CN101923024B - Method for determining elastic modulus and flexural rigidity of reinforced concrete beam with crack - Google Patents

Method for determining elastic modulus and flexural rigidity of reinforced concrete beam with crack Download PDF

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CN101923024B
CN101923024B CN2010102450103A CN201010245010A CN101923024B CN 101923024 B CN101923024 B CN 101923024B CN 2010102450103 A CN2010102450103 A CN 2010102450103A CN 201010245010 A CN201010245010 A CN 201010245010A CN 101923024 B CN101923024 B CN 101923024B
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China
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reinforced concrete
value
modulus
reinforced
elastic modulus
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CN2010102450103A
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Chinese (zh)
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CN101923024A (en
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何晓婷
孙俊贻
许劲
郑周练
胡兴健
朱海桥
宁全润
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重庆大学
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Abstract

The invention discloses a method for determining the elastic modulus and flexural rigidity of a reinforced concrete beam with a crack, relating to a tension Young's elastic modulus of a reinforced concrete beam with a crack in working, a measuring method of the tension Young's elastic modulus and a determining method of the flexural rigidity. A reinforced concrete beam with a rectangular cross section is manufactured as a test piece to be detected, and the length, width and height of the reinforced concrete beam are shown in the specification; the two ends of the test piece are supported by hinged supports; loads are intensively and symmetrically applied on the positions some distance away from at two points of the supports; the deflection value of the middle part of the test piece span and the strain value of the lowest end of the middle part of the test piece span are detected; a sum computed expression is deduced according to the analytic solution which is given by at theory of different tension-compression modulus under the condition that loading is performed on two points of a simple beam with a rectangular section intensively and symmetrically; and the sum can be accurately calculated by the load value, the defection value and the strain value. The sum determined by the invention contains a crack factor of the reinforced concrete beam within the given load range, and can be used for structural mechanic accurate analysis.

Description

A kind of definite band splits the method for reinforced beam elastic modulus and bendind rigidity
Technical field
The present invention relates with cracks work reinforced concrete beams tensile Young's modulus and compression Young's modulus The measuring method of as well as flexural stiffness method for determining.
Background technology
Adopt the precast reinforced concrete beam load test, measure its Young's modulus of elasticity and bendind rigidity, the reinforced concrete structure design theory is had directive significance.At present, the elastic modulus of reinforced beam is measured and the confirming of bendind rigidity, great majority based on classics etc. modulus elasticity theory, promptly under the identical tension and compression stress of absolute value, material will produce the identical tension and compression strain of absolute value.Lot of test and research show that material under absolute value identical tension or action of compressive stress different stretching strain of absolute value and compressive strain can take place, and promptly material has the nonlinear characteristic of tension and compression different modulus.Growing along with science and technology, to researching and proposing of the mechaanical property of materials higher requirement, the potentiality of development new material and excavated material self-characteristic become new research trend.Most engineering structure ubiquity the tension and compression different modulus Elasticity characteristic of material, especially as pottery, organic glass, reinforced concrete etc.The Elasticity character that material has the tension and compression different modulus is nonlinear problem (bilinearity) in essence.If in the engineering structure design this nonlinear characteristic of material is downplayed, still continue to use modulus elasticity theory such as classical, can cause the error of calculation excessive because of constitutive relation does not meet in some cases, this might be the real hidden danger of structural failure.In fact, most of reinforced concrete works structures are in band crackle duty, especially reinforced beam usually, and this moment, the different Young's modulus of elasticity characteristics of tension and compression of member were particularly outstanding.Therefore, still continue to use modulus elasticity theory such as classical and confirm that band splits the bendind rigidity of reinforced beam, certainly will cause the excessive error of calculation, be unfavorable for the appropriate design of engineering structure.
Summary of the invention
To adopt modulus elasticity theory such as classical to confirm that band splits the deficiency of reinforced beam bendind rigidity in order overcoming, to the invention provides a kind of band and split the measuring method of the different Young'ss modulus of elasticity of reinforced beam tension and compression and definite method of bendind rigidity.The different Young'ss modulus of elasticity of tension and compression that this method is measured comprised the cracking factor of reinforced beam in giving the constant load scope, thereby determined bendind rigidity are applicable to the reinforced beam of band crackle work.Thereby solved in the reinforced concrete structure design theory major issue of generally being concerned about.
The objective of the invention is to realize like this:
Make one longly be , wide for , high rectangular reinforced concrete beam for ; As test specimen to be detected, wherein .The hinged-support supporting is taked at the two ends of test specimen; And locate 2 concentrated symmetrical load applications apart from bearing , as shown in Figure 1.Measure the deflection value at test specimen span middle part; And the strain value of test specimen span middle part lowermost end, as shown in Figure 2.The square-section free beam that provides according to tension and compression different modulus theory is concentrated the analytic solution of symmetry under loading at 2; Derive the calculation expression of different Young'ss modulus of elasticity of reinforced beam tension and compression and bendind rigidity; By payload values , deflection value , strain value , just can accurately calculate tension and compression Young's modulus of elasticity value and bendind rigidity value.
Theoretical according to the small deflection plain bending of shallow beam, free beam is under load action, and beam can deflection, and is in the bottom and is drawn and the stress of upper portion pressurized, is neither drawn also the not neutral line of pressurized thereby form.If by modulus elasticity theory such as classical, this neutral line is positioned at half eminence of xsect just.Yet if consider that the elastic modulus of structured material when stretching and compress of formation beam is inequality, neutral line no longer is positioned at xsect half eminence so, but on certain height that is not located on the cross section according to the tension and compression elastic mould value, is shown below:
(1a,b)
Wherein, expression cross section under tension height; expression pressurized depth of section; and representes the tension and compression Young's modulus of elasticity of member respectively, and the unit of each amount adopts International System of Units.Simultaneously, the bendind rigidity of beam can be expressed as
or (2a, b)
According to different modulus elasticity theory (C.A. A Mubaerchumiyang work. Wu Ruifeng; Zhang Yunzhen etc. translate. different modulus elasticity theory [M]. and Beijing: China Railway Press; 1986.); Consider the free beam of tension and compression different modulus; And locating 2 concentrated symmetrical load applications apart from bearing , the Calculation of Deflection expression formula of its span centre is:
(3)
With expression formula (2b) the substitution formula (3) of bendind rigidity , can only get the relational expression that contains and :
(4)
Simultaneously, the calculation expression that receives the stretch bending transverse stress most greatly of span centre bottom is:
(5)
Wherein, is the mid span moment of free beam; ; With ; The expression formula substitution of and can obtain the relational expression that another one only contains and :
(6)
Simultaneous formula (4) and formula (6) can solve and respectively as follows:
(7a,b)
That like this, has just tried to achieve reinforced concrete member is drawn Young's modulus of elasticity and pressurized Young's modulus of elasticity .Then, can be by formula (2b) in the hope of bendind rigidity .
The invention has the beneficial effects as follows: parameter to be measured is few, and deflection value and the strain value that only need measure test specimen span centre bottom get final product; The different Young'ss modulus of elasticity of tension and compression that this method is measured comprised the cracking factor of reinforced beam in giving the constant load scope, thereby determined bendind rigidity are applicable to the reinforced beam of band crackle work.Thereby solved in the reinforced concrete structure design theory major issue of generally being concerned about.
Description of drawings
Fig. 1 is the mechanical models of reinforced beam under 2 concentrated symmetries load of the both sides freely-supported of the present invention's employing.Among the figure, 1 is reinforced beam; 2 are thickening rectangle loading billet.
Fig. 2 is an instrument scheme of installation of the present invention, and among the figure, 1 is that resistance strain gage, 2 is the clock gauge fleximeter.
Embodiment
test specimen is made
Make one longly be , wide for , high rectangular reinforced concrete beam for ; As test specimen to be detected, wherein .The hinged-support supporting is taked at the two ends of test specimen; Upper surface at beam is located apart from bearing ; A thickening rectangle respectively is set loads billet; Wherein is the length that loads billet along deck-siding direction rectangle; is the length that loads billet along the span direction rectangle of beam; Require ; To satisfy the mechanical model of free beam under the load effect, as shown in Figure 1.
experimental apparatus is installed
As shown in Figure 2, paste one piece of resistance strain gage in test specimen span centre bottom, resistance strain gage links to each other with strainmeter; In test specimen span centre bottom (or top) the clock gauge fleximeter is installed.
loads for the first time and measures
Adopt concentrate symmetrical loading mode at 2; Load on the billet at two, respectively apply a load .Deng malformation stable after; Accurately record the deflection value at test specimen span middle part, the strain value of test specimen span middle part lowermost end, the payload values that record is corresponding.
unloading and loading are for the second time measured
Slowly lay down load ; Observe reinforced beam and whether can recover distortion fully; If reinforced beam can recover distortion fully, then be regarded as " perfect elasticity " (otherwise the payload values that is applied has exceeded the elastic response of structure).Then in test specimen span centre bottom; Again paste one piece of resistance strain gage, to reinforced beam load application to primary payload values for the second time.Deng malformation stable after, accurately record the deflection value at test specimen span middle part, the strain value of test specimen span middle part lowermost end.
calculates
Get the deflection value , the strain value that calculate usefulness; Utilize payload values , calculate deflection value , calculate strain value , distance , beam length , deck-siding and deck-molding apart from bearing, the Yi Xia formula of Cai Yonging calculate utilization split reinforced beam drawn Young's modulus of elasticity value with pressurized Young's modulus of elasticity value and bendind rigidity value :
The unit of each physical quantity adopts International System of Units.
Explanation is at last; Above embodiment is only unrestricted in order to technical scheme of the present invention to be described; Although with reference to preferred embodiment the present invention is specified, those of ordinary skill in the art should be appreciated that and can make amendment or be equal to replacement technical scheme of the present invention; And not breaking away from the aim and the scope of technical scheme of the present invention, it all should be encompassed in the middle of the claim scope of the present invention.

Claims (1)

1. confirm that band splits the method for reinforced beam elastic modulus and bendind rigidity for one kind; It is characterized in that: make one long for , wide for , high rectangular reinforced concrete beam for ; As test specimen to be detected; Wherein ; The hinged-support supporting is taked at the two ends of test specimen; And locating 2 concentrated symmetrical load applications apart from bearing ; Measure the deflection value at test specimen span middle part; And the strain value of test specimen span middle part lowermost end, that utilizes that following formula confirms that band splits reinforced beam is drawn Young's modulus of elasticity value and pressurized Young's modulus of elasticity value and bendind rigidity value :
Where is the mount point and mount the distance between, rectangular cross-section reinforced concrete beam beam width, as the beam length, for the high beam; various physical quantities The unit adopts the international system of units.
CN2010102450103A 2010-08-04 2010-08-04 Method for determining elastic modulus and flexural rigidity of reinforced concrete beam with crack CN101923024B (en)

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CN102359228B (en) * 2011-08-05 2013-06-05 重庆大学 Method for determining relationship between cracking height and reinforcement ratio of steel-concrete beam under use bending moment
CN102866061B (en) * 2012-09-03 2014-05-14 中交第二公路勘察设计研究院有限公司 Method for measuring elastic modulus of lightweight aggregate
CN102901673A (en) * 2012-10-11 2013-01-30 山东理工大学 Method for measuring tensile and compression elastic modulus of sheets with inconsistent tensile and compression modulus
CN102914470B (en) * 2012-11-15 2014-12-31 上海城建市政工程(集团)有限公司 Device and method for testing concrete sample beam stiffness
CN103245554A (en) * 2013-04-07 2013-08-14 河海大学 Early-stage elasticity modulus measurement method and device for cement-based materials based on simple support structure
CN103439177B (en) * 2013-09-06 2016-12-07 金陵科技学院 Cement paste macroscopic elastic modulus computational methods in early days under uniaxial force state
CN103499497B (en) * 2013-10-11 2015-11-18 华北电力大学(保定) A kind of pole line measurer for curve rigid
CN104330305B (en) * 2014-09-10 2017-02-01 宁夏大学 Method for measuring uniaxial tension and elastic modulus of concrete
CN107462477A (en) * 2017-06-22 2017-12-12 中国电力科学研究院 A kind of test method and lever that load is continuously applied for concrete sample
CN107665272B (en) * 2017-08-30 2021-01-29 西安建构实业有限责任公司 Bending rigidity calculation method for prefabricated reinforced concrete bottom plate in construction stage
CN109297817A (en) * 2018-11-16 2019-02-01 江苏开放大学(江苏城市职业学院) A kind of test device and method of reinforced beam elasticity modulus
CN109342225A (en) * 2018-12-05 2019-02-15 郑州大学 Elasticity modulus test method is drawn in Polypropylene Fiber Reinforced Cement Stabilized Macadam bending resistance

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JP3067016B2 (en) * 1997-04-18 2000-07-17 前田建設工業株式会社 Concrete strength estimation method
CN101701882B (en) * 2009-11-13 2011-04-06 南京工业大学 Fast identification method of tower structure stiffness
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