Method for calculating bending moment and displacement of variable cross-section continuous composite beam

Abstract

The invention discloses a variable cross-section continuous composite beam bending moment and displacement calculation method. The method comprises the following steps: S1, segmenting a variable cross-section continuous composite beam structure; s2, calculating anti-bending inertia moments of combined sections of different beam sections, and segmenting the variable-section continuous combined beam according to the anti-bending inertia moments of the sections to obtain a segmented uniform-section model; s3, geometric morphology equivalence is conducted on the variable-cross-section continuous composite beam according to a segmented uniform-cross-section model, half span is selected through symmetry to conduct theoretical analysis calculation, and the bending moment Mr at the segment point of the equivalent model section is obtained; s4, determining an actual inflection point position, and according to the actual inflection point position, performing further equivalent segmentation on the variable cross-section continuous composite beam; and S5, dividing the half-span variable cross-section continuous composite beam into three sections according to the positions of the cross-section segmentation points and the actual inflection points, establishing an equation based on the stress balance and deformation coordination relationship of the cross-section segmentation points and the actual inflection points, and providing a typical cross-section displacement, corner and bending moment calculation method.

Description

Technical Field

[0001] The invention relates to the technical field of variable-section continuous composite beams, and in particular to a method for calculating bending moment and displacement of variable-section continuous composite beams. Background Art

[0002] Under the action of uniformly distributed load, the combined action of the positive moment zone in the mid-span of the uniform cross-section steel-concrete composite beam is significantly greater than that of the negative moment zone, which makes the mid-span section bearing capacity surplus of the uniform cross-section continuous composite beam significantly higher than that of the end section. When the end reaches a high material utilization rate, the material utilization rate in the mid-span is low. The use of variable cross-section continuous composite beams can not only reduce the mid-span structural height and increase the net height of the building, but also achieve a high material utilization rate at the same time through the safety design principle of the beam end and the span, reduce the amount of structural steel, achieve dual optimization of the net height of the composite beam component and the economic efficiency of the structure, improve the efficiency of material use, give full play to its advantages of strong bearing capacity and green and low carbon, and help the "dual carbon" strategic goal.

[0003] Although the variable cross-section continuous composite beam structure is elegant in shape and widely distributed, and has significant application and promotion value in engineering practice, there are still some problems that need to be solved in the design process. For example, the stiffness distribution characteristics of the variable cross-section composite beam are different from those of the uniform cross-section composite beam, so there is a difference in the length of the negative moment zone between the two. The relative position relationship between the beam inflection point and the variable cross-section point cannot be simply judged by experience, which increases the complexity of the force analysis. In addition, the stiffness magnification coefficient of the negative moment zone of the composite beam is small, and the length of the negative moment zone has a significant impact on the stiffness distribution of the variable cross-section continuous composite beam, making the calculation process of the section moment and displacement of the variable cross-section continuous composite beam complicated.

[0004] At present, the calculation of bending moment and displacement of variable cross-section beams is generally obtained by using finite element analysis method through commercial design software, and there is a lack of high-precision and direct analytical calculation (hand calculation) method. The use of finite element analysis method brings a lot of modeling work, and it is difficult to intuitively reflect the influence of various material parameters and geometric parameters on the bending moment and displacement of variable cross-section continuous composite beams. Therefore, it is necessary to propose a method for analytical calculation of bending moment and displacement of variable cross-section continuous composite beams. Summary of the invention

[0005] The object of the present invention is to provide a method for calculating bending moment and displacement of a continuous composite beam with variable cross-section, so as to solve the problems raised in the above-mentioned background technology.

[0006] To achieve the above object, the present invention provides a method for calculating bending moment and displacement of a variable cross-section continuous composite beam, comprising the following steps:

[0007] S1. Segment a variable-section continuous composite beam structure with rigid connections at both ends and symmetrically distributed geometric characteristics under a uniformly distributed load to obtain a variable-section model, wherein the variable-section continuous composite beam structure is divided into beam end section sections located on both sides, a mid-span section section located in the middle, and two variable-section transition sections connecting the beam end section sections and the mid-span section sections;

[0008] S2. Calculate the bending inertia moment of the combined sections of different beam segments, divide the variable cross-section continuous composite beam into sections according to the bending inertia moment of the section, and obtain a segmented equal cross-section model;

[0009] S3. The variable cross-section continuous composite beam is geometrically equivalent in the form of a segmented equal cross-section model. The half span is selected for theoretical analysis and calculation based on symmetry to obtain the bending moment M at the segmented point of the equivalent model section. r , and according to M r The positive and negative signs determine the relative position relationship between the actual inflection point and the cross-section segmentation point;

[0010] S4. Determine the actual inflection point position, and further divide the variable cross-section continuous composite beam into equivalent segments according to the actual inflection point position, and obtain M r >0 and M r <0, actual inflection point position and beam stiffness distribution;

[0011] S5. Divide the half-span variable-section continuous composite beam into three sections according to the section segmentation points and the actual inflection points. Establish equations based on the force balance and deformation coordination relationship between the section segmentation points and the actual inflection points, and propose a calculation method for typical section displacement, rotation angle and bending moment.

[0012] In a preferred embodiment, in step S2, the bending moment of inertia of the combined cross-section of different beam segments is calculated according to the following formula:

[0013] I i =α i I i,s ……(1);

[0014] Among them I i,s is the bending inertia moment of the steel beam section of different composite beam segments, α i In order to obtain the corresponding stiffness amplification coefficients of different composite beam sections after considering the contribution of floor slab stiffness, the variable cross-section transition section is divided into two sections according to its length, and each section takes the cross-section of the adjacent equal-section beam section connected to it.

[0015] In a preferred embodiment, in step S3, the variable cross-section continuous composite beam is geometrically equivalent in the form of a segmented equal cross-section model, and a half span is selected for theoretical analysis to obtain the bending moment M at the segmented point of the equivalent model section. r , and according to M r The positive and negative signs determine the relative position relationship between the actual inflection point and the cross-section segmentation point, including:

[0016] According to formula (1) and formula (2), the bending moment M at the section point of the equivalent model is obtained: r :

[0017]

[0018] Among them, the distances from the end and the mid-span of the equivalent model section segment point o are s1 and s2 respectively, and it is assumed that the stiffness magnification coefficient of the beam segment in the range of s1 is α - , the stiffness magnification factor of the beam section in the range of s2 is taken as α + .

[0019] In a preferred embodiment, in step S4, the actual inflection point position is determined, and the variable cross-section continuous composite beam is further divided into equivalent segments according to the actual inflection point position to obtain M r >0 and M r <0, the actual inflection point position and beam stiffness distribution, including:

[0020] Assume that the bending moment is positive when the bottom of the beam is in tension and is drawn below the beam in the bending moment diagram. r >0, the actual inflection point is located in the s1 segment, and the half-span variable-section continuous composite beam is based on the section bending stiffness k i It is divided into three sections with lengths of x1, x2, and x3. The x1 section is the negative moment area. At this time, the relationship between the beam segment geometry and internal forces is as follows:

[0021] x1+x2=s1=l1+0.5l2……(3);

[0022] x3=s2=0.5l2+l3……(4);

[0023] M x1 =0……(5);

[0024] k1=α - EI1, k2 = α + EI1, k3 = α + EI2:

[0025] When M r <0, the actual inflection point is located in the s2 segment, the x1+x2 segment is the negative moment area, and the relationship between the beam segment geometry and internal force is as follows:

[0026] x1=s1=l1+0.5l2……(6);

[0027] x2+x3=s2=0.5l2+l3……(7);

[0028] M x2 =0……(8);

[0029] k1=α - EI1, k2 = α - EI2, k3 = α + EI2;

[0030] Among them, E is the elastic modulus of steel, the spans of the beam end section, variable section transition section and mid-span section are l1, l2 and l3 respectively, and the section bending inertia moments considering the combined effect of the floor are I1, I2 and I3 respectively.

[0031] In a preferred embodiment, in step S5, the half-span variable cross-section continuous composite beam is divided into three sections according to the cross-section segmentation points and the actual inflection point positions, and an equation is established based on the force balance and deformation coordination relationship between the cross-section segmentation points and the actual inflection points, and a typical cross-section displacement, rotation angle and bending moment calculation method is proposed, including:

[0032] For M r >0 and M r <0, in both cases, the half-span variable cross-section continuous composite beam needs to be divided into three sections according to the section segmentation point o and the actual inflection point position, and the three-section beam stress analysis is performed. The rotation angles at the two segmentation points under the uniformly distributed load are and The vertical deflections are ω1 and ω2 respectively, and the linear stiffness of each beam segment is i j Calculate according to formula (9):

[0033]

[0034] Among them, the stiffness magnification factor α is assigned a corresponding value according to the actual situation in the positive bending moment or negative bending moment area.

[0035] In a preferred embodiment, step S5 further includes: establishing a set of equations according to the shear force and bending moment equilibrium conditions at the two segment points:

[0036]

[0037]

[0038] In a preferred embodiment, according to the bending moment formulas (14) and (15) at the two segment points, formulas (10)-(13) are combined to solve the rotation angle at the segment point: And vertical deflections ω1, ω2:

[0039]

[0040] In a preferred embodiment, the beam end bending moment M is calculated according to the following formula: end and mid-span bending moment M mid :

[0041]

[0042] In a preferred embodiment, it also includes: according to the principle of symmetry, obtaining the bending moment of the end section, the bending moment of the mid-span section, the angular displacement and the vertical deflection of each stiffness segment point of the entire variable cross-section continuous composite beam, and based on the obtained bending moment of the end section, the bending moment of the mid-span section, the angular displacement and the vertical deflection of each stiffness segment point of the variable cross-section continuous composite beam, obtaining the influence of the design parameters of the variable cross-section continuous composite beam with rigid connection at both ends and symmetrical distribution of geometric characteristics under uniformly distributed load on the bending moment distribution and displacement of the variable cross-section continuous composite beam, wherein the design parameters include cross-sectional size, stiffness, spans of each section, and external load.

[0043] Compared with the prior art, the present invention has the following beneficial effects:

[0044] Under the action of load, accurately calculating the bending moment values ​​at the mid-span and beam ends of the variable cross-section continuous composite beam structure is helpful to control the design parameters of the beam section. The calculation method of the present invention can obtain the bending moment and displacement of the main stiffness variable section of the variable cross-section continuous composite beam through basic geometric parameters and material parameters, avoiding a large number of finite element modeling processes; the bending moment and displacement of the beam end section and the mid-span section of the variable cross-section continuous composite beam structure can be obtained by substituting the parameters into analytical formulas, which has the advantages of accuracy and versatility. Through the analytical solution of the bending moment and displacement of the variable cross-section continuous composite beam provided by the present invention, the influence of design parameters such as cross-sectional size, stiffness, spans of each section, external loads, etc. on the bending moment and displacement of the variable cross-section continuous composite beam can be obtained more intuitively. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 is a flow chart of the method of the present invention;

[0046] Figure 2 It is a schematic diagram of a variable cross-section model of the present invention;

[0047] Figure 3 It is a schematic diagram of a segmented equal-section model of the present invention;

[0048] Figure 4 It is a schematic diagram of geometric equivalent of the present invention;

[0049] Figure 5 M of the present invention r >0, the actual inflection point position and beam stiffness distribution diagram;

[0050] Figure 6 M of the present invention r Schematic diagram of the actual inflection point position and beam stiffness distribution when <0;

[0051] Figure 7 It is a simplified diagram of the force analysis of the three-section beam of the present invention;

[0052] Figure 8It is a schematic diagram of the cross-section position of the variable-cross-section continuous composite beam of the present invention. DETAILED DESCRIPTION

[0053] The technical solutions in the embodiments of the present invention are described clearly and completely below. The embodiments of the present invention and all other embodiments obtained by ordinary technicians in the field without creative work are within the scope of protection of the present invention.

[0054] like Figures 1 to 8 As shown, the method for calculating bending moment and displacement of a variable cross-section continuous composite beam according to a preferred embodiment of the present invention comprises the following steps:

[0055] Step S1, segmenting a variable cross-section continuous composite beam structure with rigid connections at both ends and symmetrical geometric characteristics under uniform load to obtain a variable cross-section model, wherein the variable cross-section continuous composite beam structure is divided into beam end cross-section segments located on both sides, a mid-span cross-section segment located in the middle, and two variable cross-section transition segments connecting the beam end cross-section segments and the mid-span cross-section segments. Figure 2 As shown, the spans of the beam end section, variable section transition section and mid-span section are l1, l2 and l3 respectively, the section moments of inertia considering the combined effect of the floor are I1, I2 and I3 respectively, α is the beam section stiffness magnification factor considering the combined effect of the floor, q is the uniformly distributed load value, h1 is the beam height of the connecting beam end section, h3 is the beam height of the mid-span section, and r = (h1-h3) / l2.

[0056] Step S2, calculate the bending inertia moment of the combined section of different beam segments, divide the variable cross-section continuous composite beam into sections according to the bending inertia moment of the section, and obtain a segmented equal cross-section model. The bending inertia moment of the combined section of different beam segments is calculated according to the following formula:

[0057] I i =α i I i,s ……(1);

[0058] Among them I i,s is the bending inertia moment of the steel beam section of different composite beam segments, α i The stiffness magnification coefficients corresponding to different composite beam sections after considering the contribution of floor slab stiffness are calculated. The variable cross-section transition section is divided into two sections according to the length, and each section takes the cross section of the adjacent equal cross-section beam section connected to it, such as Figure 3 As shown, Figure 2 The five sections of the beam are equivalent to three sections.

[0059] Step S3: In order to simplify the analytical process, the variable cross-section continuous composite beam is geometrically equivalent in the manner of the segmented equal cross-section model, and the half span is selected for theoretical analysis and calculation by using symmetry. The use of symmetry can reduce the number of unknowns to be solved, reduce the computational workload, and improve efficiency. First, the variable cross-section continuous composite beam is geometrically equivalent in the manner of the segmented equal cross-section model step S2, such as Figure 4 As shown in the figure, the distances from the end and the mid-span of the equivalent model section segment point o are s1 and s2 respectively. It is assumed that the stiffness magnification coefficient of the beam segment in the range of s1 is α - , the stiffness magnification factor of the beam section in the range of s2 is taken as α + According to formula (1) and formula (2), the bending moment M at the section point of the equivalent model is obtained: r , according to M r The positive and negative signs determine the relative position relationship between the actual inflection point and the cross-section segmentation point o.

[0060]

[0061] Step S4: determine the actual inflection point position, and further perform equivalent segmentation on the variable cross-section continuous composite beam according to the actual inflection point position to obtain M r >0 and M r <0. Actual inflection point position and beam stiffness distribution.

[0062] The inflection point is the position where the beam bending moment under load is equal to 0. The bending moment is assumed to be positive when the beam is in tension at the bottom and is plotted below the beam in the bending moment diagram. r >0, the actual inflection point is located in the s1 segment, and the half-span variable-section continuous composite beam is based on the section bending stiffness k i Divide into three segments of length x1, x2, and x3, such as Figure 5 As shown in the figure, the x1 segment shown in the shaded area is the negative moment area. At this time, the relationship between the beam segment geometry and internal force is as follows:

[0063] x1+x2=s1=l1+0.5l2……(3);

[0064] x3=s2=0.5l2+l3……(4);

[0065] M x1 =0……(5);

[0066] k1=α - EI1, k2 = α + EI1, k3 = α + EI2.

[0067] When M r <0, the actual inflection point is located in the s2 segment, and its section stiffness value and variation range are as follows Figure 6As shown, the x1+x2 segment shown in the shaded area is the negative moment area, and the relationship between the beam segment geometry and internal forces is as follows:

[0068] x1=s1=l1+0.5l2……(6);

[0069] x2+x3=s2=0.5l2+l3……(7);

[0070] M x2 =0……(8);

[0071] k1=α - EI1, k2 = α - EI2,k3=α + EI2, E is the elastic modulus of steel.

[0072] Step S5: for M r >0 and M r <0, in both cases, the half-span variable-section continuous composite beam needs to be divided into three sections according to the section segmentation point o and the actual inflection point. Based on the force balance and deformation coordination relationship between the section segmentation point and the actual inflection point, an equation is established, and a calculation method for typical section displacement, rotation and bending moment is proposed.

[0073] Specifically, the three-section beam stress analysis is performed, such as Figure 6 In the force diagram shown in the figure, the rotation angles at the two segment points under the action of uniformly distributed load are and The vertical deflections are ω1 and ω2 respectively, and the linear stiffness of each beam segment is i j Calculate according to formula (9):

[0074]

[0075] Among them, the stiffness magnification factor α is assigned a corresponding value according to the actual situation in the positive bending moment or negative bending moment zone.

[0076] Step S5 also includes: establishing an equation group according to the shear force and bending moment equilibrium conditions at the two segment points:

[0077]

[0078]

[0079] According to the bending moment formulas (14) and (15) at the two segment points, the rotation angle at the segment point is solved by combining formulas (10) to (13) And vertical deflections ω1, ω2:

[0080]

[0081] The beam end bending moment M is calculated according to the following formulaend and mid-span bending moment M mid :

[0082]

[0083] Furthermore, the method further includes: obtaining the bending moment of the end section of the entire variable cross-section continuous composite beam, the bending moment of the mid-span section, the angular displacement and the vertical deflection of each stiffness segment point through the aforementioned steps according to the principle of symmetry. The positions of each section are shown in FIG. Figure 8 As shown. So far, the necessary parameters required for the design of variable cross-section continuous composite beams have been obtained. Based on the obtained bending moment of the end section, the bending moment of the mid-span section, the angular displacement and vertical deflection of each stiffness segment point of the variable cross-section continuous composite beam, the influence of the design parameters of the variable cross-section continuous composite beam with rigid connection at both ends and symmetrical distribution of geometric characteristics on the bending moment distribution and displacement of the variable cross-section continuous composite beam under uniformly distributed load is obtained. Among them, the design parameters include section size, stiffness, span of each section, and external load. Under the action of load, accurately calculating the bending moment values ​​at the mid-span and end of the variable cross-section continuous composite beam structure is helpful to control the design parameters of the beam section.

[0084] In order to verify the accuracy of the above theoretical derivation, the example models were established in the finite element software SAP2000 and midas Gen, and the bending moment at the beam end, the deflection at the variable section position and the mid-span bending moment were calculated and compared with the analytical results. The elastic modulus of the steel is taken as E = MPa, the moment of inertia I1 = 1.302 × 10-4m4, I2 = 6.667 × 10-5m4, I3 = 8.333 × 10-6m4. The length of each section of the beam is x1 = 2m, x2 = 1.5m, x3 = 1.5m, and the uniformly distributed load is 1kN / m. The analytical results and the finite element analysis results are shown in Table 1. It can be seen that the calculated values ​​of the beam bending moment are consistent, and the maximum deflection error is 0.8%, which meets the engineering design accuracy requirements.

[0085] Table 1 Comparison of calculation results

[0086]

[0087] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for calculating bending moment and displacement of a continuous composite beam with variable cross-section, characterized in that: The steps include: S1. Segment a variable-section continuous composite beam structure with rigid connections at both ends and symmetrically distributed geometric characteristics under a uniformly distributed load to obtain a variable-section model, wherein the variable-section continuous composite beam structure is divided into beam end section sections located on both sides, a mid-span section section located in the middle, and two variable-section transition sections connecting the beam end section sections and the mid-span section sections; S2. Calculate the bending inertia moment of the combined sections of different beam segments, divide the variable cross-section continuous composite beam into sections according to the bending inertia moment of the section, and obtain a segmented equal cross-section model; S3. The variable cross-section continuous composite beam is geometrically equivalent in the form of a segmented equal cross-section model. The half span is selected for theoretical analysis and calculation to obtain the bending moment M at the segmented point of the equivalent model section. r , and according to M r The positive and negative signs determine the relative position relationship between the actual inflection point and the cross-section segmentation point; S4. Determine the actual inflection point position, and further divide the variable cross-section continuous composite beam into equivalent segments according to the actual inflection point position, and obtain M r >0 and M r <0, actual inflection point position and beam stiffness distribution; S5. Divide the half-span variable-section continuous composite beam into three sections according to the section segmentation points and the actual inflection points. Establish equations based on the force balance and deformation coordination relationship between the section segmentation points and the actual inflection points, and propose a calculation method for typical section displacement, rotation angle and bending moment.

2. The method for calculating bending moment and displacement of a variable cross-section continuous composite beam according to claim 1, characterized in that: In step S2, the bending inertia moment of the combined section of different beam segments is calculated according to the following formula: I i =α i I i,s ……(1); Among them I i,s is the bending inertia moment of the steel beam section of different composite beam segments, α i In order to obtain the corresponding stiffness amplification coefficients of different composite beam sections after considering the contribution of floor slab stiffness, the variable cross-section transition section is divided into two sections according to its length, and each section takes the cross-section of the adjacent equal-section beam section connected to it.

3. The method for calculating bending moment and displacement of a variable cross-section continuous composite beam according to claim 2, characterized in that: In step S3, the variable cross-section continuous composite beam is geometrically equivalent in the form of a segmented equal cross-section model, and a half span is selected for theoretical analysis to obtain the bending moment M at the segment point of the equivalent model section. r , and according to M r The positive and negative signs determine the relative position relationship between the actual inflection point and the cross-section segmentation point, including: According to formula (1) and formula (2), the bending moment M at the section point of the equivalent model is obtained: r : Among them, the distances from the end and the mid-span of the equivalent model section segment point o are s1 and s2 respectively, and it is assumed that the stiffness magnification coefficient of the beam segment in the range of s1 is α - , the stiffness magnification factor of the beam section in the range of s2 is taken as α + .

4. The method for calculating bending moment and displacement of a variable cross-section continuous composite beam according to claim 3 is characterized in that: In step S4, the actual inflection point position is determined, and the variable cross-section continuous composite beam is further divided into equivalent segments according to the actual inflection point position to obtain M r >0 and M r <0, the actual inflection point position and beam stiffness distribution, including: Assume that the bending moment is positive when the bottom of the beam is in tension and is drawn below the beam in the bending moment diagram. r >0, the actual inflection point is located in the s1 segment, and the half-span variable-section continuous composite beam is based on the section bending stiffness k i It is divided into three sections with lengths of x1, x2, and x3. The x1 section is the negative moment area. At this time, the relationship between the beam segment geometry and internal forces is as follows: x1+x2=s1=l1+0.5l2……(3); x3=s2=0.5l2+l3……(4); M x1 ＝0 ……(5)； k1=a - EI1, k2=α + EI1, k3=a + EI2; When M r <0, the actual inflection point is located in the s2 segment, the x1+x2 segment is the negative moment area, and the relationship between the beam segment geometry and internal force is as follows: x1=s1=l1+0.5l2……(6); x2+x3=s2=0.5l2+l3……(7); M x2 ＝0 ……(8)； k1=a - EI1, k2=α-EI2, k3=α + EI2; Among them, E is the elastic modulus of steel, the spans of the beam end section, variable section transition section and mid-span section are l1, l2 and l3 respectively, and the section bending inertia moments considering the combined effect of the floor are I1, I2 and I3 respectively.

5. The method for calculating bending moment and displacement of a variable cross-section continuous composite beam according to claim 4 is characterized in that: In step S5, the half-span variable cross-section continuous composite beam is divided into three sections according to the cross-section segmentation points and the actual inflection point positions, and an equation is established based on the force balance and deformation coordination relationship between the cross-section segmentation points and the actual inflection points, and a typical cross-section displacement, rotation angle and bending moment calculation method is proposed, including: For M r >0 and M r <0, in both cases, the half-span variable cross-section continuous composite beam needs to be divided into three sections according to the section segmentation point o and the actual inflection point position, and the three-section beam stress analysis is performed. The rotation angles at the two segmentation points under the uniformly distributed load are and The vertical deflections are ω1 and ω2 respectively, and the linear stiffness of each beam segment is i j Calculate according to formula (9): Among them, the stiffness magnification factor α is assigned a corresponding value according to the actual situation in the positive bending moment or negative bending moment area.

6. The method for calculating bending moment and displacement of a variable cross-section continuous composite beam according to claim 5, characterized in that: Step S5 also includes: establishing an equation group according to the shear force and bending moment equilibrium conditions at the two segment points:

7. The method for calculating bending moment and displacement of a variable cross-section continuous composite beam according to claim 6, characterized in that: According to the bending moment formulas (14) and (15) at the two segment points, the rotation angle at the segment point is solved by combining formulas (10)-(13) And vertical deflections ω1, ω2:

8. The method for calculating bending moment and displacement of a variable cross-section continuous composite beam according to claim 7, characterized in that: The beam end bending moment M is calculated according to the following formula end and mid-span bending moment M mid :

9. The method for calculating bending moment and displacement of a variable cross-section continuous composite beam according to claim 8, characterized in that: According to the principle of symmetry, the bending moment of the end section, the bending moment of the mid-span section, the angular displacement and the vertical deflection of each stiffness segment point of the entire variable cross-section continuous composite beam are obtained. Based on the obtained bending moment of the end section, the bending moment of the mid-span section, the angular displacement and the vertical deflection of each stiffness segment point of the variable cross-section continuous composite beam, the influence of the design parameters of the variable cross-section continuous composite beam with rigid connection at both ends and symmetrical distribution of geometric characteristics under uniformly distributed load on the bending moment distribution and displacement of the variable cross-section continuous composite beam is obtained, among which the design parameters include section size, stiffness, span of each section and external load.

Images