Roof structure

Abstract

This provides a roof structure in which the roof and roof rafters are neatly fitted together. [Solution] The roof structure 1 comprises a roof 10 that descends in a second direction Y as it moves from the inside to the outside in a first direction X, and a support part 30 that is located on the outside of the roof 10 in the first direction X and supports the roof 10 from below in the second direction Y. The support part 30 includes a fixing part 31 that is on the side of the roof 10 in the second direction Y and fixed to the roof 10. The fixing part 31 includes a first portion 33 that extends in the first direction X and a second portion 34 attached to the first portion 33. The second portion 34 reduces the gap between the fixing part 31 and the roof 10 and is fixed to the roof 10.

Description

Technical Field

[0001] The present invention relates to a roof structure, and more specifically, to a roof structure including an inclined roof.

Background Art

[0002] Conventionally, a roof structure including an inclined roof has been known (see, for example, Patent Document 1).

Prior Art Documents

Patent Documents

[0003]

Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0004] In the roof structure as described in Patent Document 1, since the roof is inclined, a gap occurs between the roof and the eaves beams and girders (joists) (hereinafter, the eaves beams and girders (joists) are collectively referred to as "roof girders") connected to the outer ends of the roof. Therefore, due to this gap, it may be difficult to attach the roof and the roof girders in a well-fitting manner.

[0005] The present invention has been made in view of the above points, and an example of the problem is to provide a roof structure in which the roof and the roof girders are attached in a well-fitting manner.

Means for Solving the Problems

[0006] (1) The roof structure of the present invention comprises a roof that descends in a second direction intersecting the first direction as it extends from the inside to the outside in a first direction, and a support portion that is located on the outside of the roof in the first direction and supports the roof from below in the second direction, wherein the support portion includes a fixing portion that is on the side of the roof in the second direction and fixed to the roof, and the fixing portion includes a first portion that extends in the first direction and a second portion attached to the first portion, the second portion reducing the gap between the fixing portion and the roof and being fixed to the roof.

[0007] (2): In the roof structure of (1), the roof may be formed of deck plates in which peaks and valleys are alternately formed in a third direction intersecting the first and second directions.

[0008] (3): In the roof structure of (2), the second portion may be fixed to the valley portion of the deck plate.

[0009] (4): In the roof structure of (1), the roof may be a corrugated metal roof.

[0010] (5) In any of the roof structures of (1) to (4), in the first direction, the outer end of the roof is on the side of the inner end of the first portion, and the second portion rises in the second direction toward the inside of the first portion toward the first portion, and the angle of inclination of the second portion toward the first portion may be equal to the angle of inclination of the roof toward the first portion.

[0011] (6): In any of the roof structures of (1) to (4), in the first direction, the outer end of the roof is on the side of the outer end of the first portion, and the second portion slopes downward in the second direction outward from the outer end of the first portion in the first direction, and the angle of inclination of the second portion with respect to the first portion may be equal to the angle of inclination of the roof with respect to the first portion.

[0012] (7) In any of the roof structures of (1) to (4), in the first direction, the outer end of the roof is outward relative to the inner end of the first portion, and in the second direction, the second portion may rest on the first portion.

[0013] (8): In the roof structure of (7), in the second direction, the portion of the second part that is on the side of the roof may be inclined at an angle equal to the angle of inclination of the roof with respect to the first part. [Effects of the Invention]

[0014] According to the present invention, a roof structure is provided in which the roof and roof beams are fitted together neatly. [Brief explanation of the drawing]

[0015] [Figure 1] This is a schematic diagram showing a building equipped with a roof structure according to the first embodiment of the present invention. [Figure 2] This is a schematic perspective view showing a part of the roof structure according to the first embodiment of the present invention. [Figure 3] This is a view of a portion of the roof structure shown in Figure 2, with the line of sight directed in a third direction. [Figure 4] This is a view of a part of the roof structure according to the second embodiment of the present invention, with the line of sight directed in a third direction. [Figure 5] This is a view of a part of the roof structure according to the third embodiment of the present invention, with the line of sight directed in a third direction. [Figure 6] This is a view of a part of the roof structure according to the fourth embodiment of the present invention, with the line of sight directed in a third direction. [Modes for carrying out the invention]

[0016] Hereinafter, embodiments for implementing the roof structure according to the present invention are illustrated together with the accompanying drawings. The embodiments illustrated below are for facilitating the understanding of the present invention and are not for limiting the interpretation of the present invention. The present invention can be changed and improved from the following embodiments without departing from its gist. In addition, in the above accompanying drawings, the dimensions of each member may be exaggerated or reduced for easy understanding, or the hatching may be omitted.

[0017] (First Embodiment) FIG. 1 is a schematic view of a building including a roof structure according to the first embodiment. As shown in FIG. 1, the building 2 includes a plurality of columns 50, one ridge beam 20, and a pair of roof structures 1, 1.

[0018] In the first direction X, the pair of roof structures 1, 1 are on both sides of the ridge beam 20. In the first direction X, one end of each of the pair of roof structures 1, 1 is supported by the ridge beam 20. One end of the roof structure 1 is typically fixed to the ridge beam 20. Hereinafter, one side (the side of the ridge beam 20) in the first direction X is represented by the term "inside", and the other side (the side opposite to the side of the ridge beam 20) is represented by the term "outside". The ridge beam 20 is supported by some of the plurality of columns 50 extending in the second direction Y (orthogonal in this embodiment) intersecting the first direction X. The second direction Y is typically the vertical direction. Hereinafter, in the second direction Y, the side toward the ridge beam 20 is represented by the term "up", and the side away from the ridge beam 20 is represented by the term "down".

[0019] The column 50 is not particularly limited. For example, it may be made of wood or steel. In this embodiment, the column 50 is made of steel, for example, H-shaped steel.

[0020] FIG. 2 is a perspective view schematically showing a part of the roof structure 1, specifically, a perspective view showing the vicinity of the outer end of the roof structure 1. As shown in FIGS. 1 and 2, the roof structure 1 includes a roof 10 and a support portion 30.

[0021] The roof 10 is sloped, specifically descending in the second direction as it moves from the inside to the outside in the first direction X. That is, the outer end 13 of the roof 10 (hereinafter referred to as the "outer end 13") is lower than the inner end 14 of the roof 10 (hereinafter referred to as the "inner end 14"). The roof 10 is not particularly limited, and may be a corrugated metal roof, or it may have other shapes.

[0022] In this embodiment, the roof 10 is formed by a deck plate. Specifically, the deck plate serving as the roof 10 is a deck plate in which peaks 11 and valleys 12 are alternately formed in a third direction Z that intersects the first direction X and the second direction Y (in this embodiment, is perpendicular to the first direction X and the second direction Y), and is a deck plate capable of forming a composite slab structure. The peaks 11 and valleys 12 are connected by inclined portions 17 that slope away from the peaks 11 in the third direction Z as they move downwards. Each of the peaks 11 and valleys 12 has a substantially flat plate-like shape, and when viewed with a line of sight in the second direction Y, it has a rectangular shape with the first direction X as the longer side and the third direction Z as the shorter side.

[0023] Figure 3 is a view of a part of the roof structure 1 shown in Figure 2 (near the outer end) with the line of sight directed in the third direction Z. As shown in Figures 2 and 3, the support part 30 is located on the outside of the roof 10 in the first direction X and supports the roof 10 from below in the second direction Y. The support part 30 includes a support part body 32. The support part body 32 is a member that extends in the third direction Z and functions as a eaves beam or beam (roof beam) of the building 2. In this embodiment, the support part body 32 functions as an eaves beam.

[0024] As shown in Figure 1, in the first direction X, a support body 32 on one side of the ridge beam 20 and a support body 32 on the other side are connected by a member 40 that extends in the first direction X. In this embodiment, the member 40 may function as a beam (roof beam). The support body 32 and the member 40 are not particularly limited, but may be made of wood or steel, for example. In this embodiment, the support body 32 and the member 40 are made of steel, for example, H-shaped steel.

[0025] As shown in Figures 2 and 3, the support portion 30 includes a fixing portion 31 that is located on the side (upper side) of the roof 10 in the second direction Y and is fixed to the roof 10. The fixing portion 31 includes a first portion 33 extending in the first direction X and a second portion 34 attached to the first portion 33. In this embodiment, the first portion 33 is part of the support portion body 32, which is a eaves beam, and more specifically, it is the upper flange (upper flange) of the support portion body 32, which is an H-shaped steel beam. In this embodiment, the outer end portion 13 of the roof 10 is located on the side of the inner end portion 33A (hereinafter referred to as "inner end portion 33A") of the first portion 33 in the first direction X.

[0026] The second portion 34 of the fixed portion 31 is a plate-shaped member (for example, a metal plate) extending in the third direction Z, and is attached to the first portion 33. In this embodiment, the second portion 34 is joined to the inner end 33A of the first portion 33, for example by welding, and rises inward in the second direction Y from the inner end 33A of the first portion 33 in the first direction X. The inclination angle of the second portion 34 with respect to the first portion 33 is an inclination angle α that is equal to the inclination angle of the roof 10 with respect to the first portion 33.

[0027] In the first direction X, the outer end 13 of the roof 10 is in approximately the same position as, or inside of, the inner end 33A of the first portion 33. Therefore, when viewed from the second direction Y, the outer end 13 of the roof 10 and the portion near the outer end 13 overlap with the second portion 34. As described above, the inclination angle of the second portion 34 with respect to the first portion 33 is the same inclination angle α as the inclination angle of the roof 10 with respect to the first portion 33. Therefore, the valley portion 12 at the outer end 13 of the roof 10 and the valley portion 12 in the portion near the outer end 13 are in full contact with the second portion 34, as shown in Figures 2 and 3. As a result, the presence of the second portion 34 in the fixing portion 31 reduces the gap between the fixing portion 31 and the roof 10 compared to, for example, the case where the fixing portion 31 consists only of the first portion 33.

[0028] In the roof structure 1, the portion of the valley 12 that is in full contact with the second portion 34 is joined to the second portion 34 by, for example, bolting, welding, or any other method, thereby fixing the roof 10 to the fixing portion 31 of the support portion 30.

[0029] As described above, the roof structure 1 according to this embodiment includes a roof 10 that descends in the second direction Y as it moves from the inside to the outside in the first direction X, and a support portion 30 that is located on the outside of the roof 10 in the first direction X and supports the roof 10 from below in the second direction Y. The support portion 30 includes a fixing portion 31 that is on the side of the roof 10 in the second direction Y and fixed to the roof 10. The fixing portion 31 includes a first portion 33 that extends in the first direction X and a second portion 34 attached to the first portion 33. The second portion 34 reduces the gap between the fixing portion 31 and the roof 10 and is fixed to the roof 10.

[0030] According to this roof structure 1, the second portion 34 of the fixing portion 31 of the support portion 30 reduces the gap between the fixing portion 31 and the roof 10. In particular, in this embodiment, as described above, the second portion 34 allows a part of the roof 10 (valley portion 12) to come into full contact with a part of the fixing portion 31 (second portion 34). Thus, according to the roof structure 1, the gap that occurs at the joint between the roof 10 and the support portion 30 is reduced, making it possible to install the roof and the roof beams together neatly.

[0031] Furthermore, according to roof structure 1, since the roof 10 is formed of a deck plate capable of forming a composite slab structure, the weight of the roof 10 can be made relatively light, and it becomes possible to construct the roof with the same building materials as the floor, which is advantageous from the standpoint of construction management and transportation of building materials.

[0032] Furthermore, according to roof structure 1, the second portion 34 is fixed to the valley portion 12 (or the valley-shaped portion of the corrugated metal roof) of the roof 10 formed from the deck plate, so that the roof 10 and the support body 32 are fixed together with a close distance between them in the second direction Y. Therefore, according to roof structure 1, the joint strength between the roof 10 and the support body 32 can be increased.

[0033] (Second Embodiment) Next, a roof structure 200 according to the second embodiment will be described. The roof structure 200 can be applied to building 2 as a replacement for the roof structure 1 according to the first embodiment. For the roof structure 200 according to this embodiment, only the differences from the roof structure 1 according to the first embodiment will be described, and other components will be denoted by the same reference numerals as in the first embodiment, and will not be described unless specifically required.

[0034] Figure 4 is a diagram showing the roof structure 200 from a similar viewpoint to Figure 3, and is a view of a part of the roof structure 200 (near the outer end) with the line of sight directed in the third direction Z. As shown in Figure 4, the roof structure 200 comprises a roof 10 and a support portion 230. The support portion 230 includes a fixing portion 231 that is on the side of the roof 10 in the second direction Y and fixed to the roof 10. The fixing portion 231 includes a first portion 33 (the upper flange of the H-shaped steel constituting the support portion body 32) extending in the first direction X and a second portion 234 attached to the first portion 33.

[0035] The second part 234 is joined (for example, welded) to the outer end 33B of the first part 33 (hereinafter referred to as the "outer end 33B"), and slopes downward in the second direction Y toward the outside from the outer end 33B. The inclination angle of the second part 234 with respect to the first part 33 is equal to the inclination angle of the roof 10 with respect to the first part 33, and is inclination angle α.

[0036] In this embodiment, in the first direction X, the outer end 13 of the roof 10 is on the side of the outer end 33B of the first portion 33 and is outward relative to the outer end 33B. Therefore, when viewed from the second direction Y, the outer end 13 of the roof 10 and the portion near the outer end 13 overlap with the second portion 234. Here, as described above, the inclination angle of the second portion 234 with respect to the first portion 33 is the same inclination angle α as the inclination angle of the roof 10 with respect to the first portion 33. Therefore, the valley portion 12 at the outer end 13 of the roof 10 and the valley portion 12 in the portion near the outer end 13 are in full contact with the second portion 234. As a result, by having the second portion 234 in the fixing portion 231, the gap between the fixing portion 231 and the roof 10 is reduced compared to, for example, the case where the fixing portion 231 consists only of the first portion 33.

[0037] In the roof structure 200, the portion of the valley 12 that is in full contact with the second portion 234 is joined to the second portion 234 by, for example, bolting, welding, or any other method, thereby fixing the roof 10 to the fixing portion 231 of the support portion 230.

[0038] As described above, the roof structure 200 according to this embodiment comprises a roof 10 that descends in a second direction Y as it moves from the inside to the outside in a first direction X, and a support portion 230 that is located on the outside of the roof 10 in the first direction X and supports the roof 10 from below in the second direction Y. The support portion 230 includes a fixing portion 231 that is on the side of the roof 10 in the second direction Y and fixed to the roof 10. The fixing portion 231 includes a first portion 33 that extends in the first direction X and a second portion 234 attached to the first portion 33. The second portion 234 reduces the gap between the fixing portion 231 and the roof 10 and is fixed to the roof 10.

[0039] According to this roof structure 200, the second portion 234 of the fixing portion 231 of the support portion 230 reduces the gap between the fixing portion 231 and the roof 10. In particular, in this embodiment, as described above, the second portion 234 allows a part of the roof 10 (valley portion 12) to come into full contact with a part of the fixing portion 231 (second portion 234).

[0040] Therefore, the roof structure 200 can achieve the same effects as the roof structure 1 according to the first embodiment.

[0041] (Third embodiment) Next, a roof structure 300 according to the third embodiment will be described. The roof structure 300 can be applied to building 2 as a replacement for the roof structure 1 according to the first embodiment. For the roof structure 300 according to this embodiment, only the differences from the roof structure 1 according to the first embodiment will be described, and other components will be denoted by the same reference numerals as in the first embodiment, and will not be described unless specifically required.

[0042] Figure 5 is a diagram showing the roof structure 300 from the same viewpoint as Figure 3, and is a view of a part of the roof structure 300 (near the outer end) with the line of sight directed in the third direction Z. As shown in Figure 5, the roof structure 300 comprises a roof 10 and a support portion 330. The support portion 330 includes a fixing portion 331 that is on the side of the roof 10 in the second direction Y and fixed to the roof 10. The fixing portion 331 includes a first portion 33 (the upper flange of the H-shaped steel constituting the support portion body 32) that extends in the first direction X and a second portion 334 attached to the first portion 33.

[0043] The second part 334 rests on the upper surface 33U (the upper surface in the second direction Y) of the first part 33. The second part 334 includes a vertical section 334B that extends generally in the second direction Y, and an inclined section 334A connected to the upper end of the vertical section 334B. In the second direction Y, the inclined section 334A is the portion of the second part 334 that faces the roof 10. The second part 334 is not particularly limited, but may be made of a predetermined steel material, for example. The inclined section 334A is inclined to descend as it moves away from the vertical section 334B in the first direction X. The second part 334 is fixed to the first part 33 by, for example, welding the lower end of the vertical section 334B and the end 334Ae of the inclined section 334A opposite to the vertical section 334B side in the first direction X to the upper surface 33U of the first part 33. Furthermore, the second part 334 is placed on the upper surface 33U of the first part 33 such that the vertical part 334B is on the inside and the end part 334Ae of the inclined part 334A is on the outside. The inclination angle of the inclined part 334A with respect to the first part 33 is equal to the inclination angle of the roof 10 with respect to the first part 33, and is inclination angle α.

[0044] In this embodiment, in the first direction X, the outer end 13 of the roof 10 is located outside the inner end 33A of the first portion 33 and is in approximately the same position as the outer end 33B. Therefore, when viewed from the second direction Y, the outer end 13 of the roof 10 and the portion near the outer end 13 overlap with the inclined portion 334A of the second portion 334. Here, as described above, the inclination angle of the inclined portion 334A (the portion of the second portion 334 on the roof 10 side) with respect to the first portion 33 is the same inclination angle α as the inclination angle of the roof 10 with respect to the first portion 33. Therefore, the valley portion 12 at the outer end 13 of the roof 10 and the valley portion 12 in the portion near the outer end 13 are in full contact with the inclined portion 334A. As a result, by having the inclined portion 334A of the second portion 334 in the fixing portion 331, the gap between the fixing portion 331 and the roof 10 is reduced compared to, for example, the case where the fixing portion 331 consists only of the first portion 33.

[0045] In the roof structure 300, the portion of the valley 12 that makes full contact with the inclined portion 334A is joined to the inclined portion 334A by, for example, bolting, welding, or any other method, thereby fixing the roof 10 to the fixing portion 331 of the support portion 330.

[0046] As described above, the roof structure 300 according to this embodiment comprises a roof 10 that descends in a second direction Y as it moves from the inside to the outside in a first direction X, and a support portion 330 that is located on the outside of the roof 10 in the first direction X and supports the roof 10 from below in the second direction Y. The support portion 330 includes a fixing portion 331 that is on the side of the roof 10 in the second direction Y and fixed to the roof 10. The fixing portion 331 includes a first portion 33 that extends in the first direction X and a second portion 334 attached to the first portion 33. The second portion 334 reduces the gap between the fixing portion 331 and the roof 10 and is fixed to the roof 10.

[0047] According to this roof structure 300, the second portion 334 of the fixing portion 331 of the support portion 330 reduces the gap between the fixing portion 331 and the roof 10. In particular, in this embodiment, as described above, the second portion 334 allows a part of the roof 10 (valley portion 12) to come into full contact with a part of the fixing portion 231 (second portion 334).

[0048] Therefore, the roof structure 300 can provide the same effects as the roof structure 1 according to the first embodiment.

[0049] (Fourth Embodiment) Next, a roof structure 400 according to the fourth embodiment will be described. The roof structure 400 can be applied to building 2 as a replacement for the roof structure 1 according to the first embodiment. For the roof structure 400 according to this embodiment, only the differences from the roof structure 1 according to the first embodiment will be described, and other components will be denoted by the same reference numerals as in the first embodiment, and will not be described unless specifically required.

[0050] Figure 6 is a diagram showing the roof structure 400 from the same viewpoint as Figure 3, and is a view of a part of the roof structure 400 (near the outer end) with the line of sight directed in the third direction Z. As shown in Figure 6, the roof structure 400 comprises a roof 10 and a support portion 430. The support portion 430 includes a fixing portion 431 that is on the side of the roof 10 in the second direction Y and fixed to the roof 10. The fixing portion 431 includes a first portion 33 (the upper flange of the H-shaped steel constituting the support portion body 32) extending in the first direction X and a second portion 434 attached to the first portion 33.

[0051] The second part 434 rests on the upper surface 33U of the first part 33. The second part 434 has a substantially inverted U-shape when viewed from a third direction Z. Specifically, the second part 434 includes a pair of vertical sections 434B, 434B extending in the second direction Y, and a horizontal section 434A connected to the upper ends of each of the pair of vertical sections 434B, 434B and extending in the first direction X. In the second direction Y, the horizontal section 434A is the part of the second part 434 that faces the roof 10. The second part 434 is not particularly limited, but may be, for example, channel steel. The second part 434 is fixed to the first part 33 by, for example, welding the lower ends of each of the pair of vertical sections 434B, 434B to the upper surface 33U of the first part 33.

[0052] In this embodiment, in the first direction X, the outer end 13 of the roof 10 is located outside the inner end 33A of the first portion 33 and outside the outer end 33B. Therefore, when viewed from the second direction Y, the outer end 13 of the roof 10 and the portion near the outer end 13 overlap with the lateral portion 434A of the second portion 334. Thus, in this embodiment, since the second portion 434 is positioned between the first portion 33 and the roof 10 in the second direction Y, the gap between the fixing portion 31 (first portion 33) and the roof 10 is reduced compared to the case where the fixing portion 31 consists only of the first portion 33.

[0053] In the roof structure 400, the portion of the valley 12 facing the lateral portion 434A in the second direction Y is joined to the lateral portion 434A by, for example, bolting, welding, or any other method, thereby fixing the roof 10 to the fixing portion 431 of the support portion 430.

[0054] As described above, the roof structure 400 according to this embodiment comprises a roof 10 that descends in a second direction Y as it moves from the inside to the outside in a first direction X, and a support portion 430 that is located on the outside of the roof 10 in the first direction X and supports the roof 10 from below in the second direction Y. The support portion 430 includes a fixing portion 431 that is on the side of the roof 10 in the second direction Y and fixed to the roof 10. The fixing portion 431 includes a first portion 33 that extends in the first direction X and a second portion 434 attached to the first portion 33. The second portion 434 reduces the gap between the fixing portion 431 and the roof 10 and is fixed to the roof 10.

[0055] According to this roof structure 400, the gap between the fixing part 431 and the roof 10 is reduced by the second part 434 of the fixing part 431 of the support part 430. In other words, according to the roof structure 400, the gap that occurs at the joint between the roof 10 and the support part 430 is reduced, making it possible to install the roof and the roof beam in a neat and tidy manner.

[0056] Although the present invention has been described above using the above-described embodiments as examples, the present invention is not limited thereto. Those skilled in the art can modify the roof structure according to the present invention as appropriate in accordance with conventionally known knowledge. As long as such modifications still possess the configuration of the present invention, they are of course included within the scope of the present invention. [Explanation of Symbols]

[0057] 1,200,300,400…Roof structure, 10…Roof, 11…Rump section, 12…Valley section, 13…Outer end section, 30,230,330,430…Support section, 31,231,331,431…Fixed section, 33…First section, 33A…Inner end section, 33B…Outer end section, 34,234,334,434…Second section

Claims

1. A roof that descends in a second direction intersecting the first direction, as it moves from the inside out in the first direction, A support portion is positioned on the outside of the roof in the first direction and supports the roof from below in the second direction, Equipped with, The support portion includes a fixing portion that is located on the roof side in the second direction and is fixed to the roof, The fixing portion includes a first portion extending in the first direction and a second portion attached to the first portion. The second part is a roof structure that reduces the gap between the fixing part and the roof and is fixed to the roof.

2. The roof structure according to claim 1, wherein the roof is formed of deck plates in which peaks and valleys are alternately formed in a third direction intersecting the first and second directions.

3. The roof structure according to claim 2, wherein the second portion is fixed to the valley portion of the deck plate.

4. The roof structure according to claim 1, wherein the roof is a corrugated metal roof.

5. In the first direction, the outer end of the roof is on the side of the inner end of the first portion. The second portion rises inward from the inner end of the first portion in the first direction, and rises in the second direction. The roof structure according to any one of claims 1 to 4, wherein the angle of inclination of the second portion with respect to the first portion is equal to the angle of inclination of the roof with respect to the first portion.

6. In the first direction, the outer end of the roof is on the side of the outer end of the first portion. The second portion descends outward in the second direction from the outer end of the first portion in the first direction, The roof structure according to any one of claims 1 to 4, wherein the angle of inclination of the second portion with respect to the first portion is equal to the angle of inclination of the roof with respect to the first portion.

7. In the first direction, the outer end of the roof is located outward relative to the inner end of the first portion. The roof structure according to any one of claims 1 to 4, wherein in the second direction, the second portion is placed on the first portion.

8. The roof structure according to claim 7, wherein in the second direction, the portion of the second portion that is on the side of the roof is inclined at an angle equal to the inclination angle of the roof with respect to the first portion.

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