Bearing capacity and moment calculation method for increasing small eccentric compression of section secondary reinforcement column

Abstract

The invention relates to a bearing capacity and torque calculation method for small eccentric compression of a secondary reinforcing column with an increased cross section. The method comprises the following steps: 1, determining basic parameters of the secondary reinforcing column with the increased cross section; 2, calculating an equivalent rectangular stress diagram coefficient of the concrete compression area according to the constitutive model; 3, according to the height of the theoretical compression area of the concrete of the secondary reinforcement column and the height of the theoretical compression area of the concrete of the primary reinforcement column, calculating the distance from the small compression side of the concrete of the secondary reinforcement column to the vertex of the similar triangle and the distance from the small compression side of the concrete of the primary reinforcement column to the vertex of the similar triangle, and drawing a strain diagram; and 4, according to the basic assumption, calculating the strain of the secondary reinforcing column with the increased cross section, the strain of steel bars, profile steel and concrete, the small eccentric bearing capacity and the torque. According to the method, the eccentric compression performance of the secondary reinforcement column with the increased section and the bearing capacity improvement level relative to primary reinforcement can be estimated, and therefore theoretical guidance is provided for engineering practice.

Description

Technical Field

[0001] The present invention relates to the technical field of building structure engineering, and in particular to a method for calculating the bearing capacity and moment of a small eccentric compression of a column with enlarged cross-section and secondary reinforcement. Background Technique

[0002] In the field of building engineering, reinforced concrete columns, as key load-bearing members, the improvement of their bearing capacity has always been the focus of research. The technique of enlarging the cross-section for reinforcement, as a mature reinforcement method, increases the concrete at the bottom of the column to improve the mechanical properties of the column, and thus has received extensive attention and application. Although many scholars have studied the calculation method of the bearing capacity of small eccentric compression of columns with enlarged cross-section and secondary reinforcement, there are still the following unstudied aspects: 1) The calculation of the bearing capacity of traditional reinforced columns mostly targets single reinforcement (only enlarging the cross-section or only externally bonding steel profiles), without considering the synergistic effect of secondary reinforcement, resulting in a large error in the calculation result of the bearing capacity formula of the secondary reinforced column when directly superimposing the bearing capacity formulas of single reinforcement; 2) Factors such as the strength difference between new and old materials and the change of eccentricity during secondary reinforcement lead to a large deviation in the calculation result of the existing code formulas (such as GB 50367-2013); 3) The bearing capacity formulas of the method of enlarging the cross-section and the method of externally bonding steel profiles in GB 50367-2013 are independent, and no superposition calculation rules for secondary reinforced columns are provided, resulting in the inability of the existing formulas to directly calculate and predict the bearing capacity of columns with enlarged cross-section and secondary reinforcement. Summary of the Invention

[0003] The present invention is to solve the above-mentioned deficiencies existing in the prior art, and proposes a method for calculating the bearing capacity and moment of a small eccentric compression of a column with enlarged cross-section and secondary reinforcement, in order to predict the eccentric compression performance of the column with enlarged cross-section and secondary reinforcement and the improvement level of the bearing capacity relative to the first reinforcement, so as to provide theoretical guidance for engineering practice.

[0004] The present invention adopts the following technical solutions to achieve the above-mentioned invention purpose:

[0005] A method for calculating the bearing capacity and moment of a small eccentric compression of a column with enlarged cross-section and secondary reinforcement according to the present invention is characterized in that it includes the following steps:

[0006] Step 1: Determine the basic parameters of the reinforced column under the condition of enlarged cross-section and secondary reinforcement, including: concrete parameters, steel bar parameters and steel profile parameters:

[0007] The concrete parameters include: the design value of the axial compressive strength of the concrete of the combined cross-section of new and old concrete 、the design value of the axial compressive strength of the new concrete 、the design value of the axial compressive strength of the old concrete ; the cross-section width b of the reinforced column; the height x of the compression zone of the concrete;

[0008] The steel bar parameters include: the newly added longitudinal bars under secondary reinforcement , the cross-sectional area of the newly added longitudinally compressed steel bars under secondary reinforcement , the design value of the compressive strength of the longitudinal bars , the cross-sectional area of the longitudinal bars on the side with larger compression under the first reinforcement , the cross-sectional area of the steel bars on the tension side or the side with smaller compression under secondary reinforcement , the stress of the longitudinal bars on the tension side or the side with smaller compression under the first reinforcement , the stress of the newly added longitudinal bars on the tension side or the side with smaller compression under secondary reinforcement , the cross-sectional area of the longitudinal bars on the tension side or the side with smaller compression under the first reinforcement , the distance from the resultant force point of the longitudinal bars on the side with larger compression in the cross-section under the first reinforcement to the near side of the cross-section under secondary reinforcement , the distance from the resultant force point of the longitudinal bars on the tension side or the side with smaller compression under the first reinforcement to the near side of the cross-section under secondary reinforcement , the distance from the resultant force point of the newly added longitudinal bars on the tension side or the side with smaller compression under secondary reinforcement to the near side of the cross-section under secondary reinforcement , the distance from the resultant force point of the newly added longitudinal bars on the side with larger compression under secondary reinforcement to the near side of the cross-section under secondary reinforcement ;

[0009] The section steel parameters include: the utilization coefficient of section steel strength ; the design value of the compressive strength of section steel ; the cross-sectional area of section steel for all compression limbs ; the stress of section steel for the tension limb or the limb with smaller compression ; the cross-sectional area of section steel for all tension limbs ; the distance from the centroid of the section steel of the tension limb or the limb with smaller compression to the side with larger compression in the cross-section under secondary reinforcement , the distance from the centroid of the section steel of the limb with larger compression to the near side of the cross-section under secondary reinforcement , the distance from the centroid of the section steel of the tension limb or the limb with smaller compression to the near side of the cross-section under secondary reinforcement ;

[0010] Step 2. When 0 < ε c ≤ ε0, the compressive force resultant F of the reinforced column under secondary reinforcement is obtained from Equation (4) c , and thus the distance y from the resultant force point of the reinforced column to the edge of the concrete compression zone is obtained from Equation (5) c :

[0011] (4)

[0012] (5)

[0013] In Equations (4) and (5), y is the integration variable; ε c is the strain of concrete, and ε0 is the strain of concrete when it reaches the peak stress;

[0014] When < ≤ , the resultant force F c of the compression zone of the strengthened column is obtained from Equation (6), and then the distance y c from the resultant force point of the strengthened column to the edge of the concrete compression zone is obtained from Equation (5):

[0015] (6)

[0016] (7)

[0017] In Equations (6) and (7), is the ultimate compressive strain of concrete, is the height of the compression zone corresponding to the maximum concrete stress, is the theoretical height of the concrete compression zone;

[0018] Step 3: Use Equations (8) and (9) to obtain the distance from the smaller compressed side of the concrete of the strengthened column to the vertex of the strain similarity triangle under secondary strengthening and the distance from the smaller compressed side of the concrete of the strengthened column to the vertex of the similarity triangle under primary strengthening:

[0019] (8)

[0020] (9)

[0021] In Equations (8) and (9), is the yield strain of the steel bar, is the distance from the resultant force point of the longitudinal steel bars on the larger compressed side under primary strengthening to the near side of the cross-section of the strengthened column under secondary strengthening;

[0022] Step 4: Use Equations (10) to (14) to obtain the strain of the shape steel on the smaller compressed side under primary strengthening, the strain of the shape steel on the smaller compressed side under secondary strengthening, the strain [[ID= of the shape steel on the larger compressed side under secondary strengthening, the strain of the newly added steel bars on the smaller compressed side under secondary strengthening, and the strain of the steel bars on the smaller compressed side under primary strengthening; ;

[0023] (10)

[0024] (11)

[0025] (12)

[0026] (13)

[0027] (14)

[0028] In formulas (10) to (14), is the distance from the section steel on the less-compressed side under the first reinforcement to the near side of the transverse section of the column under the second reinforcement;

[0029] Step 5: Obtain the design value N of the axial pressure of the column under the second reinforcement according to formulas (15) to (17), which is the bearing capacity:

[0030] (15)

[0031] (16)

[0032] (17)

[0033] In formulas (15) to (17), N1 is the bearing capacity provided by the steel bars and concrete under the second reinforcement, and N2 is the bearing capacity provided by the section steel lacing plates under the second reinforcement. represents the ratio of the bearing capacity provided by the section steel under the first reinforcement to the bearing capacity provided by the section steel under the second reinforcement;

[0034] Obtain the moment of the centroid of the section steel on the less-compressed side under the second reinforcement according to formulas (18) to (20) :

[0035] (18)

[0036] (19)

[0037] (20)

[0038] In formulas (18) to (20), is the eccentricity of the column under the second reinforcement, is the moment taken about the centroid of the section steel on the less-compressed side by the steel bars and concrete under the second reinforcement, is the moment taken about the centroid of the section steel on the less-compressed side by the section steel under the second reinforcement, represents the ratio of the moment provided by the section steel under the first reinforcement to the moment provided by the section steel under the second reinforcement, and there is:

[0039] (21)

[0040] (22)

[0041] Another feature of the method for calculating the bearing capacity and moment of a small eccentrically compressed column with enlarged cross-section in the present invention is that in step 2, the stress-strain relationship of concrete is obtained using Equation (1), the stress-strain relationship of steel bars is obtained using Equation (2), and the stress-strain relationship of profiled steel is obtained using Equation (3), so as to obtain the relationship between and the theoretical compression zone height of concrete :

[0042] (1)

[0043] (2)

[0044] (3)

[0045] In Equations (1)-(3), is the strain of the steel bar; E s is the elastic modulus before the steel bar yields, is the strain when the steel bar yields; f y is the stress when the compression steel bar yields; is the ultimate strain of the compression steel bar, is the strain of the profiled steel; is the strain when the profiled steel yields; E a is the elastic modulus before the profiled steel yields; is the stress when the profiled steel yields; is the ultimate strain of the profiled steel.

[0046] Furthermore, the strain similar triangle is that the entire cross-section satisfies the plane section assumption, that is, under the plane section assumption, the strain of any point in the cross-section is proportional to its distance from the neutral axis and forms a linear strain distribution.

[0047] An electronic device of the present invention, including a memory and a processor, is characterized in that the memory is used to store a program for supporting the processor to execute the method for calculating the bearing capacity and moment, and the processor is configured to execute the program stored in the memory.

[0048] A computer-readable storage medium of the present invention, on which a computer program is stored, is characterized in that when the computer program is run by a processor, it executes the steps of the method for calculating the bearing capacity and moment.

[0049] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0050] 1. The present invention breaks through the limitations of traditional single-stage strengthening and realizes the quantitative evaluation of the synergistic effect of two-stage strengthening. Most traditional strengthening methods calculate the bearing capacity for single-stage strengthening. However, the method of the present invention establishes for the first time a mechanical model of the "steel bonding + section enlargement" two-stage strengthening system, which can directly calculate and estimate the eccentric compression performance of columns with section enlargement for two-stage strengthening based on existing data, thereby reducing engineering costs, transforming the synergistic effect from qualitative description into a quantitative analysis tool, and providing a scientific design basis for two-stage strengthening.

[0051] 2. The present invention realizes the quantitative comparison of performance throughout the life cycle. It establishes a three-level performance comparison system of "unstrengthened column - first-stage strengthened column - second-stage strengthened column", which can quantitatively show the bearing capacity improvement rate of the second-stage strengthening compared with the first-stage strengthening, helping to transform the synergistic effect of the second-stage strengthening from qualitative description into quantifiable engineering parameters and accelerating the intelligent process of the renovation of existing buildings.

[0052] 3. The present invention proposes a "strengthening correction coefficient", especially the coefficient for the second-stage strengthened steel section 、 , filling the gap in the current "Code for Design of Strengthening of Concrete Structures" (GB50367) regarding the collaborative calculation of multiple-stage strengthening. It can simply and conveniently calculate and estimate the bearing capacity and moment of columns with section enlargement for two-stage strengthening, thus providing assistance for the optimal selection and economic evaluation of the design scheme for the second-stage strengthening of existing buildings.

[0053] 4. Based on the existing concrete constitutive relationship under compression and the stress-strain relationship of steel bars in actual engineering situations, the present invention proposes how to calculate the small eccentric compression bearing capacity of columns with section enlargement for two-stage strengthening after steel bonding strengthening of reinforced concrete columns. The method steps are clear and the calculation is simple, providing a new method for calculating the small eccentric compression bearing capacity of columns with section enlargement for two-stage strengthening. Brief Description of the Drawings

[0054] Figure 1 is the calculation flow chart of the small eccentric bearing capacity and moment of columns with section enlargement for two-stage strengthening of the present invention;

[0055] Figure 2a is the curve graph of the stress-strain of steel bars;

[0056] Figure 2b is the curve graph of the stress-strain of steel sections;

[0057] Figure 3a is the schematic diagram of the size and strengthening of the first-stage strengthened specimens;

[0058] Figure 3b is the schematic diagram of the size and strengthening of the second-stage strengthened specimens;

[0059] Figure 4aThe graph of the normal cross-section strain distribution of the secondary reinforced column ZC1 with enlarged cross-section;

[0060] Figure 4b The graph of the normal cross-section strain distribution of the secondary reinforced column ZC2 with enlarged cross-section;

[0061] Figure 4c The graph of the normal cross-section strain distribution of the secondary reinforced column ZC3 with enlarged cross-section;

[0062] Figure 5a Schematic diagram of the parameters of the secondary reinforced column;

[0063] Figure 5b Model diagram for calculating the equivalent rectangular stress in the concrete compression zone;

[0064] Figure 5c Schematic diagram of the height of the concrete compression zone;

[0065] Figure 6a Distribution diagram of the normal cross-section strain of the first reinforced column;

[0066] Figure 6b Distribution diagram of the normal cross-section strain of the secondary reinforced column. Specific implementation mode

[0067] The present invention will be clearly and completely described below with reference to the accompanying drawings and specific embodiments. It should be noted that the described embodiments are only one embodiment of the present invention, rather than all embodiments. Based on the embodiments of the present invention, other embodiments obtained by those of ordinary skill in the art all fall within the scope of protection of the present invention.

[0068] In this embodiment, taking the un-reinforced column, the first bonded steel reinforced column, and the secondary reinforced column with enlarged cross-section as the research objects, a small eccentric compression test was carried out to explore the bearing capacity improvement level and failure characteristics of the secondary reinforced column, and a calculation method for the bearing capacity and moment of the small eccentric compression of the secondary reinforced column with enlarged cross-section was proposed. It is proposed for the first bonded steel reinforcement and the secondary cross-section enlargement of reinforced concrete columns, calculating the strain of the secondary reinforced column with enlarged cross-section, as well as the strains of steel bars, steel sections, and concrete and the small eccentric bearing capacity and proposing calculation formulas. As Figure 1 shown, the method specifically includes the following steps:

[0069] Step 1: Determine the basic parameters of the secondary reinforced column with enlarged cross-section, including: concrete parameters, steel bar parameters, and steel section parameters;

[0070] Concrete parameters, including: the design value of the axial compressive strength of the concrete for the combined cross-section of new and old concrete , the design value of the axial compressive strength of the new concrete , the design value of the axial compressive strength of the old concrete ; The cross-sectional width b of the reinforced column; The height x of the compression zone of the concrete;

[0071] Steel bar parameters, including: The newly added longitudinal bars under secondary reinforcement , The cross-sectional area of the newly added longitudinal compression steel bars under secondary reinforcement , The design value of the compressive strength of the longitudinal bars , The cross-sectional area of the longitudinal bars on the side with larger compression under the first reinforcement , The cross-sectional area of the steel bars on the tension side or the side with smaller compression under secondary reinforcement , The stress of the longitudinal bars on the tension side or the side with smaller compression under the first reinforcement , The stress of the newly added longitudinal bars on the tension side or the side with smaller compression under secondary reinforcement , The cross-sectional area of the longitudinal bars on the tension side or the side with smaller compression under the first reinforcement , The distance from the resultant force point of the longitudinal bars on the side with larger compression in the cross-section under the first reinforcement to the near side of the cross-section under secondary reinforcement , The distance from the resultant force point of the longitudinal bars on the tension side or the side with smaller compression under the first reinforcement to the near side of the cross-section under secondary reinforcement , The distance from the resultant force point of the newly added longitudinal bars on the tension side or the side with smaller compression under secondary reinforcement to the near side of the cross-section under secondary reinforcement , The distance from the resultant force point of the newly added longitudinal bars on the side with larger compression under secondary reinforcement to the near side of the cross-section under secondary reinforcement ;

[0072] Steel shape parameters, including: The utilization coefficient of the steel shape strength ; The design value of the compressive strength of the steel shape ; The cross-sectional area of the steel shape of all compression limbs ; The stress of the steel shape of the tension limb or the limb with smaller compression ; The cross-sectional area of the steel shape of all tension limbs ; The distance from the centroid of the cross-section of the steel shape of the tension limb or the limb with smaller compression under secondary reinforcement to the side with larger compression in the cross-section , The distance from the centroid of the cross-section of the steel shape of the limb with larger compression under secondary reinforcement to the near side of the cross-section , The distance from the centroid of the cross-section of the steel shape of the tension limb or the limb with smaller compression under secondary reinforcement to the near side of the cross-section ;

[0073] Among them, the schematic diagram of the first reinforcement is as shown in Figure 3a , and the schematic diagram of the secondary reinforcement is as shown in Figure 3b . The model diagrams specifically showing each parameter are as shown in Figure 5a , Figure 5b .

[0074] Step 2: Obtain the concrete stress-strain relationship of the constitutive model using Equation (1), obtain the steel bar stress-strain relationship of the constitutive model using Equation (2), and obtain the shape steel stress-strain relationship of the constitutive model using Equation (3):

[0075] (1)

[0076] (2)

[0077] (3)

[0078] In Equations (1)-(3), is the strain of the steel bar; E s is the elastic modulus before the steel bar yields, is the strain when the steel bar yields; f y is the stress when the compression steel bar yields; is the ultimate strain of the compression steel bar, is the strain of the shape steel; is the strain when the shape steel yields; E a is the elastic modulus before the shape steel yields; is the stress when the shape steel yields; is the ultimate strain of the shape steel. Among them, the curve diagram of the steel bar stress-strain is as shown in Figure 2a and the curve diagram of the shape steel stress-strain is as shown in Figure 2b .

[0079] Obtain the relationship between the distance from the resultant force point to the edge of the concrete compression zone and the theoretical height of the concrete compression zone according to Equations (1)-(3):

[0080] When 0 < ε c ≤ ε0, obtain the resultant force F c of the compression zone of the strengthened column from Equation (4), and thus obtain the distance y c from the resultant force point to the edge of the concrete compression zone from Equation (5):

[0081] (4)

[0082] (5)

[0083] In Equations (4) and (5), y is the integration variable; ε c is the concrete strain, and ε0 is the strain at the peak stress of the concrete. Among them, the schematic diagram of the theoretical height of the concrete compression zone is as shown in Figure 5c .

[0084] When < ≤ When , the resultant force F in the compression zone of the reinforced column is obtained by formula (6): c , and thus the distance y from the resultant point to the edge of the concrete compression zone is obtained from formula (5): c :

[0085] (6)

[0086] (7)

[0087] In formula (6) and formula (7), is the ultimate compressive strain of concrete, The height of the compression zone corresponding to the maximum concrete stress.

[0088] Distance from the centroid of the resultant force to the edge of the compression zone The height of the concrete compression zone can also be obtained by taking 1 / 2 of the height x of the equivalent stress rectangle .in, .when =0.0033, we can calculate from formula (7) combined with Table 1 .

[0089] Table 1 Equivalent rectangular stress conversion coefficients in the compression zone

[0090]

[0091] Step 3: In this embodiment, the strain similarity triangle is the entire cross section that satisfies the plane section assumption. That is, under the plane section assumption, the strain at any point in the cross section is proportional to its distance from the neutral axis, forming a linear strain distribution. Therefore, the stress distribution of concrete and steel bars can be derived from the strain similarity triangle, and the bearing capacity and moment can be solved by combining the equilibrium condition. The positive cross section strain distribution curves of the secondary reinforced columns ZC1, ZC2, and ZC3 with increased cross section are shown as follows: Figure 4a 、 Figure 4b 、 Figure 4c As shown, the plane section assumption is basically satisfied.

[0092] Using equations (8) and (9), we can get the distance from the side with less compression of the secondary reinforced column concrete to the vertex of the strain similarity triangle: The distance from the side with smaller compression of the first reinforced concrete to the vertex of the similar triangle :

[0093] (8)

[0094] (9)

[0095] In formula (8) and formula (9), is the yield strain of the first reinforcement steel bar, is the distance from the resultant force point of the longitudinal reinforcement on the side with larger compression in the first reinforcement to the near side of the transverse section after reinforcement, is the distance from the steel bars on the compressed side in the first reinforcement to the near side, and are known. The strain similar triangles are as shown in Figure 6a 、 Figure 6b .

[0096] Step 4: Obtain the strain of the steel section on the side with smaller compression in the first reinforcement using Equations (10) to (14) the strain of the steel section on the side with smaller compression in the secondary reinforcement the strain of the steel section on the compressed side in the secondary reinforcement and the strain of the original steel bars on the side with smaller compression in the secondary reinforcement ; Substitute them into Equations (2) and (3) to obtain the corresponding stresses.

[0097] (10)

[0098] (11)

[0099] (12)

[0100] (13)

[0101] (14)

[0102] In Equations (10) to (14), is the distance from the steel section on the side with smaller compression in the first reinforcement to the near side.

[0103] Step 5: Obtain the design value N of the axial compression force of the component after reinforcement according to Equations (15) to (17):

[0104] (15)

[0105] (16)

[0106] (17)

[0107] where N is the design value of the axial compression force of the component after reinforcement; N1 is the bearing capacity provided by the steel bars and concrete, N2 is the bearing capacity provided by the angle steel and the steel section batten plates, represents the ratio of the bearing capacity provided by the steel section in the first reinforcement to the bearing capacity provided by the steel section in the secondary reinforcement.

[0108] Obtain the moment about the centroid of the steel section on the side with smaller compression according to Equations (18) to (20) :

[0109] (18)

[0110] (19)

[0111] (20)

[0112] Among them, is the moment taken about the centroid of the shape steel on the side with less compression by the steel bars and concrete, is the moment taken about the centroid of the shape steel on the side with less compression by the shape steel, represents the ratio of the moment provided by the shape steel in the first strengthening and the moment provided by the shape steel in the second strengthening, and there is:

[0113] (21)

[0114] (22)

[0115] Based on the actual engineering situation, the present invention adopts the existing concrete compression constitutive relationship and steel bar stress-strain relationship, and proposes how to calculate the small eccentric compression bearing capacity and moment of the column strengthened by increasing the section after bonding steel plates for the second time. The method steps are clear and the calculation is simple, providing a new method for calculating the small eccentric compression bearing capacity and moment of the column strengthened by increasing the section for the second time.

[0116] In this embodiment, an electronic device includes a memory and a processor. The memory is used to store a program that supports the processor to execute the above method, and the processor is configured to execute the program stored in the memory.

[0117] In this embodiment, a computer-readable storage medium stores a computer program, and when the computer program is run by a processor, it executes the steps of the above method.

[0118] In this actual embodiment, 3 specimens of columns strengthened by increasing the section for the second time in a certain structural laboratory are selected, and the specimen numbers are LC1, LC2, and LC3 respectively.

[0119] 1) Determine the basic parameters of the specimens of columns strengthened by increasing the section for the second time:

[0120] Table 2 Related parameters of specimens of columns strengthened by increasing the section for the second time

[0121]

[0122] Table 3 Concrete compressive strength

[0123]

[0124] Table 4 Mechanical property parameters of steel bars

[0125]

[0126] Table 5 Mechanical property parameters of section steel

[0127]

[0128] 2) Calculate the coefficients of the equivalent rectangular stress diagram in the compression zone of concrete, as shown in Table 1.

[0129] The concrete in the compression zone of specimens LC1 - LC3 was crushed = 0.0033, take = 0.84. Substitute into Formulas (21) and (22) to obtain , 0.788. Then calculate the bearing capacity of small eccentricity.

[0130] Table 6 Compression zone height of the column with secondary reinforcement, strains of steel bars, section steel and concrete, and bearing capacity of small eccentricity

[0131]

[0132] The failure modes of specimens LC1 - LC3 were all that the newly added tension steel bars yielded and the concrete in the compression zone was crushed.

[0133] Table 7 Test values and calculated values of the bearing capacity of small eccentricity of the column with enlarged section and secondary reinforcement

[0134]

[0135] As can be seen from Table 7, the average value of the ratio of the test value to the calculated value of the bearing capacity of small eccentricity of the 3 specimens is 0.958, indicating that the bearing capacity calculation method of the column with enlarged section and secondary reinforcement provided by the present invention has good accuracy and strong practicability.

[0136] The above is only the specific implementation manner of the present invention, but the protection scope of the invention is not limited thereto. Any staff familiar with the technical field of the present invention can easily think of various equivalent modifications or replacements within the technical scope of the present invention. These modifications or replacements should all be covered within the protection scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.

Claims

1. A method for calculating the bearing capacity and moment of a small eccentrically compressed column with a secondary reinforcement of increased cross-section, characterized in that, It includes the following steps: Step 1: Determine the basic parameters of the reinforced column under the secondary reinforcement of increasing the cross-section, including: concrete parameters, steel bar parameters and section steel parameters: The concrete parameters include the design value of the axial compressive strength of the combined cross-section of new and old concrete , the design value of the axial compressive strength of the new concrete , the design value of the axial compressive strength of the old concrete ; the cross-sectional width b of the reinforced column; the height x of the concrete compression zone; The steel bar parameters include: newly added longitudinal bars under secondary reinforcement , cross-sectional area of newly added longitudinally compressed steel bars under secondary reinforcement , design value of compressive strength of longitudinal bars , cross-sectional area of longitudinal bars on the side with larger compression under primary reinforcement , cross-sectional area of steel bars on the tension side or the side with smaller compression under secondary reinforcement , stress of longitudinal bars on the tension side or the side with smaller compression under primary reinforcement , stress of newly added longitudinal bars on the tension side or the side with smaller compression under secondary reinforcement , cross-sectional area of longitudinal bars on the tension side or the side with smaller compression under primary reinforcement , distance from the resultant force point of longitudinal bars on the side with larger compression in the cross-section under primary reinforcement to the near side of the cross-section under secondary reinforcement , distance from the resultant force point of longitudinal bars on the tension side or the side with smaller compression under primary reinforcement to the near side of the cross-section under secondary reinforcement , distance from the resultant force point of newly added longitudinal bars on the tension side or the side with smaller compression under secondary reinforcement to the near side of the cross-section under secondary reinforcement , distance from the resultant force point of newly added longitudinally bars on the side with larger compression under secondary reinforcement to the near side of the cross-section under secondary reinforcement ; The section steel parameters include: the utilization coefficient of section steel strength ; the design value of the compressive strength of the section steel ; the cross-sectional area of the section steel of all compression limbs ; the stress of the section steel of the tension limb or the compression limb with smaller compression ; the cross-sectional area of the section steel of all tension limbs ; the distance from the centroid of the cross-section of the section steel of the tension limb or the compression limb with smaller compression to the side with larger compression of the cross-section under secondary reinforcement , the distance from the centroid of the cross-section of the section steel of the compression limb with larger compression to the near side of the transverse cross-section under secondary reinforcement , the distance from the centroid of the cross-section of the section steel of the tension limb or the compression limb with smaller compression to the near side of the transverse cross-section under secondary reinforcement ; Step 2. When 0 < ε c ≤ ε0, the resultant force F c of the compression zone of the strengthened column under secondary strengthening is obtained from Equation (4), and thus the distance y c from the resultant force point of the strengthened column to the edge of the concrete compression zone is obtained from Equation (5): (4) (5) In equations (4) and (5), y is the integration variable; ε c is the strain of concrete, and ε0 is the strain of concrete when it reaches the peak stress; When < ≤ , the resultant force F c of the compression zone of the strengthened column is obtained from Equation (6), and thus the distance y c from the resultant force point of the strengthened column to the edge of the concrete compression zone is obtained from Equation (5): (6) (7) In Formulas (6) and (7), is the ultimate compressive strain of concrete, is the height of the compression zone corresponding to the maximum value of the concrete stress, is the theoretical height of the compression zone of concrete; Step 3: Use Equation (8) and Equation (9) to obtain the distance from the smaller compression side of the concrete of the reinforced column under secondary reinforcement to the vertex of the strain similar triangle and the distance from the smaller compression side of the concrete of the reinforced column under primary reinforcement to the vertex of the similar triangle : (8) (9) In Formula (8) and Formula (9), is the yield strain of the steel bar, is the distance from the resultant force point of the longitudinal steel bars on the larger compression side under the first reinforcement to the near side of the cross-section of the secondary reinforced column under the first reinforcement; Step 4: Obtain the steel strain on the smaller compression side under the first strengthening by using Equations (10) to (14) Steel strain on the smaller compression side under the secondary strengthening Steel strain on the larger compression side of the section under the secondary strengthening Steel bar strain on the newly added smaller compression side under the secondary strengthening And the steel bar strain on the smaller compression side under the first strengthening ; (10) (11) (12) (13) (14) In formulas (10) to (14), is the distance from the section steel on the less compressed side under the first reinforcement to the near side of the transverse section of the column under the second reinforcement; Step 5: According to Equations (15) to (17), obtain the design value N of the axial pressure of the reinforced column under the secondary reinforcement, which is the bearing capacity: (15) (16) (17) In formulas (15) to (17), N1 is the bearing capacity provided by steel bars and concrete under secondary reinforcement, and N2 is the bearing capacity provided by the profiled steel batten under secondary reinforcement. It represents the ratio of the bearing capacity provided by the profiled steel under primary reinforcement to the bearing capacity provided by the profiled steel under secondary reinforcement. Obtain the moment of the centroid of the steel shape on the smaller compression side under secondary reinforcement according to Equations (18) to (20). : (18) (19) (20) In Formulas (18) to (20), is the eccentricity of the reinforced column under secondary reinforcement, is the moment of inertia of the steel bars and concrete about the centroid of the steel section on the less compressed side under secondary reinforcement, is the moment of inertia of the steel section about the centroid of the steel section on the less compressed side under secondary reinforcement, represents the ratio of the moment provided by the steel section under the first reinforcement to the moment provided by the steel section under the secondary reinforcement, and there is: (21) (22)。 2. A method for calculating the bearing capacity and moment of a small eccentrically compressed column with an increased cross-section and secondary reinforcement according to claim 1, characterized in that, In step 2, the stress-strain relationship of concrete is obtained by using Equation (1), the stress-strain relationship of steel bars is obtained by using Equation (2), and the stress-strain relationship of profiled steel is obtained by using Equation (3), so as to obtain the relationship between and the theoretical compression zone height of concrete : (1) (2) (3) In Formulas (1)-(3), is the strain of the steel bar; E s is the elastic modulus before the steel bar yields, is the strain when the steel bar yields; f y is the stress when the compression steel bar yields; is the ultimate strain of the compression steel bar, is the strain of the profiled steel; is the strain when the profiled steel yields; E a is the elastic modulus before the profiled steel yields; is the stress when the profiled steel yields; is the ultimate strain of the profiled steel.

3. A method for calculating the bearing capacity and moment of a small eccentrically compressed column with a secondary reinforcement of increased cross-section according to claim 1, characterized in that, The strain similar triangle is that the whole cross-section satisfies the plane section assumption, that is, under the plane section assumption, the strain of any point in the cross-section is proportional to its distance from the neutral axis and forms a linear strain distribution.

4. An electronic device, comprising a memory and a processor, characterized in that The memory is used to store a program that supports the processor to execute the bearing capacity and moment calculation method described in any one of Claims 1-3, and the processor is configured to execute the program stored in the memory.

5. A computer-readable storage medium, on which a computer program is stored, characterized in that, When the computer program is run by the processor, it executes the steps of the bearing capacity and moment calculation method described in any one of Claims 1-3.

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