CN107563049B - Design method of steel fiber recycled concrete beam - Google Patents
Design method of steel fiber recycled concrete beam Download PDFInfo
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Abstract
The invention belongs to the technical field of building design structures, particularly relates to a design method of a steel fiber recycled concrete beam, and mainly aims to provide a brand-new design structure method of the steel fiber recycled concrete, effectively overcome the technical problems of easy cracking and poor rigidity of the recycled concrete, and provide a design method of the steel fiber recycled concrete beam, wherein the design method of the steel fiber recycled concrete beam comprises the following steps: 1. determining the section width b and the section height h, 2 of the designed reinforced steel fiber recycled concrete beam, and determining the reinforcement ratio of the reinforced steel fiber recycled concrete beamρ Mu Value, 3. determining the deflection of the reinforced steel fiber recycled concrete beamf4, checking and calculating cracking; 5. checking and calculating the width of the crack; the structural design method not only effectively overcomes the technical problems of easy cracking and poor rigidity of the recycled concrete, but also effectively ensures the structural stability of the steel fiber recycled concrete, and is also effectively applied to the weighed or non-weighed structural beam.
Description
The technical field is as follows:
the invention belongs to the technical field of building design structures; in particular to a design method of a steel fiber recycled concrete beam.
Background art:
the recycled concrete is new concrete prepared by crushing, cleaning and grading waste concrete blocks, mixing the crushed, cleaned and graded concrete blocks with a grading agent according to a certain proportion, partially or completely replacing natural aggregates (mainly coarse aggregates) such as sand stones and the like, and then adding cement, water and the like; the recycled concrete can be combined into aggregates in the following cases: all aggregates are regenerated aggregates; the coarse aggregate is regenerated aggregate, and the fine aggregate is natural sand; the coarse aggregate is natural gravel or cobble, and the fine aggregate is regenerated aggregate; the regenerated aggregate replaces part of coarse aggregate or fine aggregate; the recycled concrete is an effective means for treating construction waste, however, the recycled concrete is mainly applied to non-bearing structures at present, the structural stability is poor, and particularly the technical problems that the recycled concrete is easy to crack and poor in rigidity cannot be effectively guaranteed in the design process of the steel fiber recycled concrete are solved, so that the construction engineering technology specially used for designing the steel fiber recycled concrete is very necessary.
The invention content is as follows:
the invention aims to:
the method is mainly used for providing a brand new structural design method for the steel fiber recycled concrete, not only effectively solving the technical problems of easy cracking and poor rigidity of the recycled concrete, but also effectively ensuring the structural stability of the steel fiber recycled concrete, and the steel fiber recycled concrete structure designed by the method can be effectively applied to a weighed or unweighted structural beam, and the steel fiber recycled concrete beam structure designed by the structural method also effectively meets various performance indexes of beam body structural design, so that a brand new design concept is opened for the design of the steel fiber recycled concrete structure.
The technical scheme of the invention is as follows:
a method for designing a steel fiber recycled concrete beam is provided, the steel fiber recycled concrete beam
The design method of the soil beam comprises the following steps:
(1) preliminarily determining the section height h of the reinforced steel fiber recycled concrete beam according to the high span ratio empirical value of the common reinforced concrete beam, and determining the protective layer thickness α of the longitudinal tension steel bar according to the environment type of the reinforced steel fiber recycled concrete beamsThereby obtaining the effective section height h of the designed reinforced steel fiber recycled concrete beam0＝h-αs(ii) a Determining the section width b of the designed reinforced steel fiber recycled concrete beam according to the empirical value of the width-to-height ratio of the beam section;
(2) determining the reinforcement ratio rho of the reinforced steel fiber recycled concrete beam according to the bearing capacity limit stateMuValue, determining the reinforcement ratio rho of the reinforced steel fiber recycled concrete beam in the limit state of carrying out bearing capacityMuWhen the value is measured, firstly, the tensile stress effect of the steel fiber recycled concrete in the tension area of the section is considered, and the height x of the compression area is obtained according to the bending moment balance of the sectionMuThe specific calculation procedure of the value is as followsThe following formula (1):
in the formula (1), MuThe coefficient is a bending moment design value, α is a conversion coefficient of a stress value of an equivalent rectangular stress diagram, and is 0.87 when the strength grade does not exceed C45, β is a height conversion coefficient of a compression area of the equivalent rectangular stress diagram, and is 0.73 when the strength grade does not exceed C45, ffrcThe design value of the axial compressive strength of the steel fiber recycled concrete is obtained; sigmafrtThe equivalent tensile stress of the steel fiber recycled concrete in the tension zone of the flexural member and the replacement rate of the rest recycled aggregateRAnd the characteristic mixing amount lambda of the fiberfIn this regard, it is calculated by the formula (2) based on the test result of the reinforced steel fiber recycled concrete beam.
σfrt＝(1-0.798R)(1+4.791λf)ft(2) Formula (II)
In the formula (2), ftThe tensile strength of the common concrete is the same as the tensile strength of the steel fiber recycled concrete.
From the balance of the cross-sectional forces:
(3) checking and calculating the deflection; obtaining the deflection f value of the reinforced steel fiber recycled concrete beam according to the material mechanics theory and experimental analysis; when the deflection f value of the reinforced steel fiber recycled concrete beam is calculated, the adopted deflection f solves the formula:
in the formula (3), S is the load and support condition coefficient, M is the use load, l is the calculated span, αfrcβ is the influence coefficient of the replacement rate of recycled aggregate on the short-term rigidity of the steel fiber recycled concrete beamfrcα is the influence coefficient of steel fiber on the short-term rigidity of the recycled concrete beamfrcAnd βfrcRespectively-0.3284 and 0.04652. B is the same cross sectionAnd the short-term stiffness of the reinforced concrete reference beam at the strength level; f. ofbIs an allowable deflection value.
(4) Checking and calculating the cracking; cracking bending moment M for the reinforced steel fiber recycled concrete beamfrcrChecking and calculating; the cracking bending moment M of the reinforced steel fiber recycled concrete beamfrcrThe following formula (4) is adopted when the detection calculation is carried out,
Mfrcr＝[(2.452+0.686R)×(0.6728-0.1496λf)]Wfr0[ft(1-0.2776R+0.8139λf)]
in the formula (4), the reaction mixture is,
wherein
Where A isSArea of longitudinal tension bar at bottom of concrete beam regenerated by steel fiber and αEIs the ratio of the modulus of elasticity of the steel bar and the concrete.
(5) Checking and calculating the width of the crack; the maximum crack width w of the reinforced steel fiber recycled concrete beamfrmChecking and calculating; the maximum crack width w of the reinforced steel fiber recycled concrete beamfrmIn the process of detection and calculation, a formula is adopted:
in formula (5), αcr、ψ、σs、Es、deq、ρteThe meaning and calculation of (A) are the same as the item of concrete structure design Specification (7.1.2).
2. The method of designing a steel fiber recycled concrete beam according to claim 1, wherein: other structures of the steel fiber recycled concrete beam meet the requirements of concrete structure design specifications.
The invention has the beneficial effects that:
the structural design method of the steel fiber recycled concrete provided by the invention not only effectively overcomes the technical problems of easy cracking and poor rigidity of the recycled concrete, but also effectively ensures the structural stability of the steel fiber recycled concrete, and the steel fiber recycled concrete structure designed by the structural design method can be effectively applied to a weighed or unweighted structural beam, and the steel fiber recycled concrete beam structure designed by the structural design method also effectively meets various performance indexes of the structural design of a beam body, thereby opening a brand new design concept for the design of the steel fiber recycled concrete structure.
The specific implementation mode is as follows:
the design is illustrated by a concrete structural design of the steel fiber recycled concrete with a specific structural data;
the span l of the simple support beam with the rectangular section of the known steel bar fiber recycled concrete is 3m, and the width l is calculated0The design bending moment is 50kN m, 2.7 m. Quasi-permanent value coefficient psi of live loadq0.5, regenerating concrete with C45 steel fiber, selecting and cutting bow steel fiber, |f35mm, nominal diameter df0.55mm, tensile strength is more than or equal to 1345N/mm2. The mechanical property index of the steel fiber recycled concrete is obtained by tests, and only the replacement rate of recycled aggregate is givenR50% by volume of steel fiber ρf1.5% (in this case,
) Under the condition, the mechanical property indexes of the C45 steel fiber recycled concrete are as follows: standard value f of compressive strength of axis of steel fiber recycled concretefrck46MPa, standard value f of tensile strength of axle center of steel fiber recycled concretefrtk5.22MPa, designed axial compressive strength f of steel fiber recycled concretefrc32.9MPa, the design value f of the tensile strength of the axle center of the steel fiber recycled concretefrt3.73MPa, modulus of elasticity E of steel fiber recycled concretefrc3.38 GPa; the strength design value fy of the HRB400 steel bar is 360MPa, and the elastic modulus E of the HRB400 steel barf20 GPa; the limit value of the crack width is 0.5mm, the limit value of mid-span deflection is l/200, and the appropriate beam section size and reinforcing bars are selected by trial.
(1) Determination of initial size of cross section and calculation of internal force
When h is 300mm, b is 150mm, as is 25mm, h is0＝275mm。
The design bending moment M is 50 kN.m.
(2) Determining reinforcement ratio rho under limit state of bearing capacityMu
Obtaining the height x of the compression zone according to the balance of the bending moment of the cross sectionMuThe value:
looking up the concrete structure design Specification Table 4.1.4-2, the designed value f of the C45 concrete axial tensile strength can be obtainedt1.8MPa, then
σfrt＝(1-0.798×0.5)(1+4.791×0.945)×1.8＝5.98MPa (1)
xMuAccording to the calculation formula, the following results are obtained: x is the number ofMu＝86.09mm (2)
From the balance of the cross-sectional forces:
HRB 400-grade steel bars are selected as the bottom tensioned longitudinal bars and the press area erection bars, and HPB 335-grade steel bars are adopted as the stirrups
2 HRB400 steel bars with the diameter of 16mm are selected as bottom longitudinal tension steel bars, the actual reinforcement ratio of the bottom tension steel bars is 0.89% to 0.48%, the diameter of the stirrups is 8mm, the longitudinal distance of the stirrups is 150mm, and the thickness of the protective layer is 25 mm. Meanwhile, the steel fiber reinforced concrete beam is designed by considering other structural requirements of concrete structure design specifications. The test was carried out and the ultimate bearing capacity was found to be 55.32kN m >50kN m.
(3) Checking deflection
The bending moment M corresponding to the use load between 0.2Mu and 0.7Mu is selected, the deflection of the beam is checked by adopting the formula (3), the calculated value and the measured value are shown in the table 1, and obviously, under the normal use load, the deflection value is less than the allowable deflection value l/200, namely 2700/200, namely 13.5 mm.
TABLE 1 calculation and actual measurement of deflection of steel fiber recycled concrete beams
(4) Checking calculation of cracking
Mfrcr＝[(2.452+0.686R)(0.6728-0.1496λf)]Wfr0[ft(1-0.2776R+0.8139λf)]＝8.88kN·m
The observed value was 8.30kN · m, which substantially corresponds to the calculated value.
(5) Checking calculation of crack width
As＝25mm、R＝50％、λfα, 1.5%, available from concrete structural design Specificationscr＝1.9、deq＝16mm、ρte1.79%, the other main parameters calculated are shown in table 2, wherein σsCalculating the longitudinal tensile common steel bar stress of the steel fiber recycled concrete beam under the load according to 7.1.4 bars of concrete structure design Specification; psi is the uneven coefficient of the longitudinal tension steel bar strain among the cracks, and the calculation is carried out according to the concrete structure design specification 7.1.2-2 hours. Selecting a bending moment M corresponding to the use load between 0.2Mu and 0.7Mu, checking and calculating the width w of the crack of the beam by adopting a formula (4), wherein the calculated value and the measured value are shown in a table 2, and obviously, the calculated value and the measured value are well matched and are all less than the limit of 0.5 mm.
TABLE 2 comparison of calculated and measured values of crack widths of steel fiber recycled concrete beams
| M | σs | ψ | Measured of w | w calculation |
| 13.5 | 140.36 | 0.45 | 0.03 | 0.04 |
| 27 | 280.73 | 0.77 | 0.12 | 0.14 |
| 31.5 | 327.52 | 0.82 | 0.13 | 0.17 |
| 40.5 | 421.09 | 0.88 | 0.18 | 0.23 |
Claims (2)
1. A design method of a steel fiber recycled concrete beam is characterized by comprising the following steps: the design method of the steel fiber recycled concrete beam comprises the following steps:
(1)、according to the empirical value of the high span ratio of the common reinforced concrete beam, the section height h of the reinforced steel fiber recycled concrete beam is preliminarily determined, and the protective layer thickness α of the longitudinal tension steel bar is determined according to the type of the environment where the reinforced steel fiber recycled concrete beam is locatedsThereby obtaining the effective section height h of the designed reinforced steel fiber recycled concrete beam0＝h-αs(ii) a Determining the section width b of the designed reinforced steel fiber recycled concrete beam according to the empirical value of the width-to-height ratio of the beam section;
(2) determining the reinforcement ratio rho of the reinforced steel fiber recycled concrete beam according to the bearing capacity limit stateMuValue, determining the reinforcement ratio rho of the reinforced steel fiber recycled concrete beam in the limit state of carrying out bearing capacityMuWhen the value is measured, firstly, the tensile stress effect of the steel fiber recycled concrete in the tension area of the section is considered, and the height x of the compression area is obtained according to the bending moment balance of the sectionMuThe specific calculation procedure for the value is as follows:
in the above formula, MuThe coefficient is a bending moment design value, α is a conversion coefficient of a stress value of an equivalent rectangular stress diagram, and is 0.87 when the strength grade does not exceed C45, β is a height conversion coefficient of a compression area of the equivalent rectangular stress diagram, and is 0.73 when the strength grade does not exceed C45, ffrcThe design value of the axial compressive strength of the steel fiber recycled concrete is obtained; sigmafrtThe equivalent tensile stress of the steel fiber recycled concrete in the tension zone of the flexural member and the replacement rate of the rest recycled aggregateRAnd the characteristic mixing amount lambda of the fiberfIn relation to the above, according to the test result of the reinforced steel fiber recycled concrete beam, it is calculated by formula (2);
σfrt＝(1-0.798R)(1+4.791λf)ftformula (2)
In the formula (2), ftThe design value of the tensile strength of the common concrete is the same as the strength grade of the steel fiber recycled concrete;
from the balance of the cross-sectional forces:
(3) checking and calculating the deflection; obtaining the deflection f value of the reinforced steel fiber recycled concrete beam according to the material mechanics theory and experimental analysis; when the deflection f value of the reinforced steel fiber recycled concrete beam is calculated, the adopted deflection f solves the formula:
in the formula (3), S is the load and support condition coefficient, M is the use load, l is the calculated span, αfrcβ is the influence coefficient of the replacement rate of recycled aggregate on the short-term rigidity of the steel fiber recycled concrete beamfrcα is the influence coefficient of steel fiber on the short-term rigidity of the recycled concrete beamfrcAnd βfrc-0.3284 and 0.04652, respectively; b is the short-term rigidity of the reinforced concrete reference beam with the same section and strength grade; f. ofbIs an allowable deflection value;
(4) checking and calculating the cracking; cracking bending moment M for the reinforced steel fiber recycled concrete beamfrcrChecking and calculating; the cracking bending moment M of the reinforced steel fiber recycled concrete beamfrcrThe following formula is adopted when the detection calculation is carried out,
Mfrcr＝[(2.452+0.686R)×(0.6728-0.1496λf)]Wfr0[ft(1-0.2776R+0.8139λf)]
in the above formula, the first and second carbon atoms are,
wherein
Where A isSArea of longitudinal tension bar at bottom of concrete beam regenerated by steel fiber and αEThe ratio of the elastic modulus of the steel bar to the concrete;
(5) checking and calculating the width of the crack; the maximum crack width w of the reinforced steel fiber recycled concrete beamfrmChecking and calculating; the reinforcing steel fiber is regeneratedMaximum crack width w of concrete beamfrmIn the process of detection and calculation, a formula is adopted:
in formula (5), αcr、ψ、σs、Es、deq、ρteThe meaning and calculation of (A) are the same as the item of concrete structure design Specification (7.1.2).
2. The method of designing a steel fiber recycled concrete beam according to claim 1, wherein: other structures of the steel fiber recycled concrete beam meet the requirements of concrete structure design specifications.
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| CN109632219A (en) * | 2018-12-26 | 2019-04-16 | 启迪设计集团股份有限公司 | The test method of armored concrete beam deflection |
| CN109914691A (en) * | 2019-02-25 | 2019-06-21 | 河海大学 | Bamboo-steel fiber reinforced concrete combination beam |
| CN109781501B (en) * | 2019-03-12 | 2020-04-07 | 西南交通大学 | Method for calculating crack width of steel bar-steel fiber concrete shield segment |
| CN111220467B (en) * | 2020-03-11 | 2020-11-13 | 中铁科学研究院有限公司 | Method for measuring normal section bearing capacity and reinforcing bar of steel bar-steel fiber concrete shield segment |
| CN111797449B (en) * | 2020-05-28 | 2021-11-02 | 广西交科集团有限公司 | Method for judging reasonable height of layered pouring concrete beam |
| CN112069578B (en) * | 2020-09-01 | 2023-12-26 | 武汉工程大学 | Method and device for processing cracking bending moment data of regenerated concrete beam and storage medium |
| CN116383594B (en) * | 2023-04-06 | 2023-09-01 | 安徽吾兴新材料有限公司 | Method for calculating maximum crack width of high-strength reinforced concrete flexural member |
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