A method for calculating the ultimate load of the side columns of double-span and multi-span floors under fire

Abstract

The present invention discloses a method for calculating the ultimate load of the failure of the side columns of double-span and multi-span floor slabs under fire, which includes the following steps: S1, dividing the plate into arc-shaped micro-elements, and assuming the force of three adjacent beams of the failed side columns; S2, determining the distribution of the force on the beam based on conservative estimation; S3, calculating the deflection curve equation of the beam at normal temperature according to the deflection definition of the beam; S4, determining the deflection curve equation caused by the thermal gradient, substituting the deflection curve equation at normal temperature into the deflection curve equation to calculate the deflection curve equation caused by the thermal gradient at the top and bottom of the beam; S5, calculating the change of unit bearing capacity of fan-shaped areas of different radii caused by the stretching membrane effect based on the plate balance method and the principle of additional moment caused by the plastic hinge line; finally, based on the principle of the force of the double-span floor slab, further obtaining the calculation method of the floor slab bearing capacity of the failure of the side columns of the multi-span floor slab. The present invention proposes a new bearing capacity calculation method, which is faster and more convenient than the existing method.

Description

Technical Field

[0001] The invention relates to the technical field of building structure bearing capacity, and in particular to a method for calculating the ultimate load of failure of side columns of double-span and multi-span floor slabs under fire. Background Art

[0002] When the side columns of a multi-span floor fail under fire, the existing prediction of the floor bearing capacity mainly relies on numerical simulation software to determine it. However, the numerical simulation steps are cumbersome and the calculation time is long. When the boundary conditions change slightly, it is often necessary to re-model and calculate. In the existing technical system, there is no theoretical formula that can systematically reflect the changing trend of the floor bearing capacity when the side columns fail under fire. In addition, the conventional method for calculating the ultimate load of the floor corner column failure under fire is only applicable to the case of corner column failure, and cannot effectively predict the ultimate bearing capacity of the floor under the failure of the side columns, making it difficult to perform accurate load calculations. Summary of the invention

[0003] The object of the present invention is to provide a method for calculating the ultimate load of failure of side columns of double-span and multi-span floor slabs under fire, which has higher speed and convenience in bearing capacity calculation than numerical software.

[0004] To achieve the above object, the present invention provides a method for calculating the ultimate load of failure of a double-span floor column under fire, characterized in that it comprises the following steps:

[0005] S1. Divide the plate into arc-shaped micro-elements and make force assumptions on the three adjacent beams of the failed side column;

[0006] S2. Determine the distribution of forces on the beam based on conservative estimates;

[0007] S3. According to the definition of beam deflection, calculate the deflection curve equation of the beam at room temperature;

[0008] S4, determining the deflection curve equation caused by the thermal gradient, and substituting it into the deflection curve equation at room temperature to calculate the deflection curve equation caused by the thermal gradient at the top and bottom of the beam;

[0009] S5. Based on the plate balance method and the principle of additional moment caused by plastic hinge line, the change of unit bearing capacity of fan-shaped areas with different radii caused by the tensile membrane effect is calculated.

[0010] Further, in step S1, the three adjacent beams of the failed side column are named as beam I, beam II, and beam III, and the lengths are all L, wherein beam I and beam II are located at the outer edge of the plate, and beam III is located in the middle of the plate and is perpendicular to beam I and beam II; based on the experimental cracking law of the double-span floor after the failure of the side column, it is assumed that the main cracks on the top surface of the plate around the side column after the failure of the double-span floor and roof are distributed in an arc shape, and an arc-shaped fault zone is assumed, and the number of arc-shaped fault zones is assumed to be n; the annular area between the i-th and i+1-th fault zones is called the i-th annular plate; the center of the annular plate coincides with the position of the failed beam, which is called point O. When considering the force on the beam, it is assumed that the adjacent assumed beams act with completely symmetrically distributed forces, and there is:

[0011] F1+2F n(i) =F2+G (i) ;

[0012] Where: F1 represents the tensile force of the combined force of the steel bar and concrete on the lower fracture zone, F n(i) represents the support force of the beam on the i-th fault zone, F2 represents the combined force of the steel bars and concrete caused by the fault zone below, G (i) is the gravity of the i-th fault zone, and it is assumed that the beam is subjected to the following force:

[0013]

[0014] Furthermore, in step S2, the force distribution on the beam under conservative conditions is determined using the following formula:

[0015] Where: ρ is the density of each annular unit plate; g is the acceleration due to gravity, which is 9.8 m / s 2 ; y is the thickness of the plate; x is the distance between point O and the i-th arc plate; dx is the differential symbol; q i is the external load on the plate within this arc plate; d is the width of each infinitesimal element.

[0016] Furthermore, in step S3, according to the definition of beam deflection, the displacement of the beam at room temperature that is only affected by external force but not affected by temperature is:

[0017]

[0018] Among them, x1 and x2 are symbols of integral variables, which are used to integrate the original formula; i1 represents a temporary symbol in the accumulation, which is used to accumulate to i; ω y,max It is the maximum vertical displacement of the beam end under the ultimate stress state under the influence of external load only, [σ0] is the allowable normal stress of the beam, W is the bending section coefficient, and EI is the stiffness coefficient of the beam;.

[0019] Further, in step S4, the beam displacement affected only by temperature is:

[0020]

[0021] Where: yx(T) is the required temperature deflection curve equation; is the thermal expansion coefficient; T yx is the temperature gradient on the AO beam; L is the length of the plate; x is the position variable.

[0022] Combining the deflection equation of the beam under stress and the beam displacement formula under the influence of temperature, the total displacements ω1 and ω2 of beams I and II are obtained as follows:

[0023]

[0024]

[0025] Where: 1,max ,ω 2,max They are the maximum vertical displacements at the ends of beams I and II under the influence of temperature and external force and under the ultimate stress state;

[0026] The displacement equation of beam III is calculated as:

[0027]

[0028] Furthermore, in step S5, the relationship between the load and the plate force is calculated by the plate balance method of the stretch film effect as follows:

[0029]

[0030] In the formula, F Ti1 is the upward pulling force per unit length of the annular edge, i.e., along the radius r i The total plastic hinge line resistance moment in the arc direction, r i is the distance between the ith annular plate and point O, that is, the radius of the ith annular plate, ρgy is the deadweight per unit area of ​​the floor slab, f(x) is the uniformly distributed load per unit area of ​​the slab, W1 is the moment of resistance per unit length of the annular edge, and θ is the angle between the ith and i-1th annular plates in the direction parallel to the slab normal. The formula obtained by the plate balance method is simply rearranged to obtain the total calculation formula for the unit bearing capacity f(x):

[0031]

[0032] In addition, the present invention provides a method for calculating the ultimate load of the failure of side columns of a multi-span floor under fire, which divides the multi-span floor into a double-span floor adjacent to the failed corner column, and other non-adjacent floor slabs, wherein the failure of the corner column does not affect the other non-adjacent floor slabs; the adjacent single-span floor slabs are calculated using the method described above.

[0033] The beneficial effects of the present invention are: by summarizing the failure characteristics of the existing multi-span floor side columns, a new bearing capacity calculation method is proposed, which has higher speed and convenience in bearing capacity calculation than numerical software. Compared with the prior art, it is shown that the present invention has good accuracy within a considerable range and can describe the ultimate load of the failure of the side columns of double-span and multi-span floor under fire at the theoretical formula level. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 The actual crack pattern diagram of the upper surface of the floor with failed side columns;

[0035] Figure 2 This is a hypothetical schematic diagram of a small angled floor;

[0036] Figure 3 It is a schematic diagram of a double-span floor after dividing the circular arc microelement;

[0037] Figure 4 is the display map of the ith region;

[0038] Figure 5 It is a diagram showing the beam deflection state and the coordinate system used;

[0039] Figure 6 It is the small angle sector element diagram assumed in the beam force analysis;

[0040] Figure 7 This is a rendering of the four-span floor slab;

[0041] Figure 8 It is a flow chart of the calculation method of the present invention. DETAILED DESCRIPTION

[0042] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0043] like Figure 8 FIG. 1 is a flow chart of a method for calculating the ultimate load of the side columns of double-span and multi-span floor slabs that fail under fire. The calculation method includes the following steps:

[0044] Step 1, divide the plate into arc-shaped micro-elements and make force assumptions on the three adjacent beams of the failed side column;

[0045] Step 2, based on conservative estimates, determine the distribution of forces on the beam;

[0046] Step 3, according to the definition of beam deflection, calculate the deflection curve equation of the beam at room temperature;

[0047] Step 4, determine the deflection curve equation caused by the thermal gradient, and substitute it into the deflection curve equation at room temperature to calculate the deflection curve equation caused by the thermal gradient at the top and bottom of the beam;

[0048] Step 5, based on the plate balance method and the principle of additional moment caused by the plastic hinge line, calculate the change of unit bearing capacity of the fan-shaped area with different radii caused by the tensile membrane effect;

[0049] Step 6, based on the stress principle of double-span floor, deduce the calculation method of floor bearing capacity in case of failure of side columns of multi-span floor.

[0050] Based on the cracking law of the double-span slab after the failure of the side columns (such as Figure 1 As shown in the figure, O is a failed side column, A, B, A', B', O are all unfailed side columns, AB, BO, B'O, B'A', AO', A'O', OO' are all beams), assuming that the main cracks on the top surface of the plate around the side columns after the failure of the double-span floor and roof are distributed in an arc shape, so an arc fault zone is assumed. Figure 1 It can be seen that the starting and ending positions of the arc crack with the largest radius are located at the three adjacent side columns (B, O, B') of the failed side column (O), which defines the maximum range of the fault zone. When the plate is subjected to a load far greater than the deadweight of the plate, the plate failure first occurs in the arc crack area. Here, it is assumed that the relatively small deformation is negligible to the large deformation during fracture, that is, the crack area where the large deformation occurs accounts for the main part of the floor deformation, and the area without cracks ( Figure 1 The slight deformation of the ABO' and A'B'O' triangle areas is not taken into account, that is, the crack-free triangle area is regarded as a rigid body and is completely fixed.

[0051] Assume that there is a concrete floor slab, which is shaped like a sector with O as the center and an angle dθ (see Figure 2 ), where the two straight sides of the plate are supported by beams OI and OA respectively, and the distance between these two beams is very close, which are called super-close distance beams. Since beam OI and beam AO have only a small angle, the two super-close distance beams bear exactly the same forces caused by the deadweight and load of the plate, respectively, so as to determine the relevant inequality relationship and determine the gravity and external forces of all micro-element arcs borne by the two related beams when making conservative estimates. The purpose of assuming a small-angle concrete floor here is to divide the double-span floor into countless fan-shaped micro-elements in the subsequent analysis, and each fan-shaped micro-element can be assumed to be a small-angle floor for analysis.

[0052] Division of finite arcs: The shape of the double-span floor is composed of two square floor plates (ABOO' and OB'A'O'), so the divided finite arcs tend to be positive 1 / 2 arcs: Figure 1The crack condition that is close to a circular arc can be simplified to a standard 1 / 2 circular arc shape (such as Figure 3 shown).

[0053] Assume that there are n arcs in total, all with O as the center, spreading out to the largest arc at equal distances d. It is easy to get d = L / n, and the distance from the i-th arc to the center point O, that is, the radius of the i-th arc is:

[0054]

[0055] The default failure criteria for floor slabs: only for area i ( Figure 4 The shaded area) is considered in the analysis. There is a tensile force of the steel bars between each arc (original crack) (causing the tensile membrane effect on the upper surface) and an additional section bending moment caused by the plastic hinge line. When the divided part is subjected to a load exceeding the maximum load, the force caused by the tensile membrane effect approaches the limit, and the combined force of the section bending moment and the force caused by the tensile membrane cannot resist the load. A large degree of cracks appear on the floor slab, and the floor slab is considered to have failed.

[0056] Redundant factors: Consider the influence of the deadweight of the slab: The traditional bearing capacity test of the slab with any column intact does not consider the deadweight of the floor slab, because when the side columns have not failed, the deadweight is extremely small compared with the external load. However, in the double-span slab test after the side columns failed, the slab has a slight deformation due to its deadweight when no load is applied, so it is necessary to consider the deadweight of the slab.

[0057] Beam load assumptions: When the side columns fail, Figure 4 The external forces on the i-th area shown in the figure mainly come from the support of beams BO, B'O, OO', and the steel bar tension and additional resistance bending moment between arcs k1-k2, k2-k3. After the side column fails, the three beams B'O, BO, O'O between the adjacent columns B', B, O' of O lose their bearing capacity and deflect after losing the support force at one end, as shown in Figure (3).

[0058] In the process of analyzing the stress of the beam in the i-th area, Figure (6) shows the shaded parts of the hypothetical i-th area and the i+1-th area after dividing the arc. Since the tensile force F1 of the combined force of the steel bars and concrete at (2) on the fan-shaped area below (i.e., the shaded part representing the i+1-th area) is slightly greater than the force F2 of the same nature caused by the steel bars and concrete in the fan-shaped part below (1) (i.e., the shaded part representing the i-th area), F1>F2 always holds true. Therefore, when it is assumed that the beams OI and OA on the small-angle floor have only a small angle, the two super-close beams have completely symmetrical forces distributed on OA and OI. And:

[0059] F1+2F n(i) =F2+G (i)

[0060] When 2F n(i) =G (i) When

[0061] F1+G (i) >F2+G (i)

[0062] From this inequality, we can see that when When , the force carried by the beam in this assumption is greater than the actual force. When the weight is the same, the unilateral deflection of the beam will be greater, and the load it can carry will be smaller, so the result is more conservative. When dθ expands to π, and when The results obtained are necessarily conservative.

[0063] Calculate beam displacement: Since the three related beams are subjected to symmetrical forces, the OO' beam is subjected to force analysis:

[0064] Take O as the origin and establish Figure 5 -b coordinate system, the bending curve of the beam is roughly as follows Figure 5 -a. The distribution model of the force on the beam is established in this coordinate system. The unit weight of each annular micro-element plate is conservatively estimated to be ρgy (where y is the thickness of the plate, ρ is the density of each annular unit plate, and g is the gravitational acceleration, which is taken as 9.8m / s 2 ), and the load q i All contribute to the deflection of the beam, then the unit length bearing capacity F of the i-th (counting from the center O outward) micro-element ring plate affected by the beam is n(i) for:

[0065]

[0066] Where d = L / n, d is a small increment on the x-axis. For the constant term ρgy that can be integrated, this small increment is set to dx, and for the non-constant term q i , still expressed in d, since there is an equation x = i·d, we can get:

[0067]

[0068] The above formula reflects how the magnitude of the force on the beam changes with the distance x from the center of the circle 0, and is used to calculate the bending moment generated at point A by all the forces on the beam.

[0069] Since the unit weight ρgy of each annular microelement plate is equal to the load q i All contribute to the deflection of the beam, then the unit length bearing capacity k of the i-th (counting from the center O outward) micro-element ring plate under the beam is (i) as follows:

[0070] k (i) =ρgy+q i

[0071] The unit total bearing capacity can be expressed as:

[0072] F n(i)(x) =d·(ρgy+q i )

[0073] where q i is the limit load that the i-th unit ring plate can bear. i It changes with the distance x. Therefore, the above formula reflects the change of the force on the beam with the distance x, and is used to calculate the bending moment at any point in the deflection curve equation.

[0074] Calculate the displacement-deflection curve equation of the beam under the influence of thermal gradient: When a fire occurs, the plates and beams are subjected to burning temperatures of hundreds or even thousands of degrees. The temperature will greatly affect the deformation of the beams. Therefore, it is particularly important to consider the influence of thermal gradient on beam deflection.

[0075] For deflection considering only the temperature effect: ω yx(T) is the required temperature deflection curve equation. At this time, it is assumed that the edge beam is simply supported and there is no constraint between the plate and the beam. The thermal gradient T on the AO beam is yx for:

[0076]

[0077] Where T 2b1 With T 1b1 are the temperatures of the bottom and top of the beam, respectively, b1 is the section height, h b1 =h sb1 +h s , where h sb1 is the cross-sectional height of the edge beam, h s is the plate thickness, and due to the thermal gradient, a uniform curvature is caused along the length Where α is the thermal expansion coefficient, the following equation is given:

[0078]

[0079] The boundary conditions are x=L, y t = 0, and we can obtain the deflection curve equation ω caused by temperature. yx ( T ):

[0080]

[0081] Then the total deflection formula of AO beam w1 is as follows:

[0082]

[0083] Due to q iIt does not exist in any area of ​​the board, it may only exist in such a fan-shaped range: O is the fan corner point, and the outer edge of the i-th board is the fan arc boundary line. Therefore, q outside this range i is 0, and ρgy remains the same. Therefore, the maximum deflection ω is calculated 1,max When x=x limit Time i If the beam fails, then x limit —L has no external load, and since when x=L, ω 1,max =0, represented by ω 1,max Follow x limit The value changes are as follows:

[0084]

[0085] Where EI is the stiffness coefficient of the beam. Substituting it into the total deflection, the modified total deflection equation of the AO beam under the influence of thermal gradient can be obtained.

[0086] Similarly, the deflection equation of the BO beam is as follows:

[0087]

[0088] in,

[0089]

[0090] It can be seen that the deflection curve equations of the B'O and BO beams are the same, and the deflection of the OO' beam at any point is twice that of the B'O beam, so the deflection equation of the OO' beam is as follows:

[0091]

[0092]

[0093] Based on the above considerations, the above two beam deflection curve equations can be regarded as equivalent, that is, L can replace l.

[0094] Calculation of the stretch film effect and total load-bearing capacity ：

[0095] Assumptions for calculation of stretched film effects based on plate balance method

[0096] When considering the deformation of the beam, it has been assumed that the gravity and load of each ring unit are supported by the beams on both sides. In fact, not only is there support from the beam, but there are also additional resistance moments caused by plastic hinges on both sides of a single arc, and the tensile membrane effect provided by the tension of the steel bars. Therefore, the above assumptions about the beam are conservative, but not too conservative, because when the column fails, the maximum bending angle of the beam due to the force will not be too obvious, otherwise it will cause the beam to fail, resulting in failure of the assumption. Based on the above considerations, it can be assumed that the bearing capacity of the beam is between 0 and F. ni 0 means the beam is completely unloaded, F ni When there is no force at all, all load forces are offset by the film and the resistance moment. At this time, the calculated membrane force must be the limit state, and the actual membrane force will be less than this. ni When , the beam will have the largest deformation. In the next step of calculating the tensile membrane effect, the angle θ will be the largest, so the membrane force calculated based on this premise must also be the limit state. In summary, the deformation of the beam when fully loaded is taken as the definition standard of θ, and the subsequent calculation of the membrane force does not consider the support force of the beam but only the tensile membrane force, resistance moment, deadweight, and load weight.

[0097] Plate balance calculation of stretched film effect:

[0098] For the upper surface of the sector plate within the i-th annular plate (such as Figure 4 , where the sector plate being analyzed is the shaded part), the forces are as follows:

[0099] The upward pulling force per unit length of the annular edge (along the radius r i The total plastic hinge line resistance moment in the arc direction) F Ti1 , the unit weight of the floor slab is ρgy, the uniformly distributed load per unit area in the fan-shaped area is f(x), and the resistance moment per unit length of the annular edge is W1,

[0100]

[0101] The following relationship can be obtained from the improved plate balance method considering the tensile film effect of the plate:

[0102]

[0103] Where r i , x represents the radius of the sector, y is the height of the plate, ρgy is the deadweight of the plate per unit area, θ is the angle between the i-th and i-1-th annular plates parallel to the plate normal, θ=θ i -θ i-1 , and there are:

[0104]

[0105] where k i , k i-1 can be obtained by derivation of the beam deflection curve equation. Since the deflection curve equations of beams OB and OB' are the same, and the deflection curve equation of OO' is twice that of OB, k can be calculated in the OO'B sector area. i , k i-1 as follows:

[0106]

[0107]

[0108] In the OO'B' sector, k can be calculated i , k i-1 as follows:

[0109]

[0110]

[0111] Calculate the plastic hinge resistance moment:

[0112] For the fan-shaped area, the plastic hinge line resistance moment W1 on the right side of the area is as follows:

[0113]

[0114] Among them, m x is the plastic hinge resistance moment per unit length along the arc direction. According to the concrete structure design theory,

[0115] m x =f yx A x (h0-βc)=T x (h0-βc)=T x γ s h0

[0116] m x =Cz=α1f c 'γ s h0

[0117] Where c is the horizontal length of the studied plate from the study plane when the studied plate is deflected, C is the resultant force in the concrete compression zone, β is the influence coefficient of the section height, when h0 is not greater than 800mm, the value is 1.0, when h0 is not less than 2000mm, the value is 0.9, and the linear interpolation method is used in between; f yx A is the yield strength of steel bar; x is the reinforcement area per unit width; sis the distance coefficient from the steel bar resultant force point to the concrete compression resultant force point, generally taken as 0.85-0.90; h0 is the effective height of the section; Z is the steel bar resultant force at the unit width plastic hinge line; α1 is the calculation parameter of the concrete stress diagram in the compression zone, which can be obtained by referring to the Code for Design of Concrete Structures (GB50010-2010); f c ' is the compressive strength of concrete cube.

[0118] Calculate the total bearing capacity: The original formula obtained by the plate balance method is simply rearranged to obtain the total calculation formula for the unit bearing capacity f(x):

[0119]

[0120] The unknown quantity in the formula is F Ti1 , is the radius r i The total plastic hinge line resistance moment in the arc direction is the resultant force of the reinforcement at the position of the reinforcement. For the reinforcement mesh in the entire slab under study, Where T x Along the radius r i The resultant force of the reinforcement at the plastic hinge line of unit width in the arc direction is:

[0121]

[0122] For the unknown quantity T yx (θ), as the first independent variable in this formula.

[0123] For the unknown quantity x, it serves as the second independent variable.

[0124] For the unknown quantity i, it can be described by replacing it with x in the equation x=id.

[0125] The known quantities in the formula include: slab height y, unit volume density ρ of the concrete slab, gravitational acceleration g, slab length L, stiffness coefficient EI of the steel bars, and thermal expansion coefficient α.

[0126] Analysis of multi-span floor with side column failure: Figure 7 When the side column O fails, it will also cause a large deflection of the beams around O. Experimental observations show that the failure of a side column only affects the two adjacent single-span floor slabs, while the impact on the non-adjacent floor slabs can be ignored. Therefore, in the case of Figure 7 When the bearing capacity analysis of the four-span floor with side column failure is performed for the shown four-span floor, after the failure of O, only the double-span floor AA'B'B is analyzed for the bearing capacity of the double-span floor, and the bearing capacity analysis of the remaining area is still performed using the traditional analysis method when the side columns are not lost.

[0127] The embodiments of the present invention are described in detail above in conjunction with the accompanying drawings, but the present invention is not limited thereto. Various changes that can be made within the knowledge scope of technicians in the relevant technical field without departing from the spirit of the present invention are all within the protection scope of the claims of the present invention.

Claims

1. A method for calculating the ultimate load of the side columns of a double-span floor under fire, characterized in that: The steps include: S1. Divide the plate into arc-shaped micro-elements and make force assumptions on the three adjacent beams of the failed side column; S2. Determine the distribution of forces on the beam based on conservative estimates; S3. According to the definition of beam deflection, calculate the deflection curve equation of the beam at room temperature; S4, determining the deflection curve equation caused by the thermal gradient, and substituting it into the deflection curve equation at room temperature to calculate the deflection curve equation caused by the thermal gradient at the top and bottom of the beam; S5. Based on the plate balance method and the principle of additional moment caused by plastic hinge line, the change of unit bearing capacity of fan-shaped areas with different radii caused by the tensile membrane effect is calculated; In step S1, the three adjacent beams of the failed side column are named as beam I, beam II, and beam III, and the lengths are all L, wherein beam I and beam II are located at the outer edge of the plate, and beam III is located in the middle of the plate and is perpendicular to beam I and beam II; based on the experimental cracking law of the double-span floor after the failure of the side column, it is assumed that the main cracks on the top surface of the plate around the side column after the failure of the double-span floor and roof are distributed in an arc shape, and an arc-shaped fracture zone is assumed, and the number of arc-shaped fracture zones is assumed to be n; the annular area between the i-th and i+1-th fracture zones is called the i-th annular plate; the center of the annular plate coincides with the position of the failed beam, which is called point O. When considering the force on the beam, it is assumed that the adjacent assumed beams act with completely symmetrically distributed forces, and there is: <h2 style=";text-align:left;direction:ltr">F1+2F<h2 style=";text-align:left;direction:ltr"> n(i) <h2 style=";text-align:left;direction:ltr"> <F2+G<h2 style=";text-align:left;direction:ltr"> (i) <h2 style=";text-align:left;direction:ltr"> ; Where: F1 represents the tensile force of the combined force of the steel bar and concrete on the lower fracture zone, F n(i) represents the support force of the beam on the i-th fault zone, F2 represents the combined force of the steel bars and concrete caused by the fault zone below, G (i) is the gravity of the i-th fault zone, and it is assumed that the beam is subjected to the following force: Combining the deflection equation of the beam under stress and the beam displacement formula under the influence of temperature, the total displacements ω1 and ω2 of beams I and II are obtained as follows: Where: 1,max ,ω 2,max They are the maximum vertical displacements at the ends of beams I and II under the influence of temperature and external force and under the ultimate stress state; The displacement equation of beam III is calculated as: Where: is the density of each annular unit plate; g is the acceleration due to gravity, which is 9.8m / s 2 ; y is the thickness of the plate; x is the distance between point O and the i-th arc plate; dx is the differential symbol; q i is the external load on the plate in this arc plate; d is the width of each microelement; x1 and x2 are the symbols of the integral variables, which are used to integrate the original formula; i1 represents the temporary symbol in the accumulation, which is used to accumulate to i; ω y,max It is the maximum vertical displacement of the beam end under the ultimate stress state under the influence of external load only, [σ0] is the allowable normal stress of the beam, W is the bending section coefficient, and EI is the stiffness coefficient of the beam.

2. The method for calculating the ultimate load of the failure of the side columns of a double-span floor under fire according to claim 1 is characterized in that: In step S2, the force distribution on the beam under conservative conditions is determined using the following formula: 。 3. The method for calculating the ultimate load of the failure of the side columns of a double-span floor under fire according to claim 2 is characterized in that: In step S3, according to the definition of beam deflection, the displacement of the beam at room temperature that is only affected by external force but not affected by temperature is: 。 4. The method for calculating the ultimate load of the failure of the side columns of a double-span floor under fire according to claim 3 is characterized in that: In step S4, the beam displacement affected only by temperature is: Where: yx(T) is the required temperature deflection curve equation; is the thermal expansion coefficient; T yx is the temperature gradient on the AO beam; L is the length of the plate; x is the position variable.

5. The method for calculating the ultimate load of the failure of the side columns of a double-span floor under fire according to claim 1 is characterized in that: In step S5, the relationship between the load and the plate force is calculated by the plate balance method of the stretch film effect as follows: In the formula, F Ti1 is the upward pulling force per unit length of the annular edge, i.e., along the radius r i The total plastic hinge line resistance moment in the arc direction, r i is the distance between the ith annular plate and point O, i.e., the radius of the ith annular plate, ρgy is the deadweight per unit area of ​​the floor slab, f(x) is the uniformly distributed load per unit area of ​​the slab, W1 is the moment of resistance per unit length of the annular edge, and θ is the angle between the ith and i-1th annular plates in the direction parallel to the plate normal; The total calculation formula of unit bearing capacity f(x) can be obtained by simply rearranging the formula obtained by plate balance method:

6. A method for calculating the ultimate load of failure of side columns of multi-span floor under fire, characterized in that: The multi-span floor is split into a double-span floor adjacent to the failed corner column and other non-adjacent floor slabs, wherein the failure of the corner column does not affect the other non-adjacent floor slabs; the adjacent single-span floor slabs are calculated using the method described in claims 1-5.

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