A calculation method for bending moment and displacement of a variable cross-section continuous composite beam

Abstract

The present invention discloses a method for calculating the bending moment and displacement of a variable cross-section continuous composite beam, which comprises the following steps: S1, segment the variable cross-section continuous composite beam structure; S2, calculate the flexural moment of inertia of the composite cross-section of different beam segments, and segment the variable cross-section continuous composite beam according to the flexural moment of inertia of the cross-section to obtain a segmented equal cross-section model; S3, geometrically equivalent the variable cross-section continuous composite beam in the manner of the segmented equal cross-section model, select a half-span for theoretical analysis and calculation by using symmetry, and obtain the bending moment M at the sectional segmentation point of the equivalent model cross-section r ; S4, determine the position of the actual inflection point, and further segment the variable cross-section continuous composite beam according to the position of the actual inflection point; S5, divide the half-span variable cross-section continuous composite beam into three segments according to the sectional segmentation point and the position of the actual inflection point, establish equations based on the force balance and deformation coordination relationships at the sectional segmentation point and the actual inflection point, and propose calculation methods for the displacement, rotation angle and bending moment of the typical cross-section.

Description

Technical Field

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

[0002] Under the action of uniform load, the composite action in the positive bending moment area of the equal cross-section steel-concrete composite beam is significantly greater than that in the negative bending moment area. This makes the bearing capacity redundancy of the mid-span cross-section of the equal cross-section continuous composite beam significantly higher than that of the end cross-section. When the material utilization rate at the end reaches a relatively high level, the material utilization rate at the mid-span is relatively low. After adopting the variable cross-section continuous composite beam form, not only can the structural height at the mid-span be reduced, increasing the net building use height, but also through the design principle of equal safety at the beam end and mid-span, the mid-span cross-section and the beam end cross-section can reach a relatively high material utilization rate at the same time, reducing the steel consumption of the structure, realizing the dual optimization of the net use height and structural economy of the composite beam component, improving the material use efficiency, giving full play to its advantages of strong bearing capacity, green and low-carbon, and contributing to the "dual carbon" strategic goal.

[0003] Although the variable cross-section continuous composite beam has an elegant structure and is widely distributed, and has significant application and promotion value in engineering practice, there are still some problems 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 equal cross-section composite beam, so there are differences in the length of the negative bending moment area between the two. The relative position relationship between the beam inflection point and the variable cross-section point cannot be simply judged by experience, increasing the complexity of the force analysis. In addition, the stiffness amplification coefficient in the negative bending moment area of the composite beam is small, and the length of the negative bending moment area has a significant impact on the stiffness distribution of the variable cross-section continuous composite beam, making the calculation process of the sectional bending moment and displacement of the variable cross-section continuous composite beam complex.

[0004] At present, the calculation of the bending moment and displacement of the variable cross-section beam is generally obtained by the finite element analysis method using commercial design software, and there is a lack of an analytical calculation (hand calculation) method with high accuracy and directness. The use of the finite element analysis method brings a large amount of modeling work, and it is difficult to intuitively reflect the influence law of various material parameters and geometric parameters on the bending moment and displacement of the variable cross-section continuous composite beam. Therefore, an analytical calculation method for the bending moment and displacement of the variable cross-section continuous composite beam needs to be proposed. Summary of the Invention

[0005] The purpose of the present invention is to provide a method for calculating the bending moment and displacement of a variable cross-section continuous composite beam to solve the problems raised in the above background technique.

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

[0007] S1. Segment the variable cross-section continuous composite beam structure with both ends rigidly connected and symmetric geometric characteristics under uniformly distributed load to obtain a variable cross-section model. Among them, the variable cross-section continuous composite beam structure is divided into beam end cross-section segments on both sides, a mid-span cross-section segment in the middle, and two variable cross-section transition segments connecting the beam end cross-section segments and the mid-span cross-section segments;

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

[0009] S3. Geometrically equivalent the variable cross-section continuous composite beam in the way of the segmented equal cross-section model, select half of the span for theoretical analysis and calculation, and obtain the moment M r at the cross-section segmentation point of the equivalent model, and judge the relative position relationship between the actual inflection point and the cross-section segmentation point according to the positive and negative signs of M r ;

[0010] S4. Determine the position of the actual inflection point, and further equivalently segment the variable cross-section continuous composite beam according to the position of the actual inflection point to obtain the position of the actual inflection point and the beam stiffness distribution when M r >0 and M r <0 respectively;

[0011] S5. Divide the half-span variable cross-section continuous composite beam into three segments according to the cross-section segmentation point and the position of the actual inflection point, establish equations based on the force balance and deformation coordination relationships at the cross-section segmentation point and the actual inflection point, and propose calculation methods for the displacement, rotation angle and moment of typical cross-sections.

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

[0013] I i = α i I i,s ......(1);

[0014] Where I i,s is the flexural moment of inertia of the steel beam cross-section of different composite beam segments, and α i is the stiffness amplification coefficient corresponding to different composite beam segments considering the contribution of the floor slab stiffness. The variable cross-section transition segment is divided into two segments according to the length, and the beam cross-section of the adjacent equal cross-section segment connected to each segment is taken respectively.

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

[0016] Calculate the bending moment M at the sectional point of the equivalent model according to Formula (1) and Formula (2). r :

[0017]

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

[0019] In a preferred embodiment, in step S4, determine the actual inflection point position. According to the actual inflection point position, further equivalently segment the variable-section continuous composite beam to obtain M r >0 and M r <0 when the actual inflection point position and the beam stiffness distribution, including:

[0020] Assume that the bending moment is positive when the bottom of the beam is in tension and is plotted below the beam in the bending moment diagram. When M r >0, the actual inflection point is located within the s1 section. The variable-section continuous composite beam in half-span is divided into three sections with lengths x1, x2, and x3 according to the sectional flexural stiffness k i . The x1 section is the negative bending moment area. At this time, the geometric and internal force relationships of the beam section are 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 within the s2 section. The x1 + x2 section is the negative bending moment area. The geometric and internal force relationships of the beam section are 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, the variable cross-section transition section, and the mid-span section are l1, l2, and l3 respectively. The section bending moment of inertia considering the combined effect of the floor slab is I1, I2, and I3 respectively.

[0031] In a preferred embodiment, in step S5, according to the section segmentation points and the actual inflection point positions, the semi-span variable cross-section continuous composite beam is divided into three segments. Based on the force balance and deformation coordination relationships of the section segmentation points and the actual inflection point, equations are established, and calculation methods for the displacement, rotation angle, and bending moment of typical sections are proposed, including:

[0032] For M r >0 and M r <0 for both cases, it is necessary to divide the semi-span variable cross-section continuous composite beam into three segments according to the section segmentation point o and the actual inflection point position, conduct a force analysis of the three-segment beam, and the rotation angles at the two segmentation points under the uniform load are respectively and The vertical deflections are ω1 and ω2 respectively, and the linear stiffness i of each beam segment j is calculated according to formula (9):

[0033]

[0034] Among them, the stiffness amplification coefficient α is given corresponding values according to the actual situation in its positive or negative bending moment area.

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

[0036]

[0037]

[0038] In a preferred embodiment, according to the bending moment formulas (14) and (15) at the two segmentation points, by combining formulas (10)-(13), the rotation angles and the vertical deflections ω1, ω2 at the segmentation points are obtained:

[0039]

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

[0041]

[0042] In a preferred embodiment, it further includes: according to the symmetry principle, obtaining the bending moment of the beam end section, the bending moment of the mid-span section, the rotational displacement and vertical deflection of each stiffness segmentation point of the entire variable cross-section continuous composite beam, and based on the obtained bending moment of the beam end section, the bending moment of the mid-span section, the rotational displacement and vertical deflection of each stiffness segmentation 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 both ends rigidly connected and geometrically symmetrically distributed under uniform load on the bending moment distribution and displacement of the variable cross-section continuous composite beam, wherein the design parameters include cross-sectional dimensions, stiffness, spans of each section, and external loads.

[0043] Compared with the prior art, the beneficial effects of the present invention are:

[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 helps to regulate 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-changing sections 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 mid-span section of the variable cross-section continuous composite beam structure can both be obtained by substituting parameters into the analytical formula, having the advantages of accuracy and generality. Through the analytical solutions of the bending moment and displacement of the variable cross-section continuous composite beam provided by the present invention, the influence laws of design parameters such as cross-sectional dimensions, stiffness, spans of each section, and external loads 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 the flowchart of the method of the present invention;

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

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

[0048] Figure 4 is the schematic diagram of the geometric shape equivalence of the present invention;

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

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

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

[0052] Figure 8Schematic diagram of the cross-section position of the variable cross-section continuous composite beam of the present invention. Detailed implementation manners

[0053] The technical solutions in the embodiments of the present invention will be clearly and completely described below. All other embodiments obtained by those of ordinary skill in the art without creative efforts fall within the protection scope of the present invention.

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

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

[0056] Step S2: Calculate the combined cross-section flexural moment of inertia of different beam segments. Segment the variable cross-section continuous composite beam according to the combined cross-section flexural moment of inertia to obtain a segmented equal cross-section model. The combined cross-section flexural moment of inertia of different beam segments is calculated according to the following formula:

[0057] I i = α i I i,s ……(1);

[0058] Where I i,s is the flexural moment of inertia of the steel beam cross-section of different combined beam segments, α i is the corresponding stiffness amplification coefficient considering the contribution of the floor stiffness for different combined beam segments. Divide the variable cross-section transition segment into two segments according to the length, and take the beam cross-sections of the adjacent equal cross-section segments connected to each segment respectively. As Figure 3 shown, Figure 2 the five beams in it are equivalent to three beams.

[0059] Step S3: To simplify the analysis process, the geometric shape of the variable cross-section continuous composite beam is geometrically equivalent according to the segmented equal cross-section model, and the theoretical analysis and calculation are carried out by selecting half of the span using symmetry. Using symmetry can reduce the number of unknowns in the calculation and solution, reduce the computational workload, and improve efficiency. First, the variable cross-section continuous composite beam is geometrically equivalent according to the method in Step S2 of the segmented equal cross-section model. As Figure 4 shown, the sectional point o of the equivalent model is at distances s1 and s2 from the end and the mid-span respectively. Assume that the stiffness amplification factor of the beam segment in the s1 range is taken as α - , and the stiffness amplification factor of the beam segment in the s2 range is taken as α + . Calculate the bending moment M r at the sectional point of the equivalent model section according to formulas (1) and (2). According to the positive and negative signs of M r , judge the relative position relationship between the actual inflection point and the sectional point o.

[0060]

[0061] Step S4: Determine the position of the actual inflection point. According to the position of the actual inflection point, further equivalently segment the variable cross-section continuous composite beam to obtain the position of the actual inflection point and the beam stiffness distribution when M r >0 and M r <0.

[0062] The inflection point is the position where the bending moment value of the beam is equal to 0 under the action of the load. 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. When M r >0, the actual inflection point is located within the s1 segment. The half-span variable cross-section continuous composite beam is divided into three segments with lengths x1, x2, and x3 according to the sectional flexural stiffness k i . As Figure 5 shown, the x1 segment shown in the shaded area in the figure is the negative bending moment area. At this time, the geometric and internal force relationships of the beam segment are 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 within the s2 segment, and its sectional stiffness value and variation range are as Figure 6As shown, the x1 + x2 section in the shaded area is the negative moment area, and the geometric and internal force relationships of the beam section are 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, where E is the elastic modulus of steel.

[0072] Step S5: For the two cases of M r > 0 and M r < 0, it is necessary to divide the semi-span variable cross-section continuous composite beam into three segments according to the section segmentation point o and the actual inflection point position, establish equations based on the force balance and deformation coordination relationships at the section segmentation point and the actual inflection point, and propose calculation methods for the displacement, rotation angle, and bending moment of the typical section.

[0073] Specifically, conduct a force analysis of the three-segment beam. As Figure 6 shown in the force diagram, the rotation angles at the two segmentation points under the uniform load are respectively and the vertical deflections are ω1 and ω2, and the linear stiffness i of each beam segment j is calculated according to formula (9):

[0074]

[0075] Among them, the stiffness amplification coefficient α is given corresponding values according to the actual situation in its positive or negative moment area.

[0076] Step S5 also includes: Establish a system of equations according to the shear force and bending moment balance conditions at the two segmentation points:

[0077]

[0078]

[0079] According to the bending moment formulas (14) and (15) at the two segmentation points, and by combining formulas (10) to (13), the rotation angles and the vertical deflections ω1 and ω2 at the segmentation points are solved:

[0080]

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

[0082]

[0083] Furthermore, it also includes: through the steps described above, according to the symmetry principle, obtaining the bending moments at the beam end sections, mid-span sections of the entire variable cross-section continuous composite beam, the rotational displacements and vertical deflections at each stiffness segmentation point, and the schematic diagrams of the positions of each section are as shown in Figure 8 shown. Thus far, all the necessary parameters required for the design of the variable cross-section continuous composite beam have been obtained. And based on the bending moments at the beam end sections, mid-span sections of the variable cross-section continuous composite beam, the rotational displacements and vertical deflections at each stiffness segmentation point, the influence of the design parameters of the variable cross-section continuous composite beam with both ends rigidly connected and geometrically symmetrically distributed under uniformly distributed load on the bending moment distribution and displacement of the variable cross-section continuous composite beam is obtained. Among them, the design parameters include cross-sectional dimensions, stiffness, spans of each section, and external loads. Under the action of the load, accurately calculating the mid-span and beam end bending moment values of the variable cross-section continuous composite beam structure helps to regulate the design parameters of the beam section.

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

[0085] Table 1 Comparison of calculation results

[0086]

[0087] Although the embodiments of the present invention have been shown and described, for those of ordinary skill in the art, it can be understood that various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the present invention. 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 zone.

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.

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