Background
The method measures the Young's modulus and the bending rigidity by adopting a load test of the precast reinforced concrete beam, and has guiding significance on a reinforced concrete structure design theory. At present, the measurement of the elastic modulus and the determination of the bending rigidity of the reinforced concrete beam are mostly based on the classic equal modulus elasticity theory, namely, under the tension and compression stress with the same absolute value, the material generates the tension and compression strain with the same absolute value. A large number of tests and researches show that under the action of tensile stress or compressive stress with the same absolute value, the material can generate tensile strain and compressive strain with different absolute values, namely the material has nonlinear characteristics of tensile modulus and compressive modulus. With the increasing development of scientific technology, higher requirements are put forward on the research of the mechanical properties of materials, and the development of novel materials and the potential of the characteristics of the materials are developed, so that a new research trend is formed. Most engineering structures generally have the tensile and compression elastic mechanical properties of different modulus of materials, such as ceramics, organic glass, reinforced concrete and the like. The elastomechanical properties of a material with different moduli in tension and compression are essentially a non-linear problem (bilinear). If the non-linear characteristic of the material is not considered in the engineering structure design, the classical equal modulus elasticity theory is still used, and the calculation error is too large due to the fact that the constitutive relation is not met in some cases, which is possibly the real hidden trouble of structure failure. In fact, most reinforced concrete engineering structures are usually in a crack working state, especially reinforced concrete beams, and the tensile and compression Young's modulus characteristics of the members are particularly outstanding. Therefore, the bending rigidity of the reinforced concrete beam with the crack is still determined by using the classical equal modulus elasticity theory, and excessive calculation errors are caused, so that the reasonable design of the engineering structure is not facilitated.
Disclosure of Invention
In order to overcome the defect that the bending rigidity of the reinforced concrete beam with cracks is determined by adopting the classical equal-modulus elasticity theory, the invention provides a method for measuring tensile and compression different Young elastic moduli of the reinforced concrete beam with cracks and a method for determining the bending rigidity. The tensile and compression different Young's elastic moduli measured by the method contain the cracking factor of the reinforced concrete beam in a given load range, so that the determined bending rigidity is suitable for the reinforced concrete beam with cracks to work. Therefore, the important problem of common concern in the design theory of the reinforced concrete structure is solved.
The purpose of the invention is realized as follows:
making a root length of
Is as wide as
High is
As a test piece to be tested, wherein
. The two ends of the test piece are supported by hinged supports and are at a distance from the supports
Two points are centralized and symmetrically applied with load
As shown in fig. 1. Measuring the deflection value of the middle of the span of the test piece
And strain value of the lowermost end of the middle of the span of the specimen
As shown in fig. 2. Deducing the tension of the reinforced concrete beam according to the analytic solution of the rectangular-section simply supported beam given by the tension-compression different modulus theory under the two-point concentrated symmetric loadingThe calculation expression of the Young's modulus and the bending rigidity is expressed according to the load value
Value of deflection
Strain value of
Therefore, the tensile and compressive Young's modulus value and the bending rigidity value can be accurately calculated.
According to the small-deflection plane bending theory of the shallow beam, under the action of load, the beam can deflect and is in a stressed state that the lower part is pulled and the upper part is pressed, so that a neutral layer which is neither pulled nor pressed is formed. The neutral layer is located exactly half way up the cross-section if according to classical equimodulus elasticity theory. However, if the modulus of elasticity of the structural material forming the beam in tension and compression is considered to be different, the neutral layer is no longer located at half height in the cross-section, but at a certain height in the cross-section depending on the magnitude of the tensile and compressive modulus, as shown in the following equation:
wherein,
the height of the cross-section in tension is indicated,
the height of the cross-section under pressure is indicated,
and
each of the tensile and compressive Young's moduli of the members is expressed in the unit of International Unit System. At the same time, the flexural rigidity of the beam
Can be expressed as
According to the theory of elasticity of different moduli (C.A. Ammbarkinje. Wu-Zhang-Kun-Shi-Wan, et al. theory of elasticity of different moduli [ M]Beijing, China railway Press, 1986.), consider simply supported beams of different moduli under tension and compression, and spaced from the support
Two points are centralized and symmetrically applied with load
The calculation expression of the deflection of the span is as follows:
will resist bending rigidity
By substituting the expression (2 b) into the formula (3), the compound can contain only
And
the relation of (1):
meanwhile, the calculation expression of the maximum tensile bending stress of the midspan bottom is as follows:
wherein,
in order to realize mid-span bending moment of the simply supported beam,
will be
,
And
by substituting the expression(s), another expression can be obtained which only contains
And
the relation of (1):
(6)
the combined vertical type (4) and the formula (6) can be obtained
And
respectively as follows:
thus, the Young's modulus in tension of the reinforced concrete member was determined
And Young's modulus of elasticity under compression
. Then, the flexural rigidity can be obtained from the formula (2 b)
。
The invention has the beneficial effects that: the parameters to be measured are few, and only the bending value of the middle-span bottom of the test piece needs to be measured
And strain value
Then the method is finished; the tensile and compression different Young's elastic moduli measured by the method contain the cracking factor of the reinforced concrete beam in a given load range, so that the determined bending rigidity is suitable for the reinforced concrete beam with cracks to work. Therefore, the important problem of common concern in the design theory of the reinforced concrete structure is solved.
Detailed Description
Making a root length of
Is as wide as
High is
As a test piece to be tested, wherein
. The two ends of the test piece are supported by hinged supports, and the distance between the supports and the upper surface of the beam
Where each is provided with a thickened rectangle
Loading a steel pad plate therein
For rectangular loading of the length of the steel backing plate in the beam width direction,
for rectangular loading of the length of the steel shim plate in the span direction of the beam, requirements are made
So as to satisfy the mechanical model of the simply supported beam under the action of concentrated load, as shown in fig. 1.
Laboratory apparatus installation
As shown in fig. 2, a resistance strain gauge is attached to the bottom of the midspan of the test piece, and the resistance strain gauge is connected with a strain gauge; and a dial indicator deflectometer is arranged at the bottom (or the top) of the span of the test piece.
First loading and measuring
Two-point centralized symmetrical loading mode is adopted, and a centralized load is respectively applied to the two loading steel base plates
. Accurately measuring the deflection value of the middle part of the span of the test piece after the structure is stably deformed
Strain value of the lowest end of span middle part of test piece
Record the corresponding load value
。
Unload and second load measurements
Slowly unload the load
Observing whether the reinforced concrete beam can completely recover deformation, and if the reinforced concrete beam can completely recover deformation, considering the reinforced concrete beam as 'complete elasticity' (otherwise, the applied load value
Already beyond the elastic response of the structure). Then, a resistance strain gauge is attached to the middle bottom of the span of the test piece again, and the load is applied to the reinforced concrete beam for the second time to reach the first load value
. Accurately measuring the deflection value of the middle part of the span of the test piece after the structure is stably deformed
Strain value of the lowest end of span middle part of test piece
。
Taking calculated deflection values
Strain value of
Using the lotusLoad value
Calculating the deflection value
Calculating the strain value
Distance from the support
Length of beam
Width of beam
Height of beam
Calculating the tensile Young's modulus value of the reinforced concrete beam with the crack by adopting the following formula
And value of Young's modulus under compression
And bending stiffness value
:
The units of the physical quantities are made by international system of units.
Finally, the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting, although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications or equivalent substitutions may be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all of them should be covered in the claims of the present invention.