Method for determining the stress and deformation of hinged beam foundation-soil system

Abstract

The present invention discloses a method for determining the stress deformation of an articulated beam foundation-foundation system, comprising the following steps: step S1, based on the structure of the articulated beam foundation-foundation system, establishing a mechanical model and a coordinate system of the articulated beam foundation-foundation system; step S2, based on the mechanical model and the coordinate system of the articulated beam foundation-foundation system, calculating the displacement, rotation angle, bending moment, and shear force of the articulated beam foundation-foundation system under the action of a concentrated force; step S3, determining the boundary and continuity conditions of the articulated beam foundation-foundation system, and based on the boundary and continuity conditions, calculating the displacement, rotation angle, bending moment, and shear force of the articulated beam foundation-foundation system under the action of a concentrated force, and being able to accurately determine the structural internal force of the articulated beam foundation-foundation system for structural design. The problem that the internal force calculation method of the traditional cast-in-place frame beam structure is not applicable to the articulated beam foundation-foundation system is solved.

Description

Technical Field

[0001] The invention belongs to the technical field of foundation stress and deformation research, and relates to a method for determining the stress and deformation of an articulated beam foundation-foundation system. Background Art

[0002] Anchor frame beams are safe and reliable in structure and beautiful in appearance, so they are widely used in slope support projects. Although the existing anchor frame beam support system has been used for more than 30 years, in actual application, the existing anchor frame beams have many problems, such as poor support and timeliness, low concrete quality, difficult deformation coordination, complex procedures, high construction risks, etc., which still make it There is a large gap between them and actual needs. In order to solve these problems existing in the construction of the existing cast-in-place frame beam anchoring system, Zhang Junhui and others developed an articulated anchor frame beam structure (Zhang Junhui, Li Feng, Zheng Jianlong, Zhang Shiping. Waterproof and moisturizing fully prefabricated lattice beam anchor support system, support and repair method [P]. Hunan Province: ZL 201910542787.7, 2021-01-01.), such as Figure 1 As shown in the figure, the articulated beam foundation-subgrade system is composed of prefabricated beams connected to each other as a whole, forming an articulated structure. The action mechanism between soil, anchor cables and frame beams is fully revealed through numerical simulation, centrifuge model test, slope monitoring, etc., and the safety and reliability of the articulated beam foundation-subgrade system are verified. The articulated beam foundation-subgrade system has been successfully applied to the slope support of K55+920-K56+050 of Guizhou Jiangyu Expressway (Jiangkou to Yuping) and K87+391.5~K87+565 of Guihuang Expressway (Guiyang to Huangping). The on-site application results show that the articulated beam foundation-subgrade system is superior to the traditional cast-in-place frame beam anchoring system in terms of construction period, personnel and machinery, safety management, economic cost, carbon emissions, and support effect. However, there is still a lack of structural design methods for the articulated anchor frame beam, which is not convenient for engineering application. However, the bending moment of the articulated beam foundation-foundation system is smaller than that of the traditional cast-in-place frame beam structure. If the internal force calculation method of the traditional cast-in-place frame beam structure is used to calculate the internal force of the articulated beam foundation-foundation system for structural design, it will cause a waste of structural resistance. Therefore, it is necessary to accurately determine the structural internal force of the articulated beam foundation-foundation system, and then perform structural design based on the maximum internal force of the articulated beam foundation-foundation system structure. Summary of the invention

[0003] The purpose of an embodiment of the present invention is to provide a method for determining the stress and deformation of an articulated beam foundation-subgrade system, so as to solve the problem that the internal force calculation method of a traditional cast-in-place frame beam structure is not applicable to the articulated beam foundation-subgrade system.

[0004] The technical solution adopted in the embodiment of the present invention is: a method for determining the stress and deformation of an articulated beam foundation-foundation system, comprising the following steps:

[0005] Step S1, based on the structure of the articulated beam foundation-foundation system, establishing a mechanical model and a coordinate system of the articulated beam foundation-foundation system;

[0006] Step S2, based on the mechanical model and coordinate system of the articulated beam foundation-foundation system, calculating the general solution of the displacement, rotation angle, bending moment and shear force of the articulated beam foundation-foundation system under the action of concentrated force;

[0007] Step S3, determine the boundary and continuity conditions of the articulated beam foundation-foundation system, and based on the boundary and continuity conditions, calculate the displacement, rotation, bending moment and shear force of the articulated beam foundation-foundation system under the action of concentrated force.

[0008] Furthermore, in step S1:

[0009] The articulated beam foundation-foundation system uses an articulated anchor frame beam consisting of three sections of precast beams as a unit, regards the connection between the precast beams as the hinge point, simplifies the foundation action into a spring action, and establishes a mechanical model;

[0010] A coordinate system is established with the left end point of the articulated anchor frame beam as the origin and the length direction of the articulated anchor frame beam as the x-axis direction. The coordinates of points A, B, C, D, E, and F from left to right on the articulated anchor frame beam are (0,0), (L1,0), (l1,0), (l2,0), (L3,0), and (l3,0), respectively. Points A and F are endpoints, points B and E are anchor points, points C and D are hinge points, and concentrated forces P1 and P3 act on points B and E, respectively. P1 represents the concentrated force on the first section of precast beam, and P3 represents the concentrated force on the third section of precast beam.

[0011] Furthermore, in step S2, the general displacement solution of the articulated beam foundation-foundation system is:

[0012]

[0013] In the formula, w i (x) represents the concentrated force P on the i-th precast beam of the articulated beam foundation-soil system i The general solution of displacement under action, i = 1, 2, 3, P2 = 0; x is the horizontal coordinate of any point on the surface of the hinged anchor frame beam, λ is the defined intermediate variable, k is the foundation reaction coefficient, b is the width of the hinged anchor frame beam, E is the elastic modulus of the hinged anchor frame beam, I is the section inertia moment of the hinged anchor frame beam, h is the height of the hinged anchor frame beam; C4i-3 , C 4i-2 , C 4i-1 , C 4i That is, C1~C 12 , is the integration constant; Indicates the concentration P i The position of action, is the Heaviside function,

[0014] Furthermore, in step S2, the general solution of the rotation angle of the articulated beam foundation-foundation system under the concentrated force is:

[0015]

[0016] Among them, θ i (x) represents the concentration force P i The rotation angle of the i-th precast beam under the action.

[0017] Furthermore, in step S2, the general solution of the bending moment of the articulated beam foundation-foundation system under the concentrated force is:

[0018]

[0019] Among them, M i (x) represents the concentration force P i Bending moment of the i-th precast beam under the action.

[0020] Furthermore, in step S2, the general solution of the shear force of the articulated beam foundation-foundation system under the concentrated force is:

[0021]

[0022] Among them, Q i (x) represents the concentration force P i The shear force of the i-th precast beam under the action.

[0023] Furthermore, in step S3, the boundary and continuity conditions of the articulated beam foundation-foundation system are:

[0024]

[0025]

[0026]

[0027]

[0028]

[0029]

[0030]

[0031]

[0032]

[0033]

[0034]

[0035]

[0036] Combining equations (10) to (21), we can obtain the integral constants C1 to C 12 ;

[0037] In step S3, C1 to C 12 Substitute the general solution of the displacement, rotation, bending moment and shear force of the articulated beam foundation-foundation system under the action of concentrated force to obtain the definite expression of the displacement, rotation, bending moment and shear force of the articulated beam foundation-foundation system.

[0038] The beneficial effects of the embodiments of the present invention are as follows: a method for determining the force and deformation of an articulated beam foundation-foundation system is provided, and the mechanical boundary conditions at the articulation are used to solve the structural internal force and deformation of the articulated beam foundation-foundation system, which is applicable to the internal force calculation of the articulated beam foundation-foundation system structure, and solves the problem that the internal force calculation method of the traditional cast-in-place frame beam structure is not applicable to the articulated beam foundation-foundation system. The main calculation process can be realized by software, which solves the problem that the manual algorithm is prone to errors and improves the calculation accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0040] Figure 1 It is a structural diagram of an articulated beam foundation-foundation system.

[0041] Figure 2 It is a structural mechanics model and coordinate system diagram of the articulated beam foundation-foundation system.

[0042] Figure 3 It is a displacement, rotation, bending moment and shear force curve diagram of the articulated beam foundation-foundation system and the traditional frame beam anchoring system.

[0043] Figure 4 It is a curve diagram of displacement, rotation, bending moment and shear force of the articulated beam foundation-foundation system under different concentrated forces.

[0044] Figure 5 It is a graph of displacement, rotation, bending moment and shear force of the articulated beam foundation-foundation system under different foundation reaction coefficients.

[0045] Figure 6 It is a graph of displacement, rotation, bending moment and shear force of the articulated beam foundation-foundation system under different cross-sectional sizes.

[0046] Figure 7 It is the displacement, rotation, bending moment and shear force curve of the articulated beam foundation-foundation system under different cantilever lengths.

[0047] Figure 8 It is the displacement, rotation, bending moment and shear force curve diagram of the articulated beam foundation-foundation system at different articulation positions. DETAILED DESCRIPTION

[0048] The following will be combined with the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0049] Example 1

[0050] This embodiment provides a method for determining the stress and deformation of an articulated beam foundation-foundation system, comprising the following steps:

[0051] Step S1, based on the structure of the articulated beam foundation-foundation system, establishing a mechanical model and a coordinate system of the articulated beam foundation-foundation system;

[0052] Step S2, based on the mechanical model and coordinate system of the articulated beam foundation-foundation system, calculating the general solution of the displacement, rotation angle, bending moment and shear force of the articulated beam foundation-foundation system under the action of concentrated force;

[0053] Step S3, determine the boundary and continuity conditions of the articulated beam foundation-foundation system, and based on the boundary and continuity conditions, calculate the displacement, rotation, bending moment and shear force of the articulated beam foundation-foundation system under the action of concentrated force.

[0054] For step S1, the articulated beam foundation-foundation system adopts an articulated anchor frame beam, such as Figure 1As shown in the figure, a simplified three-section precast beam structure consisting of an articulated anchor frame beam is used as a representative, that is, the articulated beam foundation-foundation system uses an articulated anchor frame beam consisting of three sections of precast beams as a unit. The precast beams can rotate vertically. The connection between the precast beams is regarded as a hinge point, where the deflection and shear force are continuous and the bending moment is zero. The foundation effect is simplified to a spring effect, and the following is established: Figure 2 The mechanical model shown in the figure establishes a coordinate system with the left end point of the hinged anchor frame beam as the origin and the length direction of the beam as the x-axis direction. The coordinates of points A, B, C, D, E, and F from left to right are (0,0), (L1,0), (l1,0), (l2,0), (L3,0), and (l3,0), respectively. Points A and F are endpoints, points B and E are anchor points, points C and D are hinge points, and concentrated forces P1 and P3 act on points B and E, respectively. P1 represents the concentrated force on the first section of the beam, and P3 represents the concentrated force on the third section of the beam.

[0055] For step S2, since the foundation model is assumed to be a spring, the pressure P at any point on the beam surface is proportional to the displacement of the point, so:

[0056] P(x)=kw(x); (1)

[0057] Where, P(x) is the reaction force of the foundation on any point on the surface of the articulated anchor frame beam, k is the foundation reaction coefficient, w(x) is the vertical displacement of any point on the surface of the articulated anchor frame beam, i.e. the articulated beam foundation-foundation system, and x is the horizontal coordinate of any point on the surface of the articulated anchor frame beam;

[0058] Combining equation (1), the differential equation of the beam deflection curve is established as:

[0059]

[0060] Where, E is the elastic modulus of the hinged anchor frame beam, I is the section inertia moment of the hinged anchor frame beam, h is the height of the articulated anchor frame beam, and b is the width of the articulated anchor frame beam.

[0061] Let w(x)=e λx , λ is the defined intermediate variable, Substituting it into equation (2), the general solution of the vertical displacement of the articulated beam foundation-foundation system can be obtained as:

[0062] w(x)=e λx (C1 cosλx+C2 sinλx)+e -λx (C3cosλx+C4 sinλx); (3)

[0063] In the formula, C1, C2, C3, and C4 are integral constants, which can be determined according to different load types and boundary conditions.

[0064] According to the differential relationship between the displacement, rotation, bending moment and shear force of any section on the hinged anchor frame beam, the bending moment and shear force of any section of the hinged anchor frame beam can be calculated. The specific process is as follows:

[0065] Considering the influence of concentrated force, when x≥x P (position of concentrated force), the displacement w(x) increased by the concentrated force P can be obtained from equation (3): P for:

[0066]

[0067] Combining formula (4) with the boundary and continuity conditions of each precast beam of the articulated beam foundation-soil system, the general solution of the displacement of the articulated beam foundation-soil system under concentrated force is obtained as follows:

[0068]

[0069] In the formula, w i (x) represents the concentrated force P on the i-th precast beam of the articulated beam foundation-soil system i General solution of displacement under action, i = 1, 2, 3, P2 = 0; C 4i-3 , C 4i-2 , C 4i-1 , C 4i is the integral constant, that is, C1~C 12 , determined according to different load types and boundary conditions; is the Heaviside function, Indicates the concentration P i The position of action;

[0070] The relationship between the rotation angle θ(x), bending moment M(x), shear force Q(x) and displacement of the foundation beam section is:

[0071]

[0072] Substituting equation (5) into equation (6), the general solution of the rotation angle, bending moment and shear force of the articulated beam foundation-foundation system under concentrated force is obtained as follows:

[0073]

[0074]

[0075]

[0076] Among them, θ i (x) represents the concentration force P i The rotation angle of the i-th beam (precast beam) under the action, M i (x) represents the concentration force P i The bending moment of the i-th beam under the action, Q i (x) represents the concentration force P i The shear force on the i-th beam section under the action of .

[0077] For step S3, to solve the displacement, rotation, bending moment and shear force of the articulated beam foundation-foundation system, it is necessary to establish a set of equations according to the boundary and continuity conditions to obtain the specific value of the integral constant. Figure 2 It can be seen that the bending moment and shear force at the free end of the articulated anchor frame beam are zero, the bending moment at the hinge is zero, and the displacement and shear force at the hinge are continuous.

[0078] For the first beam (precast beam):

[0079] The moment balance at point C (AC segment) is:

[0080]

[0081] Bending moment at point A M 1A is zero, we have:

[0082]

[0083] Shear force Q at point A 1A is zero, we have:

[0084]

[0085] For the second beam:

[0086] The bending moment at point C is balanced, so:

[0087]

[0088] The bending moment at point D is balanced, so:

[0089]

[0090] The displacements on both sides of point C are equal:

[0091]

[0092] The displacements on both sides of point D are equal:

[0093]

[0094] Bending moment at point C M 2C is zero, we have:

[0095]

[0096] Bending moment at point D M 2D is zero, we have:

[0097]

[0098] For the third beam:

[0099] The moment balance at point D (segment DF) is:

[0100]

[0101] The bending moment at point F is zero:

[0102]

[0103] The shear force at point F is zero:

[0104]

[0105] Combining equations (10) to (21), we can obtain C1 to C 12 , and then substitute into equations (5) and (7) to (9), we can obtain the definite expressions for the displacement, rotation, bending moment, and shear force of the articulated beam foundation-foundation system.

[0106] Example 2

[0107] based on Figure 2 The mechanical model and coordinate system shown in the figure adopt the displacement, rotation, bending moment and shear force of the hinged beam foundation-foundation system derived and solved by Example 1. The length of a single beam is 2m, the cross-sectional dimensions are the beam width b = 0.3m, the beam height h = 0.4m, and the foundation reaction coefficient k is taken as the average value of 4×10 4 kN / m 3 , the distributed concentrated force P is taken as 345kN, the commonly used C30 concrete elastic modulus is taken as 30GPa, and the distance between the hinge point and the anchor point is taken as the minimum value of 0.5m.

[0108] Figure 3The figure shows the curves of displacement, rotation, bending moment and shear force of two frame beam structures under different concentrated forces (0.5P, 1.0P) (C represents the traditional frame beam structure, and J represents the articulated anchor frame beam structure). The traditional structure is calculated by the method proposed in the document "Huang Yi, He Fangshe. Beams, plates and shells on elastic foundations [M]. Science Press, 2005", and the articulated anchor frame beam structure is calculated by the method of Example 1. The displacement, rotation, bending moment and shear force variation trends of the traditional cast-in-place frame beam structure are similar to those of the articulated anchor frame beam structure, except that the maximum deflection of the articulated anchor frame beam structure is greater than that of the traditional cast-in-place structure, and the minimum deflection of the articulated anchor frame beam structure is less than that of the traditional cast-in-place structure. This is because the articulated anchor frame beam structure is connected by an articulated structure, each section of the beam has a higher degree of freedom, and the displacement of its bottom beam is less affected by other sections; the articulated structure has discontinuous rotation angles at the 2m and 4m positions, one positive and one negative, while the traditional structure is continuous; taking the bending moment and shear force of the concentrated force of 1.0P as an example, the maximum positive and negative bending moments of the articulated anchor frame beam are 90kN·m and -70kN·m, respectively, and the shear forces are 208kN and -208kN, respectively. The maximum positive and negative bending moments of the traditional frame beam are 115kN·m and -20kN·m, respectively, and the shear forces are 182kN and -182kN, respectively. The maximum structural bending moment value of the articulated anchor frame beam is smaller than that of the traditional frame beam, which is about 70% to 80% of the traditional structure (reduced by more than 20%); the shear forces of the two are basically equivalent, with a difference of about 10%. Therefore, the hinged anchor frame beam structure can effectively reduce the maximum bending moment of the structure without changing the extreme value of the shear force, thus optimizing the stress state of the structure. Figure 3 It can also be seen that the calculation results are completely consistent with the boundary and continuity conditions, which also verifies the rationality of the derivation of Example 1.

[0109] Figure 4The figure shows the curves of the displacement, rotation, bending moment and shear force of the bottom of the beam of the hinged beam foundation-foundation system under different concentrated forces (0.5P, 0.75P, 1.0P and 1.25P). It can be seen that with the increase of concentrated force, the displacement, rotation, bending moment and shear force of the bottom of the beam of the hinged beam foundation-foundation system also increase. The maximum displacement of the bottom of the beam occurs at the positions of 2m and 4m, where the hinge points are located. This is because the existence of the hinge points makes the deformation of the beam easier. The hinge points transmit shear force and axial force, but not bending moment, that is, the translational degrees of freedom of the hinge points are equal, the rotational degrees of freedom are irrelevant, and the rotation angles can be unequal. Therefore, the rotation angles are discontinuous and one positive and one negative appear at the positions of 2m and 4m. Taking the bending moment and shear force of the concentrated force of 1.25P as an example, along the length of the beam, the bending moment at the position of 0 to 1.5m increases from 0 to 110kN. m, then the bending moment at 1.5-3.0m decreases from 100 to 0kN·m and then to -90kN·m. The curves of displacement and bending moment change are centrally symmetrically distributed at the midpoint of the calculation model. The bending moment at 0m, 2m, 4m, and 6m is zero, corresponding to the boundary conditions of zero bending moment at the hinge point and free end. The shear force increases from 0 to 170kN at 0-1.5m, and suddenly changes from 170kN to -260kN at 1.5m due to the concentrated force. The sum of its absolute values ​​is the concentrated force acting at this location. Then it increases from -260kN to 0kN at 1.5-3.0m. The shear force and rotation angle changes on the right side of the coordinate 3.0m are axially symmetrical with the left side. The shear force at 0m and 6m is zero, corresponding to the boundary conditions of zero shear force at the free end. The shear force at 2m and 4m is continuous, which meets the condition of shear force transmission at the hinge point.

[0110] Figure 5 The figure shows the curves of the displacement, rotation, bending moment and shear force of the bottom of the beam under different foundation reaction coefficients of the articulated beam foundation-foundation system. The larger the foundation reaction coefficient, the less likely the soil is to deform under the action of external forces. Figure 6 The value of the foundation reaction force is K1 = 1 × 10 5 kN / m 3 K2=2×10 5 kN / m 3 K3 = 3 × 10 5 kN / m 3 K4 = 4 × 10 5 kN / m 3 K5 = 5 × 10 5 kN / m 3 As can be seen from the figure, the size of the foundation reaction coefficient has a significant impact on the displacement and rotation of the frame beam. The larger the foundation reaction coefficient, the smaller the displacement and rotation; and under the conditions of different foundation reaction coefficients, the bending moment and shear force are slightly affected.

[0111] Figure 6 The figure shows the curves of displacement, rotation, bending moment and shear force of the articulated beam foundation-foundation system structure under different cross-sectional dimensions. The cross-sectional dimensions are S3 = b × h = 0.3m × 0.3m, S4 = b × h = 0.4m × 0.4m, S5 = b × h = 0.5m × 0.5m, S6 = b × h = 0.6m × 0.6m. It can be seen from the figure that different cross-sectional dimensions have little effect on the bending moment and shear force of the frame beam, but have a greater effect on the displacement and rotation of the frame beam. When only the cross-sectional dimensions are changed, the larger the value, the smaller the displacement and rotation of the beam. The smaller the cross-sectional dimensions, the easier it is for the beam to deform when subjected to external forces, but the magnitude of the external forces it is subjected to remains unchanged, so the shear force and bending moment of the beam change very little.

[0112] Figure 7 The figure shows the variation curves of the displacement, rotation, bending moment and shear force of the bottom of the beam under different cantilever lengths (from the free end to the anchor point) of the articulated beam foundation-foundation system. In the figure, the cantilever lengths are X1 = 0.5m, X2 = 0.75m, X3 = 1.0m, X4 = 1.25m, and X5 = 1.5m. It can be seen from the figure that the cantilever length has a significant effect on the displacement, rotation, bending moment and shear force of the beam. As the cantilever length increases, the deflection at the cantilever end decreases sharply, from 40mm to 5mm, while the deflection of the beam between the two hinge points increases, from 5mm to 12mm, which is much smaller than the end; the change in the rotation angle is similar to the displacement, the absolute value of the rotation angle on both sides of the hinge point decreases with the increase of the cantilever length, and the rotation angle value of the beam between the hinge points changes less; the positive bending moment increases with the increase of the cantilever length, and the negative bending moment decreases with the increase of the cantilever length; the maximum absolute value of the shear force on both sides of the anchor point decreases with the increase of the cantilever length, while it is just the opposite between the anchor points, increasing with the increase of the cantilever length. This is because after the cantilever length is reduced, the force area of ​​the beam is reduced, while the stiffness of the soil remains unchanged, so the deflection of the beam at both ends is greater, and the influence of the concentrated force increases, while the influence of the part between the concentrated force points decreases, so the displacement, rotation angle, bending moment, and shear force of the middle beam are smaller. Therefore, when designing the structure of the articulated beam foundation-foundation system, the distance between the anchor point near the end and the end should be reduced as much as possible, thereby effectively reducing the bending moment near the anchor point near the end of the articulated beam foundation-foundation system.

[0113] Figure 8The figure shows the curves of displacement, rotation, bending moment and shear force of the bottom of the beam under different hinge positions (from the hinge point to the adjacent anchor point) of the hinged beam foundation-foundation system. The hinge position in the figure is Y1=0.5m, Y2=0.6m, Y3=0.7m, Y4=0.8m, and Y5=0.9m, which is the length from the anchor point. It can be seen from the figure that as the distance between the hinge point and the anchor point increases, the displacement change tends to be gentle, the maximum displacement decreases, and the displacement at the end increases; as the distance between the hinge point and the anchor point increases, the absolute value of the rotation angle decreases; the positive bending moment increases with the increase of the distance between the hinge point and the anchor point, and the negative bending moment decreases with the increase of the distance between the hinge point and the anchor point. Therefore, there is a hinge point position that makes the absolute value of the maximum positive bending moment equal to the minimum negative bending moment; the distance between the hinge point and the anchor point has little effect on the shear force. Increasing the distance between the hinge point and the anchor point is equivalent to making the force-bearing structure at the position where the concentrated force acts closer to the traditional cast-in-place structure, which is manifested in a flatter displacement curve, a smaller sudden change in the angle at the hinge point, and an increase in the bending moment and negative bending moment at the point where the concentrated force acts. Therefore, when designing the structure of the hinged beam foundation-foundation system, by adjusting the distance between the hinge point and the adjacent anchor point, the bending moment on both sides of the anchor point of the hinged beam foundation-foundation system can be effectively balanced and the maximum bending moment value can be reduced.

[0114] The above description is only a preferred embodiment of the present invention and is not intended to limit the protection scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention are included in the protection scope of the present invention.

Claims

1. A method for determining the stress and deformation of an articulated beam foundation-foundation system, characterized in that: The following steps are involved: Step S1, based on the structure of the articulated beam foundation-foundation system, establishing a mechanical model and a coordinate system of the articulated beam foundation-foundation system; In step S1: The articulated beam foundation-foundation system uses an articulated anchor frame beam consisting of three sections of precast beams as a unit, regards the connection between the precast beams as the hinge point, simplifies the foundation action into a spring action, and establishes a mechanical model; With the left end of the hinged anchor frame beam as the origin and the length direction of the hinged anchor frame beam as the x-axis direction, a coordinate system is established. The coordinates of points A, B, C, D, E, and F from left to right on the hinged anchor frame beam are (0,0), ( L 1,0)、( l 1,0)、( l 2,0)、( L 3,0)、( l 3,0), points A and F are endpoints, points B and E are anchor points, points C and D are hinge points, and concentrated forces P1 and P3 act on points B and E respectively. P1 represents the concentrated force on the first section of precast beams, and P3 represents the concentrated force on the third section of precast beams; Step S2: Based on the mechanical model and coordinate system of the articulated beam foundation-foundation system, the displacement general solution of the articulated beam foundation-foundation system under the action of concentrated force is calculated as: (5) In the formula, Indicates the articulated beam foundation-soil system in i Concentrated forces on precast beams The general solution of displacement under the action is: ; is the horizontal coordinate of any point on the surface of the hinged anchor frame beam, is the intermediate variable defined, ; is the foundation reaction coefficient, is the width of the articulated anchor frame beam, is the elastic modulus of the hinged anchor frame beam, is the section inertia moment of the hinged anchor frame beam, , is the height of the articulated anchor frame beam; , is the integration constant; Indicates concentration The position of action, is the Heaviside function, ; The general solution of the angle is: (7) in, Indicates concentration Under the effect The corner of the precast beam; The bending moment solution is: (8) in, Indicates concentration Under the effect Bending moment of precast beam; General solution for shear force: (9) in, Indicates concentration Under the effect Shear force of precast beams; Step S3, determine the boundary and continuity conditions of the articulated beam foundation-foundation system, and based on the boundary and continuity conditions, calculate the displacement, rotation, bending moment and shear force of the articulated beam foundation-foundation system under the action of concentrated force.

2. The method for determining the stress and deformation of the articulated beam foundation-foundation system according to claim 1, characterized in that: In step S3, the boundary and continuity conditions of the articulated beam foundation-foundation system are: (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20) (21) Combining equations (10) to (21), we get the integral constant C 1~ C 12 ; In step S3, C 1~ C 12 Substitute the general solution of the displacement, rotation, bending moment and shear force of the articulated beam foundation-foundation system under the action of concentrated force to obtain the definite expression of the displacement, rotation, bending moment and shear force of the articulated beam foundation-foundation system.

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