CN110298133B - Method for calculating cracks of reinforced concrete beam of main control building of all-indoor substation - Google Patents

Method for calculating cracks of reinforced concrete beam of main control building of all-indoor substation Download PDF

Info

Publication number
CN110298133B
CN110298133B CN201910604725.4A CN201910604725A CN110298133B CN 110298133 B CN110298133 B CN 110298133B CN 201910604725 A CN201910604725 A CN 201910604725A CN 110298133 B CN110298133 B CN 110298133B
Authority
CN
China
Prior art keywords
concrete
strain
formula
steel bar
compressive
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN201910604725.4A
Other languages
Chinese (zh)
Other versions
CN110298133A (en
Inventor
陈幸
陈国华
李玉婷
陈盛华
彭怀德
吴浩
王敏
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
State Grid Corp of China SGCC
Economic and Technological Research Institute of State Grid Jiangxi Electric Power Co Ltd
Original Assignee
State Grid Corp of China SGCC
Economic and Technological Research Institute of State Grid Jiangxi Electric Power Co Ltd
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by State Grid Corp of China SGCC, Economic and Technological Research Institute of State Grid Jiangxi Electric Power Co Ltd filed Critical State Grid Corp of China SGCC
Priority to CN201910604725.4A priority Critical patent/CN110298133B/en
Publication of CN110298133A publication Critical patent/CN110298133A/en
Application granted granted Critical
Publication of CN110298133B publication Critical patent/CN110298133B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/13—Architectural design, e.g. computer-aided architectural design [CAAD] related to design of buildings, bridges, landscapes, production plants or roads
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/06—Power analysis or power optimisation
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E60/00—Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Geometry (AREA)
  • Theoretical Computer Science (AREA)
  • General Physics & Mathematics (AREA)
  • Computer Hardware Design (AREA)
  • Evolutionary Computation (AREA)
  • General Engineering & Computer Science (AREA)
  • Structural Engineering (AREA)
  • Computational Mathematics (AREA)
  • Civil Engineering (AREA)
  • Mathematical Analysis (AREA)
  • Mathematical Optimization (AREA)
  • Pure & Applied Mathematics (AREA)
  • Architecture (AREA)
  • Rod-Shaped Construction Members (AREA)

Abstract

本发明公开了一种全户内变电站主控楼钢筋混凝土梁裂缝计算方法，包括以下步骤：1)根据平均裂缝宽度wm的经验公式，构建出平均裂缝宽度wm用曲率

Figure DDA0002120442580000011
表达的公式；2)根据当受拉纵筋刚屈服时的两种情况(第一种情况：受压混凝土边缘应变εc≤峰值压应变ε0；第二种情况：受压混凝土边缘应变εc>峰值压应变ε0)，以及适筋梁受压混凝土达到极限压应变时的情况，构建曲率的表达式；3)将步骤2)中曲率表达式代入步骤1)的公式中，即得考虑了钢筋应力影响的裂缝宽度的计算公式。本发明推导出了受拉钢筋屈服后的钢筋混凝土梁裂缝的计算方法，相较于传统的计算方法，本发明的方法计算出的裂缝宽度与实际的裂缝宽度更贴近。

Figure 201910604725

The invention discloses a method for calculating the cracks of reinforced concrete beams of the main control building of an all-indoor substation, which comprises the following steps: 1) constructing the average crack width w m with the curvature according to the empirical formula of the average crack width w m

Figure DDA0002120442580000011
The expression formula; 2) According to the two situations when the tensile longitudinal reinforcement just yields (the first situation: the edge strain of the compressed concrete ε c ≤ the peak compressive strain ε 0 ; the second situation: the edge strain of the compressed concrete εc >Peak compressive strain ε 0 ), and when the compressive concrete of the well-reinforced beam reaches the ultimate compressive strain, construct the expression of curvature; 3) Substitute the curvature expression in step 2) into the formula of step 1), and then consider The calculation formula of crack width affected by steel stress is given. The invention deduces the calculation method for the cracks of the reinforced concrete beam after the tensile steel bar yields. Compared with the traditional calculation method, the crack width calculated by the method of the invention is closer to the actual crack width.

Figure 201910604725

Description

一种全户内变电站主控楼钢筋混凝土梁裂缝计算方法A method for calculating cracks in reinforced concrete beams of the main control building of an indoor substation

技术领域Technical Field

本发明属于土木工程技术领域，具体涉及一种全户内变电站主控楼钢筋混凝土梁裂缝计算方法。The invention belongs to the technical field of civil engineering, and in particular relates to a method for calculating cracks in reinforced concrete beams of a main control building of a fully indoor substation.

背景技术Background Art

在钢筋混凝土梁弹塑性分析时，若弯矩调幅系数取值过大，调幅后的钢筋在外荷载的作用下可能发生屈服。我们通常在计算裂缝宽度时采用规范中提出的公式，在计算时此公式中并未考虑钢筋应力的影响，而构件的裂缝宽度在钢筋屈服之后将不再发生变化，这与实际是不相符的，因而按照采用规范中提出的公式得到的裂缝宽度准确度不高。In the elastoplastic analysis of reinforced concrete beams, if the moment modulation coefficient is too large, the modulated steel bars may yield under the action of external loads. We usually use the formula proposed in the specification to calculate the crack width. This formula does not take into account the influence of steel bar stress during calculation, and the crack width of the component will no longer change after the steel bar yields, which is inconsistent with the actual situation. Therefore, the crack width obtained by using the formula proposed in the specification is not accurate.

通常钢筋混凝土结构在偶然荷载的作用下也可能发生屈服，钢筋屈服后构件的变形及裂缝宽度等是判断结构是否可修以及决定修复加固程度的重要指标，国内外针对钢筋屈服之后构件的裂缝宽度的研究很少，所以推导钢筋屈服之后的裂缝计算方法是非常必要的。Usually reinforced concrete structures may also yield under the action of accidental loads. The deformation and crack width of the components after the steel bar yields are important indicators for judging whether the structure is repairable and determining the degree of repair and reinforcement. There are few studies on the crack width of components after the steel bar yields at home and abroad, so it is very necessary to derive a method for calculating cracks after the steel bar yields.

发明内容Summary of the invention

本发明的目的是提供一种考虑钢筋应力影响的全户内变电站主控楼钢筋混凝土梁裂缝计算方法，提高计算出裂缝宽度的准确度。The purpose of the present invention is to provide a method for calculating cracks in reinforced concrete beams of a main control building of an indoor substation taking into account the influence of steel bar stress, so as to improve the accuracy of calculating the crack width.

本发明这种全户内变电站主控楼钢筋混凝土梁裂缝计算方法，包括以下步骤：The method for calculating cracks in reinforced concrete beams of the main control building of the fully indoor substation of the present invention comprises the following steps:

1)根据平均裂缝宽度的经验公式，构建出平均裂缝宽度用曲率表达的公式；1) Based on the empirical formula of average crack width, a formula for expressing the average crack width in terms of curvature is constructed;

2)根据当适筋梁受拉钢筋刚屈服时的两种情况(第一种情况：受压混凝土边缘应变εc≤峰值压应变ε0；第二种情况：受压混凝土边缘应变εc>峰值压应变ε0)，以及适筋梁受压混凝土达到极限压应变时的情况，构建曲率的表达式；2) Based on the two cases when the tension reinforcement of the properly reinforced beam just yields (the first case: the edge strain of the compressive concrete ε c ≤ the peak compressive strain ε 0 ; the second case: the edge strain of the compressive concrete ε c > the peak compressive strain ε 0 ), and the case when the compressive concrete of the properly reinforced beam reaches the ultimate compressive strain, an expression for the curvature is constructed;

3)将步骤2)中曲率表达式代入步骤1)的公式中，即得考虑了钢筋应力影响的裂缝宽度的计算公式。3) Substitute the curvature expression in step 2) into the formula in step 1) to obtain the calculation formula for the crack width that takes into account the influence of steel bar stress.

所述步骤1)中，经验公式为：In the step 1), the empirical formula is:

Figure BDA0002120442560000011
Figure BDA0002120442560000011

式中，wm为平均裂缝宽度，εsm为纵向受拉钢筋的平均拉应变，εctm为与纵向受拉钢筋相同水平处侧表面混凝土的平均拉应变，lm为平均裂缝区段的钢筋混凝土梁计算长度。Where wm is the average crack width, εsm is the average tensile strain of the longitudinal tensile reinforcement, εctm is the average tensile strain of the side surface concrete at the same level as the longitudinal tensile reinforcement, and lm is the calculated length of the reinforced concrete beam in the average crack section.

所述构建出平均裂缝宽度用曲率表达的公式，具体包括以下步骤：The formula for constructing the average crack width expressed by curvature specifically includes the following steps:

1.1根据经验公式，考虑梁屈服后裂缝附近的粘结作用的消失，

Figure BDA0002120442560000021
取为0.95，则平均裂缝计算公式为：wm＝0.95εsmlm；1.1 According to the empirical formula, considering the disappearance of the bonding effect near the crack after the beam yields,
Figure BDA0002120442560000021
Take it as 0.95, then the average crack calculation formula is: w m = 0.95ε sm l m ;

1.2构件的平均曲率

Figure BDA0002120442560000022
与εsm的关系式如下：1.2 Average curvature of the component
Figure BDA0002120442560000022
The relationship with ε sm is as follows:

Figure BDA0002120442560000023
Figure BDA0002120442560000023

其中:h0为截面有效高度；x为构件的受压区高度；Where: h0 is the effective height of the section; x is the height of the compression zone of the component;

1.3将步骤1.2中的公式代入步骤1.1公式中，得到平均裂缝宽度用曲率表达的公式为：1.3 Substitute the formula in step 1.2 into the formula in step 1.1 to obtain the formula for expressing the average crack width in terms of curvature:

Figure BDA0002120442560000024
Figure BDA0002120442560000024

所述步骤2)中，适受筋梁受拉钢筋刚屈服时的第一种情况:受压混凝土边缘应变εc≤峰值压应变ε0时,构建曲率的表达式包括以下步骤：In the step 2), the first case of the reinforced beam when the tensile reinforcement just yields: when the edge strain ε c of the compressive concrete is ≤ the peak compressive strain ε 0 , constructing the expression of the curvature includes the following steps:

2.1.1设截面屈服曲率为

Figure BDA0002120442560000025
受拉钢筋屈服时受压区混凝土水平应变为εc，受压区高度为xc,2.1.1 Assume that the yield curvature of the section is
Figure BDA0002120442560000025
When the tensile reinforcement yields, the horizontal strain of the concrete in the compression zone is ε c , and the height of the compression zone is x c .

根据平截面假定有：According to the plane section assumptions:

Figure BDA0002120442560000026
Figure BDA0002120442560000026

式中h0为截面有效高度，εy为为受拉区纵向普通钢筋应变；Where h0 is the effective height of the section, εy is the strain of the longitudinal ordinary reinforcement in the tension zone;

2.1.2根据力的平衡有：2.1.2 According to the balance of forces:

σ′sA′s+C＝fyAs σ′ s A′ s + C = f y A s

式中σ′s为受压区钢筋应力；C为混凝土受压区合力；A′s为受压区纵向钢筋的截面面积，fy为钢筋抗拉强度设计值，As为受拉区纵向钢筋的截面面积；Where σ ′s is the stress of the steel bar in the compression zone; C is the resultant force of the concrete in the compression zone; A ′s is the cross-sectional area of the longitudinal steel bar in the compression zone, fy is the design value of the tensile strength of the steel bar, and As is the cross-sectional area of the longitudinal steel bar in the tension zone;

则有：Then we have:

Figure BDA0002120442560000027
Figure BDA0002120442560000027

Figure BDA0002120442560000031
Figure BDA0002120442560000031

其中Es为钢筋的弹性模量，ε′s为受压区钢筋应变，a′s为受压区纵向钢筋合力点到截面受压边缘的距离；b为钢筋混凝土梁截面宽度，fc为混凝土轴心抗压强度设计值；Where E s is the elastic modulus of the steel bar, ε′ s is the strain of the steel bar in the compression zone, a′ s is the distance from the resultant force point of the longitudinal steel bar in the compression zone to the compression edge of the section; b is the cross-sectional width of the reinforced concrete beam, and f c is the design value of the axial compressive strength of the concrete;

2.1.3将步骤2.1.1中的公式代入步骤2.1.2中的第三个公式中得：2.1.3 Substitute the formula in step 2.1.1 into the third formula in step 2.1.2 to obtain:

Figure BDA0002120442560000032
Figure BDA0002120442560000032

2.1.4将步骤2.1.2中的第二个公式和步骤2.1.3的公式，代入步骤2.1.2中的第一个公式得：2.1.4 Substitute the second formula in step 2.1.2 and the formula in step 2.1.3 into the first formula in step 2.1.2 to obtain:

Figure BDA0002120442560000033
Figure BDA0002120442560000033

2.1.5对步骤2.1.4中的公式进行化简，在计算时忽略

Figure BDA0002120442560000034
因子，将
Figure BDA0002120442560000035
代入上式，则有：2.1.5 Simplify the formula in step 2.1.4 and ignore
Figure BDA0002120442560000034
Factor, will
Figure BDA0002120442560000035
Substituting into the above formula, we have:

Figure BDA0002120442560000036
Figure BDA0002120442560000036

则此时的屈服曲率为：The yield curvature at this time is:

Figure BDA0002120442560000037
Figure BDA0002120442560000037

式中：Where:

Figure BDA0002120442560000038
Figure BDA0002120442560000038

a2＝Esε0εyA′s+2fcbh0εy+fyAsε0 a 2 ＝E s ε 0 ε y A′ s +2f c bh 0 ε y +f y A s ε 0

Figure BDA0002120442560000039
Figure BDA0002120442560000039

所述步骤2)中，适受筋梁受拉钢筋刚屈服时的第二种情况：受压混凝土边缘应变εc＞峰值压应变ε0时，构建曲率的表达式包括以下步骤：In the step 2), the second case of the reinforced beam when the tensile reinforcement just yields: when the edge strain ε c of the compressive concrete is greater than the peak compressive strain ε 0 , constructing the expression of the curvature includes the following steps:

2.2.1设受压混凝土边缘应变达到峰值压应变ε0时的受压区高度为x0，2.2.1 Assume that the height of the compression zone when the edge strain of the compressed concrete reaches the peak compressive strain ε 0 is x 0 ,

根据平截面假定，有如下的变形协调方程：According to the plane section assumption, the following deformation coordination equation is obtained:

Figure BDA0002120442560000041
Figure BDA0002120442560000041

其中：ε为混凝土应变，x为混凝土应变达到ε时的混凝土受压区高度；Where: ε is the concrete strain, x is the height of the concrete compression zone when the concrete strain reaches ε;

2.2.2则根据受压混凝土的本构关系可知，压区混凝土的应力应变曲线为两段，一段为抛物线上升段，一段为水平段，所以对混凝土的积分应进行分段积分才能得到压应力合力C为：2.2.2 According to the constitutive relationship of compressed concrete, the stress-strain curve of the compression zone concrete is divided into two sections, one is a parabolic ascending section and the other is a horizontal section. Therefore, the integral of the concrete should be segmented to obtain the compressive stress resultant C:

Figure BDA0002120442560000042
Figure BDA0002120442560000042

则根据力平衡公式σ′sA′s+C＝fyAs和

Figure BDA0002120442560000043
可得：According to the force balance formula σ′ s A′ s + C = f y A s and
Figure BDA0002120442560000043
We can get:

Figure BDA0002120442560000044
Figure BDA0002120442560000044

其中σ′s为受压区钢筋应力，A′s为受压区纵向钢筋的截面面积，C为混凝土受压区合力，fy为钢筋抗拉强度设计值，As为受拉区纵向钢筋的截面面积；Es为钢筋的弹性模量，ε′s为受压区钢筋应变，a′s为受压区纵向钢筋合力点到截面受压边缘的距离；b为钢筋混凝土梁截面宽度，fc为混凝土轴心抗压强度设计值；Where σ′ s is the stress of the steel bar in the compression zone, A′ s is the cross-sectional area of the longitudinal steel bar in the compression zone, C is the resultant force in the compression zone of the concrete, f y is the design value of the tensile strength of the steel bar, A s is the cross-sectional area of the longitudinal steel bar in the tension zone; E s is the elastic modulus of the steel bar, ε′ s is the strain of the steel bar in the compression zone, a′ s is the distance from the resultant force point of the longitudinal steel bar in the compression zone to the compression edge of the section; b is the cross-sectional width of the reinforced concrete beam, and f c is the design value of the axial compressive strength of the concrete;

2.2.3将

Figure BDA0002120442560000045
代入步骤2.2.2最后得到的公式中，可得：2.2.3
Figure BDA0002120442560000045
Substituting into the formula obtained at the end of step 2.2.2, we get:

Figure BDA0002120442560000046
Figure BDA0002120442560000046

则此时的屈服曲率可通过上式计算得到：The yield curvature at this time can be calculated by the above formula:

Figure BDA0002120442560000047
Figure BDA0002120442560000047

式中：Where:

b1＝3EsA′s(h0-a′s)b 1 =3E s A′ s (h 0 -a′ s )

b2＝3EsA′sεy-3fcbh0+3fyAs b 2 ＝3E s A′ s ε y -3f c bh 0 +3f y A s

b3＝3fcbεy+fcbε0。b 3 =3f c bε y +f c bε 0 .

所述步骤2)中，适筋梁受压混凝土达到极限压应变εcu时，构建曲率的表达式包括以下步骤：In the step 2), when the compressive concrete of the reinforced beam reaches the ultimate compressive strain ε cu , constructing the expression of curvature includes the following steps:

2.3.1受压混凝土应力达到抗压强度fc，此时受拉钢筋应变大于屈服应变，可求得：2.3.1 When the stress of the compressed concrete reaches the compressive strength f c , the strain of the tensile reinforcement is greater than the yield strain, and we can obtain:

Figure BDA0002120442560000051
Figure BDA0002120442560000051

式中εs为受拉钢筋应变，xcu为受压混凝土达到极限压应变时的混凝土极限受压区高度；Where ε s is the strain of the tensile reinforcement, x cu is the height of the ultimate compression zone of the concrete when the compressive concrete reaches the ultimate compressive strain;

2.3.2在此种状态下，混凝土合力C的表达式为：2.3.2 Under this condition, the expression of concrete resultant force C is:

Figure BDA0002120442560000052
Figure BDA0002120442560000052

其中b为钢筋混凝土梁截面宽度，x0为受压混凝土边缘应变达到峰值压应变时的混凝土极限受压区高度，fc为混凝土轴心抗压强度设计值；Where b is the cross-sectional width of the reinforced concrete beam, x 0 is the height of the ultimate compression zone of the concrete when the edge strain of the compressed concrete reaches the peak compressive strain, and f c is the design value of the axial compressive strength of the concrete;

则根据力的平衡有σ′sA′s+C＝fyAs和

Figure BDA0002120442560000053
可得出：According to the balance of forces, we have σ′ s A′ s +C＝f y A s and
Figure BDA0002120442560000053
It can be concluded that:

Figure BDA0002120442560000054
Figure BDA0002120442560000054

σ′s为受压区钢筋应力，A′s为受压区纵向钢筋的截面面积，C为混凝土受压区合力，fy为钢筋抗拉强度设计值，As为受拉区纵向钢筋的截面面积；Es为钢筋的弹性模量，ε′s为受压区钢筋应变，a′s为受压区纵向钢筋合力点到截面受压边缘的距离；b为钢筋混凝土梁截面宽度，fc为混凝土轴心抗压强度设计值；σ′ s is the stress of the steel bar in the compression zone, A′ s is the cross-sectional area of the longitudinal steel bar in the compression zone, C is the resultant force in the compression zone of the concrete, f y is the design value of the tensile strength of the steel bar, A s is the cross-sectional area of the longitudinal steel bar in the tension zone; E s is the elastic modulus of the steel bar, ε′ s is the strain of the steel bar in the compression zone, a′ s is the distance from the resultant force point of the longitudinal steel bar in the compression zone to the compression edge of the section; b is the cross-sectional width of the reinforced concrete beam, and f c is the design value of the axial compressive strength of the concrete;

2.3.3将步骤2.3.2中最后得到的公式，用

Figure BDA0002120442560000055
的形式表示为：2.3.3 Use the formula obtained in step 2.3.2 to
Figure BDA0002120442560000055
The form is expressed as:

Figure BDA0002120442560000056
Figure BDA0002120442560000056

则此时的屈服曲率可通过上式计算得到：The yield curvature at this time can be calculated by the above formula:

Figure BDA0002120442560000057
Figure BDA0002120442560000057

c1＝3Esa′sA′s c 1 = 3E s a′ s A′ s

c2＝3EsεcuA′s-3fyAs-fcbx0 c 2 =3E s ε cu A′ s -3f y A s -f c bx 0

c3＝-2fcbεcu。c 3 = -2f c bε cu .

所述步骤3)中，将步骤2)中的曲率表达式代入步骤1)中，得到受压混凝土边缘应变εc≤峰值压应变ε0时：In step 3), the curvature expression in step 2) is substituted into step 1) to obtain the following when the edge strain ε c of the compressive concrete is ≤ the peak compressive strain ε 0 :

Figure BDA0002120442560000061
Figure BDA0002120442560000061

受压混凝土边缘应变εc＞峰值压应变ε0时：When the edge strain ε c of the compressive concrete is greater than the peak compressive strain ε 0 :

Figure BDA0002120442560000062
Figure BDA0002120442560000062

适筋梁受压混凝土达到极限压应变εcu时:When the compressive concrete of the properly reinforced beam reaches the ultimate compressive strain ε cu :

Figure BDA0002120442560000063
Figure BDA0002120442560000063

本发明的有益效果：本发明在考虑受拉钢筋屈服后的两个节点，即适筋梁受拉钢筋刚屈服时和适筋梁受压混凝土达到极限压应变时的基础上，考虑平均伸长与相应水平处构件侧表面混凝土平均伸长的差值来计算平均裂缝宽度，推导出了受拉钢筋屈服后的钢筋混凝土梁裂缝的计算方法，相较于传统的计算方法，本发明的方法计算出的裂缝宽度与实际的裂缝宽度更贴近。Beneficial effects of the present invention: The present invention calculates the average crack width by considering the difference between the average elongation and the average elongation of the concrete on the side surface of the component at the corresponding level, based on the two nodes after the yield of the tensile steel bars, namely, when the tensile steel bars of the properly reinforced beam have just yielded and when the compressive concrete of the properly reinforced beam has reached the ultimate compressive strain. The method for calculating the cracks in the reinforced concrete beam after the yield of the tensile steel bars is derived. Compared with the traditional calculation method, the crack width calculated by the method of the present invention is closer to the actual crack width.

附图说明BRIEF DESCRIPTION OF THE DRAWINGS

图1实施例2中受压混凝土边缘应变εc≤峰值压应变ε0，受力简图；FIG. 1 shows a force diagram of the compressed concrete edge strain ε c ≤ peak compressive strain ε 0 in Example 2;

图2实施例2中受压混凝土边缘应变εc＞峰值压应变ε0，受力简图；FIG2 shows the stress diagram of the edge strain ε c of the compressed concrete in Example 2, which is greater than the peak compressive strain ε 0 ;

图3实施例3中适筋梁受压混凝土达到极限压应变εcu时，受力简图。FIG3 is a schematic diagram of the forces when the compressive concrete of the properly reinforced beam in Example 3 reaches the ultimate compressive strain ε cu .

具体实施方式DETAILED DESCRIPTION

说明书中的

Figure BDA0002120442560000064
和
Figure BDA0002120442560000065
都是代表曲率，是同一参数，只是为了区分在不同情况下的推导过程，修改了下标。In the manual
Figure BDA0002120442560000064
and
Figure BDA0002120442560000065
They all represent curvature and are the same parameter, but the subscripts are modified to distinguish the derivation process in different cases.

实施例1平均裂缝宽度计算公式的构建Example 1 Construction of the average crack width calculation formula

平均裂缝宽度等于构件裂缝区段内钢筋的平均伸长与相应水平处构件侧表面混凝土平均伸长的差值：The average crack width is equal to the difference between the average elongation of the steel bars in the crack section of the component and the average elongation of the concrete on the side surface of the component at the corresponding level:

Figure BDA0002120442560000066
Figure BDA0002120442560000066

式中：εsm为纵向受拉钢筋的平均拉应变，εctm为与纵向受拉钢筋相同水平处侧表面混凝土的平均拉应变，lm为平均裂缝区段的钢筋混凝土梁计算长度。。Where: ε sm is the average tensile strain of the longitudinal tensile reinforcement, ε ctm is the average tensile strain of the side surface concrete at the same level as the longitudinal tensile reinforcement, and l m is the calculated length of the reinforced concrete beam in the average crack section.

考虑梁屈服后裂缝附近的粘结作用的消失，

Figure BDA0002120442560000071
取为0.95，则平均裂缝计算公式为：Considering the disappearance of the bonding effect near the crack after the beam yields,
Figure BDA0002120442560000071
Take it as 0.95, then the average crack calculation formula is:

wm＝0.95εsmlm (2)w m =0.95ε sm l m (2)

构件的平均曲率为

Figure BDA0002120442560000072
The average curvature of the component is
Figure BDA0002120442560000072

Figure BDA0002120442560000073
Figure BDA0002120442560000073

将式(2)用平均曲率的形式表示为：Formula (2) can be expressed in the form of mean curvature as:

Figure BDA0002120442560000074
Figure BDA0002120442560000074

式中x为构件的受压区高度。Where x is the height of the compression zone of the component.

实施例2筋梁受拉钢筋刚屈服时的裂缝计算方法Example 2 Calculation method for cracks in reinforced beam when tensile reinforcement just yields

适筋梁在受拉纵筋刚屈服时，以受压区边缘混凝土应变是否达到受压混凝土峰值应变为界限可分为以下两种情况考虑：When the tensile longitudinal reinforcement of the properly reinforced beam just yields, the following two situations can be considered based on whether the concrete strain at the edge of the compression zone reaches the peak strain of the compression concrete:

(1)当受拉纵筋刚屈服时，受压混凝土边缘应变εc≤峰值压应变ε0，受力简图如图1所示。(1) When the tensile longitudinal reinforcement just yields, the edge strain ε c of the compressive concrete is ≤ the peak compressive strain ε 0 . The force diagram is shown in Figure 1.

设截面屈服曲率为

Figure BDA0002120442560000075
受拉钢筋屈服时受压区混凝土水平应变为εc，受压区高度为xc,计算简图如图2所示：Assume the yield curvature of the section is
Figure BDA0002120442560000075
When the tensile reinforcement yields, the horizontal strain of the concrete in the compression zone is ε c , and the height of the compression zone is x c . The calculation diagram is shown in Figure 2:

根据平截面假定有：According to the plane section assumptions:

Figure BDA0002120442560000076
Figure BDA0002120442560000076

其中h0为截面有效高度，εy为为受拉区纵向普通钢筋应变。Where h0 is the effective height of the section and εy is the strain of the longitudinal ordinary reinforcement in the tension zone.

根据力的平衡有：According to the balance of forces:

σ′sA′s+C＝fyAs (7)σ′ s A′ s +C＝f y A s (7)

式中σ′s为受压区钢筋应力；C为混凝土受压区合力；A′s为受压区纵向钢筋的截面面积，fy为钢筋抗拉强度设计值，As为受拉区纵向钢筋的截面面积；Where σ ′s is the stress of the steel bar in the compression zone; C is the resultant force of the concrete in the compression zone; A ′s is the cross-sectional area of the longitudinal steel bar in the compression zone, fy is the design value of the tensile strength of the steel bar, and As is the cross-sectional area of the longitudinal steel bar in the tension zone;

则有：Then we have:

Figure BDA0002120442560000081
Figure BDA0002120442560000081

Figure BDA0002120442560000082
Figure BDA0002120442560000082

式中Es为钢筋的弹性模量，ε′s为受压区钢筋应变，a′s为受压区纵向钢筋合力点到截面受压边缘的距离；b为钢筋混凝土梁截面宽度，fc为混凝土轴心抗压强度设计值；Where E s is the elastic modulus of the steel bar, ε′ s is the strain of the steel bar in the compression zone, a′ s is the distance from the resultant force point of the longitudinal steel bar in the compression zone to the compression edge of the section; b is the cross-sectional width of the reinforced concrete beam, and f c is the design value of the axial compressive strength of the concrete;

将式(6)代入式(9)中得：Substituting formula (6) into formula (9), we get:

Figure BDA0002120442560000083
Figure BDA0002120442560000083

将式(8)和式(10)，代入式(7)中得：Substituting equation (8) and equation (10) into equation (7), we get:

Figure BDA0002120442560000084
Figure BDA0002120442560000084

对式(11)进行化简，在计算时忽略

Figure BDA0002120442560000085
因子，将
Figure BDA0002120442560000086
代入上式，则有：Simplify formula (11) and ignore
Figure BDA0002120442560000085
Factor, will
Figure BDA0002120442560000086
Substituting into the above formula, we have:

Figure BDA0002120442560000087
Figure BDA0002120442560000087

则此时的屈服曲率为：The yield curvature at this time is:

Figure BDA0002120442560000088
Figure BDA0002120442560000088

式中：Where:

Figure BDA0002120442560000089
Figure BDA0002120442560000089

a2＝Esε0εyA′s+2fcbh0εy+fyAsε0 (15)a 2 ＝E s ε 0 ε y A′ s +2f c bh 0 ε y +f y A s ε 0 (15)

Figure BDA00021204425600000810
Figure BDA00021204425600000810

将以上屈服曲率公式代入公式(4)中，可得第一种情况下的裂缝计算公式Substituting the above yield curvature formula into formula (4), we can obtain the crack calculation formula for the first case:

Figure BDA00021204425600000811
Figure BDA00021204425600000811

(2)当受拉纵筋刚屈服时，且受压混凝土边缘应变εc＞峰值压应变ε0 (2) When the tensile longitudinal reinforcement has just yielded and the compressive concrete edge strain ε c > peak compressive strain ε 0

设受压混凝土边缘应变达到峰值压应变ε0时的受压区高度为x0。Assume that the height of the compression zone when the edge strain of the compressed concrete reaches the peak compressive strain ε 0 is x 0 .

根据平截面假定，有如下的变形协调方程：According to the plane section assumption, the following deformation coordination equation is obtained:

Figure BDA0002120442560000091
Figure BDA0002120442560000091

则根据受压混凝土的本构关系可知，压区混凝土的应力应变曲线为两段，一段为抛物线上升段，一段为水平段，所以对混凝土的积分应进行分段积分才能得到压应力合力C为：According to the constitutive relationship of compressed concrete, the stress-strain curve of the compression zone concrete is divided into two sections, one is a parabolic ascending section, and the other is a horizontal section. Therefore, the integral of the concrete should be segmented to obtain the compressive stress resultant C:

Figure BDA0002120442560000092
Figure BDA0002120442560000092

则式(7)变为：Then formula (7) becomes:

Figure BDA0002120442560000093
Figure BDA0002120442560000093

将

Figure BDA0002120442560000094
代入上式，可得：Will
Figure BDA0002120442560000094
Substituting into the above formula, we can get:

Figure BDA0002120442560000095
Figure BDA0002120442560000095

则此时的屈服曲率可通过上式计算得到：The yield curvature at this time can be calculated by the above formula:

Figure BDA0002120442560000096
Figure BDA0002120442560000096

式中：Where:

Figure BDA0002120442560000097
Figure BDA0002120442560000097

b2＝3EsA′sεy-3fcbh0+3fyAs (23)b 2 ＝3E s A′ s ε y -3f c bh 0 +3f y A s (23)

b3＝3fcbεy+fcbε0 (24)b 3 =3f c bε y +f c bε 0 (24)

将屈服曲率公式代入公式(4)中，可得第二种情况下的裂缝计算公式。Substituting the yield curvature formula into formula (4), we can obtain the crack calculation formula for the second case.

Figure BDA0002120442560000101
Figure BDA0002120442560000101

实施例3适筋梁受压混凝土达到极限压应变时裂缝计算方法Example 3 Calculation method for cracks when the compression concrete of the reinforced beam reaches the ultimate compressive strain

适筋梁受压混凝土达到极限压应变εcu时，受压混凝土应力达到抗压强度fc，此时受拉钢筋应变大于屈服应变，则达到极限变形时的应力图形和应变图形如图3所示。When the compressive concrete of the properly reinforced beam reaches the ultimate compressive strain ε cu , the compressive concrete stress reaches the compressive strength f c , and the strain of the tensile reinforcement is greater than the yield strain. The stress and strain diagrams when the ultimate deformation is reached are shown in Figure 3.

通过图3中的几何条件可求得：Through the geometric conditions in Figure 3, we can obtain:

Figure BDA0002120442560000102
Figure BDA0002120442560000102

则混凝土合力为：The resultant force of concrete is:

Figure BDA0002120442560000103
Figure BDA0002120442560000103

则根据力的平衡有：According to the balance of forces:

Figure BDA0002120442560000104
Figure BDA0002120442560000104

将上式用

Figure BDA0002120442560000105
的形式表示为：Use the above formula
Figure BDA0002120442560000105
The form is expressed as:

Figure BDA0002120442560000106
Figure BDA0002120442560000106

则此时的屈服曲率可通过上式计算得到：The yield curvature at this time can be calculated by the above formula:

Figure BDA0002120442560000107
Figure BDA0002120442560000107

c1＝3Esa′sA′s (30)c 1 =3E s a′ s A′ s (30)

c2＝3EsεcuA′s-3fyAs-fcbx0 (31)c 2 ＝3E s ε cu A′ s -3f y A s -f c bx 0 (31)

c3＝-2fcbεcu (32)c 3 = -2f c bε cu (32)

将屈服曲率公式代入公式(4)中，可得第三种情况下的裂缝计算公式，Substituting the yield curvature formula into formula (4), we can obtain the crack calculation formula for the third case:

Figure BDA0002120442560000108
Figure BDA0002120442560000108

Claims (8)

1.一种全户内变电站主控楼钢筋混凝土梁裂缝计算方法，包括以下步骤：1. A method for calculating cracks in reinforced concrete beams of a main control building of an indoor substation, comprising the following steps: 1)根据平均裂缝宽度的经验公式，构建出平均裂缝宽度用曲率表达的公式；1) Based on the empirical formula of average crack width, a formula for expressing the average crack width in terms of curvature is constructed; 2)根据当受拉纵筋刚屈服时的两种情况：第一种情况：受压混凝土边缘应变εc≤峰值压应变ε0；第二种情况：受压混凝土边缘应变εc>峰值压应变ε0；以及适筋梁受压混凝土达到极限压应变时的情况，构建曲率的表达式；2) According to the two cases when the tensile longitudinal reinforcement just yields: the first case: the edge strain of the compressive concrete ε c ≤ the peak compressive strain ε 0 ; the second case: the edge strain of the compressive concrete ε c > the peak compressive strain ε 0 ; and the case when the compressive concrete of the properly reinforced beam reaches the ultimate compressive strain, construct an expression for the curvature; 适受筋梁受拉钢筋刚屈服时的第一种情况:受压混凝土边缘应变εc≤峰值压应变ε0时,构建曲率的表达式包括以下步骤：The first case of a reinforced beam with tensile reinforcement just yielding: when the edge strain of the compressive concrete ε c ≤ the peak compressive strain ε 0 , constructing the expression for the curvature includes the following steps: 2.1.1设截面屈服曲率为
Figure FDA0004118684230000011
受拉钢筋屈服时受压区混凝土水平应变为εc，受压区高度为xc,2.1.1 Assume that the yield curvature of the section is
Figure FDA0004118684230000011
When the tensile reinforcement yields, the horizontal strain of the concrete in the compression zone is ε c , and the height of the compression zone is x c . 根据平截面假定有：According to the plane section assumptions:
Figure FDA0004118684230000012
Figure FDA0004118684230000012
 式中h0为截面有效高度，εy为为受拉区纵向普通钢筋应变；Where h0 is the effective height of the section, εy is the strain of the longitudinal ordinary reinforcement in the tension zone; 2.1.2根据力的平衡有：2.1.2 According to the balance of forces: σ′sA′s+C＝fyAs σ′ s A′ s + C = f y A s 式中σ′s为受压区钢筋应力；C为混凝土受压区合力；A′s为受压区纵向钢筋的截面面积，fy为钢筋抗拉强度设计值，As为受拉区纵向钢筋的截面面积；Where σ ′s is the stress of the steel bar in the compression zone; C is the resultant force of the concrete in the compression zone; A ′s is the cross-sectional area of the longitudinal steel bar in the compression zone, fy is the design value of the tensile strength of the steel bar, and As is the cross-sectional area of the longitudinal steel bar in the tension zone; 则有：Then we have:
Figure FDA0004118684230000013
Figure FDA0004118684230000013
Figure FDA0004118684230000014
Figure FDA0004118684230000014
 式中Es为钢筋的弹性模量，ε′s为受压区钢筋应变，a′s为受压区纵向钢筋合力点到截面受压边缘的距离；b为钢筋混凝土梁截面宽度，fc为混凝土轴心抗压强度设计值；Where E s is the elastic modulus of the steel bar, ε′ s is the strain of the steel bar in the compression zone, a′ s is the distance from the resultant force point of the longitudinal steel bar in the compression zone to the compression edge of the section; b is the cross-sectional width of the reinforced concrete beam, and f c is the design value of the axial compressive strength of the concrete; 2.1.3将步骤2.1.1中的公式代入步骤2.1.2中的第三个公式中得：2.1.3 Substitute the formula in step 2.1.1 into the third formula in step 2.1.2 to obtain:
Figure FDA0004118684230000015
Figure FDA0004118684230000015
 2.1.4将步骤2.1.2中的第二个公式和步骤2.1.3的公式，代入步骤2.1.2中的第一个公式得：2.1.4 Substitute the second formula in step 2.1.2 and the formula in step 2.1.3 into the first formula in step 2.1.2 to obtain:
Figure FDA0004118684230000021
Figure FDA0004118684230000021
 2.1.5对步骤2.1.4中的公式进行化简，在计算时忽略
Figure FDA0004118684230000022
因子，将
Figure FDA0004118684230000023
代入上式，则有：2.1.5 Simplify the formula in step 2.1.4 and ignore
Figure FDA0004118684230000022
Factor, will
Figure FDA0004118684230000023
Substituting into the above formula, we have:
Figure FDA0004118684230000024
Figure FDA0004118684230000024
 则此时的屈服曲率为：The yield curvature at this time is:
Figure FDA0004118684230000025
Figure FDA0004118684230000025
 式中：Where:
Figure FDA0004118684230000026
Figure FDA0004118684230000026
 a2＝Esε0εyA′s+2fcbh0εy+fyAsε0 a 2 ＝E s ε 0 ε y A′ s +2f c bh 0 ε y +f y A s ε 0
Figure FDA0004118684230000027
Figure FDA0004118684230000027
 3)将步骤2)中曲率表达式代入步骤1)的公式中，即得考虑了钢筋应力影响的裂缝宽度的计算公式。3) Substitute the curvature expression in step 2) into the formula in step 1) to obtain the calculation formula for the crack width that takes into account the influence of steel bar stress. 2.根据权利要求1所述的全户内变电站主控楼钢筋混凝土梁裂缝计算方法，其特征在于，所述步骤1)中，经验公式为：2. The method for calculating cracks in reinforced concrete beams of the main control building of the fully indoor substation according to claim 1, characterized in that in the step 1), the empirical formula is:
Figure FDA0004118684230000028
Figure FDA0004118684230000028
 式中，wm为平均裂缝宽度，εsm为纵向受拉钢筋的平均拉应变，εctm为与纵向受拉钢筋相同水平处侧表面混凝土的平均拉应变，lm为平均裂缝区段的钢筋混凝土梁计算长度。Where wm is the average crack width, εsm is the average tensile strain of the longitudinal tensile reinforcement, εctm is the average tensile strain of the side surface concrete at the same level as the longitudinal tensile reinforcement, and lm is the calculated length of the reinforced concrete beam in the average crack section. 3.根据权利要求2所述的全户内变电站主控楼钢筋混凝土梁裂缝计算方法，其特征在于，所述构建出平均裂缝宽度用曲率表达的公式，具体包括以下步骤：3. The method for calculating cracks in reinforced concrete beams of the main control building of a fully indoor substation according to claim 2 is characterized in that the formula for expressing the average crack width in terms of curvature specifically comprises the following steps: 1.1根据经验公式，考虑梁屈服后裂缝附近的粘结作用的消失，
Figure FDA0004118684230000029
取为0.95，则平均裂缝计算公式为：wm＝0.95εsmlm；1.1 According to the empirical formula, considering the disappearance of the bonding effect near the crack after the beam yields,
Figure FDA0004118684230000029
Take it as 0.95, then the average crack calculation formula is: w m = 0.95ε sm l m ; 1.2构件的平均曲率
Figure FDA0004118684230000031
与εsm的关系式如下：1.2 Average curvature of the component
Figure FDA0004118684230000031
The relationship with ε sm is as follows:
Figure FDA0004118684230000032
Figure FDA0004118684230000032
 其中:h0为截面有效高度；x为构件的受压区高度；Where: h0 is the effective height of the section; x is the height of the compression zone of the component; 1.3将步骤1.2中的公式代入步骤1.1公式中，得到平均裂缝宽度用曲率表达的公式为：1.3 Substitute the formula in step 1.2 into the formula in step 1.1 to obtain the formula for expressing the average crack width in terms of curvature:
Figure FDA0004118684230000033
Figure FDA0004118684230000033
 4.根据权利要求3所述的全户内变电站主控楼钢筋混凝土梁裂缝计算方法，其特征在于，所述步骤2)中，适受筋梁受拉钢筋刚屈服时的第二种情况：受压混凝土边缘应变εc＞峰值压应变ε0时，构建曲率的表达式包括以下步骤：4. The method for calculating cracks in reinforced concrete beams of the main control building of the fully indoor substation according to claim 3 is characterized in that, in the step 2), in the second case when the tensile reinforcement of the reinforced beam just yields: when the edge strain ε c of the compressive concrete is greater than the peak compressive strain ε 0 , constructing the expression for the curvature comprises the following steps: 2.2.1设受压混凝土边缘应变达到峰值压应变ε0时的受压区高度为x0，2.2.1 Assume that the height of the compression zone when the edge strain of the compressed concrete reaches the peak compressive strain ε 0 is x 0 , 根据平截面假定，有如下的变形协调方程：According to the plane section assumption, the following deformation coordination equation is obtained:
Figure FDA0004118684230000034
Figure FDA0004118684230000034
 式中：ε为混凝土应变，x为混凝土应变达到ε时的混凝土受压区高度；Where: ε is the concrete strain, x is the height of the concrete compression zone when the concrete strain reaches ε; 2.2.2则根据受压混凝土的本构关系可知，压区混凝土的应力应变曲线为两段，一段为抛物线上升段，一段为水平段，所以对混凝土的积分应进行分段积分才能得到压应力合力C为：2.2.2 According to the constitutive relationship of compressed concrete, the stress-strain curve of the compression zone concrete is divided into two sections, one is a parabolic ascending section and the other is a horizontal section. Therefore, the integral of the concrete should be segmented to obtain the compressive stress resultant C:
Figure FDA0004118684230000035
Figure FDA0004118684230000035
 则根据力平衡公式σ′sA′s+C＝fyAs和
Figure FDA0004118684230000036
可得：According to the force balance formula σ′ s A′ s + C = f y A s and
Figure FDA0004118684230000036
We can get:
Figure FDA0004118684230000037
Figure FDA0004118684230000037
 其中σ′s为受压区钢筋应力，A′s为受压区纵向钢筋的截面面积，C为混凝土受压区合力，fy为钢筋抗拉强度设计值，As为受拉区纵向钢筋的截面面积；Es为钢筋的弹性模量，ε′s为受压区钢筋应变，a′s为受压区纵向钢筋合力点到截面受压边缘的距离；b为钢筋混凝土梁截面宽度，fc为混凝土轴心抗压强度设计值；Where σ′ s is the stress of the steel bar in the compression zone, A′ s is the cross-sectional area of the longitudinal steel bar in the compression zone, C is the resultant force in the compression zone of the concrete, f y is the design value of the tensile strength of the steel bar, As is the cross-sectional area of the longitudinal steel bar in the tension zone; E s is the elastic modulus of the steel bar, ε′ s is the strain of the steel bar in the compression zone, a′ s is the distance from the resultant force point of the longitudinal steel bar in the compression zone to the compression edge of the section; b is the cross-sectional width of the reinforced concrete beam, and f c is the design value of the axial compressive strength of the concrete; 2.2.3将
Figure FDA0004118684230000041
代入步骤2.2.2最后得到的公式中，可得：2.2.3
Figure FDA0004118684230000041
Substituting into the formula obtained at the end of step 2.2.2, we get:
Figure FDA0004118684230000042
Figure FDA0004118684230000042
 则此时的屈服曲率可通过上式计算得到：The yield curvature at this time can be calculated by the above formula:
Figure FDA0004118684230000043
Figure FDA0004118684230000043
 式中：Where: b1＝3EsA′s(h0-a′s)b 1 =3E s A′ s (h 0 -a′ s ) b2＝3EsA′sεy-3fcbh0+3fyAs b 2 ＝3E s A′ s ε y -3f c bh 0 +3f y A s b3＝3fcbεy+fcbε0。b 3 =3f c bε y +f c bε 0 . 5.根据权利要求4所述的全户内变电站主控楼钢筋混凝土梁裂缝计算方法，其特征在于，所述步骤2)中，适筋梁受压混凝土达到极限压应变εcu时，构建曲率的表达式包括以下步骤：5. The method for calculating cracks in reinforced concrete beams of the main control building of the fully indoor substation according to claim 4 is characterized in that, in the step 2), when the compressive concrete of the reinforced beam reaches the ultimate compressive strain ε cu , constructing the expression of curvature comprises the following steps: 2.3.1受压混凝土应力达到抗压强度fc，此时受拉钢筋应变大于屈服应变，可求得：2.3.1 When the stress of the compressed concrete reaches the compressive strength f c , the strain of the tensile reinforcement is greater than the yield strain, and we can obtain:
Figure FDA0004118684230000044
Figure FDA0004118684230000044
 式中εs为受拉钢筋应变，xcu为受压混凝土达到极限压应变时的混凝土极限受压区高度；Where ε s is the strain of the tensile reinforcement, x cu is the height of the ultimate compression zone of the concrete when the compressive concrete reaches the ultimate compressive strain; 2.3.2在此种状态下，混凝土合力C的表达式为：2.3.2 Under this condition, the expression of concrete resultant force C is:
Figure FDA0004118684230000045
Figure FDA0004118684230000045
 其中b为钢筋混凝土梁截面宽度，x0为受压混凝土边缘应变达到峰值压应变时的混凝土极限受压区高度，fc为混凝土轴心抗压强度设计值；Where b is the cross-sectional width of the reinforced concrete beam, x 0 is the height of the ultimate compression zone of the concrete when the edge strain of the compressed concrete reaches the peak compressive strain, and f c is the design value of the axial compressive strength of the concrete; 则根据力的平衡有σ′sA′s+C＝fyAs和
Figure FDA0004118684230000046
可得出：According to the balance of forces, we have σ′ s A′ s +C＝f y A s and
Figure FDA0004118684230000046
It can be concluded that:
Figure FDA0004118684230000047
Figure FDA0004118684230000047
 σ′s为受压区钢筋应力，A′s为受压区纵向钢筋的截面面积，C为混凝土受压区合力，fy为钢筋抗拉强度设计值，As为受拉区纵向钢筋的截面面积；Es为钢筋的弹性模量，ε′s为受压区钢筋应变，a′s为受压区纵向钢筋合力点到截面受压边缘的距离；b为钢筋混凝土梁截面宽度，fc为混凝土轴心抗压强度设计值；σ′ s is the stress of the steel bar in the compression zone, A′ s is the cross-sectional area of the longitudinal steel bar in the compression zone, C is the resultant force in the compression zone of the concrete, f y is the design value of the tensile strength of the steel bar, As is the cross-sectional area of the longitudinal steel bar in the tension zone; E s is the elastic modulus of the steel bar, ε′ s is the strain of the steel bar in the compression zone, a′ s is the distance from the resultant force point of the longitudinal steel bar in the compression zone to the compression edge of the section; b is the cross-sectional width of the reinforced concrete beam, and f c is the design value of the axial compressive strength of the concrete; 2.3.3将步骤2.3.2中最后得到的公式，用
Figure FDA0004118684230000051
的形式表示为：2.3.3 Use the formula obtained in step 2.3.2 to
Figure FDA0004118684230000051
The form is expressed as:
Figure FDA0004118684230000052
Figure FDA0004118684230000052
 则此时的屈服曲率可通过上式计算得到：The yield curvature at this time can be calculated by the above formula:
Figure FDA0004118684230000053
Figure FDA0004118684230000053
 c1＝3Esa′sA′s c 1 = 3E s a′ s A′ s c2＝3EsεcuA′s-3fyAs-fcbx0 c 2 =3E s ε cu A′ s -3f y A s -f c bx 0 c3＝-2fcbεcu。c 3 = -2f c bε cu . 6.根据权利要求5所述的全户内变电站主控楼钢筋混凝土梁裂缝计算方法，其特征在于，所述步骤3)中，将步骤2)中的曲率表达式代入步骤1)中，得到受压混凝土边缘应变εc≤峰值压应变ε0时：6. The method for calculating cracks in reinforced concrete beams of the main control building of the fully indoor substation according to claim 5, characterized in that, in the step 3), the curvature expression in step 2) is substituted into step 1) to obtain the compressive concrete edge strain ε c ≤ peak compressive strain ε 0 :
Figure FDA0004118684230000054
Figure FDA0004118684230000054
 7.根据权利要求6所述的全户内变电站主控楼钢筋混凝土梁裂缝计算方法，其特征在于，所述步骤3)中，将步骤2)中的曲率表达式代入步骤1)中，受压混凝土边缘应变εc＞峰值压应变ε0时：7. The method for calculating cracks in reinforced concrete beams of the main control building of the fully indoor substation according to claim 6, characterized in that, in the step 3), the curvature expression in the step 2) is substituted into the step 1), and when the edge strain ε c of the compressive concrete is greater than the peak compressive strain ε 0 :
Figure FDA0004118684230000055
Figure FDA0004118684230000055
 8.根据权利要求7所述的全户内变电站主控楼钢筋混凝土梁裂缝计算方法，其特征在于，所述步骤3)中，将步骤2)中的曲率表达式代入步骤1)中，适筋梁受压混凝土达到极限压应变εcu时:8. The method for calculating cracks in reinforced concrete beams of the main control building of the fully indoor substation according to claim 7 is characterized in that, in the step 3), the curvature expression in step 2) is substituted into step 1), and when the compressive concrete of the reinforced beam reaches the ultimate compressive strain ε cu :
Figure FDA0004118684230000061
Figure FDA0004118684230000061
CN201910604725.4A 2019-07-05 2019-07-05 Method for calculating cracks of reinforced concrete beam of main control building of all-indoor substation Active CN110298133B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201910604725.4A CN110298133B (en) 2019-07-05 2019-07-05 Method for calculating cracks of reinforced concrete beam of main control building of all-indoor substation

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201910604725.4A CN110298133B (en) 2019-07-05 2019-07-05 Method for calculating cracks of reinforced concrete beam of main control building of all-indoor substation

Publications (2)

Publication Number Publication Date
CN110298133A CN110298133A (en) 2019-10-01
CN110298133B true CN110298133B (en) 2023-05-26

Family

ID=68030463

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201910604725.4A Active CN110298133B (en) 2019-07-05 2019-07-05 Method for calculating cracks of reinforced concrete beam of main control building of all-indoor substation

Country Status (1)

Country Link
CN (1) CN110298133B (en)

Families Citing this family (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112464345B (en) * 2020-11-26 2024-02-02 北京工业大学 Earthquake damage reinforced concrete column crack width calculation method based on deformation
CN113642087B (en) * 2021-09-13 2022-11-15 东南大学 A Prediction Method for the Shear Performance of Reinforced Concrete Beams with Square Section

Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102622493A (en) * 2012-03-31 2012-08-01 广东省电力设计研究院 Method and device for determining maximum crack widths of ring-shaped members of round coal bunker
CN108614936A (en) * 2018-05-28 2018-10-02 湖南省建筑设计院有限公司 Steel-concrete composite beam analysis of calculation models method based on peg connection

Family Cites Families (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102359229B (en) * 2011-08-05 2013-05-01 重庆大学 Suitable method for determining ideal ratio of reinforcement of reinforced concrete beam under usage of bending moment
CN105040904B (en) * 2015-07-13 2017-10-10 涂建维 A kind of construction method of fracture width and the FRP Concrete Beam Reinforceds of amount of deflection control
JP6706499B2 (en) * 2015-12-28 2020-06-10 東日本旅客鉄道株式会社 Steel-concrete sandwich structure design method.
CN106485029B (en) * 2016-10-27 2019-07-09 北京市市政工程研究院 Bearing capacity evaluation method after Concrete beam bridge damage based on overstrain
CN109190309B (en) * 2018-10-25 2023-03-31 长沙理工大学 Method for evaluating shear-resisting bearing capacity of aged reinforced concrete beam bridge

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102622493A (en) * 2012-03-31 2012-08-01 广东省电力设计研究院 Method and device for determining maximum crack widths of ring-shaped members of round coal bunker
CN108614936A (en) * 2018-05-28 2018-10-02 湖南省建筑设计院有限公司 Steel-concrete composite beam analysis of calculation models method based on peg connection

Also Published As

Publication number Publication date
CN110298133A (en) 2019-10-01

Similar Documents

Publication Publication Date Title
Collins Towards a rational theory for RC members in shear
CN105956256B (en) Bearing capacity evaluation and reinforcement calculation method for complex areas of existing concrete bridges
CN109750748B (en) A Direct Performance Based Design Method for Reinforced Concrete Structures
JP6699639B2 (en) Steel beam design method used for floor structure, floor structure
CN110298133B (en) Method for calculating cracks of reinforced concrete beam of main control building of all-indoor substation
CN113642087B (en) A Prediction Method for the Shear Performance of Reinforced Concrete Beams with Square Section
CN109885925B (en) Method for calculating bearing capacity of assembled PEC (reinforced concrete) composite beam
CN114330019A (en) Calculation method of flexural capacity of composite beams with unbonded prestressed corrugated steel webs in vivo
CN110619165A (en) Method for determining shear-resisting bearing capacity of horizontal connection connecting beam of fabricated shear wall and application
CN105888289B (en) Reinforcement Treatment Structure of Head-holding Beam and Gold Column Joints in Ancient Buildings
CN110147622B (en) Method for determining crack width of fully fabricated steel-concrete composite girder bridge
CN109933838A (en) A whole-process slip calculation method for prefabricated shear connectors
CN104598723A (en) Method for predicting shear-bearing capacity of steel-concrete-steel combined deep beam
Mursi et al. Behaviour and design of fabricated high strength steel columns subjected to biaxial bending, Part II: Analysis and design codes
CN210439720U (en) Reinforced structure for increasing cross section of concrete beam side
CN109977454B (en) Rapid optimization design method for self-resetting prefabricated frame structure nodes
CN116305414B (en) Shear design method and device based on wedge-shaped section shear model
CN104462804B (en) A kind of fast determination method of PCCP pipelines geometrical characteristic
Zheng et al. Shear test of variable depth rc beams with inflection point
CN109112946B (en) Construction method of steel truss-corrugated steel web large-span combined beam bridge
CN108005248B (en) Design and evaluation method of reinforced asphalt isolation pier wall under earthquake
CN208235796U (en) A kind of FRP tendons-reinforcing bar composite strengthening ECC- Combined concrete T-type beam
CN116305413B (en) Wedge-shaped section combined shear design method and device
CN118332668B (en) A calculation method for the flexural bearing capacity of reinforced concrete beams reinforced with bonded steel
CN109635476A (en) Design method of combined beam column joint

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant