510px]]
 |- style="text-align: center; font-size: 75%;"
 | colspan="1" style="padding:10px;"| '''Figure 18'''. Comparison of capacity curves for reinforced masonry walls without and with openings (models)

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 {| style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: auto;max-width: auto;"
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-|style="padding:10px;"| [[Image:Review_149504853691-chart1.svg|510px]]
+|style="padding:10px;"| [[Image:Campbell_2019a_4831_test-image10.png|510px]]
 |- style="text-align: center; font-size: 75%;"
 | colspan="1" style="padding:10px;"| '''Figure 8'''. Capacity curves of reinforced masonry wall (test and model)
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 {| style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: auto;max-width: auto;"
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-|style="padding:10px;"| [[Image:Review_149504853691-chart2.svg|510px]]
+|style="padding:10px;"| [[Image:Campbell_2019a_3693_test-image11.png|510px]]
 |- style="text-align: center; font-size: 75%;"
 | colspan="1" style="padding:10px;"| '''Figure 9'''. Capacity curves for walls MLC-T2 (tests and model)
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 {| style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: auto;max-width: auto;"
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-|style="padding:10px;"|[[Image:Review_149504853691-chart3.svg|510px]]
+|style="padding:10px;"|[[Image:Campbell_2019a_7568_test-image12.png|510px]]
 |- style="text-align: center; font-size: 75%;"
 | colspan="1" style="padding:10px;"| '''Figure 10'''. Capacity curves for walls MLC-T3 (tests and model)
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 {| style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: auto;max-width: auto;"
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-|style="padding:10px;"|[[Image:Review_149504853691-chart4.svg|510px]]
+|style="padding:10px;"|[[Image:Campbell_2019a_9571_test-image13.png|510px]]
 |- style="text-align: center; font-size: 75%;"
 | colspan="1" style="padding:10px;"| '''Figure 11'''. Capacity curves for walls MLC-T4 (positive cycle tests and model)
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 {| style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: auto;max-width: auto;"
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-|style="padding:10px;"|[[Image:Review_149504853691-chart5.svg|510px]]
+|style="padding:10px;"|[[Image:Campbell_2019a_1639_test-image14.png|510px]]
 |- style="text-align: center; font-size: 75%;"
 | colspan="1" style="padding:10px;"| '''Figure 12'''. Capacity curves for walls MLC-T4 (negative cycle tests and model)
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 {| style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: auto;max-width: auto;"
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-|style="padding:10px;"|[[Image:Review_149504853691-chart6.svg|510px]]
+|style="padding:10px;"|[[Image:Campbell_2019a_1991_test-image15.png|510px]]
 |- style="text-align: center; font-size: 75%;"
 | colspan="1" style="padding:10px;"| '''Figure 13'''. Capacity curves for walls MLC-T6 (positive cycle tests and model)
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 {| style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: auto;max-width: auto;"
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-|style="padding:10px;"|[[Image:Review_149504853691-chart7.svg|510px]]
+|style="padding:10px;"|[[Image:Campbell_2019a_3812_test-image16.png|510px]]
 |- style="text-align: center; font-size: 75%;"
 | colspan="1" style="padding:10px;"| '''Figure 14'''. Capacity curves for walls MLC-T6 (negative cycle tests and model)
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 {| style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: auto;max-width: auto;"
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-|style="padding:10px;"|[[Image:Review_149504853691-chart8.svg|510px]]
+|style="padding:10px;"|[[Image:Campbell_2019a_6165_test-image17.png|510px]]
 |- style="text-align: center; font-size: 75%;"
 | colspan="1" style="padding:10px;"| '''Figure 15'''. Comparison of capacity curves for reinforced masonry walls 01, 02 and 03 (tests and model)
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 {| style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: auto;max-width: auto;"
 |-
-|style="padding:10px;"|[[Image:Review_149504853691-chart9.svg|510px]]
+|style="padding:10px;"|[[Image:Campbell_2019a_5271_test-image18.png|510px]]
 |- style="text-align: center; font-size: 75%;"
 | colspan="1" style="padding:10px;"| '''Figure 16'''. Comparison of capacity curves for walls MLC-T1 (tests and model)

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 - Maximum compressive strength of the concrete <math>f_c= 23.900</math> kN/m<math>^2</math> with <math>E_c =21.643.500</math> kN/m<math>^2</math>.
-- Column width 0,20 m with longitudinal reinforcement 4φ10 and stirrups φ6 [mailto:@ @] 15.
+- Column width 0,20 m with longitudinal reinforcement 4<math>\varphi</math>10 and stirrups <math>\varphi</math>6 [mailto:@ @] 15.
-- Beam height 0,20 m with longitudinal reinforcement 4φ10 and stirrups φ6 [mailto:@ @] 15.
+- Beam height 0,20 m with longitudinal reinforcement 4<math>\varphi</math>10 and stirrups <math>\varphi</math>6 [mailto:@ @] 15.
 - The size of the openings is presented on Table 1.

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 The wall had the following technical specifications:
-- Brick MqHv 7x14x29 cm, arranged in running bond with a total of 22 rows and horizontal and vertical joints of 2 cm (<math>E_b =5.450.000</math> kN/m<math>^2</math>; <math>f_b=21.800</math> kN/m<math>^2</math>).
+- Brick MqHv <math>7\times 14\times 29</math> cm, arranged in running bond with a total of 22 rows and horizontal and vertical joints of 2 cm (<math>E_b =5.450.000</math> kN/m<math>^2</math>; <math>f_b=21.800</math> kN/m<math>^2</math>).
 - Reinforced bond beam, foundation and vertical reinforcement with A630-420H steel (<math>E_s=210.000.000 </math> kN/m<math>^2</math>; <math>f_y=420.000</math> kN/m<math>^2</math>).

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 For all the walls tested the properties of the materials used were:
-- Ceramic brick MqP, grade 1 11,3x14x29 cm, arranged in running bond with a total of 16 rows and horizontal and vertical joints of 12 mm (<math>E_b=6.475.000</math> kN/m<math>^2</math>; <math>f_b=25.900</math> kN/m<math>^2</math>).
+- Ceramic brick MqP, grade 1 <math>11,3\times 14\times 29</math> cm, arranged in running bond with a total of 16 rows and horizontal and vertical joints of 12 mm (<math>E_b=6.475.000</math> kN/m<math>^2</math>; <math>f_b=25.900</math> kN/m<math>^2</math>).
 - Reinforcement steel used A630-420H (<math>E_s =210.000.000</math> kN/m<math>^2</math>; <math>f_y=420.000</math> kN/m<math>^2</math>).

@@ Line 144: / Line 144: @@
 The wall had the following technical specifications:
-- Brick MqHv 7x14x29 cm, arranged in running bond with a total of 22 rows and horizontal and vertical joints of 2 cm (E<sub>b</sub>=5.450.000 kN/m<sup>2</sup>; f<sub>b</sub>=21.800 kN/m<sup>2</sup>).
+- Brick MqHv 7x14x29 cm, arranged in running bond with a total of 22 rows and horizontal and vertical joints of 2 cm (<math>E_b =5.450.000</math> kN/m<math>^2</math>; <math>f_b=21.800</math> kN/m<math>^2</math>).
-- Reinforced bond beam, foundation and vertical reinforcement with A630-420H steel (E<sub>s</sub>=210.000.000 kN/m<sup>2</sup>; f<sub>y</sub>=420.000 kN/m<sup>2</sup>).
+- Reinforced bond beam, foundation and vertical reinforcement with A630-420H steel (<math>E_s=210.000.000 </math> kN/m<math>^2</math>; <math>f_y=420.000</math> kN/m<math>^2</math>).
-- Horizontal reinforcement diameter of 4,2 mm of AT560-500H quality (E=210.000.000 kN/m<sup>2</sup>; f<sub>y</sub>=500.000 kN/m<sup>2</sup>).
+- Horizontal reinforcement diameter of 4,2 mm of AT560-500H quality (<math>E=210.000.000</math> kN/m<math>^2</math>; <math>f_y=500.000</math> kN/m<math>^2</math>).
-- Maximum compressive strength of the mortar f<sub>m</sub>= 22.555 kN/m<sup>2</sup> with E<sub>m</sub>=3.390.000 kN/m<sup>2</sup>.
+- Maximum compressive strength of the mortar <math>f_m= 22.555</math> kN/m<math>^2</math> with <math>E_m =3.390.000</math> kN/m<math>^2</math>.
-- Maximum compressive strength of the concrete f<sub>c</sub>= 24.520 kN/m<sup>2</sup> with E<sub>c</sub>=21.922.400 kN/m<sup>2</sup>.
+- Maximum compressive strength of the concrete <math>f_c= 24.520</math> kN/m<math>^2</math> with <math>E_c=21.922.400</math> kN/m<math>^2</math>.
 - The size of the opening is 0,64 m wide and 0,54 m high.
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 | colspan="1" style="padding:10px;"| '''Figure 3.''' Geometric characteristics and layout of reinforcements (RM Wall with opening)
 |}
 ====3.1.2 Tests of confined masonry walls with openings====

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 {| style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: auto;max-width: auto;"
 |-
-|style="padding:10px;"| [[File:Campbell_2019a_9432_Figura 1.png|550px]]
+|style="padding:10px;"| [[File:Campbell_2019a_9432_Figura 1.png|500px]]
 |- style="text-align: center; font-size: 75%;"
 | colspan="1" style="padding:10px;"| '''Figure 1'''. Model of the joint between bricks and mortar [13]