Edge joist support and double floor structure
The double floor structure with a joist joist support device addresses the issues of special processing and load deflection in conventional systems by eliminating groove processing needs and distributing loads effectively, resulting in cost savings, reduced processing time, and enhanced floor stability.
Patent Information
- Application Number
- JP2023205946
- Authority / Receiving Office
- JP · JP
- Patent Type
- Patents
- Current Assignee / Owner
- Filing Date
- 2023-12-06
- Publication Date
- 2025-04-07
- Estimated Expiration
- 2043-12-06
AI Technical Summary
Conventional joist support systems require special processing of joist materials and are prone to deflection under load due to cantilevered beam structures.
A double floor structure using a joist joist support device with a joist plate and support bolt configuration that eliminates the need for groove processing on the joist material and distributes loads more effectively by supporting the upper floor material on multiple surfaces.
This solution reduces material costs and processing time, enhances the rigidity of the top floor material at the wall side, and improves the stability of the floor surface by distributing loads more evenly.
Smart Images

Figure 0007657900000001_ABST
Abstract
Description
[Technical field]
[0001] The present invention relates to an edge joist support and a double floor structure using the edge joist support. [Background technology]
[0002] A double floor structure using joist supports that are installed on a structural floor such as concrete is known (for example, Patent Document 1, Patent Document 2, etc.). The double floor structure is used, for example, on concrete structural floors in apartment buildings. A plurality of joist supports are installed on the structural floor at a predetermined interval, and the upper floor material is placed on top of them for construction. The joist supports are configured to be adjustable in height, and the interval between the structural floor and the upper floor material can be adjusted by adjusting the height of the joist supports. The double floor structure exhibits excellent effects such as sound insulation and heat insulation, depending on the material of the upper floor material and the configuration of the joist supports. Among the joist materials, those installed near the wall are called edge joists. [Prior art documents] [Patent documents]
[0003] [Patent Document 1] JP 2007-204931 A [Patent Document 2] JP 2015-224446 A Summary of the Invention [Problem to be solved by the invention]
[0004] However, in order to securely hold the joist material in the conventional joist supports, the joist material needs to be processed into a special shape. Specifically, a groove is provided on the side of the joist material that extends in the longitudinal direction, and the joist support is attached to the joist material so that it can slide by inserting the protrusion of the joist support into the groove. This requires time and money to process the joist material.
[0005] In addition, in conventional back joist supports that support joist materials for back joists, the joist material acts as a cantilever against the support bolt, making the joist support prone to bending due to the load from the upper floor material.
[0006] Therefore, the present invention provides an edge joist support that can distribute the load from the upper floor material without requiring special processing of the joists, and a double floor structure using the edge joist support. [Means for solving the problem]
[0007] The present invention has been made to solve at least some of the above-mentioned problems, and can be realized in the following aspects or application examples.
[0008] [1] One aspect of the edge joist support of the present invention is as follows: A joist support plate having a female screw hole penetrating in the vertical direction; A support bolt screwed into the female threaded hole; having The joist support plate has a joist support surface formed on the upper surface of the joist support plate, a first rising portion, a second rising portion, and a third rising portion extending above the joist support surface, and a protrusion protruding from an upper portion of the first rising portion and extending parallel to the joist support surface, The joist support surface is formed on a flat portion extending in a first direction from the female threaded hole, The first rising portion is formed at one end of the joist support surface, The third rising portion is formed lower than the second rising portion at the other end of the joist support surface on the female screw hole side, The second raised portion is formed at a position adjacent to the female threaded hole, Both side surfaces of the joist material on which the first rising portion and the third rising portion are placed on the joist support surface; Opposing, The lower surface of the protrusion faces a part of the upper surface of the joist, The upper surface of the second rising portion has a portion at the same height as the upper surface of the joist.
[0009] According to one embodiment of the edge joist support, the protrusion is located opposite the top surface of the joist material, eliminating the need to groove the side surface of the joist material. Also, since a part of the top surface of the second rising part is at the same height as the top surface of the joist material, the top surface of the second rising part also receives the load from the upper floor material. This allows the load from the upper floor material to be received not only on the joist support surface, but also at a position adjacent to the female threaded hole, i.e., near the support bolt. Therefore, the load can be distributed not only to the conventional cantilever structure, but also to the support bolt side.
[0010] [2] In one embodiment of the edge joist support, an upper surface of the second rising portion includes, in a plan view, a first portion that is located on a back side of the female screw hole relative to the first rising portion, and a second portion that extends from the first portion in a second direction perpendicular to the first direction; The second portion may have a portion that overlaps with a part of the female screw hole in the second direction in a plan view.
[0011] With this configuration, the load from the upper floor material can be received by the first portion and the second portion around the female threaded hole, making it easier to transmit the load to the support bolt.
[0012] [3] In one embodiment of the edge joist support, A side surface of the second raised portion may have a concave portion that curves along the female threaded hole.
[0013] With this configuration, the second raised portion can be formed along the female threaded hole, so that the second raised portion can receive the load from the upper floor material at a position close to the support bolt, making it easier to transmit the load to the support bolt.
[0014] [4] One aspect of the double floor structure according to the present invention is One embodiment of the above-mentioned edge joist support is arranged on the lower floor, holds the joist material on the joist support surface, and supports the upper floor material on the upper surface of the first rising portion and the upper surface of the second rising portion.
[0015] According to one aspect of the double floor structure, since groove processing of the joists is not required, it is possible to reduce material costs and shorten the material processing time. In addition, since the edge joist support is a support structure that does not rely only on a cantilever structure, the rigidity of the upper floor material at the wall edge is increased. Effect of the Invention
[0016] According to one aspect of the edge joist support of the present invention, since groove processing of the joist material is not required, material costs can be reduced and the material processing time can be shortened, and the load from the upper floor material can be distributed. According to one aspect of the double floor structure of the present invention, since groove processing of the joist material is not required, material costs can be reduced and the material processing time can be shortened, and the rigidity of the upper floor material at the wall edge can be increased. [Brief description of the drawings]
[0017] [Figure 1] FIG. 2 is a front view of an edge joist support according to one embodiment of the present invention. [Diagram 2] FIG. 2 is a plan view of an edge joist support according to one embodiment of the present invention. [Diagram 3] FIG. 2 is a right side view of an edge joist support according to one embodiment of the present invention. [Figure 4] 2 is a cross-sectional view taken along line AA in FIG. 1. [Diagram 5] 3 is a cross-sectional view of FIG. 2 taken along line B-B. [Figure 6] FIG. 13 is a front view of an edge joist support according to a modified example. [Figure 7] FIG. 13 is a plan view of an edge joist support according to a modified example. [Figure 8] 7 is a cross-sectional view taken along CC in FIG. 6. [Figure 9] FIG. 8 is a cross-sectional view taken along the line DD in FIG. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0018] Preferred embodiments of the present invention will be described in detail below with reference to the drawings. Note that the embodiments described below do not unduly limit the contents of the present invention described in the claims. In addition, not all of the configurations described below are necessarily essential components of the present invention.
[0019] 1.Double floor structure Fig. 1 is a front view of an edge joist support 10 according to one embodiment of the present invention. Fig. 1 and Fig. 6 show a part of a double floor structure 50 according to one embodiment of the present invention at a wall edge.
[0020] As shown in FIG. 1, the double floor structure 50 has an edge joist support 10 disposed on the lower floor 42, holds the joist material 30 on the joist support surface 14a, and supports the upper floor material 40 on the first upper surface 11c of the first rising portion 11 and the second upper surface 12c of the second rising portion 12. The edge joist support 10 is installed along the wall 44 and supports the joist material 30 extending along the wall 44. Although FIG. 1 shows only the wall configuration, the double floor structure 50 has a plurality of joist materials and joist supports (not shown) between the lower floor 42 and the upper floor material 40. As a joist support other than the edge joist support 10, a known joist support may be used. The lower floor 42 and the upper floor material 40 are constructed so as to have a predetermined interval between them. The double floor structure 50 allows various pipes and wiring to be constructed between the lower floor 42 and the upper floor material 40. The edge joist support 10 will be described in detail later, so a description thereof will be omitted here.
[0021] The upper floor material 40 and the lower floor 42 may be made of known materials and structures. The lower floor 42 may be, for example, a concrete structural floor. The upper floor material 40 is formed, for example, by placing a finishing material on a base panel. The base panel may be made of plywood or particle board, and the finishing material may be made of flooring material, cork material, vinyl floor tiles, sheet material, stone material, tatami mats, etc. Also, a heat insulating material may be sandwiched between the base panel and the finishing material.
[0022] The joist material 30 may be a known wooden joist material. In particular, a joist material 30 of a general size used for edge joists may be used. In particular, grooves are not required on the side of the joist material 30 supported by the edge joist support 10. Therefore, there is no need to groove the joist material 30, which reduces material costs and shortens the material processing period for the joist material 30. The joist material 30 supports the upper floor material 40 on its upper surface in the portion where the edge joist support 10 is not present, but there may be a small gap between the joist material 30 and the upper floor material 40 on the edge joist support 10.
[0023] The edge joist support 10 is disposed adjacent to the wall 44 and supports the upper floor material 40 on the first upper surface 11c of the first rising portion 11 and the second upper surface 12c of the second rising portion 12. Conventional edge joist supports the upper floor material 40 only on the joist material, but the edge joist support 10 according to the present embodiment supports the upper floor material 40 also on the second upper surface 12c of the second rising portion 12. Since the second rising portion 12 is located adjacent to the female screw hole 15a as described later, the load from the upper floor material 40 can be applied vertically to the support bolt 22, not to a cantilever beam as in the conventional case. Therefore, according to the double floor structure 50, the rigidity of the upper floor material 40 at the wall edge is increased, and the stability of the floor surface is improved.
[0024] 2. Edge joist support Fig. 1 to Fig. 5 are diagrams showing an edge joist support 10 according to this embodiment. Fig. 1 is a front view of the edge joist support 10 according to this embodiment, Fig. 2 is a plan view of the edge joist support 10 according to this embodiment, Fig. 3 is a right side view of the edge joist support 10 according to this embodiment, Fig. 4 is an AA cross-sectional view of Fig. 1, and Fig. 5 is a BB cross-sectional view of Fig. 2. The upper floor material 40 is omitted in Figs. 2 to 5.
[0025] 1, the edge joist support 10 has a joist support plate 14 having a female screw hole 15a penetrating in the vertical direction (third direction Z) and a support bolt 22 screwed into the female screw hole 15a. The edge joist support 10 is preferably made of, for example, a synthetic resin, but the support bolt 22 may be made of metal.
[0026] The joist support plate 14 has a joist support surface 14a formed on the upper surface of the joist support plate 14, a first rising portion 11, a second rising portion 12, and a third rising portion 13 extending above the joist support surface 14a, and a protrusion 16 protruding from the upper portion of the first rising portion 11 and extending parallel to the joist support surface 14a. The joist support plate 14 has a shape in which the first rising portion 11 and the second rising portion 12 rise in the third direction Z from both ends of a flat plate extending in the first direction X, and is a plate-like shape formed in a substantially U-shape when viewed from the front. Then, a female screw hole 15a and the third rising portion 13 are formed between the first rising portion 11 and the second rising portion 12. Here, with the edge joist support 10 installed on the subfloor 42, the first direction X is a horizontal direction toward the wall 44, the second direction Y is a direction perpendicular to the first direction X within the horizontal plane, and the third direction Z is a vertical direction perpendicular to the first direction X and the second direction Y.
[0027] The joist support surface 14a is formed on a flat portion extending from the female screw hole 15a in the first direction X (left in FIG. 1). The joist support surface 14a is a surface on which the joist material 30 extending in the second direction Y is placed. The first rising portion 11 is formed at one end (first end 14b) of the joist support surface 14a. The third rising portion 13 is formed at the other end (second end 14c) of the joist support surface 14a on the female screw hole 15a side, lower than the second rising portion 12. The joist support surface 14a is formed such that the length in the first direction X is slightly longer than the width of the joist material 30, as shown in FIG. 2. The length in the second direction Y of the joist support surface 14a is shorter than the length in the first direction X.
[0028] The first rising portion 11 is disposed on the wall 44 side. The first rising portion 11 may be in contact with the wall 44. The first rising portion 11 is a plate-like portion extending from the first end portion 14b in the third direction Z. As shown in FIG. 2, the width of the first rising portion 11 in the second direction Y in a plan view is the same as the width of the joist support plate 14. The first rising portion 11 is located at a position furthest from the female screw hole 15a in the first direction X. The first side surface 11a of the first rising portion 11 faces the joist support surface 14a and is a flat surface extending in the third direction Z. The first upper surface 11c at the upper end of the first rising portion 11 is located slightly higher than the upper surface of the joist material 30 supported by the joist support surface 14a. Therefore, in the edge joist support 10, the upper floor material 40 is directly supported by the first upper surface 11c and the second upper surface 12c. The height of the first upper surface 11c (height from the joist support surface 14a in the third direction Z) is preferably, for example, not more than 2 mm, and more preferably not more than 1 mm, higher than the upper surface of the joist material 30. In places where there are no edge joist supports 10, the upper surface of the joist material 30 supports the upper floor material 40, so it is preferable that there is as little difference as possible between the support height at that portion and the edge joist support 10. In addition, the height of the first upper surface 11c is preferably, for example, not more than 2 mm, and more preferably not more than 1 mm higher than the height of the second upper surface 12c (height from the joist support surface 14a in the third direction Z in both cases).
[0029] The protrusion 16 is a plate-like portion that protrudes from an upper portion, for example, the upper end, of the first rising portion 11 toward the second rising portion 12. The protrusion 16 restricts the upward movement of the joist material 30. The protrusion 16 protrudes from a position of the first rising portion 11 that is slightly higher than the height of the joist material 30. The length of the protrusion 16 in the first direction X may be such that the joist material 30 does not come off the edge joist support 10, and also such that the joist material 30 does not enter the first side surface 11a when the joist material 30 and the edge joist support 10 are assembled. It is sufficient that the width of the protrusion 16 is as wide as possible. The width of the protrusion 16 is the same as the width of the joist support surface 14a in the second direction Y, as shown in Fig. 2. The thickness of the protrusion 16 can be set appropriately as long as it does not affect the fixture above the protrusion 16, but since strength is not required in this portion, it may be 1 mm or less. By positioning the protrusion 16 in a position opposite the upper surface of the joist material 30 arranged on the joist support surface 14a, movement of the joist material 30 in the third direction Z is restricted, making it difficult for the joist material 30 to come out of the joist support fixture 10.
[0030] The second rising portion 12 is formed at a position adjacent to the female screw hole 15a. The second rising portion 12 is a plate-like portion extending in the third direction Z. The width of the second rising portion 12 in the second direction Y is, for example, the same as the width of the first rising portion 11 and the width of the joist support surface 14a as shown in FIG. 2. The second upper surface 12c of the second rising portion 12 has a portion at the same height as the upper surface of the joist material 30. "The same height" means that at least the degree of dimensional error of the wooden joist material 30 is in the same height range. In this embodiment, the entire second upper surface 12c is at the same height as the upper surface of the joist material 30. The thickness of the second rising portion 12 in the first direction X is preferably wide in order to support the upper floor material 40, and is preferably about the thickness of the protrusion 15, for example, and is preferably 4 mm or more. When the upper floor material 40 is supported only by the upper surface of the joist material 30, the joist support plate 14 is in a cantilever state and is easily deflected. However, by supporting the upper floor material 40 on the second upper surface 12c of the second rising portion 12 adjacent to the female screw hole 15a, the load can be transmitted to the support bolt 22 without significant deflection of the joist support plate 14. In this way, the edge joist support 10 makes it possible to distribute the load from the upper floor material 40 to the joist support surface 14a and the second rising portion 12. And by arranging the edge joist support 10 near the wall, the upper floor material 40 can be given a firm sense of rigidity.
[0031] The first rising portion 11 and the third rising portion 13 face both side surfaces of the joist material 30 arranged on the joist support surface 14a. The lower surface of the protrusion 16 faces a part of the upper surface of the joist material 30. Therefore, the joist material 30 is held so as to be sandwiched between the first side surface 11a of the first rising portion 11 and the third side surface 13a of the third rising portion 13 in the front and rear in the first direction X, and is held so as to be sandwiched between the joist support surface 14a and the lower surface of the protrusion 16 in the top and bottom in the third direction Z. The joist material 30 does not need to be in close contact with the protrusion 16, the first side surface 11a, and the third side surface 13a, and it is sufficient that the edge joist support 10 is held to such an extent that it does not come off the joist material 30 even if the joist material 30 is lifted during construction. During construction, with the joist material 30 held by the first rising portion 11, the third rising portion 13 and the joist support surface 14a, the edge joist support 10 can be slid to an appropriate position along the joist material 30 extending in the second direction Y. In this way, the edge joist support 10 can hold the joist material 30 even if there is no groove in the joist material 30, thereby reducing material costs and the material processing time.
[0032] The third rising portion 13 is disposed adjacent to the female threaded hole 15a. As shown in Figs. 2 and 3, two third rising portions 13 may be provided on either side of the female threaded hole 15a in the second direction Y, or a single continuous protrusion may be provided bypassing the female threaded hole 15a. The third rising portion 13 is provided at a position that does not interfere with the movement of the support bolt 22 up and down within the female threaded hole 15a. The height of the third rising portion 13 is lower than the first rising portion 11 and the second rising portion 12. The third rising portion 13 has a tapered surface 13b that is inclined from the upper end toward the third side surface 13a.
[0033] As shown in FIG. 2, the second upper surface 12c of the second rising portion 12 includes a first portion 12d located on the back side of the female screw hole 15a with respect to the first rising portion 11 in a plan view, and second portions 12e, 12e extending from the first portion 12d in a second direction Y perpendicular to the first direction X. The second portion 12e has a portion that overlaps with a part of the female screw hole 15a in the second direction Y in a plan view. The first portion 12d and the second portion 12e are portions that have the same height as the upper surface of the joist material 30. The first portion 12d and the second portion 12e that receive the load from the upper floor material 40 are arranged to surround a part of the female screw hole 15a, so that the load from the upper floor material 40 can be easily transmitted to the support bolt 22. The second side surface 12a of the second rising portion 12 has a concave portion 12b that curves along the female screw hole 15a. The second side surface 12a is provided on the female screw hole 15a side of the second rising portion 12. As a result, the second side surface 12a of the second rising portion 12 can be formed along the female threaded hole 15a without interfering with the raising and lowering of the support bolt 22. This brings the second upper surface 12c into close proximity with the female threaded hole 15a, allowing the load from the upper floor material 40 to be efficiently transmitted to the support bolt 22.
[0034] The joist support plate 14 has a protrusion 15 that protrudes downward from the bottom surface of the joist support plate 14 at a position where the female threaded hole 15a is formed. The protrusion 15 can be substantially cylindrical in shape as shown in FIG. 4. The protrusion 15 has a female threaded hole 15a formed therein that extends to the top surface of the joist support plate 14. The female threaded hole 15a has a female thread 15b formed on its inner circumferential surface. The female threaded hole 15a screws into the male thread 22a of the support bolt 22.
[0035] The support bolt 22 has a male thread 22a formed on its outer periphery, and extends along the third direction Z, which is the vertical direction. A groove 22b for inserting a flat-head screwdriver is formed at the upper end of the support bolt 22 (FIG. 2). When the support bolt 22 is turned with a flat-head screwdriver, the joist support plate 14 moves up and down along the support bolt 22 in the third direction Z, making it possible to adjust the height of the upper floor material 40 relative to the lower floor 42. A base 20 made of a material that absorbs vibrations, such as rubber or soft plastic, is fixed to the lower end of the support bolt 22.
[0036] As shown in Fig. 5, the joist material 30 is inserted from above diagonally from the third rising portion 13 side to the first rising portion 11 side, avoiding the protrusions 16, and placed on the joist support surface 14a. At this time, since the joist support plate 14 is made of synthetic resin, the joist material 30 may be pushed between the first rising portion 11 and the third rising portion 13 while slightly deforming the first rising portion 11. In addition, since the third rising portion 13 is lower than the first rising portion 11, the joist material 30 can be moved to the joist support surface 14a, and in particular, the tapered surface 13b makes it easier to move the joist material 30 toward the joist support surface 14a.
[0037] 3. Variations Fig. 6 to Fig. 9 are diagrams showing an edge joist support 100 according to a modified example of the present invention. Fig. 6 and Fig. 9 show a part of a double floor structure 50 according to a modified example of the present invention at the wall edge. Fig. 6 is a front view of the edge joist support 100 according to the modified example, Fig. 7 is a plan view of the edge joist support 100 according to the modified example, Fig. 8 is a cross-sectional view taken along CC in Fig. 6, and Fig. 9 is a cross-sectional view taken along DD in Fig. 7. In Figs. 6 to 9, parts having the same functions as those in Figs. 1 to 5 are given the same names and symbols, and explanations thereof will be omitted.
[0038] As shown in Fig. 6, in the modified example, the shape of the third rising portion 13 is different from that of the above embodiment. The third rising portion 13 is a generally cylindrical shape extending upward from the joist support surface 14a. A female screw hole 15a is formed inside the third rising portion 13, penetrating vertically. The part of the third rising portion 13 closest to the first rising portion 11 is the third side surface 13a. As shown in Fig. 7, the third side surface 13a is curved when viewed from above, but the joist material 30 can be held between the third side surface 13a and the first side surface 11a.
[0039] The edge joist support 100 does not have a protrusion 15 that protrudes downward from the joist support plate 14. Therefore, it is advantageous in that a double floor structure 52 can be formed with a narrower gap between the lower floor 42 and the upper floor material 40 than in the above embodiment.
[0040] Thus, according to the edge joist support 100 of the modified example, as in the above embodiment, groove processing of the joist material 30 is not required, which reduces material costs and shortens the material processing time, and it is possible to distribute the load from the upper floor material 40. Furthermore, according to one aspect of the double floor structure 52 of the modified example, as in the above embodiment, groove processing of the joist material 30 is not required, which reduces material costs and shortens the material processing time, and it is possible to increase the rigidity of the upper floor material 40 at the wall edge.
[0041] The present invention is not limited to the above-described embodiment, and various modifications are possible. For example, the present invention includes configurations that are substantially the same as the configurations described in the embodiments (for example, configurations with the same functions, methods, and results, or configurations with the same purpose and effect). The present invention also includes configurations in which non-essential parts of the configurations described in the embodiments are replaced. The present invention also includes configurations that achieve the same effects as the configurations described in the embodiments or that can achieve the same purpose. The present invention also includes configurations in which publicly known technology is added to the configurations described in the embodiments. [Explanation of symbols]
[0042] 10,100...edge joist support, 11...first rising portion, 11a...first side, 11c...first upper surface, 12...second rising portion, 12a...second side, 12b...concave portion, 12c...second upper surface, 12d...first portion, 12e...second portion, 13...third rising portion, 13a...third side, 13b...tapered surface, 14...joist support plate, 14a...joist support surface, 14b...first end, 14c...second end, 15...projection, 15a...female thread hole, 15b...female thread, 16...projection, 20...base, 22...support bolt, 22a...male thread, 22b...groove, 30...joist material, 40...upper floor material, 42...lower floor, 44...wall, 50...double floor structure, X...first direction, Y...second direction, Z...third direction
Claims
1. A joist support plate having a female screw hole penetrating in the vertical direction; A support bolt screwed into the female threaded hole; having The joist support plate has a joist support surface formed on the upper surface of the joist support plate, a first rising portion, a second rising portion, and a third rising portion extending above the joist support surface, and a protrusion protruding from an upper portion of the first rising portion and extending parallel to the joist support surface, The joist support surface is formed on a flat portion extending in a first direction from the female threaded hole, The first rising portion is formed at one end of the joist support surface, The third rising portion is formed lower than the second rising portion at the other end of the joist support surface on the female screw hole side, The second raised portion is formed at a position adjacent to the female threaded hole, The first rising portion and the third rising portion face both side surfaces of the joist material to be placed on the joist support surface, The lower surface of the protrusion faces a part of the upper surface of the joist, An edge joist support, characterized in that the upper surface of the second rising portion has a portion at the same height as the upper surface of the joist material.
2. In the edge joist support device according to claim 1, an upper surface of the second rising portion includes a first portion located on a back side of the female screw hole relative to the first rising portion in a plan view, and a second portion extending from the first portion in a second direction perpendicular to the first direction, The edge joist support is characterized in that the second portion has a portion that overlaps with a portion of the female threaded hole in the second direction when viewed in a plan view.
3. In the edge joist support device according to claim 2, An edge joist support, characterized in that the side of the second rising portion has a concave portion that curves along the female threaded hole.
4. A double floor structure, characterized in that a joist support as described in claim 1 or claim 2 is arranged on the lower floor, the joist material is held on the joist support surface, and an upper floor material is supported on the upper surface of the first rising portion and the upper surface of the second rising portion.
Citation Information
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