Large-cantilever viaduct pier based on ficus microcarpa bionics and design method thereof

Abstract

The invention discloses a large cantilever viaduct pier based on ficus microcarpa bionics and a design method thereof.The large cantilever viaduct pier comprises a pier body, supporting columns, plate supports and torsion bars, and the supporting columns are annularly and evenly distributed on the periphery of the pier body and arranged parallel to the pier body to assist the pier body in bearing bending moment; the plate supports are evenly arranged on the periphery of the bridge pier body, obliquely connected between the bridge pier body and the ground and used for assisting the bridge pier body to bear shearing force, and each plate support comprises a plate support round rod and a web plate welded to the lower portion of the plate support round rod. The torsion bars are evenly arranged on the periphery of the bridge pier body, connected between the bridge pier body and the ground and used for assisting the bridge pier to bear torque, in a top view, the extension lines of the plate supporting round bars should pass through the axis of the bridge pier, and the extension lines of the torsion bars penetrate through the interior of the section of the bridge pier and do not intersect with the axis. The anti-seismic problem of the large-cantilever single-column pier is expected to be solved, and the large-cantilever single-column pier is safe and reliable like a ficus microcarpa.

Description

Technical Field

[0001] The present invention belongs to the technical field of seismic design in civil engineering, and particularly relates to a large cantilever elevated bridge pier based on bionic banyan tree and its design method. Background Art

[0002] With the rapid increase of urban population, higher requirements are put forward for overpasses, that is, the smaller the space occupied by their piers, the better, and the more lanes on the bridge deck, the better. Under this background, single-column large cantilevers are increasingly used in urban overpasses. Such overpasses can better meet the stress performance requirements under dead load and vehicle load. However, due to its top-heavy and bottom-light characteristics, it is prone to be damaged under the action of earthquake along the transverse direction of the bridge.

[0003] To solve this problem, engineers, experts and scholars have proposed single-column piers with a wider transverse width, transverse double-column piers with a small spacing, and rocking piers, etc. Compared with ordinary piers, wide single-column piers have poor bending and rotating ability and shear resistance in the transverse direction of the bridge. Under transverse earthquake, short piers are prone to shear failure, and tall piers may crack or be crushed under a small earthquake. Small-spacing double-column piers are a better solution for urban elevated bridge piers. However, due to the close distance between their bearings, the main girder is prone to overturning.

[0004] Rocking piers are a novel mode proposed by experts and scholars in recent years. Its main idea is to isolate the vibration of the pier and the foundation through a rocking interface, thereby reducing the transfer of the inertial force of the main girder to the bottom of the pier. On the other hand, concentrating the cracking at the rocking interface can effectively reduce the damage of the pier. However, the scholars mainly studied its bending resistance problem. Its main problem is that the connection between the pier and the foundation is weakened, and there is no clear transmission path for the transfer of bending moment, shear force and torque between the pier and the foundation. Under actual earthquake action, although there is no problem with bending resistance, whether there will be shear resistance or torsion resistance problems is the main challenge faced by its popularization and application. Summary of the Invention

[0005] Aiming at the defects existing in the above-mentioned prior art, the present invention proposes a large cantilever elevated bridge pier based on bionic banyan tree and its design method. The stress system of the bionic banyan tree is reasonable, the force transmission path is clear, the trunk resists pressure, the prop roots mainly resist bending moment, the buttress roots resist shear force, and the twining roots resist torque. The present invention uses the main pier to resist compression, uses the prop to resist bending, uses the plate brace to resist shear, and uses the torsion bar to resist torsion. When there are clear force transmission paths and resistance mechanisms for various structural internal forces, it is expected to solve the seismic problem of large cantilever single-column piers and make them as safe and reliable as banyan trees.

[0006] The above object is achieved by the following technical solutions:

[0007] A large cantilever elevated bridge pier based on banyan tree bionics, comprising a pier main body, struts, plate braces and torsion bars, wherein:

[0008] The struts are evenly distributed in a ring around the periphery of the pier main body and are arranged parallel to the pier main body to assist the pier main body in bearing bending moments;

[0009] The plate braces are evenly arranged around the periphery of the pier main body and are obliquely connected between the pier main body and the ground to assist the pier main body in bearing shear forces. The plate braces include plate brace round bars and webs welded below the plate brace round bars. The angle between the plate brace round bars and the ground is α c , α c ∈[35°, 50°];

[0010] The torsion bars are evenly arranged around the periphery of the pier main body and are connected between the pier main body and the ground to assist the pier in bearing torques. The angle between the torsion bars and the ground is α n , α n ∈[55°, 70°];

[0011] There are 8 or more struts and plate braces, and 4 or more torsion bars. In a top view, the extension lines of the plate braces should pass through the axis of the pier, and the extension lines of the torsion bars pass through the inside of the pier cross-section and do not intersect the axis.

[0012] Furthermore, the pier main body adopts a columnar pier main body or a tree-trunk-shaped pier main body.

[0013] Furthermore, the plate braces and the torsion bars are connected to the pier by welding. The distances from the bottoms of the struts, the plate brace round bars, and the torsion bars to the bottom of the pier are within 1.5 times the diameter of the pier.

[0014] The design method of the above large cantilever elevated bridge pier based on banyan tree bionics is as follows:

[0015] S1. Determine the distances between the bottoms of the struts, the plate brace round bars, and the torsion bars and the center of the pier according to the installation position. The distances from the bottoms of the struts, the plate brace round bars, and the torsion bars to the bottom of the pier are within 1.5 times the diameter of the pier;

[0016] S2. Determine the angles between the plate brace round bars and the torsion bars and the ground;

[0017] S3. Determine the cross-sectional areas of a single strut, a plate brace round bar, and a torsion bar. The specific method is as follows:

[0018] Let the distance between the center of the bottom end of the strut and the rotation center of the pier main body be d, the heights of the pier main body and the strut be h, establish a coordinate system with the rotation center of the pier under external forces as the origin, and the angle between the line connecting the vertex of the strut and the origin and the y-axis be α, Under the action of an external force, when the system composed of the pier main body, the strut, the plate bracing round bar, and the torsion bar rotates by an angle θ around the origin z After that, the strut will undergo a deformation Δl z , and the vertex coordinates of the strut after deformation are The length l′ of the strut on the stretched side after deformation zL is:

[0019]

[0020] The included angle between the line connecting the center of the strut and the center of the pier main body and the direction of the bending moment is between 67.5° and 112.5°. Considering it as on one side, the strain ε of the single-sided strut zi is:

[0021]

[0022] From this, the stress σ of the single-sided strut zi is:

[0023] σ zi = k z ·ε zi (3)

[0024] In the formula, k z is the elastic coefficient of the material used for the strut;

[0025] Assume that the bending moment borne by the system is M. According to formula (4), the minimum cross-sectional area A required for the single-sided strut can be designed zmin :

[0026] σ zi A z min d = M (4)

[0027] Let the included angle between the plate bracing round bar and the ground be α c , the length of the plate bracing round bar be l c , the projection length of the plate bracing round bar in the horizontal direction be d c , and the projection length in the vertical direction be h c , then When the pier cross-section where the vertex of the plate bracing round bar is located undergoes a displacement u under the action of an external force, the plate bracing round bar will thus generate a strain ε s , if the included angle between the line connecting the center of the plate bracing round bar and the center of the pier main body and the shear force action line is between -22.5° and 22.5°, considering it as on one side, then:

[0028] The length l′ of the stretched side plate bracing round bar after displacement cL is:

[0029]

[0030] Similarly, the length l' of the compressed side plate support round bar cR is:

[0031]

[0032] Thus, the strain of the stretched side plate support round bar is obtained:

[0033]

[0034] The strain of the compressed side plate support round bar:

[0035]

[0036] Thus, the stress of the stretched side plate support round bar is obtained:

[0037] σ cL = k c ·ε cL (9)

[0038] Thus, the stress of the compressed side plate support round bar is obtained:

[0039] σ cR = k c ·ε cL (10)

[0040] In the formula, k c is the elastic coefficient of the material used for the plate support round bar;

[0041] Taking the shear force borne by the system as F, the minimum cross-sectional area A cm i n required for the single-side plate support round bar can be designed according to formula (11):

[0042] (|σ cL | + |σ cR |)A c min cosα c = F (11)

[0043] Let the radius of the bridge pier be R, the length of the torsion bar be l n , the height from the vertex to the ground be h n , the distance from the bottom point to the outer edge of the bridge pier be d n , the angle between the torsion bar and the ground be α n , the angle between the projection of the torsion bar on the ground and the tangent plane of the vertex on the bridge pier be β. Assuming that a displacement with a rotation angle of θ occurs at the cross-section at the vertex of the torsion bar, the torsion bar will generate corresponding strain

[0044] The distance s traveled by the vertex of the torsion bar is:

[0045] s = Rθ (12)

[0046] Flatten the side of the pier, and according to the Pythagorean theorem, the length l' of the deformed torsion bar can be obtained n is:[[]]

[0047]

[0048] From this, the strain ε of the torsion bar can be obtained s is:[[]]

[0049]

[0050] From this, the stress σ of the single-sided torsion bar can be obtained n is:[[]]

[0051] σ n = k n ·ε n (15)

[0052] In the formula, k n is the elastic coefficient of the material used for the torsion bar;

[0053] Take the torque borne by the system as T, and according to formula (16), the minimum cross-sectional area A required for a single torsion bar can be designed nmin :[[]]

[0054] nσ n A n min cosα n cosβR = T (16)

[0055] In the formula, n is the number of torsion bars.

[0056] Beneficial effects:

[0057] 1. Using the structure imitating banyan trees and the method of decoupling loads, the pier only bears pressure, and the bending moment, shear force and torque are borne separately by the struts, plate braces and torsion bars. The existing pier designs do not utilize the structure imitating banyan trees and do not use the method of decoupling loads to design the piers. Instead, the piers mainly bear composite loads by themselves. The present invention makes the resistance mechanisms of the pier to bending moment, shear force and torque clear, and avoids new collapse modes that may be caused when the shear force or torque is too large.

[0058] 2. Since the present invention adds components for resisting bending, shear and torsion, it greatly improves the ability of the pier to cope with seismic loads, wind loads and eccentric loads, and improves the anti-overturning ability of the pier. Description of the drawings

[0059] Figure 1 is the overall structural schematic diagram of the present invention, Figure 1 in which a trunk-shaped pier body is adopted;

[0060] Figure 2 This is a schematic diagram of the overall structure of another embodiment of the present invention. Figure 2 A columnar pier body is adopted.

[0061] Figure 3 This is a schematic diagram showing the struts assisting in bearing the bending moment.

[0062] Figure 4 This is a schematic diagram showing the plate braces assisting in bearing the shear force.

[0063] Figure 5 This is a schematic diagram showing the torsion bars assisting in bearing the bending moment.

[0064] Figure 6 This is a schematic diagram of the arrangement of the plate braces in the top view.

[0065] Figure 7 This is a schematic diagram of the arrangement of the torsion bars in the top view.

[0066] Figure 8 This is a schematic diagram of the structure after welding the web plate to the bottom of the plate brace in the embodiment of the present invention.

[0067] Explanation of the reference numerals in the figure: 1, pier body; 2, strut; 3, torsion bar; 4, plate brace. Specific embodiments

[0068] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments, but the protection scope of the present invention is not limited thereto.

[0069] As Figure 1-2 shown, a large cantilever elevated pier based on banyan tree bionics of the present invention includes a pier body, struts, plate braces and torsion bars, wherein:

[0070] The struts are evenly distributed in a ring around the pier body and are arranged parallel to the pier body to assist the pier body in bearing the bending moment.

[0071] The plate braces are evenly arranged around the pier body and are obliquely connected between the pier body and the ground to assist the pier body in bearing the shear force. In this embodiment, the plate braces include plate brace round bars and web plates welded below the plate brace round bars, and the angle between the plate brace round bars and the ground is α c , α c ∈[35°, 50°];

[0072] The torsion bars are evenly arranged around the pier body and are connected between the pier body and the ground to assist the pier in bearing the torque, and the angle between the torsion bars and the ground is α n , α m ∈[55°, 70°];

[0073] Considering the uncertainty of the load direction, there are 8 or more of the said struts and plate braces, and 4 or more of the said torsion bars, which can be appropriately densified according to actual needs. In the top view, the extension line of the plate brace should pass through the axis center of the bridge pier, and the extension line of the torsion bar passes through the inside of the bridge pier section and does not intersect the axis.

[0074] In this embodiment, the bridge pier main body adopts a columnar bridge pier main body as shown in Figure 2 or a tree-trunk-shaped bridge pier main body as shown in Figure 1 .

[0075] In this embodiment, the plate brace and the torsion bar are connected to the bridge pier by welding. The distances from the bottoms of the strut, the round bar of the plate brace, and the bottom of the torsion bar to the bottom of the bridge pier are within 1.5 times the diameter of the bridge pier.

[0076] In this embodiment, a variable-height equal-thickness steel plate is welded to the bottom of the round bar of the plate brace. The steel plate serves as a web. When deforming, the contribution of the round bar of the plate brace to the force is much greater than that of the web, so the force on the web is not considered. Only the force on the round bar of the plate brace is considered. The thickness of the steel plate is 8 - 10 mm. The overall plate brace after welding the steel plate is as shown in Figure 8 .

[0077] The above design method of a large cantilever elevated bridge pier based on bionic banyan tree is as follows:

[0078] S1. Determine the distances between the bottoms of the strut, the round bar of the plate brace, and the bottom of the torsion bar and the center of the bridge pier according to the installation position. The distances from the bottoms of the strut, the round bar of the plate brace, and the bottom of the torsion bar to the bottom of the bridge pier are within 1.5 times the diameter of the bridge pier;

[0079] S2. Determine the angles between the round bar of the plate brace and the torsion bar and the ground;

[0080] S3. Determine the cross-sectional areas of a single strut, the round bar of the plate brace, and the torsion bar. The specific method is as follows:

[0081] Generally speaking, bridge piers are divided into two types: ordinary bridge piers (fixed connection at the bottom of the pier) and rocking bridge piers. Among them, the rotation center of the ordinary bridge pier under the action of external forces is at the center of the bottom of the pier, and the rotation center of the rocking bridge pier under the action of external forces is around the bottom of the bridge pier. Let the distance between the center of the bottom end of the strut and the rotation center of the bridge pier main body be d, and the heights of both the bridge pier main body and the strut be h. Establish a coordinate system with the rotation center of the bridge pier under the action of external forces as the origin. The angle between the connection line of the top of the strut and the origin and the y-axis is α. Under the action of external forces, when the system composed of the bridge pier main body, the strut, the plate brace, and the torsion bar rotates by an angle θ z around the origin, at this time, the strut will generate a deformation Δl z , and the vertex coordinates of the deformed strut are The length l′ of the strut on the stretched side after deformation zL is:

[0082]

[0083] The angle between the line connecting the center of the strut and the center of the pier body and the direction of the bending moment is between 67.5° and 112.5°. Considering it as one side, the strain ε of the single-sided strut zi is:

[0084]

[0085] Thus, the stress σ of the single-sided strut zi is:

[0086] σ zi = k z ·ε zi (3)

[0087] In the formula, k z is the elastic coefficient of the material used for the strut;

[0088] Assume the bending moment borne by the system is M. According to formula (4), the minimum cross-sectional area A required for the single-sided strut can be designed zmin :

[0089] σ zi A z min d = M (4)

[0090] Let the angle between the plate bracing round bar and the ground be α c , the length of the plate bracing round bar be l c , the projected length of the plate bracing round bar in the horizontal direction be d c , and the projected length in the vertical direction be h c , then When the pier section where the vertex of the plate bracing round bar is located generates a displacement u under the action of an external force, the plate bracing round bar will generate a strain ε s . If the angle between the line connecting the center of the plate bracing round bar and the center of the pier body and the shear force action line is between -22.5° and 22.5°, considering it as one side, then:

[0091] The length l′ of the stretched side plate bracing round bar after displacement cL is:

[0092]

[0093] Similarly, the length l′ of the compressed side plate bracing round bar cR is:

[0094]

[0095] Thus, the strain of the stretched side plate supporting round bar is obtained as follows:

[0096]

[0097] The strain of the compressed side plate supporting round bar:

[0098]

[0099] Thus, the stress of the stretched side plate supporting round bar is obtained as follows:

[0100] σ cL = k c ·ε cL (9)

[0101] Thus, the stress of the compressed side plate supporting round bar is obtained as follows:

[0102] σ cR = k c ·ε cR (10)

[0103] In the formula, k c is the elastic coefficient of the material used for the plate supporting round bar;

[0104] Taking the shear force borne by the system as F, the minimum cross-sectional area A required for the single-side plate supporting round bar can be designed according to formula (11) c min :

[0105] (|σ cL | + |σ cR |)A c min cosα c = F (11)

[0106] Let the radius of the pier be R, the length of the torsion bar be l n , the height from the vertex to the ground be h n , the distance from the bottom point to the outer edge of the pier be d n , the angle between the torsion bar and the ground be α n , the angle between the projection of the torsion bar on the ground and the tangent plane of the vertex on the pier be β. Assuming that a displacement with a rotation angle of θ occurs at the cross-section at the vertex of the torsion bar, the torsion bar will generate corresponding strain accordingly.

[0107] The distance s traveled by the vertex of the torsion bar is:

[0108] s = Rθ (12)

[0109] Flatten the side surface of the pier. According to the Pythagorean theorem, the length l' of the deformed torsion bar n is:

[0110]

[0111] Thus, the strain ε of the torsion bar can be obtained. s It is:

[0112]

[0113] Thus, the stress σ of the single-sided torsion bar is obtained. n It is:

[0114] σ n = k n ·ε n (15)

[0115] Wherein, k n is the elastic coefficient of the material used for the torsion bar;

[0116] Taking the torque borne by the system as T, the minimum cross-sectional area A required for a single torsion bar can be designed according to formula (16). nmin It is:

[0117] nσ n A n min cosα n cosβR = T (16)

[0118] Wherein, n is the number of torsion bars.

[0119] During the actual design process, what needs to be designed are:

[0120] (1) The distances between the strut, the bottom of the plate brace round bar, the bottom of the torsion bar and the center of the bridge pier;

[0121] (2) The angles between the plate brace round bar and the torsion bar and the ground;

[0122] (3) The cross-sectional areas of a single strut, the plate brace round bar and the torsion bar.

[0123] The distances between the strut, the bottom of the plate brace round bar and the bottom of the torsion bar and the center of the bridge pier should not be too far, generally within 1.5 times the diameter of the bridge pier.

[0124] The angle between the plate brace round bar and the ground is generally taken as 45°, and can also be flexibly adjusted according to the actual situation, but should not be less than 35° and should not be greater than 50°. The angle between the torsion bar and the ground is generally taken as 60°, and can also be flexibly adjusted according to the actual situation, but should be between 55° and 70°.

[0125] When designing the cross-sectional area of each component, first calculate the bending moment, shear force and torque that the pier system may bear according to the current calculation method. Combine the determined distance between the component and the pier center and the angle between the component and the ground, and calculate the cross-sectional areas of a single strut, a plate bracing round bar and a single torsion bar according to the formulas (5), (11) and (16) in the above text, and arrange them evenly along the pier circumference. If a bifurcated tree-shaped pier as shown in Figure 1 is to be built, it is recommended to use concrete-filled steel tube components for the pier body. First prefabricate the steel tubes in blocks according to the trunk and branch bifurcations, transport them to the construction site, complete the splicing and then pour concrete on site, and no steel reinforcement cage needs to be placed inside. In addition, anti-corrosion treatment should also be carried out on the steel tubes.

[0126] The above embodiments are the preferred embodiments of the nodes of the present invention, but the embodiments of the present invention are not limited by the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications made without departing from the spirit and principle of the present invention shall be equivalent replacement methods and are all included in the protection scope of the present invention.

Claims

1. A large cantilever elevated bridge pier based on banyan tree bionics, comprising a pier main body, a support column, a plate brace and a torsion bar, characterized in that, The struts are evenly distributed in a ring around the periphery of the pier main body and are arranged parallel to the pier main body to assist the pier main body in bearing the bending moment; The plate braces are evenly arranged on the periphery of the pier main body and are obliquely connected between the pier main body and the ground to assist the pier main body in bearing shear force. The plate brace includes a plate brace round bar and a web plate welded below the plate brace round bar. The included angle between the plate brace round bar and the ground is α c , α c ∈[35°, 50°]; The torsion bars are evenly arranged around the pier main body and connected between the pier main body and the ground to assist the pier in bearing torque, and the included angle between the torsion bars and the ground is α n , α n ∈[55°, 70°]; There are 8 or more struts and plate braces, and 4 or more torsion bars. In the top view, the extension line of the plate brace should pass through the axis of the pier, and the extension line of the torsion bar passes through the interior of the pier cross-section and does not intersect the axis.

2. The large cantilever elevated bridge pier based on banyan tree bionics according to claim 1, characterized in that, The pier main body adopts a columnar pier main body or a tree-trunk-shaped pier main body.

3. The large cantilever elevated bridge pier based on banyan tree bionics according to claim 1, wherein The plate brace and the torsion bar are connected to the pier by welding. The distances from the bottoms of the struts, plate braces, and torsion bars to the bottom of the pier are within 1.5 times the diameter of the pier.

4. The design method of a large cantilever elevated bridge pier based on banyan tree bionics according to any one of claims 1-3, characterized in that, The method is as follows: S1. Determine the distances from the bottoms of the struts, circular bars of the plate braces, and bottoms of the torsion bars to the center of the pier according to the installation position. The distances from the bottoms of the struts, circular bars of the plate braces, and bottoms of the torsion bars to the bottom of the pier are within 1.5 times the diameter of the pier; S2. Determine the angles between the circular bars of the plate braces and the torsion bars and the ground; S3. Determine the cross-sectional areas of a single strut, circular bar of the plate brace, and torsion bar. The specific method is as follows: Let the distance between the center of the bottom end of the strut and the rotation center of the bridge pier main body be d, and the heights of both the bridge pier main body and the strut be h. Establish a coordinate system with the rotation center of the bridge pier under external force as the origin. The angle between the line connecting the vertex of the strut and the origin and the y-axis is α. Under external force, when the system composed of the bridge pier main body, the strut, the plate bracing round bar, and the torsion bar rotates by an angle θ around the origin z After that, at this time, the strut will generate a deformation Δl z , and the vertex coordinates of the deformed strut are cos(θ z -α)), and the length l′ zL of the stretched side of the deformed strut is: The included angle between the connecting line of the center of the strut and the center of the pier body and the direction of the bending moment is between 67.5° and 112.5°. Regarding it as on one side, the strain ε of the single-sided strut zi is as follows: Thus, the stress σ of the single-sided support is obtained as follows zi : σ zi = k z ·ε zi (3) where k z is the elastic coefficient of the material used for the strut; Let the bending moment borne by the system be M. According to formula (4), the minimum cross-sectional area A required for the single-sided support can be designed. z min : σ zi A z min d = M (4) Let the angle between the plate support round bar and the ground be α c , the length of the plate support round bar be l c , the projected length of the plate support round bar in the horizontal direction be d c , the projected length in the vertical direction be h c , then When the pier section where the vertex of the plate support round bar is located generates a displacement u under the action of an external force, the plate support round bar will generate a strain ε s , if the angle between the line connecting the center of the plate support round bar and the center of the pier main body and the shear force action line is between -22.5° and 22.5°, and it is regarded as on one side, then: The length l′ of the circular strut on the stretched side after displacement cL is as follows: Similarly, the length l' of the compressed side plate supporting round bar cR is as follows: Thus, the strain of the tensioned side circular bar of the plate brace is obtained: The strain of the compressed side circular bar of the plate brace: Thus, the stress of the tensioned side circular bar of the plate brace is obtained: σ cL = k c ·ε cL (9) Thus, the stress of the compressed side circular bar of the plate brace is obtained: σ cR = k c · ε cR In Equation (10), k c is the elastic coefficient of the material used for the plate support round bar; Take the shear force borne by the system as F, and the minimum cross-sectional area A required for the single-sided plate brace round bar can be designed according to formula (11). c min : (|σ cL | + |σ cR |)A c min cosα c = F(11) Let the radius of the pier be R and the length of the torsion bar be l n , the height from the vertex to the ground be h n , the distance from the bottom point to the outer edge of the pier be d n , the angle between the torsion bar and the ground be α n , the angle between the projection of the torsion bar on the ground and the tangent plane of the pier at its vertex be β. Assume that a displacement with a rotation angle of θ occurs at the cross-section at the vertex of the torsion bar, and the torsion bar will generate corresponding strains accordingly. The distance s traveled by the vertex of the torsion bar is: s = Rθ (12) Flatten the side of the pier, and according to the Pythagorean theorem, the length l' of the deformed torsion bar is obtained n as follows: The strain ε of the torsion bar can thus be obtained s as follows: Thus, the stress σ of the single-sided torsion bar is obtained as follows: n as follows: σ n = k n ·ε n (15) where k n is the elastic coefficient of the material used for the torsion bar; Taking the torque borne by the system as T, the minimum cross-sectional area A required for a single torsion bar can be designed according to formula (16). n min : nσ n A n min cosα n cosβR = T (16) In the formula, n is the number of torsion bars; Calculate the cross-sectional areas of a single strut, circular bar of the plate brace, and a single torsion bar according to formulas (5), (11), and (16) respectively, and arrange them evenly along the pier circumference.

Images