A method for calculating stress and mid-span deflection of hyperstatic plane truss structure

Abstract

The application relates to a stress and mid-span deflection calculation method for a statically indeterminate plane truss structure, which decomposes the horizontal concentrated load borne by the statically indeterminate plane truss into symmetrical horizontal concentrated load and antisymmetrical horizontal concentrated load, obtains the internal force of each rod of the statically indeterminate plane truss under the action of the symmetrical horizontal concentrated load by utilizing the symmetry of the structure and the load; simplifies the statically indeterminate plane truss under the action of the antisymmetrical horizontal concentrated load into a beam with fixed connection at both ends, calculates the bending moment and shear force at the same section of the statically indeterminate plane truss by calculating the bending moment and shear force at a section of the beam with fixed connection at both ends, and obtains the internal force of each rod of the statically indeterminate plane truss under the action of the antisymmetrical horizontal concentrated load by combining the symmetry of the structure and the load; and superimposes the internal force of each rod of the statically indeterminate plane truss under the action of the symmetrical horizontal concentrated load and the antisymmetrical horizontal concentrated load, so that the internal force of each rod of the statically indeterminate plane truss under the action of the horizontal concentrated load is obtained.

Description

Technical Field

[0001] This invention relates to the field of stress and mid-span deflection analysis of power engineering frame beam structures, and particularly to a method for calculating the stress and mid-span deflection of statically indeterminate plane truss structures. Background Technology

[0002] In power engineering construction, the frame beam is an important structural structure connecting electrical conductors within a substation. The bottom truss of the frame beam is a highly redundant statically indeterminate planar truss structure, and the calculation of its internal forces and mid-span deflection under horizontal concentrated loads is of paramount importance in structural design.

[0003] Currently, the calculation of internal forces and mid-span deflection of statically indeterminate plane truss structures under horizontal concentrated loads mainly relies on computer simulation.

[0004] The "Substation Structure Design Manual" proposes a "simply supported beam manual method" for calculating the internal forces of statically indeterminate plane truss structures under horizontal concentrated loads. This method is essentially an envelope internal force method. The basic idea is to treat the statically indeterminate plane truss at the bottom of the structure beam as a simply supported beam at both ends under horizontal concentrated loads. By solving for the maximum bending moment of the simply supported beam, the maximum axial force of the chord members is obtained. Then, the maximum axial force of the chord members is used to envelop the entire cross-section of the chord members in the design. Simultaneously treating the statically indeterminate plane truss at the bottom of the structure beam as a simply supported beam at both ends under horizontal concentrated loads allows for the calculation of shear forces at each section of the truss, thereby obtaining the axial forces of the web members at the corresponding sections.

[0005] Furthermore, there are currently no studies on manual calculation methods for calculating the mid-span deflection of statically indeterminate planar truss structures under horizontal concentrated loads.

[0006] Relying on computer simulation to calculate the internal forces and mid-span deflection of statically indeterminate planar truss structures under concentrated horizontal loads suffers from the complexity of specialized software and the long modeling and calculation cycle, making it unsuitable for the early stages of engineering construction. The "manual method for simply supported beams" proposed in the *Substation Structure Design Manual*, in practical engineering applications, yields a maximum axial force in the chord members that is far greater than the axial force value output by the calculation software, resulting in insufficient calculation accuracy. This leads to the selection of oversized chord member sections, and the envelope design concept of the simply supported method makes it impossible to calculate the axial force of chord members at arbitrary cross-sections of the truss. Summary of the Invention

[0007] To address the aforementioned problems, the present invention aims to provide a method for calculating the stress and mid-span deflection of statically indeterminate plane truss structures. This method can accurately calculate the internal forces of members at any cross-section of a statically indeterminate plane truss and accurately calculate the mid-span deflection. Furthermore, the calculation is simple and can eliminate the reliance on specialized computer calculation software in the early stages of engineering.

[0008] To achieve the above objectives, the present invention adopts the following technical solution:

[0009] As one aspect of the present invention, a method for calculating the stress of a statically indeterminate plane truss structure is provided. The statically indeterminate plane truss structure includes two parallel chords connected as a whole by several straight web members arranged between them. Two X-shaped diagonal web members are provided between adjacent straight web members and between the ends of the end straight web members and the ends of the two chords. The ends of each diagonal web member are connected to the corresponding connection points between the chords and the straight web members. The stress calculation method is as follows: the horizontal concentrated load on the statically indeterminate plane truss is decomposed into a symmetrical horizontal concentrated load and an anti-symmetrical horizontal concentrated load. The symmetry of the structure and the load is used to derive the statically indeterminate plane truss structure. The internal forces of each member of the truss under symmetrical horizontal concentrated loads are calculated as follows: The statically indeterminate plane truss under antisymmetric horizontal concentrated loads is simplified to a beam fixed at both ends. The bending moment and shear force at a certain section of the beam are calculated to determine the bending moment and shear force of the statically indeterminate plane truss at the same section. The internal forces of each member of the statically indeterminate plane truss under antisymmetric horizontal concentrated loads are then obtained by combining the symmetric and antisymmetric horizontal concentrated loads. Finally, the internal forces of each member of the statically indeterminate plane truss under horizontal concentrated loads are obtained by superimposing the internal forces of each member under symmetrical and antisymmetric horizontal concentrated loads.

[0010] As another aspect of the present invention, a method for calculating mid-span deflection of a statically indeterminate plane truss structure is provided. The statically indeterminate plane truss structure includes two parallel chords connected as a whole by several straight web members arranged between them. Two X-shaped diagonal web members are provided between adjacent straight web members and between the ends of the end straight web members and the ends of the two chords. The two ends of each diagonal web member are connected to the corresponding connection points of the chords and straight web members. The mid-span deflection calculation method is as follows: The statically indeterminate plane truss under a horizontal concentrated load is simplified to a structure with both ends fixed. For the connecting beam, the mid-span deflection caused by the axial deformation of the chord is calculated by calculating the mid-span deflection of the fixed beam. Based on the force calculation method used for statically indeterminate plane truss structures, the internal forces of the straight and diagonal web members are obtained. Combined with the internal force analysis of the straight and diagonal web members, the graphical method is used to calculate the mid-span deflection caused by the axial deformation of the straight and diagonal web members. The sum of the mid-span deflections caused by the axial deformation of the chord members and the axial deformation of the straight and diagonal web members when the statically indeterminate plane truss is subjected to a horizontal concentrated load is the total mid-span deflection of the statically indeterminate plane truss structure under the action of a horizontal concentrated load.

[0011] The present invention has the following beneficial effects:

[0012] This invention provides a method for calculating internal forces and mid-span deflection without the cumbersome modeling and calculation process required by specialized computer software, saving design time and making it suitable for the early stages of engineering design discussions. Compared to traditional manual methods, it significantly improves calculation accuracy and can calculate the axial forces of members at any cross-section of a statically indeterminate plane truss. The mid-span deflection calculation method of this invention fills a gap in the research on manual calculation of mid-span deflection for statically indeterminate plane trusses. By calculating the mid-span deflection of the simplified beams fixed at both ends, the method calculates the mid-span deflection caused by the axial deformation of the chords of the statically indeterminate plane truss, which not only greatly simplifies deflection calculation but also reveals the essence of truss structural deformation. Attached Figure Description

[0013] Figure 1 This is a schematic diagram of the force model of a statically indeterminate planar truss.

[0014] Figure 2 This is a schematic diagram of the force model decomposition of a statically indeterminate plane truss under symmetrical loads.

[0015] Figure 3 This is a schematic diagram of the force model decomposition of a statically indeterminate plane truss under antisymmetric loads.

[0016] Figure 4 for Figure 3 A simplified force model of a statically indeterminate planar truss as a beam with fixed ends;

[0017] Figure 5 This is a schematic diagram of the shear force on a beam fixed at both ends.

[0018] Figure 6 This is a schematic diagram of the bending moment of a beam fixed at both ends.

[0019] Figure 7 A schematic diagram of bending moment and shear force at any cross section of a statically indeterminate plane truss;

[0020] Figure 8 for Figure 1 A simplified force model of a statically indeterminate planar truss as a beam with fixed ends;

[0021] Figure 9 This is a schematic diagram of the axial forces in the web members of a statically indeterminate plane truss under a concentrated horizontal load.

[0022] Figure 10 This is a schematic diagram of the axial force of the web members of a statically indeterminate plane truss under a unit horizontal concentrated load at mid-span. Detailed Implementation

[0023] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0024] A method for calculating the stress and mid-span deflection of statically indeterminate plane truss structures.

[0025] See Figure 1 The statically indeterminate planar truss structure is a statically indeterminate planar truss at the bottom of the substation frame beam. It includes two parallel chords 101, with several straight web members 102 positioned between them. Preferably, the straight web members 102 are evenly distributed between the two chords 101. Each straight web member 102 is perpendicular to the chord 101 and its ends are connected to both chords 101. Two X-shaped diagonal web members 103 are positioned between adjacent straight web members 102 and between the end straight web members 102 and the end supports of the two chords 101. The ends of each diagonal web member 103 are connected to the corresponding connection points of the chord 101 and the straight web member 102. In general, the above-mentioned statically indeterminate planar truss structure is symmetrically arranged about the centerline between the two chords 101, parallel to the chord 101.

[0026] The calculation method for the axial force of each member of the above-mentioned statically indeterminate plane truss is as follows:

[0027] See the force model of the statically indeterminate planar truss. Figure 1 Establish an XOZ plane coordinate system in the figure, taking the midpoint of the line connecting the endpoints of the two chord members at the left support as point O. The OZ axis coincides with the centerline, and the OX axis is perpendicular to the OZ axis. In the figure, L is the span of the statically indeterminate plane truss, H is the distance between the chord members, and F... x Let A be the horizontal concentrated load F. x The distance to the left support, B, represents the distance from the horizontal concentrated load F. x The distance to the right end support. The connection between the chord and the column head of the support in the statically indeterminate plane truss is simplified to a hinge, and the connection between the web members and the chord members by bolts through the gusset plates is also simplified to a hinge. The chord members are continuous members and have a uniform cross-section. All diagonal web members have the same cross-section, and preferably all diagonal web members have the same length.

[0028] Figure 1 The horizontal concentrated load F on the statically indeterminate plane truss shown x It can be decomposed into symmetrical loads and anti-symmetrical loads, as follows: Figure 2 , Figure 3 As shown, solve them respectively. Figure 2 structure, Figure 3 The internal forces of the structure can be obtained by superimposing them. Figure 1 Structural internal forces.

[0029] exist Figure 2 Under the symmetrical load shown, neglecting the influence of the axial deformation of the straight web members directly bearing the concentrated load on the internal forces of the structure, it can be considered that... Figure 2 Under the operating conditions, the axial force of the straight web members of the statically indeterminate planar truss, except for those directly bearing concentrated loads, is 0.5F. x Apart from that, all other members are zero members.

[0030] exist Figure 3Under the action of the antisymmetric load shown, the internal forces of each member of the statically indeterminate plane truss are antisymmetric about the Z axis. That is, Figure 3 all straight web members are zero-force members; at any section of the truss, the axial forces of the top chords are equal in magnitude and opposite in direction, and the axial forces of the diagonal web members are equal in magnitude and opposite in direction. The Figure 3 shown statically indeterminate plane truss is simplified as a fixed-end beam, as shown in Figure 4 , the bending moment and shear force at any section (e.g., section 1-1) of the fixed-end beam are solved to obtain the bending moment and shear force at the same section of the statically indeterminate plane truss.

[0031] Figure 5 is the shear diagram of the fixed-end beam, and in the illustrated XOZ plane coordinate system, the following is obtained:

[0032] when 0≤z<a1L,

[0033] when a1L≤z≤L,

[0034] in the formula: z is Figure 5 the Z-axis coordinate in the illustrated XOZ plane coordinate system, representing the section position of the shear force to be obtained; V z is the shear force value at the position where the Z-axis coordinate of the fixed-end beam is z; F x is the applied horizontal concentrated load; a1=A / L, b1=B / L, L is the span of the fixed-end beam, that is, the span of the statically indeterminate plane truss, A and B are respectively the distances from the horizontal concentrated load F x to the left end support and the right end support.

[0035] Figure 6 is the bending moment diagram of the fixed-end beam, and in the illustrated XOZ plane coordinate system, the following is obtained:

[0036] when 0≤z<a1L,

[0037] when a1L≤z≤L,

[0038] in the formula: z is Figure 6 the Z-axis coordinate in the illustrated XOZ plane coordinate system, representing the section position of the bending moment to be obtained; M z is the bending moment value at the position where the Z-axis coordinate of the fixed-end beam is z; L is the span of the fixed-end beam; F x is the applied horizontal concentrated load; a1=A / L, b1=B / L, A and B are respectively the distances from the horizontal concentrated load F x to the left end support and the right end support.

[0039] It can be obtained from the foregoing analysis that the schematic diagram of bending moment and shear force at any section of the statically indeterminate plane truss is as shown in Figure 7 , where V z, M z See details in Formula (1), Formula (2), Formula (3) and Formula (4).

[0040] Combined with the foregoing symmetry analysis, for Figure 7 the stress working condition of the statically indeterminate plane truss shown in, all straight web members are zero-force members. The axial forces of the top chord members on any section of the statically indeterminate plane truss are equal in magnitude and opposite in direction, and the axial forces of the diagonal web members are equal in magnitude and opposite in direction. Based on this conclusion and neglecting the tiny shear force existing in the chord section, the following can be obtained:

[0041]

[0042]

[0043] Substituting Formula (1), Formula (2), Formula (3) and Formula (4) into Formula (5) and Formula (6) gives:

[0044] when 0≤z<a1L,

[0045] when a1L≤z≤L,

[0046] when 0≤z<a1L,

[0047] when a1L≤z≤L,

[0048] Where: z is Figure 3 the Z-axis coordinate in the XOZ plane coordinate system shown in, representing the section position where the requested member is located; N cz is the axial force of the truss chord at the position where the Z-axis coordinate is z, for Figure 3 the XOZ plane coordinate system shown in, for chords located in the first quadrant, tension is positive, and for chords located in the third quadrant, compression is positive; N wz is the axial force of the truss diagonal web member at the position where the Z-axis coordinate is z, which is an absolute value; M z is the bending moment value of the fixed-end beam at the position where the Z-axis coordinate is z; V z is the shear force value of the fixed-end beam at the position where the Z-axis coordinate is z; L is the span of the statically indeterminate plane truss; H is the limb spacing of the chord; F x is the horizontal concentrated load applied to the statically indeterminate plane truss; a1=A / L, b1=B / L, where A and B are the distances from the horizontal concentrated load F x to the left end support and the right end support, respectively; θ is the included angle between the web member and the chord.

[0049] Superimposing the internal forces of the Figure 2 structure and the Figure 3 structure gives the internal forces of each member of the Figure 1 structure. For Figure 1The statically indeterminate planar truss structure shown has axial forces in its chords as detailed in equations (7) and (8), and axial forces in its diagonal web members as detailed in equations (9) and (10). Except for the straight web members directly bearing concentrated loads, the axial force is 0.5F. x Apart from that, all other straight-webbed rods are zero rods.

[0050] The method for calculating the mid-span deflection of a statically indeterminate plane truss is as follows:

[0051] 1. Calculation of mid-span deflection caused by axial deformation of the chord:

[0052] Bundle Figure 1 The statically indeterminate planar truss shown is simplified as follows: Figure 8 The beam shown is fixed at both ends. The mid-span deflection caused by the axial deformation of the chord is calculated by calculating the mid-span deflection of this fixed beam. The simplified bending stiffness and mid-span deflection along the X-axis of the statically indeterminate plane truss beam are as follows:

[0053]

[0054]

[0055] Where: E is the elastic modulus of steel; I z I is the moment of inertia of the section of the statically indeterminate planar truss about the Z-axis; 1z A is the moment of inertia of a single chord member of a statically indeterminate planar truss about the Z-axis. c is the cross-sectional area of ​​the chord; H is the distance between the chord members; f1 is the mid-span deflection of the statically indeterminate plane truss caused by the axial deformation of the chord members under a concentrated horizontal load; F x Let F be the horizontal concentrated load; L be the span of the truss; e1 = min(c1, d1), c1 = C / L, d1 = D / L, where C and D are the horizontal concentrated loads F and D, respectively. x Distance to the proximal and distal supports.

[0056] 2. Calculation of mid-span deflection caused by axial deformation of the web member:

[0057] The graphical method is used to calculate the mid-span deflection caused by the axial deformation of the web member. Figure 9 For a statically indeterminate planar truss under a concentrated horizontal load F x The diagram shows the axial force of the web members under load. For the sake of simplicity in subsequent graphical calculations, the statically indeterminate plane truss structure is divided into three segments for graphical calculation, as shown in the diagram. The first segment is the diagonal web members with a horizontal concentrated load to the near-end support, the second segment is the diagonal web members with a horizontal concentrated load to the mid-span, and the third segment is the remaining diagonal web members. Figure 9 In the first section, F1 below “Ⅰ” represents the absolute value of the axial force of the diagonal web members within the first truss section. In the second and third sections, F2 below “Ⅱ” and “Ⅲ” represents the absolute value of the axial force of the diagonal web members within the second and third truss sections.

[0058] As can be seen from the foregoing analysis, for Figure 9 The statically indeterminate planar truss shown has a straight web member with an internal force of 0.5F at the point where it directly bears a concentrated load. x Apart from the straight web members, all other straight web members are zero-force members. The axial forces of the diagonal web members are as follows:

[0059]

[0060]

[0061] In the formula: F1 and F2 are the horizontal concentrated loads F x The axial force of the diagonal web members between the proximal and distal supports is taken as the absolute value; F x The horizontal concentrated load is C1 = C / L, d1 = D / L, where C and D are the horizontal concentrated loads F and D, respectively. x The distance to the near and far supports; θ is the angle between the web member and the chord member.

[0062] Similarly, to solve the schematic diagram of the axial force of the web members of a statically indeterminate plane truss under a unit horizontal concentrated load at mid-span, see [reference needed]. Figure 10 Except for the straight web members that directly bear concentrated loads, where the internal force is 0.5, all other straight web members are zero-force members, and the axial force of the diagonal web members is 1 / 4sinθ.

[0063] Using graph multiplication method Figure 9 and Figure 10 The mid-span deflection caused by the axial deformation of the web members is calculated using the internal force information of the web members. Analysis shows that the mid-span deflection caused by the graphical product of the axial forces in the first and third web member segments is downward, while the mid-span deflection caused by the graphical product of the second web member segment is upward. Figure 9 and Figure 10 If the number of diagonal web members in the first, second, and third segments are n1, n2, and n3 respectively, then the mid-span deflection caused by the axial deformation of the web members under a horizontal concentrated load on the statically indeterminate plane truss is as follows:

[0064]

[0065] In the formula: f2 is the mid-span deflection of the statically indeterminate planar truss caused by the axial deformation of the web members under a horizontal concentrated load; l0 is the length of the diagonal web member; E is the elastic modulus of steel; A w Let n be the cross-sectional area of ​​the diagonal web member; θ be the angle between the web member and the chord member; and n1 be the horizontal concentrated load F. x The number of diagonal web members up to the near-end support; n2 is the horizontal concentrated load F. x n3 is the number of diagonal web members from mid-span to the far end support; F1 and F2 are the number of diagonal web members from mid-span to the far end support, respectively. xThe axial forces of the diagonal web members between the near and far supports are taken as absolute values, as detailed in equations (13) and (14); F3 is the internal force of the straight web member at mid-span, and when the horizontal concentrated load acts at mid-span, F3 = 0.5F x Otherwise, take F3 = 0; H is the length of the straight web member at mid-span, which is also Figure 1 The distance between the legs of the middle chord; A wv Let be the cross-sectional area of ​​the straight web member at mid-span.

[0066] 3. Calculation of mid-span deflection of a statically indeterminate plane truss:

[0067] From the foregoing analysis, it can be concluded that... Figure 1 The statically indeterminate plane truss shown has the following mid-span deflection under a concentrated horizontal load:

[0068] f = f1 + f2 (16)

[0069] In the formula: f is the total mid-span deflection of the statically indeterminate plane truss under the action of a horizontal concentrated load; f1 and f2 are the mid-span deflections caused by the axial deformation of the chord members and the axial deformation of the web members when the statically indeterminate plane truss is subjected to a horizontal concentrated load, respectively, as detailed in formula (12) and formula (15).

[0070] The calculation is performed using a statically indeterminate plane truss at the bottom of the main transformer frame beam in a substation as an example. The span of the frame beam is 16m, and the chord section is... The steel pipe has a straight web member section of 2L100×10 at the point directly bearing the load, while the remaining web members are all L70×5. The chord member spacing is 1m, and the horizontal projection of the diagonal web members is 1m. The chord members are continuous members, with all four supports at both ends of the chord members being hinged. The web members are also hinged to the chord members at both ends. A concentrated load of 15kN is applied at mid-span to the statically indeterminate plane truss, and the elastic modulus of the steel is taken as E = 206000MPa. The above statically indeterminate plane truss is calculated using this method, and the results are compared with those calculated by the MIDAS professional software.

[0071] The internal forces and mid-span deflection of the members obtained using this calculation method are almost completely consistent with the results calculated by MIDAS. In the MIDAS calculation model, the chord members are modeled using beam elements. The 16m long chord is divided into 16 beam element segments. Due to the characteristics of beam elements, the output internal forces of each beam element segment are the internal forces at the midpoint of that element. The maximum axial force of the chord member output by the MIDAS calculation model is 26.1kN, located in the end chord beam elements and the mid-span chord beam elements. Figure 3The coordinate systems shown are z = 0.5m and z = 7.5m. Substituting z = 0.5m and z = 7.5m into the calculation formula of this method, the corresponding internal force is 26.3kN. The error between the result calculated by this method and MIDAS is only 0.8%. The mid-span deflection output by the MIDAS calculation model is 2.025mm, while the mid-span deflection calculated by this method is 2.057mm. The error between the result calculated by this method and MIDAS is 1.6%. It can be seen that after eliminating the cumbersome modeling and calculation process of professional software, the calculation method using this method can still guarantee high calculation accuracy and even meet the requirements of construction drawing design.

[0072] The above description is merely a specific embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent structural transformations made based on the content of the present invention specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of the present invention.

Claims

1. A method for calculating the forces on statically indeterminate planar truss structures. The statically indeterminate planar truss structure includes two parallel chords connected as a whole by several straight web members arranged between them. Two X-shaped diagonal web members are provided between adjacent straight web members and between the ends of the end straight web members and the ends of the two chords. Each diagonal web member is connected at both ends to the corresponding connection point between the chord and the straight web member. Its features are, The force calculation method is as follows: The horizontal concentrated load on the statically indeterminate plane truss is decomposed into a symmetrical horizontal concentrated load and an antisymmetric horizontal concentrated load. The internal forces of each member of the statically indeterminate plane truss under the symmetrical horizontal concentrated load are obtained by utilizing the symmetry of the structure and the load. The statically indeterminate plane truss under the antisymmetric horizontal concentrated load is simplified to a beam with fixed ends. The bending moment and shear force at a certain section of the beam with fixed ends are calculated to calculate the bending moment and shear force of the statically indeterminate plane truss at the same section. The internal forces of each member of the statically indeterminate plane truss under the antisymmetric horizontal concentrated load are obtained by combining the symmetry of the structure and the load. By superimposing the internal forces of each member of the statically indeterminate plane truss under symmetrical and antisymmetric horizontal concentrated loads, the internal forces of each member of the statically indeterminate plane truss under horizontal concentrated loads can be obtained. The axial force of the chord is calculated using equations (7) and (8). The axial force of the diagonal web member is calculated using equations (9) and (10). In the force model of the statically indeterminate plane truss, establish the XOZ plane coordinate system, take the midpoint of the line connecting the endpoints of the two chords at the left end support as point O, the OZ axis coincides with the midline between the two chords parallel to the chords, and the OX axis is perpendicular to the OZ axis. In the formula The Z-axis coordinate in the XOZ plane coordinate system represents the cross-sectional position of the member in question; Z-axis coordinate is The axial force of the truss chord at the location is positive for tension in the chord in the first quadrant of the XOZ plane coordinate system, and positive for compression in the chord in the third quadrant. Z-axis coordinate is The axial force of the diagonal web member of the truss at the location is an absolute value; For the span of a statically indeterminate planar truss; The distance between the chord members; For a statically indeterminate plane truss subjected to a concentrated horizontal load; , , , They are respectively horizontal concentrated loads Distance to the left and right supports; The angle between the web member and the chord member; Except for the axial force of the straight web members directly bearing concentrated loads, Apart from that, all other straight-webbed rods are zero rods.

2. The method for calculating the force on a statically indeterminate planar truss structure according to claim 1, characterized in that: The shear force at a certain cross section is calculated using equations (1) and (2). In the force model of the statically indeterminate plane truss, establish the XOZ plane coordinate system, take the midpoint of the line connecting the endpoints of the two chords at the left end support as point O, the OZ axis coincides with the midline between the two chords parallel to the chords, and the OX axis is perpendicular to the OZ axis. In the formula: The Z-axis coordinate in the XOZ plane coordinate system represents the cross-sectional location of the shear force to be determined. The Z-axis coordinate of the beam fixed at both ends is The shear force value at the location; The load is a concentrated horizontal load. , , , They are respectively horizontal concentrated loads Distance to the left and right supports.

3. The method for calculating the force of a statically indeterminate plane truss structure according to claim 1, characterized in that: The bending moment at a certain section is calculated using equations (3) and (4). In the force model of the statically indeterminate plane truss, establish the XOZ plane coordinate system, take the midpoint of the line connecting the endpoints of the two chords at the left end support as point O, the OZ axis coincides with the midline between the two chords parallel to the chords, and the OX axis is perpendicular to the OZ axis. In the formula: The Z-axis coordinate in the XOZ plane coordinate system represents the cross-sectional location of the bending moment to be determined. The Z-axis coordinate of the beam fixed at both ends is The bending moment value at the location; This refers to the span of the beam that is fixed at both ends. The load is a concentrated horizontal load. , , , They are respectively horizontal concentrated loads Distance to the left and right supports.

4. A method for calculating mid-span deflection of statically indeterminate plane truss structures. The statically indeterminate planar truss structure includes two parallel chords connected as a whole by several straight web members arranged between them. Two X-shaped diagonal web members are provided between adjacent straight web members and between the ends of the end straight web members and the ends of the two chords. Each diagonal web member is connected at both ends to the corresponding connection point between the chord and the straight web member. Its features are, The method for calculating mid-span deflection is as follows: The statically indeterminate plane truss under a horizontal concentrated load is simplified to a beam fixed at both ends. The mid-span deflection caused by the axial deformation of the chord members is calculated by calculating the mid-span deflection of this fixed beam. The internal forces of the straight and diagonal web members obtained by the force calculation method for statically indeterminate plane truss structures according to any one of claims 1 to 3 are combined with the internal force analysis of the straight and diagonal web members and the graphical method is used to calculate the mid-span deflection caused by the axial deformation of the straight and diagonal web members. The sum of the mid-span deflections caused by the axial deformation of the chord members and the axial deformation of the straight and diagonal web members when the statically indeterminate plane truss is subjected to a horizontal concentrated load is the total mid-span deflection of the statically indeterminate plane truss structure under a horizontal concentrated load.

5. The method for calculating mid-span deflection of statically indeterminate plane truss structures according to claim 4, characterized in that: Mid-span deflection of the statically indeterminate plane truss caused by axial deformation of the chord members under a concentrated horizontal load. The results are obtained by calculation using equations (11) and (12): In the formula The elastic modulus of steel; Let be the moment of inertia of the section of the statically indeterminate plane truss about the Z-axis; Let be the moment of inertia of a single chord member of a statically indeterminate plane truss about the Z-axis. Let be the cross-sectional area of ​​the chord. The distance between the chord members; The load is a concentrated horizontal load. The span of the truss; , , , , They are respectively horizontal concentrated loads Distance to the proximal and distal supports.

6. The method for calculating mid-span deflection of statically indeterminate plane truss structures according to claim 4, characterized in that: The statically indeterminate plane truss structure is divided into three sections for graphical representation. The first section consists of diagonal web members with horizontal concentrated loads applied to the near-end supports. The second section consists of diagonal web members with horizontal concentrated loads applied to the mid-span. The third section consists of the remaining diagonal web members.

7. The method for calculating mid-span deflection of statically indeterminate plane truss structures according to claim 6, characterized in that: Mid-span deflection of the statically indeterminate planar truss caused by axial deformation of the web members under a concentrated horizontal load. The results are obtained by calculation using equations (13), (14), and (15): In the formula , They are respectively horizontal concentrated loads The absolute values ​​of the axial forces of the diagonal web members between the proximal and distal supports are taken. The load is a concentrated horizontal load. , , , They are respectively horizontal concentrated loads Distance to the proximal and distal supports; The angle between the web member and the chord member. The length of the diagonal web member; The elastic modulus of steel; Let be the cross-sectional area of ​​the diagonal web member; For horizontal concentrated loads The number of diagonal web members extending to the proximal support; For horizontal concentrated loads The number of diagonal web members extending to the mid-span; The number of diagonal web members from mid-span to the far-end support; For the internal forces of the straight web members at mid-span, when a concentrated horizontal load acts at mid-span, take... Otherwise take ; The length of the straight web member at mid-span is the distance between the chord members; Let be the cross-sectional area of ​​the straight web member at mid-span.

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