阅读说明：本技术 一种地基上格子梁节点集中荷载分配方法及结构设计方法 (Method for distributing concentrated loads of lattice beam nodes on foundation and structural design method ) 是由 樊军伟 杨仕教 孙冰 彭成 江俊设 邓波 尹裕 陈文昭 龙慧 戴纳新 方耀楚 于 2021-09-08 设计创作，主要内容包括：本发明提供一种地基上格子梁节点集中荷载分配方法及结构设计方法,涉及地基上格子梁结构分析领域,包括：步骤一：将任意两个相交于i节点上的格子梁分为纵梁、横梁及重叠区；步骤二：根据纵梁、横梁及重叠区的静力平衡条件以及变形协调条件建立三者受力以及变形的关系式；步骤三：根据横梁上的静力平衡条件分析并建立ω-(ix)与F-(ix)的关系式；根据纵梁上的静力平衡条件分析并建立ω-(iy)与F-(iy)的关系式；根据重叠区底面地基上各点沉降一致,得出重叠区所受荷载力以及其变形的关系式；步骤四：根据重叠区静力平衡条件及变形协调条件求解后即可得到荷载分配情况；本发明提供的方案能够提高荷载分配计算结果的准确性,为地基上交叉基础梁的结构设计做出更加准确的指导。(The invention provides a method for distributing concentrated loads of lattice beam nodes on a foundation and a structure design method, which relate to the field of analysis of lattice beam structures on the foundation and comprise the following steps: the method comprises the following steps: dividing any two lattice beams intersected on the i node into longitudinal beams, transverse beams and overlapping areas; step two: establishing a relation of stress and deformation of the longitudinal beam, the transverse beam and the overlapped area according to the static balance condition and the deformation coordination condition of the longitudinal beam, the transverse beam and the overlapped area; step three: analyzing and establishing omega according to static balance condition on the cross beam ix And F ix The relational expression of (1); analyzing and establishing omega according to static balance condition on longitudinal beam iy And F iy The relational expression of (1); obtaining a relational expression of the load force borne by the overlapping area and the deformation of the load force according to the consistent settlement of each point on the foundation on the bottom surface of the overlapping area; step four: static balancing according to overlap regionSolving the conditions and the deformation coordination conditions to obtain the load distribution condition; the scheme provided by the invention can improve the accuracy of the load distribution calculation result and provide more accurate guidance for the structural design of the crossed foundation beam on the foundation.)

1. A method for distributing concentrated loads of lattice beam nodes on a foundation is characterized by comprising the following steps: the method comprises the following steps:

the method comprises the following steps: dividing any two lattice beams intersected on the i node on the foundation into longitudinal beams, transverse beams and overlapping areas; the overlapping area is an overlapping area of the longitudinal beam and the cross beam at a node i, and the longitudinal beam and the cross beam are the residual parts of the original lattice beam after the overlapping area is deducted;

step two: the following equation is established according to static balance conditions and deformation coordination conditions of the longitudinal beams, the cross beams and the overlapping area:

F_i＝F_ix+F_iy+F_ica (1)

ω_ix＝ω_iy＝ω_ica (2)

in the formula: f_i-the total concentrated load acting on the i-node of the lattice beam in kN;

F_ix-concentrated loads assigned to said cross-beam in kN;

F_iy-concentrated loads assigned to said stringers in kN;

F_ica-a concentrated load assigned to said overlapping area in kN;

w_ix-concentrated force F along the connecting ends of said cross-member with said overlapping area_iDeformation in direction, in m;

w_iy-concentrated forces F along the connecting ends of said stringers to said overlap_iDeformation in direction, in m;

w_ica-concentration force F along said overlapping area_iDeformation in direction, in m;

step three: analyzing and establishing omega according to the static balance condition on the cross beam_ixAnd F_ixThe relational expression of (1); analyzing and establishing omega according to static balance conditions on the longitudinal beam_iyAnd F_iyThe relational expression of (1);

according to the consistent settlement of each point on the foundation of the bottom surface of the overlapping area, particularly under the action of long-term load, the ground surface settlement of the overlapping area tends to be uniform, and the following results are obtained:

in the formula: k-foundation bed coefficient in kN/m³(ii) a A is the bottom area of the overlapping area of the longitudinal and transverse beams, and the unit is m²；

Step four: substituting the relational expression established in the third step into the formula (1) and the formula (2) and respectively establishing F_ixAnd F_i、F_iyAnd F_iAnd F_icaAnd F_iThe load distribution condition can be obtained after the relation.

2. The method for distributing the concentrated load of the lattice beam node on the foundation according to claim 1, wherein: in the third step, omega is calculated by adopting Wencher elastic foundation upper beam theoretical analysis_ixAnd F_ix、ω_iyAnd F_iyThe relational expression (c) of (c).

3. The method for distributing the concentrated load of the lattice beam node on the foundation according to claim 2, wherein: analyzing and calculating omega by adopting an infinite long beam superposition method in the third step_ixAnd F_ix、ω_iyAnd F_iyThe relational expression (c) of (c).

4. The method for distributing the concentrated load of the lattice beam node on the foundation according to claim 3, wherein: analyzing and calculating by adopting the infinite long beam superposition method to obtain:

in the formula: z when the beam is a semi-infinite beam_x＝1+e^-2λx(1+2cos²λ x-2cos λ xsin λ x); z when the beam I is a semi-infinite beam and the left-hand outer elongation is 0_x4; when the beam I is an infinite beam, Z_x＝1；

S is the characteristic length of the foundation beam, and the unit is m;

k-foundation bed coefficient in kN/m³；

Lambda-characteristic value of compliance of foundation beam in m^-1；

b-the width of the foundation beam, with the unit of m;

x-is the left outside elongation of the beam I;

F₀-concentrated load on the beam I in kN;

ω₀deformation of the point of concentrated load of the beam I in the direction of the force, in m.

5. The method for distributing the concentrated load of the lattice beam node on the foundation according to claim 2, wherein: in calculation, lattice beam node types are classified in advance to determine Z₀The value of (d);

(1) corner joint: the cross beam and the longitudinal beam are regarded as semi-infinite long beams extending outwards for a certain length;

(2) side node: one of the cross beam or the longitudinal beam is a semi-infinite beam, and the other one is an infinite beam;

(3) an inner node: both the cross beam and the longitudinal beam are regarded as infinite long beams.

6. The method for distributing the concentrated load of the lattice beam node on the foundation according to claim 2, wherein: substituting the formula (3) and the formula (6) into the formula (1) and the formula (2) to obtain

7. The method for distributing the concentrated load of the lattice beam node on the foundation according to claim 2, wherein: in the second step, the influence of concentrated loads of other nodes on the lattice beam is ignored, and only the action of the concentrated loads on the i node is considered.

8. A structure design method is characterized in that: the method comprises the following steps: after the distribution condition of the concentrated load at each node is calculated by using the calculation method for the concentrated load distribution of lattice beam nodes on the foundation according to any one of claims 1 to 7, the overlapping area is abstracted to be a point with zero area, and the influence of the concentrated load obtained by the distribution of the overlapping area is not considered, the elastic foundation upper lattice beams are disassembled into a plurality of one-dimensional foundation upper beams with the concentrated load, wherein the concentrated load is the distributed concentrated load, and then the static balance method, the inverted beam method, the Winkler foundation method or the American ACI method are adopted to respectively perform internal force analysis and structural design on all the disassembled one-dimensional foundation upper beams, wherein the internal force refers to bending moment and shearing force.

Technical Field

The invention relates to the field of analysis of lattice beam structures on a foundation, in particular to a method for distributing concentrated loads of lattice beam nodes on the foundation and a structure design method.

Background

The lattice beam structure on the foundation in civil engineering is most commonly a cross strip foundation; for high-rise buildings with large loads, the foundation is soft, the compression uniformity of foundation soil is poor or column loads are greatly different in size along the longitudinal direction and the transverse direction, the foundation needs to have certain bending rigidity in the longitudinal direction and the transverse direction so as to reduce foundation deformation and avoid excessive uneven settlement, and a crossed strip foundation with a reinforced concrete beam body arranged in two directions is often adopted. The foundation has higher rigidity, can effectively reduce the settlement difference between the column bases, and meets the requirements of foundation bearing capacity and foundation deformation, thereby ensuring the reliability of buildings.

The crossed strip foundation is a space system formed by strip foundations which are rigidly connected in the longitudinal direction and the transverse direction and arranged below the columns, and the theoretical analysis of the interaction between the crossed strip foundations and the foundation is quite complex. At present, a common action theory of a superstructure-foundation (SSI) is not mature, and for preliminary design of a crossed strip foundation, some approximate calculation methods are often adopted to solve the problem of distribution of column loads of longitudinal and transverse foundation beam joints.

The application of lattice beams on foundations in civil engineering also relates to another commonly used situation, namely anchor cable lattice beam slope anchoring technology.

The residual sliding force or soil pressure of the slope rock-soil body is born by anchor rods or anchor cables arranged at the crossing points of the longitudinal and transverse lattice beams, and the residual sliding force or soil pressure is transmitted to the slope deep stable stratum through the anchor rods, so that the slope rock-soil body is in a stable state under the action of the anchoring force provided by the anchor rods. Therefore, the lattice beam is used as an outer anchor structure to uniformly disperse the anchoring force provided by the anchor rod to the slope surface of the whole side slope, so that the condition that the rock soil body under the anchor rod generates large plastic deformation and even is damaged, the slope rock soil body slides out of the outer anchor section of the anchor rod to cause the anchor rod to lose efficacy is avoided, and the adverse geological operation influencing the overall stability of the side slope is mainly born by the anchor rod or the anchor cable arranged at the lattice intersection point.

The prestressed anchor rod (or anchor cable) concrete lattice beam actively reinforces the rock-soil mass of the side slope and controls the deformation of the side slope by applying larger prestress to the anchor rod, is a high-light supporting and retaining structure which has strong applicability, reasonable stress, material saving and attractive and environment-friendly concept, and is widely applied to the reinforcement and treatment of various types and different heights of side slopes in China, particularly high and steep side slopes with poor stability.

Although the technology of anchoring the crossed strip foundation and the prestressed anchor lattice beam side slope in the civil engineering practice process of the past decades is widely applied, the analysis theory of the lattice beam is still not perfect in the design stage. At present, it is a common practice to simplify the load (upper structure frame column load or anchor rod prestress locking value) acting on the intersection point of a lattice beam (cross bar foundation or lattice beam) into a concentrated force, distribute the concentrated load to bar foundation beams in longitudinal and transverse directions, after the concentrated load distribution is completed, artificially disassemble the spatial rigid frame structure of the lattice beam (cross bar foundation or lattice beam) into a plurality of one-dimensional bar foundation beam structures under the action of the concentrated load on an elastic foundation for internal force analysis, and then perform internal force analysis and structural design on the disassembled one-dimensional foundation beam by using a static balance method, an inverted beam method, a Winkler foundation beam method or an American ACI method according to specific conditions.

The above node concentrated load distribution method mainly faces the following disadvantages: when the lattice beams carry out load distribution according to longitudinal and transverse strip-shaped foundation beams, the areas of the cross nodes of the longitudinal and transverse beams (namely the overlapping areas of the longitudinal and transverse lattice beams) are repeatedly used twice, if the proportion of the sum of the areas of the overlapping areas of the cross nodes to the total area of the bottom surface of the lattice beam is large, the concentrated load obtained after the longitudinal and transverse foundation beams are distributed is small, and the analysis and design of the internal force of the foundation beam are unsafe; secondly, in order to avoid the disadvantage that the distributed concentrated load is smaller in the first step, the conventional method is to adjust the concentrated load at the intersection nodes linearly according to the area of the overlapping area of the longitudinal and transverse beams artificially and subjectively, however, when the concentrated loads at the intersection nodes of the whole lattice beam are different greatly, the method for adjusting the concentrated load at the intersection points artificially and subjectively does not obviously increase the load at the action point of the larger concentrated load, so that the secondary load distribution mechanism on the whole lattice beam is unreasonable; abstracting the lattice beam with a certain width into a linear cross structure for node concentrated load distribution and performing internal force analysis, wherein the complexity of the stress state of the overlapping area at the cross position of the longitudinal and transverse foundation beams with a certain width cannot be considered; fourthly, considering that the stress state of the overlapping area of the lattice beam is very complex, simultaneously is restrained by bending moment, shearing force, torque and pressure, is restrained by upper structure frame columns (cross bar-shaped foundation) or steel base plates (lattice beam prestress anchor cable anchoring system), and is directly positioned under concentrated load, correspondingly, the rock-soil body on the surface of the foundation right below the overlapping area deforms greatly and presents a uniform settlement form, so the rigid body characteristic of the overlapping area at the intersection of the longitudinal and transverse foundation beams cannot be considered; therefore, a new node centralized load distribution scheme is needed to solve the above problems.

Disclosure of Invention

The invention aims to provide a method for distributing concentrated loads of lattice beam nodes on a foundation and a structural design method, which are used for solving the problems in the prior art, improving the accuracy of the calculation result of node load distribution and giving more accurate guidance to the structural design of a foundation beam.

In order to achieve the purpose, the invention provides the following scheme:

the invention provides a method for distributing concentrated loads of lattice beam nodes on a foundation, which comprises the following steps:

the method comprises the following steps: dividing any two lattice beams intersected on the i node into longitudinal beams, transverse beams and overlapping areas; the overlapping area is an overlapping area of the longitudinal beam and the cross beam at a node i, and the longitudinal beam and the cross beam are the residual parts of the original lattice beam after the overlapping area is deducted;

step two: the following equation is established according to static balance conditions and deformation coordination conditions of the longitudinal beams, the cross beams and the overlapping area:

F_i＝F_ix+F_iy+F_ica (1)

ω_ix＝ω_iy＝ω_ica (2)

in the formula: f_i-the total concentrated load acting on the i-node of the lattice beam in kN;

F_ix-concentrated loads assigned to said cross-beam in kN;

F_iy-concentrated loads assigned to said stringers in kN;

F_ica-a concentrated load assigned to said overlapping area in kN;

w_ix-concentrated force F along the connecting ends of said cross-member with said overlapping area_iDeformation in direction, in m;

w_iy-concentrated forces F along the connecting ends of said stringers to said overlap_iDeformation in direction, in m;

w_ica-concentration force F along said overlapping area_iDeformation in direction, in m;

step three: analyzing and establishing omega according to the static balance condition on the cross beam_ixAnd F_ixThe relational expression of (1); analyzing and establishing omega according to static balance conditions on the longitudinal beam_iyAnd F_iyThe relational expression of (1);

according to the consistent settlement of each point on the foundation of the bottom surface of the overlapping area, particularly under the action of long-term load, the ground surface settlement of the overlapping area tends to be uniform, and the following results are obtained:

in the formula: k-foundation bed coefficient in kN/m³(ii) a A is the bottom area of the overlapping area of the longitudinal and transverse beams, and the unit is m²；

Step four: substituting the relational expression established in the third step into the formula (1) and the formula (2) and respectively establishing F_ixAnd F_i、F_iyAnd F_iAnd F_icaAnd F_iThe load distribution condition can be obtained after the relation.

Preferably, in the third step, the Wencher elastic foundation upper beam theoretical analysis is adopted to calculate omega_ixAnd F_ix、ω_iyAnd F_iyThe relational expression (c) of (c).

Preferably, in the third step, the infinite long beam superposition method is adopted to analyze and calculate omega_ixAnd F_ix、ω_iyAnd F_iyThe relational expression (c) of (c).

Preferably, the infinite long beam superposition method is adopted for analysis and calculation to obtain:

in the formula: z when the beam is a semi-infinite beam_x＝1+e^-2λx(1+2cos²λ x-2cos λ xsin λ x); z when the beam I is a semi-infinite beam and the overhanging length is 0_x4; when the beam I is an infinite beam, Z_x＝1；

S is the characteristic length of the foundation beam, and the unit is m;

k-foundation bed coefficient in kN/m³；

b-the width of the foundation beam, with the unit of m;

F₀-concentrated force load on the beam I in kN;

ω₀-the beam I is subjected to a concentrated load F₀In m, in the direction of the force.

Preferably, in the calculation, the lattice beam node types are classified in advance to determine Z_xThe value of (d);

(1) corner joint: the cross beam and the longitudinal beam are regarded as semi-infinite long beams extending outwards for a certain length; (see FIG. 3)

(2) Side node: one of the cross beam or the longitudinal beam is a semi-infinite beam, and the other one is an infinite beam; (see FIG. 4)

(3) An inner node: both the cross beam and the longitudinal beam are regarded as infinite long beams. (see FIG. 5)

Preferably, the compounds represented by the formulae (3) and (6) are substituted into the compounds represented by the formulae (1) and (2) to give

Preferably, the influence of concentrated loads of other nodes on the lattice beam is neglected in the step two, and only the action of the concentrated loads on the i node is considered.

The invention provides a structure design method, which comprises the following steps: after the load distribution condition of each node is calculated by using the grid beam node load distribution calculation method, the overlapping area is abstracted to be a point with zero area, the influence of the load distributed by the overlapping area is not considered, the elastic foundation upper grid beam is disassembled into a plurality of one-dimensional foundation upper beams with concentrated force load, then the static balance method, the inverted beam method, the Winkler foundation method or the American ACI method are adopted to respectively carry out internal force analysis and structural design on all the disassembled one-dimensional foundation upper beams, and the internal force refers to bending moment and shearing force.

Compared with the prior art, the invention has the following technical effects:

the method for distributing the load of the grid beam nodes on the foundation separates the overlapped areas when concentrated loads at the i-node are distributed, analyzes and deduces the load and deformation relations of the longitudinal beam, the transverse beam and the overlapped area, and is different from the traditional method for distributing the grid beam into the longitudinal beam and the transverse beam only.

Drawings

In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without creative efforts.

FIG. 1 is a schematic view of a lattice beam node concentrated load distribution structure on a foundation;

FIG. 2 is a schematic diagram of the structure and stress of a beam I and a beam II assumed in the derivation process in the first embodiment;

FIG. 3 is a schematic structural diagram of an i-node as an angle node;

FIG. 4 is a schematic structural diagram of an inode as an edge node;

FIG. 5 is a schematic structural diagram of an inode when the inode is an internal node;

in the figure: 1-cross beam, 2-longitudinal beam and 3-overlapping area.

Detailed Description

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.

The invention aims to provide a method for distributing concentrated loads of lattice beam nodes on a foundation and a structural design method, which are used for solving the problems in the prior art, improving the accuracy of load distribution calculation results and giving more accurate guidance to the structural design of a foundation beam.

In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.

Example one

The embodiment provides a method for distributing concentrated loads of lattice beam nodes on a foundation, which is suitable for distributing concentrated loads of lattice beams on an elastic foundation, and as shown in fig. 1 to 5, the method includes:

the method comprises the following steps: dividing any two beams intersected on the i node into a longitudinal beam 2, a transverse beam 1 and an overlapping area 3; the overlapping area 3 is an overlapping area of the longitudinal beam 2 and the cross beam 1 at a node i, and the longitudinal beam 2 and the cross beam 1 are the rest parts of the original lattice beam after the overlapping area 3 is deducted;

step two: the following equation is established according to the static balance conditions and deformation coordination conditions of the longitudinal beams 2, the cross beams 1 and the overlapping area 3:

F_i＝F_ix+F_iy+F_ica (1)

ω_ix＝ω_iy＝ω_ica (2)

in the formula: f_i-the total concentrated load acting on the i-node of the lattice beam in kN;

F_ix-concentrated load distributed to the beam 1 in kN;

F_iyconcentrated loads assigned to the stringers 2, in kN;

F_ica-concentrated load assigned to the overlap zone 3 in kN;

w_ixthe force F concentrated along the edges of the connection of the cross-member 1 to the overlap 3_iDeformation in direction, in m;

w_iyconcentrated forces F along the edges of the connection of the longitudinal beams 2 to the overlap region 3_iDeformation in direction, in m;

w_icaconcentration of force F along the overlap zone 3_iDeformation in direction, in m;

step three: omega is analyzed and established according to the static balance condition on the cross beam 1_ixAnd F_ixThe relational expression of (1); omega is analyzed and established according to the static equilibrium condition on the longitudinal beam 2_iyAnd F_iyThe relational expression of (1);

researches show that the proportion of the load shared by the longitudinal and transverse overlapping areas 3 of the lattice beam to the total load is considerable, and the load sharing effect is not negligible. In fact, the contact area of the overlap area and the foundation is large, and the concentrated load F is directly positioned at the node_iUnder the action, the corresponding settlement is larger, so that the overlapped area bears a part of concentrated load under the action of the foundation reaction force. Because the stress state of the overlapping area is extremely complex and the bending rigidity of the bottom surface of the overlapping area is very high, the settlement of each point on the foundation of the bottom surface of the overlapping area is consistent, and particularly the settlement of the ground surface of the overlapping area tends to be uniform under the action of long-term load. Thereby assuming a total concentrated load F at the inode_iLoad F assigned to the overlap region_icaThe earth surface of the overlap area generates uniform settlement w under the action_iacCan be expressed as:

in the formula: k-foundation bed coefficient in kN/m³(ii) a A is the bottom area of the overlapping area of the longitudinal and transverse beams, and the unit is m²(ii) a The longitudinal and transverse beams have A ═ b in the orthogonal state_xb_y。

Step four: substituting the relational expression established in the third step into the formula (1) and the formula (2) and respectively establishing F_ixAnd F_i、F_iyAnd F_iAnd F_icaAnd F_iThe load distribution condition can be obtained after the relation.

The method for distributing concentrated loads of lattice beam nodes on the foundation provided by the embodiment separates the overlapping areas independently when distributing the concentrated loads of the i-node, analyzes and deduces the load and deformation relationship of three parts of structures of the longitudinal beam, the cross beam and the overlapping areas respectively, and is different from the traditional distribution method in which the lattice beam is only divided into the longitudinal beam and the cross beam, the distribution method provided by the invention fully considers the complexity of the stress state of the overlapping areas and the magnitude of the load force borne by the lattice beam, improves the accuracy of the load distribution calculation result, and can provide more accurate guidance for the structural design of the foundation beam;

in addition, the defect that the overlapping area of the lattice beam is repeatedly utilized twice is avoided during node concentrated load distribution, the node concentrated load distribution is completed once, the distributed node concentrated load does not need to be adjusted manually and subjectively, and the program is simple and reliable; the node concentrated load is distributed at one time, and no matter whether the concentrated loads acting on each intersection point on the whole lattice beam are greatly different, the lattice beam load distribution method provided by the embodiment is applicable, the node load distribution mechanism is widely applied, and the method can be applied to the node concentrated load distribution of the crossed strip foundation and the distribution of the side slope lattice beam node concentrated loads; the method for distributing the concentrated load of the lattice beams on the foundation provided by the embodiment can be applied no matter whether the spacing of the lattice beams is uniform or not and whether the longitudinal and transverse beam bodies are orthogonal or not.

Further, in the third step, the Wenkeler (Winkler) elastic foundation upper beam theoretical analysis is adopted to calculate omega_ixAnd F_ix、ω_iyAnd F_iyThe relational expression (c) of (c).

Further, in the third step, omega is analyzed and calculated by adopting an infinite long beam superposition method_ixAnd F_ix、ω_iyAnd F_iyThe relational expression (c) of (c).

Further, the method is obtained by analyzing and calculating by adopting an infinite long beam superposition method:

in the formula: z when the beam I is a semi-infinite beam_x＝1+e^-2λx(1+2cos²λ x-2cos λ xsin λ x); when the beam I is halfZ when the beam is infinitely long and the left-side external elongation is 0_x4; when the beam I is an infinite beam, Z_x＝1；

S is the characteristic length of the foundation beam, and the unit is m;

k-foundation bed coefficient in kN/m³；

b-the width of the foundation beam, with the unit of m;

F₀-concentrated force load on the beam I in kN;

ω₀deformation of the beam I in the direction of the force, in m, at the point where it is subjected to a concentrated force load.

The specific analysis and calculation process by using an infinite long beam superposition method is as follows:

as shown in fig. 2, a semi-infinite beam (beam I) with an outer elongation x towards the left side has a vertical concentrated load F acting on the beam at point O₀. The deflection of the overhanging semi-infinite long beam at the O point is obtained according to an infinite long beam superposition method shown by a beam II under the condition that the boundary condition force F is at the beam end_A、M_AAnd a concentrated load F₀Under the combined action of the two beams, the bending moment and the shearing force of the point A on the beam II are zero. According to this condition:

in the formula:C_x＝e^-λx(cosλx-sinλx)；D_x＝e^-λxcosλx

s-characteristic Length of ground Beam (m)

Lambda-characteristic value of compliance (m) of foundation beam^-1)

E-modulus of elasticity (kPa) of the ground beam

I-area moment of inertia (m) of the ground beam⁴)

k-foundation bed coefficient (kN/m)³)

b-width of ground beam (m)

Solving equation (4) yields:

at a concentrated load F₀And boundary condition force F_A、M_AUnder the combined action, the deflection of a semi-infinite beam (beam I) O point can be obtained by an overlapping method according to an infinite beam theory on a Wenkeler (Winkler) elastic foundation:

in the formula: a. the_x＝e^-λx(cosλx+sinλx)；

B_x＝e^-λxsinλx，Z_x＝1+e^-2λx(1+2cos²λx-2cosλxsinλx)；

In the formula (6), Z is a semi-infinite beam when the left-side external elongation is 0_x4; z when the left-hand outer elongation approaches infinity (infinite beam)_x＝l。

Further, in performing the calculation, lattice beam node types are classified in advance to determine Z₀The value of (d);

(1) corner joint: the cross beam and the longitudinal beam are regarded as semi-infinite long beams extending outwards for a certain length; (see FIG. 3)

(2) Side node: one of the cross beam or the longitudinal beam is a semi-infinite beam, and the other one is an infinite beam; (see FIG. 4)

(3) An inner node: both the cross beam and the longitudinal beam are regarded as infinite long beams. (see FIG. 5)

Further, substituting the formula (3) and the formula (6) into the formula (1) and the formula (2) to obtain

In the formula

F_i-is the total concentrated load (kN) acting on the lattice beam joints; f_ix、F_iy-the concentrated loads (kN) assigned to the beams and stringers at node i, respectively;

F_ica-a concentrated load (kN) assigned to the overlap zone at node i;

b_x、b_y-the widths of the bottom edges of the cross beams and the longitudinal beams respectively (m);

S_x、S_y-characteristic lengths (m) of the cross beam and the longitudinal beam, respectively:

λ_x、λ_ycharacteristic values of compliance (m) for the transverse and longitudinal beams, respectively^-1)；

I_x、I_ySection moments of inertia (m) for the transverse and longitudinal beams, respectively⁴)；

Z_x、Z_yEach is λ_xx、λ_yy (dimensionless).

Furthermore, the influence of concentrated loads of other nodes on the lattice beam is ignored in the step two, and only the action of the concentrated loads on the i node is considered, so that the concentrated load distribution mode at the nodes can be greatly simplified.

Example two

The structure design method provided by the embodiment comprises the following steps: after the load distribution condition of each node is calculated by using the method for calculating the load distribution of the lattice beam on the foundation in the embodiment, the overlapping area is abstracted to be a point with zero area, and the influence of the load distributed by the overlapping area is not considered, the lattice beam on the elastic foundation is disassembled into a plurality of one-dimensional foundation upper beams with concentrated loads (distributed concentrated loads), and then the static balance method, the inverted beam method, the Winkler foundation method or the American ACI method is adopted to respectively perform internal force analysis and structural design on all the disassembled one-dimensional foundation upper beams, wherein the internal force refers to bending moment and shearing force.

The principle and the implementation mode of the invention are explained by applying a specific example, and the description of the embodiment is only used for helping to understand the method and the core idea of the invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.