CN105550418B - CFRP plate reinforces the calculation method for setting the Ultimate flexural strength of core beam - Google Patents

Abstract

The invention provides a method for calculating the ultimate bearing capacity of a normal section of a core-placed beam reinforced by CFRP plates, which belongs to the technical field of beam reinforcement. The calculation method includes the following steps: (1) make basic assumptions about the reinforcement process; (2) calculate the stress-strain relationship of the cross-section of the core material under the failure conditions of each material; (3) calculate the stress-strain relationship of the core material under the failure conditions of each material The height of the compression zone of the cross section; (4) Calculate the height of the plastic development of the compression zone of the cross section of the core material under the failure conditions of each material; (5) According to the failure conditions of each material, the cross section of the core material The height of the compression zone and the height of the plastic development of the compression zone are used to calculate the flexural bearing capacity of the normal section of the reinforced core beam under the corresponding failure conditions of each material, and the ultimate bearing capacity of the normal section considering the plastic development of the reinforced core beam is obtained. The invention can effectively calculate the ultimate bearing capacity of the normal section considering the plastic development of the core beam reinforced by the CFRP plate, and provides powerful theoretical guidance for engineering application.

Description

Calculation method of ultimate bearing capacity of normal section of CFRP plate-reinforced beam with core

technical field

The invention belongs to the technical field of beam reinforcement, and relates to a method for calculating the ultimate bearing capacity, in particular to a method for calculating the ultimate bearing capacity of a reinforced core-placed beam.

Background technique

The vast majority of ancient Chinese buildings belong to wooden structures. Due to the long-term exposure to the sun and rain, termite erosion, and corrosion and aging of the surface of the components, the safety of the buildings decreases year by year. At present, the reinforcement and repair of the wooden components of ancient buildings generally adopts the replacement of the whole beam, or the grouting filling of holes and cracks. These methods improve the safety of ancient buildings to a certain extent; the disadvantage is that the beams and columns of the building need to be unloaded before replacing the beams and columns, which has potential safety hazards, and the construction speed is slow and the cost is high. In addition, the appearance of the replaced components is obviously different from the original parts, which violates the principle of "repairing the old as the old" for ancient buildings with cultural relic value.

The corrosion of beams and trusses in wooden buildings mainly occurs at the two ends and upper parts of the components, and the beams near patios, doors and porches are generally more seriously damaged than those inside the building, especially some ancestral halls, Hui-style buildings such as government offices and temples have been in disrepair for a long time, and there are many phenomena such as rain and water leakage in the cornice position, resulting in the appearance of beam components in good condition, but the core part is a special kind of damage. The phenomenon is also more common.

For the reinforcement and repair methods of wooden beams, there are a large number of theoretical and experimental analyses at home and abroad, but basically all reinforcement methods such as steel, cloth and embedded ribs are directly attached to the surface of the original beam members. It is a reinforcement technique with the bearing capacity or stiffness of the specimen as the main objective, and the reinforcement treatment method is unidirectional, irreversible, and non-reinforcing, and has a great influence on the appearance of the wooden beam. What is particularly important is that, for the reinforcement technology that can protect the appearance of the building and can be reinforced twice, how to systematically study the design theory of its structural system, there is currently no theoretical basis and analysis and design methods to guide engineering applications, let alone. Corresponding normative procedures can be followed. Especially when calculating the ultimate bearing capacity of reinforced beams, usually only the ultimate bearing capacity of elastic development is considered, but the ultimate bearing capacity of plastic development is not considered, which cannot reflect the performance of reinforced beams objectively, and cannot provide a reasonable theoretical basis for engineering applications. .

SUMMARY OF THE INVENTION

The object of the present invention is to provide a method for calculating the ultimate bearing capacity of the normal section of a beam that can realize the reinforcement technology capable of protecting the appearance of the building and enabling secondary reinforcement.

In order to achieve the above object, the solution of the present invention is:

A method for calculating the ultimate bearing capacity of the normal section of a CFRP plate reinforced with a core-mounted beam, wherein the CFRP plate is used as a reinforcement material and is attached to the bottom of the core material to strengthen the core material, and the core material is then arranged on the outer shell of the beam. in a tension zone to reinforce the beam; the method includes the steps of:

(1) Make basic assumptions about the reinforcement process;

(2) Calculate the stress-strain relationship of the cross-section of the core material under the failure of each material in the reinforced core beam;

(3) Calculate the height of the compression zone of the cross-section of the core material and the height of the plastic development of the compression zone of the cross-section of the core material under each material failure condition;

(4) According to the height of the compression zone of the cross-section of the core material and the height of the plastic development of the compression zone under each material failure condition, calculate the flexural load of the normal section of the reinforced core beam under each material failure condition The ultimate bearing capacity of the normal section considering the plastic development of the core beam is obtained.

The basic assumptions of the step (1) include:

(11) Assume that the contribution of the original beam shell to the reinforcement of the core beam is zero;

(12) It is assumed that the cross-section of the core beam remains flat before and after deformation;

(13) It is assumed that before the cracking of the tension zone of the core beam, the coordinated deformation between the reinforcement material and the core material does not occur, and there is no bond slip phenomenon;

(14) It is assumed that the compression constitutive model of the core material adopts the ideal elastic-plastic model, and the tension constitutive model adopts the linear elastic model;

(15) It is assumed that the constitutive model of the CFRP board is the linear elastic model.

The core material is wood, including wood fibers; the failure situations of the materials include:

Damage caused by the breaking of the wood fibers of the core material under tension;

failure of the wood fibers of the compressed core material to the ultimate strain;

The CFRP panels reach ultimate strength-induced failure.

Described step (2) comprises:

Calculate the stress-strain relationship of the cross-section of the core material when the wood fiber of the core material under tension is broken by the following formula:

in: represents the ultimate tensile strain of the wood fibers of the core;

represents the compressive strain at yield of the wood fibers of the core;

h represents the height of the cross section of the core material;

x _c represents the height of the compression zone of the cross-section of the core material;

x _cp represents the height of the plastic development of the compression zone of the cross section of the core material;

represents the ultimate tensile stress of the wood fiber of the core material considering the strength reduction;

represents the yield compressive stress of the wood fiber of the core material without considering the strength reduction;

R _σ represents the ratio of the maximum tensile stress to the maximum compressive stress of the wood fiber of the core material;

Calculate the stress-strain relationship of the cross-section of the core material when the wood fiber of the compressed core material reaches the ultimate compressive strain and causes failure as follows:

in: represents the ultimate compressive strain of the wood fibers of the core material;

γ _ε represents the ratio of the ultimate plastic strain to elastic strain of the wood fiber of the core material;

Calculate the stress-strain relationship of the cross-section of the core material when the CFRP board reaches the ultimate strength and causes damage as follows:

in: represents the ultimate tensile strain in the constitutive model of the CFRP plate;

represents the ultimate tensile stress in the constitutive model of the CFRP plate;

α _E represents the ratio of the elastic modulus of the CFRP sheet to the elastic modulus of the core material;

h represents the height of the cross section of the core material.

In step (3), in the case of calculating the failure of each material, the height of the compression zone of the cross section of the core material includes:

Calculate the height of the compression zone of the cross-section of the core material when the wood fiber of the core material under tension is broken by the following formula:

Among them: A ^F represents the area of reinforcement material;

b represents the width of the cross section of the core material;

Calculate the height of the compression zone of the cross section of the core material when the wood fiber of the compressed core material reaches the ultimate compressive strain and causes failure as follows:

Calculate the height of the compression zone of the cross-section of the core material when the CFRP board reaches the ultimate strength and causes damage as follows:

In the case of calculating the failure of each material in the step (3), the height of the plastic development of the compression zone of the cross-section of the core material includes: combining the cross-section of the core material under the failure conditions of each material calculated in the step (2) The stress-strain relationship is calculated, and the height x _cp of the plastic development of the compression zone of the cross-section of the core material under the corresponding failure conditions of each material is calculated.

Described step (4) comprises:

The flexural bearing capacity of the normal section of the reinforced core beam under the failure conditions of each material is calculated as follows:

Among them: M represents the flexural bearing capacity of the normal section of the core beam after reinforcement;

x _c is calculated according to the value of x _c under the corresponding damage situation in step (3);

x _cp is calculated according to the value of x _cp in the corresponding damage situation in step (3).

The step (4) also includes:

In the obtained normal section flexural bearing capacity of the reinforced core beam under each material failure condition, the smallest value is taken as the normal section ultimate bearing capacity of the reinforced core beam considering the plastic development.

Due to the adoption of the above scheme, the beneficial effects of the present invention are as follows: the present invention proposes a method for calculating the bearing capacity of the normal section of the CFRP plate reinforced core beam, which provides theoretical guidance for the design of the CFRP plate reinforced core beam, and ensures that the The core beam reinforced in this way can meet the design requirements, so as to effectively protect the integrity of the building's appearance, the strength meets the requirements and can be reinforced twice.

Description of drawings

Figure 1a is a schematic diagram of a core material reinforced with CFRP plates in an embodiment of the present invention;

Fig. 1b is the schematic diagram of the original beam shell in the embodiment of the present invention;

Fig. 1c is a schematic diagram of a reinforced core beam obtained by using the reinforcing core material shown in Fig. 1a to reinforce the shell of the original beam shown in Fig. 1b in an embodiment of the present invention;

Fig. 2 is the graph of the constitutive relation model of the core material in the embodiment of the present invention;

Fig. 3 is the graph of the constitutive relation model of CFRP board in the embodiment of the present invention;

4a is one of the schematic diagrams for calculating the height of the compression zone of the cross section of the core material in the embodiment of the present invention;

4b is the second schematic diagram of the calculation of the height of the compression zone of the cross section of the core material in the embodiment of the present invention;

Fig. 5a is one of the schematic diagrams of the calculation of the bending bearing capacity of the normal section of the core beam in the embodiment of the present invention;

5b is the second schematic diagram of the calculation of the bending bearing capacity of the front section of the core-mounted wooden beam in the embodiment of the present invention;

Fig. 5c is the third schematic diagram of the calculation of the bending bearing capacity of the front section of the core-mounted wooden beam in the embodiment of the present invention.

In the attached drawings: 1. Core material; 2. Original beam shell; 3. CFRP board.

Detailed ways

The present invention will be further described below with reference to the embodiments shown in the accompanying drawings.

Aiming at the lack of theoretical research technology on the technology that can protect the appearance of ancient buildings and can reinforce beams twice in the prior art, the present invention proposes a CFRP (carbon fiber reinforced composite material) plate reinforced core beam with positive cross-section ultimate bearing capacity calculation method. In the technology of reinforcing the core beam with the CFRP plate, the CFRP plate 3 is used as the reinforcing material to reinforce the core material 1, and the reinforced core material 1 is placed in the tension zone of the shell 2 of the original beam. Among them, the CFRP board 3 is attached to the bottom of the core material 1 . Figure 1a is a schematic diagram of the core material reinforced with CFRP plates; Figure 1b is a schematic diagram of the original beam shell, wherein the vacant area is the tension zone; Figure 1c is the reinforcement core material of Figure 1a after reinforcing the original beam shell of Figure 1b Schematic diagram of a reinforced core beam. In this embodiment, the core material is wood, including wood fibers.

The method for calculating the ultimate bearing capacity of the normal section of the CFRP plate-reinforced core-placed beam proposed by the present invention includes the following steps:

The first step is to make the following basic assumptions about the reinforcement process:

1) It is assumed that the contribution of the original beam shell to the reinforced core beam is not considered, that is, the contribution of the original beam to the reinforced core beam is assumed to be zero;

2) It is assumed that the cross section of the core beam remains flat before and after deformation, that is, the assumption of flat section is satisfied;

3) It is assumed that before the cracking of the tension zone of the core beam, the coordination deformation between the reinforcement material (ie CFRP plate) and the core material does not occur, and there is no bond slip phenomenon;

4) Assume that the ideal elastic-plastic model is used for the compression constitutive model of the core material, and the linear elastic model is used for the tension constitutive model, as shown in Figure 2. Among them, the compressive elastic modulus of the core material and tensile modulus of elasticity take the same value, Pick in, is the ultimate compressive strain of the wood fiber of the core material, is the yield compressive strain of the wood fibers of the core material, is the ultimate tensile strain of the wood fibers of the core material. represents the yield compressive stress of the wood fiber of the core material; σ ^w represents the stress of the wood fiber of the core material; ε ^w represents the strain of the wood fiber of the core material.

5) Assuming that the CFRP board only considers the strength along the wood fiber direction of the core material, the stress is equal to the product of the strain and its elastic modulus, but its absolute value is not greater than its corresponding strength design value, and the linear elastic model is selected as the constitutive model, as shown in the figure 3 shown. in, represents the ultimate tensile strain of the CFRP plate; represents the ultimate tensile stress in the constitutive model of the CFRP plate. σ ^F represents the stress of the CFRP plate; Represents the tensile modulus of elasticity of the CFRP board; represents the ultimate tensile strain of the CFRP plate; ε ^F represents the strain of the CFRP plate.

In the second step, according to the assumption of the plane section, find the stress-strain relationship of the cross-section of the core material under the failure of each material in the core beam after reinforcement, including:

Calculate the stress-strain relationship of the cross-section of the core material when the wood fiber of the tensioned core material breaks and causes damage according to the following formula:

Where: represents the ultimate tensile strain of the wood fiber of the core material;

represents the compressive strain at yield of the wood fibers of the core;

h represents the height of the cross section of the core material;

x _c represents the height of the compression zone of the cross section of the core material;

x _cp represents the height of the plastic development of the cross-sectional compression zone of the core material;

Represents the ultimate tensile stress of the wood fiber of the core material under the consideration of strength reduction (that is, considering the reduction of tensile strength by defects such as knots, holes and shrinkage cracks in the tensile zone of the wood);

Represents the yield compressive stress of the wood fiber of the core material without considering the reduction of strength (that is, without considering the reduction of tensile strength by defects such as knots, holes and shrinkage cracks in the tensile area of the wood);

_Rσ represents the ratio of the maximum tensile stress to the maximum compressive stress of the wood fibers of the core material.

Calculate the stress-strain relationship of the cross-section of the core material when the wood fiber of the compressed core material reaches the ultimate compressive strain and causes failure according to the following formula:

in: represents the ultimate compressive strain of the wood fibers of the core material;

γ _ε represents the ratio of the ultimate plastic strain to the elastic strain of the wood fiber of the core material.

Calculate the stress-strain relationship of the cross-section of the core material when the CFRP board reaches the ultimate strength and causes damage according to the following formula:

in: represents the ultimate tensile strain in the constitutive model of the CFRP plate;

represents the ultimate tensile force in the constitutive model of the CFRP plate;

α _E represents the ratio of the elastic modulus of the CFRP sheet to the elastic modulus of the core material;

h represents the height of the cross section of the core material.

In the third step, according to the various equations in the second step and the static equilibrium conditions of the section, find the height of the compression zone of the cross section of the core material, as shown in Figure 4a and Figure 4b, including:

Calculate the height of the compression zone of the cross-section of the core material under the condition that the wood fiber of the tensile core material breaks and causes damage according to the following formula:

Where: x _c represents the height of the compression zone of the cross-section of the core material in the failure caused by the breaking of the wood fiber of the core material under tension;

A ^F represents the area of reinforcement material;

b represents the width of the cross section of the core material;

Calculate the height of the compression zone of the cross-section of the core material when the wood fiber of the compressed core material reaches the ultimate compressive strain and causes failure according to the following formula:

Where: x _c represents the height of the compression zone of the cross-section of the core material when the wood fibers of the compressed core material reach the ultimate compressive strain and cause failure.

Calculate the height of the compression zone of the cross section of the core material when the CFRP board reaches the ultimate strength and causes damage according to the following formula:

Where: x _c represents the height of the compression zone of the cross-section of the core material when the CFRP board reaches the ultimate strength and causes failure.

In Figure 4b, represents the compressive strain of the wood fibers of the core; represents the tensile strain of the wood fibers of the core; Indicates the tensile strain of the tensile reinforcement material (CFRP plate).

In the fourth step, combined with the stress-strain relationship of the cross-section of the core material under the failure conditions of each material calculated in the second step, the height x _cp of the plastic development of the compression zone of the cross-section of the core material under the corresponding failure conditions of each material is calculated.

The fifth step, as shown in Figure 5a, Figure 5b and Figure 5c, calculates the flexural bearing capacity of the normal section of the reinforced core beam under the failure of each material according to the following formula:

Among them: M represents the flexural bearing capacity of the normal section of the core beam after reinforcement; x _c is calculated according to the value of x _c under the corresponding failure situation in the third step; x _cp is calculated according to the corresponding failure situation in the fourth step. Calculate the value of x _cp below.

In the obtained flexural bearing capacity of the normal section of the reinforced core beam under each material failure condition, the minimum value is taken as the normal section ultimate bearing capacity of the reinforced core beam considering the plastic development.

In Figure 5c, represents the tensile stress of the wood fiber of the core material; F ^F represents the resultant force of the reinforcing material (CFRP board).

In the obtained flexural bearing capacity of the normal section of the reinforced core beam under each material failure condition, the minimum value is taken as the normal section ultimate bearing capacity of the reinforced core beam considering the plastic development.

The ultimate bearing capacity of the normal section of the core-set wooden beam obtained according to the above method can be used as a guide for relevant theoretical research and engineering application, and assist in obtaining a reinforced core-set wooden beam that can meet the design requirements.

Generally, the core-set timber beams reinforced with CFRP panels that have completed the design shall meet the following functional requirements within the specified design service life:

(1) It can withstand various effects that may occur during normal construction and normal use;

(2) It can meet the control requirements of various indicators of the structure during normal construction and normal use;

(3) It has good working performance during normal use;

(4) Sufficient durability under normal maintenance;

(5) The necessary overall stability can be maintained during and after the occurrence of accidental events specified in the design.

The above-mentioned requirements for the function of core-set wood beam structural members reinforced with CFRP plates are essentially to have sufficient strength to withstand the internal force generated by the most unfavorable load effect, and to meet the limit state requirements of bearing capacity. In addition, the economy and operability of the design scheme must also be considered.

The design of core-set wood beam structural members reinforced with CFRP plates is mainly carried out according to the following steps, and an economical, reasonable and feasible design scheme often needs to be modified and calculated several times to obtain:

(1) Determine the secondary internal force of the structure;

(2) According to the use requirements and the overall plan and structural form formulated, with reference to the existing design and related materials, the section size of the reinforced core wood beam and the thickness and length of the CFRP board are preliminarily determined;

(3) Use the internal force analysis model to calculate the load effect combination and the maximum effect of the control section;

(4) According to the design internal force of the control section under the ultimate limit state of bearing capacity and the limit state of normal service and the preliminary proposed section size, estimate the number, size and arrangement of CFRP panels, and make a reasonable arrangement. If the CFRP board cannot be reasonably arranged, go back to step (2) and modify the section size;

(5) Check and calculate the section stress in the construction stage, transportation and installation stage and use stage;

(6) Check the anchorage length.

To sum up, the present invention proposes a method for calculating the bearing capacity of the normal section of a beam reinforced with CFRP plates, which provides theoretical guidance for the design of beams reinforced with CFRP plates and ensures that the beams reinforced by this method are used. The core beam can meet the design requirements, so as to effectively protect the integrity of the building appearance, the strength meets the requirements and can be reinforced twice.

The above description of the embodiments is for the convenience of those of ordinary skill in the art to understand and apply the present invention. It will be apparent to those skilled in the art that various modifications to these embodiments can be readily made, and the generic principles described herein can be applied to other embodiments without inventive step. Therefore, the present invention is not limited to the embodiments herein, and improvements and modifications made by those skilled in the art according to the disclosure of the present invention without departing from the scope of the present invention should all fall within the protection scope of the present invention.

Claims (6)

1. A calculation method for the ultimate bearing capacity of the normal section of a CFRP plate reinforced with a core beam, wherein the CFRP plate is used as a reinforcement material, and is attached to the bottom of the core material to reinforce the core material, and the core material is then arranged on the beam. The beam is strengthened in the tension zone of the shell, characterized in that: the method comprises the following steps: (1) Make basic assumptions about the reinforcement process; The basic assumptions include: (11) It is assumed that the contribution of the original beam shell to the reinforcement of the core beam is zero; (12) The cross section of the core beam is assumed to remain flat before and after deformation; (13) It is assumed that the tension zone of the core beam is cracked Before, the deformation between the reinforcement material and the core material is coordinated, and there is no bond-slip phenomenon; (14) It is assumed that the compression constitutive model of the core material adopts the ideal elastic-plastic model, and the tension constitutive model adopts the linear elastic model; (15) ) assumes that the constitutive model of the CFRP plate takes the linear elastic model; (2) Calculate the stress-strain relationship of the cross-section of the core material under the failure of each material in the reinforced core beam; The core material is wood and contains wood fibers; the failure conditions of each material include: damage caused by the breaking of the wood fibers of the core material under tension; damage caused by the wood fibers of the compressed core material reaching the ultimate compressive strain; The damage caused by the CFRP board reaching the ultimate strength; (3) Calculate the height of the compression zone of the cross-section of the core material and the height of the plastic development of the compression zone of the cross-section of the core material under each material failure condition; (4) According to the height of the compression zone of the cross section of the core material and the height of the plastic development of the compression zone under each material failure condition, calculate the bending load of the normal section of the reinforced core beam under each material failure condition The ultimate bearing capacity of the normal section considering the plastic development of the core beam is obtained. 2. The calculation method of the normal section ultimate bearing capacity of the CFRP plate reinforced core beam according to claim 1, is characterized in that: described step (2) comprises: Calculate the stress-strain relationship of the cross-section of the core material when the wood fiber of the core material under tension is broken by the following formula: in: represents the ultimate tensile strain of the wood fibers of the core; represents the compressive strain at yield of the wood fibers of the core; h represents the height of the cross section of the core material; x _c represents the height of the compression zone of the cross-section of the core material; x _cp represents the height of the plastic development of the compression zone of the cross section of the core material; represents the ultimate tensile stress of the wood fiber of the core material considering the strength reduction; represents the yield compressive stress of the wood fiber of the core material without considering the strength reduction; R _σ represents the ratio of the maximum tensile stress to the maximum compressive stress of the wood fiber of the core material; Calculate the stress-strain relationship of the cross-section of the core material when the wood fiber of the compressed core material reaches the ultimate compressive strain and causes failure as follows: in: represents the ultimate compressive strain of the wood fibers of the core material; γ _ε represents the ratio of the ultimate plastic strain to elastic strain of the wood fiber of the core material; Calculate the stress-strain relationship of the cross-section of the core material when the CFRP board reaches the ultimate strength and causes damage as follows: in: represents the ultimate tensile strain in the constitutive model of the CFRP plate; represents the ultimate tensile stress in the constitutive model of the CFRP plate; α _E represents the ratio of the elastic modulus of the CFRP sheet to the elastic modulus of the core material; h represents the height of the cross section of the core material. 3. The method for calculating the ultimate bearing capacity of the normal section of the CFRP plate reinforced core beam according to claim 2, characterized in that: in step (3), under the condition of calculating the failure of each material, the cross section of the core material is subjected to the calculation method. The height of the nip includes: Calculate the height of the compression zone of the cross-section of the core material when the wood fiber of the core material under tension is broken by the following formula: Among them: A ^F represents the area of reinforcement material; b represents the width of the cross section of the core material; Calculate the height of the compression zone of the cross section of the core material when the wood fiber of the compressed core material reaches the ultimate compressive strain and causes failure as follows: Calculate the height of the compression zone of the cross-section of the core material when the CFRP board reaches the ultimate strength and causes failure as follows: 4. The method for calculating the ultimate bearing capacity of the normal section of the CFRP plate reinforced core beam according to claim 3, characterized in that: in the step (3), in the case of calculating the failure of each material, the cross section of the core material The height of the plastic development of the compression zone includes: in combination with the stress-strain relationship of the cross-section of the core material under the failure conditions of each material calculated in step (2), calculate the corresponding compression of the cross-section of the core material under the failure conditions of each material. The height x _cp of the plastic development of the zone. 5. the calculation method of the normal section ultimate bearing capacity of the CFRP plate reinforced core beam according to claim 4, it is characterized in that: described step (4) comprises: strengthen the core beam under the following formula calculation under each material damage situation The normal section flexural capacity of : Among them: M represents the flexural bearing capacity of the normal section of the core beam after reinforcement; x _c is calculated according to the value of x _c under the corresponding damage situation in step (3); x _cp is calculated according to the value of x _cp in the corresponding damage situation in step (3). 6. The calculation method of the normal section ultimate bearing capacity of the CFRP plate reinforced core beam according to claim 5, characterized in that: the step (4) further comprises: strengthening the CFRP plate under the obtained damage situation of each material Among the flexural bearing capacity of the normal section of the core beam, the smallest value is taken as the normal section ultimate bearing capacity of the reinforced core beam considering the plastic development.