JP7718704B2 - Scissor structure panel units, telescopic panels and panel-type scissor bridges - Google Patents

Description

The present invention relates to a scissor-structured panel unit suitable for use as a structural material for constructing structures such as temporary bridges, a telescopic panel constructed by connecting the panel units lengthwise and widthwise, and a panel-type scissors bridge constructed using the telescopic panels as bridge structural materials.

The inventors have previously researched and developed temporary bridges (single-stage scissors) that use a scissors mechanism, a type of deployable structure, to serve as alternatives to small bridges washed away by disasters (see Non-Patent Documents 1 and 2, bottom left of Figure 7). Furthermore, by adopting hanging scissors that also use cables, the inventors have demonstrated the possibility of enlarging the size of scissors bridges (see top right of Figure 7).

A scissors structure is a structure in which a pair of links arranged in an X-shape can be opened and closed around a pin joint formed at the intersection, and a bridge is constructed using a single-stage scissors configuration in which these are arranged in a linear row. The components of a scissors structure can be transported to the temporary bridge installation site in a folded (contracted) state in the material axis direction, and then unfolded (extended) in the material axis direction at the installation site, making them easy to transport and easy to construct. Telescopic bridges with such a scissors structure are proposed, for example, in Patent Documents 1 and 2.

K. Chanthamanivong, I. Ario, Y. Chikahiro: Smart design of coupling scissors-type bridge, Structures, 30, 206-216, 2021. Y. Chikahiro, I. Ario, P. Pawlowski C. Graczykowski, J. Holnicki-Szulc: Optimization of reinforcement layout of scissor type bridge using differential evolution algorithm, Computer-Aided Civil and Infrastructure Engineering, 34(6), 523-538, 2019.

JP 2014-145203 A International Publication No. 2015/193930

There is a need for temporary bridges that can be quickly restored, even for medium-sized bridges that are constantly subject to washout damage. Even in the case of temporary bridges for medium-sized bridges, reducing the amount of bridge components transported and assembly work required on-site is important in order to quickly erect the temporary bridge during the initial response after a disaster. For this reason, it is possible to use scissors-structured bridges for temporary bridges for medium-sized bridges, which have not been the subject of previous research.

As shown in Figure 7, scissors structures can be applied to small bridges by arranging them in a straight line, and can be made larger, like suspension bridges, by using them in combination with cables. However, applying them to medium-sized bridges is difficult from the perspective of ease of construction and strength. For example, as a structural material for a temporary bridge made up of scissors structures, it is possible to ensure the necessary strength by using multi-stage scissors, in which scissors structures are arranged not only horizontally but also vertically. However, simply increasing the number of stages in the scissors structure increases the material used, the weight, and manufacturing costs. Furthermore, it also reduces the ease of construction when unfolding the heavy multi-stage scissors structure components at the installation site and installing the bridge.

This issue arises not only when multi-scissor structure members are used as bridge structural materials, but also when multi-scissor structure members are used to increase the strength of structural members such as beams and girders used in building structures.

In light of these points, the object of the present invention is to provide a scissors-structured panel unit that is stronger and allows for longer spans than members with a single-stage scissors structure, and that is lighter and easier to install while suppressing a decrease in strength compared to members with a multi-stage scissors structure, as well as an expandable panel constructed by connecting such panel units vertically and horizontally.

Another object of the present invention is to provide a panel-type scissors bridge, a medium-sized temporary bridge that can be easily constructed by a small number of people by deploying such expandable panels at the disaster site and assembling several of them on-site (see Figure 7).

In order to solve the above problems, the panel unit of the scissors structure of the present invention comprises:
It has a rectangular frame with a scissors structure that can be stretched vertically and horizontally,
The four sides of the rectangular frame are defined by left and right vertical frame members and top and bottom horizontal frame members,
Each of the vertical frame members and the horizontal frame members includes a plurality of sets of unit scissors linearly arranged in one direction,
the unit scissors includes a pair of links arranged crossing in an X shape along a pair of diagonal lines of the rectangular frame, and intersections of these links are connected to each other to form intersection pin joints;
Between a pair of adjacently arranged unit scissors in the vertical frame member and the horizontal frame member, the ends of the links inclined in opposite directions are connected to each other to form outer peripheral edge side pin nodes arranged along the outer peripheral edge of the rectangular frame and inner peripheral edge side pin nodes arranged along the inner peripheral edge of the rectangular frame,
The unit scissors located at each of the four corners of the rectangular frame are characterized by being common unit scissors that serve both as the unit scissors located at the ends of the vertical frame material and as the unit scissors located at the ends of the horizontal frame material.

The panel unit of the present invention can be a double-panel unit or a multiple-panel unit in which rectangular frames of the above configuration are connected vertically or horizontally. For example, a panel unit is made up of multiple sets of rectangular frames connected horizontally. In this case, the rectangular frames are connected to each other so that the vertical frame member located between adjacent rectangular frames connected horizontally serves as both the vertical frame member of one rectangular frame and the vertical frame member of the other rectangular frame.

Furthermore, in the panel unit of the present invention, it is desirable that a diagonal member be attached to the rectangular frame. The diagonal member is bridged between links extending in the diagonal direction of at least one pair of unit scissors located at both ends of the rectangular frame in that diagonal direction.

It is desirable to connect the diagonal member to the links across which it spans so that it is positioned on the same plane as those links. In this case, the diagonal member and the pair of links across which it spans can be integrated and arranged as a single member.

In addition, the scissors-structured stretchable panel of the present invention is
Let m and n be positive integers of 1 or more.
The panel unit has m×n sets of panel units connected in a plane direction to form m rows and n columns,
The panel unit is characterized by being a panel unit with the above-described scissors structure.
In this case, between a pair of adjacent panel units, the outer edge side pin node on one panel unit side and the outer edge side pin node on the other panel unit side are each connected or integrated with each other to form a common pin node.

Next, the panel-type scissors bridge of the present invention is characterized in that the telescopic panels having the above-described configuration are arranged as bridge structural materials.

In this invention, instead of the conventional linearly arranged scissors structure (single-stage scissors) used in beam structures, a telescopic panel is constructed using panel units with a scissors structure that takes into account the upper chord, lower chord, and diagonal members of a truss structure. This appropriately distributes the load generated in each part, increasing strength and allowing for longer spans compared to single-stage scissors structure members, while also minimizing the decline in strength compared to multi-stage scissors structure members, reducing weight and improving workability. Pre-assembled telescopic panels can be deployed at the disaster site, and several of them can be combined on site to construct panel-type bridge members. This makes it possible to easily construct medium-sized temporary bridges with a small number of people.

1A is a front view of a panel unit, (b1) and (b2) are front and side views of unit scissors that constitute the panel unit, and (c) is an explanatory diagram showing the expansion and contraction operation of the panel unit. (a1) and (a2) are a front view and a partially enlarged view of a telescopic panel with one row and six columns, (b) is a front view of a telescopic panel with two rows and six columns, and (c) is an explanatory diagram showing an example of a panel-type scissors bridge using telescopic panels as bridge beams. (a1) and (a2) are front and side views of a rectangular frame without diagonal members, (b1) and (b2) are front and side views of a rectangular frame with one diagonal member arranged within the link plane, (c1) and (c2) are front and side views of a rectangular frame with one diagonal member arranged outside the link plane, (d1) and (d2) are front and side views of a rectangular frame with two diagonal members arranged within the link plane, and (e1) and (e2) are front and side views of a rectangular frame with two diagonal members arranged outside the link plane. (a) is a front view of a double panel unit, (b) is a front view of an expandable panel with one row and three columns made up of double panel units, and (c) is a front view of an expandable panel with two rows and three columns made up of double panel units. 10A to 10F are front views of models 1 to 6 to be analyzed in analysis 1. 10 is a graph showing the stress-strain relationship of a link member given in the analysis. This is an explanatory diagram showing the boundary conditions and loading positions of the analysis model in Analysis 1 (assuming a through-type scissors bridge after construction). 10 is a graph showing the relationship between mass and stiffness of each model obtained in analysis 1. 10 is a graph showing the relationship between the mass and the maximum bending moment, the relationship between the mass and the maximum tensile force, and the relationship between the mass and the maximum compressive force of each model obtained in Analysis 1. 10A to 10F are front views of models 1' to 6' that are the analysis targets in analysis 2. This is an explanatory diagram showing the boundary conditions and loading positions of the analysis model in Analysis 2 (assuming a through-type scissors bridge after construction). 10 is a graph showing the relationship between mass and stiffness of each model obtained in analysis 2. 10 is a graph showing the relationship between the mass and the maximum bending moment, the relationship between the mass and the maximum tensile force, and the relationship between the mass and the maximum compressive force of each model obtained in Analysis 2. FIG. 1 is an explanatory diagram showing the positioning of a panel-type scissors bridge to which the present invention is applied.

Embodiments of the present invention will be described below with reference to the drawings. Note that the embodiments are merely examples of the present invention and are not intended to limit the present invention to the embodiments.

(Panel unit)
1(a) is a front view showing an example of a panel unit with a scissors structure according to the present invention. Note that the vertical direction Y and the horizontal direction X in the following description are given for convenience, and these directions may be any two directions that are perpendicular to each other. When used as a bridge structural material or the like, the panel unit 1 is used in an upright position facing vertically.

The panel unit 1 is composed of a rectangular frame 2 with a scissors structure that can expand and contract in two perpendicular directions: the vertical direction Y and the horizontal direction X. A pair of diagonal members 3A, 3B is strung across the rectangular frame 2 in an X-shape along each of its diagonals. The rectangular frame 2 is defined by a pair of vertical frame members 4A, 4B that define the left and right sides of the rectangular frame 2, and a pair of horizontal frame members 5A, 5B that define the top and bottom sides of the rectangular frame 2. Each of the vertical frame members 4A, 4B is composed of multiple sets of unit scissors 6 connected in a row in the vertical direction Y, five sets in this example. Similarly, each of the horizontal frame members 5A, 5B is composed of multiple sets of unit scissors 6 connected in a row in the horizontal direction X, five sets in this example.

The vertical frame members 4A and 4B on the left and right sides of the rectangular frame 2 have the same shape and structure, and in the following explanation, when there is no need to distinguish between them, they will be referred to as vertical frame members 4. Similarly, the horizontal frame members 5A and 5B on the top and bottom have the same shape and structure, and when there is no need to distinguish between them, they will be referred to as horizontal frame members 5.

Figures 1(b1) and (b2) are a front view and a side view showing unit scissors 6 that make up vertical frame member 4 and horizontal frame member 5. Unit scissors 6 includes a first link 7 and a second link 8 that are arranged in an X-shaped cross-section along a pair of diagonal lines of rectangular frame 2. At their intersections, the first and second links 7 and 8 are connected in a manner that allows them to rotate around a hinge pin that defines intersection pin node 9. In this example, the first and second links 7 and 8 are straight members of the same length and cross section, and are made of, for example, steel, aluminum alloy, or the like with a hollow cross section or a channel cross section.

In each of the vertical frame members 4 and horizontal frame members 5, one of a pair of unit scissors 6 arranged adjacently along the vertical direction Y or horizontal direction X, as indicated by the arrows in the figure, is designated as the front unit scissors, and the other as the rear unit scissors. For example, in Figure 1(b1), the unit scissors 6 indicated by the solid lines is designated as the front unit scissors, and the unit scissors 6 adjacent to it indicated by the imaginary lines is designated as the rear unit scissors. The rear end 7b of the first link 7 of the front unit scissors 6 and the front end 8a of the second link 8 of the rear unit scissors 6, which is inclined in the opposite direction, are rotatably connected via a hinge pin that defines a first pin joint 11. Furthermore, the rear end 8b of the second link 8 of the front unit scissors 6 and the front end 7a of the first link 7 of the rear unit scissors 6 are rotatably connected via a hinge pin that defines a second pin joint 12. In this way, in the rectangular frame 2 defined by the vertical frame members 4 and horizontal frame members 5 obtained by connecting the unit scissors 6, as shown in Figure 1(a), the ends of the first and second links 7 and 8, which are inclined in opposite directions, are connected to each other, and one of the first and second pin nodes 11 and 12 is arranged as an outer edge side pin node along the outer periphery of the rectangular frame, and the other of the first and second pin nodes 11 and 12 is arranged as an inner edge side pin node along the inner periphery of the rectangular frame. Also, at each of the four corners of the rectangular frame 2, the unit scissors 6 located at the top and bottom ends of the vertical frame members 4 in the vertical direction Y are arranged as unit scissors that also serve as unit scissors 6 located at the left and right ends of the horizontal frame members 5 in the horizontal direction X.

(Diagonal member: in-plane arrangement)
Next, the pair of diagonal members 3A, 3B attached to the rectangular frame 2 are arranged as follows in this example. The diagonal member 3A is spanned between the first link 7 of the unit scissors 6 located in the upper left corner of the rectangular frame 2 and the first link 7 of the unit scissors 6 located in the lower right corner of the rectangular frame 2. In this example, the diagonal member 3A is arranged so as to be located on the same vertical plane as the first link 7 (in-plane arrangement of diagonal members). For example, the diagonal member 3A and both first links 7 are arranged as a single member extending linearly. The other diagonal member 3B is spanned between the second link 8 of the unit scissors 6 located in the upper right corner of the rectangular frame 2 and the second link 8 of the unit scissors 6 located in the lower left corner of the rectangular frame 2. The diagonal member 3B is also arranged so as to be located on the same vertical plane as the second link 8 (in-plane arrangement of diagonal members). For example, the diagonal member 3B and both second links 8 are arranged as a single member extending linearly. In this example, the diagonal members 3A and 3B have a pin joint 13 formed at the central intersection point in the material axis direction (the center of the rectangular frame 2), and are connected in a state where they can rotate around this center, ensuring rigidity in the out-of-plane direction.

As shown in Figure 1(c), the rectangular panel unit 1, with its square state considered to be its neutral state, can expand and contract from the neutral state to a vertically elongated state stretched in the vertical direction Y and a horizontally elongated state stretched in the horizontal direction X. The first and second links 7 and 8 of the unit scissors 6, which are connected via the first and second pin joints 11 and 12, respectively, open and close around the intersection pin joint 9 while maintaining an orientation facing in a direction along a pair of diagonals of the rectangular frame 2 of the panel unit 1. This allows the rectangular panel unit 1 as a whole to expand and contract in the vertical direction Y and the horizontal direction X.

(stretchable panel)
Fig. 2(a1) is an explanatory diagram showing a telescopic panel 20 formed by connecting six panel units 1 of the above-described configuration in a planar direction. In the telescopic panel 20, a pair of adjacent panel units 1 are connected in the horizontal direction X, which is the panel unit arrangement direction. As shown in an enlarged view in Fig. 2(a2), if one panel unit 1 is panel unit 1A and the other is panel unit 1B, each of the four first pin nodes 11 on the rectangular frame outer periphery of the rear vertical frame member 4B of panel unit 1A is coaxially connected to each of the four second pin nodes 12 on the front vertical frame member 4A of the other panel unit 1B adjacent to the vertical frame member 4B, thereby forming four common unit connection pin nodes. In other words, between a pair of horizontally adjacent panel units 1A and 1B, the first pin node 11, which is the pin node on the outer edge of the vertical frame material 4B of one panel unit 1A, and the second pin node 12, which is the pin node on the outer edge of the vertical frame material 4A of the other panel unit 1B, are each connected or integrated with each other to form a common pin node.

Furthermore, at the upper ends of the vertical frame members 4A and 4B, the upper end of the second link 8 of the vertical frame member 4B and the upper end of the first link 7 of the vertical frame member 4A are connected via a common unit connection pin joint 14. Furthermore, at the lower ends of the vertical frame members 4A and 4B, the lower end of the first link 7 of the vertical frame member 4B and the lower end of the second link 8 of the vertical frame member 4A are connected via a common unit connection pin joint 14.

In a similar manner, an expandable panel can be constructed by connecting panel units 1 in a row in the vertical direction Y. Although not shown in the figures, in this case, a pair of adjacent panel units 1 in the vertical direction Y are connected via unit connection pin nodes as follows: Each of the four first pin nodes 11 on the outer periphery of the rectangular frame of the horizontal frame member 5B of the upper panel unit 1 is connected to each of the four second pin nodes 12 on the outer periphery of the rectangular frame of the upper vertical frame member 5A of the panel unit 1 adjacent to the lower side of that horizontal frame member 5B, thereby defining four unit connection pin nodes. Furthermore, at the left ends of the horizontal frame members 5A and 5B, the lower end of the second link 8 of the horizontal frame member 5B is coaxially connected to the upper end of the first link 7 of the horizontal frame member 5A, forming a unit connection pin node. At the right ends of the horizontal frame members 5A and 5B, the lower end of the first link 7 of the upper horizontal frame member 5B and the upper end of the second link 8 of the lower horizontal frame member 5A are coaxially connected to form a unit connection pin joint.

Figure 2(b) is an explanatory diagram showing an example of a telescopic panel constructed by connecting panel units 1 vertically and horizontally. The telescopic panel 30 shown in this figure is a two-tiered, six-column telescopic panel, with two panel units 1 connected vertically and six connected horizontally. A telescopic panel 30 of this configuration is used, for example, as a bridge structural material for constructing a medium-sized temporary bridge.

(Panel-type scissors bridge)
Figure 2(c) is a conceptual diagram showing an example of a medium-sized panel-type scissors bridge constructed using expandable panels as bridge structural materials. The panel-type scissors bridge 40 shown in this figure is constructed by connecting the left and right bridge girders spanning between abutments (not shown) installed on opposite banks of a river or the like, using the expandable panels 30 shown in Figure 2(b). A deck slab 41 is placed between the left and right expandable panels 30, which are arranged parallel to each other in a vertical position with a certain distance between them.

In order to quickly erect temporary bridges during the initial response after a disaster, it is important to reduce the amount of bridge components transported and the amount of assembly work required at the site. By using the expandable panels 30 (foldable panels) configured as described above, pre-assembled expandable panels 30 can be deployed at the disaster site and several of them can be combined on-site, making it possible to easily construct a temporary bridge with a small number of people.

In this example, to create a medium-sized temporary bridge, the scissors structure, which has traditionally been arranged in a straight line like a beam structure, is replaced with a truss structure-like arrangement that takes into account the upper chord, lower chord, and diagonal members. This effectively distributes the load on each component of the panel-type scissors bridge 40, making it possible to achieve a longer span. Another feature is that the panel units 1 that make up the expandable panel 30 are hollowed-out rectangular frames rather than multi-stage scissors structure panels, thereby reducing the weight of the expandable panel 30 while minimizing the loss of strength compared to multi-stage scissors structure panels. The use of the expandable panel 30 in this example makes it possible to address medium-sized bridges, which have previously been considered difficult to restore in an emergency after a disaster, and is expected to contribute to addressing disaster prevention issues such as the isolation of settlements after a disaster and regional reconstruction.

(Examples of modified panel units and expandable panels)
Figure 3 shows a modified example of the panel unit 1. Figures 3(a1) and (a2) show a panel unit 1A consisting of a rectangular frame 2 without diagonal members 3A and 3B. Figures 3(b1) and (b2) show a panel unit 1B (in-plane arrangement) in which one diagonal member 3 is arranged in the same plane as the link, while Figures 3(c1) and (c2) show a panel unit 1C (out-of-plane arrangement) in which one diagonal member 3 is not in the same plane as the link. Figures 3(d1) and (d2) show a panel unit 1D (in-plane arrangement) in which two diagonal members are arranged in the same plane as the link, while Figures 3(e1) and (e2) show a panel unit 1E (out-of-plane arrangement) in which two diagonal members are not in the same plane as the link. These panel units can be selected and used depending on the strength and weight restrictions required for the telescopic panel.

Figure 4(a) shows yet another example of a panel unit. The panel unit 1A shown in this figure is a double panel unit made by connecting two sets of the above-mentioned rectangular panel units 1. The double panel unit 1A is configured so that when the above-mentioned rectangular panel units 1 are lined up, adjacent vertical frame members 4 or horizontal frame members 5 form a single common frame member. In the figure, the vertical frame member 4 is shown as a common vertical frame member 4C. In a similar manner, multiple panel units such as a triple panel unit can be constructed.

Extendable panels are constructed by connecting multiple panel units 1A vertically and horizontally as basic units. For example, as shown in Figure 4(b), three double-panel units 1A are connected horizontally to construct an extendable panel 20A with one row and three columns. Also, as shown in Figure 4(c), two double-panel units 1A are connected vertically and three horizontally to construct an extendable panel 30A with two rows and three columns.

[Analysis example]
The inventors conducted FEM analysis of the load-bearing capacity of the scissors-structured telescopic panel (folding panel) and the multi-stage scissors-structured panel of the present invention. In particular, they investigated the influence on the load-bearing capacity of the rectangular frame-shaped panel unit in comparison with the multi-stage scissors-structured panel. An example of the analysis conducted by the inventors is described below.

<Analysis 1: Load-bearing capacity of the expandable panel (one double panel unit)>
(Analysis model)
The analysis object is shown in Figure 5.1. Model 1 is a panel unit with a five-row, nine-column multi-scissor structure, used for comparison with Models 2 to 6, which are double-panel units according to the present invention. All models are 1,800 mm long and 1,000 mm high. Model 2 connects two square panel units with five rows and five columns, each with vertical and horizontal frames made up of five sets of 200 mm x 200 mm unit scissors, and shares adjacent vertical frames (vertical members). Model 3 adds two diagonal members by extending and connecting the links at a pair of corners of Model 2. Model 5 similarly adds four diagonal members, two each in an X-shape. Furthermore, Models 4 and 6 are structures in which the diagonal members of Models 3 and 5 are attached out of plane to reinforce Model 2.

All members (links) were created using beam elements. At each of the member intersections and hinges (pin nodes) at the member connection points, constraints were imposed to ensure that the displacement of both intersecting members was equal and that bending moments were not transmitted. The mass, number of members, number of hinges, number of nodes, and number of elements for each model are shown in Table 1.1. The members were hollow members with a width of 30 mm, height of 70 mm, and thickness of 2 mm. The cross-sectional area of this member was A = 384 ^mm2 , and the second moment of area was I = 2.35 x ^{105 mm4} .

(Material properties)
The material used for the components was assumed to be aluminum alloy A6063, with Young's modulus E = 62.5 GPa, Poisson's ratio ν = 0.31, and density ρ = 2.71 g/cm ^3. Taking into account the nonlinearity of the material, a bilinear stress-strain relationship was applied with a yield stress σ _y = 216.0 MPa, as shown in Figure 5.2.

<Boundary conditions>
As shown in Figure 5.3, boundary conditions were applied assuming a through-type scissors bridge after construction. Here, out-of-plane displacement was restrained at all nodes to prevent lateral collapse in the out-of-plane direction. All models were in a pin-support state at both ends, and a concentrated load of up to 50 kN was applied to the lower hinge in the center of the panel unit at each of the two intersecting points, assuming a live load applied to the center. This load was applied monotonically with a time step of 0.001 s, so that a total of 100 kN was applied at t = 1.0 s.

(Analysis results/discussion)
The end time of the analysis and the load at that time are shown in Table 1.2. Model 1 completed the analysis up to t = 1.0 s, while the analysis for the other models was interrupted at a load of around 30 kN. Only Model 2, which does not have diagonal members, did not reach a load of 30 kN, confirming the effectiveness of the diagonal members.

(Load-displacement curve)
Load-displacement curves were created at the loading positions of models 1, 2, 3, and 5. The load-displacement curves of all models clearly showed elastic and nonlinear regions.
Regarding the yielding condition of the members, Table 1.3 shows the load and displacement at the time of member yielding.
When calculating the percentage of load for each shape based on Model 1, it was 43% for Model 2, 51% for Model 3, and 68% for Model 5. The load to yield tends to increase as the number of diagonal members increases, and Model 5 had the best load-bearing performance, excluding Model 1.

Looking at the displacement under a constant load, for example, the displacement at a load of 5.0 kN, which is in the elastic range, is, in order from smallest to largest, Models 1, 6, 5, 4, 3, and 2. This is also the order of greatest rigidity, and the relationship between rigidity and mass is shown in Figure 5.4. In this regard, Models 3 and 5 are aligned on the line connecting the reference Models 1 and 2, suggesting a proportional relationship, but Models 4 and 6, which have diagonal members attached out-of-plane, are 8% and 12% lower, respectively, from the line.

(bending moment/axial force)
Table 1.4 shows the maximum values of bending moment and axial force for each model, and Figure 5.5 shows the relationship between mass and maximum bending moment/axial force.

Model 2 was the largest in all bending moments, tension forces, and compression forces.
Models 3 to 6 with diagonal members are compared with Model 1 for examination.
Model 5 had the next smallest values for both bending moment and tensile force after Model 1, but the bending moment was 68% and the tensile force was 21%, both of which were larger than Model 1.
Focusing on the bending moment, Model 5 and Model 6 also have relatively small values, but as can be seen from the relationship between mass and maximum bending moment shown in Figure 5.5(a), Model 6 has not been able to be made lighter efficiently. From a similar perspective, it can be seen that Models 3 and 5 were able to be made lighter relatively efficiently.
In the relationship between mass and maximum and minimum axial forces shown in Figures 5.5(b) and (c), model 5 was the most efficient at reducing weight in terms of tensile force, and models 3 to 6 were the most efficient at reducing weight in terms of compressive force. Therefore, excluding model 1, model 5 can be said to be the most advantageous shape overall.

<Analysis 2: Load-bearing capacity of the expansion panel (four double panel units)>
(Analysis model)
In Analysis 2, four double panel units defined in Analysis 1 were connected in the bridge axis direction to clarify their load-bearing capacity. Models 1' to 6', each 5,400 mm long and 1,000 mm high, were created by connecting four of Models 1 to 6 from Analysis 1. These are shown in Figure 6.1. All adjacent nodes were connected using hinges (pin nodes). The mass, number of members, number of hinges, number of nodes, and number of elements for each model are shown in Table 2.1.

As with Analysis 1, the boundary conditions assumed all models were pin-supported at both ends, with a live load applied at the center. A concentrated load of up to 10 kN was applied to the lower hinge connecting the second and third panels of the double-panel unit, at each of the two intersecting points. This load was applied monotonically with a time step of 0.001 s, so that a total of 20 kN was applied at t = 1.0 s. This is shown in Figure 6.2. In addition, to prevent lateral collapse in the out-of-plane direction, displacement in the out-of-plane direction was restrained.

(Analysis results/discussion)
The end time of the analysis and the load at the end time are shown in Table 2.2. Model 6' completed up to t = 1.0 s, while the analysis of the other models was suspended. Comparing the number and shape of diagonal members, the load at the end was relatively large for the model with four diagonal members, followed by the model with two diagonal members, which underwent a longer analysis.

(Load-displacement curve)
Load-displacement curves were created for the loading positions of models 1', 2', 3', and 5'.
Regarding the yielding status of the members, Table 2.3 shows the load and displacement at member yielding. All models yielded within the elastic region and immediately thereafter began to exhibit nonlinear behavior. The load at member yielding for each shape was almost the same, and when the load ratio for each shape was calculated based on Model 1', it was 29% for Model 2', 34% for Model 3', and 44% for Model 5'. These ratios were inferior to the case of a single double-panel unit.
As the number of diagonal members increases, the load until yielding tends to increase, and there was no change in the fact that Model 5' had the best load-bearing performance, except for Model 1.

Focus on the displacement under a constant load. For example, the displacement at a load of 5.0 kN, where all models are in the elastic range, is, in order from smallest to largest, Models 1', 6', 5', 4', 3', and 2'. This is also the order of greatest rigidity, and the relationship between rigidity and mass is shown in Figure 6.3. As an auxiliary line, a straight line connecting the reference Models 1' and 2' has been added. The relationship between mass and rigidity shows the same trend as for a single double-panel unit, with Models 4' and 6' showing low rigidity relative to their mass.

(bending moment/axial force)
The maximum bending moment and the maximum and minimum axial force are shown in Table 2.4.

Model 2' had the highest bending moment and tensile force, while Model 4' had the highest compressive force. Model 1' also had the lowest values in both cases.

Models 3' to 6' with diagonal members are compared with Model 1'.
Models 6' and 5' had the next smallest values for bending moment, tensile force, and compressive force after Model 1', but their bending moment was 130%, tensile force was 23%, and compressive force was 151% greater than Model 1'.
Focusing on the bending moment, Model 6' and Model 5' also have relatively small values, but as can be seen from the relationship between mass and maximum bending moment shown in Figure 6.4 (a), Model 6' has not been able to be made lighter efficiently. From the same perspective, it can be seen that Models 3' and 5' have been able to be made lighter relatively efficiently. This is the same as the result for a single panel.
Figures 6.4(b) and (c) show the relationship between mass and maximum tensile and compressive forces. Looking at tensile force, all models were successfully lightweighted, with model 5' in particular showing a large reduction in tensile force relative to mass.
However, from the viewpoint of compressive force, it can be seen that none of the models were successful in reducing weight. Models 3' and 4' even had larger maximum values than Model 2', which had no diagonal members.
With the exception of Model 1', Model 5' was found to be superior overall. Of the models considered in this analysis, Model 5' can be said to have the most appropriate shape.

1, 1B, 1C, 1D, 1E Panel unit 1A Double panel unit 2 Rectangular frame 3A, 3B Diagonal members 4, 4A, 4B, 4C Vertical frame members 5, 5A, 5B Horizontal frame members 6 Unit scissors 7 First link 7a Front end 7b Rear end 8 Second link 8a Front end 8b Rear end 9 Intersection pin joint 11 First pin joint 12 Second pin joint 13 Pin joint 14 Unit connection pin joint 20, 20A, 30, 30A Telescopic panel 40 Panel-type scissors bridge 41 Deck X Horizontal direction Y Vertical direction

Claims (6)

It has a rectangular frame with a scissors structure that can be stretched vertically and horizontally,
The four sides of the rectangular frame are defined by left and right vertical frame members and top and bottom horizontal frame members,
Each of the vertical frame members and the horizontal frame members includes a plurality of sets of unit scissors linearly arranged in one direction,
the unit scissors includes a pair of links arranged crossing in an X shape along a pair of diagonal lines of the rectangular frame, and intersections of these links are connected to each other to form intersection pin joints;
Between a pair of adjacently arranged unit scissors in the vertical frame member and the horizontal frame member, the ends of the links inclined in opposite directions are connected to each other to form outer peripheral edge side pin nodes arranged along the outer peripheral edge of the rectangular frame and inner peripheral edge side pin nodes arranged along the inner peripheral edge of the rectangular frame,
The unit scissors located at each of the four corners of the rectangular frame are common unit scissors that serve as both the unit scissors located at the ends of the vertical frame members and the unit scissors located at the ends of the horizontal frame members, in a panel unit with a scissors structure. In claim 1,
The rectangular frame is provided with a plurality of sets connected in the horizontal direction,
A panel unit with a scissors structure in which the rectangular frames are interconnected so that the vertical frame material located between adjacent rectangular frames becomes a common vertical frame material that serves as both the vertical frame material of one of the rectangular frames and the vertical frame material of the other rectangular frame. In claim 1 or 2, further comprising:
A diagonal member is attached to the rectangular frame,
The diagonal member is a panel unit having a scissors structure that is spanned between the links extending in the diagonal direction of a pair of unit scissors located at both ends of at least one diagonal direction of the rectangular frame. In claim 3,
The diagonal member is a panel unit of a scissors structure that is located on the same plane as the link of the unit scissors across which the diagonal member is spanned. Let m and n be positive integers of 1 or more.
The panel unit has m×n sets of panel units connected in a plane direction to form m rows and n columns,
The panel unit is a panel unit having a scissors structure according to any one of claims 1 to 4,
Between a pair of adjacent panel units, the outer edge side pin node on one panel unit and the outer edge side pin node on the other panel unit are connected or integrated with each other to form a common pin node, in an expandable panel with a scissors structure. A panel-type scissors bridge, characterized in that the expandable panel described in claim 5 is arranged as a bridge structural material.