A method for analyzing the bearing capacity of reinforced concrete floor considering the influence of beam deformation

Abstract

The present invention discloses a reinforced concrete floor bearing capacity analysis method considering the influence of beam deformation. The analysis method considers the influence of the vertical deformation of the beam on the bearing capacity of the concrete slab. By calculating the position parameters of the yield line of the reinforced concrete slab, the displacement coefficients of the long beam and the short beam, the yield line load value of the reinforced concrete slab, and the improvement coefficient of the reinforced concrete slab, the bearing capacity of the reinforced concrete floor considering the influence of beam deformation is obtained. By establishing a new equilibrium equation, the analysis method analyzes the ultimate bearing capacity of the reinforced concrete slab, and the error is smaller than the data obtained from actual tests. The analysis method has great significance for the study of the bearing capacity of reinforced concrete floors.

Description

Technical Field

[0001] The present invention relates to a reinforced concrete floor bearing capacity analysis method, and in particular to a reinforced concrete floor bearing capacity analysis method taking into account the influence of beam deformation. Background Art

[0002] The calculation of bearing capacity is of great significance to structures and buildings, and scholars have never stopped their theoretical research on it, such as the yield line theory, Bailey theory, and steel bar strain difference method. However, it is undeniable that these theories always have certain errors compared with the experimental values.

[0003] It is a common situation that the beams of reinforced concrete floor slabs undergo vertical deformation during normal operation. Under this condition, the ultimate bearing capacity of the slab also changes. Therefore, it is of great significance to consider the vertical deformation of the beams when calculating the bearing capacity of the reinforced concrete floor slabs. Summary of the Invention

[0004] The purpose of the present invention is to provide a reinforced concrete floor bearing capacity analysis method taking into account the influence of beam deformation, and the reinforced concrete floor bearing capacity analyzed by this method has a smaller error than the actual situation.

[0005] To achieve the above objectives, the present invention provides a method for analyzing the bearing capacity of reinforced concrete floors that takes into account the influence of beam deformation. The reinforced concrete floors supported by beams are reinforced concrete slabs composed of rectangular two-way slabs, and the beams include long beams and short beams supported by columns. The method is characterized in that it includes the following steps:

[0006] S1. Divide the reinforced concrete slab into four equal rectangular areas. Each rectangular area is further divided into a right-angled trapezoidal plate and a right-angled triangular plate. The right-angled trapezoidal plate is numbered as plate 1 in the rectangular area, and the right-angled triangular plate is numbered as plate 2 in the rectangular area. In each pair of adjacent rectangular areas, plates 1 and 2 are arranged axially symmetrically along the butting edge between the two rectangular areas, and one of the right-angled edges of each plate 2 coincides with the edge of the reinforced concrete slab.

[0007] S2. Establish an elliptical area based on the reinforced concrete slab to distinguish the tensile and compressive membrane effect areas;

[0008] S3. Ignoring beam torsion and horizontal displacement, determine the location parameter n of the yield line of the reinforced concrete slab based on the length L, width l, and reinforcement parameters of the reinforced concrete slab, where the boundary conditions for the reinforced concrete slab and the beam are simply supported on both sides;

[0009] S4. Based on the length L and width l of the reinforced concrete slab, the location parameter n of the yield line of the reinforced concrete slab, and the displacement calculation formulas for the beam and reinforced concrete slab, determine the displacement coefficient λ1 of the long beam and the displacement coefficient λ2 of the short beam, respectively;

[0010] S5. Based on the length L and width l of the reinforced concrete slab, the location parameter n of the yield line of the reinforced concrete slab, the displacement coefficient λ1 of the long beam, and the displacement coefficient λ2 of the short beam, determine the yield line load value q of the reinforced concrete slab according to the principle of virtual work, where the vertical load on the reinforced concrete slab is a uniformly distributed load;

[0011] S6. Based on the length L and width l of the reinforced concrete slab, determine the membrane force parameters of the reinforced concrete slab according to the elliptical area;

[0012] S7. Based on the membrane force parameters of the reinforced concrete slab and the principle of membrane effect, determine the bearing capacity improvement factors of plate 1 and plate 2, as well as the bearing capacity improvement factors caused by the axial force of plates 1 and 2;

[0013] S8. Determine the improvement factor for the reinforced concrete slab based on the increased bearing capacity factors of plates 1 and 2, and the increased bearing capacity factors due to the axial forces of plates 1 and 2, and in accordance with the principle of equivalent concentrated forces;

[0014] S9. Based on the yield line load value q and the improvement factor of the reinforced concrete slab, the ultimate bearing capacity of the reinforced concrete slab is calculated, and then the bearing capacity of the reinforced concrete floor considering the influence of beam deformation is obtained.

[0015] As a preferred technical solution of the present invention: the method for dividing the elliptical area in step S2 is: dividing the length and width of the reinforced concrete slab into four equal parts, dividing the reinforced concrete slab into 16 rectangular areas, for the 16 rectangular areas, the four central rectangular areas together constitute a central rectangular area, and an elliptical area is divided on the reinforced concrete slab through the four vertices of the central rectangular area, the area inside the ellipse is the tensile membrane effect area, and the area outside the ellipse is the compressive membrane effect area.

[0016] As a preferred technical solution of the present invention: the position parameter n of the yield line of the reinforced concrete slab determined in step S3 is as follows:

[0017]

[0018] Wherein, the reinforcement parameters include the preset orthogonal parameter μ, the aspect ratio a of the reinforced concrete slab, and the angle difference α between the obtuse angle of the right-angled trapezoid in the rectangular area plate 2 divided by the reinforced concrete slab and the right angle.

[0019] As a preferred technical solution of the present invention, the steps of calculating the displacement coefficient λ1 of the long beam and the displacement coefficient λ2 of the short beam in step S4 include:

[0020] S41: Calculate the mid-span vertical displacement of the beam in the long and short span directions, as well as the mid-span vertical displacement of the reinforced concrete slab:

[0021]

[0022]

[0023] Where q 长 ,q 短 ,q 板 is the uniformly distributed load on the reinforced concrete slab, E is the elastic modulus of concrete, I 板 is the moment of inertia of the reinforced concrete slab, I 梁 is the moment of inertia of the beam, Δ 长 , Δ 短 are the mid-span vertical displacements of the beam in the long span and short span directions, Δ 板 is the mid-span vertical displacement of the reinforced concrete slab;

[0024] S42: Based on the mid-span vertical displacements of the beam in the long and short span directions, as well as the mid-span vertical displacements of the reinforced concrete slab, the displacement coefficients λ1 and λ2 of the long beam and short beam are calculated as follows:

[0025]

[0026] As a preferred technical solution of the present invention: the yield line load value q of the reinforced concrete slab in step S5 is as follows:

[0027]

[0028] Where M x 、M y are the unit ultimate bending moments of reinforced concrete slabs along the x and y directions, m1 and m2 are the unit ultimate bending moments of long beams and short beams respectively, and b ′ is the beam width, λ1 is the displacement coefficient of the long beam, and λ2 is the displacement coefficient of the short beam.

[0029] As a preferred technical solution of the present invention: the membrane force parameters of the reinforced concrete slab in step S6 include membrane force related quantity k, membrane force related quantity k ′ , membrane force related quantity k ″ , film force related quantity b, where the film force related quantity k is as follows:

[0030]

[0031] Where:

[0032]

[0033] Where B0 is the length of the minor axis of the ellipse;

[0034]

[0035] Membrane force related quantity k ′ As follows:

[0036]

[0037] Where T0 is the yield strength of steel bar per unit width, f c is the compressive strength of concrete, x c is the width of the thin film effect under edge pressure;

[0038] Membrane force related quantity k ″ As follows:

[0039]

[0040] Where:

[0041]

[0042] The film force related quantity b is as follows:

[0043]

[0044] Where C1 is the resultant force of concrete pressure at yield line AG, T2 is the resultant force of steel tension at yield line BG, K is the ratio of the yield force of steel per unit width in the y-direction to the yield force of steel per unit width in the x-direction, and α is the angle difference between the obtuse angle and the right angle of the right trapezoid in plate 2 of the rectangular area divided by the reinforced concrete slab.

[0045] As a preferred technical solution of the present invention: the load-bearing capacity improvement coefficient in step S7 includes the load-bearing capacity improvement coefficient e of plate 1 and plate 2 along the x direction. 1m,x 、e 2m,x , the bearing capacity improvement factor e of plate 1 and plate 2 along the y direction 1m,y 、e 2m,y , the load-bearing capacity improvement coefficient e caused by the axial force of plate 1 and plate 2 1b 、e 2b ;

[0046] The bearing capacity improvement factor e of plate 1 along the x direction 1m,x As follows:

[0047]

[0048] Where:

[0049] M 1m,x =C1cosαh C1 +T4h T4 -Ssinαh s -T2cosαh T2 -C2h C2

[0050] The bearing capacity improvement factor e of plate 1 along the y direction 1m,y As follows:

[0051]

[0052] Where:

[0053] M 1m,y =T2sinαh T2 +T1h T1 -C1sinαh C1 -Scosαh s

[0054] The bearing capacity improvement factor e of plate 2 along the x direction 2m,x As follows:

[0055]

[0056] Where:

[0057] M 2m,x =T2sinαh T2 +Ssinαh s -C1cosαh C1

[0058] The bearing capacity improvement factor e of plate 2 along the y direction 2m,y As follows:

[0059]

[0060] Where:

[0061] M 2m,y =C1sinαh C1 +Scosαh s +T3h T3 -T2sinαh T2 -C3h C3

[0062] in:

[0063]

[0064] Where C1 is the resultant force of concrete pressure at yield line AG, C2 is the resultant force of concrete pressure at yield line ED, C3 is the resultant force of concrete pressure at yield line IF, T1 is the resultant force of steel tension at yield line BC, T2 is the resultant force of steel tension at yield line BG, T3 is the resultant force of steel tension at yield line BI, T4 is the resultant force of steel tension at yield line DC, h i is the vertical displacement of the support of the reinforced concrete slab under the equivalent membrane force in the i direction, α is the angle difference between the obtuse angle of the right-angled trapezoid in plate 2 of the rectangular area divided by the reinforced concrete slab and the right angle;

[0065] The load-bearing capacity enhancement factor e caused by the axial force of plate 1 1b As follows:

[0066]

[0067] Where:

[0068]

[0069]

[0070] in:

[0071]

[0072] L AE is the length of the bottom side of plate 1, k, k ′ is the membrane force parameter, K is the ratio of the yield strength of the steel bar per unit width in the y direction to the yield strength of the steel bar per unit width in the x direction, T0 is the yield strength of the steel bar per unit width, f c is the compressive strength of concrete, x c is the width of the thin film effect under edge pressure;

[0073] The load-bearing capacity enhancement factor e caused by the axial force of plate 2 2b As follows:

[0074]

[0075] Where:

[0076]

[0077] in:

[0078]

[0079] Where A0 is the length of the major axis of the ellipse, k ″ is the film force parameter;

[0080] in:

[0081]

[0082] i=1,2,

[0083] Where g i is the compressive stress zone parameter under bending in long span or short span.

[0084] As a preferred technical solution of the present invention: the analysis method of the improvement coefficient e of the reinforced concrete slab in step S8 is as follows:

[0085]

[0086] Where:

[0087] e ′ =(1-n)e 1x +ne 2x

[0088] e ″ =(1-n)e 1y +ne 2y

[0089] in:

[0090] e 1x =e 1m,x +e 1b

[0091] e 2x =e 2m,x +e 2b

[0092] e 1y =e 1m,y +e 1b

[0093] e 2y =e 2m,y +e 2b

[0094] Where, e 1m,x is the load-bearing capacity enhancement factor of plate 1 along the x direction, e 2m,x is the load-bearing capacity enhancement factor of plate 2 along the x direction, e 1m,y is the load-bearing capacity enhancement factor of plate 1 along the y direction, e 2m,y is the load-bearing capacity enhancement factor of plate 2 along the y direction, e 1b is the load-bearing capacity enhancement factor caused by the axial force of plate 1, e 2b is the bearing capacity enhancement coefficient caused by the axial force of plate 2.

[0095] As a preferred technical solution of the present invention: the ultimate bearing capacity q of the reinforced concrete slab in step S9limit As follows:

[0096] q limit =q×e

[0097] Where e is the enhancement factor of reinforced concrete slab, and q is the yield line load value of reinforced concrete slab.

[0098] Beneficial effects: Compared with the prior art, the advantages of the present invention include:

[0099] The present invention designs a reinforced concrete floor bearing capacity analysis method that considers the influence of beam deformation. This analysis method considers the influence of the vertical deformation of the beam on the bearing capacity of the concrete slab. By calculating the position parameters of the yield line of the reinforced concrete slab, the displacement coefficients of the long beam and the short beam, the yield line load value of the reinforced concrete slab, and the improvement coefficient of the reinforced concrete slab, the bearing capacity of the reinforced concrete floor that considers the influence of beam deformation is obtained. By establishing a new equilibrium equation, this analysis method analyzes the ultimate bearing capacity of the reinforced concrete slab and compares it with the data obtained from actual tests, with a smaller error. BRIEF DESCRIPTION OF THE DRAWINGS

[0100] Figure 1 is a schematic diagram of the plates divided in a reinforced concrete slab provided in an embodiment of the present invention;

[0101] Figure 2 is an internal force distribution diagram of a reinforced concrete slab under a uniformly distributed load provided by an embodiment of the present invention;

[0102] 3 is a diagram showing the internal force distribution of a reinforced concrete slab when the load is transferred to a beam according to an embodiment of the present invention;

[0103] Figure 4 Schematic diagram of elliptical areas divided on a reinforced concrete slab for distinguishing tension-compression membrane effect areas according to an embodiment of the present invention;

[0104] FIG5 is a diagram showing the internal force distribution of a plate according to an embodiment of the present invention. DETAILED DESCRIPTION

[0105] The present invention will be further described below in conjunction with the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solutions of the present invention and are not intended to limit the scope of protection of the present invention.

[0106] The present invention provides a method for analyzing the bearing capacity of a reinforced concrete floor slab that takes into account the influence of beam deformation. The reinforced concrete floor slab supported by the beams is a reinforced concrete slab composed of a rectangular two-way slab, and the beams include long beams and short beams, and are supported by columns. The method for analyzing the bearing capacity of the reinforced concrete floor slab comprises the following steps:

[0107] S1. References Figure 1 , the reinforced concrete slab is divided into four rectangular areas of equal size, and each rectangular area is further divided into a right-angled trapezoidal plate and a right-angled triangle plate, and the right-angled trapezoidal plate is numbered as plate 1 of the rectangular area, and the right-angled triangle plate is numbered as plate 2 of the rectangular area, and plates 1 and 2 in each group of two adjacent rectangular areas are respectively distributed axially symmetrically along the butt joint between the two rectangular areas, and one of the right-angled sides of each plate 2 coincides with the edge of the reinforced concrete slab; according to symmetry, only the two adjacent right-angled trapezoidal and right-angled triangle plates, i.e., plates 1 and 2, are analyzed;

[0108] S2. Establish an elliptical area based on the reinforced concrete slab to distinguish the tensile and compressive membrane effect areas;

[0109] S3. In practice, beams are not rigid but deformable under load. Since the horizontal displacement at mid-span is small, the beam torsion and horizontal displacement are neglected. Based on the length L, width l, and reinforcement parameters of the reinforced concrete slab, the location parameter n of the yield line of the reinforced concrete slab is determined. The boundary conditions for the reinforced concrete slab and the beam are both simply supported on both sides.

[0110] S4. Based on the length L and width l of the reinforced concrete slab, the location parameter n of the yield line of the reinforced concrete slab, and the displacement calculation formulas for the beam and reinforced concrete slab, determine the displacement coefficient λ1 of the long beam and the displacement coefficient λ2 of the short beam, respectively;

[0111] S5. References Figure 2 Figure 3. Based on the length L and width l of the reinforced concrete slab, the location parameter n of the yield line of the reinforced concrete slab, the displacement coefficient λ1 of the long beam, and the displacement coefficient λ2 of the short beam, the yield line load value q of the reinforced concrete slab is determined according to the principle of virtual work. The vertical load on the reinforced concrete slab is a uniformly distributed load. When the load on the reinforced concrete slab is transferred to the beam, the load transfer principle of the two-way slab is used for analysis.

[0112] S6. Based on the length L and width l of the reinforced concrete slab, determine the membrane force parameters of the reinforced concrete slab according to the elliptical area;

[0113] S7. Based on the membrane force parameters of the reinforced concrete slab and the principle of membrane effect, determine the bearing capacity improvement factors of plate 1 and plate 2, as well as the bearing capacity improvement factors caused by the axial force of plates 1 and 2;

[0114] S8. Determine the improvement factor for the reinforced concrete slab based on the increased bearing capacity factors of plates 1 and 2, and the increased bearing capacity factors due to the axial forces of plates 1 and 2, and in accordance with the principle of equivalent concentrated forces;

[0115] S9. Based on the yield line load value q and the improvement factor of the reinforced concrete slab, the ultimate bearing capacity of the reinforced concrete slab is calculated, and then the bearing capacity of the reinforced concrete floor considering the influence of beam deformation is obtained.

[0116] The vertical displacement of the reinforced concrete slab will increase as the vertical load gradually increases, so under the ultimate state, the reinforced concrete slab will enter a membrane effect stage that can improve the ultimate bearing capacity of the slab;

[0117] In the reinforced concrete floor bearing capacity analysis method considering the influence of beam deformation provided by the embodiment of the present invention, the method for dividing the elliptical area in step S2 is: Figure 4 , divide the length and width of the reinforced concrete slab into four equal parts, and divide the reinforced concrete slab into 16 rectangular areas. For these 16 rectangular areas, the four central rectangular areas together constitute the central rectangular area. An elliptical area is divided on the reinforced concrete slab through the four vertices of the central rectangular area. The area inside the ellipse is the tensile membrane effect area, and the area outside the ellipse is the compressive membrane effect area.

[0118] In the reinforced concrete floor bearing capacity analysis method considering the influence of beam deformation provided by an embodiment of the present invention, referring to FIG5 , the position parameter n of the reinforced concrete slab yield line determined in step S3 is as follows:

[0119]

[0120] Wherein, the reinforcement parameters include the preset orthogonal parameter μ, the aspect ratio a of the reinforced concrete slab, and the angle difference α between the obtuse angle of the right-angled trapezoid in the rectangular area plate 2 divided by the reinforced concrete slab and the right angle.

[0121] In the reinforced concrete floor bearing capacity analysis method considering the influence of beam deformation provided by an embodiment of the present invention, the step of calculating the displacement coefficient λ1 of the long beam and the displacement coefficient λ2 of the short beam in step S4 includes:

[0122] S41: Calculate the mid-span vertical displacement of the beam in the long and short span directions, as well as the mid-span vertical displacement of the reinforced concrete slab:

[0123]

[0124] Where q 长 ,q 短 ,q 板 is the uniformly distributed load on the reinforced concrete slab, E is the elastic modulus of concrete, I 板 is the moment of inertia of the reinforced concrete slab, I 梁 is the moment of inertia of the beam, Δ 长 , Δ 短 are the mid-span vertical displacements of the beam in the long span and short span directions, Δ板 is the mid-span vertical displacement of the reinforced concrete slab;

[0125] S42: Based on the mid-span vertical displacements of the beam in the long and short span directions, as well as the mid-span vertical displacements of the reinforced concrete slab, the displacement coefficients λ1 and λ2 of the long beam and short beam are calculated as follows:

[0126]

[0127] In the reinforced concrete floor bearing capacity analysis method considering the influence of beam deformation provided by an embodiment of the present invention, the yield line load value q of the reinforced concrete slab in step S5 is as follows:

[0128]

[0129] Where M x 、M y are the unit ultimate bending moments of reinforced concrete slabs along the x and y directions, m1 and m2 are the unit ultimate bending moments of long beams and short beams respectively, and b ′ is the beam width, λ1 is the displacement coefficient of the long beam, and λ2 is the displacement coefficient of the short beam.

[0130] In the reinforced concrete floor bearing capacity analysis method considering the influence of beam deformation provided by an embodiment of the present invention, the elliptic equation in step S6 is as follows:

[0131]

[0132] Where A0 is the length of the major axis of the ellipse, and B0 is the length of the minor axis of the ellipse;

[0133] The parameters of the ellipse equation passing through the point (L / 4, l / 4) with a major-minor axis ratio of L / l are:

[0134]

[0135] For each rectangular area divided on the reinforced concrete slab, the four vertices of plate 1 are numbered: the vertex where the lower base and the hypotenuse of the right-angled trapezoidal plate intersect is A, the vertex where the hypotenuse intersects the upper base is B, the vertex where the waist intersects the upper base is C, and the vertex where the waist intersects the lower base is E; the three vertices of plate 2 in the rectangular area are numbered: the vertex where the two right-angled sides of the right-angled triangle plate intersect is F, and the vertices where the hypotenuse intersects the two right-angled sides are A and B respectively; the hypotenuse of the right-angled triangle plate coincides with the hypotenuse of the right-angled trapezoidal plate, and the hypotenuse line segment is numbered AB;

[0136] Based on the elliptical area and each rectangular area divided on the reinforced concrete slab, the ellipse intersects with the waist and hypotenuse of the right-angled trapezoidal plate in the rectangular area, and the intersection points are D and G respectively. The ellipse intersects with the hypotenuse and right-angled side of the right-angled triangle plate in the rectangular area, and the intersection points are H and I respectively.

[0137] Substituting the coordinates of point G into the ellipse equation, the membrane force related quantity k of the reinforced concrete slab is obtained as follows:

[0138]

[0139] Where:

[0140]

[0141] The lengths of line segments ED and BI are:

[0142]

[0143] According to symmetry, only the plate 1 and plate 2 in a rectangular area divided by the reinforced concrete slab are subjected to force analysis. According to the force balance equation of plate 2 along the x direction, the force balance equation is expressed as follows:

[0144] T2cosα+Ssinα-C1cosα=0

[0145] Where:

[0146]

[0147] Where C1 is the resultant force of concrete pressure at the yield line AG, T2 is the resultant force of steel tension at the yield line BG, and α is the angle difference between the obtuse angle of the right-angled trapezoid in plate 2 and the right angle of the rectangular area divided by the reinforced concrete slab;

[0148] According to the force balance equation of plate 1 along the x direction, the force balance equation is expressed as follows:

[0149]

[0150] Get the membrane force related quantity k ′ As follows:

[0151]

[0152] Where T0 is the yield strength of steel bar per unit width, f c is the compressive strength of concrete, x c is the width of the thin film effect under edge pressure;

[0153] According to the force balance equation of plate 1 along the y direction, the force balance equation is expressed as follows:

[0154]

[0155] Where K is the ratio of the yield strength of the steel bar per unit width in the y direction to the yield strength of the steel bar per unit width in the x direction;

[0156] The film force related quantity b is as follows:

[0157]

[0158] Finally, according to the force balance equation of plate 2 along the y direction, the force balance equation is expressed as follows:

[0159]

[0160] Get the membrane force related quantity k ″ As follows:

[0161]

[0162] In the reinforced concrete floor bearing capacity analysis method considering the influence of beam deformation provided in an embodiment of the present invention, in step S7, a semi-ellipsoid is fitted with the center point of the reinforced concrete slab as the origin, the major axis of the ellipse as the x-axis, the minor axis of the ellipse as the y-axis, and the vertical displacement direction of the mid-span of the reinforced concrete slab as the z-axis, where the z-axis is downward as the positive direction. Assuming that the displacement of the center point of the reinforced concrete slab on the z-axis is greater than or equal to 1 / 20 of the length of the reinforced concrete slab in the short span direction, the reinforced concrete slab is considered to be in the load limit state;

[0163] The equation of the semi-ellipsoid is:

[0164]

[0165] When z = 0, the ellipse passes through the geometric center of the four cylinders. According to the ratio of the major and minor axes of the ellipse, the following formula is obtained:

[0166]

[0167] Where:

[0168]

[0169] Among them, A0 is the length of the major axis of the ellipse, and B0 is the length of the minor axis of the ellipse;

[0170] When analyzing the improvement coefficient, the horizontal displacement of the reinforced concrete slab is ignored, and the bearing capacity of plate 1 along the x direction is improved by the coefficient e 1m,x As follows:

[0171]

[0172] Where:

[0173] M 1m,x =C1cosαh C1 +T4h T4 -Ssinαh s -T2cosαh T2 -C2h C2

[0174] The bearing capacity improvement factor e of plate 1 along the y direction 1m,y As follows:

[0175]

[0176] Where:

[0177] M 1m,y =T2sinαh T2 +T1h T1 -C1sinαh C1 -Scosαh s

[0178] The bearing capacity improvement factor e of plate 2 along the x direction 2m,x As follows:

[0179]

[0180] Where:

[0181] M 2m,x =T2sinαh T2 +Ssinαh s -C1cosαh C1

[0182] The bearing capacity improvement factor e of plate 2 along the y direction 2m,y As follows:

[0183]

[0184] Where:

[0185] M 2m,y =C1sinαh C1 +Scosαh s +T3h T3 -T2sinαh T2 -C3h C3

[0186] in:

[0187]

[0188] Where C1 is the resultant force of concrete pressure at yield line AG, C2 is the resultant force of concrete pressure at yield line ED, C3 is the resultant force of concrete pressure at yield line IF, T1 is the resultant force of steel tension at yield line BC, T2 is the resultant force of steel tension at yield line BG, T3 is the resultant force of steel tension at yield line BI, T4 is the resultant force of steel tension at yield line DC, h i is the vertical displacement of the support of the reinforced concrete slab under the equivalent membrane force in the i direction, α is the angle difference between the obtuse angle of the right-angled trapezoid in plate 2 of the rectangular area divided by the reinforced concrete slab and the right angle;

[0189] The load-bearing capacity enhancement factor e caused by the axial force of plate 1 1b As follows:

[0190]

[0191] Where:

[0192]

[0193] in:

[0194]

[0195] L AE is the length of the bottom side of plate 1, k, k ′ is the membrane force parameter, K is the ratio of the yield strength of the steel bar per unit width in the y direction to the yield strength of the steel bar per unit width in the x direction, T0 is the yield strength of the steel bar per unit width, f c is the compressive strength of concrete, x c is the width of the thin film effect under edge pressure;

[0196] The load-bearing capacity enhancement factor e caused by the axial force of plate 2 2b As follows:

[0197]

[0198] Where:

[0199]

[0200] in:

[0201]

[0202] Where A0 is the length of the major axis of the ellipse, k ″ is the film force parameter;

[0203] in:

[0204]

[0205] Where g i is the compressive stress zone parameter under bending in long span or short span.

[0206] In the reinforced concrete floor bearing capacity analysis method considering the influence of beam deformation provided by an embodiment of the present invention, in step S8, since both plate 1 and plate 2 have bearing capacity enhancement coefficients in the x and y directions, the following formula is obtained by analysis:

[0207] e 1x =e 1m,x +e 1b

[0208] e 1y =e 1m,y +e 1b

[0209] e 2x =e 2m,x +e 2b

[0210] e 2y =e 2m,y +e 2b

[0211] According to the equivalence principle of force, we get the following formula:

[0212] 2qA1e1+2qA2e2=q limit Ll

[0213] Where A1 is the geometric area of ​​plate 1, A2 is the geometric area of ​​plate 2, e1 is the improvement coefficient of plate 1, and e2 is the improvement coefficient of plate 2;

[0214] Simplified:

[0215] q[(1-n)Lle1+nLle2]=q limit Ll

[0216] Therefore, the improvement coefficient e of reinforced concrete slab can be obtained as follows:

[0217] e=(1-n)e1+ne2

[0218] Taking the x and y directions respectively, the average value of the improvement coefficient e of the reinforced concrete slab can be obtained as follows:

[0219]

[0220] Where:

[0221] e ′ =(1-n)e 1x +ne 2x

[0222] e ″ =(1-n)e 1y +ne 2y

[0223] In the reinforced concrete floor bearing capacity analysis method considering the influence of beam deformation provided by an embodiment of the present invention, the reinforced concrete floor bearing capacity is obtained in step S9 based on the yield line theory and the influence of the membrane effect as follows:

[0224] q limit =q×e

[0225] Where e is the enhancement factor of reinforced concrete slab, and q is the yield line load value of reinforced concrete slab.

[0226] The embodiments of the present invention are described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Various changes can be made within the scope of knowledge possessed by ordinary technicians in this field without departing from the spirit of the present invention.

Claims

1. A method for analyzing the bearing capacity of reinforced concrete floor slabs considering the influence of beam deformation, wherein: The reinforced concrete floor supported by the beams is a reinforced concrete slab composed of rectangular two-way slabs, and the beams include long beams and short beams, and are supported by columns. The method for analyzing the bearing capacity of the reinforced concrete floor comprises the following steps: S1. Divide the reinforced concrete slab into four equal rectangular areas. Each rectangular area is further divided into a right-angled trapezoidal plate and a right-angled triangular plate. The right-angled trapezoidal plate is numbered as plate 1 in the rectangular area, and the right-angled triangular plate is numbered as plate 2 in the rectangular area. In each pair of adjacent rectangular areas, plates 1 and 2 are arranged axially symmetrically along the butting edge between the two rectangular areas, and one of the right-angled edges of each plate 2 coincides with the edge of the reinforced concrete slab. S2. Establish an elliptical area based on the reinforced concrete slab to distinguish the tensile and compressive membrane effect areas; S3. Ignoring beam torsion and horizontal displacement, determine the location parameter n of the yield line of the reinforced concrete slab based on the length L, width l, and reinforcement parameters of the reinforced concrete slab, where the boundary conditions for the reinforced concrete slab and the beam are simply supported on both sides; S4. Based on the length L and width l of the reinforced concrete slab, the location parameter n of the yield line of the reinforced concrete slab, and the displacement calculation formulas for the beam and reinforced concrete slab, determine the displacement coefficient λ1 of the long beam and the displacement coefficient λ2 of the short beam, respectively; S5. Based on the length L and width l of the reinforced concrete slab, the location parameter n of the yield line of the reinforced concrete slab, the displacement coefficient λ1 of the long beam, and the displacement coefficient λ2 of the short beam, determine the yield line load value q of the reinforced concrete slab according to the principle of virtual work, where the vertical load on the reinforced concrete slab is a uniformly distributed load; S6. Based on the length L and width l of the reinforced concrete slab, determine the membrane force parameters of the reinforced concrete slab according to the elliptical area; S7. Based on the membrane force parameters of the rectangular area demarcated by the reinforced concrete slab and the principle of membrane effect, determine the bearing capacity improvement coefficients of plate 1 and plate 2, as well as the bearing capacity improvement coefficients due to the axial force of plates 1 and 2, respectively; S8. Determine the improvement factor for the reinforced concrete slab based on the increased bearing capacity factors of plates 1 and 2, and the increased bearing capacity factors due to the axial forces of plates 1 and 2, and in accordance with the principle of equivalent concentrated forces; S9. Based on the yield line load value q and the improvement factor of the reinforced concrete slab, the ultimate bearing capacity of the reinforced concrete slab is calculated, and then the bearing capacity of the reinforced concrete floor considering the influence of beam deformation is obtained.

2. The reinforced concrete floor bearing capacity analysis method considering the influence of beam deformation according to claim 1 is characterized in that: The method for dividing the elliptical area in step S2 is as follows: divide the length and width of the reinforced concrete slab into four equal parts, and divide the reinforced concrete slab into 16 rectangular areas. For these 16 rectangular areas, the four central rectangular areas together constitute a central rectangular area. An elliptical area is divided on the reinforced concrete slab through the four vertices of the central rectangular area. The area inside the ellipse is the tensile membrane effect area, and the area outside the ellipse is the compressive membrane effect area.

3. The reinforced concrete floor bearing capacity analysis method considering the influence of beam deformation according to claim 1 is characterized in that: The position parameter n of the yield line of the reinforced concrete slab determined in step S3 is as follows: Wherein, the reinforcement parameters include the preset orthogonal parameter μ, the aspect ratio a of the reinforced concrete slab, and the angle difference α between the obtuse angle of the right-angled trapezoid in the rectangular area plate 2 divided by the reinforced concrete slab and the right angle.

4. The reinforced concrete floor bearing capacity analysis method considering the influence of beam deformation according to claim 1 is characterized in that: The calculation steps of the displacement coefficient λ1 of the long beam and the displacement coefficient λ2 of the short beam in step S4 include: S41: Calculate the mid-span vertical displacement of the beam in the long and short span directions, as well as the mid-span vertical displacement of the reinforced concrete slab: Where q 长 ,q 短 ,q 板 is the uniformly distributed load on the reinforced concrete slab, E is the elastic modulus of concrete, I 板 is the moment of inertia of the reinforced concrete slab, I 梁 is the moment of inertia of the beam, Δ 长 , Δ 短 are the mid-span vertical displacements of the beam in the long span and short span directions, Δ 板 is the mid-span vertical displacement of the reinforced concrete slab; S42: Based on the mid-span vertical displacements of the beam in the long and short span directions, as well as the mid-span vertical displacements of the reinforced concrete slab, the displacement coefficients λ1 and λ2 of the long beam and short beam are calculated as follows:

5. The reinforced concrete floor bearing capacity analysis method considering the influence of beam deformation according to claim 1 is characterized in that: The yield line load value q of the reinforced concrete slab in step S5 is as follows: Where M x 、M y are the unit ultimate bending moments of reinforced concrete slabs along the x and y directions, m1 and m2 are the unit ultimate bending moments of long beams and short beams respectively, and b ′ is the beam width, λ1 is the displacement coefficient of the long beam, and λ2 is the displacement coefficient of the short beam.

6. The reinforced concrete floor bearing capacity analysis method considering the influence of beam deformation according to claim 1 is characterized in that: The membrane force parameters of the reinforced concrete slab in step S6 include membrane force related quantity k, membrane force related quantity k ′ , membrane force related quantity k ″ , film force related quantity b, where the film force related quantity k is as follows: Where: Where B0 is the length of the minor axis of the ellipse; Membrane force related quantity k ′ As follows: Where T0 is the yield strength of steel bar per unit width, f c is the compressive strength of concrete, x c is the width of the thin film effect under edge pressure; Membrane force related quantity k ″ As follows: Where: The film force related quantity b is as follows: For each rectangular area divided on the reinforced concrete slab, the four vertices of plate 1 are numbered: the vertex where the lower base and the hypotenuse of the right-angled trapezoidal plate intersect is A, the vertex where the hypotenuse intersects with the upper base is B, the vertex where the waist intersects with the upper base is C, and the vertex where the waist intersects with the lower base is E; the three vertices of plate 2 in the rectangular area are numbered: the vertex where the two right-angled sides of the right-angled triangle plate intersect is F, and the vertices where the hypotenuse intersects with the two right-angled sides are A and B respectively; the hypotenuse of the right-angled triangle plate coincides with the hypotenuse of the right-angled trapezoidal plate, and the hypotenuse line segment is numbered AB; Based on the elliptical area and each rectangular area divided on the reinforced concrete slab, the ellipse intersects with the waist and hypotenuse of the right-angled trapezoidal plate in the rectangular area, and the intersection points are D and G respectively. The ellipse intersects with the hypotenuse and right-angled side of the right-angled triangle plate in the rectangular area, and the intersection points are H and I respectively. Where C1 is the resultant force of concrete pressure at yield line AG, T2 is the resultant force of steel tension at yield line BG, K is the ratio of the yield force of steel per unit width in the y-direction to the yield force of steel per unit width in the x-direction, and α is the angle difference between the obtuse angle and the right angle of the right trapezoid in plate 2 of the rectangular area divided by the reinforced concrete slab.

7. The reinforced concrete floor bearing capacity analysis method considering the influence of beam deformation according to claim 6 is characterized in that: The load-bearing capacity improvement coefficient in step S7 includes the load-bearing capacity improvement coefficient e of plate 1 and plate 2 along the x direction. 1m,x 、e 2m,x , the bearing capacity improvement factor e of plate 1 and plate 2 along the y direction 1m,y 、e 2m,y , the load-bearing capacity improvement coefficient e caused by the axial force of plate 1 and plate 2 1b 、e 2b ; The bearing capacity improvement factor e of plate 1 along the x direction 1m,x As follows: Where: M 1m,x =C1cosαh C1 +T4h T4 -Ssinαh s -T2cosαh T2 -C2h C2 The bearing capacity improvement factor e of plate 1 along the y direction 1m,y As follows: Where: M 1m,y =T2sinαh T2 +T1h T1 -C1sinαh C1 -Scosαh s The bearing capacity improvement factor e of plate 2 along the x direction 2m,x As follows: Where: M 2m,x =T2sinαh T2 +Ssinαh s -C1cosαh C1 The bearing capacity improvement factor e of plate 2 along the y direction 2m,y As follows: Where: M 2m,y =C1sinαh C1 +Scosαh s +T3h T3 -T2sinαh T2 -C3h C3 in: Where C1 is the resultant force of concrete pressure at yield line AG, C2 is the resultant force of concrete pressure at yield line ED, C3 is the resultant force of concrete pressure at yield line IF, T1 is the resultant force of steel tension at yield line BC, T2 is the resultant force of steel tension at yield line BG, T3 is the resultant force of steel tension at yield line BI, T4 is the resultant force of steel tension at yield line DC, h i is the vertical displacement of the support of the reinforced concrete slab under the equivalent membrane force in the i direction, α is the angle difference between the obtuse angle of the right-angled trapezoid in plate 2 of the rectangular area divided by the reinforced concrete slab and the right angle; The load-bearing capacity enhancement factor e caused by the axial force of plate 1 1b As follows: Where: in: L AE is the length of the bottom side of plate 1, k, k ′ is the membrane force parameter, K is the ratio of the yield strength of the steel bar per unit width in the y direction to the yield strength of the steel bar per unit width in the x direction, T0 is the yield strength of the steel bar per unit width, f c is the compressive strength of concrete, x c is the width of the thin film effect under edge pressure; The load-bearing capacity enhancement factor e caused by the axial force of plate 2 2b As follows: Where: in: Where A0 is the length of the major axis of the ellipse, k ″ is the film force parameter; in: Where g i is the compressive stress zone parameter under bending in long span or short span.

8. The reinforced concrete floor bearing capacity analysis method considering the influence of beam deformation according to claim 1 is characterized in that: The analysis method of the improvement coefficient e of the reinforced concrete slab in step S8 is as follows: Where: e′=(1-n)e 1x +no 2x e″=(1-n)e 1y +no 2y in: And 1x =and 1m,x +e 1b And 2x =and 2m,x +e 2b And 1y =and 1m,y +e 1b And 2y =and 2m,y +e 2b Where, e 1m,x is the load-bearing capacity enhancement factor of plate 1 along the x direction, e 2m,x is the load-bearing capacity enhancement factor of plate 2 along the x direction, e 1m,y is the load-bearing capacity enhancement factor of plate 1 along the y direction, e 2m,y is the load-bearing capacity enhancement factor of plate 2 along the y direction, e 1b is the load-bearing capacity enhancement factor caused by the axial force of plate 1, e 2b is the bearing capacity enhancement coefficient caused by the axial force of plate 2.

9. The reinforced concrete floor bearing capacity analysis method considering the influence of beam deformation according to claim 1, characterized in that: The ultimate bearing capacity q of the reinforced concrete slab in step S9 limit As follows: q limit =q×e Where e is the enhancement factor of reinforced concrete slab, and q is the yield line load value of reinforced concrete slab.

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