CN110298133A - A kind of full indoor substation master control building cracks in steel reinforced concrete beam calculation method - Google Patents

A kind of full indoor substation master control building cracks in steel reinforced concrete beam calculation method Download PDF

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CN110298133A
CN110298133A CN201910604725.4A CN201910604725A CN110298133A CN 110298133 A CN110298133 A CN 110298133A CN 201910604725 A CN201910604725 A CN 201910604725A CN 110298133 A CN110298133 A CN 110298133A
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concrete
strain
compressive
compression
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CN110298133B (en
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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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Economic and Technological Research Institute of State Grid Jiangxi Electric Power Co Ltd
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    • 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
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Abstract

The invention discloses a kind of full indoor substation master control building cracks in steel reinforced concrete beam calculation methods, comprising the following steps: 1) according to average crack width wmEmpirical equation, construct average crack width wmUse curvatureThe formula of expression；2) two kinds of situations (the first situation: compression concrete edge strain stress when muscle is just surrendered is indulged according to when tensionc≤ peak value compressive strain ε0；Second situation: compression concrete side strainεc> peak value compressive strain ε0) and under-reinforced beam compression concrete reach capacity compressive strain when the case where, construct the expression formula of curvature；3) step 2) mean curvature expression formula is substituted into the formula of step 1) to get the calculation formula for the fracture width for considering reinforcement stresses influence.The present invention is deduced the calculation method of the cracks in steel reinforced concrete beam after tension reinforcement surrender, compared to traditional calculation method, the calculated fracture width of method of the invention and actual fracture width closer to.

Description

A kind of full indoor substation master control building cracks in steel reinforced concrete beam calculation method
Technical field
The invention belongs to technical field of civil engineering, and in particular to a kind of full indoor substation master control building reinforced beam Crack calculation method.
Background technique
In reinforced beam elastic-plastic analysis, if moment modified factor value is excessive, the reinforcing bar after amplitude modulation is in outer lotus It may be surrendered under the action of load.The formula that we usually propose in code requirement when calculating fracture width, when calculating The influence of reinforcement stresses is not considered in this formula, and the fracture width of component will be no longer changed after reinforcement yielding, This be not consistent really, thus it is according to the fracture width accuracy that the formula proposed in code requirement obtains not high.
Usual reinforced concrete structure is under the action of accidental load it can also happen that surrender, the change of reinforcement yielding rear part Shape and fracture width etc. are to judge whether structure can repair and determine the important indicator of repairing and reinforcement degree, are directed to reinforcing bar both at home and abroad The research of the fracture width of the rear part of surrender is seldom, so the crack calculation method after deriving reinforcement yielding is very necessary 's.
Summary of the invention
The object of the present invention is to provide a kind of full indoor substation master control building armored concrete that consideration reinforcement stresses influence Beam crack calculation method improves the accuracy for calculating fracture width.
This full indoor substation master control building of the invention cracks in steel reinforced concrete beam calculation method, comprising the following steps:
1) according to the empirical equation of average crack width, the formula of average crack width curvature expression is constructed；
2) it (the first situation: is answered at compression concrete edge according to two kinds of situations when under-reinforced beam tension reinforcement is just surrendered Become εc≤ peak value compressive strain ε0；Second situation: compression concrete edge strain stressc> peak value compressive strain ε0) and under-reinforced beam by Pressure concrete reach capacity compressive strain when the case where, construct the expression formula of curvature；
3) step 2) mean curvature expression formula is substituted into the formula of step 1) to get the crack for considering reinforcement stresses influence The calculation formula of width.
In the step 1), empirical equation are as follows:
In formula, wmFor average crack width, εsmFor the average stretching strain of longitudinal tensile reinforcing bar, εctmFor with longitudinal tensile steel The average stretching strain of side surface concrete, l at muscle phase same levelmFor the reinforced beam computational length of average crack section.
The formula for constructing the expression of average crack width curvature, specifically includes the following steps:
1.1 rule of thumb formula consider the disappearance of the cementation after beam surrender near crack,0.95 is taken as, Then average crack calculation formula are as follows: wm=0.95 εsmlm；
The average curvature of 1.2 componentsWith εsmRelational expression it is as follows:
Wherein: h0For effective depth of section；X is the depth of compressive zone of component；
1.3 substitute into the formula in step 1.2 in step 1.1 formula, obtain the public affairs of average crack width curvature expression Formula are as follows:
In the step 2), the first situation when just being surrendered by muscle beam tension reinforcement: compression concrete side strain is fitted εc≤ peak value compressive strain ε0When, construct the expression formula of curvature the following steps are included:
2.1.1 set section yield curvature asThe strain of compressive region concrete horizontal is ε when tension reinforcement is surrenderedc, compressive region Height is xc,
Had according to plane cross-section assumption:
H in formula0For effective depth of section, εyTo be strained for tensile region longitudinal direction regular reinforcement；
2.1.2 had according to the balance of power:
σ′sA′s+ C=fyAs
σ ' in formulasFor compressive region reinforcement stresses；C is concrete compression area resultant force；A′sFor the section of compressive region longitudinal reinforcement Area, fyFor Steel Bar Tensile Strength design value, AsFor the area of section of tensile region longitudinal reinforcement；
Then have:
Wherein EsFor the elasticity modulus of reinforcing bar, ε 'sFor the strain of compressive region reinforcing bar, a 'sIt is arrived for compressive region longitudinal reinforcement Resultant force The distance at section compression edge；B is Sectional Dimension of Reinforced Concrete Beam width, fcFor concrete axial compressive strength design value；
2.1.3 the formula in step 2.1.1 is substituted into the third formula in step 2.1.2 and is obtained:
2.1.4 by the formula of second formula and step 2.1.3 in step 2.1.2, first in step 2.1.2 is substituted into A formula obtains:
2.1.5 abbreviation is carried out to the formula in step 2.1.4, ignored when calculatingThe factor, willIt substitutes into Above formula then has:
Then yield curvature at this time are as follows:
In formula:
a2=Esε0εyA′s+2fcbh0εy+fyAsε0
In the step 2), second situation when just being surrendered by muscle beam tension reinforcement: compression concrete side strain is fitted εc> peak value compressive strain ε0When, construct the expression formula of curvature the following steps are included:
2.2.1 it sets compression concrete side strain and reaches peak value compressive strain ε0When depth of compressive zone be x0,
According to plane cross-section assumption, there is following Coordinate deformation equation:
Wherein: ε is concrete strain, and x is concrete compression area height when concrete strain reaches ε；
2.2.2 then according to compression coagulation Soil Constitutive Relation it is found that the stress-strain diagram of compressive concrete be two sections, one Section is the parabola ascent stage, and one section is horizontal segment, so should carry out subsection integral to the integral of concrete can just obtain compression Resultant force C are as follows:
Then according to dynamic balance formula σ 'sA′s+ C=fyAsWithIt can obtain:
Wherein σ 'sFor compressive region reinforcement stresses, A 'sFor the area of section of compressive region longitudinal reinforcement, C is concrete compression area With joint efforts, fyFor Steel Bar Tensile Strength design value, AsFor the area of section of tensile region longitudinal reinforcement；EsFor the elasticity modulus of reinforcing bar, ε′sFor the strain of compressive region reinforcing bar, a 'sIt is pressurized the distance at edge for compressive region longitudinal reinforcement Resultant force to section；B is reinforced concrete Native beam section width, fcFor concrete axial compressive strength design value；
2.2.3 willIt substitutes into the formula that step 2.2.2 is finally obtained, can obtain:
Then yield curvature at this time can be calculated by above formula:
In formula:
b1=3EsA′s(h0-a′s)
b2=3EsA′sεy-3fcbh0+3fyAs
b3=3fcbεy+fcbε0。
In the step 2), under-reinforced beam compression concrete reaches capacity compressive strain εcuWhen, the expression formula for constructing curvature includes Following steps:
2.3.1 compression concrete stress reaches compression strength fc, tension reinforcement, which strains, at this time is greater than yield strain, can ask :
ε in formulasFor tension reinforcement strain, xcuReach capacity for compression concrete compressive strain when concrete limit compressive region Highly；
2.3.2 under such state, the expression formula of concrete resultant force C are as follows:
Wherein b is Sectional Dimension of Reinforced Concrete Beam width, x0When reaching peak value compressive strain for compression concrete side strain Concrete limit depth of compressive zone, fcFor concrete axial compressive strength design value；
σ ' is then had according to the balance of powersA′s+ C=fyAsWithIt can obtain:
σ′sFor compressive region reinforcement stresses, A 'sFor the area of section of compressive region longitudinal reinforcement, C is concrete compression area resultant force, fyFor Steel Bar Tensile Strength design value, AsFor the area of section of tensile region longitudinal reinforcement；EsFor the elasticity modulus of reinforcing bar, ε 'sFor by The strain of pressure area reinforcing bar, a 'sIt is pressurized the distance at edge for compressive region longitudinal reinforcement Resultant force to section；B cuts for reinforced beam Face width, fcFor concrete axial compressive strength design value；
2.3.3 the formula that will be finally obtained in step 2.3.2 is usedForm indicate are as follows:
Then yield curvature at this time can be calculated by above formula:
c1=3Esa′sA′s
c2=3EsεcuA′s-3fyAs-fcbx0
c3=-2fcbεcu。
In the step 3), the curvature expression formula in step 2) is substituted into step 1), compression concrete edge is obtained and answers Become εc≤ peak value compressive strain ε0When:
Compression concrete edge strain stressc> peak value compressive strain ε0When:
Under-reinforced beam compression concrete reaches capacity compressive strain εcuWhen:
Beneficial effects of the present invention: two nodes of the present invention after considering tension reinforcement surrender, i.e. under-reinforced beam tension steel When muscle is just surrendered and under-reinforced beam compression concrete reach capacity compressive strain when on the basis of, consider at average elongation and respective horizontal The difference of component side surface concrete average elongation calculates average crack width, the reinforcing bar after being deduced tension reinforcement surrender The calculation method in beams of concrete crack, compared to traditional calculation method, the calculated fracture width of method of the invention and reality The fracture width on border closer to.
Detailed description of the invention
Compression concrete edge strain stress in Fig. 1 embodiment 2c≤ peak value compressive strain ε0, stress sketch；
Compression concrete edge strain stress in Fig. 2 embodiment 2c> peak value compressive strain ε0, stress sketch；
Under-reinforced beam compression concrete reaches capacity compressive strain ε in Fig. 3 embodiment 3cuWhen, stress sketch.
Specific embodiment
In specificationWithAll it is to represent curvature, is same parameters, is intended merely to distinguish in different situations Under derivation process, have modified subscript.
The building of 1 average crack width calculation formula of embodiment
Average crack width is mixed equal to component side surface at the average elongation and respective horizontal of reinforcing bar in structure member crevices section The difference of solidifying soil average elongation:
In formula: εsmFor the average stretching strain of longitudinal tensile reinforcing bar, εctmFor with side surface at longitudinal tensile reinforcing bar phase same level The average stretching strain of concrete, lmFor the reinforced beam computational length of average crack section.
Consider the disappearance of the cementation after beam is surrendered near crack,It is taken as 0.95, then average crack calculates public Formula are as follows:
wm=0.95 εsmlm (2)
The average curvature of component is
Formula (2) is indicated with the form of average curvature are as follows:
X is the depth of compressive zone of component in formula.
Crack calculation method when 2 muscle beam tension reinforcement of embodiment is just surrendered
Whether under-reinforced beam reaches compression concrete peak value when tension is indulged muscle and just surrendered, with compression area edge concrete strain Strain is that boundary can be divided into the consideration of following two situation:
(1) when tension, which indulges muscle, just surrenders, compression concrete edge strain stressc≤ peak value compressive strain ε0, stress sketch such as Fig. 1 It is shown.
If section yield curvature isThe strain of compressive region concrete horizontal is ε when tension reinforcement is surrenderedc, depth of compressive zone For xc, calculation diagram is as shown in Figure 2:
Had according to plane cross-section assumption:
Wherein h0For effective depth of section, εyTo be strained for tensile region longitudinal direction regular reinforcement.
Had according to the balance of power:
σ′sA′s+ C=fyAs (7)
σ ' in formulasFor compressive region reinforcement stresses；C is concrete compression area resultant force；A′sFor the section of compressive region longitudinal reinforcement Area, fyFor Steel Bar Tensile Strength design value, AsFor the area of section of tensile region longitudinal reinforcement；
Then have:
E in formulasFor the elasticity modulus of reinforcing bar, ε 'sFor the strain of compressive region reinforcing bar, a 'sIt is arrived for compressive region longitudinal reinforcement Resultant force The distance at section compression edge；B is Sectional Dimension of Reinforced Concrete Beam width, fcFor concrete axial compressive strength design value；
Formula (6) are substituted into formula (9) and are obtained:
By formula (8) and formula (10), substitutes into formula (7) and obtains:
Abbreviation is carried out to formula (11), is ignored when calculatingThe factor, willAbove formula is substituted into, then is had:
Then yield curvature at this time are as follows:
In formula:
a2=Esε0εyA′s+2fcbh0εy+fyAsε0 (15)
The above yield curvature formula is substituted into formula (4), the crack calculation formula in the case of the first can be obtained
(2) when tension, which indulges muscle, just surrenders, and compression concrete edge strain stressc> peak value compressive strain ε0
If compression concrete side strain reaches peak value compressive strain ε0When depth of compressive zone be x0。
According to plane cross-section assumption, there is following Coordinate deformation equation:
Then according to compression coagulation Soil Constitutive Relation it is found that the stress-strain diagram of compressive concrete is two sections, one section is The parabola ascent stage, one section is horizontal segment, so should carry out subsection integral just to the integral of concrete can obtain compression resultant force C Are as follows:
Then formula (7) becomes:
It willAbove formula is substituted into, can be obtained:
Then yield curvature at this time can be calculated by above formula:
In formula:
b2=3EsA′sεy-3fcbh0+3fyAs (23)
b3=3fcbεy+fcbε0 (24)
Yield curvature formula is substituted into formula (4), the crack calculation formula under second situation can be obtained.
3 under-reinforced beam compression concrete of embodiment reach capacity compressive strain when crack calculation method
Under-reinforced beam compression concrete reaches capacity compressive strain εcuWhen, compression concrete stress reaches compression strength fc, at this time Tension reinforcement strain is greater than yield strain, then stress pattern when deforming of reaching capacity and strain figures are as shown in Figure 3.
It can be acquired by the geometrical condition in Fig. 3:
Then concrete resultant force are as follows:
Then had according to the balance of power:
Above formula is usedForm indicate are as follows:
Then yield curvature at this time can be calculated by above formula:
c1=3Esa′sA′s (30)
c2=3EsεcuA′s-3fyAs-fcbx0 (31)
c3=-2fcbεcu (32)
Yield curvature formula is substituted into formula (4), the crack calculation formula in the case of the third can be obtained,

Claims (9)

1. a kind of full indoor substation master control building cracks in steel reinforced concrete beam calculation method, comprising the following steps:
1) according to the empirical equation of average crack width, the formula of average crack width curvature expression is constructed；
2) two kinds of situations when muscle is just surrendered: the first situation: compression concrete edge strain stress are indulged according to when tensionc≤ peak value pressure Strain stress0；Second situation: compression concrete edge strain stressc> peak value compressive strain ε0；And under-reinforced beam compression concrete reaches pole The case where when pressure limiting strains, construct the expression formula of curvature；
3) step 2) mean curvature expression formula is substituted into the formula of step 1) to get the fracture width for considering reinforcement stresses influence Calculation formula.
2. full indoor substation master control building according to claim 1 cracks in steel reinforced concrete beam calculation method, feature exist In, in the step 1), empirical equation are as follows:
In formula, wmFor average crack width, εsmFor the average stretching strain of longitudinal tensile reinforcing bar, εctmFor with longitudinal tensile reinforcing bar phase The average stretching strain of side surface concrete, l at same levelmFor the reinforced beam computational length of average crack section.
3. full indoor substation master control building according to claim 1 or 2 cracks in steel reinforced concrete beam calculation method, feature It is, the formula for constructing the expression of average crack width curvature, specifically includes the following steps:
1.1 rule of thumb formula consider the disappearance of the cementation after beam surrender near crack,Be taken as 0.95, then it is average Crack calculation formula are as follows: wm=0.95 εsmlm；
The average curvature of 1.2 componentsWith εsmRelational expression it is as follows:
Wherein: h0For effective depth of section；X is the depth of compressive zone of component；
1.3 substitute into the formula in step 1.2 in step 1.1 formula, obtain the formula of average crack width curvature expression are as follows:
4. full indoor substation master control building according to claim 1 cracks in steel reinforced concrete beam calculation method, feature exist In, in the step 2), suitable the first situation when just being surrendered by muscle beam tension reinforcement: compression concrete edge strain stressc≤ peak It is worth compressive strain ε0When, construct the expression formula of curvature the following steps are included:
2.1.1 set section yield curvature asThe strain of compressive region concrete horizontal is ε when tension reinforcement is surrenderedc, depth of compressive zone For xc,
Had according to plane cross-section assumption:
H in formula0For effective depth of section, εyTo be strained for tensile region longitudinal direction regular reinforcement；
2.1.2 had according to the balance of power:
σ′sA′s+ C=fyAs
σ ' in formulasFor compressive region reinforcement stresses；C is concrete compression area resultant force；A′sFor the area of section of compressive region longitudinal reinforcement, fyFor Steel Bar Tensile Strength design value, As is the area of section of tensile region longitudinal reinforcement；
Then have:
E in formulasFor the elasticity modulus of reinforcing bar, ε 'sFor the strain of compressive region reinforcing bar, a 'sFor compressive region longitudinal reinforcement Resultant force to section The distance at compression edge；B is Sectional Dimension of Reinforced Concrete Beam width, fcFor concrete axial compressive strength design value；
2.1.3 the formula in step 2.1.1 is substituted into the third formula in step 2.1.2 and is obtained:
2.1.4 by the formula of second formula and step 2.1.3 in step 2.1.2, first public affairs in step 2.1.2 are substituted into Formula obtains:
2.1.5 abbreviation is carried out to the formula in step 2.1.4, ignored when calculatingThe factor, willAbove formula is substituted into, Then have:
Then yield curvature at this time are as follows:
In formula:
a2=Esε0εyA′s+2fcbh0εy+fyAsε0
5. full indoor substation master control building according to claim 1 cracks in steel reinforced concrete beam calculation method, feature exist In, in the step 2), suitable second situation when just being surrendered by muscle beam tension reinforcement: compression concrete edge strain stresscThe peak > It is worth compressive strain ε0When, construct the expression formula of curvature the following steps are included:
2.2.1 it sets compression concrete side strain and reaches peak value compressive strain ε0When depth of compressive zone be x0, according to plane section vacation It is fixed, there is following Coordinate deformation equation:
In formula: ε is concrete strain, and x is concrete compression area height when concrete strain reaches ε；
2.2.2 then according to compression coagulation Soil Constitutive Relation it is found that the stress-strain diagram of compressive concrete is two sections, one section is The parabola ascent stage, one section is horizontal segment, so should carry out subsection integral just to the integral of concrete can obtain compression resultant force C Are as follows:
Then according to dynamic balance formula σ 'sA′s+ C=fyAsWithIt can obtain:
Wherein σ 'sFor compressive region reinforcement stresses, A 'sFor the area of section of compressive region longitudinal reinforcement, C is concrete compression area resultant force, fyFor Steel Bar Tensile Strength design value, AsFor the area of section of tensile region longitudinal reinforcement；EsFor the elasticity modulus of reinforcing bar, ε 'sFor by The strain of pressure area reinforcing bar, a 'sIt is pressurized the distance at edge for compressive region longitudinal reinforcement Resultant force to section；B cuts for reinforced beam Face width, fcFor concrete axial compressive strength design value；
2.2.3 willIt substitutes into the formula that step 2.2.2 is finally obtained, can obtain:
Then yield curvature at this time can be calculated by above formula:
In formula:
b1=3EsA′s(h0-a′s)
b2=3EsA′sεy-3fcbh0+3fyAs
b3=3fcbεy+fcbε0。
6. full indoor substation master control building according to claim 1 cracks in steel reinforced concrete beam calculation method, feature exist In in the step 2), under-reinforced beam compression concrete reaches capacity compressive strain εcuWhen, the expression formula for constructing curvature includes following step It is rapid:
2.3.1 compression concrete stress reaches compression strength fc, tension reinforcement, which strains, at this time is greater than yield strain, it can acquire:
ε in formulasFor tension reinforcement strain, xcuReach capacity for compression concrete compressive strain when concrete limit compressive region it is high Degree；
2.3.2 under such state, the expression formula of concrete resultant force C are as follows:
Wherein b is Sectional Dimension of Reinforced Concrete Beam width, x0Reach concrete when peak value compressive strain for compression concrete side strain Limit depth of compressive zone, fcFor concrete axial compressive strength design value；
σ ' is then had according to the balance of powersA′s+ C=fyAsWithIt can obtain:
σ′sFor compressive region reinforcement stresses, A 'sFor the area of section of compressive region longitudinal reinforcement, C is concrete compression area resultant force, fyFor Steel Bar Tensile Strength design value, AsFor the area of section of tensile region longitudinal reinforcement；EsFor the elasticity modulus of reinforcing bar, ε 'sFor compressive region Reinforcing bar strain, a 'sIt is pressurized the distance at edge for compressive region longitudinal reinforcement Resultant force to section；B is that Sectional Dimension of Reinforced Concrete Beam is wide Degree, fcFor concrete axial compressive strength design value；
2.3.3 the formula that will be finally obtained in step 2.3.2 is usedForm indicate are as follows:
Then yield curvature at this time can be calculated by above formula:
c1=3Esa′sA′s
c2=3EsεcuA′s-3fyAs-fcbx0
c3=-2fcbεcu。
7. full indoor substation master control building according to claim 1 or 4 cracks in steel reinforced concrete beam calculation method, feature It is, in the step 3), the curvature expression formula in step 2) is substituted into step 1), compression concrete edge strain stress is obtainedc ≤ peak value compressive strain ε0When:
8. full indoor substation master control building cracks in steel reinforced concrete beam calculation method according to claim 1 or 5, feature It is, in the step 3), the curvature expression formula in step 2) is substituted into step 1), compression concrete edge strain stresscThe peak > It is worth compressive strain ε0When:
9. full indoor substation master control building cracks in steel reinforced concrete beam calculation method according to claim 1 or 6, feature It is, in the step 3), the curvature expression formula in step 2) is substituted into step 1), under-reinforced beam compression concrete reaches capacity Compressive strain εcuWhen:
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