CN114266098A - Calculation method for collapse load power increase coefficient of prestressed BFRP (bidirectional reinforced concrete) reinforced concrete frame - Google Patents
Calculation method for collapse load power increase coefficient of prestressed BFRP (bidirectional reinforced concrete) reinforced concrete frame Download PDFInfo
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Abstract
The invention discloses a calculation method for a collapse load power increase coefficient of a prestressed BFRP (bidirectional Forwarding-reinforced concrete) reinforced concrete frame, and belongs to the technical field of engineering structures. The invention provides a calculation method of a collapse load power increase coefficient DIF and a simplified calculation model of the DIF based on an energy conservation principle and combined with the damage characteristic of a prestressed BFRP rib. Based on a calculation model of the DIF, the value of the static collapse load power increase coefficient DIF can be determined by predicting the vertical displacement of the corresponding structural part after the frame column of the type fails, and the collapse load adopted in the static collapse analysis is the product of the static collapse load and the DIF. The method can provide direct basis for the static collapse analysis of the prestressed BFRP reinforced concrete frame.
Description
Technical Field
The invention belongs to the technical field of engineering structures, and particularly relates to a calculation method for a collapse load power increase coefficient of a prestressed BFRP (bidirectional Forwarding-reinforced concrete) reinforced concrete frame.
Background
Reinforced concrete frame structures have been widely used throughout the world. The reinforced concrete frame structure has the advantages of good structural integrity, convenient construction, lower price and the like, but the reinforced concrete frame structure is easily influenced by environmental corrosion and sudden disasters, so that more and more early building structures are aged and damaged, and the problems of high cost and the like of maintaining and reinforcing the building structures are increasingly obvious. How to reduce the maintenance cost and improve the utilization rate of novel materials becomes a problem to be solved urgently in the current building structure. The Fiber Reinforced Plastic (FRP) has the advantages of high strength, corrosion resistance, light weight and the like, and is an ideal material for replacing the steel bar in the existing reinforced concrete structure. Basalt Fiber (BFRP) is one of the commonly used fiber materials, and has a thermal expansion coefficient close to that of concrete, and excessive temperature stress is not generated between the two. However, due to the low modulus of elasticity of the BFRP bead, it is generally necessary to prestress the BFRP bead to play its main role. At present, BFRP reinforced concrete structures have been applied to some pilot engineering structures.
The load bearing columns of concrete frame structures may fail in the event of an explosion, fire, earthquake, etc., thereby causing partial or total collapse damage to the structure. Prestressed BFRP concrete frame structures are also at risk of collapse damage, and their resistance to progressive collapse is still less studied at present. When the frame structure is designed to resist collapse, a column drawing method and other static collapse analysis methods are often adopted. However, the collapse process of the structure is a dynamic process, and the dynamic impact effect cannot be reflected when the static collapse analysis is carried out, so that the collapse load needs to be corrected to reflect the influence of the dynamic impact effect.
Disclosure of Invention
The invention aims to solve the problems in the prior art and provides a scientific and reasonable dereferencing method for the collapse load increase coefficient in the static collapse analysis of a prestressed BFRP (bidirectional Forwarding-reinforced concrete) reinforced concrete frame, which has high accuracy and good applicability. The invention particularly provides a calculation method of a collapse load dynamic increasing coefficient DIF, and provides a simplified calculation model, which provides a basis for correcting a collapse load during static collapse analysis of a prestressed BFRP reinforced concrete frame.
In order to achieve the purpose, the technical scheme of the invention is as follows:
the calculation method of the collapse load power increase coefficient of the prestressed BFRP reinforced concrete frame comprises the following steps:
(1) calculating the total elongation delta L of the central shaft of the frame beam, calculating the strain epsilon of the central shaft of the frame beam at the beam end of the side column, and calculating the strain increment delta epsilon of the prestressed BFRP rib at the bottom of the beam end according to the similar triangle principleB1And the strain increment delta epsilon of the beam-end top prestress BFRP ribB2;
(2) Calculating the prestress increment delta sigma of the beam bottom prestress BFRP rib at the beam end of the side column1Prestress increment delta sigma of beam top prestress BFRP rib2Calculating the beam end bending moment M according to the initial prestress and the increment thereof, and calculating the vertical displacement delta of the failure columnsCalculating the corner theta of the end section of the side column beam from the net span L of the frame beamsAccording to the angle theta of the cross section of the end of the side column beamsAnd the beam end bending moment M is used for solving the total work W of the bending moment M at the beam ends of the two side columns of the frame beamM;
(3) The total work W is done according to the bending moments of the beam ends of two side columns of the frame beamMCalculating the equivalent dynamic load P of the total external force by doing work with the load P of the failure columnd,eq;
(4) The total work W is done according to the bending moments of the beam ends of two side columns of the frame beamMCalculating total equivalent static load P with vertical load P of failure columns;
(5) According to equivalent dynamic load Pd,eqAnd total equivalent dead load PsAnd calculating a collapse load power increase coefficient DIF, and multiplying the design collapse load of the structure by the DIF to obtain a collapse load correction value considering the impact influence of load power.
Further, the total elongation delta L of the central shaft of the frame beam in the step (1),Strain epsilon of frame beam central shaft at side column beam end and strain increment delta epsilon of beam bottom prestress BFRP ribB1And the strain increment delta epsilon of the beam top prestress BFRP ribB2Respectively according to the following formula:
in the formula,. DELTA.sIs the vertical displacement of the failure column caused by the load P; l is the clear span of the frame beam; h is the section height of the frame beam; e is the distance from the center of gravity of the prestressed BFRP rib to the neutral axis of the beam section; lbTaking (1.5-2.0) hours for the length of the damaged section of the frame beam end.
Further, in the step (2), the prestress increment delta sigma of the bottom prestress BFRP rib at the beam end of the side column1Prestress increment delta sigma of prestressed BFRP web at beam top2Beam end bending moment M, side column beam end section corner thetasAnd total work W made by bending moments M at two side column beam ends of the frame beamMRespectively according to the following formula:
Δσ1=ΔεB1e (formula 5)
Δσ2=ΔεB2E (formula 6)
In the formula, E is the elastic modulus of the prestressed BFRP rib; a. the1The total cross-sectional area of the prestressed BFRP rib at the bottom of the beam is shown; a. the2The total cross-sectional area of the prestressed BFRP rib at the top of the beam is shown, when the prestressed BFRP rib is arranged on the beam bottom only, A2=0;σ01And σ02Initial prestressing of the bottom and top prestressed BFRP-ribs of the beam, respectively.
Further, the equivalent dynamic load P of the total external force in the step (3)d,eqCalculated according to the following formula:
further, the total equivalent static load P in the step (4)sCalculated according to the following formula:
further, the collapse load power increase coefficient DIF in the step (5) is calculated by the following formula
DIF=Ps/Pd,eq(formula 12).
Further, when calculating the DIF value of the concrete frame collapse load power increase coefficient, the following basic assumptions are made: firstly, all damages are concentrated at the beam ends, and the middle part of the beam is in an elastic working state; not considering the energy loss caused by concrete cracking; the work of the non-prestressed tendons at the end parts of the side columns and the beams in the collapse process is not considered; and fourthly, the ends of the frame beams close to the side columns have the same rotating angle.
The invention also provides a calculation model, and the calculation model is used for increasing the collapse load power of the prestressed BFRP reinforced concrete frameFitting the DIF value obtained by the coefficient calculation method, wherein the calculation model is DIF along with the flex span ratio deltasA calculation model of/L change, wherein a calculation formula of the calculation model is as follows:
the invention also provides a collapse load value taking method for performing static collapse analysis on the prestressed BFRP reinforced concrete frame by using the mathematical computation model, which comprises the following steps:
(1) setting the displacement limit value of the structure at the failure column to be delta'sCalculating flex span ratio delta's/L;
(2) Determination of Δ 'from (formula 13)'sDIF value corresponding to/L;
(3) and (3) during static collapse analysis, taking the product of the static collapse load and the DIF value calculated in the step (2) as the collapse load actually applied to the structure.
The invention provides a calculation method of a collapse load power increase coefficient DIF and a simplified calculation model of the DIF based on an energy conservation principle and combined with the damage characteristic of a prestressed BFRP rib. Based on a calculation model of the DIF, the value of the static collapse load power increase coefficient DIF can be determined by predicting the vertical displacement of the corresponding structural part after the frame column of the type fails, and the collapse load adopted in the static collapse analysis is the product of the static collapse load and the DIF. The method can provide direct basis for the static collapse analysis of the prestressed BFRP reinforced concrete frame.
The invention has the following beneficial effects:
(1) the invention considers the influence of the work done by the prestressed BFRP rib in the process of structure collapse and can more truly reflect the dynamic effect when the prestressed BFRP reinforced concrete frame structure collapses.
(2) The DIF calculation process of the prestressed BFRP reinforced concrete frame structure adopts a mechanical derivation process, and the proposed DIF mathematical calculation model provides a reliable basis for the anti-collapse risk control of the prestressed BFRP reinforced concrete frame.
Drawings
FIG. 1 is an overall schematic view of a prestressed BFRP concrete frame structure;
FIG. 2 is a schematic diagram of the deformation of a prestressed BFRP concrete frame substructure; notation in the figure: 1 is the clear span L of the frame beam, and 2 is the vertical displacement delta of the failure column s3 is a vertical load P of the failure column, 4 is a beam column joint detail part, 5 is a side column, and 6 is the failure column;
FIG. 3 is a detailed view of a side column beam end node in a prestressed BFRP reinforced concrete frame structure; notation in the figure: 7 is the strain increment delta epsilon corresponding to the beam bottom prestress BFRP rib B18 is the distance e from the center of gravity of the prestressed BFRP rib to the neutral axis of the beam section, and 9 is the corner theta of the beam end section of the side columnsAnd 10 is the prestress increment delta sigma of the prestressed BFRP rib at the bottom of the beam 111 is a beam bottom prestress BFRP rib, 12 is a beam section neutral axis, and 13 is the strain of a frame beam neutral axis at the end of a side column beamεAnd 14 is the strain increment delta epsilon corresponding to the top prestress BFRP rib of the beam end B215 is a beam top prestressed BFRP rib, 16 is a prestressed increment delta sigma of the beam top prestressed BFRP rib2;
FIG. 4 shows DIF and ΔsGraph of the/L relationship.
Detailed Description
The invention is further described with reference to the following figures and specific examples.
Examples
As shown in fig. 1, in this embodiment, a first-layer two-span substructure in a prestressed BFRP reinforced concrete frame structure is selected as a research object, and the calculation of the concrete frame collapse load dynamic increase coefficient DIF value includes the following steps:
the following basic assumptions are made prior to the calculation: firstly, all damages are concentrated at the beam ends, and the middle part of the beam is in an elastic working state; not considering the energy loss caused by concrete cracking; the work of the non-prestressed tendons at the end parts of the side columns and the beams in the collapse process is not considered; and fourthly, the ends of the frame beams close to the side columns have the same rotating angle.
The specific calculation steps are as follows:
(1) calculating the total elongation delta L of the central shaft of the frame beam, calculating the strain epsilon of the central shaft of the frame beam at the beam end of the side column, and calculating the strain increment delta epsilon of the prestressed BFRP rib at the bottom of the beam end according to the similar triangle principleB1And the strain increment delta epsilon of the beam-end top prestress BFRP ribB2(as shown in fig. 2), the calculation formula is as follows:
in the formula,. DELTA.sIs the vertical displacement of the failure column caused by the load P; l is the clear span of the frame beam; h is the section height of the frame beam; e is the distance from the center of gravity of the prestressed BFRP rib to the neutral axis of the beam section; lbTaking (1.5-2.0) hours for the length of the damaged section of the frame beam end.
(2) Calculating the prestress increment delta sigma of the beam bottom prestress BFRP rib at the beam end of the side column1Prestress increment delta sigma of beam top prestress BFRP rib2Calculating the beam end bending moment M according to the initial prestress and the increment thereof, and calculating the vertical displacement delta of the failure columnsCalculating the corner theta of the end section of the side column beam from the net span L of the frame beamsAccording to the angle theta of the cross section of the end of the side column beamsAnd the beam end bending moment M is used for solving the total work W of the bending moment M at the beam ends of the two side columns of the frame beamM(as shown in fig. 3), the calculation formula is as follows:
Δσ1=Δε11e (formula 5)
Δσ2=ΔδB2E (formula 6)
In the formula, E is the elastic modulus of the prestressed BFRP rib; a. the1The total cross-sectional area of the prestressed BFRP rib at the bottom of the beam is shown; a. the2The total cross-sectional area of the prestressed BFRP rib at the top of the beam is shown, when the prestressed BFRP rib is arranged on the beam bottom only, A2=0;σ01And σ02Initial prestressing of the bottom and top prestressed BFRP-ribs of the beam, respectively.
(3) The total work W is done according to the bending moments of the beam ends of two side columns of the frame beamMCalculating the equivalent dynamic load P of the total external force by doing work with the load P of the failure columnd,eqThe calculation formula is as follows:
(4) the total work W is done according to the bending moments of the beam ends of two side columns of the frame beamMCalculating total equivalent static load P with vertical load P of failure columnsThe calculation formula is as follows:
(5) according to equivalent dynamic load Pd,eqAnd total equivalent dead load PsCalculating DIF, wherein the calculation formula is as follows:
DIF=Ps/Ps,eq(formula 12).
In the embodiment, a large number of prestressed BFRP reinforced concrete frame structures are simulated through finite element software and extractedAnd (4) load and displacement relation data. Calculating corresponding DIF value according to the calculation method, and finally fitting DIF span ratio deltasA mathematical calculation model of the/L variation (as shown in FIG. 4), the model calculation formula is as follows:
in practical application, the implementation steps of the static collapse analysis by using the DIF of the invention are as follows:
(1) setting the displacement limit value of the structure at the failure column as delta, and calculating the bending span ratio delta/L;
(2) the DIF value corresponding to Δ/L is determined using (equation 13).
(3) And (3) during static collapse analysis, taking the product of the static collapse load and the DIF value calculated in the step (2) as the collapse load actually applied to the structure.
Although the present invention has been described with respect to the preferred embodiments, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.
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