A wall corner element restraint method for a rocking wall structural system

Abstract

This invention discloses a method for constraining corner elements in a rocking wall structure system. Based on the structural parameters of the rocking wall and the frame structure, the shear stiffness of the frame structure is obtained. A first lateral displacement expression and a second lateral displacement expression are constructed using the shear stiffness and the first and second equilibrium equations. An inter-story drift angle expression is then constructed using these expressions to solve for the stiffness of the rotating combined disc springs. The bending moment of the rotating combined disc springs is obtained from the stiffness of the rotating combined disc springs. The number of single disc springs stacked in the same direction and the number of combined disc springs are determined by the deformation requirement and the bearing capacity requirement of the combined disc springs obtained from the bending moment. This yields the combined height of the disc springs. The combined height of the disc springs is then used to constrain the length of the core rod and the support height in the corner element, achieving rapid constraint of the core rod length and support height in the corner element based on statics.

Description

Technical Field

[0001] This invention relates to the field of corner element constraint for rocker walls, and more particularly to a corner element constraint method for rocker wall structural systems. Background Technology

[0002] Reinforced concrete frame structures are a widely used structural form in buildings. However, post-earthquake disaster investigations show that these structures are prone to irreparable damage during earthquakes. Statistics indicate that damage to frame structures often stems from the yielding mechanism formed by concentrated deformation in a few floors. To reduce irreparable damage during earthquakes and improve the seismic performance of structures, swaying walls were introduced into frame structures, leading to the development of frame-hinged swaying wall structures. This structure consists of a frame and swaying walls. Under horizontal loads, the frame structure exhibits a shear deformation mode, with the maximum inter-story drift occurring at the bottom of the structure. The swaying walls, under horizontal loads, exhibit a bending deformation mode. The two structures are connected only at the floor levels by shear keys, working together synergistically. Therefore, the overall deformation mode of the frame-hinged swaying wall structure is bending-shear, significantly reducing deformation concentration. Furthermore, the horizontal forces borne by the frame structure are transferred to the swaying wall structure, resulting in a redistribution of internal forces. This alleviates the stress on the frame. Studies have shown that, provided the swaying wall possesses sufficient stiffness and strength, it can effectively control the deformation mode of a frame structure, making the inter-story lateral displacement more uniform and mitigating or preventing story yield failure. Existing research primarily focuses on frame-swaying wall structures where the swaying wall and foundation are connected by hinges, i.e., frame-hinged swaying wall structures. However, in actual structures, additional restoring force devices are usually added to the bottom layer of the swaying wall, generating a certain bending stiffness. Therefore, it is necessary to introduce rotational constraint springs reflecting the restoring force of corner elements at the bottom layer of the swaying wall structure. Wu Dayang et al. introduced rotational constraint springs at the bottom of the swaying structure, with a stiffness of Kr, and established a new distributed parameter mathematical model based on dynamics. However, modeling based on dynamics, due to the introduction of variables such as time and acceleration, makes the calculation of the corner element structural parameters very complex, resulting in time-consuming calculations and making it difficult to quickly constrain the corner element structural parameters for swaying wall structures, thus hindering the use by designers. Summary of the Invention

[0003] To simplify the calculation of the structural parameters of corner elements and to achieve rapid constraint of the structural parameters of corner elements based on the structural parameters of the swaying wall structure system, this invention proposes a method for constraining corner elements in a swaying wall structure system. The corner element includes an upper constraint plate, a combined disc spring, and a lower constraint plate arranged sequentially from top to bottom. One end of the combined disc spring abuts against the upper constraint plate, and the other end abuts against the lower constraint plate. The lower constraint plate has a through hole and a support at its bottom. The upper constraint plate has a mandrel that passes through the combined disc spring and the through hole sequentially from top to bottom. The method includes the following steps:

[0004] S01: Set the structural parameters of the swaying wall and the frame structure, and obtain the shear stiffness of the frame structure through the structural parameters of the frame structure; set the expressions for the top concentrated load F and the horizontal inverted triangular load; set the target inter-story drift angle θ. tar The horizontal inverted triangular load expression includes the variable ξ, which is the vertical height ξ of the rocking wall structure system.

[0005] S02: Construct the first equilibrium equation by considering the differential relationship between the force balance, bending moment, shear force, and load intensity of the swaying wall; define the lateral horizontal load on the frame structure as a horizontal inverted triangular load, and transform the first equilibrium equation using the expression for the horizontal inverted triangular load. Then, construct the first lateral displacement expression for the swaying wall structure system under the horizontal inverted triangular load using the transformed first equilibrium equation, shear stiffness, and structural parameters of the swaying wall; construct the second equilibrium equation by defining the lateral horizontal load on the frame structure as a top concentrated load and setting the top concentrated load F to be non-zero. Finally, construct the second lateral displacement expression for the swaying wall structure system under the top concentrated load using the second equilibrium equation.

[0006] S03: Construct the inter-story drift angle expression using the first and second lateral drift expressions, and differentiate the inter-story drift angle expression to solve for the inter-story drift angle θ when it is the target inter-story drift angle. tar The corresponding vertical height ξ max By substituting the vertical height ξ max The stiffness K of the rotating combined disc spring is obtained from the expression for the inter-story drift angle. r ;

[0007] S04: Calculation formulas for the angle of rotation of the bottom surface of the swaying wall relative to the foundation plane, the bending moment calculation formula for the rotating disc spring, and the stiffness K of the rotating disc spring. r Obtain the bending moment M of the rotating combined disc spring. r ;

[0008] S05: Construct bending moment M rWith the combined disc spring load-bearing capacity requirement F z The relationship is expressed, and the bending moment M is obtained by applying the formula. r Substituting into the formula, we obtain the load-bearing capacity requirement F of the combined disc spring. z ;

[0009] S06: By combining disc springs, the load-bearing capacity requirement F is met. z Determine the number N of single disc springs stacked in the same direction, and obtain the required deformation f of the combined disc springs. z Through deformation demand f z Obtain the number i of mating disc springs in the combined disc spring; obtain the combined height H of the disc spring by combining the number N of individual disc springs stacked in the same direction with the number i of mating disc springs. z The height H is achieved by combining disc springs. z Constrain the length of the mandrel and the height of the support in the corner element.

[0010] Furthermore, step S01 also includes: setting a target value γ for the restoring force coefficient to be shared by the corner element. tar The process between steps S03 and S04 also includes:

[0011] S31: Obtain the stiffness K of the rotating combined disc spring by using the formula for calculating the restoring force coefficient of the corner element. r The corresponding restoring force coefficient to be shared by the corner element; the calculation formula for the restoring force coefficient to be shared by the corner element is: In the formula, γ represents the coefficient of restoring force to be shared by the corner element, u f K represents r When =∞, relative to K r The amount of displacement decrease when u = 0 r express When, relative to K r The amount of displacement reduction when = 0;

[0012] S32: Determine if γ is greater than or equal to γ tar If so, proceed to step S04.

[0013] Furthermore, in step S01, the structural parameters of the swaying wall include the elastic modulus E of the concrete. w and the width b of the sway wall section w and length h w The structural parameters of the frame structure include: the elastic modulus E of the concrete. f The total height H of the frame structure, the floor height h, the number of columns n per floor, and the beam cross-sectional width b. b With cross-sectional length h b The width of the column section b c With cross-sectional length h c ;

[0014] The formula for obtaining the shear stiffness of the frame structure is as follows:

[0015] In the formula, I c Let I be the moment of inertia of the column; b Let be the moment of inertia of the beam, and K be the shear stiffness.

[0016] The expression for the horizontal inverted triangular load is:

[0017] P(ξ)=qξ; where, Where H is the total height of the frame structure; x is any height of the frame structure; P(ξ) is the uniformly distributed lateral horizontal load on the swaying wall and the overall frame structure; and q is the maximum vertical axis value.

[0018] Furthermore, in step S02, the formula expression for the first equilibrium equation is:

[0019]

[0020] In the formula, I w Let u be the moment of inertia of the swaying wall section in the plane, and u in the first equilibrium equation. β This represents the lateral displacement of the rocking wall structure system under a horizontal inverted triangular load.

[0021] The first equilibrium equation is transformed using the horizontal inverted triangular load expression. The transformed first equilibrium equation is expressed as follows:

[0022] The formula for the first lateral displacement expression is:

[0023]

[0024] In the formula, Where λ is a dimensionless parameter reflecting the relative magnitude of the shear stiffness of the frame structure and the bending stiffness of the swaying wall section; β is a dimensionless parameter reflecting the relative magnitude of the stiffness of the rotating combined disc spring and the bending stiffness of the swaying wall section; K r To determine the stiffness of the rotating disc spring.

[0025] Further, in step S02, the formula expression for the second equilibrium equation is:

[0026] u in the second equilibrium equation β This indicates the lateral displacement of the rocking wall structure system under a concentrated load at the top;

[0027] The formula for the second lateral displacement expression is:

[0028]

[0029] In the formula,

[0030] Further, in step S03, the inter-story drift angle expression is constructed using the first lateral drift expression and the second lateral drift expression, specifically as follows:

[0031] The inter-story drift angle θ under horizontal inverted triangular load is obtained using the first lateral displacement expression. tri The formula is:

[0032]

[0033] The inter-story drift angle θ under the concentrated load at the top is obtained using the second lateral displacement expression. con The formula is:

[0034]

[0035] via θ tri With θ con The expression for the inter-story drift angle is constructed as follows:

[0036]

[0037]

[0038] In the formula, θ z The inter-story drift angle is the angle between the horizontal inverted triangular load and the top concentrated load.

[0039] In step S03, the derivative of the expression for the inter-story drift angle is obtained, and the derivative formula is as follows:

[0040] The target inter-layer displacement angle θ tar This is the limit value for the inter-story drift angle.

[0041] Furthermore, step S04 specifically includes:

[0042] The angle calculation formula for the rotation of the bottom surface of the swaying wall relative to the foundation plane is obtained through a preset rotation angle calculation formula; the preset rotation angle calculation formula is:

[0043] In the formula, y represents the lateral displacement of the overall frame structure, which is the sum of the corresponding lateral displacements of the swaying wall structure system under the action of the horizontal inverted triangular load and the action of the top concentrated load; x represents the actual height of the frame structure; θ represents the angle of rotation of the swaying wall relative to the foundation plane.

[0044] The formula for calculating the angle is:

[0045] In the formula, ξ=0 indicates that the vertical height of the rocking wall structure system is 0; θ0 indicates the angle of rotation of the bottom surface of the rocking wall relative to the foundation plane;

[0046] By connecting θ0 with K r Substitute the values ​​into the formula for calculating the bending moment of a rotating disc spring to obtain the bending moment M of the rotating disc spring. r The expression for the bending moment calculation formula is: M r =K r θ0.

[0047] Furthermore, in step S05, the bending moment M r With the combined disc spring load-bearing capacity requirement F z The relational expression is:

[0048] In the formula, b r b is the width of the corner element. w Width b of the sway wall section w .

[0049] Furthermore, in step S06, the formula for obtaining the number N of single disc springs stacked in the same direction is:

[0050] F z =N·F spr In the formula, F spr Let f ≈ 0.75h0 be the load-bearing capacity of a single disc spring, where f represents the deformation of a single disc spring and h0 represents the deformation of a single disc spring without support surface when compressed.

[0051] In step S06, the deformation requirement f z The formula for obtaining it is:

[0052] In the formula, θ max This indicates the maximum angle of rotation of the bottom surface of the swing wall relative to the foundation plane.

[0053] In step S06, the formula for obtaining the number i of disc springs engaged is:

[0054] f z =i·f;

[0055] In step S06, the height H of the disc spring assembly z The formula for obtaining it is:

[0056] H z =i·(H0+(N-1)·t); where H0 is the free height of a single disc spring, and t represents the thickness of a single disc spring.

[0057] Furthermore, in step S06, the height H is determined by combining disc springs. z The constraints used in the corner element include: the length of the mandrel and the height of the support.

[0058] First constraint: l x >H z +t x In the formula, l x t represents the length of the mandrel. x Indicates the thickness of the lower constraint plate; second constraint condition: h d >l x -H z -t x +f z In the formula, h d Indicates the support height.

[0059] Compared with the prior art, the present invention has at least the following beneficial effects:

[0060] (1) This invention obtains the shear stiffness of the frame structure based on the structural parameters of the swaying wall and the frame structure. Using the shear stiffness, structural parameters, and the constructed first and second equilibrium equations, it constructs a first lateral displacement expression under a horizontal inverted triangular load and a second lateral displacement expression under a top concentrated load. Furthermore, it constructs an inter-story drift angle expression using the first and second lateral displacement expressions to solve for the stiffness of the rotating combined disc spring when the inter-story drift angle is the target inter-story drift angle. The bending moment of the rotating combined disc spring is obtained using the angle calculation formula, the bending moment calculation formula, and the stiffness of the rotating combined disc spring. The bending moment is used to determine the load-bearing capacity requirement of the combined disc springs and the deformation requirement. Then, the number of single disc springs stacked in the same direction and the number of disc springs in combination are determined by the load-bearing capacity requirement and the deformation requirement of the combined disc springs. The height of the disc spring combination is then obtained. The length of the core rod and the height of the support in the corner element are constrained by the height of the disc spring combination. The expression is constructed to determine the height of the disc spring combination without using dynamic variables such as time and acceleration. This achieves rapid constraint on the length of the core rod and the height of the support in the corner element based on statics, which greatly improves the design efficiency of the corner element.

[0061] (2) This invention calculates the stiffness of the rotating combined disc spring by setting the target inter-layer displacement angle, and obtains the corner element's proposed restoring force coefficient corresponding to the stiffness of the rotating combined disc spring through the calculation formula of the corner element's proposed restoring force coefficient. The target value of the corner element's proposed restoring force coefficient is used to determine whether the currently calculated stiffness of the rotating combined disc spring meets the preset requirements, which further improves the rationality and safety of the corner element design. Attached Figure Description

[0062] Figure 1 A flowchart of a corner element constraint method for a rocking wall structure system;

[0063] Figure 2 This is a structural diagram of a corner component;

[0064] Figure 3 This is a schematic diagram of the forces acting on the cross-section of a rocking wall with corner elements. Detailed Implementation

[0065] The following are specific embodiments of the present invention, which are described in conjunction with the accompanying drawings. However, the present invention is not limited to these embodiments.

[0066] Example 1

[0067] To simplify the calculation of the structural parameters of corner elements and to quickly constrain the structural parameters of corner elements based on the structural parameters of the rocking wall structure system, such as... Figure 1 As shown, this invention proposes a method for constraining corner elements in a rocking wall structure system, wherein, as... Figure 2 As shown, the corner element includes an upper constraint plate, a combined disc spring, and a lower constraint plate arranged sequentially from top to bottom; one end of the combined disc spring abuts against the upper constraint plate, and the other end of the combined disc spring abuts against the lower constraint plate; the lower constraint plate has a through hole, and the bottom of the lower constraint plate has a support; the upper constraint plate has a mandrel, and the mandrel passes through the combined disc spring and the through hole sequentially from top to bottom, including the following steps:

[0068] S01: Set the structural parameters of the swaying wall and the frame structure, and obtain the shear stiffness of the frame structure through the structural parameters of the frame structure; set the expressions for the top concentrated load F and the horizontal inverted triangular load; set the target inter-story drift angle θ. tar The horizontal inverted triangular load expression includes the variable ξ, which is the vertical height ξ of the rocking wall structure system; step S01 further includes: setting the target value γ of the restoring force coefficient to be shared by the corner elements. tar ;

[0069] In step S01, the structural parameters of the swaying wall include the elastic modulus E of the concrete. w and the width b of the sway wall section w and length h w The structural parameters of the frame structure include: the elastic modulus E of the concrete. f The total height H of the frame structure, the floor height h, the number of columns n per floor, and the beam cross-sectional width b. b With cross-sectional length h b The width of the column section b c With cross-sectional length h c ;

[0070] The formula for obtaining the shear stiffness of the frame structure is as follows:

[0071] In the formula, I c Let I be the moment of inertia of the column; b Let be the moment of inertia of the beam, and K be the shear stiffness.

[0072] The expression for the horizontal inverted triangular load is:

[0073] P(ξ)=qξ; where, Where H is the total height of the frame structure; x is any height of the frame structure; P(ξ) is the uniformly distributed lateral horizontal load on the overall structure of the swaying wall and frame; and q is the maximum vertical axis value.

[0074] S02: Construct the first equilibrium equation by considering the differential relationship between the force balance, bending moment, shear force, and load intensity of the swaying wall; define the lateral horizontal load on the frame structure as a horizontal inverted triangular load, and transform the first equilibrium equation using the expression for the horizontal inverted triangular load. Then, construct the first lateral displacement expression for the swaying wall structure system under the horizontal inverted triangular load using the transformed first equilibrium equation, shear stiffness, and structural parameters of the swaying wall; construct the second equilibrium equation by defining the lateral horizontal load on the frame structure as a top concentrated load and setting the top concentrated load F to be non-zero. Finally, construct the second lateral displacement expression for the swaying wall structure system under the top concentrated load using the second equilibrium equation.

[0075] In step S02, the formula expression for the first equilibrium equation is:

[0076]

[0077] In the formula, I w Let u be the moment of inertia of the swaying wall section in the plane, and u in the first equilibrium equation. β This represents the lateral displacement of the rocking wall structure system under a horizontal inverted triangular load.

[0078] The first equilibrium equation is transformed using the horizontal inverted triangular load expression. The transformed first equilibrium equation is expressed as follows:

[0079] Neglecting the higher-order differentials of the transformed first equilibrium equation (their effect is negligible, so they are omitted), we obtain:

[0080] The general solution of Equation 1.1 is obtained by using the solution method for nonhomogeneous differential equations:

[0081] in, For a particular solution of Equation 1.2, C1, C2 and A, B are constants, which can be determined from Table 1 below:

[0082]

[0083]

[0084] In Table 1:

[0085] In the formula, x represents the actual height of the frame structure; θ represents the angle of rotation of the sway wall relative to the foundation plane; V w V represents the shear force of the swaying wall. F M represents the inter-story shear force in a frame structure. w Indicates the bending moment of the swaying wall;

[0086] set up Combining the boundary conditions and expressions in Table 1, we can solve the equations to obtain:

[0087]

[0088]

[0089]

[0090]

[0091] Substituting formulas 1.3 to 1.6 into formula 1.2, we obtain the formula for the first lateral displacement expression as follows:

[0092]

[0093] In the formula, Where λ is a dimensionless parameter reflecting the relative magnitude of the shear stiffness of the frame structure and the bending stiffness of the swaying wall section; β is a dimensionless parameter reflecting the relative magnitude of the stiffness of the rotating combined disc spring and the bending stiffness of the swaying wall section; K r The stiffness of the rotating disc spring is used to reflect the rotational stiffness of the corner element attached to the bottom of the rocking wall to provide restoring force to the structure in the actual structure. K r =0 indicates that the bottom of the sway wall is hinged to the foundation; when K r When =∞, it means that the bottom of the rocking wall is fixed to the foundation, and the rocking wall structure system with corner elements is a frame-shear wall structure.

[0094] In this embodiment, using the known first lateral displacement expression, the bending moment M of the swaying wall structure system under the action of a horizontal inverted triangular load can also be obtained: w(See Formula 1.7); Shear force V of the swaying wall w (See Formula 1.8); Inter-story shear force V of frame structure F (See Formula 1.9);

[0095]

[0096]

[0097]

[0098] In step S02, the formula expression for the second equilibrium equation is:

[0099] u in the second equilibrium equation β This indicates the lateral displacement of the rocking wall structure system under a concentrated load at the top;

[0100] Solving the second equilibrium equation using the method for solving non-homogeneous differential equations, we obtain the general solution of the second equilibrium equation:

[0101] u β =C1+C2ξ+Asinhλξ+Bcoshλξ (Formula 2.1); where C1, C2 and A, B are constants, which can be determined from Table 2 below:

[0102]

[0103] In Table 2: j represents the number of layers in the frame structure. This represents the inter-story shear force of the j-th story in the frame structure;

[0104] set up Combining the boundary conditions and expressions in Table 2, we can solve the equations to obtain:

[0105]

[0106]

[0107]

[0108]

[0109] Substituting equations 2.2 to 2.5 into equation 2.1, we obtain the second lateral displacement expression as follows:

[0110]

[0111] In this embodiment, using the known second lateral displacement expression, the bending moment M of the swaying wall structure system under the action of a concentrated load at the top can also be obtained: w(See Formula 2.6); Shear force V of the swaying wall w (See Formula 2.7); Inter-story shear force V of frame structure F (See Formula 2.8);

[0112]

[0113]

[0114]

[0115] S03: Construct the inter-story drift angle expression using the first and second lateral drift expressions, and differentiate the inter-story drift angle expression to solve for the inter-story drift angle θ when it is the target inter-story drift angle. tar The corresponding vertical height ξ max By substituting the vertical height ξ max The stiffness K of the rotating combined disc spring is obtained from the expression for the inter-story drift angle. r ;

[0116] In step S03, the inter-story drift angle expression is constructed using the first lateral drift expression and the second lateral drift expression, specifically as follows:

[0117] The inter-story drift angle θ under horizontal inverted triangular load is obtained using the first lateral displacement expression. tri The formula is:

[0118]

[0119] The inter-story drift angle θ under the concentrated load at the top is obtained using the second lateral displacement expression. con The formula is:

[0120]

[0121] via θ tri With θ con The expression for the inter-story drift angle is constructed as follows:

[0122]

[0123] In the formula, θ z The inter-story drift angle is the angle between the horizontal inverted triangular load and the top concentrated load.

[0124] In step S03, the derivative of the expression for the inter-story drift angle is obtained, and the derivative formula is as follows:

[0125] The target inter-layer displacement angle θ tar This is the limit value for the inter-story drift angle.

[0126] The process between steps S03 and S04 also includes:

[0127] S31: Obtain the stiffness K of the rotating combined disc spring by using the formula for calculating the restoring force coefficient of the corner element. r The corresponding restoring force coefficient to be shared by the corner element; the calculation formula for the restoring force coefficient to be shared by the corner element is: In the formula, γ represents the coefficient of restoring force to be shared by the corner element, u f K represents r When =∞, relative to K r The amount of displacement decrease when u = 0 r K represents r When ≠∞, relative to K r When γ = 0, it represents the reduction in displacement; when γ = 1, it indicates that the restoring force provided by the corner element reaches its maximum value, meaning the wall corresponds to a traditional shear wall. When γ = 0, it indicates that the corner element does not provide restoring force, meaning there is no corner element at the bottom of the wall; based on the actual requirements of the project, the target value γ for the restoring force sharing coefficient of the corner element is determined. tar The design requires γ ≥ γ tar .

[0128] S32: Determine if γ is greater than or equal to γ tar If so, proceed to step S04.

[0129] This invention calculates the stiffness of the rotating combined disc spring by setting a target inter-story displacement angle, and obtains the restoring force coefficient of the corner element corresponding to the stiffness of the rotating combined disc spring through the calculation formula of the restoring force coefficient to be shared by the corner element. The target value of the restoring force coefficient to be shared by the corner element is used to determine whether the currently calculated stiffness of the rotating combined disc spring meets the preset requirements, which further improves the rationality and safety of the corner element design.

[0130] S04: Calculation formulas for the angle of rotation of the bottom surface of the swaying wall relative to the foundation plane, the bending moment calculation formula for the rotating disc spring, and the stiffness K of the rotating disc spring. r Obtain the bending moment M of the rotating combined disc spring. r ;

[0131] The S04 step specifically includes:

[0132] The angle calculation formula for the rotation of the bottom surface of the swaying wall relative to the foundation plane is obtained through a preset rotation angle calculation formula; the preset rotation angle calculation formula is:

[0133] In the formula, y represents the lateral displacement of the overall frame structure, which is the sum of the corresponding lateral displacements of the swaying wall structure system under the action of the horizontal inverted triangular load and the action of the top concentrated load; x represents the actual height of the frame structure; θ represents the angle of rotation of the swaying wall relative to the foundation plane.

[0134] The formula for calculating the angle is:

[0135] In the formula, ξ=0 indicates that the vertical height of the rocking wall structure system is 0; θ0 indicates the angle of rotation of the bottom surface of the rocking wall relative to the foundation plane;

[0136] By connecting θ0 with K r Substitute the values ​​into the formula for calculating the bending moment of a rotating disc spring to obtain the bending moment M of the rotating disc spring. r The expression for the bending moment calculation formula is: M r =K r θ0.

[0137] S05: Through such Figure 3 The bending moment M shown r With the combined disc spring load-bearing capacity requirement F z The relationship is used to construct the bending moment M. r With the combined disc spring load-bearing capacity requirement F z The relationship is expressed, and the bending moment M is obtained by applying the formula. r Substituting into the formula, we obtain the load-bearing capacity requirement F of the combined disc spring. z ;

[0138] In step S05, the bending moment M r With the combined disc spring load-bearing capacity requirement F z The relational expression is:

[0139] In the formula, b r b is the width of the corner element. w Width b of the sway wall section w .

[0140] In this embodiment, the required load-bearing capacity F of the combined disc spring is obtained. z Subsequently, by consulting the book "Disc Springs," a disc spring was selected, and its specifications were determined, including its main dimensions: outer diameter D, inner diameter d, flattening height h0, thickness t, free height H0, and the load-bearing capacity F of a single disc spring when f ≈ 0.75h0. spr .

[0141] S06: By combining disc springs, the load-bearing capacity requirement F is met. z Determine the number N of single disc springs stacked in the same direction, and obtain the required deformation f of the combined disc springs. zThrough deformation demand f z Obtain the number i of mating disc springs in the combined disc spring; obtain the combined height H of the disc spring by combining the number N of individual disc springs stacked in the same direction with the number i of mating disc springs. z The height H is achieved by combining disc springs. z Constrain the length of the mandrel and the height of the support in the corner element.

[0142] In step S06, the formula for obtaining the number N of single disc springs stacked in the same direction is:

[0143] F z =N·F spr In the formula, F spr Let f ≈ 0.75h0 be the load-bearing capacity of a single disc spring, where f represents the deformation of a single disc spring and h0 represents the deformation of a single disc spring without support surface when compressed.

[0144] In step S06, the deformation requirement f z The formula for obtaining it is:

[0145] In the formula, θ max This indicates the maximum angle of rotation of the bottom surface of the swing wall relative to the foundation plane.

[0146] In step S06, the formula for obtaining the number i of disc springs engaged is:

[0147] f z =i·f;

[0148] In this embodiment, to facilitate the alignment of the disc spring axis and the mandrel axis, the mandrel diameter is slightly smaller than the disc spring's inner diameter, and the lower constraint plate's inner diameter is slightly larger than the mandrel's diameter. Furthermore, the outer diameters of the upper and lower constraint plates should be larger than the maximum outer diameter that the disc spring can reach after compression.

[0149] In step S06, the height H of the disc spring assembly z The formula for obtaining it is:

[0150] H z =i·(H0+(N-1)·t); where H0 is the free height of a single disc spring, and t represents the thickness of a single disc spring.

[0151] In step S06, the height H is achieved by combining disc springs. z The constraints used in the corner element include: the length of the mandrel and the height of the support.

[0152] First constraint: l x >H z +t x In the formula, lx t represents the length of the mandrel. x Indicates the thickness of the lower constraint plate; second constraint condition: h d >l x -H z -t x +f z In the formula, h d Indicates the support height.

[0153] This invention, based on the structural parameters of the swaying wall and frame structure, obtains the shear stiffness of the frame structure. Using the shear stiffness, structural parameters, and the constructed first and second equilibrium equations, it establishes a first lateral displacement expression under a horizontal inverted triangular load and a second lateral displacement expression under a top concentrated load. Furthermore, it constructs an inter-story drift angle expression using the first and second lateral displacement expressions to solve for the stiffness of the rotating combined disc spring when the inter-story drift angle is the target inter-story drift angle. The bending moment of the rotating combined disc spring is obtained using angle calculation formulas, bending moment calculation formulas, and the stiffness of the rotating combined disc spring. The load-bearing capacity and deformation requirements of the combined disc springs are determined. Based on these requirements, the number of individual disc springs stacked in the same direction and the total number of disc springs in combination are calculated. This yields the combined height of the disc springs. The combined height then constrains the length of the mandrel and the height of the support in the corner element. By constructing various expressions to determine the combined height of the disc springs without using dynamic variables such as time and acceleration, a rapid constraint on the length of the mandrel and the height of the support in the corner element is achieved based on statics, greatly improving the design efficiency of the corner element.

[0154] It should be noted that all directional indications (such as up, down, left, right, front, back, etc.) in the embodiments of the present invention are only used to explain the relative positional relationship and movement of each component in a certain specific posture (as shown in the figure). If the specific posture changes, the directional indication will also change accordingly.

[0155] Furthermore, in this invention, descriptions involving terms such as "first," "second," and "a" are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this invention, "a plurality of" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0156] In this invention, unless otherwise explicitly specified and limited, the terms "connection," "fixed," etc., should be interpreted broadly. For example, "fixed" can mean a fixed connection, a detachable connection, or an integral part; it can mean a mechanical connection or an electrical connection; it can mean a direct connection or an indirect connection through an intermediate medium; it can mean the internal communication of two components or the interaction between two components, unless otherwise explicitly limited. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0157] Furthermore, the technical solutions of the various embodiments of the present invention can be combined with each other, but only if they are feasible for those skilled in the art. If the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention.

Claims

1. A method for constraining corner elements in a rocking wall structure system, wherein, The corner element includes an upper constraint plate, a combined disc spring, and a lower constraint plate arranged sequentially from top to bottom; one end of the combined disc spring abuts against the upper constraint plate, and the other end of the combined disc spring abuts against the lower constraint plate; the lower constraint plate has a through hole, and a support is provided at the bottom of the lower constraint plate; a core rod is provided on the upper constraint plate, and the core rod passes through the combined disc spring and the through hole sequentially from top to bottom. The feature is that it includes the following steps: S01: Set the structural parameters of the swaying wall and the frame structure, and obtain the shear stiffness of the frame structure through the structural parameters of the frame structure; set the expressions for the top concentrated load F and the horizontal inverted triangular load; set the target inter-story drift angle θ. tar The horizontal inverted triangular load expression includes the variable ξ, which is the vertical height ξ of the rocking wall structure system. S02: Construct the first equilibrium equation by considering the differential relationship between the force balance, bending moment, shear force, and load intensity of the swaying wall; define the lateral horizontal load on the frame structure as a horizontal inverted triangular load, and transform the first equilibrium equation using the expression for the horizontal inverted triangular load. Then, construct the first lateral displacement expression for the swaying wall structure system under the horizontal inverted triangular load using the transformed first equilibrium equation, shear stiffness, and structural parameters of the swaying wall; construct the second equilibrium equation by defining the lateral horizontal load on the frame structure as a top concentrated load and setting the top concentrated load F to be non-zero. Finally, construct the second lateral displacement expression for the swaying wall structure system under the top concentrated load using the second equilibrium equation. S03: Construct the inter-story drift angle expression using the first and second lateral drift expressions, and differentiate the inter-story drift angle expression to solve for the inter-story drift angle θ when it is the target inter-story drift angle. tar The corresponding vertical height ξ max By substituting the vertical height ξ max The stiffness K of the rotating combined disc spring is obtained from the expression for the inter-story drift angle. r ; S04: Calculation formulas for the angle of rotation of the bottom surface of the swaying wall relative to the foundation plane, the bending moment calculation formula for the rotating disc spring, and the stiffness K of the rotating disc spring. r Obtain the bending moment M of the rotating combined disc spring. r ; S05: Construct bending moment M r With the combined disc spring load-bearing capacity requirement F z The relationship is expressed by using the obtained bending moment M. r Substituting into the formula, we obtain the load-bearing capacity requirement F of the combined disc spring. z ; S06: By combining disc springs, the load-bearing capacity requirement F is met. z Determine the number N of single disc springs stacked in the same direction, and obtain the required deformation f of the combined disc springs. z Through deformation demand f z Obtain the number i of mating disc springs in the combined disc spring; obtain the combined height H of the disc spring by combining the number N of individual disc springs stacked in the same direction with the number i of mating disc springs. z The height H is achieved by combining disc springs. z Constrain the length of the mandrel and the height of the support in the corner element.

2. The corner element constraint method for a rocking wall structure system according to claim 1, characterized in that, The S01 step also includes: setting the target value γ of the restoring force coefficient to be shared by the corner element. tar The process between steps S03 and S04 also includes: S31: Obtain the stiffness K of the rotating combined disc spring by using the formula for calculating the restoring force coefficient of the corner element. r The corresponding restoring force coefficient to be shared by the corner element; the calculation formula for the restoring force coefficient to be shared by the corner element is: In the formula, γ represents the coefficient of restoring force to be shared by the corner element, u f K represents r When =∞, relative to K r The amount of displacement decrease when u = 0 r K represents r When ≠∞, relative to K r The amount of displacement reduction when = 0; S32: Determine if γ is greater than or equal to γ tar If so, proceed to step S04.

3. The corner element constraint method for a rocking wall structure system according to claim 2, characterized in that, In step S01, the structural parameters of the swaying wall include the elastic modulus E of the concrete. w and the width b of the sway wall section w and length h w The structural parameters of the frame structure include: the elastic modulus E of the concrete. f The total height H of the frame structure, the floor height h, the number of columns n per floor, and the beam cross-sectional width b. b With cross-sectional length h b The width of the column section b c With cross-sectional length h c ; The formula for obtaining the shear stiffness of the frame structure is as follows: In the formula, I c Let I be the moment of inertia of the column; b Let K be the moment of inertia of the beam, and K be the shear stiffness. The expression for the horizontal inverted triangular load is: P(ξ)=qξ; where, Where H is the total height of the frame structure; x is any height of the frame structure; P(ξ) is the uniformly distributed lateral horizontal load on the swaying wall and the overall frame structure; and q is the maximum vertical axis value.

4. A method for constraining corner elements in a rocking wall structure system according to claim 3, characterized in that, In step S02, the formula expression for the first equilibrium equation is: In the formula, I w Let u be the moment of inertia of the swaying wall section in the plane, and u in the first equilibrium equation. β This represents the lateral displacement of the rocking wall structure system under a horizontal inverted triangular load. The first equilibrium equation is transformed using the horizontal inverted triangular load expression. The transformed first equilibrium equation is expressed as follows: The formula for the first lateral displacement expression is: In the formula, Where λ is a dimensionless parameter reflecting the relative magnitude of the shear stiffness of the frame structure and the bending stiffness of the swaying wall section; β is a dimensionless parameter reflecting the relative magnitude of the stiffness of the rotating combined disc spring and the bending stiffness of the swaying wall section; K r To determine the stiffness of the rotating disc spring.

5. A method for constraining corner elements in a rocking wall structure system according to claim 4, characterized in that, In step S02, the formula expression for the second equilibrium equation is: u in the second equilibrium equation β This indicates the lateral displacement of the rocking wall structure system under a concentrated load at the top; The formula for the second lateral displacement expression is: In the formula, 6. A method for constraining corner elements in a rocking wall structure system according to claim 4, characterized in that, In step S03, the inter-story drift angle expression is constructed using the first lateral drift expression and the second lateral drift expression, specifically as follows: The inter-story drift angle θ under horizontal inverted triangular load is obtained using the first lateral displacement expression. tri The formula is: The inter-story drift angle θ under the concentrated load at the top is obtained using the second lateral displacement expression. con The formula is: via θ tri With θ con The expression for the inter-story drift angle is constructed as follows: In the formula, θ z The inter-story drift angle is the angle between the horizontal inverted triangular load and the top concentrated load. In step S03, the derivative of the expression for the inter-story drift angle is obtained, and the derivative formula is as follows: The target inter-layer displacement angle θ tar This is the limit value for inter-story drift angle.

7. A method for constraining corner elements in a rocking wall structure system according to claim 5, characterized in that, The S04 step specifically includes: The angle calculation formula for the rotation of the bottom surface of the swaying wall relative to the foundation plane is obtained through a preset rotation angle calculation formula; the preset rotation angle calculation formula is: In the formula, y represents the lateral displacement of the overall frame structure, which is the sum of the corresponding lateral displacements of the swaying wall structure system under the action of the horizontal inverted triangular load and the action of the top concentrated load; x represents the actual height of the frame structure; θ represents the angle of rotation of the swaying wall relative to the foundation plane. The formula for calculating the angle is: In the formula, ξ=0 indicates that the vertical height of the rocking wall structure system is 0; θ0 indicates the angle of rotation of the bottom surface of the rocking wall relative to the foundation plane; By connecting θ0 with K r Substitute the values ​​into the formula for calculating the bending moment of a rotating disc spring to obtain the bending moment M of the rotating disc spring. r The expression for the bending moment calculation formula is: M r =K r θ0.

8. A method for constraining corner elements in a rocking wall structure system according to claim 7, characterized in that, In step S05, the bending moment M r With the combined disc spring load-bearing capacity requirement F z The relational expression is: In the formula, b r b is the width of the corner element. w Width b of the sway wall section w .

9. A method for constraining corner elements in a rocking wall structure system according to claim 8, characterized in that, In step S06, the formula for obtaining the number N of single disc springs stacked in the same direction is: F z =N·F spr In the formula, F spr Let f ≈ 0.75h0 be the load-bearing capacity of a single disc spring, where f represents the deformation of a single disc spring and h0 represents the deformation of a single disc spring without support surface when compressed. In step S06, the deformation requirement f z The formula for obtaining it is: In the formula, θ max This indicates the maximum angle of rotation of the bottom surface of the swing wall relative to the foundation plane. In step S06, the formula for obtaining the number i of disc springs engaged is: f z =i·f; In step S06, the height H of the disc spring assembly z The formula for obtaining it is: H z =i·(H0+(N-1)·t); where H0 is the free height of a single disc spring, and t represents the thickness of a single disc spring.

10. A method for constraining corner elements in a rocking wall structure system according to claim 8, characterized in that, In step S06, the height H is achieved by combining disc springs. z The constraints used in the corner element include: the length of the mandrel and the height of the support. First constraint: l x >H z +t x In the formula, l x t represents the length of the mandrel. x Indicates the thickness of the lower constraint plate; second constraint condition: h d >l x -H z -t x +f z In the formula, h d Indicates the support height.

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