CN109868937B - Post-tensioned unbonded prestressed concrete composite beam and its design and construction method - Google Patents
Post-tensioned unbonded prestressed concrete composite beam and its design and construction method Download PDFInfo
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Abstract
本发明涉及一种后张无粘结的预应力混凝土叠合梁及其施工方法，该叠合梁是一种为满足使用需求，在叠合梁叠合成型之后对整根梁施加后张无粘结预应力。相对传统的叠合梁，其采用了后张无粘结预应力技术，既秉承下叠合结构预制装配程度高、施工便捷等特点，还能提升构件的抗裂抗弯性能。由于其在整体施工后能够施加后张预应力，其特别适用于对变形控制、承载力要求较高的大跨、重载等高性能要求的结构中，并在满足设计要求的同时也能体现装配式结构的优越性。
The invention relates to a post-tensioned unbonded prestressed concrete composite beam and a construction method thereof. The composite beam is a kind of post-tensioned concrete composite beam applied to the whole beam after the composite beam is stacked and formed to meet the requirements of use. Bonding prestress. Compared with the traditional laminated beam, it adopts the post-tensioning unbonded prestressing technology, which not only inherits the characteristics of high prefabricated assembly and convenient construction of the lower laminated structure, but also improves the crack resistance and bending performance of the components. Because it can apply post-tensioning prestress after the overall construction, it is especially suitable for structures with high performance requirements such as large spans and heavy loads that require high deformation control and bearing capacity, and can also reflect the design requirements while meeting the design requirements. The advantages of prefabricated structure.
Description
Technical Field
The invention relates to the technical field of civil engineering design, in particular to a fractional tensioning prestressed concrete superposed beam stretched after unbonded tensioning in a large-span heavy-load structure and a design and construction method thereof.
Background
In recent years, with the improvement of the construction technology of China, the corresponding construction level is higher and higher. The building has new concepts and requirements in various aspects such as building appearance, building quality, building efficiency, green, low-carbon and energy-saving of buildings and the like. However, the labor cost of manpower and the environmental impact control requirement during the construction are increased, which is a little test for improving the construction level. Building industrialization is receiving more and more attention because the design and construction integrated production mode can meet the requirements of buildings and construction and manufacturing.
The construction process of prestressed concrete includes pre-tensioning method and post-tensioning method. The pre-tensioning construction process can ensure the effective binding force between the prestressed tendon and the concrete, and is simple in construction, but is only suitable for industrial production of small and medium-sized components. For the industrial production of large-scale components, a post-tensioning construction process is usually adopted, post-tensioning prestressed concrete can be divided into bonded prestressed concrete and unbonded prestressed concrete, the bonded prestressed concrete structure is reliable, the bearing capacity is high, but the construction is complex, a pore passage and grouting are required to be reserved, and the construction quality of the post-tensioning bonded prestressed concrete is difficult to control because a construction technology and an effective detection means for ensuring the complete compactness of the grouting are not available; the unbonded prestressed concrete prestressed tendon is not bonded with the surrounding concrete, the prestressed tendon can be freely deformed, the construction is simpler than the bonded prestressed concrete, a hole channel and grouting are not required to be reserved, and the friction loss can be reduced. The proposed unbonded prestressed structure has been developed more rapidly, and although the mechanical properties of the unbonded prestressed structure are not as excellent as those of the bonded prestressed structure, the construction performance is better and the quality is relatively more reliable.
Disclosure of Invention
The invention aims to provide a post-tensioned unbonded prestressed concrete superposed beam and a construction method thereof, which is a novel prestressed member adopting unbonded prestressed bars. The composite structure combines two traditional structures of a composite structure and an unbonded prestressed structure, introduces the innovative special design and construction technology of prestress, completely inherits the good construction performance of the composite structure and the unbonded prestressed structure, and can make up the defects of low bearing capacity of the composite structure and insufficient mechanical performance of the pure unbonded structure.
In order to achieve the purpose, the invention adopts the following scheme:
the utility model provides a post-tensioned unbonded prestressed concrete composite beam, includes concrete prefabricated component, superimposed layer 2, top vertical reinforcement 1, bottom vertical reinforcement 5 and stirrup 6 the upper portion of concrete prefabricated component of superimposed beam is provided with superimposed layer 2, top vertical reinforcement 1 and bottom vertical reinforcement 5 set up respectively in the top and the bottom of superimposed beam, top vertical reinforcement 1 is located in superimposed layer 2, stirrup 6 set up in the inside of superimposed beam and parcel top vertical reinforcement 1 and bottom vertical reinforcement 5, be provided with bonding reinforcement 7 in the middle part of superimposed beam, be provided with lumbar muscle 3 at every layer the lower extreme of bonding reinforcement 7 all be provided with waist muscle 3 in the superimposed beam lower part is equipped with a plurality of post-tensioned unbonded prestressed tendons 4, post-tensioned unbonded prestressed reinforcement 4 sets up in the pore in the concrete prefabricated component, post-tensioned unbonded prestressed reinforcement 4 is reserved for curve or straight line arrangement, and passes through the superposed layer 2, and two ends of the superposed layer extend out of the superposed beam, and two ends of the superposed layer are respectively and fixedly provided with an anchorage device 9 and a clamp 8.
Preferably, both ends of the post-tensioned unbonded prestressed tendon 4 extend out of the laminated layer 2 of the laminated beam, and the end part of the laminated layer 2 is further provided with a post-cast area 10.
Preferably, the stirrups 6 in the range of twice the height of the beam on both sides of the position where the post-tensioned unbonded prestressed tendon 4 passes through the laminated layer need to be doubly and densely arranged.
Preferably, the vertical clear distance of the reserved hole channel of the post-tensioned unbonded prestressed tendon 4 is not less than 50mm and not less than 1.25 times of the particle size of the coarse aggregate, and the clear distance from the hole channel to the edge of the superposed beam member is not less than 30mm and not less than half of the diameter of the hole channel.
The invention also provides a design method of the post-tensioned unbonded prestressed concrete composite beam, which comprises the following stages according to the construction and using stress conditions of the post-tensioned unbonded prestressed concrete composite beam:
(a) determining the cross-sectional dimensions b, h1，h2
(b) Area A of the pre-estimated post-tensioning unbonded ribp2
(c) Determining the area A of non-prestressed tendons designed for bondings
(d) Calculating post-tension unbonded pre-stress loss
(e) Checking calculation of reinforcement limit value of post-tensioned unbonded prestressed concrete composite beam
(f) Calculating the primary stress of the prestressed precast beam
(g) Prestress applied to laminated beam by calculating post-tensioning method
(h) And calculating the integral stress of the post-tensioned unbonded prestressed concrete composite beam.
The invention also provides a construction method of the post-tensioned unbonded prestressed concrete composite beam, which comprises the following steps:
a. arranging common steel bars and unbonded prestressed tendons in advance before pouring the prefabricated part;
b. pouring, maintaining and forming, transporting, hoisting in place on site, and pouring a superposed layer;
c. stretching the pre-buried unbonded prestressed tendons when the maintenance of the laminated layer reaches the standard and the requirement of stretching prestress is met;
d. the non-adhesive material in the non-adhesive prestressed tendon slowly produces adhesive force along with the time, and finally reaches a completely adhesive state to form the post-tensioned non-adhesive prestressed concrete composite beam.
Compared with the traditional prestressed composite beam, the post-tensioned unbonded prestressed concrete composite beam has the following advantages:
(1) improving the crack and bending resistance of the component
If the precast beam is cracked due to self weight and the weight of the upper structure borne by the precast beam as a construction formwork, the original crack can be closed or the width of the original crack can be reduced by applying secondary prestress. If the precast beam does not crack, the secondary prestress can improve the cracking load of the test piece. The stiffness of the component can be increased because the prestressing delays the occurrence of cracks and limits the width of cracks.
(2) Can improve the weather resistance of the member
In general, if a prestressed design is not a design method using full prestressing, a member will have a certain degree of microcracks at the initial stage of use, and cracks will continuously propagate with the passage of time, and the carbonization degree of concrete will also increase. The traditional prestressed tendons inevitably interact with a corrosion medium under a high stress state, so that the stress corrosion condition is caused. If the prestressed tendon of post-tensioning adopts the form of unbonded prestressed tendon, the oversheath of tendon and the unbonded material of packing can be relied on to a great extent and the corrosive medium separates to the deformability of sheath and unbonded material is better under the general condition, can satisfy under the high strain still guarantee not to break, thereby guarantee the weatherability of component.
(3) Enhancing the connection and structural integrity of a node
The secondary pre-stress may not only strengthen the strength of the structural member, but it may also serve as a way of linking between structural members. The beam columns are connected in series into a whole through the prestressed tendons, and the normal stress between the beam columns generated by the prestress can increase the friction force and the biting force between the members at the joints. In terms of seismic resistance, the pre-stress can provide self-resetting capability for relative displacement between the components at the node.
Drawings
FIG. 1 is a schematic cross-sectional view of a post-tensioned unbonded prestressed concrete composite beam;
FIG. 2 is a front view of a post-tensioned unbonded prestressed concrete composite beam (without post-cast sections);
FIG. 3 is a front view of a post-tensioned unbonded prestressed concrete composite beam (with post-cast sections);
FIG. 4 is a schematic view of a post-tensioned unbonded prestressed concrete composite beam joint (with post-cast sections);
FIG. 5 is a computational flow diagram;
FIG. 6 is a schematic view of a post-tensioned unbonded tendon;
FIG. 7 is an extra-rib limit reinforcement strain analysis plot;
FIG. 8 is a diagram of calculation of the stress of the prestressed precast beam;
FIG. 9 is a simplified calculation diagram of the prestressed precast beam once stressed and the concrete in an elastic state;
FIG. 10 is a simplified calculation diagram of a precast beam cracking time;
FIG. 11 is a schematic diagram of calculation of post-tensioning prestress applied to a once-stressed uncracked composite beam;
FIG. 12 is a graph of strain analysis of a concrete portion at a compression zone of a precast beam during decompression;
FIG. 13 is a strain analysis diagram of concrete at a compression area of a precast beam without decompression;
FIG. 14 is a stress analysis diagram of a concrete part in a compression area of a precast beam during decompression;
FIG. 15 fracture re-opening stress analysis plot of fracture closed section;
FIG. 16 is a force analysis diagram of the laminated beam at the extreme load state;
the reference numbers in the figures include:
1-top longitudinal bar, 2-laminated layer, 3-waist bar, 4-post-tensioning unbonded prestressed bar, 5-bottom longitudinal bar, 6-stirrup, 7-tie bar, 8-clamp, 9-anchor, 10-post-pouring area, 11 column, 12-concrete, 13-side wire, 14-core wire and 15-corrugated pipe.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings.
Referring to fig. 1-4, a post-tensioned unbonded prestressed concrete composite beam is provided, in which an unbonded prestressed is applied to the composite beam by a post-tensioning method, a top longitudinal rib 1 is arranged at the top of the composite beam, a bottom longitudinal rib 5 is arranged at the bottom of the composite beam, a composite layer 2 is arranged at the upper part of the composite beam, two layers of tie bars 7 are arranged at the middle part of the composite beam, a wale 3 is arranged at the lower end of each layer of tie bar 7, a plurality of unbonded prestressed ribs 4 are arranged at the lower part of the composite beam, stirrups 6 are arranged at the periphery of the composite beam, two ends of the post-tensioned unbonded prestressed ribs 4 extend out of a composite beam member, an anchorage device 9 and a clamp 8 are respectively fixedly arranged at two ends of the post-tensioned unbonded prestressed ribs 4, and a post-cast region 10 can be arranged at the end part of the composite layer according to requirements.
As shown in fig. 4, which is a schematic node diagram (provided with a post-cast area) of a post-tensioned unbonded prestressed concrete composite beam, a schematic node diagram of the combination of two composite beams and a column 11 can be seen.
The post-tensioned unbonded prestressed concrete superposed beam applies unbonded prestress to the superposed beam by adopting a post-tensioning method, so that the member meets the requirements of bearing capacity and service performance at each stage.
The post-tensioned unbonded prestressed tendons 4 can adopt a linear or curvilinear arrangement mode according to the actual stress condition of the components and the construction requirements. The straight line or curved line arrangement selection is suggested as follows: if the component is under the condition of simple support and mainly bears uniform stress, or the component does not need to be designed finely and adopts a linear arrangement mode;
in order to make the prestressed tendon play a larger bearing role in the structure, the linear loss height of the prestressed tendon should be increased as much as possible in the design. The beam height can be effectively used in the design process to allow the post-tensioned unbonded tendons 4 to span the overlap plane and extend into the overlap layer 2.
As shown in fig. 6, which is a schematic diagram of the post-tensioned unbonded prestressed tendon, a plurality of heel side wires 13 are arranged outside a core wire 14, and a corrugated pipe 15 is wrapped outside the core wire.
In order to facilitate the space arrangement of node assembly, tensioning of the post-tensioning unbonded prestressed tendon 4 and the like, the superposed layer 2 can be arranged with the precast beam in unequal length, and a post-pouring area 10 is arranged at the end position of the superposed layer. The design can increase the geometric diversity of the member, and facilitates the node design and installation construction. For the post-tensioned unbonded prestressed tendons 4 which are arranged in a curve and penetrate through the laminated layer, in order to prevent the concrete penetrating through the laminated layer from being damaged due to complex stress action, stirrups in the range of one-time beam height on the left side and the right side of the penetrating point are required to be encrypted by one time and do not exceed the standard requirement. If the encryption range is in the stirrup encryption area where the beam end is resistant to shear damage and the encryption degree of the stirrups is the same or lower than that of the original encryption design, the arrangement of the stirrups does not need to be additionally increased. According to a bending moment diagram of the stress of the component, the height losing direction is zoomed according to a certain proportion, and the linear shape of the prestressed tendon can meet the requirements of geometric dimension and structure, so that the most economical linear arrangement of the prestressed tendon can be obtained. If the curved line shape cannot be arranged according to the shape of the bending moment diagram, the line shape and the bending moment diagram should be ensured to be similar as much as possible so as to obtain relatively economic design effect.
In order to meet the requirements of ensuring local concrete pressure bearing at the anchoring part of the prestressed tendon, compact concrete pouring, enough space for prestressed tendon tensioning construction and the like, the arrangement of the prestressed tendon has the following requirements: the vertical clear distance of the reserved hole channel is not smaller than 50mm and not smaller than 1.25 times of the particle size of the coarse aggregate, and the clear distance from the hole channel to the edge of the member is not smaller than 30mm and not smaller than half of the diameter of the hole channel.
The construction method of the post-tensioned unbonded prestressed concrete composite beam comprises the following steps: arranging common steel bars and prestressed tendons in a prearranged manner before the prefabricated part is poured; tensioning a prestressed tendon on the pedestal; pouring, maintaining and forming, transporting, hoisting in place on site, and pouring a superposed layer; stretching the pre-buried post-tensioned prestressed tendons when the maintenance of the laminated layer reaches the standard and the requirement of stretching secondary prestress is met; and after the tensioning meets the requirements, forming the post-tensioned unbonded prestressed concrete composite beam.
If no end plate is arranged at the whole height of the beam end or the whole height of the cast-in-place net piece is arranged, the joint pressure bearing effect of the precast beam and the laminated layer cannot be considered simultaneously during the checking calculation of local pressure bearing.
The method for calculating the expansion design of the post-tensioned unbonded prestressed concrete composite beam according to the four stages and the limit reinforcing bar values is explained below. The calculation flow is shown in fig. 5.
1. Determining the cross-sectional dimensions b, h1，h2
For the post-tensioned unbonded prestressed concrete composite beam, the consideration of the section size needs to consider the stress conditions under the construction state and the normal use state simultaneously. Its height h before and after folding1And h2Width b, height-to-span ratio h1L and h2/l(h1Height of the precast beam, h2Height after superposition, and l is the span of the beam), the load and other factors, and the selected section size needs to meet the corresponding specification requirement.
2. Area A of post-tensioned unbonded rib in pre-estimated precast beamp2
According to the bonding design and the requirement of the normal use limit state, the total area of the prestressed tendons is determined according to crack control, and the prestressed concrete can be calculated according to the uncracked state. Under the conditions of construction and use and under the action of design load and prestress, the area A of the unbonded rib is estimated according to the criterion that the maximum tensile stress and the nominal tensile stress of concrete edge fibers in a tension area do not exceed the tensile strength of the concretep2。
And (4) calculating the prestress of the post-tensioned unbonded prestressed tendon according to the structure type and the control requirement of the normal section crack according to the following formula, and taking a larger value of the result.
Wherein M is1kAnd M1qRespectively calculating bending moment design values of the stress of one stage of the precast beam according to the load standard combination and the quasi-permanent combination; m2kAnd M2qRespectively calculating bending moment design values of the superposed forming rear beam according to load standard combination and quasi-permanent combination; [ sigma ]ctk，lim]And [ sigma ]ctq，lim]The tensile limit values of the concrete under the load standard combination and the load quasi-permanent combination can be taken by reference to the standard; w2Elastic resisting moment of tension edge of member section of the superposed composite beam; a. the2The cross section area of the component of the superposed composite type beam; e.g. of the type02The eccentricity of the center of the prestressed tendon relative to the superposed beam is obtained; beta is a beam structure coefficient, for example, for a simply supported structure, beta is 1.0, for a hogging moment section of a continuous structure, beta is 0.9, and for a positive bending moment section of the continuous structure, beta is 1.2.
Effective prestressing force N according to prestressing tendonspe2Estimating the area A of the post-tensioned unbonded tendonp2Can be estimated as follows
Wherein σcon2Controlling the stress for the tensioning of the post-tensioned unbonded prestressed tendon; sigmal，tot2The pre-stressed loss of the post-tensioned unbonded prestressed tendon is estimated.
3. Determining the area A of non-prestressed tendons designed for bondings
From the area A of the tendonp2Degree of prestress λ, minimumReinforcement ratio ρminAnd the construction requirement determines the area A of the non-prestressed tendons1.
The reinforcement distribution rate of non-prestressed tendons in a tension area in the unbonded prestressed concrete flexural member is not less than the specification of table 1 and the requirement of the prestress degree lambda, the prestress degree lambda is determined according to the earthquake resistance grade of the member, and meanwhile, the configuration of the non-prestressed tendons meets the construction requirement.
TABLE 1 minimum reinforcement ratio of non-prestressed reinforcement of unbonded prestressed concrete flexural member
| Kind of reinforcing bar | HPB235 stage | HRB335 stage | HRB400 stage |
| Minimum reinforcement ratio ρmin | 0.367％ | 0.257％ | 0.213％ |
Namely, the method comprises the following steps: a. thes≥ρminbh2And is and
wherein f ispyThe design value of the tensile strength of the post-tensioned unbonded prestressed tendon is obtained; h ispThe effective distance from the longitudinal prestressed rib resultant force action point to the pressed edge of the superposed beam; f. ofyThe design value of the tensile strength of the common steel bar is obtained; h iss2For longitudinally-tensioned non-prestressed tendonsThe effective distance from the resultant force action point to the pressed edge of the section of the superposed beam.
4. Post-tensioning unbonded pre-stress loss calculation
The calculation of the prestress loss is divided into two parts of instantaneous loss and long-term loss. Transient losses include anchor losses, friction losses, elastic compression losses, long term losses include stress relaxation of the tendons and shrinkage creep of the concrete.
5. Checking calculation of reinforcement limit value of post-tensioned unbonded prestressed concrete composite beam
The boundary reinforcement can be divided into boundary reinforcement of 'proper reinforcement' and 'excessive reinforcement' and boundary reinforcement of 'proper reinforcement' and 'few reinforcement'. Because the laminated beam has the characteristics of leading stress of a tension steel bar and lagging strain of the concrete of the laminated layer, the ultimate bearing capacity and the stress and the strain of a cracking state of the laminated beam are different from those of a common integrally cast beam, and the limit reinforcement value of the laminated beam is also different.
(1) Boundary reinforcement of ' suitable reinforcement ' and ' extra reinforcement
The calculation diagram is shown in figure 7. The relative compression zone height of the boundary can be divided into two parts to show
In the above formula,. DELTA.xn、ξb1And xib2According to the transformation coordination relationship can be expressed as
In the formula (I), the compound is shown in the specification,
Δεpc14according to the deformation coordination condition, the method comprises the following steps of,
the height xi of the compression zone of the rib fitting and extra rib boundary can be obtained by combining the above formulasb。
(2) Boundary reinforcement of ' suitable reinforcement ' and ' less reinforcement
The method for calculating the minimum reinforcement ratio of the composite beam is as follows
6. One-time stress analysis checking calculation for prestressed precast beam
(1) Analysis under elastic State of Cross section
The calculation diagram is shown in figure 9.
When the once stressed load is small, the concrete fiber at the edge of the tension area does not enter a plastic state, the section is still in an elastic state, and the analysis can be carried out according to a material mechanics method.
At an acting force M1Stress variation of concrete under action
If it is
It indicates that the concrete is in an elastic state. On the contrary, the calculation should be carried out with the concrete in the tension area in the elastoplastic state or the cracking state
(2) Cross section cracking load calculation
The cracking load of the section can be calculated by a normative method utilizing the concrete plasticity influence coefficient, and can also be accurately calculated by a theoretical derivation method. For convenient calculation, a more conservative standard calculation method can be adopted. In order to economically and accurately calculate the cracking load, a theoretical derivation method can be adopted.
Theoretical calculation method is given below
Compared with the calculation method adopted by the standard, the invention needs to accurately calculate the cracking of the post-tensioned unbonded prestressed concrete composite beam, so that the theoretical calculation method is recommended to be adopted for estimating the cracking load
The calculation diagram is shown in figure 10
Calculate the compression zone height according to
After the height of the concrete compression area is calculated, the pressure action point can be set to 0 according to the bending moment balance condition sigma M, and the bending moment of the concrete section at the moment is obtained
Mcr0＝Mc2+Ms2＝Tc2lA+Ts2lB (5)
In the formula, Tc2、Ts2Respectively showing the resultant force of concrete and ordinary steel bar in the tension areaA、lBRespectively representing the distance from the resultant force action point of the concrete in the tension area and the common steel bar to the concrete in the compression area, and respectively calculating according to the following formulas
(3) Checking calculation after section cracking
If the stress of one stage is large and the design is conservative, the precast beam can crack in the stress of one stage, but the width of the crack needs to be within the limit value. Crack control level and maximum crack control width limit ω of structural memberlimAs shown in the following tableThe following steps:
| grade of crack control | ωlim(mm) |
| Three-stage | 0.2 |
| Class II | 0.1 |
| Class I of two | It is generally required that no cracks occur |
| First stage | No crack is allowed to appear |
Note: if the influence of the secondary internal force (secondary axial force and secondary bending moment) cannot be ignored, the influence of the secondary internal force is considered by the crack width calculation formula, and the calculation can be carried out by referring to relevant specifications.
7. Analysis and checking calculation of prestress applied to laminated beam by post-tensioning method
For the beam which cracks in one stress, the application of prestress by adopting a post-tensioning method can reduce the width of the originally cracked crack and even can reclose the crack, thereby greatly helping the durability of the beam. Therefore, whether the primary stressed beam cracks needs to be discussed separately, wherein the beam which is cracked under the primary stress needs to be checked whether the crack is closed or not.
(1) Does not crack under one-time stress
If a load force M1Less than the crack resistance bearing capacity M of the precast beamcr1I.e. M1＜Mcr1At this time, the stress level of the section is small, and the stress condition of the section is considered in an elastic state. The calculation diagram is shown in figure 11.
Stress variation of concrete at any point
In the formula, An2And In2Respectively calculating the cross-sectional area and the moment of inertia of the converted cross section of the composite beam after deducting the post-tensioned pore channel; e.g. of the type02The eccentricity of the center of the prestressed tendon relative to the superposed beam is obtained; y is the distance from the stress position of the concrete to the centroid of the converted section; n is a radical ofpe2The prestress of the post-tensioned prestressed tendon.
Applying secondary prestress on the superposed beam by a post-tensioning method to ensure that the tensile stress of the concrete of the whole cross section does not exceed the corresponding limit value, checking and calculating the concrete fiber stress of the edge of the superposed layer and the edge of the precast beam to meet the requirement of not being more than tensile strength, namely, the following two formulas:
in the formula (f)tAnd fcRespectively designing values of tensile strength and compressive strength of the concrete;
and
the stress of the concrete at the bottom and the top of the section respectively;
the stress of the concrete at the bottom of the section in a first stress stage; a isp2The center of gravity of the post-tensioned prestressed tendon is far away from the beam bottomThe distance of (c).
(2) Stress of the section of the primary stress cracking
According to whether the concrete in the compression area of the precast beam is decompressed or not, the two conditions can be divided, and corresponding strain analysis is shown in the attached figures 12 and 13. In order to conveniently calculate whether the primary stress cracking section can close the crack under the action of secondary prestress, a conservative calculation method is uniformly adopted to estimate the two conditions, and the method comprises the following steps:
calculating the area of the converted section
An2＝bh-Dtbxn2+αEs(As+As′) (9)
In the formula, DtThe variable of concrete compression damage caused by concrete cracking; x is the number ofn2The height of the concrete in the tension area of the precast beam in the first stage stress state is determined; alpha is alphaEsThe ratio of the elastic modulus of the steel bar to the concrete; a. thes' is the area of the rebar under compression.
Calculating the distance of the mandrel from the bottom surface of the beam
In the formula, asAnd as' distances from the center of gravity of the tensioned and stressed reinforcement bars to the tensioned and stressed edges, respectively;
calculating the converted moment of inertia of the cross section
Calculating the concrete mean stress variation at the bottom edge
When in use
When the following formula is satisfiedConsider concrete crack closure
In the formula, EcIs the modulus of elasticity of concrete; sigmac0The compressive stress of the concrete when the crack is closed can be 1-2 MPa;
is the average strain of a concrete section under a primary force.
8. Analysis and checking calculation for integral stress of post-tensioned unbonded prestressed concrete composite beam
(1) Cracking load of one-stage stressed uncracked member
The calculation diagram is shown in figure 14.
The cracking load can be determined by taking the moment of the concrete edge in the tension area, i.e.
Mcr＝M1+M2＝Mc1+Mc2+Ms2+MTc+Ms1+Mp2 (14)
The respective moments of the above formula are
Ms2＝-Cs2·(h-as′) (17)
Ms1＝Ts1·as (19)
Mp1＝Np2ap2 (20)
(2) Crack re-opening load of one-stage stress-cracked post-tensioning crack closing component
The calculation diagram is shown in figure 15.
Calculating the area of the converted section
An2′＝Dcbh-(Dt-Dc)xn2+αEs(As+As′)+αEpAp2 (21)
In the formula, DcThe damage variable of the precast beam top concrete fiber is shown; dtThe variable of concrete compression damage caused by concrete cracking.
Calculating the distance of the mandrel from the bottom surface of the beam
Calculating the converted moment of inertia of the cross section
Calculating the tensile stress increment of the concrete at the bottom edge
When in use
The concrete crack is opened again when the following formula is satisfied
In the formula (I), the compound is shown in the specification,
the concrete strain at the edge of the bottom part under the action of secondary tension force.
(3) Ultimate bending resistance bearing capacity of cross section
The calculation diagram is shown in figure 16.
According to the balance condition of section force ∑ X ═ 0, obtain
fyAs+σp14Ap1+σp24Ap2＝K1K3fcbxn+fyAs′ (26)
Obtaining the bending moment according to the bending moment balance condition sigma M equal to 0
Mu＝M1+M2＝σp24Ap2(h-a21-K2xn)+fy(As-As′)(h0-K2xn)+fyAs′(h0-as′) (27)
Wherein the deformation coordination relationship is
In the formula, delta phi4Is the corner curvature increment of the cross section.
The post-tensioning rib stress can be valued according to the standard
If the normal reinforcement is matched, the common steel bar can yield, so that the stress of the common steel bar can be changed into yield stress fyConsider.
If the normal reinforcement is matched, the common steel bar can yield, so that the stress of the common steel bar can be changed into yield stress fyConsider.
The deformation coordination relation and the stress condition of the prestressed tendon in the above formulas are brought into the section stress balance condition sigma X as 0, and the section stress balance condition sigma X can be calculatedCalculating to obtain delta phi4. Solve to obtain delta phi4And then obtaining the stress-strain conditions of all materials on the cross section, wherein whether the prestressed tendon is yielding or not is determined, and if the stress expression does not accord with the stress expression which is supposed to be substituted, the calculation is substituted again. And finally, according to the bending moment balance condition sigma M being 0, the section bending moment under the action of the ultimate bearing force can be obtained.
Thus, the design calculation work is completed.
The above description is only for the specific embodiments of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can easily conceive of the changes or substitutions within the technical scope of the present invention, and all the changes or substitutions should be covered within the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the appended claims.
Claims (4)
1. The utility model provides a post-tensioned unbonded prestressed concrete composite beam, includes that precast concrete component, superimposed layer (2), top are indulged muscle (1), bottom and are indulged muscle (5) and stirrup (6) the upper portion of the precast concrete component of superimposed beam is provided with superimposed layer (2), muscle (1) is indulged in the top and bottom are indulged muscle (5) and are set up respectively in the top and the bottom of superimposed beam, muscle (1) is located is indulged in the top in superimposed layer (2), stirrup (6) set up in inside and the parcel of superimposed beam muscle (1) is indulged in the top and bottom are indulged muscle (5), its characterized in that: a tie bar (7) is arranged in the middle of the superposed beam, a waist bar (3) is arranged at the lower end of each layer of the tie bar (7), a plurality of post-tensioned unbonded prestressed tendons (4) are arranged at the lower part of the superposed beam, the post-tensioned unbonded prestressed tendons (4) are arranged in a reserved hole channel in the concrete prefabricated part, the post-tensioned unbonded prestressed tendons (4) are arranged in a curve or straight line, penetrate through the laminated layer (2) and extend out of the laminated beam from two ends, the two ends of the post-tensioned unbonded prestressed concrete composite beam are respectively and fixedly provided with an anchorage device (9) and a clamp (8), the composite beam and the post (11) are connected in series into a whole through the post-tensioned unbonded prestressed tendon (4), the design method of the post-tensioned unbonded prestressed concrete composite beam is provided, the construction method is characterized by comprising the following steps according to the construction and use stress conditions of the post-tensioned unbonded prestressed concrete composite beam:
(a) determining the cross-sectional dimensions b, h1，h2
Determining the height h of the post-tensioned unbonded prestressed concrete composite beam before and after the composite1And h2Width b, height-to-span ratio h1L and h2/l，h1Height of the precast beam, h2The height after superposition is determined, i is the span of the beam, and the selected section size needs to meet the corresponding specification requirement;
(b) area A of the pre-estimated post-tensioning unbonded ribp2
According to the bonding design, determining the total area of the prestressed tendons according to the requirements of the normal use limit state and crack control, and calculating the prestressed concrete according to the uncracked state; under the conditions of construction and use and under the action of design load and prestress, the area A of the unbonded rib is estimatedp2；
According to the structure type and the control requirement of the normal section crack, the prestress of the post-tensioned unbonded prestressed tendon is calculated according to the following formula, and the larger value of the result is taken:
Wherein M is1kAnd M1qRespectively calculating bending moment design values of the stress of one stage of the precast beam according to the load standard combination and the quasi-permanent combination; m2kAnd M2qRespectively calculating bending moment design values of the superposed forming rear beam according to load standard combination and quasi-permanent combination; [ sigma ]ctk，lim]And [ sigma ]ctq，lim]The tensile limit values of the concrete under the load standard combination and the load quasi-permanent combination can be taken by reference to the standard; w2Elastic resisting moment of tension edge of member section of the superposed composite beam; a. the2The cross section area of the component of the superposed composite type beam; e.g. of the type02The center of the prestressed tendon is deviated from the superposed composite beamThe distance between the heart and the heart; beta is a beam structure coefficient, for example, for a simply supported structure, beta is 1.0, for a hogging moment section of a continuous structure, beta is 0.9, and for a positive bending moment section of the continuous structure, beta is 1.2;
effective prestressing force N according to prestressing tendonspe2Estimating the area A of the post-tensioned unbonded tendonp2The estimation is performed as follows:
wherein σcon2Controlling the stress for the tensioning of the post-tensioned unbonded prestressed tendon; sigmal，tot2Predicting all prestress losses of the post-tensioned unbonded prestressed tendon;
(c) determining the area A of non-prestressed tendons designed for bondings
From the area A of the tendonp2Degree of prestress λ, minimum reinforcement ratio ρminAnd the construction requirement determines the area A of the non-prestressed tendons；
As≥ρminbh2And is and
wherein f ispyThe design value of the tensile strength of the post-tensioned unbonded prestressed tendon is obtained; h ispThe effective distance from the longitudinal prestressed rib resultant force action point to the pressed edge of the superposed beam; f. ofyThe design value of the tensile strength of the common steel bar is obtained; h iss2The effective distance from the resultant force action point of the longitudinally-tensioned non-prestressed tendons to the pressed edge of the section of the superposed beam;
(d) calculating post-tension unbonded pre-stress loss
Calculating the prestress loss into an instantaneous loss and a long-term loss, wherein the instantaneous loss comprises anchoring loss, friction loss and elastic compression loss, and the long-term loss comprises stress relaxation of prestressed tendons and shrinkage creep of concrete;
(e) checking calculation of reinforcement limit value of post-tensioned unbonded prestressed concrete composite beam
Because the stress of the tensile steel bar of the superposed beam is advanced and the strain of the concrete of the superposed layer is lagged, the ultimate bearing capacity and the stress and the strain of the cracking state of the superposed beam are different from those of a common integrally cast beam, and the limit reinforcement values are also different; therefore, when the checking calculation is carried out, the boundary reinforcement is divided into the boundary reinforcement of 'proper reinforcement' and 'excessive reinforcement' and the boundary reinforcement of 'proper reinforcement' and 'few reinforcement' for calculation respectively;
(f) calculating the primary stress of the prestressed precast beam
(g) Prestress applied to laminated beam by calculating post-tensioning method
Whether the primary stressed beam cracks or not is separately discussed, wherein the primary stressed beam which cracks needs to be checked whether the crack is closed or not;
if a load force M1Less than the crack resistance bearing capacity M of the precast beamcr1I.e. M1＜Mcr1At the moment, the stress level of the section is smaller, the stress condition of the section is considered in an elastic state,
stress variation of concrete at any point
In the formula, An2And In2Respectively calculating the cross-sectional area and the moment of inertia of the converted cross section of the composite beam after deducting the post-tensioned pore channel; e.g. of the type02The eccentricity of the center of the prestressed tendon relative to the superposed beam is obtained; y is the distance from the stress position of the concrete to the centroid of the converted section; n is a radical ofpe2Effective pre-stress of the post-tensioned prestressed tendons;
applying secondary prestress on the superposed beam by a post-tensioning method to ensure that the tensile stress of the concrete of the whole cross section does not exceed the corresponding limit value, checking and calculating the concrete fiber stress of the edge of the superposed layer and the edge of the precast beam to meet the requirement of not being more than tensile strength, namely, the following two formulas:
in the formula (f)tAnd fcRespectively designing values of tensile strength and compressive strength of the concrete;
and
the stress of the concrete at the bottom and the top of the section respectively;
the stress of the concrete at the bottom of the section in a first stress stage; a isp2The distance between the gravity center of the post-tensioned prestressed tendon and the beam bottom is;
if the fracture is stressed once, the stress of the section is calculated as follows:
according to the method, two conditions are divided into two conditions according to whether the concrete in the compression area of the precast beam is decompressed, in order to conveniently calculate whether the primary stress cracking section can close the crack under the action of secondary prestress, a conservative calculation method is uniformly adopted to estimate the two conditions, and the method comprises the following steps:
calculating the area of the converted section
An2＝bh-Dtbxn2+αEs(As+As′)
In the formula, DtThe variable of concrete compression damage caused by concrete cracking; x is the number ofn2The height of the concrete in the tension area of the precast beam in the first stage stress state is determined; alpha is alphaEsThe ratio of the elastic modulus of the steel bar to the concrete; a. thes' is the area of the compressed rebar;
calculating the distance of the mandrel from the bottom surface of the beam
In the formula, asAnd as' distances from the center of gravity of the tensioned and stressed reinforcement bars to the tensioned and stressed edges, respectively;
calculating the converted moment of inertia of the cross section
Calculating the concrete mean stress variation at the bottom edge
When in use
Concrete cracks can be considered to be closed when the following formula is satisfied
In the formula, EcIs the modulus of elasticity of concrete; sigmac0The compressive stress of the concrete when the crack is closed can be 1-2 MPa;
the average strain of the concrete section under the primary acting force;
(h) and calculating the integral stress of the post-tensioned unbonded prestressed concrete composite beam.
2. The post-tensioned unbonded prestressed concrete composite beam of claim 1, characterized in that the stirrups (6) in the range of twice the beam height on both sides of the position where said post-tensioned unbonded prestressed tendons (4) pass through the composite layer need to be doubly densely arranged.
3. The post-tensioned unbonded prestressed concrete composite beam of claim 2, wherein said post-tensioned unbonded prestressed tendons (4) have a clear vertical spacing of the pre-openings of not less than 50mm and not less than 1.25 times the grain size of the coarse aggregate, and a clear spacing of not less than 30mm and not less than half the diameter of the openings from the openings to the edge of the composite beam member.
4. The construction method of the post-tensioned unbonded prestressed concrete composite girder according to claim 1, comprising the steps of:
a. arranging common steel bars and unbonded prestressed tendons in advance before pouring the prefabricated part;
b. pouring, maintaining and forming, transporting, hoisting in place on site, and pouring a superposed layer;
c. stretching the pre-buried unbonded prestressed tendons when the maintenance of the laminated layer reaches the standard and the requirement of stretching prestress is met;
d. the non-adhesive material in the non-adhesive prestressed tendon slowly produces adhesive force along with the time, and finally reaches a completely adhesive state to form the post-tensioned non-adhesive prestressed concrete composite beam.
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