CN102650579A - Flexural bearing capacity designing method for frame beam adopting pre-stressed steel reinforced concrete structure - Google Patents

Flexural bearing capacity designing method for frame beam adopting pre-stressed steel reinforced concrete structure Download PDF

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CN102650579A
CN102650579A CN2011104369011A CN201110436901A CN102650579A CN 102650579 A CN102650579 A CN 102650579A CN 2011104369011 A CN2011104369011 A CN 2011104369011A CN 201110436901 A CN201110436901 A CN 201110436901A CN 102650579 A CN102650579 A CN 102650579A
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shaped steel
prime
bearing capacity
reinforced concrete
concrete structure
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熊学玉
高峰
熊斌
李明
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SHANGHAI TONGJI CONSTRUCTION ENGINEERING DESIGN Co Ltd
Tongji University
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SHANGHAI TONGJI CONSTRUCTION ENGINEERING DESIGN Co Ltd
Tongji University
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Abstract

The invention relates to a flexural bearing capacity designing method for a frame beam adopting a pre-stressed steel reinforced concrete structure and belongs to the field of civil engineering. The flexural bearing capacity designing method for the frame beam adopting the pre-stressed steel reinforced concrete structure is characterized in that when the frame beam adopting the pre-stressed steel reinforced concrete structure is designed, the influence on a flexural bearing capacity and bending moment of a front section of the frame beam caused by lateral restraint is considered; and by adopting a method that the calculation is influenced by the restraint during the structure construction, a new formula for calculating the flexural bearing capacity and the bending moment is provided. According to the design method disclosed by the invention, complex restraint conditions of the pre-stressed steel reinforced concrete structure and the influence on the calculation of the flexural bearing capacity of the front section of the frame beam caused by the restraint and distribution of the pre-stressed steel reinforced concrete structure are fully considered, so that the design of the structure better meets the requirement of an actual structure and better safety performance is obtained.

Description

The Vierendeel girder anti-bending bearing capacity method for designing of prestress steel reinforced concrete structure
Technical field
The present invention relates to the design of prestress steel reinforced concrete structure ultimate bearing capacity, relate in particular to the Vierendeel girder anti-bending bearing capacity method for designing of prestress steel reinforced concrete structure.
Background technology
Modern prestressed structure system is meant the prestressed structure system of getting up with high performance material, modern Design and advanced construction technology construction with high-strength, be current technological most advanced, purposes the most extensively, one of the most rising a kind of building structure pattern.At large public building, encorbelment greatly, stride greatly in the buildingss such as heavily loaded industrial building, skyscraper, big-and-middle span bridge, large special structure, television tower, nuclear power plant containment shell, ocean platform and be used widely.Prestress steel reinforced concrete (PSRC) structure is as a kind of new modern prestressed structure, can very effective adaptation modern architecture Development Trend, satisfy the demand of modern structure.Girder with rolled steel section en cased in concrete is applied prestress, can enlarge the elastic range of material, make full use of Materials with High Strength more, the performance material behavior alleviates dead load; Improve ultimate bearing capacity, reduce malformation; Postpone the appearance of hogging moment area distress in concrete; The rigidity of enhanced type steel beams of concrete reduces stress amplitude effectively, the fatigue lifetime of enhanced type steel beams of concrete.
Compare with common prestressed concrete, the prestress girder with rolled steel section en cased in concrete has following characteristics: (1) good seismic resistance; (2) easy construction; (3) shear-carrying capacity is big; (4) section rigidity is big, and amount of deflection control easily.Compare girder with rolled steel section en cased in concrete, the PSRC beam then has following characteristics: (1) span-depth radio can suitably be amplified; (2) delay crack developing; (3) amount of deflection control more is prone to satisfy; (4) steel using amount reduces; (5) construction is complicated, with high content of technology.
Using the earliest of prestress steel reinforced concrete structure mainly is the conversion layer structure of skyscraper, after multidigit scholar and practitioner's development and perfect, gradually because its excellent characteristic is used expansion gradually.But from method for designing; The principle of work that current inner forces calculation method about prestressed reinforced concrete construction mainly is based on the prestressed concrete continuous beam structure is set up; In fact the structure that calculates during design is based on the prestressed reinforced concrete construction of ignoring constraint (lateral confinement); The vertical members such as post, shear wall and tube of promptly not considering prestressed concrete frame structure, plate-column structure, frame-shear structure, framed-tube structure etc. are to prestressed influence, and vertical members such as true upper prop, shear wall and tube have very big influence to prestressed transmission.And show through the long-term research of this seminar; Have in the complicated structure that retrains above-mentioned; Because receive the influence of post lateral deformation stiffness, the effective prestress in the prestressed concrete beam has bigger reduction, if according to the design of not considering in the present design to retrain; Then the normal use of actual prestressed concrete beam and ultimate bearing capacity just can't satisfy structural requirement; And the prestress steel reinforced concrete structure with respect to common prestressed reinforced concrete construction because the existence of built-in shaped steel, in rigidity, the crack development of load action lower member and to work in coordination with load-bearing capacity different, when the complicated prestress steel reinforced concrete structure that retrains being arranged by the current methods designing and calculating; To bring potential safety hazard to engineering, therefore reasonably design must be considered constraint and built-in shaped steel and concrete Structural Influence.
At present, the prestress steel reinforced concrete structure is not seen abroad has theoretical research and practical applications.At home; A small amount of experimental study with the prestress steel reinforced concrete structure is only arranged; And shortage is to the research of prestress steel reinforced concrete structure System Design theoretical system; This emerging unitized construction form of prestress steel reinforced concrete structure is only done preliminary trial, also do not formed theoretical foundation, the analysis design method that instructs practical applications, more do not had corresponding standard rules to according to.
Summary of the invention
Technical matters to be solved by this invention provides a kind of Vierendeel girder anti-bending bearing capacity method for designing of prestress steel reinforced concrete structure; Ignore constraint when solving present method for designing owing to calculating; Cause the normal use and the ultimate bearing capacity of actual prestressed concrete beam can't satisfy structural requirement, and bring the defective of potential safety hazard to engineering.
Technical scheme
A kind of Vierendeel girder anti-bending bearing capacity method for designing of prestress steel reinforced concrete structure; It is characterized in that: to adopting the Vierendeel girder of prestress steel reinforced concrete structure; Normal section for Vierendeel girder during design receives curved bearing capacity to require to calculate according to following formula, and need meet following requirement to moment of flexure:
(1) about non-seismic design,
M - [ M 2 - N 2 ( h 2 - a s ) ] ≤ α 1 f c bx ( h 0 - x 2 ) + f y ′ A s ′ ( h 0 - a s ′ ) + f a A af ( a a - a s )
+ f a ′ A af ′ ( h 0 - a a ′ ) + M aw
α 1f cbx+f′ yA′ s+f′ aA′ af-f yA s-f pyA p-f aA af-N 2+N aw=0;
(2) about seismic design,
M - [ M 2 - N 2 ( h 2 - a s ) ] ≤ 1 γ RE [ α 1 f c bx ( h 0 - x 2 ) + f y ′ A s ′ ( h 0 - a s ′ ) + f a A af ( a a - a s )
+ f a ′ A af ′ ( h 0 - a a ′ ) + M aw ]
α 1f cbx+f′ yA′ s+f′ aA′ af-f yA s-f pyA p-f aA af-N 2+N aw=0;
Wherein, M---moment of flexure design load;
α 1---coefficient, when strength grade of concrete was no more than C50, α 1 was taken as 1.0, and when strength grade of concrete was C80, α 1 was taken as 0.94, confirmed by linear interpolation therebetween;
β 1---coefficient, when strength grade of concrete is no more than C50, be taken as 0.8, when strength grade of concrete is C80, be taken as 0.74, confirm by linear interpolation therebetween;
f c---concrete axial compressive strength design load;
M Aw---what the shaped steel web bore axially receives pull wing edge and the longitudinal tensile reinforcing bar moment of point with joint efforts to shaped steel with joint efforts;
N Aw---what the shaped steel web bore axially makes a concerted effort;
F ' a, f aThe resistance to compression of-shaped steel, the tensile strength design load; f y', f y-drawn the intensity of the vertical muscle of pressurized;
f Py---the tensile strength of prestress wire;
N 2-secondary axes power; A ' Af, A Af-shaped steel pressurized, receive pull wing edge area;
A ' s, A s---the Vierendeel girder pressurized, drawn vertical rib area.
Further, said normal section for Vierendeel girder receives the requirement of curved bearing capacity and moment of flexure, when depth of compressive zone satisfies δ 1h 0<1.25x, δ 2h 0During>1.25x, moment of flexure with receive curved bearing capacity and h 0Require to calculate according to following formula:
M aw=[0.5(δ 1 22 2)-(δ 12)+2.5ξ-(1.25ξ) 2]t wh 0 2f a
N aw=[2.5ξ-(δ 12)]t wh 0f a
h 0 = f a A af ( δ 2 h 0 + 0.5 t w ) + f y A y ( h - a s ) + f py A p ( h - a p ) f a A af + f y A y + f py A p
Wherein: ξ---relative height of compression zone, ξ=x/h 0
ξ b---relative balanced depth of compression zone, ξ b=x b/ h 0
x b---balanced depth of compression zone;
δ 1---shaped steel web upper end to the cross section top margin from the ratio of h0;
δ 2---shaped steel web lower end to the cross section top margin from the ratio of h0;
M Aw---what the shaped steel web bore axially receives pull wing edge and the longitudinal tensile reinforcing bar moment of point with joint efforts to shaped steel with joint efforts;
N Aw---what the shaped steel web bore axially makes a concerted effort;
t w---the shaped steel web thickness;
t f'---shaped steel compression flange thickness;
h w---the shaped steel web height;
h 0---shaped steel receives pull wing edge, longitudinal tensile reinforcing bar and presstressed reinforcing steel to make a concerted effort point to the concrete compression Edge Distance.
Further, said concrete compression district height x meets the formula requirement:
X≤x b=min{x s, x a, x p, and x>=a ' a+ t ' f
Wherein: when surrendering in regular reinforcement, deformed bar and the shaped steel lower flange, depth of compressive zone is respectively x s, x p, x aA ' a-shaped steel compression flange is to the distance at Vierendeel girder pressurized edge.
Further, the Vierendeel girder of said prestress steel reinforced concrete structure adopts and is full of the real abdomen shaped steel of type.
Beneficial effect
Method for designing of the present invention has taken into full account the complicated restraint condition of prestress steel reinforced concrete structure; When design for the Vierendeel girder normal section receive the calculating of curved bearing capacity and moment of flexure the time will retrain and the distribution joint account; On this basis; The structure of design will more meet the requirement of practical structure because of having considered shaped steel and concrete influence, and security performance is more outstanding.
Description of drawings
Fig. 1 is the shaped steel sectional reinforcement form synoptic diagram of prestress girder with rolled steel section en cased in concrete of the present invention.
Fig. 2 is a Vierendeel girder synoptic diagram of the present invention.
Fig. 3 is a boundary of the present invention district high computational simplified schematic diagram.
Fig. 4 receives curved bearing capacity calculation synoptic diagram for Vierendeel girder normal section of the present invention.
Embodiment
Below in conjunction with specific embodiment and accompanying drawing, further set forth the present invention.
The long-term research of this seminar shows; In the prestress steel reinforced concrete structure that complicated constraint is arranged; Because receive the influence of post lateral deformation stiffness; Effective prestress in the prestressed concrete beam has bigger reduction, so the normal use of actual prestressed concrete beam and ultimate bearing capacity can't satisfy structural requirement, can produce potential safety hazard to engineering.Therefore consider to propose a kind of prestress steel reinforced concrete structure method for designing, solve above-mentioned two kinds of requirements, thereby eliminate safe hidden trouble based on the complicacy constraint.The present invention is a kind of new method for designing that at first proposes ultimate bearing capacity.
For the shaped steel of prestress steel reinforced concrete frame beam, should adopt to be full of the real abdomen shaped steel of type, a side wing edge of its shaped steel should be positioned at compressive region, and the opposite side edge of a wing is positioned at the tensile region, shown in accompanying drawing 1.When the beam section height is higher, join the prestress girder with rolled steel section en cased in concrete of truss-like shaped steel in can adopting.
When carrying out structural internal force and The deformation calculation, cross section bendind rigidity, axial rigidity and the shear stiffness of prestress steel reinforced concrete structure member, can calculate by following regulation:
EI=E cI c+E aI a
EA=E cA c+E aA a
GA=G cA c+G aA a
EI, EA, GA in the formula---member section bendind rigidity, axial rigidity, shear stiffness; E cI c, E cA c, G cA c---cross section bendind rigidity, axial rigidity, the shear stiffness of reinforced concrete part; E aI a, E aA a, G aA a---cross section bendind rigidity, axial rigidity, the shear stiffness of shaped steel or steel pipe part.
For prestress steel reinforced concrete frame beam and conversion beam, its normal section should be calculated according to following fundamental assumption by curved bearing capacity:
1. the cross section should keep the plane;
2. do not consider concrete tensile strength;
3. pressurized edge ultimate compressive strain of concrete ε CuGet 0.003, corresponding maximum crushing stress is got concrete axial compressive strength design load f cMultiply by alpha 1, when strength grade of concrete is no more than C50, α 1Be taken as 1.0; When strength grade of concrete is C80, α 1Be taken as 0.94, confirm by linear interpolation therebetween; The compressive region stress diagram is reduced to the rectangular stress figure of equivalence, and it is highly got by the determined depth of neutral axis of plane cross-section assumption and multiply by factor beta 1, when strength grade of concrete is no more than C50, β 1Be taken as 0.8, when strength grade of concrete is C80, β 1Be taken as 0.74, confirm by linear interpolation therebetween;
4. the stress pattern of shaped steel web is the trapezoidal stress patterns of tension and compression, during designing and calculating, is reduced to equivalent rectangular stress block shape, and owing to the build-in and the effect of contraction of concrete to shaped steel, the bearing capacity limit stage is not considered the flexing of shaped steel;
5. reinforcement stresses equals the product of reinforcing bar strain and its elastic modulus, but its absolute value should be greater than its corresponding strength design load; Longitudinal tensile reinforcing bar and shaped steel receive the ultimate tensile strength ε of pull wing edge SuGet 0.01.
And when surrendering in regular reinforcement, deformed bar and the shaped steel lower flange; The minimum value of depth of compressive zone can be thought the cross section boundary nip height of prestress girder with rolled steel section en cased in concrete; Shown in accompanying drawing 3; When wherein surrendering in regular reinforcement, deformed bar and the shaped steel lower flange, depth of compressive zone is respectively x s, x p, x a
Therefore: x s = β 1 1 + f y / ( E s ϵ Cu ) h s , x p = β 1 1 + 0.002 ϵ Cu + f Py - σ p 0 E p ϵ Cu h p , x a = β 1 1 + f a / ( E a ϵ Cu ) h Ss .
Thereby obtain the shaped steel cross section is prestress steel reinforced concrete frame beam and the conversion beam that is full of the real abdomen shaped steel of type, and its normal section should be calculated by following formula by curved bearing capacity:
For non-seismic design,
M - [ M 2 - N 2 ( h 2 - a s ) ] ≤ α 1 f c bx ( h 0 - x 2 ) + f y ′ A s ′ ( h 0 - a s ′ ) + f a A af ( a a - a s )
+ f a ′ A af ′ ( h 0 - a a ′ ) + M aw
α 1f cbx+f′ yA′ s+f′ aA′ af-f yA s-f pyA p-f aA af-N 2+N aw=0;
For seismic design,
M - [ M 2 - N 2 ( h 2 - a s ) ] ≤ 1 γ RE [ α 1 f c bx ( h 0 - x 2 ) + f y ′ A s ′ ( h 0 - a s ′ ) + f a A af ( a a - a s ) ,
+ f a ′ A af ′ ( h 0 - a a ′ ) + M aw ]
α 1f cbx+f′ yA′ s+f′ aA′ af-f yA s-f pyA p-f aA af-N 2+N aw=0。
Work as δ 1h 0<1.25x, δ 2h 0During>1.25x,
M aw=[0.5(δ 1 22 2)-(δ 12)+2.5ξ-(1.25ξ) 2]t wh 0 2f a
N aw=[2.5ξ-(δ 12)]t wh 0f a
h 0 = f a A af ( δ 2 h 0 + 0.5 t w ) + f y A y ( h - a s ) + f py A p ( h - a p ) f a A af + f y A y + f py A p .
And concrete compression district height x still should meet formula requirement (promptly can not be in the overreinforced state):
x≤x b=min{x s,x a,x p},x≥a′ a+t′ f
In the above formula, M---moment of flexure design load;
α 1---coefficient, when strength grade of concrete was no more than C50, α 1 was taken as 1.0, and when strength grade of concrete was C80, α 1 was taken as 0.94, confirmed by linear interpolation therebetween;
β 1---coefficient, when strength grade of concrete is no more than C50, be taken as 0.8, when strength grade of concrete is C80, be taken as 0.74, confirm by linear interpolation therebetween;
f c---concrete axial compressive strength design load;
M Aw---what the shaped steel web bore axially receives pull wing edge and the longitudinal tensile reinforcing bar moment of point with joint efforts to shaped steel with joint efforts;
N Aw---what the shaped steel web bore axially makes a concerted effort;
ξ---relative height of compression zone, ξ=x/h 0
ξ b---relative balanced depth of compression zone, ξ b=x b/ h 0
x b---balanced depth of compression zone;
δ 1---shaped steel web upper end to the cross section top margin from the ratio of h0;
δ 2---shaped steel web lower end to the cross section top margin from the ratio of h0;
M Aw---what the shaped steel web bore axially receives pull wing edge and the longitudinal tensile reinforcing bar moment of point with joint efforts to shaped steel with joint efforts;
N Aw---what the shaped steel web bore axially makes a concerted effort;
t w---the shaped steel web thickness;
t f'---shaped steel compression flange thickness;
h w---the shaped steel web height;
h 0---shaped steel receives pull wing edge, longitudinal tensile reinforcing bar and presstressed reinforcing steel to make a concerted effort point to the concrete compression Edge Distance.
Above-mentioned requirement to prestress steel reinforced concrete structure function in fact promptly has enough intensity, can bear the internal force that the least favorable load effect produces, and satisfies the ultimate limit states requirement.In addition, also need consider the economy and the operability of design proposal.
The total design is mainly carried out according to following steps, and economy, reasonable, a feasible design proposal often need just can obtain through revising repeatedly to calculate several times.
(1) confirms the inferior internal force of structure
(2),, tentatively confirm prestressing force steel reinforced concrete structure section form and sectional dimension with reference to existing design and related data based on instructions for use and overall plan of working out and version;
(3) adopt model for internal force analysis, calculate the maximum effect in combination of load effect and control cross section;
(4) adopt the inventive method according to the control design force of cross section under ultimate limit states and serviceability limit state and the sectional dimension of tentatively working out, the quantity of estimation presstressed reinforcing steel, and carry out reasonable Arrangement.If presstressed reinforcing steel can't reasonable Arrangement, then should return for (2) step, revise sectional dimension;
(5) calculate the cross section geometric characteristic;
(6) confirm the control stress for prestressing of presstressed reinforcing steel, calculate loss of prestress and each stage corresponding effective stress;
(7) the checking computations construction stage, transport the section stress with installation phase and operational phase;
(8) checking computations anchoring position partial pressing.

Claims (4)

1. the Vierendeel girder anti-bending bearing capacity method for designing of a prestress steel reinforced concrete structure; It is characterized in that: to adopting the Vierendeel girder of prestress steel reinforced concrete structure; Normal section for Vierendeel girder during design receives curved bearing capacity to require to calculate according to following formula, and need meet following requirement to moment of flexure:
(1) about non-seismic design,
M - [ M 2 - N 2 ( h 2 - a s ) ] ≤ α 1 f c bx ( h 0 - x 2 ) + f y ′ A s ′ ( h 0 - a s ′ ) + f a A af ( a a - a s )
+ f a ′ A af ′ ( h 0 - a a ′ ) + M aw
α 1f cbx+f′ yA′ s+f′ aA′ af-f yA s-f pyA p-f aA af-N 2+N aw=0;
(2) about seismic design,
M - [ M 2 - N 2 ( h 2 - a s ) ] ≤ 1 γ RE [ α 1 f c bx ( h 0 - x 2 ) + f y ′ A s ′ ( h 0 - a s ′ ) + f a A af ( a a - a s )
+ f a ′ A af ′ ( h 0 - a a ′ ) + M aw ]
α 1f cbx+f′ yA′ s+f′ aA′ af-f yA s-f pyA p-f aA af-N 2+N aw=0;
Wherein, M---moment of flexure design load;
α 1---coefficient, when strength grade of concrete was no more than C50, α 1 was taken as 1.0, and when strength grade of concrete was C80, α 1 was taken as 0.94, confirmed by linear interpolation therebetween;
β 1---coefficient, when strength grade of concrete is no more than C50, be taken as 0.8, when strength grade of concrete is C80, be taken as 0.74, confirm by linear interpolation therebetween;
f c---concrete axial compressive strength design load;
M Aw---what the shaped steel web bore axially receives pull wing edge and the longitudinal tensile reinforcing bar moment of point with joint efforts to shaped steel with joint efforts;
N Aw---what the shaped steel web bore axially makes a concerted effort;
F ' a, f aThe resistance to compression of-shaped steel, the tensile strength design load; f y', f y-drawn the intensity of the vertical muscle of pressurized;
f Py---the tensile strength of prestress wire;
N 2-secondary axes power; A ' Af, A Af-shaped steel pressurized, receive pull wing edge area;
A ' s, A s---the Vierendeel girder pressurized, drawn vertical rib area.
2. the Vierendeel girder anti-bending bearing capacity method for designing of prestress steel reinforced concrete structure as claimed in claim 1 is characterized in that: said normal section for Vierendeel girder receives the requirement of curved bearing capacity and moment of flexure, when depth of compressive zone satisfies δ 1h 0<1.25x, δ 2h 0During>1.25x, moment of flexure with receive curved bearing capacity and h 0Require to calculate according to following formula:
M aw=[0.5(δ 1 22 2)-(δ 12)+2.5ξ-(1.25ξ) 2]t wh 0 2f a
N aw=[2.5ξ-(δ 12)]t wh 0f a
h 0 = f a A af ( δ 2 h 0 + 0.5 t w ) + f y A y ( h - a s ) + f py A p ( h - a p ) f a A af + f y A y + f py A p
Wherein: ξ---relative height of compression zone, ξ=x/h 0
ξ b---relative balanced depth of compression zone, ξ b=x b/ h 0
x b---balanced depth of compression zone;
δ 1---shaped steel web upper end to the cross section top margin from the ratio of h0;
δ 2---shaped steel web lower end to the cross section top margin from the ratio of h0;
M Aw---what the shaped steel web bore axially receives pull wing edge and the longitudinal tensile reinforcing bar moment of point with joint efforts to shaped steel with joint efforts;
N Aw---what the shaped steel web bore axially makes a concerted effort;
t w---the shaped steel web thickness;
t f'---shaped steel compression flange thickness;
h w---the shaped steel web height;
h 0---shaped steel receives pull wing edge, longitudinal tensile reinforcing bar and presstressed reinforcing steel to make a concerted effort point to the concrete compression Edge Distance.
3. according to claim 1 or claim 2 the Vierendeel girder anti-bending bearing capacity method for designing of prestress steel reinforced concrete structure, it is characterized in that: said concrete compression district height x meets formula and requires:
X≤x b=min{x s, x a, x p, and x>=a ' a+ t ' f
Wherein: when surrendering in regular reinforcement, deformed bar and the shaped steel lower flange, depth of compressive zone is respectively x s, x p, x aA ' a-shaped steel compression flange is to the distance at Vierendeel girder pressurized edge.
4. the Vierendeel girder anti-bending bearing capacity method for designing of prestress steel reinforced concrete structure as claimed in claim 1 is characterized in that: the Vierendeel girder of said prestress steel reinforced concrete structure adopts and is full of the real abdomen shaped steel of type.
CN2011104369011A 2011-12-22 2011-12-22 Flexural bearing capacity designing method for frame beam adopting pre-stressed steel reinforced concrete structure Pending CN102650579A (en)

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