CN101923024A - A Method for Determining Elastic Modulus and Bending Stiffness of Cracked Reinforced Concrete Beams - Google Patents

A Method for Determining Elastic Modulus and Bending Stiffness of Cracked Reinforced Concrete Beams Download PDF

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CN101923024A
CN101923024A CN 201010245010 CN201010245010A CN101923024A CN 101923024 A CN101923024 A CN 101923024A CN 201010245010 CN201010245010 CN 201010245010 CN 201010245010 A CN201010245010 A CN 201010245010A CN 101923024 A CN101923024 A CN 101923024A
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reinforced concrete
value
test piece
modulus
span
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CN101923024B (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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CHONGQING ZHONGKE CONSTRUCTION (GROUP) Co Ltd
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Chongqing University
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Abstract

本发明公开了一种确定带裂钢筋混凝土梁弹性模量E+和受压杨氏弹性模量E-的测量方法以及抗弯刚度D的确定方法。制作一根长为l、宽为b、高为h的矩形截面钢筋混凝土梁，作为待检测的试件，其中l≥5h，试件的两端采取铰支座支承，并在距离支座a处两点集中对称施加荷载P，测出试件跨度中部的挠度值w，以及试件跨度中部最底端的应变值ε，根据拉压不同模量理论给出的矩形截面简支梁在两点集中对称加载下的解析解，推导出E+、E-和D的计算表达式，由荷载值P、挠度值w、应变值ε，便可以精确地计算出E+、E-和D。该方法所确定的E+、E-和D，包含了钢筋混凝土梁在给定荷载P范围内的开裂因素，因而可用于结构的力学精细分析。The invention discloses a measuring method for determining the elastic modulus E + and the compressed Young's elastic modulus E- of a cracked reinforced concrete beam and a method for determining the bending stiffness D. Make a reinforced concrete beam of rectangular section with length l, width b, and height h as the test piece to be tested, where l≥5h, the two ends of the test piece are supported by hinge supports, and at a distance from the support a Centrally and symmetrically apply a load P at two points, measure the deflection value w in the middle of the span of the specimen, and the strain value ε at the bottom end of the middle span of the specimen, and the rectangular cross-section simply supported beam given by the theory of different moduli in tension and compression is at two points Based on the analytical solution under concentrated symmetric loading, the calculation expressions of E + , E - and D are deduced, and E + , E - and D can be accurately calculated from the load value P, deflection value w, and strain value ε. The E + , E - and D determined by this method include the cracking factors of reinforced concrete beams within a given load P range, so they can be used for fine mechanical analysis of structures.

Description

一种确定带裂钢筋混凝土梁弹性模量及抗弯刚度的方法 A Method for Determining Elastic Modulus and Bending Stiffness of Cracked Reinforced Concrete Beams

技术领域technical field

本发明涉及带裂纹工作的钢筋混凝土梁的受拉杨氏弹性模量                                               

Figure 2010102450103100002DEST_PATH_IMAGE002
和受压杨氏弹性模量
Figure 2010102450103100002DEST_PATH_IMAGE004
的测量方法以及抗弯刚度
Figure 2010102450103100002DEST_PATH_IMAGE006
的确定方法。The present invention relates to Young's modulus of elasticity in tension for reinforced concrete beams working with cracks
Figure 2010102450103100002DEST_PATH_IMAGE002
and Young's modulus of elasticity under compression
Figure 2010102450103100002DEST_PATH_IMAGE004
The measurement method and the bending stiffness
Figure 2010102450103100002DEST_PATH_IMAGE006
method of determination.

背景技术Background technique

采用预制钢筋混凝土梁加载试验，测量其杨氏弹性模量及抗弯刚度，对钢筋混凝土结构设计理论具有指导意义。目前，钢筋混凝土梁的弹性模量测量及抗弯刚度的确定，大多数基于经典的等模量弹性理论，即在绝对值相同的拉压应力下，材料将产生绝对值相同的拉压应变。大量的试验和研究表明，材料在绝对值相同的拉应力或压应力作用下，会发生绝对值不同的拉应变和压应变，即材料具有拉压不同模量的非线性特性。随着科学技术的日益发展，对材料力学性质的研究提出了更高的要求，研制新型材料以及挖掘材料自身特性的潜力，成为新的研究动向。大多数工程结构普遍存在着材料的拉压不同模量弹性力学特性，尤其像陶瓷、有机玻璃、钢筋混凝土等。材料具有拉压不同模量的弹性力学性质本质上是非线性问题(双线性) 。如果工程结构设计中对材料的这种非线性特性不予重视，仍然沿用经典的等模量弹性理论，在某些情况下会因本构关系不符合而造成计算误差过大，这有可能是结构失效的真正隐患。事实上，大多数钢筋混凝土工程结构，通常处于带裂纹工作状态，尤其是钢筋混凝土梁，此时构件的拉压不同杨氏弹性模量特征尤为突出。因此，仍沿用经典的等模量弹性理论确定带裂钢筋混凝土梁的抗弯刚度，势必造成过大的计算误差，不利于工程结构的合理设计。The prefabricated reinforced concrete beams are used for loading tests to measure Young's modulus of elasticity and flexural stiffness, which has guiding significance for the design theory of reinforced concrete structures. At present, the measurement of the elastic modulus and the determination of the flexural stiffness of reinforced concrete beams are mostly based on the classic theory of equal modulus elasticity, that is, under the same absolute value of tensile and compressive stress, the material will produce the same absolute value of tensile and compressive strain. A large number of tests and studies have shown that under the same absolute value of tensile stress or compressive stress, materials will have different absolute values of tensile strain and compressive strain, that is, materials have nonlinear characteristics of different tensile and compressive moduli. With the increasing development of science and technology, higher requirements are put forward for the study of the mechanical properties of materials. The development of new materials and the potential of tapping the properties of materials have become new research trends. Most engineering structures generally have different tensile and compressive modulus elastic mechanical properties of materials, especially ceramics, plexiglass, and reinforced concrete. The elastic mechanical properties of materials with different modulus in tension and compression are essentially nonlinear problems (bilinear). If the nonlinear characteristics of materials are ignored in the design of engineering structures, and the classic theory of equal modulus elasticity is still used, in some cases, the calculation error will be too large due to the inconsistency of the constitutive relationship, which may be The real danger of structural failure. In fact, most reinforced concrete engineering structures are usually in the working state with cracks, especially reinforced concrete beams. At this time, the characteristics of different Young's elastic moduli of components are particularly prominent. Therefore, still using the classic equal modulus elasticity theory to determine the flexural stiffness of cracked reinforced concrete beams will inevitably cause excessive calculation errors, which is not conducive to the rational design of engineering structures.

发明内容Contents of the invention

为了克服采用经典的等模量弹性理论确定带裂钢筋混凝土梁抗弯刚度的不足，本发明提供了一种带裂钢筋混凝土梁拉压不同杨氏弹性模量的测量方法以及抗弯刚度的确定方法。该方法所测得的拉压不同杨氏弹性模量，包含了钢筋混凝土梁在给定荷载范围内的开裂因素，因而所确定的抗弯刚度适用于带裂纹工作的钢筋混凝土梁。从而解决了钢筋混凝土结构设计理论中，普遍关心的一个重要问题。In order to overcome the disadvantages of using the classic equal modulus elasticity theory to determine the flexural stiffness of cracked reinforced concrete beams, the present invention provides a method for measuring Young's modulus of elasticity in tension and compression of cracked reinforced concrete beams and a method for determining the flexural stiffness. The different Young's elastic moduli measured by this method include the cracking factors of reinforced concrete beams within a given load range, so the determined flexural stiffness is suitable for reinforced concrete beams working with cracks. Thus, it solves an important problem of general concern in the design theory of reinforced concrete structures.

本发明的目的是这样实现的：The purpose of the present invention is achieved like this:

制作一根长为

Figure 2010102450103100002DEST_PATH_IMAGE008
、宽为
Figure 2010102450103100002DEST_PATH_IMAGE010
、高为
Figure 2010102450103100002DEST_PATH_IMAGE012
的矩形截面钢筋混凝土梁，作为待检测的试件，其中
Figure 2010102450103100002DEST_PATH_IMAGE014
。试件的两端采取铰支座支承，并在距离支座
Figure 2010102450103100002DEST_PATH_IMAGE016
处两点集中对称施加荷载
Figure 2010102450103100002DEST_PATH_IMAGE018
，如图1所示。测出试件跨度中部的挠度值
Figure 2010102450103100002DEST_PATH_IMAGE020
，以及试件跨度中部最底端的应变值
Figure 2010102450103100002DEST_PATH_IMAGE022
，如图2所示。根据拉压不同模量理论给出的矩形截面简支梁在两点集中对称加载下的解析解，推导出钢筋混凝土梁拉压不同杨氏弹性模量和抗弯刚度的计算表达式，由荷载值
Figure 374798DEST_PATH_IMAGE018
、挠度值
Figure 229622DEST_PATH_IMAGE020
、应变值
Figure 947042DEST_PATH_IMAGE022
，便可以精确地计算出拉压杨氏弹性模量值和抗弯刚度值。make a length of
Figure 2010102450103100002DEST_PATH_IMAGE008
, width is
Figure 2010102450103100002DEST_PATH_IMAGE010
, Gao Wei
Figure 2010102450103100002DEST_PATH_IMAGE012
Rectangular cross-section reinforced concrete beam, as the specimen to be tested, where
Figure 2010102450103100002DEST_PATH_IMAGE014
. Both ends of the specimen are supported by hinge supports, and the distance between the supports
Figure 2010102450103100002DEST_PATH_IMAGE016
Centralized symmetrical load at two points
Figure 2010102450103100002DEST_PATH_IMAGE018
,As shown in Figure 1. Measure the deflection value in the middle of the span of the specimen
Figure 2010102450103100002DEST_PATH_IMAGE020
, and the strain value at the bottom end of the middle part of the specimen span
Figure 2010102450103100002DEST_PATH_IMAGE022
,as shown in picture 2. According to the analytical solution of simply supported rectangular beams under two-point concentrated symmetrical loading given by the theory of different moduli in tension and compression, the calculation expressions of Young's modulus of elasticity and flexural stiffness of reinforced concrete beams in tension and compression are deduced. value
Figure 374798DEST_PATH_IMAGE018
, deflection value
Figure 229622DEST_PATH_IMAGE020
, strain value
Figure 947042DEST_PATH_IMAGE022
, the value of Young's modulus of elasticity in tension and compression and the value of bending stiffness can be accurately calculated.

根据浅梁的小挠度平面弯曲理论，简支梁在荷载作用下，梁会挠曲，并处于下部受拉而上部受压的受力状态，从而形成既不受拉也不受压的中性层。如果按经典的等模量弹性理论，该中性层恰好位于横截面的半高处。然而，如果考虑构成梁的结构材料在拉伸和压缩时的弹性模量不相同，那么中性层则不再位于横截面半高处，而是根据拉压弹性模量值的不同位于截面的某个高度上，如下式所示：According to the small deflection plane bending theory of shallow beams, under the load of a simply supported beam, the beam will deflect and be in a state where the lower part is under tension and the upper part is under compression, thus forming a neutral state where neither tension nor compression layer. According to the classic theory of equal modulus elasticity, the neutral layer is exactly located at the half-height of the cross section. However, if it is considered that the elastic modulus of the structural material constituting the beam is different in tension and compression, then the neutral layer is no longer located at the half-height of the cross section, but is located at the center of the section according to the difference in tension and compression elastic modulus values. At a certain height, as shown in the following formula:

Figure 2010102450103100002DEST_PATH_IMAGE024
             （1a,b）
Figure 2010102450103100002DEST_PATH_IMAGE024
(1a,b)

其中，

Figure 2010102450103100002DEST_PATH_IMAGE026
表示受拉截面高度，表示受压截面高度，
Figure 155300DEST_PATH_IMAGE002
和
Figure 907356DEST_PATH_IMAGE004
分别表示构件的拉压杨氏弹性模量，各个量的单位采用国际单位制。同时，梁的抗弯刚度
Figure 667501DEST_PATH_IMAGE006
可表示为in,
Figure 2010102450103100002DEST_PATH_IMAGE026
Indicates the tension section height, is the height of the compression section,
Figure 155300DEST_PATH_IMAGE002
and
Figure 907356DEST_PATH_IMAGE004
Respectively represent the tensile and compressive Young's modulus of elasticity of the component, and the units of each quantity adopt the International System of Units. At the same time, the bending stiffness of the beam
Figure 667501DEST_PATH_IMAGE006
can be expressed as

 或 

Figure DEST_PATH_IMAGE032
   (2a,b) or
Figure DEST_PATH_IMAGE032
(2a,b)

根据不同模量弹性理论（C.A.阿姆巴尔楚米扬著. 邬瑞锋, 张允真等译. 不同模量弹性理论[M]. 北京:中国铁道出版社,1986.），考虑拉压不同模量的简支梁，并在距离支座

Figure 809901DEST_PATH_IMAGE016
处两点集中对称施加荷载
Figure 946484DEST_PATH_IMAGE018
，其跨中的挠度计算表达式为：According to the different modulus elasticity theory (CA Ambal Chumiyan. Wu Ruifeng, Zhang Yunzhen et al. translation. Different modulus elasticity theory [M]. Beijing: China Railway Press, 1986.), considering the simple girders, and supports at distances
Figure 809901DEST_PATH_IMAGE016
Centralized symmetrical load at two points
Figure 946484DEST_PATH_IMAGE018
, the calculation expression of the deflection in the span is:

Figure DEST_PATH_IMAGE034
                            （3）
Figure DEST_PATH_IMAGE034
(3)

将抗弯刚度

Figure 553046DEST_PATH_IMAGE006
的表达式（2b）代入公式（3），可得仅含有
Figure 484093DEST_PATH_IMAGE002
和
Figure 176105DEST_PATH_IMAGE004
的关系式：Bending stiffness
Figure 553046DEST_PATH_IMAGE006
The expression (2b) of is substituted into the formula (3), it can be obtained that only contains
Figure 484093DEST_PATH_IMAGE002
and
Figure 176105DEST_PATH_IMAGE004
The relational formula:

Figure DEST_PATH_IMAGE036
                            （4）
Figure DEST_PATH_IMAGE036
(4)

同时，跨中底部的最大受拉弯曲应力的计算表达式为：At the same time, the calculation expression of the maximum tensile bending stress at the bottom of the mid-span is:

Figure DEST_PATH_IMAGE038
                               （5）
Figure DEST_PATH_IMAGE038
(5)

其中，

Figure DEST_PATH_IMAGE040
为简支梁的跨中弯矩，
Figure DEST_PATH_IMAGE042
，将
Figure 726166DEST_PATH_IMAGE040
，和
Figure 554762DEST_PATH_IMAGE026
的表达式代入，可得到另外一个仅含有
Figure 734071DEST_PATH_IMAGE002
和
Figure 9194DEST_PATH_IMAGE004
的关系式：in,
Figure DEST_PATH_IMAGE040
is the mid-span bending moment of the simply supported beam,
Figure DEST_PATH_IMAGE042
,Will
Figure 726166DEST_PATH_IMAGE040
, and
Figure 554762DEST_PATH_IMAGE026
Substituting the expression of , we can get another one containing only
Figure 734071DEST_PATH_IMAGE002
and
Figure 9194DEST_PATH_IMAGE004
The relational formula:

                               （6） (6)

联立式（4）和式（6），可解得

Figure 528032DEST_PATH_IMAGE002
和
Figure 800881DEST_PATH_IMAGE004
分别如下：Simultaneous formula (4) and formula (6), can be solved to get
Figure 528032DEST_PATH_IMAGE002
and
Figure 800881DEST_PATH_IMAGE004
They are as follows:

Figure DEST_PATH_IMAGE046
           （7a,b）
Figure DEST_PATH_IMAGE046
(7a,b)

这样，就求得了钢筋混凝土构件的受拉杨氏弹性模量

Figure 467486DEST_PATH_IMAGE002
和受压杨氏弹性模量。然后，由公式（2b）可以求得抗弯刚度
Figure 919644DEST_PATH_IMAGE006
。In this way, the tensile Young's modulus of the reinforced concrete member is obtained
Figure 467486DEST_PATH_IMAGE002
and Young's modulus of elasticity under compression . Then, the bending stiffness can be obtained from formula (2b)
Figure 919644DEST_PATH_IMAGE006
.

本发明的有益效果是：待测量的参数少，仅需要测量试件跨中底部的挠度值

Figure 691291DEST_PATH_IMAGE020
和应变值
Figure 591331DEST_PATH_IMAGE022
即可；该方法所测得的拉压不同杨氏弹性模量，包含了钢筋混凝土梁在给定荷载范围内的开裂因素，因而所确定的抗弯刚度适用于带裂纹工作的钢筋混凝土梁。从而解决了钢筋混凝土结构设计理论中，普遍关心的一个重要问题。The beneficial effects of the present invention are: there are few parameters to be measured, and only the deflection value of the mid-span bottom of the test piece needs to be measured
Figure 691291DEST_PATH_IMAGE020
and strain value
Figure 591331DEST_PATH_IMAGE022
That is; the different Young's modulus of elasticity measured by this method includes the cracking factors of reinforced concrete beams within a given load range, so the determined flexural stiffness is suitable for reinforced concrete beams working with cracks. Thus, it solves an important problem of general concern in the design theory of reinforced concrete structures.

附图说明Description of drawings

图1为本发明采用的两边简支的钢筋混凝土梁在两点集中对称加载下的力学模型。图中，1为钢筋混凝土梁；2为加厚矩形

Figure DEST_PATH_IMAGE048
加载钢垫板。Fig. 1 is the mechanical model of the reinforced concrete beam simply supported on both sides adopted by the present invention under two-point concentrated symmetrical loading. In the figure, 1 is a reinforced concrete beam; 2 is a thickened rectangle
Figure DEST_PATH_IMAGE048
Load the steel backing plate.

图2为本发明仪器安装示意图，图中，1为电阻应变片、2为千分表挠度计。Fig. 2 is the schematic diagram of the installation of the instrument of the present invention, in which, 1 is a resistance strain gauge, and 2 is a dial gauge deflection gauge.

具体实施方式Detailed ways

Figure DEST_PATH_IMAGE050
 试件制作
Figure DEST_PATH_IMAGE050
Test piece production

制作一根长为

Figure 349203DEST_PATH_IMAGE008
、宽为
Figure 639370DEST_PATH_IMAGE010
、高为
Figure 519601DEST_PATH_IMAGE012
的矩形截面钢筋混凝土梁，作为待检测的试件，其中。试件的两端采取铰支座支承，在梁的上表面距离支座
Figure 315836DEST_PATH_IMAGE016
处，各设置一块加厚矩形
Figure 726088DEST_PATH_IMAGE048
加载钢垫板，其中为沿梁宽方向矩形加载钢垫板的长度，
Figure DEST_PATH_IMAGE054
为沿梁的跨度方向矩形加载钢垫板的长度，要求
Figure DEST_PATH_IMAGE056
，以满足简支梁在集中荷载作用下的力学模型，如图1所示。make a length of
Figure 349203DEST_PATH_IMAGE008
, width is
Figure 639370DEST_PATH_IMAGE010
, Gao Wei
Figure 519601DEST_PATH_IMAGE012
Rectangular cross-section reinforced concrete beam, as the specimen to be tested, where . Both ends of the specimen are supported by hinged supports, and the distance between the upper surface of the beam and the supports
Figure 315836DEST_PATH_IMAGE016
At each place, set a thickened rectangle
Figure 726088DEST_PATH_IMAGE048
Load the steel backing plate, where is the length of the steel backing plate loaded rectangularly along the beam width direction,
Figure DEST_PATH_IMAGE054
For the length of the rectangularly loaded steel backing plate along the span direction of the beam, the required
Figure DEST_PATH_IMAGE056
, to meet the mechanical model of a simply supported beam under concentrated load, as shown in Figure 1.

Figure DEST_PATH_IMAGE058
 实验仪器安装
Figure DEST_PATH_IMAGE058
Experimental instrument installation

如图2所示，在试件跨中底部贴一枚电阻应变片，电阻应变片与应变仪相连；在试件跨中底部(或顶部)安装千分表挠度计。As shown in Figure 2, a resistance strain gauge is attached to the bottom of the middle span of the test piece, and the resistance strain gauge is connected to the strain gauge; a dial gauge deflection gauge is installed on the bottom (or top) of the middle span of the test piece.

 第一次加载及测量 First loading and measurement

采用两点集中对称加载模式, 在两块加载钢垫板上，各施加一个集中荷载

Figure 527954DEST_PATH_IMAGE018
。等结构变形稳定后，准确测得试件跨度中部的挠度值
Figure DEST_PATH_IMAGE062
、试件跨度中部最底端的应变值，记录对应的荷载值
Figure 328550DEST_PATH_IMAGE018
。A two-point concentrated symmetrical loading mode is adopted, and a concentrated load is applied to each of the two loaded steel backing plates
Figure 527954DEST_PATH_IMAGE018
. After the structural deformation is stable, accurately measure the deflection value in the middle of the span of the specimen
Figure DEST_PATH_IMAGE062
, The strain value at the bottom end of the middle part of the specimen span , record the corresponding load value
Figure 328550DEST_PATH_IMAGE018
.

Figure DEST_PATH_IMAGE066
 卸载及第二次加载测量
Figure DEST_PATH_IMAGE066
Unloading and second loading measurement

缓慢卸掉荷载，观察钢筋混凝土梁是否能够完全恢复变形，若钢筋混凝土梁能够完全恢复变形，则视为“完全弹性”（否则所施加的荷载值已经超出结构的弹性响应）。然后在试件跨中底部，重新贴一枚电阻应变片，对钢筋混凝土梁第二次施加荷载至第一次的荷载值

Figure 711755DEST_PATH_IMAGE018
。等结构变形稳定后，准确测得试件跨度中部的挠度值
Figure DEST_PATH_IMAGE068
、试件跨度中部最底端的应变值
Figure DEST_PATH_IMAGE070
。slow unloading , observe whether the reinforced concrete beam can fully recover the deformation, if the reinforced concrete beam can fully recover the deformation, it is regarded as "completely elastic" (otherwise the applied load value has exceeded the elastic response of the structure). Then, at the bottom of the mid-span of the specimen, re-attach a resistance strain gauge, and apply the load to the reinforced concrete beam for the second time to the load value of the first time
Figure 711755DEST_PATH_IMAGE018
. After the structural deformation is stable, accurately measure the deflection value in the middle of the span of the specimen
Figure DEST_PATH_IMAGE068
, The strain value at the bottom end of the middle part of the specimen span
Figure DEST_PATH_IMAGE070
.

Figure DEST_PATH_IMAGE072
 计算
Figure DEST_PATH_IMAGE072
calculate

取计算用的挠度值

Figure DEST_PATH_IMAGE074
、应变值
Figure DEST_PATH_IMAGE076
，利用荷载值
Figure 812698DEST_PATH_IMAGE018
、计算挠度值、计算应变值
Figure 897645DEST_PATH_IMAGE022
、距离支座的距离
Figure 25001DEST_PATH_IMAGE016
、梁长
Figure 924824DEST_PATH_IMAGE008
、梁宽
Figure 428618DEST_PATH_IMAGE010
和梁高
Figure 667969DEST_PATH_IMAGE012
，采用以下公式计算出带裂钢筋混凝土梁的受拉杨氏弹性模量值和受压杨氏弹性模量值
Figure 353346DEST_PATH_IMAGE004
以及抗弯刚度值
Figure 660830DEST_PATH_IMAGE006
：Take the deflection value for the calculation
Figure DEST_PATH_IMAGE074
, strain value
Figure DEST_PATH_IMAGE076
, using the load value
Figure 812698DEST_PATH_IMAGE018
, Calculate the deflection value , Calculate the strain value
Figure 897645DEST_PATH_IMAGE022
, the distance from the support
Figure 25001DEST_PATH_IMAGE016
, Liang Chang
Figure 924824DEST_PATH_IMAGE008
, beam width
Figure 428618DEST_PATH_IMAGE010
and Liang Gao
Figure 667969DEST_PATH_IMAGE012
, using the following formula to calculate the tensile Young's modulus of the cracked reinforced concrete beam and Young's modulus of elasticity under compression
Figure 353346DEST_PATH_IMAGE004
and the value of the bending stiffness
Figure 660830DEST_PATH_IMAGE006
:

Figure DEST_PATH_IMAGE080
Figure DEST_PATH_IMAGE080

Figure 426792DEST_PATH_IMAGE032
Figure 426792DEST_PATH_IMAGE032

各个物理量的单位采用国际单位制。The units of each physical quantity adopt the International System of Units.

最后说明的是，以上实施例仅用以说明本发明的技术方案而非限制，尽管参照较佳实施例对本发明进行了详细说明，本领域的普通技术人员应当理解，可以对本发明的技术方案进行修改或者等同替换，而不脱离本发明技术方案的宗旨和范围，其均应涵盖在本发明的权利要求范围当中。Finally, it is noted that the above embodiments are only used to illustrate the technical solutions of the present invention without limitation. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that the technical solutions of the present invention can be carried out Modifications or equivalent replacements without departing from the spirit and scope of the technical solution of the present invention shall be covered by the claims of the present invention.

Claims (1)

1. A method for determining the elastic modulus and the bending rigidity of a reinforced concrete beam with cracks is characterized by comprising the following steps of: making a root length of
Figure DEST_PATH_IMAGE002
Is as wide as
Figure DEST_PATH_IMAGE004
High is
Figure DEST_PATH_IMAGE006
As a test piece to be tested, wherein
Figure DEST_PATH_IMAGE008
The two ends of the test piece are supported by hinged supports and are at a distance from the supports
Figure DEST_PATH_IMAGE010
Two points are centralized and symmetrically applied with load
Figure DEST_PATH_IMAGE012
Measuring the deflection value of the middle part of the test piece span and the strain value of the bottommost end of the test piece span
Figure DEST_PATH_IMAGE014
Determining the tensile Young's modulus value of the reinforced concrete beam with cracks by using the following formula
Figure DEST_PATH_IMAGE016
And value of Young's modulus under compression
Figure DEST_PATH_IMAGE018
And bending stiffness value
Figure DEST_PATH_IMAGE020
：
Figure DEST_PATH_IMAGE022
Figure DEST_PATH_IMAGE026
Wherein
Figure DEST_PATH_IMAGE028
Is the distance between the loading point and the support,Is a rectangular section reinforced concrete beam with wide beam,
Figure 278044DEST_PATH_IMAGE002
Is long and,
Figure 665163DEST_PATH_IMAGE006
Is the beam height; the units of the physical quantities are made by international system of units.
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