Pipeline support reconstruction structure based on existing concrete column
By setting up tensioned beam groups and pressed beam groups on old concrete columns to form a triangular structure, offsetting the lateral bending moment and fixing them with chemical anchor bolts, the problem of safely adding pipeline support on reinforced concrete structures is solved, and the safety and stability of the structure are improved.
Patent Information
- Application Number
- CN202422507296.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Utility models(China)
- Current Assignee / Owner
- Filing Date
- 2024-10-16
- Publication Date
- 2025-08-05
- Estimated Expiration
- 2034-10-16
AI Technical Summary
Pipe support is added safely and reliably on the old reinforced concrete structure to avoid damage to the concrete structure and affecting the stress system of the original structure.
The tension beam group and the pressed beam group are connected to the concrete column to form a stable triangular structure. The lateral bending moments acting on the concrete column by the tension beam group and the pressed beam group are offset by each other, reducing the influence of adverse loads, and using chemical anchor bolts to fix the beam group to reduce disturbance to the concrete.
It effectively reduces the impact of adverse loads on concrete columns, improves the safety and stability of the structure after renovation, avoids cracking of concrete columns and corrosion of steel bars, and enhances the load-bearing capacity of pipeline support.
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Figure CN223190115U_ABST
Abstract
Description
Technical Field
[0001] The present disclosure relates to the technical field of old building reconstruction, and in particular to a pipe support reconstruction structure based on existing concrete columns. Background Art
[0002] With the continuous advancement of industrial technology and the upgrading of production equipment, most old industrial plants can no longer meet the needs of production and must be renovated or expanded. Various pipelines in the plant, as important components necessary for industrial production, also need to be rearranged or new pipelines added to meet the needs in order to improve the production efficiency of the old plant.
[0003] Pipe supports and pipelines work together as a spatial system. In actual production, improper pipe support design or construction often leads to pipe loss, bent tie rods, or tilting due to load loss. Failure of pipe supports can damage pipeline components during operation, causing changes in the stress of the entire piping system and, in more serious cases, even damaging the original building structure. Therefore, the proper placement of pipe supports is directly related to the safety and stability of the piping system.
[0004] Usually, due to the limitations of space and existing equipment in old factories, it is impossible to set up pipe supports separately. Instead, it is necessary to use the original structure as the rooting point for the pipe supports. In the existing technology, the technology of rooting pipe supports on steel structures is relatively mature. The pipe supports can be directly welded or screwed to the steel structure, and the design and construction are relatively flexible and convenient. However, a considerable number of old factories use reinforced concrete structures. Due to the relatively single design bearing capacity of the reinforced concrete structural columns during construction, they cannot withstand large lateral bending moments. Therefore, adding pipe supports for bearing loads to the old structure will not only damage the concrete structure, but also cause great disturbances to the force system of the original structure, posing a huge safety risk. Utility Model Content
[0005] A technical problem to be solved by the present disclosure is: how to safely and reliably add pipe supports to old reinforced concrete structures.
[0006] In order to solve the above technical problems, an embodiment of the present disclosure provides a pipe support modification structure based on an existing concrete column, including: a tension beam group and a compression beam group connected to the concrete column, the first end of the tension beam group is connected to the concrete column at a first height, the first end of the compression beam group is connected to the concrete column at a second height, the second end of the tension beam group and the second end of the compression beam group are connected to each other at a third height, the first height is higher than the second height, and the third height is not higher than the first height and not lower than the second height; wherein, the second end of the tension beam group is used to receive the pipeline, and the second end of the compression beam group is connected to be supported on the second end of the tension beam group.
[0007] In some embodiments, the first end of the tension beam group and the first end of the compression beam group are respectively connected to the concrete column through anchoring steel plates, and the anchoring steel plates are fixed to the concrete column through chemical anchor bolts.
[0008] In some embodiments, the concrete column further includes a shear member located between the first height and the second height and disposed on the concrete column.
[0009] In some embodiments, the tension beam group includes two tension steel beams arranged in parallel on a first side surface and an opposite second side surface of the concrete column, and the compression beam group includes two compression steel beams arranged in parallel on the first side surface and the second side surface.
[0010] In some embodiments, the concrete column further includes a tensile member located on the third side and / or the opposite fourth side of the concrete column.
[0011] In some embodiments, the tension steel beam is an H-shaped steel beam, and the compression steel beam is a box-shaped steel beam.
[0012] In some embodiments, multiple groups of tension bolts are provided between the two tension steel beams and / or the two compression steel beams.
[0013] In some embodiments, the tension beam group further includes a plurality of connecting steel beams for connecting two tension steel beams.
[0014] In some embodiments, a supporting assembly is provided at the second end of the tension beam group, and the supporting assembly includes a bearing plate arranged on the top of the tension steel beam and the connecting steel beam, a plurality of vibration-damping springs connected to the bearing plate, and a support plate connected to the top of the plurality of vibration-damping springs.
[0015] In some embodiments, stiffening ribs are provided in the tension steel beams and the connecting steel beams.
[0016] Through the above technical solution, the present invention provides a pipe support modification structure based on existing concrete columns, in which the tension beam group, the compression beam group and the concrete column form a stable triangular structure, and most of the lateral bending moments generated by the tension beam group and the compression beam group acting on the concrete column can offset each other, greatly reducing the impact of adverse loads on the concrete column and improving the safety of the modified structure. BRIEF DESCRIPTION OF THE DRAWINGS
[0017] In order to more clearly illustrate the embodiments of the present disclosure or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present disclosure. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.
[0018] Figure 1 It is a schematic structural diagram of the pipe support disclosed in the embodiment of the present disclosure;
[0019] Figure 2 This is disclosed in the embodiment of the present disclosure Figure 1 AA cross-sectional schematic diagram;
[0020] Figure 3 This is disclosed in the embodiment of the present disclosure Figure 2 BB cross-sectional schematic diagram;
[0021] Figure 4 is a partial cross-sectional view showing a chemical anchor disclosed in an embodiment of the present disclosure;
[0022] Figure 5 This is a schematic diagram of the structure of the embodiment of the present disclosure after ignoring the tension beam group and the compression beam group.
[0023] Description of reference numerals:
[0024] 1. Tension beam group; 101. Tension steel beam; 102. Connecting steel beam; 103. Stiffening rib; 104. Second connecting plate; 105. Third connecting plate; 2. Compression beam group; 201. Compression steel beam; 202. First connecting plate; 3. Anchor steel plate; 301. Chemical anchor; 4. Support assembly; 401. Bearing plate; 402. Vibration-damping spring; 403. Support plate; 5. Concrete column; 6. Shear member; 7. Tensile member; 8. Tension bolt. DETAILED DESCRIPTION
[0025] The following embodiments of the present disclosure are further described in detail with reference to the accompanying drawings and examples. The detailed description of the following examples and the accompanying drawings are intended to illustrate the principles of the present disclosure, but are not intended to limit the scope of the present disclosure. The present disclosure can be implemented in many different forms and is not limited to the specific embodiments disclosed herein, but rather includes all technical solutions within the scope of the claims.
[0026] The present disclosure provides these embodiments in order to make this disclosure thorough and complete, and to fully convey the scope of the present disclosure to those skilled in the art. It should be noted that: unless otherwise specifically stated, the relative arrangement of parts and steps, the composition of materials, numerical expressions and numerical values set forth in these embodiments should be interpreted as merely exemplary, and not as limiting.
[0027] It should be noted that, in the description of this disclosure, unless otherwise specified, "plurality" means greater than or equal to two; terms such as "upper," "lower," "left," "right," "inner," and "outer" indicating directions or positional relationships are intended solely to facilitate and simplify the description of this disclosure, and do not indicate or imply that the devices or elements referred to must have a specific orientation, be constructed, or operate in a specific orientation. Therefore, they should not be construed as limitations on this disclosure. When the absolute position of the object being described changes, the relative positional relationship may also change accordingly.
[0028] In addition, the terms "first," "second," and similar terms used in this disclosure do not denote any order, quantity, or importance, but are merely used to distinguish different parts. "Perpendicular" does not mean perpendicular in the strict sense, but rather means within the tolerance range. "Parallel" does not mean parallel in the strict sense, but rather means within the tolerance range. "Include" or "comprising" and similar terms mean that the elements preceding the term include the elements listed after the term, and do not exclude the possibility of also including other elements.
[0029] It should also be noted that, in the description of this disclosure, unless otherwise expressly specified or limited, the terms "installed," "connected," and "connected" should be understood in a broad sense. For example, they can refer to fixed connections, detachable connections, or integral connections; they can refer to direct connections or indirect connections through an intermediary. Those skilled in the art will understand the specific meanings of the above terms in this disclosure depending on the specific circumstances. When a specific device is described as being located between a first device and a second device, there may or may not be an intervening device between the specific device and the first or second device.
[0030] All terms used in this disclosure have the same meaning as understood by one of ordinary skill in the art to which this disclosure belongs, unless otherwise specifically defined. It should also be understood that terms defined in, for example, common dictionaries should be interpreted as having a meaning consistent with their meaning in the context of the relevant art, and should not be interpreted in an idealized or highly formal sense, unless explicitly defined as such herein.
[0031] Technologies, methods, and equipment known to ordinary technicians in the relevant art may not be discussed in detail, but where appropriate, the technologies, methods, and equipment should be considered part of the specification.
[0032] like Figure 1 As shown, the present disclosure provides a pipe support modification structure based on an existing concrete column, comprising: a tension beam group 1 and a compression beam group 2 connected to the concrete column 5, the first end of the tension beam group 1 being connected to the concrete column 5 at a first height, the first end of the compression beam group 2 being connected to the concrete column 5 at a second height, the second end of the tension beam group 1 and the second end of the compression beam group 2 being connected to each other at a third height, the first height being higher than the second height, and the third height being no higher than the first height and no lower than the second height; wherein, the second end of the tension beam group 1 is used to receive the pipe, and the second end of the compression beam group 2 is connected to be supported on the second end of the tension beam group 1.
[0033] Specifically, under the same conditions, the tensile strength of concrete is only 10-20% of its compressive strength. Therefore, when concrete column 5 is subjected to a transverse horizontal load, the lateral bending moment generated by the load will cause cracking and damage on the tensile side surface of concrete column 5, exposing the steel bars inside the structure and causing them to rust, seriously affecting the structure's bearing capacity. To eliminate the impact of lateral bending moment on the structure, a tension beam group 1 and a compression beam group 2 are provided. The action of the pipeline load causes tension beam group 1 and compression beam group 2 to generate equal and opposite forces on concrete column 5 in the horizontal direction. The lateral bending moments imposed by tension beam group 1 and compression beam group 2 on concrete column 5 are largely offset, preventing cracking of the concrete on its side under the action of tension, effectively improving the safety of the modified structure.
[0034] exist Figure 1 In the embodiment shown, the third height is equal to the first height and greater than the second height. At this time, the tension beam group 1 is placed horizontally, and together with the compression beam group 2 and the concrete column 5, a triangular stability system is formed. The load center of the subsequently installed pipeline acts on the connection point of the tension beam group 1 and the compression beam group 2 to facilitate load transfer. In addition, if Figure 1 As shown, the first end or the second end for connection between the tension beam group 1 and the compression beam group 2 and between them and the concrete column 5 is not limited to their end heads. In order to facilitate the placement of pipelines and installation structures, the points of mutual connection between the structures can be located near one side of their end heads.
[0035] In some embodiments, the third height can be between the first and second heights or equal to the second height, which can also ensure that the tension beam group 1 and the compression beam group 2 exert forces of the same magnitude and direction on the concrete column 5 in the horizontal direction. If the third height is less than the first height, the tension beam group 1 is tilted downward. To facilitate pipe support, a straight section for pipe support can be provided near its second end. The center of the pipe load still acts at the connection between the tension beam group 1 and the compression beam group 2, facilitating load transfer.
[0036] like Figure 5As shown, in some embodiments, to ensure structural stability and facilitate retrofit construction, the third height is equal to the first height and greater than the second height, and the compression beam group 2 forms a 45° angle with the vertical. Specifically, setting the third height equal to the first height can meet the installation clearance requirements of some pipelines. During construction, the length of the tension beam group 1 should be as short as possible to reduce installation costs while also minimizing the size of the bracket to improve structural stability. The tension beam group 1 has a minimum length, influenced by the diameter of the pipeline to be installed. Once the length of the tension beam group 1 is determined, a larger angle increases the horizontal force component generated by the tension beam group 1 and the compression beam group 2 under the pipeline load, which is less favorable for the existing concrete column 5. A smaller angle increases the length of the compression beam group 2, increasing costs and susceptibility to on-site space constraints. Therefore, based on actual on-site installation experience, adopting a 45° installation angle ensures structural stability while controlling installation costs. In other embodiments, the appropriate installation angle should be selected based on actual on-site installation conditions.
[0037] like Figures 1 to 5 As shown, in some embodiments, the first end of the tension beam group 1 and the first end of the compression beam group 2 are respectively connected to the concrete column 5 through the anchoring steel plate 3, and the anchoring steel plate 3 is fixed to the concrete column 5 through the chemical anchor bolt 301.
[0038] Specifically, compared to methods such as directly embedding the tension beam group 1 and the compression beam group 2 into the concrete column 5 or using expansion bolts to secure the anchor steel plate 3, chemical anchor bolts 301, unlike mechanical anchor bolts, rely on adhesives for fixation, thus preventing expansion and compression stress on the concrete. Furthermore, their installation process is relatively simple and quick, allowing for use within smaller installation spaces and spacings, making them suitable for construction sites with limited space. Therefore, indirectly attaching the tension beam group 1 and the compression beam group 2 to the concrete column 5 via the anchor steel plate 3 reduces disturbance to the concrete column 5. Furthermore, the use of chemical anchor bolts 301 effectively reduces the expansion stress on the concrete column 5 at the fixing point, thus minimizing the impact of the modified structure on the original concrete column.
[0039] like Figure 1 、 Figure 3 and Figure 5 As shown, in some embodiments, a shear member 6 is further included, which is located between the first height and the second height and is provided on the concrete column 5 .
[0040] Specifically, since the shear resistance of the concrete structure is better than its tensile resistance, the pipe support modification structure splits the lateral bending moment into lateral bending moments that can offset each other through the tension beam group 1 and the compression beam group 2, thereby reducing the impact of adverse loads on the original structure. However, between the first height and the second height, a shear superposition area will appear on the concrete column 5. The shear member 6 is installed in the shear superposition area of the concrete column 5 to resist the load influence and maintain the stability of the structure.
[0041] In some embodiments, the shear member 6 can be a fiber polymer wrapped around the concrete column 5, which can effectively improve the shear resistance of the structure. In other embodiments, the shear member 6 can also be a stirrup or steel plate wrapped around the shear superposition area of the concrete column 5, which can also improve the shear resistance of the structure and achieve the purpose of maintaining structural stability.
[0042] like Figure 2 and Figure 3 As shown, in some embodiments, the tension beam group 1 includes two tension steel beams 101 arranged parallel to a first side surface and an opposite second side surface of the concrete column 5, and the compression beam group 2 includes two compression steel beams 201 arranged parallel to the first side surface and the second side surface. Specifically, the two tension steel beams 101 and the two compression steel beams 201 are symmetrically arranged on either side of the concrete column 5 to prevent torsional stress in the concrete column 5 under load. In other embodiments, the tension beam group 1 and the compression beam group 2 may also include more steel beams symmetrically arranged on the concrete column 5.
[0043] like Figure 1 and Figure 5 As shown, the structure further includes tensile members 7 located on the third side and / or the opposite fourth side of the concrete column 5. The pipe support modification structure applies equal and opposite horizontal forces to the concrete column 5 at the first and second heights, respectively. Therefore, the tensile members 7 should be positioned accordingly based on the distribution of the first and second heights on the concrete column 5.
[0044] Specifically, when the first height is close to the top anchorage end of the concrete column 5, the lateral bending moment that can be generated by the tension beam group 1 will be smaller than the lateral bending moment that can be generated by the compression beam group 2. The tensile member 7 should be installed on the fourth side of the concrete column 5 facing away from the pipeline. To save costs, the tensile member 7 can be installed only below the second height to resist the tensile stress. Similarly, when the second height is close to the bottom anchorage end of the concrete column 5, the tensile member 7 can be installed only above the first height on the third side of the concrete column 5. When the distance between the first height and the top anchorage end and the distance between the second height and the bottom anchorage end are similar, it can be decided whether to install the tensile member 7 at the same time based on the actual load size. The tensile member 7 here can be a steel plate fixed to the side of the concrete column 5 or a component with prestressed fiber reinforcement that can improve the tensile strength of the structure surface.
[0045] In some embodiments, the tension steel beam 101 is an H-shaped steel beam, and the compression steel beam 201 is a box-shaped steel beam. Specifically, the tension steel beam 101, the compression steel beam 201, and the anchoring steel plate 3 are connected by welding. The use of H-shaped and box-shaped steel beams ensures effective contact between the two and the anchoring steel plate 3 before welding, facilitates stable welding construction, and effectively improves the fixing strength. Furthermore, when the pipeline support is displaced under load, the use of an H-shaped steel beam for the tension steel beam 101 effectively resists bending deformation, while the box-shaped cross-section of the compression steel beam 201 also better supports the tension steel beam 101.
[0046] like Figure 1 and Figure 2 As shown, in some embodiments, a plurality of groups of tension bolts 8 are provided between the two tension steel beams 101 and / or the two compression steel beams 201 .
[0047] Specifically, the tension bolts 8 can strengthen the connection between the steel beams, enhance their integrity, and avoid uneven deformation under load, which causes the concrete column 5 to be subjected to torsional stress.
[0048] In some embodiments, as Figure 1 and Figure 2 As shown, the ends of the two tension steel beams 101 connected to the first ends of the concrete column 5 both extend beyond the fourth side surface of the concrete column 5. Tension bolts 8 are provided at the ends of the tension steel beams 101 extending beyond the fourth side surface and at the locations extending beyond the third side surface. The two sets of tension bolts 8 and the two tension steel beams 101 form a closed constraint surrounding the concrete column 5, allowing the tension steel beams 101 to be more firmly installed on the concrete column 5. In other embodiments, tension bolts 8 may also be added to the two compression steel beams 201 on both sides of the concrete column 5 to ensure their fixed connection to the concrete column 5.
[0049] like Figure 2 As shown, in some embodiments, the tension beam group 1 further includes a plurality of connecting steel beams 102 for connecting two tension steel beams 101 .
[0050] Specifically, multiple connecting steel beams 102 are arranged at the second end of the tension beam group 1. The connecting steel beams 102 are H-shaped steel beams welded vertically to the tension steel beams 101. The multiple connecting steel beams 102 and the two tension steel beams 101 form a rectangular bearing area at the second end of the tension beam group 1 that can bear the pipeline.
[0051] like Figure 1 and Figure 3As shown, in some embodiments, a supporting assembly 4 is provided at the second end of the tension beam group 1, and the supporting assembly 4 includes a bearing plate 401 arranged on the top of the tension steel beam 101 and the connecting steel beam 102, a plurality of vibration-damping springs 402 connected to the bearing plate 401, and a support plate 403 connected to the top of the plurality of vibration-damping springs 402.
[0052] Specifically, the load-bearing plate 401 is a steel plate installed above the rectangular bearing area. The shape of the support plate 403 is adapted to the arc shape of the pipeline. A plurality of vibration-damping springs 402 of different lengths are provided on the load-bearing plate 401 to fit the bottom of the support plate 403. When the supported pipeline vibrates due to the flow of the medium inside it, the plurality of vibration-damping springs 402 arranged between the load-bearing plate 401 and the support plate 403 can absorb the vibration, thereby reducing the impact of the vibration on the joints in the modified structure and extending the life of the structure.
[0053] like Figure 2 As shown, in some embodiments, stiffening ribs 103 are provided in the tension steel beams 101 and the connecting steel beams 102. Specifically, to improve stability under load, stiffening ribs 103 are provided in the tension steel beams 101 and the connecting steel beams 102 within the rectangular load-bearing area. The stiffening ribs 103 are steel plates welded between the web and flange plates of the H-shaped steel beam. They can significantly increase the bending modulus of the steel beam and effectively reduce deformation of the steel beam under load.
[0054] like Figure 2 and Figure 3 As shown, in some embodiments, in order to save modification costs, the cross-sectional size of the compression steel beam 201 that mainly bears compressive stress is smaller than the tension steel beam 101 that bears tensile stress and bending stress. To facilitate the connection between the two, a horizontally placed first connecting plate 202 is welded at the groove of the compression steel beam 201. The first connecting plate 202 is welded to the inner flange plate of the tension steel beam 101 near the concrete column 5 through a vertically placed second connecting plate 104. At the same time, the first connecting plate 202 is connected to the web of the tension steel beam 101 through a third connecting plate 105, and stiffening ribs 103 are provided at both ends of the third connecting plate 105 along the length direction of the tension steel beam 101, and the two ends of the third connecting plate 105 are welded to the two stiffening ribs 103 to form a whole, which is conducive to reducing structural deformation and improving stability after being put into use.
[0055] In some embodiments, the tension steel beam 101 , the connection steel beam 102 and the compression steel beam 201 may also be connected by bolting or bolt welding.
[0056] Thus far, various embodiments of the present disclosure have been described in detail. To avoid obscuring the concept of the present disclosure, some details known in the art have not been described. Based on the above description, those skilled in the art can fully understand how to implement the technical solutions disclosed herein.
[0057] Although some specific embodiments of the present disclosure have been described in detail through examples, those skilled in the art will understand that the above examples are for illustrative purposes only and are not intended to limit the scope of the present disclosure. Those skilled in the art will understand that the above embodiments may be modified or some technical features may be replaced with equivalents without departing from the scope and spirit of the present disclosure. In particular, as long as there are no structural conflicts, the various technical features mentioned in the various embodiments may be combined in any manner.
Claims
1. A pipe support modification structure based on an existing concrete column, characterized in that: include: A tension beam group (1) and a compression beam group (2) connected to a concrete column (5), wherein a first end of the tension beam group (1) is connected to the concrete column (5) at a first height, a first end of the compression beam group (2) is connected to the concrete column (5) at a second height, a second end of the tension beam group (1) and a second end of the compression beam group (2) are connected to each other at a third height, the first height being higher than the second height, and the third height being no higher than the first height and no lower than the second height; The second end of the tension beam group (1) is used to receive the pipeline, and the second end of the compression beam group (2) is connected to be supported on the second end of the tension beam group (1).
2. The pipe support reconstruction structure based on the existing concrete column according to claim 1 is characterized in that: The first end of the tension beam group (1) and the first end of the compression beam group (2) are respectively connected to the concrete column (5) through an anchoring steel plate (3), and the anchoring steel plate (3) is fixed to the concrete column (5) through a chemical anchor bolt (301).
3. The pipe support reconstruction structure based on the existing concrete column according to claim 1 is characterized in that: It also includes a shear member (6) located between the first height and the second height and arranged on the concrete column (5).
4. The pipe support reconstruction structure based on the existing concrete column according to claim 1 is characterized in that: The tension beam group (1) includes two tension steel beams (101) arranged in parallel on a first side surface and an opposite second side surface of the concrete column (5), and the compression beam group (2) includes two compression steel beams (201) arranged in parallel on the first side surface and the second side surface.
5. The pipe support reconstruction structure based on the existing concrete column according to claim 4 is characterized in that: It also includes a tensile member (7) located on the third side surface and / or the opposite fourth side surface of the concrete column (5).
6. The pipe support reconstruction structure based on the existing concrete column according to claim 4 is characterized in that: The tension steel beam (101) is an H-shaped steel beam, and the compression steel beam (201) is a box-shaped steel beam.
7. The pipe support reconstruction structure based on the existing concrete column according to claim 4 is characterized in that: A plurality of groups of tension bolts (8) are provided between the two tension steel beams (101) and / or the two compression steel beams (201).
8. The pipe support reconstruction structure based on the existing concrete column according to claim 4 is characterized in that: The tension beam group (1) further comprises a plurality of connecting steel beams (102) for connecting two tension steel beams (101).
9. The pipe support reconstruction structure based on the existing concrete column according to claim 8, characterized in that: The second end of the tension beam group (1) is provided with a supporting assembly (4), and the supporting assembly (4) includes a bearing plate (401) arranged on the top of the tension steel beam (101) and the connecting steel beam (102), a plurality of vibration-damping springs (402) connected to the bearing plate (401), and a supporting plate (403) connected to the top of the plurality of vibration-damping springs (402).
10. The pipe support reconstruction structure based on the existing concrete column according to claim 9, characterized in that: Stiffening ribs (103) are provided inside the tension steel beam (101) and the connection steel beam (102).