CN105426691B - Bar planting method reinforces the computational methods for the Ultimate flexural strength for putting core beam - Google Patents
Bar planting method reinforces the computational methods for the Ultimate flexural strength for putting core beam Download PDFInfo
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Abstract
The present invention proposes the computational methods that a kind of bar planting method reinforces the Ultimate flexural strength for putting core beam, belongs to beam reinforcement technique field.The computational methods comprise the following steps：(1) basic assumption is done to reinforcing process；(2) calculate under each material damage situation, the stress-strain relation of the cross section of core；(3) calculate under each material damage situation, the height of the compressive region of the cross section of core；(4) calculate under each material damage situation, the height of the plasticity of the compressive region of the cross section of core；(5) according to the height of the plasticity of the height of the compressive region of the cross section of core and compressive region under each material damage situation, the flexure bearing capacity for putting core beam is reinforced under each material damage situation corresponding to calculating, obtains reinforcing the Ultimate flexural strength for the consideration plasticity for putting core beam.The present invention can effectively calculate the Ultimate flexural strength that bar planting method reinforces the consideration plasticity for putting core beam, and strong theoretical direction is provided for engineer applied.
Description
Technical Field
The invention belongs to the technical field of beam reinforcement, and relates to a method for calculating ultimate bearing capacity, in particular to a method for calculating ultimate bearing capacity of a reinforced core beam.
Background
The ancient Chinese buildings are mostly belonged to wood structure buildings, and because the ancient Chinese buildings are damaged by sunlight and rain for a long time and are damaged by termite, the surfaces of the members are corroded and aged, and the safety of the buildings is reduced year by year. At present, the reinforcing and repairing of the ancient building timber components are generally carried out by replacing the whole beam or grouting and filling holes and cracks. The methods improve the safety of the ancient buildings to a certain extent; the method has the disadvantages that the beam column of the building needs to be unloaded before the beam column is replaced, potential safety hazards exist, the construction speed is low, and the manufacturing cost is high. In addition, the appearance of the replaced component is obviously different from the original part, and the principle of 'repairing old as old' of the historic building with cultural relic value is violated.
The corrosion of beams and purlin members in the wood structure building mainly occurs at two ends and the upper part of the members, the beam members close to a patio, a door and a corridor are generally more seriously damaged than the beam members inside the building, particularly, in some hui buildings such as a temple, a house Xian and a temple, the buildings are overhauled all the year round, rain and water leakage can occur at the cornice position, the appearance of the beam members is good, but the medullary part is in a special damage form under the rotten condition, and the phenomenon is also relatively common.
The method and the technology for reinforcing and repairing the wood beam have a large number of theories and experimental analyses at home and abroad, but basically, the method is a reinforcing method of directly sticking steel, cloth materials, embedded ribs and the like on the surface of an original beam member, a reinforcing technology which mainly aims at improving the bearing capacity or rigidity of a damaged test piece is adopted, and the reinforcing treatment mode is unidirectional, irreversible and irreversible, and has large influence on the appearance of the wood beam. Particularly, for the reinforcement technology which can protect the appearance of the building and can perform secondary reinforcement, how to systematically research the design theory of the structural system of the reinforcement technology does not form a theoretical basis and an analysis design method for guiding engineering application at present, and no corresponding specification can be followed. Particularly, when the ultimate bearing capacity of the reinforcing beam is calculated, only the ultimate bearing capacity of elastic development is usually considered, but the ultimate bearing capacity of plastic development is not considered, so that the performance of the reinforcing beam cannot be objectively reflected, and a reasonable theoretical basis cannot be provided for engineering application.
Disclosure of Invention
The invention aims to provide a method for calculating the ultimate bearing capacity of a normal section of a beam reinforced by a reinforcing technology which can protect the appearance of a building and can be reinforced secondarily.
In order to achieve the above purpose, the solution of the invention is:
a method for calculating the ultimate bearing capacity of a normal section of a reinforced core beam by a bar planting method, wherein the bar is used as a reinforcing material and is implanted into the bottom of a core material to reinforce the core material, and the core material is arranged in a tension area of a shell of the beam to reinforce the beam; the method comprises the following steps:
(1) making basic assumption on the reinforcing process;
(2) calculating the stress-strain relationship of the cross section of the core material under the condition that each material in the reinforced core beam is damaged;
(3) calculating the height of the compression area of the cross section of the core material and the height of the plastic development of the compression area of the cross section of the core material under the condition that each material is damaged;
(4) and calculating the bending bearing capacity of the normal section of the reinforced core beam under the corresponding material damage condition according to the height of the compression area of the cross section of the core material under the condition that each material is damaged and the height of the plastic development of the compression area, so as to obtain the limit bearing capacity of the normal section of the reinforced core beam, which takes the plastic development into consideration.
The ribs are CFRP ribs or reinforcing steel bars.
The basic assumption of step (1) includes:
(11) assuming that the contribution of the beam's outer shell to the reinforcement of the core beam is zero;
(12) the cross section of the core beam is supposed to keep a plane before and after deformation;
(13) before the core beam tension area is cracked, the reinforcing material and the core material are in coordinated deformation, and the bonding slippage phenomenon does not occur;
(14) assuming that the compression constitutive model of the core material is an ideal elastic-plastic model, and the tension constitutive model is an linear elastic model;
(15) when the rib is a CFRP rib, assuming that a constitutive model of the CFRP rib takes a linear elastic model; when the reinforcing steel bar is a reinforcing steel bar, an ideal elastic-plastic model is selected as the constitutive model of the reinforcing steel bar.
The core material is wood and comprises wood fibers; the material failure situations comprise:
failure by wood fiber stretch-breaking of the core material under tension;
failure of the wood fibers of the compressed core material to reach ultimate strain;
when the rib is a CFRP rib, the CFRP rib reaches the damage caused by the ultimate strength; when the reinforcing steel bar is a reinforcing steel bar, the reinforcing steel bar is buckled, and the wood fiber of the core material is broken and cracked to cause damage.
The step (2) comprises the following steps:
the stress-strain relationship of the cross section of the core material in the case of breakage of the wood fiber of the core material under tension caused failure was calculated as follows:
wherein:represents the ultimate tensile strain of the wood fibers of the core material;
represents the yield stress strain of the wood fibers of the core material;
h0representing the distance from the stressed geometric center of the rib to the stressed edge of the core material;
xca height of the compression zone representing a cross-section of the core material;
xcpa height of development of a plastic region of the compression region representing a cross section of the core material;
represents the ultimate tensile stress of the wood fibers of the core material in consideration of the reduction in strength;
represents the yield compressive stress of the wood fiber of the core material without considering the strength reduction;
Rσrepresents the ratio of the maximum tensile stress to the maximum compressive stress of the wood fibers of the core material;
the stress-strain relationship of the cross section of the core material in the case where the wood fiber of the compressed core material reached the ultimate compressive strain to cause failure was calculated as follows:
wherein:represents the ultimate compressive strain of the wood fibers of the core material;
γεrepresents a ratio of ultimate plastic strain to elastic strain of the wood fiber of the core material;
when the rib is a CFRP rib, calculating the stress-strain relationship of the cross section of the core material under the condition that the CFRP rib reaches the ultimate strength and causes damage according to the following formula:
wherein:representing ultimate tensile strain in the CFRP tendon constitutive model;
representing ultimate tensile stress in the CFRP rib constitutive model;
αEexpressing the ratio of the elastic modulus of the CFRP rib to the elastic modulus of the core material;
when the reinforcement is a steel bar, calculating the stress-strain relationship of the cross section of the core material under the condition that the steel bar is subjected to yield and the wood fiber of the core material is broken and cracked to cause damage according to the following formula:
in the step (3), calculating the height of the compression area of the cross section of the core material under the condition that each material is damaged comprises the following steps: the method comprises calculating the height x of the pressure zone of the cross section of the core material when the wood fiber of the core material under tension is broken, when the wood fiber of the core material under compression reaches the ultimate compressive strain to cause breakage, when the CFRP bar is a CFRP bar and reaches the ultimate strength to cause breakage, when the bar is a steel bar and when the wood fiber of the core material is broken and cracked to cause breakage, according to the following formulac：
Wherein: fiRepresenting the internal forces of the respective materials or components;
h represents the height of the cross section of the core material;
σw(xc) Height x of compression zone representing cross section of core materialcStress of wood fibers;
b(xc) Height x of compression zone representing cross section of core materialcThe cross-sectional width of;
representing the tensile stress of the tensile reinforcement material;
AFindicating the area of the reinforcing material in tension.
Calculating the plastic development height of the compression area of the cross section of the core material under the condition that each material is damaged in the step (3) comprises the following steps: and (3) calculating the height x of the plastic development of the compression area of the cross section of the core material under the corresponding material failure condition by combining the stress-strain relation of the cross section of the core material under the condition that each material fails, calculated in the step (2)cp。
The step (4) comprises the following steps:
and (3) calculating the normal section bending bearing capacity of the reinforcing core beam under the condition of damage of each material according to the following formula:
wherein: m represents the bending bearing capacity of the normal section of the reinforced core beam;
b represents the width of the cross section of the core material;
xcaccording to x in the corresponding damage situation in step (3) respectivelycValue calculation;
xcpaccording to x in the corresponding damage situation in step (3) respectivelycpAnd (5) value calculation.
The step (4) further comprises: taking the minimum value of the flexural bearing capacity of the normal section of the reinforcing core beam under the condition of failure of each material as the limit bearing capacity of the normal section of the reinforcing core beam considering the plastic development.
Due to the adoption of the scheme, the invention has the beneficial effects that: the invention provides a method for calculating the ultimate bearing capacity of the normal section of a reinforced core beam by a bar planting method, provides theoretical guidance for the design of reinforcing the reinforced core beam by the bar planting method, and ensures that the reinforced core beam reinforced by the method can meet the design requirement, thereby effectively protecting the intact appearance of a building, ensuring that the strength meets the requirement and realizing secondary reinforcement.
Drawings
FIG. 1a is a schematic diagram of a core material reinforced by a bar planting manner in the embodiment of the present invention;
FIG. 1b is a schematic illustration of the shell of the primary beam in an embodiment of the present invention;
FIG. 1c is a schematic view of a reinforced core beam resulting from the core material of FIG. 1a reinforcing the original beam shell of FIG. 1 b;
FIG. 2 is a graph of a constitutive relation model of a core material in an embodiment of the present invention;
FIG. 3 is a graph of a constitutive relation model of CFRP tendon in the embodiment of the present invention;
FIG. 4 is a graph of a constitutive relation model of a normal steel bar in the embodiment of the invention;
FIG. 5a is one of the schematic diagrams of calculation of the height of the compression zone of the cross section of the core material in the embodiment of the present invention;
FIG. 5b is a second schematic diagram illustrating the calculation of the height of the compression zone of the cross-section of the core material in an embodiment of the present invention;
FIG. 6a is one of the schematic diagrams of the calculation of the normal section bending bearing capacity of the core-mounted wood beam in the embodiment of the invention;
FIG. 6b is a second schematic diagram illustrating the calculation of the flexural bearing capacity of the core-embedded wooden beam in the embodiment of the invention;
fig. 6c is a third schematic diagram of the calculation of the flexural bearing capacity of the front section of the core-mounted wood beam in the embodiment of the invention.
In the drawings: 1. a rib; 2. a core material; 3. original beam shell.
Detailed Description
The invention will be further described with reference to examples of embodiments shown in the drawings.
Aiming at the problem that the technology which can protect the appearance of an ancient building and can strengthen a beam for the second time is lack of a technology for theoretical research in the prior art, the invention provides a method for calculating the ultimate bearing capacity of a normal section of a reinforced core beam by a bar planting method. In the technology for reinforcing the core beam by the bar planting method, the bar 1 is used as a reinforcing material to reinforce the core material 2, and the reinforced core material 2 is placed in a tension area of an original beam shell 3. The process of reinforcing the core material by adopting the bar planting method is to put the bar 1 into the bottom of the core material 2 to reinforce the core material 2. FIG. 1a is a schematic illustration of a core material reinforced with CFRP (carbon fiber reinforced composite) sheets; FIG. 1b is a schematic view of the original beam shell, wherein the void region is the tension region; fig. 1c is a schematic view of a reinforced core beam obtained by reinforcing the original beam shell of fig. 1b with the reinforcing core of fig. 1 a. In this embodiment, the core material 2 is wood, including wood fibers.
The invention provides a method for calculating the ultimate bearing capacity of a normal section of a reinforced core beam by a bar planting method, which comprises the following steps:
in the first step, the following basic assumptions are made about the consolidation process:
1) the contribution of the original beam shell to the reinforced core beam is not considered, namely the contribution of the original beam to the reinforced core beam is zero;
2) assuming that the cross section of the reinforced core beam keeps a plane before and after deformation, namely, the assumption of a flat section is met;
3) assuming that before the tension area of the reinforced core beam cracks, the reinforcing material (namely ribs) and the core material deform coordinately, and the bonding slippage phenomenon does not occur;
4) assuming that the core material compression constitutive model is an ideal elastic-plastic model, a tension constitutive modelThe model is taken as a linear elastic model, as shown in FIG. 2. Wherein the core material has a modulus of elasticity under compressionAnd modulus of elasticity in tensionThe same numerical value is taken as the numerical value,getWherein,is the ultimate compressive strain of the wood fibers of the core material,is the yield pressure strain of the wood fibres of the core material,is the ultimate tensile strain of the wood fibers of the core material. In FIG. 2,. epsilonwRepresents strain of the wood fiber of the core material; sigmawRepresents the stress of the wood fibers of the core material;represents the ultimate compressive stress of the wood fibers of the core material;the ultimate tensile stress of the wood fibers of the core material is indicated.
5) When the rib is a CFRP rib, assuming that the CFRP rib considers only the strength in the wood fiber direction of the core material, the stress is equal to the product of the strain and the elastic modulus thereof, but the absolute value thereof is not greater than the corresponding strength design value thereof, and the constitutive model selects a linear elastic model, as shown in fig. 3. Wherein,representing the ultimate tensile strain of the CFRP rib;representing the ultimate tensile stress of the CFRP rib;representing the tensile elastic modulus of the CFRP rib; sigmaFRepresenting the stress of the CFRP rib; epsilonFIndicating strain of the CFRP tendon.
When the bar is a common bar, the stress of the common bar is equal to the product of the strain and the elastic module, but the absolute value is not more than the designed strength value, and the ultimate tensile strainTaking 0.01, the constitutive model selects an ideal elastic-plastic model, as shown in FIG. 4. In FIG. 4, σsRepresenting the stress of ordinary steel bars;representing the yield tensile strain of ordinary steel bars;representing the yield stress of ordinary steel bars;representing the yield stress strain of ordinary steel bars;representing the yield tensile stress of ordinary steel bars; epsilonsRepresenting the strain of ordinary steel bars;representing the tensile elastic modulus of ordinary steel bars.
And secondly, calculating the stress-strain relationship of the cross section of the core material under the condition that each material of the reinforced core beam is damaged according to the assumption of the flat section, wherein the stress-strain relationship comprises the following steps:
the stress-strain relationship of the cross section of the core material in the case of breakage of the wood fiber of the core material under tension caused failure was calculated as follows:
wherein:represents the ultimate tensile strain of the wood fibers of the core material;
represents the yield stress strain of the wood fibers of the core material;
h0representing the distance from the stressed geometric center of the rib to the stressed edge of the core material;
xca height of the compression zone representing a cross-section of the core material;
xcpa plastic development height of the compression zone representing a cross section of the core material;
the ultimate tensile stress of the wood fiber of the core material under the condition of considering the strength reduction (namely, under the condition of considering the reduction of the tensile strength by defects such as wood knots, holes, drying shrinkage cracks and the like in a tensile area of the core material);
representing the yield compressive stress of the wood fibers of the core material without considering the reduction of the strength (i.e. without considering the reduction of the tensile strength by defects such as knots, holes and drying shrinkage cracks in the tensile region of the core material);
Rσindicating the maximum tensile stress of the wood fibres of the coreRatio to maximum compressive stress.
The stress-strain relationship of the cross section of the core material in the case where the wood fiber of the compressed core material reached the ultimate compressive strain to cause failure was calculated as follows:
wherein:represents the ultimate compressive strain of the wood fibers of the core material;
γεthe ratio of the ultimate plastic strain to the elastic strain of the wood fibers of the core material is indicated.
When the reinforcement is a CFRP reinforcement, calculating the stress-strain relationship of the cross section of the core material under the condition that the CFRP reinforcement reaches the ultimate strength and causes damage according to the following formula:
wherein:representing ultimate tensile strain in the CFRP plate constitutive model;
representing ultimate tensile force in the CFRP plate constitutive model;
αEthe ratio of the modulus of elasticity of the CFRP sheet to the modulus of elasticity of the core material is shown.
When the steel bar is a common steel bar, calculating the stress-strain relationship of the cross section of the core material under the conditions that the common steel bar embedded material yields and the wood fiber of the core material is broken and cracked according to the following formula:
thirdly, according to the formulas and the static balance conditions of the sections in the second step, calculating the damage condition of each material according to the following formula, namely, the damage condition caused by the tensile breakage of the wood fiber of the core material, the damage condition caused by the ultimate compressive strain of the wood fiber of the core material, the damage condition caused by the ultimate strength of the CFRP rib when the rib is a CFRP rib, the yield of the common steel bar when the rib is the common steel bar and the damage condition caused by the tensile breakage and cracking of the wood fiber of the core material, and the height x of the compression area of the cross section of the core materialcAs shown in fig. 5a and 5 b:
wherein: fiRepresenting the internal forces of the respective materials or components;
h represents the height of the cross section of the core material;
σw(xc) Height x representing the cross-section of the core materialcStress of wood fibers;
b(xc) Height x representing the cross-section of the core materialcThe width of the cross section;
representing the tensile stress of the tensile reinforcement material;
AFindicating the area of the reinforcing material in tension.
In the context of figure 5b of the drawings,representing the compressive strain of the wood fibers of the core material;representing the tensile strain of the wood fibers of the core material;indicating the tensile strain of the tensile reinforcement material.
Fourthly, calculating the height x of the plastic development of the compression area of the cross section of the core material under the corresponding material failure condition by combining the stress-strain relation of the cross section of the core material under the condition that each material is failed calculated in the second stepcp。
Fifthly, as shown in fig. 6a, 6b and 6c, calculating the normal section bending bearing capacity of the reinforced core beam according to the following formula:
wherein: m represents the bending bearing capacity of the normal section of the reinforced core beam;
b represents the width of the cross section of the core material;
xcaccording to x in the corresponding destruction situation in the third stepcValue calculation;
xcpaccording to x in the corresponding damage situation in the fourth stepcpAnd (5) value calculation.
And taking the minimum value as the ultimate bearing capacity of the normal section of the reinforced core beam considering the plastic development in the bending bearing capacity of the normal section of the reinforced core beam under the condition that each material is damaged.
In fig. 6a, a denotes the distance from the geometric centre of the tendon to the tensioned edge of the core material. FFRepresenting the resultant force of the reinforcement material (plain rebar or CFRP rebar);showing the tensile stress of the wood fibers of the core material.
The ultimate bearing capacity of the normal section of the core-placed wood beam obtained by the method can be used as a guide for relevant theoretical research and engineering application, and a reinforced core-placed wood beam which can meet the design requirement can be obtained in an auxiliary manner.
Generally, the designed reinforced core-placed wood beam reinforced by the bar planting method meets the following functional requirements within the specified design service life:
(1) can bear various possible effects during normal construction and normal use;
(2) the control requirements of various indexes of the structure can be met during normal construction and normal use;
(3) the working performance is good when the device is used normally;
(4) sufficient durability under normal maintenance;
(5) the necessary overall stability is maintained during and after design-specified contingencies.
The requirements for the functions of the core-placed wood beam structural member reinforced by the bar planting method are that the core-placed wood beam structural member has enough strength, can bear the internal force generated by the worst load effect, and meets the requirement of the bearing capacity limit state. In addition to this, the economics and operability of the design must be considered.
The design of the core-placed wood beam structural member reinforced by the bar planting method is mainly carried out according to the following steps, and an economic, reasonable and feasible design scheme is often obtained by repeatedly modifying and calculating for several times:
(1) determining a secondary internal force of the structure;
(2) according to the use requirements and the drawn overall scheme and structural form, the sectional dimension of the reinforced core-placed wood beam and the sectional dimension and length of the bar-planting material are preliminarily determined by referring to the existing design and related data;
(3) calculating the maximum effect of the load effect combination and the control section by adopting an internal force analysis model;
(4) and estimating the type, the quantity, the size and the arrangement mode of the bar-planting materials according to the design internal force and the preliminarily drawn section size of the control section in the bearing capacity limit state and the normal use limit state, and carrying out reasonable arrangement. If the bar planting materials cannot be reasonably arranged, returning to the step (2) and modifying the section size;
(5) checking and calculating section stress in a construction stage, a conveying and mounting stage and a using stage;
(6) and checking and calculating the anchoring length.
In conclusion, the invention provides a method for calculating the ultimate bearing capacity of the normal section of the reinforced core beam by the bar planting method, provides theoretical guidance for the design of reinforcing the core beam by the bar planting method, and ensures that the core beam reinforced by the method can meet the design requirements, thereby effectively protecting the intact appearance of the building, meeting the strength requirement and realizing secondary reinforcement.
The embodiments described above are intended to facilitate one of ordinary skill in the art in understanding and using the present invention. It will be readily apparent to those skilled in the art that various modifications to these embodiments may be made, and the generic principles described herein may be applied to other embodiments without the use of the inventive faculty. Therefore, the present invention is not limited to the embodiments described herein, and those skilled in the art should make improvements and modifications within the scope of the present invention based on the disclosure of the present invention.
Claims (7)
1. A method for calculating the ultimate bearing capacity of a normal section of a reinforced core beam by a bar planting method, wherein the bar is used as a reinforcing material, the bottom of a core material is implanted to reinforce the core material, and the core material is arranged in a tension area of a shell of the beam to reinforce the beam, and the method is characterized in that: the method comprises the following steps:
(1) making basic assumption on the reinforcing process;
(2) calculating the stress-strain relationship of the cross section of the core material under the condition that each material in the reinforced core beam is damaged;
(3) calculating the height of the compression area of the cross section of the core material and the height of the plastic development of the compression area of the cross section of the core material under the condition that each material is damaged;
(4) calculating the normal section bending bearing capacity of the reinforced core beam under the damage condition of each material according to the height of the compression area of the cross section of the core material under the damage condition of each material and the height of the plastic development of the compression area, and obtaining the normal section limit bearing capacity of the reinforced core beam considering the plastic development;
the basic assumption of step (1) includes:
(11) assuming that the contribution of the beam's outer shell to the reinforcement of the core beam is zero;
(12) the cross section of the core beam is supposed to keep a plane before and after deformation;
(13) before the core beam tension area is cracked, the reinforcing material and the core material are in coordinated deformation, and the bonding slippage phenomenon does not occur;
(14) assuming that the compression constitutive model of the core material is an ideal elastic-plastic model, and the tension constitutive model is an linear elastic model;
(15) when the rib is a CFRP rib, assuming that a constitutive model of the CFRP rib takes a linear elastic model; when the reinforcement is a steel bar, an ideal elastic-plastic model is selected on the assumption that the constitutive model of the steel bar is an ideal elastic-plastic model;
the material failure situations comprise:
failure by wood fiber stretch-breaking of the core material under tension;
the wood fibers of the compressed core material reach damage caused by extreme compressive strain;
when the rib is a CFRP rib, the CFRP rib reaches the damage caused by the ultimate strength; when the reinforcing steel bar is a reinforcing steel bar, the reinforcing steel bar is buckled, and the wood fiber of the core material is broken and cracked to cause damage.
2. The method for calculating the ultimate bearing capacity of the normal section of the reinforced core beam by the bar planting method according to claim 1, wherein the method comprises the following steps: the ribs are CFRP ribs or reinforcing steel bars.
3. The method for calculating the ultimate bearing capacity of the normal section of the reinforced core beam by the bar planting method according to claim 1, wherein the method comprises the following steps: the core material is wood and comprises wood fibers.
4. The method for calculating the ultimate bearing capacity of the normal section of the reinforced core beam by the bar planting method according to claim 1, wherein the method comprises the following steps: the step (2) comprises the following steps:
the stress-strain relationship of the cross section of the core material in the case of breakage of the wood fiber of the core material under tension caused failure was calculated as follows:
<mrow> <mfrac> <msubsup> <mi>&epsiv;</mi> <mrow> <mi>t</mi> <mi>u</mi> </mrow> <mi>w</mi> </msubsup> <msubsup> <mi>&epsiv;</mi> <mrow> <mi>c</mi> <mi>y</mi> </mrow> <mi>w</mi> </msubsup> </mfrac> <mo>=</mo> <mfrac> <mrow> <msub> <mi>h</mi> <mn>0</mn> </msub> <mo>-</mo> <msub> <mi>x</mi> <mi>c</mi> </msub> </mrow> <mrow> <msub> <mi>x</mi> <mi>c</mi> </msub> <mo>-</mo> <msub> <mi>x</mi> <mrow> <mi>c</mi> <mi>p</mi> </mrow> </msub> </mrow> </mfrac> <mo>=</mo> <mfrac> <msubsup> <mi>&sigma;</mi> <mrow> <mi>t</mi> <mi>u</mi> </mrow> <mi>w</mi> </msubsup> <msubsup> <mi>&sigma;</mi> <mrow> <mi>c</mi> <mi>y</mi> </mrow> <mi>w</mi> </msubsup> </mfrac> <mo>=</mo> <msub> <mi>R</mi> <mi>&sigma;</mi> </msub> </mrow>
wherein:wood fiber representing core materialUltimate tensile strain of;
represents the yield stress strain of the wood fibers of the core material;
h0representing the distance from the stressed geometric center of the rib to the stressed edge of the core material;
xca height of the compression zone representing a cross-section of the core material;
xcpa height of development of a plastic region of the compression region representing a cross section of the core material;
represents the ultimate tensile stress of the wood fibers of the core material in consideration of the reduction in strength;
represents the yield compressive stress of the wood fiber of the core material without considering the strength reduction;
Rσrepresents the ratio of the maximum tensile stress to the maximum compressive stress of the wood fibers of the core material;
the stress-strain relationship of the cross section of the core material in the case where the wood fiber of the compressed core material reached the ultimate compressive strain to cause failure was calculated as follows:
<mrow> <mfrac> <msub> <mi>x</mi> <mrow> <mi>c</mi> <mi>p</mi> </mrow> </msub> <mrow> <msub> <mi>x</mi> <mi>c</mi> </msub> <mo>-</mo> <msub> <mi>x</mi> <mrow> <mi>c</mi> <mi>p</mi> </mrow> </msub> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <msubsup> <mi>&epsiv;</mi> <mrow> <mi>c</mi> <mi>u</mi> </mrow> <mi>w</mi> </msubsup> <mo>-</mo> <msubsup> <mi>&epsiv;</mi> <mrow> <mi>c</mi> <mi>y</mi> </mrow> <mi>w</mi> </msubsup> </mrow> <msubsup> <mi>&epsiv;</mi> <mrow> <mi>c</mi> <mi>y</mi> </mrow> <mi>w</mi> </msubsup> </mfrac> <mo>=</mo> <msub> <mi>&gamma;</mi> <mi>&epsiv;</mi> </msub> </mrow>
wherein:represents the ultimate compressive strain of the wood fibers of the core material;
γεrepresents a ratio of ultimate plastic strain to elastic strain of the wood fiber of the core material;
when the rib is a CFRP rib, calculating the stress-strain relationship of the cross section of the core material under the condition that the CFRP rib reaches the ultimate strength and causes damage according to the following formula:
<mrow> <mfrac> <msubsup> <mi>&epsiv;</mi> <mrow> <mi>t</mi> <mi>u</mi> </mrow> <mi>F</mi> </msubsup> <msubsup> <mi>&epsiv;</mi> <mrow> <mi>c</mi> <mi>y</mi> </mrow> <mi>w</mi> </msubsup> </mfrac> <mo>=</mo> <mfrac> <msubsup> <mi>&sigma;</mi> <mrow> <mi>t</mi> <mi>u</mi> </mrow> <mi>F</mi> </msubsup> <mrow> <msub> <mi>&alpha;</mi> <mi>E</mi> </msub> <msubsup> <mi>&sigma;</mi> <mrow> <mi>c</mi> <mi>y</mi> </mrow> <mi>w</mi> </msubsup> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <msub> <mi>h</mi> <mn>0</mn> </msub> <mo>-</mo> <msub> <mi>x</mi> <mi>c</mi> </msub> </mrow> <mrow> <msub> <mi>x</mi> <mi>c</mi> </msub> <mo>-</mo> <msub> <mi>x</mi> <mrow> <mi>c</mi> <mi>p</mi> </mrow> </msub> </mrow> </mfrac> </mrow>
wherein:representing ultimate tensile strain in the CFRP tendon constitutive model;
representing ultimate tensile stress in the CFRP rib constitutive model;
αEexpressing the ratio of the elastic modulus of the CFRP rib to the elastic modulus of the core material;
when the reinforcement is a steel bar, calculating the stress-strain relationship of the cross section of the core material under the condition that the steel bar is subjected to yield and the wood fiber of the core material is broken and cracked to cause damage according to the following formula:
<mrow> <mfrac> <msubsup> <mi>&epsiv;</mi> <mrow> <mi>t</mi> <mi>u</mi> </mrow> <mi>w</mi> </msubsup> <msubsup> <mi>&epsiv;</mi> <mrow> <mi>c</mi> <mi>y</mi> </mrow> <mi>w</mi> </msubsup> </mfrac> <mo>=</mo> <mfrac> <msubsup> <mi>&sigma;</mi> <mrow> <mi>t</mi> <mi>u</mi> </mrow> <mi>w</mi> </msubsup> <msubsup> <mi>&sigma;</mi> <mrow> <mi>c</mi> <mi>y</mi> </mrow> <mi>w</mi> </msubsup> </mfrac> <mo>=</mo> <mfrac> <mrow> <msub> <mi>h</mi> <mn>0</mn> </msub> <mo>-</mo> <msub> <mi>x</mi> <mi>c</mi> </msub> </mrow> <mrow> <msub> <mi>x</mi> <mi>c</mi> </msub> <mo>-</mo> <msub> <mi>x</mi> <mrow> <mi>c</mi> <mi>p</mi> </mrow> </msub> </mrow> </mfrac> <mo>.</mo> </mrow>
5. the method for calculating the ultimate bearing capacity of the normal section of the reinforced core beam by the bar planting method according to claim 4, wherein the method comprises the following steps: in the step (3), calculating the height of the compression area of the cross section of the core material under the condition that each material is damaged comprises the following steps: the method comprises calculating the height x of the pressure zone of the cross section of the core material when the wood fiber of the core material under tension is broken, when the wood fiber of the core material under compression reaches the ultimate compressive strain to cause breakage, when the CFRP bar is a CFRP bar and reaches the ultimate strength to cause breakage, when the bar is a steel bar and when the wood fiber of the core material is broken and cracked to cause breakage, according to the following formulac：
<mrow> <msub> <mi>&Sigma;F</mi> <mi>i</mi> </msub> <mo>=</mo> <msubsup> <mo>&Integral;</mo> <mrow> <mo>-</mo> <mi>h</mi> <mo>/</mo> <mn>2</mn> </mrow> <mrow> <mi>h</mi> <mo>/</mo> <mn>2</mn> </mrow> </msubsup> <msup> <mi>&sigma;</mi> <mi>w</mi> </msup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>c</mi> </msub> <mo>)</mo> </mrow> <mi>b</mi> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>c</mi> </msub> <mo>)</mo> </mrow> <msub> <mi>dx</mi> <mi>c</mi> </msub> <mo>+</mo> <msubsup> <mi>&sigma;</mi> <mi>t</mi> <mi>F</mi> </msubsup> <msup> <mi>A</mi> <mi>F</mi> </msup> <mo>=</mo> <mn>0</mn> </mrow>
Wherein: fiRepresenting the internal forces of the respective materials or components;
h represents the height of the cross section of the core material;
σw(xc) Height x of compression zone representing cross section of core materialcStress of wood fibers;
b(xc) Height x of compression zone representing cross section of core materialcThe cross-sectional width of;
representing the tensile stress of the tensile reinforcement material;
AFindicating the area of the reinforcing material in tension.
6. The method for calculating the ultimate bearing capacity of the normal section of the reinforced core beam by the bar planting method according to claim 5, wherein the method comprises the following steps: the step (4) comprises the following steps:
and (3) calculating the normal section bending bearing capacity of the reinforcing core beam under the condition of damage of each material according to the following formula:
<mrow> <mi>M</mi> <mo>=</mo> <msubsup> <mi>&sigma;</mi> <mrow> <mi>c</mi> <mi>y</mi> </mrow> <mi>w</mi> </msubsup> <mi>b</mi> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mrow> <mi>c</mi> <mi>p</mi> </mrow> </msub> <mo>(</mo> <mrow> <msub> <mi>x</mi> <mi>c</mi> </msub> <mo>-</mo> <mfrac> <msub> <mi>x</mi> <mrow> <mi>c</mi> <mi>p</mi> </mrow> </msub> <mn>2</mn> </mfrac> </mrow> <mo>)</mo> <mo>+</mo> <mfrac> <mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>c</mi> </msub> <mo>-</mo> <msub> <mi>x</mi> <mrow> <mi>c</mi> <mi>p</mi> </mrow> </msub> <mo>)</mo> </mrow> <mn>3</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mi>h</mi> <mo>-</mo> <msub> <mi>x</mi> <mi>c</mi> </msub> <mo>)</mo> </mrow> <mn>3</mn> </msup> </mrow> <mrow> <mn>3</mn> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>c</mi> </msub> <mo>-</mo> <msub> <mi>x</mi> <mrow> <mi>c</mi> <mi>p</mi> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <mrow> <msub> <mi>&alpha;</mi> <mi>E</mi> </msub> <msubsup> <mi>&sigma;</mi> <mrow> <mi>c</mi> <mi>y</mi> </mrow> <mi>w</mi> </msubsup> <msup> <mi>A</mi> <mi>F</mi> </msup> <msup> <mrow> <mo>(</mo> <mi>h</mi> <mo>-</mo> <msub> <mi>x</mi> <mi>c</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> <mrow> <msub> <mi>x</mi> <mi>c</mi> </msub> <mo>-</mo> <msub> <mi>x</mi> <mrow> <mi>c</mi> <mi>p</mi> </mrow> </msub> </mrow> </mfrac> </mrow>
wherein: m represents the bending bearing capacity of the normal section of the reinforced core beam;
b represents the width of the cross section of the core material;
xcaccording to x in the corresponding damage situation in step (3) respectivelycValue calculation;
xcpaccording to x in the corresponding damage situation in step (3) respectivelycpAnd (5) value calculation.
7. The method for calculating the ultimate bearing capacity of the normal section of the reinforced core beam by the bar planting method according to claim 1, wherein the method comprises the following steps: the step (4) further comprises: taking the minimum value of the flexural bearing capacity of the normal section of the reinforcing core beam under the condition of failure of each material as the limit bearing capacity of the normal section of the reinforcing core beam considering the plastic development.
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