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

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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
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陈幸
陈国华
李玉婷
陈盛华
彭怀德
吴浩
王敏
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State Grid Corp of China SGCC
Economic and Technological Research Institute of State Grid Jiangxi Electric Power Co Ltd
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Abstract

The invention discloses a method for calculating cracks of reinforced concrete beams of a main control building of a full indoor transformer substation, which comprises the following steps: 1) According to the average crack width w m The empirical formula of (2) constructs the average crack width w m By curvature
Figure DDA0002120442580000011
An expressed formula; 2) According to two cases when the tensile longitudinal bar just yields (first case: edge strain epsilon of pressed concrete c Peak compressive strain epsilon less than or equal to 0 The method comprises the steps of carrying out a first treatment on the surface of the Second case: edge strain of pressed concrete εc >Peak compressive strain epsilon 0 ) Constructing an expression of curvature under the condition that the concrete pressed by the adaptive beam reaches the limit compressive strain; 3) Substituting the curvature expression in the step 2) into the formula of the step 1) to obtain a calculation formula of the crack width considering the influence of the steel bar stress. Compared with the traditional calculation method, the method for calculating the crack of the reinforced concrete beam after the tensile steel bar is yielded is closer to the actual crack width.

Description

Method for calculating cracks of reinforced concrete beam of main control building of all-indoor substation
Technical Field
The invention belongs to the technical field of civil engineering, and particularly relates to a method for calculating cracks of reinforced concrete beams of a main control building of a full indoor transformer substation.
Background
When the elastoplasticity analysis is performed on the reinforced concrete beam, if the amplitude modulation coefficient of the bending moment is excessively large, the amplitude-modulated reinforced concrete beam may yield under the action of external load. We generally use the formula set forth in the specification when calculating the crack width, where the effect of the bar stress is not taken into account, and where the crack width of the member will not change after the bar yields, which is not practical and therefore the accuracy of the crack width obtained according to the formula set forth in the specification is not high.
In general, the reinforced concrete structure may yield under the action of accidental load, and the deformation, crack width and the like of the member after the steel bar yields are important indexes for judging whether the structure can be repaired and determining the repair and reinforcement degree, so that the research on the crack width of the member after the steel bar yields is very little at home and abroad, and a crack calculation method after the steel bar yields is very necessary.
Disclosure of Invention
The invention aims to provide a method for calculating the crack of the reinforced concrete beam of the main control building of the whole indoor transformer substation, which considers the influence of the stress of the reinforced concrete, and improves the accuracy of calculating the width of the crack.
The invention discloses a method for calculating cracks of reinforced concrete beams of a main control building of a full indoor transformer substation, which comprises the following steps:
1) Constructing a formula for expressing the average crack width by using curvature according to an empirical formula of the average crack width;
2) According to two cases when the tendon is pulled by the tendon but is just yielding (first case: edge strain epsilon of pressed concrete c Peak compressive strain epsilon less than or equal to 0 The method comprises the steps of carrying out a first treatment on the surface of the Second case: edge strain epsilon of pressed concrete c >Peak compressive strain epsilon 0 ) Constructing an expression of curvature under the condition that the concrete pressed by the adaptive beam reaches the limit compressive strain;
3) Substituting the curvature expression in the step 2) into the formula of the step 1) to obtain a calculation formula of the crack width considering the influence of the steel bar stress.
In the step 1), the empirical formula is:
Figure BDA0002120442560000011
wherein w is m For average crack width ε sm Epsilon for average tensile strain of a longitudinally tensioned steel bar ctm For the average tensile strain of the side surface concrete at the same level as the longitudinal tensile bars, l m The length is calculated for the reinforced concrete beam of the average crack section.
The formula for constructing the curvature expression of the average crack width specifically comprises the following steps:
1.1 according to an empirical formula, considering the disappearance of the adhesion near the crack after yielding of the beam,
Figure BDA0002120442560000021
taking 0.95, the average fracture calculation formula is: w (w) m ＝0.95ε sm l m ；
1.2 mean curvature of the Member
Figure BDA0002120442560000022
And epsilon sm The relation of (2) is as follows:
Figure BDA0002120442560000023
wherein h is 0 Is the effective height of the section; x is the compressed zone height of the component;
1.3 substituting the formula in step 1.2 into the formula in step 1.1 to obtain the formula for expressing the average crack width by curvature, wherein the formula is as follows:
Figure BDA0002120442560000024
in the step 2), the first condition of the tensile steel bar of the stressed beam when being just bent is that the edge strain epsilon of the stressed concrete c Peak compressive strain epsilon less than or equal to 0 When constructing an expression for curvature, comprising the steps of:
2.1.1 setting the section yield curvature as
Figure BDA0002120442560000025
The horizontal strain of the concrete in the compression area is epsilon when the tension steel bar yields c The height of the pressed area is x c ,
Based on the plain section, it is assumed that:
Figure BDA0002120442560000026
h in 0 Epsilon is the effective height of the section y Is a longitudinal common steel bar strain in a tension zone;
2.1.2 according to the balance of forces:
σ′ s A′ s +C＝f y A s
sigma 'in' s Is the stress of the steel bars in the pressed area; c is the resultant force of the concrete compression area; a's' s Is the cross-sectional area of the longitudinal steel bar of the compression zone, f y Is designed as the tensile strength of the steel bar, A s The cross-sectional area of the longitudinal steel bar in the tension zone;
then there are:
Figure BDA0002120442560000027
Figure BDA0002120442560000031
wherein E is s Is the elastic modulus of the steel bar, epsilon' s For the strain of the reinforcement bar in the pressed area, a' s The distance from the longitudinal steel bar combining force point of the compression area to the compression edge of the section; b is the section width of the reinforced concrete beam, f c The design value of the compressive strength of the concrete axle center is designed;
2.1.3 substituting the formula in step 2.1.1 into the third formula in step 2.1.2:
Figure BDA0002120442560000032
2.1.4 substituting 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
2.1.5 reduce the formula in step 2.1.4, neglecting the calculation
Figure BDA0002120442560000034
Factor, will->
Figure BDA0002120442560000035
Substituting the above, there are:
Figure BDA0002120442560000036
the yield curvature at this time is:
Figure BDA0002120442560000037
wherein:
Figure BDA0002120442560000038
a 2 ＝E s ε 0 ε y A′ s +2f c bh 0 ε y +f y A s ε 0
Figure BDA0002120442560000039
in the step 2), the second condition of the tensile steel bar of the adaptive beam when the tensile steel bar just yields is as follows: edge strain epsilon of pressed concrete c Peak compressive strain epsilon 0 When constructing an expression for curvature, comprising the steps of:
2.2.1 setting the edge Strain of the compressed concrete to reach the peak compressive Strain ε 0 The height of the pressed area is x 0 ，
From the plain section assumption, there is the following deformation coordination equation:
Figure BDA0002120442560000041
wherein: epsilon is the concrete strain, and x is the height of a concrete compression zone when the concrete strain reaches epsilon;
2.2.2 according to constitutive relation of the pressed concrete, the stress-strain curve of the concrete in the pressing area is two sections, one section is a parabolic ascending section and the other section is a horizontal section, so that the integral of the concrete is subjected to sectional integral to obtain the resultant force C of the compressive stress, wherein the resultant force C is:
Figure BDA0002120442560000042
then according to the force balance formula sigma' s A′ s +C＝f y A s And
Figure BDA0002120442560000043
the method can obtain:
Figure BDA0002120442560000044
wherein sigma' s A 'is the stress of the steel bars in the pressed area' s The cross section area of the longitudinal steel bar in the compression area is C is the resultant force of the concrete compression area, f y Is designed as the tensile strength of the steel bar, A s Cross-sectional surface of longitudinal steel bar in tension zoneAccumulating; e (E) s Is the elastic modulus of the steel bar, epsilon' s For the strain of the reinforcement bar in the pressed area, a' s The distance from the longitudinal steel bar combining force point of the compression area to the compression edge of the section; b is the section width of the reinforced concrete beam, f c The design value of the compressive strength of the concrete axle center is designed;
2.2.3 will
Figure BDA0002120442560000045
Substituting the obtained formula in the step 2.2.2 to obtain the following formula:
Figure BDA0002120442560000046
the yield curvature at this time can be calculated by the formula:
Figure BDA0002120442560000047
wherein:
b 1 ＝3E s A′ s (h 0 -a′ s )
b 2 ＝3E s A′ s ε y -3f c bh 0 +3f y A s
b 3 ＝3f c bε y +f c bε 0 。
in the step 2), the concrete pressed by the appropriate reinforcement beam reaches the limit compressive strain epsilon cu When constructing an expression for curvature, comprising the steps of:
2.3.1 the stress of the compressed concrete reaches the compressive strength f c At this time, the tensile bar strain is larger than the yield strain, and can be obtained by:
Figure BDA0002120442560000051
epsilon in s To strain the steel bar, x cu Concrete pole for compression concrete reaching limit compressive strainLimiting the height of the compression zone;
2.3.2 in this state, the expression of the concrete resultant force C is:
Figure BDA0002120442560000052
wherein b is the section width of the reinforced concrete beam, x 0 For the limit compression zone height of the concrete when the edge strain of the compression concrete reaches the peak compressive strain, f c The design value of the compressive strength of the concrete axle center is designed;
then there is sigma 'according to the balance of forces' s A′ s +C＝f y A s And
Figure BDA0002120442560000053
it can be derived that:
Figure BDA0002120442560000054
σ′ s a 'is the stress of the steel bars in the pressed area' s The cross section area of the longitudinal steel bar in the compression area is C is the resultant force of the concrete compression area, f y Is designed as the tensile strength of the steel bar, A s The cross-sectional area of the longitudinal steel bar in the tension zone; e (E) s Is the elastic modulus of the steel bar, epsilon' s For the strain of the reinforcement bar in the pressed area, a' s The distance from the longitudinal steel bar combining force point of the compression area to the compression edge of the section; b is the section width of the reinforced concrete beam, f c The design value of the compressive strength of the concrete axle center is designed;
2.3.3 Using the formula obtained in step 2.3.2
Figure BDA0002120442560000055
Is expressed in terms of:
Figure BDA0002120442560000056
the yield curvature at this time can be calculated by the formula:
Figure BDA0002120442560000057
c 1 ＝3E s a′ s A′ s
c 2 ＝3E s ε cu A′ s -3f y A s -f c bx 0
c 3 ＝-2f c bε cu 。
in the step 3), substituting the curvature expression in the step 2) into the step 1) to obtain the edge strain epsilon of the pressed concrete c Peak compressive strain epsilon less than or equal to 0 When (1):
Figure BDA0002120442560000061
edge strain epsilon of pressed concrete c Peak compressive strain epsilon 0 When (1):
Figure BDA0002120442560000062
the concrete pressed by the rib-adapted beam reaches the limit compressive strain epsilon cu When (1):
Figure BDA0002120442560000063
the invention has the beneficial effects that: according to the method, on the basis of considering two nodes after the tensile steel bar is subjected to yielding, namely when the tensile steel bar of the adaptive beam is subjected to the steel bar yielding and when the compressive concrete of the adaptive beam reaches the ultimate compressive strain, the average crack width is calculated 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, and the calculation method of the crack of the reinforced concrete beam after the tensile steel bar is subjected to yielding is deduced.
Drawings
FIG. 1 edge strain ε of the compressed concrete in example 2 c Peak compressive strain epsilon less than or equal to 0 A stress diagram is formed;
FIG. 2 edge strain ε of the pressed concrete in example 2 c Peak compressive strain epsilon 0 A stress diagram is formed;
FIG. 3 example 3 concrete under compression of compliant beams reaches ultimate compressive strain ε cu And when the force is applied, the force is simple.
Detailed Description
In the specification
Figure BDA0002120442560000064
And->
Figure BDA0002120442560000065
Are all representative of curvature and are the same parameters, with the subscripts modified merely to distinguish between the derivation processes in different situations.
Example 1 construction of an average crack width calculation formula
The average crack width is equal to the difference between the average elongation of the steel bars in the crack sections of the components and the average elongation of the concrete on the side surface of the components at the corresponding level:
Figure BDA0002120442560000066
wherein: epsilon sm Epsilon for average tensile strain of a longitudinally tensioned steel bar ctm For the average tensile strain of the side surface concrete at the same level as the longitudinal tensile bars, l m The length is calculated for the reinforced concrete beam of the average crack section. .
Considering the disappearance of the adhesion near the crack after yielding of the beam,
Figure BDA0002120442560000071
taking 0.95, the average fracture calculation formula is:
w m ＝0.95ε sm l m (2)
of membersAverage curvature of
Figure BDA0002120442560000072
Figure BDA0002120442560000073
Equation (2) is expressed as an average curvature:
Figure BDA0002120442560000074
where x is the height of the compression zone of the member.
Example 2 method for calculating cracks when tensile bars of a beam are just yielding
When the tensile longitudinal rib is just yielding, the adaptive rib beam can be considered by taking whether the edge concrete strain of the compression area reaches the peak stress of the compression concrete as a limit or not as follows:
(1) When the tensile longitudinal rib just yields, the edge strain epsilon of the pressed concrete c Peak compressive strain epsilon less than or equal to 0 The stress diagram is shown in figure 1.
Let the yield curvature of the section be
Figure BDA0002120442560000075
The horizontal strain of the concrete in the compression area is epsilon when the tension steel bar yields c The height of the pressed area is x c The computational diagram is shown in figure 2:
based on the plain section, it is assumed that:
Figure BDA0002120442560000076
wherein h is 0 Epsilon is the effective height of the section y Is a strain of a common longitudinal steel bar in a tension zone.
According to the balance of forces:
σ′ s A′ s +C＝f y A s (7)
sigma 'in' s Is the stress of the steel bars in the pressed area; c is the resultant force of the concrete compression area; a's' s Is the cross-sectional area of the longitudinal steel bar of the compression zone, f y Is designed as the tensile strength of the steel bar, A s The cross-sectional area of the longitudinal steel bar in the tension zone;
then there are:
Figure BDA0002120442560000081
Figure BDA0002120442560000082
in E s Is the elastic modulus of the steel bar, epsilon' s For the strain of the reinforcement bar in the pressed area, a' s The distance from the longitudinal steel bar combining force point of the compression area to the compression edge of the section; b is the section width of the reinforced concrete beam, f c The design value of the compressive strength of the concrete axle center is designed;
substituting formula (6) into formula (9):
Figure BDA0002120442560000083
substituting the formula (8) and the formula (10) into the formula (7):
Figure BDA0002120442560000084
the formula (11) is simplified and ignored in the calculation
Figure BDA0002120442560000085
Factor, will->
Figure BDA0002120442560000086
Substituting the above, there are:
Figure BDA0002120442560000087
the yield curvature at this time is:
Figure BDA0002120442560000088
wherein:
Figure BDA0002120442560000089
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
substituting the above yield curvature formula into formula (4) to obtain a fracture calculation formula in the first case
Figure BDA00021204425600000811
(2) When the tensile longitudinal rib just yields, the edge strain epsilon of the pressed concrete c Peak compressive strain epsilon 0
Setting the edge strain of the pressed concrete to reach the peak compressive strain epsilon 0 The height of the pressed area is x 0 。
From the plain section assumption, there is the following deformation coordination equation:
Figure BDA0002120442560000091
according to constitutive relation of the pressed concrete, the stress-strain curve of the concrete in the pressing area is two sections, one section is a parabolic ascending section, and the other section is a horizontal section, so that integration of the concrete is carried out in a sectional way to obtain compressive stress resultant force C which is:
Figure BDA0002120442560000092
then equation (7) becomes:
Figure BDA0002120442560000093
will be
Figure BDA0002120442560000094
Substituting the above formula, the following can be obtained:
Figure BDA0002120442560000095
the yield curvature at this time can be calculated by the formula:
Figure BDA0002120442560000096
wherein:
Figure BDA0002120442560000097
b 2 ＝3E s A′ s ε y -3f c bh 0 +3f y A s (23)
b 3 ＝3f c bε y +f c bε 0 (24)
substituting the yield curvature formula into formula (4) can obtain a fracture calculation formula in the second case.
Figure BDA0002120442560000101
Example 3 method for calculating cracks when compressed concrete of adapted beam reaches ultimate compressive strain
The concrete pressed by the rib-adapted beam reaches the limit compressive strain epsilon cu When the stress of the pressed concrete reaches the compressive strength f c The stress pattern and strain pattern when the tensile bar strain is greater than the yield strain and the ultimate deformation is reached are shown in fig. 3.
The geometry in fig. 3 can be determined by:
Figure BDA0002120442560000102
the concrete resultant force is:
Figure BDA0002120442560000103
then there is a balance according to the forces:
Figure BDA0002120442560000104
for the purpose of
Figure BDA0002120442560000105
Is expressed in terms of:
Figure BDA0002120442560000106
the yield curvature at this time can be calculated by the formula:
Figure BDA0002120442560000107
c 1 ＝3E s a′ s A′ s (30)
c 2 ＝3E s ε cu A′ s -3f y A s -f c bx 0 (31)
c 3 ＝-2f c bε cu (32)
substituting the yield curvature formula into formula (4) to obtain a crack calculation formula under the third condition,
Figure BDA0002120442560000108

Claims (8)

1. a method for calculating cracks of reinforced concrete beams of a main control building of a full indoor transformer substation comprises the following steps:
1) Constructing a formula for expressing the average crack width by using curvature according to an empirical formula of the average crack width;
2) According to two cases when the tensile longitudinal bars just yield: first case: edge strain epsilon of pressed concrete c Peak compressive strain epsilon less than or equal to 0 The method comprises the steps of carrying out a first treatment on the surface of the Second case: edge strain epsilon of pressed concrete c >Peak compressive strain epsilon 0 The method comprises the steps of carrying out a first treatment on the surface of the And constructing an expression of curvature under the condition that the pressed concrete of the adaptive beam reaches the limit compressive strain;
the first condition of the tensile steel bar of the stressed beam when the tensile steel bar just yields is that the edge strain epsilon of the stressed concrete c Peak compressive strain epsilon less than or equal to 0 When constructing an expression for curvature, comprising the steps of:
2.1.1 setting the section yield curvature as
Figure FDA0004118684230000011
The horizontal strain of the concrete in the compression area is epsilon when the tension steel bar yields c The height of the pressed area is x c ,
Based on the plain section, it is assumed that:
Figure FDA0004118684230000012
h in 0 Epsilon is the effective height of the section y Is a longitudinal common steel bar strain in a tension zone;
2.1.2 according to the balance of forces:
σ′ s A′ s +C＝f y A s
sigma 'in' s Is the stress of the steel bars in the pressed area; c is the resultant force of the concrete compression area; a's' s Is the cross-sectional area of the longitudinal steel bar of the compression zone, f y As is the cross-sectional area of the longitudinal steel bar in the tension zone, which is the design value of the tensile strength of the steel bar;
then there are:
Figure FDA0004118684230000013
Figure FDA0004118684230000014
in E s Is the elastic modulus of the steel bar, epsilon' s For the strain of the reinforcement bar in the pressed area, a' s The distance from the longitudinal steel bar combining force point of the compression area to the compression edge of the section; b is the section width of the reinforced concrete beam, f c The design value of the compressive strength of the concrete axle center is designed;
2.1.3 substituting the formula in step 2.1.1 into the third formula in step 2.1.2:
Figure FDA0004118684230000015
2.1.4 substituting 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
2.1.5 reduce the formula in step 2.1.4, neglecting the calculation
Figure FDA0004118684230000022
Factor, will->
Figure FDA0004118684230000023
Substituting the above, there are:
Figure FDA0004118684230000024
the yield curvature at this time is:
Figure FDA0004118684230000025
wherein:
Figure FDA0004118684230000026
a 2 ＝E s ε 0 ε y A′ s +2f c bh 0 ε y +f y A s ε 0
Figure FDA0004118684230000027
3) Substituting the curvature expression in the step 2) into the formula of the step 1) to obtain a calculation formula of the crack width considering the influence of the steel bar stress.
2. The method for calculating the crack of the reinforced concrete beam of the building controlled by the whole indoor transformer substation according to claim 1, wherein in the step 1), the empirical formula is as follows:
Figure FDA0004118684230000028
wherein w is m For average crack width ε sm Epsilon for average tensile strain of a longitudinally tensioned steel bar ctm Is a steel with longitudinal tensionAverage tensile strain of side surface concrete at the same level of the ribs, l m The length is calculated for the reinforced concrete beam of the average crack section.
3. The method for calculating the crack of the reinforced concrete beam of the building controlled by the whole indoor transformer substation according to claim 2, wherein the formula for constructing the average crack width expressed by curvature specifically comprises the following steps:
1.1 according to an empirical formula, considering the disappearance of the adhesion near the crack after yielding of the beam,
Figure FDA0004118684230000029
taking 0.95, the average fracture calculation formula is: w (w) m ＝0.95ε sm l m ；
1.2 mean curvature of the Member
Figure FDA0004118684230000031
And epsilon sm The relation of (2) is as follows:
Figure FDA0004118684230000032
wherein h is 0 Is the effective height of the section; x is the compressed zone height of the component;
1.3 substituting the formula in step 1.2 into the formula in step 1.1 to obtain the formula for expressing the average crack width by curvature, wherein the formula is as follows:
Figure FDA0004118684230000033
4. the method for calculating the crack of the reinforced concrete beam of the main control building of the whole indoor transformer substation according to claim 3, wherein in the step 2), the second condition when the tensile steel bar of the receiving beam just yields is that: edge strain epsilon of pressed concrete c Peak compressive strain epsilon 0 When constructing curvatureThe expression comprises the following steps:
2.2.1 setting the edge Strain of the compressed concrete to reach the peak compressive Strain ε 0 The height of the pressed area is x 0 ，
From the plain section assumption, there is the following deformation coordination equation:
Figure FDA0004118684230000034
wherein: epsilon is the concrete strain, and x is the height of a concrete compression zone when the concrete strain reaches epsilon;
2.2.2 according to constitutive relation of the pressed concrete, the stress-strain curve of the concrete in the pressing area is two sections, one section is a parabolic ascending section and the other section is a horizontal section, so that the integral of the concrete is subjected to sectional integral to obtain the resultant force C of the compressive stress, wherein the resultant force C is:
Figure FDA0004118684230000035
then according to the force balance formula sigma' s A′ s +C＝f y A s And
Figure FDA0004118684230000036
the method can obtain:
Figure FDA0004118684230000037
wherein sigma' s A 'is the stress of the steel bars in the pressed area' s The cross section area of the longitudinal steel bar in the compression area is C is the resultant force of the concrete compression area, f y As is the cross-sectional area of the longitudinal steel bar in the tension zone, which is the design value of the tensile strength of the steel bar; e (E) s Is the elastic modulus of the steel bar, epsilon' s For the strain of the reinforcement bar in the pressed area, a' s The distance from the longitudinal steel bar combining force point of the compression area to the compression edge of the section; b is the section width of the reinforced concrete beam, f c Is coagulationA design value of the compressive strength of the soil axis;
2.2.3 will
Figure FDA0004118684230000041
Substituting the obtained formula in the step 2.2.2 to obtain the following formula:
Figure FDA0004118684230000042
the yield curvature at this time can be calculated by the formula:
Figure FDA0004118684230000043
wherein:
b 1 ＝3E s A′ s (h 0 -a′ s )
b 2 ＝3E s A′ s ε y -3f c bh 0 +3f y A s
b 3 ＝3f c bε y +f c bε 0 。
5. the method for calculating cracks of reinforced concrete beams of main control building of all-indoor transformer substation according to claim 4, wherein in the step 2), the prestressed concrete of the compliant beam reaches a limit compressive strain epsilon cu When constructing an expression for curvature, comprising the steps of:
2.3.1 the stress of the compressed concrete reaches the compressive strength f c At this time, the tensile bar strain is larger than the yield strain, and can be obtained by:
Figure FDA0004118684230000044
epsilon in s To strain the steel bar, x cu Concrete limit compression zone height when the compression concrete reaches limit compression strain；
2.3.2 in this state, the expression of the concrete resultant force C is:
Figure FDA0004118684230000045
wherein b is the section width of the reinforced concrete beam, x 0 For the limit compression zone height of the concrete when the edge strain of the compression concrete reaches the peak compressive strain, f c The design value of the compressive strength of the concrete axle center is designed;
then there is sigma 'according to the balance of forces' s A′ s +C＝f y A s And
Figure FDA0004118684230000046
it can be derived that:
Figure FDA0004118684230000047
σ′ s a 'is the stress of the steel bars in the pressed area' s The cross section area of the longitudinal steel bar in the compression area is C is the resultant force of the concrete compression area, f y As is the cross-sectional area of the longitudinal steel bar in the tension zone, which is the design value of the tensile strength of the steel bar; e (E) s Is the elastic modulus of the steel bar, epsilon' s For the strain of the reinforcement bar in the pressed area, a' s The distance from the longitudinal steel bar combining force point of the compression area to the compression edge of the section; b is the section width of the reinforced concrete beam, f c The design value of the compressive strength of the concrete axle center is designed;
2.3.3 Using the formula obtained in step 2.3.2
Figure FDA0004118684230000051
Is expressed in terms of:
Figure FDA0004118684230000052
the yield curvature at this time can be calculated by the formula:
Figure FDA0004118684230000053
c 1 ＝3E s a′ s A′ s
c 2 ＝3E s ε cu A′ s -3f y A s -f c bx 0
c 3 ＝-2f c bε cu 。
6. the method for calculating cracks of reinforced concrete beams of a building controlled by a full indoor transformer substation according to claim 5, wherein in the step 3), the curvature expression in the step 2) is substituted into the step 1), so as to obtain the edge strain epsilon of the pressed concrete c Peak compressive strain epsilon less than or equal to 0 When (1):
Figure FDA0004118684230000054
7. the method for calculating cracks of reinforced concrete beams of building controlled by full indoor transformer substation according to claim 6, wherein in the step 3), the curvature expression in the step 2) is substituted into the step 1), and the edge strain epsilon of the pressed concrete is calculated c Peak compressive strain epsilon 0 When (1):
Figure FDA0004118684230000055
8. the method for calculating the crack of the reinforced concrete beam of the main control building of the whole indoor transformer substation according to claim 7, wherein in the step 3), the curvature expression in the step 2) is substituted into the step 1), and the prestressed concrete of the compliant beam reaches the limit compressive strain epsilon cu When (1):
Figure FDA0004118684230000061
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