Lifting device and method for erecting box girder bridges

Abstract

To provide a box girder block capable of suppressing future deterioration.SOLUTION: A lifting device 20 for a box girder block 14 includes an upper floor slab 5, lower floor slab 6, and multiple webs 7; and a pair of lifting units 22 that are placed at a distance from each other in the direction perpendicular to the bridge axis of the box girder block 14 and connected to each other by a connecting member 21. Each of the lifting units includes: a beam 23 that is longer than the length of the upper floor slab 5 in the bridge axis direction and placed above the upper floor slab 5 along the bridge axis direction; a first support arm 24 that is provided to one end of the beam 23 and includes a first support piece 26 for supporting the upper floor slab 5 from the bottom; and a second support arm 25 that is slidably arranged on the other end of beam 23, and has a second support piece 27 for supporting the upper floor slab 5 from the bottom on the lower end. Since box girder block 14 can be supported from the bottom and lifted, there is no need to provide an insert member on the top surface of the box girder block 14.SELECTED DRAWING: Figure 4

Description

Technical Field

[0001] The present invention relates to a lifting device for box girder blocks and a method for erecting box girder bridges.

Background Art

[0002] As a construction method for manufacturing structures such as bridges, there is a precast segment method. This method is a method of joining precast concrete blocks (segments) on site and integrating them by introducing prestress with a tensioning material. The heavy precast segments are lifted using a crane and erected at a predetermined position. As a lifting structure for precast segments of a box girder bridge, a configuration is known in which through holes are formed in a floor slab, and a fixed frame (lifting jig) is attached to PC steel bars inserted into these through holes to lift the segments (FIG. 2 of Patent Document 1).

[0003] Also, as a lifting structure for precast members, as shown in FIG. 10(A), an anchor material 52 is embedded in a member body 51, and a lifting jig 53 is attached to the anchor material 52 to lift the precast member. The anchor material 52 is provided in a hollowed-out portion 54 formed in the member body 51. After the precast member is lifted and erected at a predetermined position, the hollowed-out portion 54 is filled with a backfill material 55 such as non-shrink mortar or expansive concrete and processed to be flat, as shown in FIG. 10(B). The through holes as disclosed in Patent Document 1 are also processed with the backfill material 55 after the erection of the precast member.

Prior Art Documents

Patent Documents

[0004]

Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0005] However, in conventional lifting structures, the post-fill material is exposed on the top surface of the box girder block. Over time, the post-fill material deteriorates, which can lead to cracking or delamination between the post-fill material and the box girder block. Alternatively, if expansive concrete is used as the post-fill material, sufficient expansion may not be achieved depending on the environmental conditions during filling. In such cases, the bond between the post-fill material and the box girder block is more likely to break, and cracking is more likely to occur. If cracks appear on the top surface, the deterioration of the precast members progresses due to erosion by water that penetrates through the cracks, freezing of the penetrated water, and rusting of metal members such as reinforcing bars by water.

[0006] In view of the above background, the present invention aims to suppress future deterioration of box girder blocks. [Means for solving the problem]

[0007] To solve the above problems, one aspect of the present invention provides a lifting device (20) for a box girder block (14) comprising an upper deck (5), a lower deck (6), and a plurality of webs (7), comprising a pair of lifting units (22) spaced apart from each other in the direction perpendicular to the bridge axis of the box girder block and connected to each other by a connecting member (21), each of which includes a beam (23) longer than the length of the upper deck in the bridge axis direction and positioned above the upper deck along the bridge axis direction, a first support arm (24) provided at one end of the beam and having a first support piece (26) at its lower end for supporting the upper deck from below, and a second support arm (25) slidably provided on the other end of the beam and having a second support piece (27) at its lower end for supporting the upper deck from below.

[0008] In this embodiment, the upper deck slab is supported from below by the first support piece of the first support arm and the second support piece of the second support arm, allowing the box girder block to be lifted. Furthermore, the support of the upper deck slab can be easily released by sliding the second support arm. Since the box girder block can be supported and lifted from below by this lifting device, there is no need to provide an insert member on the upper surface of the box girder block, and deterioration of the upper surface of the box girder block is suppressed.

[0009] In the above embodiment, the lower surface of the upper deck slab is preferably formed with a thickened portion (7b) of the web or a pair of ribs (8) extending perpendicular to the bridge axis, and the first support piece and the second support piece are preferably in contact with the lower surface of the thickened portion of the web or the lower surface of the ribs.

[0010] According to this embodiment, the thickened portion or rib of the web, which has high bending rigidity against upward forces, can be supported from below. Therefore, there is no need to thicken the plate portion of the upper deck for lifting purposes.

[0011] In the above embodiment, the beam may have a plurality of through holes (29) arranged to be spaced apart in the longitudinal direction, and the second support arm may be fixed to the beam by pins (30) that are inserted into and removed from the through holes.

[0012] According to this embodiment, the second support arm can be easily fixed to and released from the beam by inserting and removing a pin into the through hole.

[0013] In the above embodiment, each of the lifting units may further include at least one pressing member (31) that presses down on the upper floor slab from above.

[0014] In this embodiment, the upper deck can be sandwiched between the first support piece of the first support arm and the second support piece of the second support arm, which support the upper deck from below, and the pressing member that presses the upper deck from above. Therefore, rattling of the box girder block when it is suspended is suppressed.

[0015] In the above embodiment, the retaining member preferably includes a base member (33) provided on the beam and a contact member (34) provided on the base member so as to be movable in the vertical direction and in contact with the upper surface of the upper floor slab.

[0016] According to this embodiment, the contact member can be easily pressed against and released from above the upper floor slab by moving the contact member vertically relative to the base member.

[0017] Furthermore, in order to solve the above problems, one aspect of the present invention is a method for erecting a box girder bridge (4) which is constructed by connecting a plurality of box girder blocks (14) arranged in the bridge axis direction, comprising the steps of: placing an erection frame (40) below the erection position of the box girder bridge; providing a pair of rails (42) extending in the bridge axis direction on the erection frame; providing a traveling trolley (43) on the rails; lifting the box girder blocks using the lifting device configured above and placing the box girder blocks on the traveling trolley, and The method includes the steps of: moving the traveling carriage on which the box girder block is placed to move the box girder block to a predetermined position above the erection frame; placing a support member (45) on the erection frame and switching the support of the box girder block placed at the predetermined position from the traveling carriage to the support member; repeating the steps from placing the box girder block to switching the support of the box girder block; and connecting the plurality of box girder blocks supported at each of the predetermined positions.

[0018] The lifting device with the above configuration lifts the box girder block with the first support arm and the second support arm arranged on both sides of the upper floor slab in the bridge axis direction. Therefore, when adjacent box girder blocks are arranged at predetermined positions, the box girder block lifted by the lifting device cannot be arranged at the predetermined position. On the other hand, according to this aspect, the box girder block lifted by the lifting device can be placed on the traveling trolley and moved to a predetermined position by the traveling trolley. Further, at the predetermined position, since the support of the box girder block is switched from the traveling trolley to the support member, the traveling trolley can be repeatedly diverted for the movement of other box girder blocks. And since the insert member is not provided on the upper surface of the box girder block, deterioration of the upper surface of the box girder block is suppressed.

Effect of the Invention

[0019] According to the above aspect, future deterioration of the precast member can be suppressed.

Brief Description of the Drawings

[0020] [Figure 1] Side view of the box girder bridge according to the embodiment [Figure 2] Cross-sectional view of the box girder bridge shown along the line II-II in FIG. 1 [Figure 3] Front view showing the lifted state of the box girder block [Figure 4] Side cross-sectional view showing the lifted state of the box girder block [Figure 5] Explanatory drawing of the lifting procedure of the box girder block [Figure 6] Explanatory drawing of the lifting procedure of the box girder block [Figure 7] [[ID=!33]]Side view for explaining the erection procedure of the box girder bridge [Figure 8] Front view for explaining the erection procedure of the box girder bridge [Figure 9] Front view for explaining the erection procedure of the box girder bridge [Figure 10] Explanatory drawing of the lifting structure of the precast member according to the prior art

Mode for Carrying Out the Invention

[0021] Embodiments of the present invention will be described in detail below with reference to the drawings.

[0022] Figure 1 is a side view of a box girder bridge 4 according to an embodiment. As shown in Figure 1, the bridge 1 is used as a road bridge or railway bridge and has two abutments 2 (only the right abutment 2 is shown in the figure), one or more piers 3 constructed between the two abutments 2, and a box girder bridge 4 that spans these to form a continuous girder. Note that Figure 1 shows a general side view centered on one span from the right abutment 2 to the adjacent pier 3.

[0023] Figure 2 is a cross-sectional view of the box girder bridge 4 along the line II-II in Figure 1. As shown in Figures 1 and 2, the box girder bridge 4 has an upper deck 5, a lower deck 6, and a pair of webs 7 that extend roughly vertically. The pair of webs 7 are connected at their upper ends to the middle of the upper deck 5 in the direction perpendicular to the bridge axis, and at their lower ends to both ends of the lower deck 6. The upper deck 5 is configured to protrude from the pair of webs 7. Ribs 8 (Figure 2) extending in the direction perpendicular to the bridge axis are integrally formed on the lower surface of the upper deck 5. Wall railings 9 (Figure 1) are constructed at both ends of the upper deck 5 in the direction perpendicular to the bridge axis. In this embodiment, the box girder bridge 4 is configured as a single box girder bridge with a box-shaped cross-section in which the internal space enclosed by the pair of webs 7, the upper deck 5, and the lower deck 6 is rectangular.

[0024] These pair of webs 7, upper slab 5, lower slab 6, and wall parapet 9 are formed from high-strength concrete of the same mix, and are further made of prestressed unreinforced concrete. For the high-strength concrete, it is preferable to use concrete with a design strength of 80 N / mm2 reinforced with steel fibers to achieve high shear strength characteristics. The upper slab 5, lower slab 6, and web 7 may also be formed from reinforced concrete. Furthermore, the web 7 may be formed from a steel member.

[0025] Multiple external cables 11 are stretched within the internal space of the box girder bridge 4. As shown in Figure 1, these external cables 11 are positioned at their highest point at the column heads 12, which are directly above the abutments 2 and piers 3. The external cables 11 extend diagonally downward from the column heads 12 toward the two bulkheads 10 located in the middle of the box girder bridge 4, and are stretched so that their lowest point between the two bulkheads 10 is parallel to the box girder bridge 4. Both ends of these external cables 11 are anchored to the column heads 12 under tension. In this way, the tension of the diagonally stretched external cables 11 introduces prestress, improving the shear strength and bending strength of the box girder bridge 4.

[0026] The box girder bridge 4 is composed of multiple box girder blocks 14 (segments) arranged in the direction of the bridge axis. Post-tensioning tension members 15 extending in the direction of the bridge axis are embedded in appropriate locations within each box girder block 14. Tension members (not shown) extending perpendicular to the bridge axis are also embedded in the box girder blocks 14. As the tension members 15, for example, aramid rods (FRP tension members) can be used, which are made by shaping aramid fibers into a desired form (mainly string-like) and hardening them with a binder such as a hardening plastic.

[0027] Figure 3 is a front view showing the box girder block 14 in a lifted state, and Figure 4 is a side cross-sectional view showing the box girder block 14 in a lifted state. As shown in Figures 3 and 4, each box girder block 14 has a portion of the upper deck 5 in the bridge axis direction (simply referred to as the upper deck 5), a portion of the lower deck 6 in the bridge axis direction (simply referred to as the lower deck 6), and a portion of the pair of webs 7 in the bridge axis direction (simply referred to as the webs 7). Two ribs 8 (see Figure 4) are provided on the lower surface of the upper deck 5, positioned near the end in the bridge axis direction.

[0028] As shown in Figure 4, each web 7 has a plate-like portion 7a that exhibits a butterfly shape, with its length in the bridge axis direction gradually increasing from the middle in the height direction towards its upper and lower edges. An upper thickened portion 7b is provided at the upper end of the plate-like portion 7a, which is thicker than the upper part of the plate (in the dimension perpendicular to the bridge axis). A lower thickened portion 7c is provided at the lower end of the plate-like portion 7a, which is thicker than the plate-like portion 7a. Shear keys 17 and keyways 18 are formed at appropriate locations on the joint surface of the box girder block 14 in the bridge axis direction.

[0029] The box girder block 14 is lifted using a lifting device 20 suspended from a wire of a lifting device such as a crane (not shown). The lifting device 20 comprises a pair of lifting units 22, which are spaced apart from each other in the direction perpendicular to the bridge axis of the box girder block 14 and connected to each other by a connecting member 21 (Figure 3). Both lifting units 22 have the same or symmetrical configuration. The lifting units 22 will be described below.

[0030] As shown in Figure 4, the lifting unit 22 comprises a beam 23 positioned above the upper deck 5 along the bridge axis direction, a first support arm 24 provided at the right end (one end) of the beam 23, and a second support arm 25 provided at the left end (other end) of the beam 23. The beam 23 has a length longer than the bridge axis direction length of the upper deck 5. The first support arm 24 hangs down from the right end of the beam 23 and has a first support piece 26 at its lower end. The first support piece 26 extends to the left from the first support arm 24 toward the second support arm 25. The first support piece 26 supports the upper deck 5 from below by abutting against the lower surface of the right end of the upper thickened portion 7b of the web 7. The second support arm 25 hangs down from the middle left portion of the beam 23 and has a second support piece 27 at its lower end. The second support piece 27 extends to the right from the second support arm 25 toward the first support arm 24. The second support piece 27 supports the upper floor slab 5 from below by contacting the lower surface of the left end of the upper thickened portion 7b of the web 7.

[0031] In this way, the first support piece 26 and the second support piece 27 abut against the lower surface of the thickened upper portion 7b of the web 7, thereby supporting the web 7, which has high bending rigidity against upward forces, from below. Therefore, there is no need to thicken the plate portion of the upper floor slab 5 for lifting purposes. The same applies when the first support piece 26 and the second support piece 27 abut against the lower surface of the rib 8 and support the upper floor slab 5 via the rib 8. Accordingly, in other embodiments, the first support piece 26 and the second support piece 27 may abut against the lower surfaces of the right and left ribs 8 to support the upper floor slab 5 from below.

[0032] Furthermore, the second support arm 25 has a slider 28 at its upper end. The slider 28 is engaged with the beam 23 so as to be movable in the longitudinal direction of the beam 23. As the slider 28 moves along the beam 23, the distance between the second support piece 27 and the first support piece 26 changes. In the lifted state of the box girder block 14 shown in Figure 4, the second support arm 25 is fixed to the beam 23 at a position where it abuts against or is close to both end faces of the box girder block 14 in the bridge axis direction, along with the first support arm 24. The beam 23 has a plurality of through holes 29 arranged to be spaced apart in the longitudinal direction, and the slider 28 of the second support arm 25 has two pin insertion holes for inserting pins 30. The second support arm 25 is fixed to the beam 23 by inserting the pins 30 into the pin insertion holes of the slider 28 and the through holes 29 of the beam 23. When the pin 30 is removed from the through hole 29, the second support arm 25 is released from its fixation to the beam 23, and the second support arm 25 becomes able to slide along the beam 23. In this way, the second support arm 25 can be easily fixed to and released from the beam 23 by inserting and removing the pin 30 from the through hole 29.

[0033] Two retaining members 31 are provided in the middle of the beam 23, positioned at intervals in the bridge axis direction. As a result, the upper deck 5 is sandwiched between the first support piece 26 of the first support arm 24 and the second support piece 27 of the second support arm 25, which support the upper deck 5 from below, and the retaining members 31 which press down on the upper deck 5 from above. Therefore, rattling of the box girder block 14 when it is suspended is suppressed.

[0034] The retaining member 31 includes a base member 33 fixed to the beam 23 via a bracket 32, and a contact member 34 provided on the base member 33. The contact member 34 is provided so as to be movable in the vertical direction relative to the base member 33, and by moving downwards, it contacts the upper surface of the upper deck 5. By moving the contact member 34 in the vertical direction relative to the base member 33, the upper deck 5 can be easily pressed down and released from above.

[0035] The contact member 34 should preferably be movable up and down by a screw. This allows the contact member 34 to contact the upper floor slab 5 with a predetermined pressing force. Furthermore, the contact member 34 should preferably be slidable relative to the base member 33 and fixed by a pin 30. This allows the vertical position of the contact member 34 to be changed quickly by sliding, and the desired pressing force to be generated by the screw.

[0036] The lifting device 20 is configured as described above. Next, the procedure for lifting the box girder block 14 using the lifting device 20 will be explained with reference to Figures 5 and 6. Each step described below will be performed by a worker.

[0037] Figures 5 and 6 are explanatory diagrams of the procedure for lifting the box girder block 14. As shown in Figure 5, the worker moves the contact member 34 upward to shorten the retaining member 31. The worker also moves the second support arm 25 to the left end of the beam 23 and fixes it to the beam 23. The gap between the first support piece 26 and the second support piece 27 is longer than the length of the upper deck slab 5 in the bridge axis direction. The lifting device 20 is lowered to a position where the first support arm 24 and the second support arm 25 are positioned on both sides of the box girder block 14 in the bridge axis direction, and the lifting device 20 is further moved horizontally so that the first support arm 24 contacts the joint surface of the upper deck slab 5. As a result, the box girder block 14 and the lifting device 20 are in the state shown in Figure 6.

[0038] In this state, the second support arm 25 is slid toward the box girder block 14 and brought into contact with the joint surface of the upper deck 5. Next, the lifting device 20 is raised until the first support piece 26 and the second support piece 27 come into contact with the lower surface of the upper thickened portion 7b of the corresponding web 7. In this state, the contact member 34 is moved downward until it comes into contact with the upper surface of the upper deck 5, thereby extending the pressing member 31. This brings the box girder block 14 and the lifting device 20 into a state suitable for lifting as shown in Figure 4.

[0039] After the box girder block 14 is lifted by the lifting device 20 and moved to a predetermined transport position, the lifting device 20 can be removed from the box girder block 14 by performing the reverse procedure described above.

[0040] Each unit of the lifting device 20 comprises a beam 23, a first support arm 24 with a first support piece 26 at its lower end for supporting the upper deck 5 from below, and a second support arm 25 with a second support piece 27 at its lower end for supporting the upper deck 5 from below. This allows the upper deck 5 to be supported from below by the first support piece 26 of the first support arm 24 and the second support piece 27 of the second support arm 25, enabling the box girder block 14 to be lifted. Furthermore, since the second support arm 25 is slidably provided on the other end of the beam 23, the support for the upper deck 5 can be easily released by sliding the second support arm 25. As the box girder block 14 can be supported and lifted from below by this lifting device 20, there is no need to provide an insert member on the upper surface of the box girder block 14. Therefore, deterioration of the upper surface of the box girder block 14 is suppressed.

[0041] Next, with reference to Figures 7 to 9, the method for erecting the box girder bridge 4 using this lifting device 20 will be described. Figures 7 to 9 are explanatory diagrams of the procedure for erecting the box girder bridge 4. Figure 7 is a side view of the box girder bridge 4, Figure 8 is a cross-sectional view VIII in Figure 7, and Figure 9 is a cross-sectional view IX in Figure 7. The work in each step for erecting the box girder bridge 4, as described below, will be carried out by workers.

[0042] As shown in Figures 7 to 9, first, a scaffolding frame 40 is placed below the erection site of the box girder bridge 4. A pair of rail frames 41 extending in the direction of the bridge axis are placed on top of the scaffolding frame 40, and a pair of rails 42 are placed on top of the rail frames 41. A trolley 43 is placed on top of the rails 42. The trolley 43 is preferably an electric vehicle equipped with an electric drive unit. Alternatively, the trolley 43 may not be equipped with an electric drive unit and may be moved along the rails by the power of workers. In this case, it is preferable to use tools such as a chain hoist. A pair of support frames 44 extending in the direction of the bridge axis are placed on the outside of the rail frames 41 in the width direction.

[0043] Next, the workers use the lifting device 20 configured above to lift the box girder block 14 and place it on the trolley 43. Then, as shown in Figures 7 and 8, the trolley 43 with the box girder block 14 on it is moved to a predetermined position (predetermined erection position) above the erection frame 40. After that, as shown in Figures 7 and 9, support members 45 are placed on the erection frame 40, specifically on a pair of support frames 44, and the support of the box girder block 14 placed in the predetermined position is switched from the trolley 43 to the support members 45. After the support is switched, the trolley 43 is moved away from below the box girder block 14 to allow for the movement of the next box girder block 14. For each box girder block 14, the process from placing it on the trolley 43 to switching the support from the trolley 43 to the support frame 44 is repeated. After all the box girder blocks 14 are placed in their designated positions, these box girder blocks 14 are connected using tensioning members 15.

[0044] The lifting device 20 lifts the box girder block 14 with the first support arms 24 and the second support arms 25 positioned on both sides of the upper deck 5 in the bridge axis direction. Therefore, when an adjacent box girder block 14 is positioned in a predetermined location, the box girder block 14 lifted by the lifting device 20 cannot be positioned in the predetermined location. In this embodiment, the box girder block 14 lifted by the lifting device 20 can be placed on a traveling trolley 43 and moved to a predetermined location by the traveling trolley 43. Furthermore, at the predetermined location, the support of the box girder block 14 is switched from the traveling trolley 43 to the support member 45, so the traveling trolley 43 can be repeatedly reused to move other box girder blocks 14. In addition, since no insert member is provided on the upper surface of the box girder block 14, deterioration of the upper surface of the box girder block 14 is suppressed.

[0045] This concludes the description of specific embodiments, but the present invention is not limited to the above embodiments or modifications and can be broadly modified and implemented.

[0046] For example, the box girder bridge 4 in the above embodiment is configured as a single box girder bridge in which the upper deck 5 and the lower deck 6 are connected by a pair of webs 7. In other embodiments, the box girder bridge 4 may be configured as a multi-girder box girder bridge having two or more box-shaped sections, or as a multi-tiered box girder bridge with continuous box-shaped sections, and so on.

[0047] In addition, the specific configuration, arrangement, quantity, materials, or construction procedures of each component or part can be modified as appropriate, as long as they do not depart from the spirit of the present invention. Furthermore, not all of the components shown in the above embodiments are necessarily essential, and can be selected as appropriate. [Explanation of symbols]

[0048] 4: Box girder bridge 5:Upper floor version 6: Lower floor version 7: Web 8: Rib 14: Box girder block 20: Lifting device 21: Connecting member 22: Lifting Unit 23: Beam 24: First support arm 25: Second support arm 26: 1st support piece 27:Second support piece 29: Through hole 30: Pin 31: Retaining member 33: Base component 34: Contact member 40: Erection platform 42: Rail 43: Running bogie 45: Support member

Claims

1. A lifting device for a box girder block comprising an upper deck, a lower deck and multiple webs, The box girder block is provided with a pair of lifting units that are spaced apart from each other in the direction perpendicular to the bridge axis and connected to each other by connecting members, Each of the aforementioned lifting units, A beam that is longer than the length of the upper deck in the bridge axis direction and is positioned above the upper deck along the bridge axis direction, A first support arm is provided at one end of the beam and has a first support piece at its lower end that supports the upper floor slab from below, A lifting device including a second support arm slidably provided on the other end of the beam and having a second support piece at its lower end for supporting the upper floor slab from below.

2. A pair of ribs extending in the direction perpendicular to the bridge axis or in the thickened portion of the web is formed on the lower surface of the upper deck slab. The lifting device according to claim 1, wherein the first support piece and the second support piece abut against the lower surface of the thickened portion or the lower surface of the rib.

3. The beam has a plurality of through holes formed therein, which are spaced apart in the longitudinal direction. The lifting device according to claim 1, wherein the second support arm is fixed to the beam by a pin that is inserted into and removed from the through hole.

4. The lifting device according to claim 1, wherein each of the lifting units further includes at least one pressing member that presses down on the upper floor slab from above.

5. The lifting device according to claim 4, wherein the pressing member comprises a base member provided on the beam and a contact member provided on the base member so as to be movable in the vertical direction and in contact with the upper surface of the upper floor slab.

6. A method for constructing a box girder bridge, which is constructed by connecting multiple box girder blocks arranged in the direction of the bridge axis, The steps include: positioning a support structure below the construction site of the box girder bridge; The steps include: installing a pair of rails extending in the direction of the bridge axis on the aforementioned erection frame, A step of installing a trolley on the aforementioned rail, A step of lifting the box girder block using the lifting device described in any one of claims 1 to 5, and placing the box girder block on the traveling carriage, The steps include: moving the trolley on which the box girder block is placed to a predetermined position above the erection frame; The steps include: placing a support member on the erection frame, and switching the support of the box girder block positioned at the predetermined location from the traveling trolley to the support member; The steps of repeating the steps from the step of placing the box girder block to the step of switching the support of the box girder block, A method for erecting a box girder bridge, comprising the step of connecting a plurality of box girder blocks supported at each of the predetermined positions.

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