CN109868940B - Post-tensioned bonded co-tensioned prestressed concrete composite beam and design and construction method thereof - Google Patents
Post-tensioned bonded co-tensioned prestressed concrete composite beam and design and construction method thereof Download PDFInfo
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Abstract
The invention relates to a post-tensioned and bonded co-tensioned prestressed concrete composite beam and a design and construction method thereof. Compared with the traditional prestressed composite beam, the post-tensioned prestressed composite beam adopts the post-tensioned bonded prestressed technology, has the characteristics of high prefabricated assembly degree of the lower composite structure, convenience and quickness in construction and the like, has unique advantages, can improve the anti-cracking and anti-bending performance of components, meets the structural requirements in different periods by batch tensioning, can be matched with the design of assembling integral prestressed node connection to enhance the integrity and the anti-seismic performance of the structure, is particularly suitable for the structures with high performance requirements on deformation control, high bearing capacity, high span, heavy load and the like, and can embody the superiority of the assembled structure while meeting the design requirements.
Description
Technical Field
The invention relates to the technical field of civil engineering design, in particular to a split tensioning prestressed concrete superposed beam with post-bonding tensioning and a construction method thereof in a large-span heavy-load structure.
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 bonded prestressed concrete, the bonded prestressed concrete structure is reliable, the bearing capacity is high, but the construction is complex, a pore passage and grouting need 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 grouting do not exist; the bonded prestressed concrete prestressed tendon is not bonded with the surrounding concrete, the prestressed tendon can be freely deformed, and compared with the bonded prestressed concrete, the construction of the bonded prestressed concrete prestressed tendon is simple, a pore channel does not need to be reserved, grouting is not needed, and the friction loss can be reduced. The bonded prestressed structure has been proposed earlier, and has been developed, and although the mechanical property of the bonded prestressed structure is not as excellent, the construction performance is better and the quality is relatively more reliable.
Disclosure of Invention
The invention aims to provide a post-tensioned and bonded co-tensioned prestressed concrete superposed beam and a construction method thereof, which is a novel prestressed member adopting a prestressed rib mixed by bonding and bonding. The laminated structure and the bonded prestressed structure are combined with two traditional structures, namely a laminated structure and a bonded prestressed structure, and a co-tensioned prestressing innovative special design and construction technology are introduced, so that the good construction performance of the laminated structure and the bonded prestressed structure is completely inherited, and meanwhile, the defects of low bearing capacity of the laminated structure and insufficient mechanical performance of the pure bonded structure can be overcome.
In order to achieve the purpose, the invention adopts the following scheme:
a post-tensioned bonded co-tensioned prestressed concrete composite beam comprises concrete prefabricated components, a composite layer 2, top longitudinal reinforcements 1, bottom longitudinal reinforcements 6 and stirrups 7, wherein the composite layer 2 is arranged on the upper portion of the concrete prefabricated components of the composite beam, the top longitudinal reinforcements 1 and the bottom longitudinal reinforcements 6 are respectively arranged on the top and the bottom of the composite beam, the top longitudinal reinforcements 1 are positioned in the composite layer 2, the stirrups 7 are arranged in the composite beam and wrap the top longitudinal reinforcements 1 and the bottom longitudinal reinforcements 6, two layers of tie reinforcements 8 are arranged in the middle of the composite beam, waist reinforcements 3 are arranged at the lower ends of each layer of the tie reinforcements 8, a plurality of pre-tensioned prestressed reinforcements 5 and reserved holes are further arranged in the concrete prefabricated components positioned on the lower portion of the composite beam, a plurality of post-tensioned bonded prestressed reinforcements 4 are further arranged on the lower portion of the composite beam, the post-tensioned adhesive prestressed tendon 4 is arranged in the reserved hole channel; two ends of the post-tensioned adhesive prestressed tendon 4 extend out of the superposed beam, and two ends of the post-tensioned adhesive prestressed tendon are respectively and fixedly provided with an anchorage device 10 and a clamp 9.
Preferably, a post-cast zone 11 is provided at the end of the stack 2.
Preferably, the post-tensioned bonded tendons 4 are arranged in a curved or straight line, able to pass through the superimposed layers.
Preferably, the stirrups 7 in the range of twice the height of the beam on two sides of the position where the post-tensioned bonded 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 with the post-tensioned adhesive 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.
Preferably, the post-tensioned prestressed tendons 4 are formed by arranging a core wire 13 and a plurality of heel side wires 14 outside the core wire 13, coating the side wires 14 with grouting material 15, and then sleeving the outermost layer in a sheath 16.
The invention also provides a design method for the post-tensioned and bonded co-tensioned prestressed concrete composite beam, which comprises the following stages according to the construction and use stress conditions of the post-tensioned and bonded co-tensioned prestressed concrete composite beam:
(a) determining cross-sectional dimensions
(b) Estimating the area of the precast beam with bonding and post-tensioning bonding ribs
(c) Determining the area of non-prestressed tendons designed for bonding
(d) Calculating pre-tensioned and post-tensioned with bond prestress losses
(e) Checking calculation of reinforcement limit value of post-tensioned bonded co-tensioned prestressed concrete composite beam
(f) Pretensioning method for applying prestress to precast beam
(g) Calculating the primary stress of the prestressed precast beam
(h) Prestress applied to laminated beam by calculating post-tensioning method
(i) And calculating the integral stress of the post-tensioned and bonded co-tensioned prestressed concrete composite beam.
The invention also provides a construction method of the post-tensioned bonded co-tensioned prestressed concrete superposed beam, which comprises the following steps:
a. arranging common steel bars, common prestressed tendons and bonded prestressed tendons in advance before pouring the prefabricated part;
b. tensioning common prestressed tendons on the pedestal;
c. pouring, maintaining and forming, transporting, hoisting in place on site, and pouring a superposed layer;
d. stretching the pre-buried bonded prestressed tendons when the curing of the laminated layer reaches the standard and the requirement of stretching secondary prestress is met;
e. after tensioning meets the requirements, grouting the pore passages;
f. and slowly solidifying the grouting material in the pore channel to finally reach a completely bonded state, namely finishing the main construction of the post-tensioned bonded co-tensioned prestressed concrete superposed beam.
Compared with the traditional prestressed composite beam, the post-tensioned bonded co-tensioned 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) Meet the requirements of structures at different periods on components
The sectional dimension of the precast beam is smaller than that of the formed superposed beam, and if the prestressed tendons are configured and prestressed directly according to the design requirements of the final superposed beam, the precast member may be deformed too much and cracked and damaged. If the prestress is applied in multiple times, the prestress precast beam can only meet the load in the construction period, and the residual prestress is applied after being superposed and molded, so that the load requirement in the use stage is met, and the method is particularly suitable for large-span and heavy-load structures.
(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 bonded co-tensioned prestressed concrete composite beam
FIG. 2 is a front view of a post-tensioned prestressed concrete composite beam with adhesive joint (without post-cast zone)
FIG. 3 is a front view of a post-tensioned prestressed concrete composite beam with adhesive joint (with post-cast section)
FIG. 4 is a schematic view of a joint of a post-tensioned prestressed concrete composite beam with adhesive (with post-cast section)
FIG. 5 is a calculation flow chart
FIG. 6 is a schematic view of a post-tensioned bonded tendon
FIG. 7 is a strain analysis diagram of reinforcement at the reinforcement exceeding limit
Figure 8 prestress precast beam stress calculation diagram
FIG. 9 is a simplified calculation diagram of a prestressed precast beam under one stress and concrete in an elastic state
FIG. 10 is a schematic diagram of calculation of cracking of a prestressed precast beam
FIG. 11 is a schematic diagram of calculation of secondary prestress applied to a once-stressed uncracked composite beam
FIG. 12 graph of strain analysis of concrete part at compression zone of precast beam during decompression
FIG. 13 is a graph of the concrete strain analysis without decompression in the compression zone of the precast beam
FIG. 14 is a graph showing the stress analysis of the concrete portion of the compression zone of the precast beam during decompression
FIG. 15 fracture re-opening stress analysis chart of fracture closed section
FIG. 16 stress analysis diagram of laminated beam in extreme bearing capacity state
The reference numbers in the figures are as follows:
1-top longitudinal bar, 2-laminated layer, 3-waist bar, 4-post-tensioned binding prestressed bar, 5-pre-tensioned prestressed bar, 6-bottom longitudinal bar, 7-stirrup, 8-tie bar, 9-clamp, 10-anchor, 11 post-cast region, 12 columns, 13-core wire, 14-side wire, 15-grouting material and 16-sheath.
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 bonded co-tensioned prestressed concrete composite girder is a composite girder applied with bonding and bonding prestress by pre-tensioning and post-tensioning, the top of the composite girder is provided with a layer of top longitudinal reinforcement 1, the bottom of the composite girder is provided with a layer of bottom longitudinal reinforcement 6, the upper part of the composite girder is provided with a composite layer 2, the middle part of the composite girder is provided with two layers of tie reinforcements 8, the lower end of each layer of the tie reinforcements 8 is provided with a waist reinforcement 3, the lower part of the composite girder is provided with a plurality of pre-tensioned prestressed reinforcements 5, the lower part of the composite girder is provided with a plurality of bonding prestressed reinforcements 4 or arranged between the pre-tensioned prestressed reinforcements 5, the periphery of the composite girder is provided with a hoop reinforcement 7, the two ends of the post-tensioned bonding prestressed reinforcements 4 extend out of the composite girder component, and two ends thereof are respectively and fixedly provided with an anchor 10 and a clamp 9, a post-cast zone 11 may be provided at the end of the laminated layer as desired.
As shown in fig. 4, which is a schematic node diagram (provided with a post-cast area) of a post-tensioned bonded prestressed concrete composite beam, a node diagram of the combination of two composite beams and a column 12 can be seen.
The post-tensioned and bonded co-tensioned prestressed concrete superposed beam adopts a pre-tensioning method and a post-tensioning method to apply bonding and bonded prestress to the superposed beam, so that the member meets the requirements of bearing capacity and service performance of each stage.
The pretensioned prestressed tendons 5 and the pretensioned bonded prestressed tendons 4 can be arranged in a straight line or a curve mode according to the actual stress condition of the component and the construction requirement. 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; if the component is simply supported in the construction process, the end part support is changed into fixed or elastic restraint after the node construction, the beam end generates negative bending moment, at the moment, the pre-tensioned bonded prestressed tendons can adopt linear tendon distribution, and the post-tensioned bonded prestressed tendons adopt a curve tendon distribution method according to the stress condition of the component in the use stage; if the components have complex constraint and stress conditions in the construction stage and the use stage, the pre-stressed reinforcing bars can be arranged in a curve mode according to the actual conditions.
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, and the post-tensioned adhesive tendons 4 are allowed to cross the laminated surface and extend into the laminated layer 2.
As shown in figure 6, which is a schematic diagram of the post-tensioned unbonded prestressed tendon, a plurality of heel side wires 14 are arranged outside a core wire 13, a grouting material 15 is coated outside the heel side wires, and then the outermost layer is integrally sleeved in a sheath 16.
In order to facilitate the space arrangement of node assembly, post-tensioning and the like with the bonded prestressed tendons 4, the superposed layers 2 can be arranged with the precast beams in unequal lengths, and the end parts of the superposed layers are provided with post-pouring areas 11. The design can increase the geometric diversity of the member, and facilitates the node design and installation construction.
The post-tensioning adhesive prestressed tendons 4 which are arranged in a curve and penetrate through the superposed layer are used for preventing the concrete penetrating through the superposed layer from being damaged due to complex stress action, and the stirrups penetrating through the left side and the right side of the penetrating point of the superposed layer within the range of one-time beam height 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 bonded co-tensioned prestressed concrete superposed beam comprises the following steps: arranging common steel bars and prestressed tendons in a prearranged manner before the prefabricated part is poured; tensioning common prestressed tendons 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; after tensioning meets the requirements, grouting the pore passages; and (3) slowly solidifying the grouting material in the pore channel to finally reach a completely bonded state, and finishing the main construction of the post-tensioned bonded co-tensioned 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 development design of the post-tensioned 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 theThe consideration of the section size of the post-tensioned bonded co-tensioned prestressed concrete superposed beam 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. Estimating the area A of the precast beam with bonding and post-tensioning bonding ribsp1And Ap2
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 with bonding and bonding ribs 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 concretep1And Ap2。
According to the structure type and the control requirement of the normal section crack, the prestress of the pre-tensioned bonding prestressed tendon and the post-tensioned bonding prestressed tendon can be calculated according to the following formula, and the larger value of the result is taken.
(1) Pretensioned with cohesive pre-stress
(2) Post-tensioned with cohesive pre-stress
Wherein M is1kA bending moment design value is calculated for the stress of the precast beam at one stage according to the load standard combination; m2kAnd M2qRespectively of superposed typeCalculating a bending moment design value according to the load standard combination and the 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; w1And W2Elastic resisting moments of tension edges of the sections of the components of the precast beam and the superposed composite beam respectively; a. the01And A2Respectively the section areas of the components of the precast beam and the superposed composite beam after the pore channel is deducted; e.g. of the type01And e02The eccentricity of the center of the prestressed tendon relative to the precast beam and the superposed composite beam is respectively; 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 tendonspe1And Npe2Estimating the area A of the pre-tensioned bonded and post-tensioned bonded tendonsp1And Ap2Can be estimated as follows
3. determining the area A of non-prestressed tendons designed for bondings
From the area A of the tendonp1And Ap2Degree of prestress λ, minimum reinforcement ratio ρminAnd the construction requirement determines the area A of the non-prestressed tendons1.
The reinforcement ratio of the non-prestressed tendons in the tension area of the bonded prestressed concrete flexural member is not less than the specification of table 1 and the requirement of the prestress degree lambda, wherein the prestress degree lambda is determined according to the earthquake resistance grade of the member, and the configuration of the non-prestressed tendons meets the construction requirement.
TABLE 1 minimum reinforcement ratio of non-prestressed reinforcement with bonded 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, lambda is the prestress degree; f. ofpyThe tensile strength of the pre-tensioned prestressed tendon is larger than that of the post-tensioned prestressed tendon; h ispThe effective distance from the reasonable action point of the longitudinal prestressed tendon to the pressed edge of the superposed composite 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 composite beam.
4. Pretensioned with bond and post-tensioned with bond prestress loss sigmal1And σl2
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 bonded co-tensioned 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, xip12The ratio of the height of the compression area to the distance from the center of gravity of the pretensioned rib to the top of the precast beam under the action of one stress, namely
Δεpc14According to the deformation coordination condition, the method comprises the following steps of,
the proper rib and the extra rib boundary can be obtained by combining the above formulasHeight xi of compression limiting zoneb。
(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. Analysis and checking calculation of prestress applied to precast beam by pre-tensioning method
The calculation diagram is shown in figure 8.
Stress of concrete at any point
In the formula, A01The area of the cross section of the converted cross section of the precast beam after deducting the area of the bonded prestressed tendon; i is01The calculated section inertia moment of the precast beam after deducting the area of the bonded prestressed tendon is obtained; e.g. of the type01The distance from the center of the acting force of the pretensioned rib to the centroid of the converted section; y is1The distance from the stress position of the concrete to the centroid of the converted section is calculated.
Checking concrete stress at the edge of compression zone and tension zone of cross section
Pressing:
in tension:
and calculating the stress of the prestressed tendon after the pretensioned prestressed tendon is released into
σp11＝σcon1-σlI1-αEpσpc1 (5)
In the formula, alphaEpThe ratio of the elastic modulus of the prestressed tendons to the elastic modulus of the precast beam concrete; sigmapc1Concrete normal stress acting on the combined force of prestressed tendons after the loss of the first batch of prestressed reinforcements occursForce.
Stress of ordinary steel bar
σs1＝αEsσsc1 (6)
In the formula, alphaEsThe ratio of the elastic modulus of the common steel bar to the elastic modulus of the precast beam concrete; sigmasc1The normal stress of the concrete on which the prestress rib acts after the I-th batch of prestress loss occurs.
7. 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
Calculating the stress of the concrete at the bottom edge of the section
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 elastoplasticity state or the cracking state when the sigma is calculatedc2＝ftWhen the concrete section is in an elastic state, the concrete section can bear the maximum external bending moment
(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.
1) Calculation method for standard adoption
Mcr＝(σpc0II+γft)W0 (10)
In the formula, σpc0IIAfter all prestress loss is deducted, the prestress stress generated by the prestressed tendon at the anti-cracking checking edge is calculated; gamma is the influence coefficient of concrete plasticity; gamma raymThe cross section resistance plasticity influence coefficient basic value of the concrete member.
2) Calculation method for theoretical calculation of prestressed concrete section cracking bending moment
Compared with the calculation method adopted by the standard, the invention needs to accurately calculate the cracking of the post-tensioned bonded co-tensioned prestressed concrete composite beam, so that the theoretical calculation method is recommended to be adopted to estimate 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+Mp2＝Tc2lA+Ts2lB+Tp2Ap1lc (13)
In the formula, Tc2、Ts2And Tp2Respectively showing the resultant force of the concrete, the ordinary steel bar and the prestressed bar in the tension area, lA、lBAnd lCRespectively showing the distance from the resultant action point of the concrete in the tension zone, the common steel bar and the prestressed tendon to the concrete in the compression zone, 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 table:
| 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.
8. 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 the primary loading force does not cause concrete cracking, i.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 distance from the acting force center of the post-tensioned rib to the centroid of the converted section; and y is the distance from the stress position of the concrete to the centroid of the converted section.
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:
(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 adopted to estimate the two conditions, and the method comprises the following steps:
calculating the area of the converted section
An2＝bh-Dtxn2+αEs(As+As′)+αEpAp1 (18)
In the formula, 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 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 (I), the compound is shown in the specification,
is the average strain of a concrete section under a primary force.
9. Analyzing and checking the whole stress of the post-tensioned bonded co-tensioned prestressed concrete composite beam (1) to calculate the cracking load of the stressed uncracked member at the stage
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+Mp1+Mp2 (23)
The respective moments of the above formula are
Ms2＝-Cs2·(h-as′) (26)
Ms1＝Ts1·as (28)
Mp1＝Np1ap1 (29)
Mp1＝Np2ap2 (30)
(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′)+αEp(Ap1+Ap2) (31)
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,
in the second time of tensioningThe concrete strains at the bottom edge of the force bed.
(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′ (36)
Obtaining the bending moment according to the bending moment balance condition sigma M equal to 0
Mu＝M1+M2＝σp14Ap1(h-ap1-K2xn)+σp24Ap2(h-a21-K2xn)+fy(As-As′)(h0-K2xn)+fyAs′(h0-as′) (37)
Wherein the deformation coordination relationship is
In the formula, delta phi4Is the corner curvature increment of the cross section.
According to the deformation coordination relation, the stress of the prestressed tendon can be obtained, and whether the prestressed tendon is yielding or not is considered
a. Pre-tensioned tendon stress
Unyielding: sigmap14＝σp12+EpΔεpc14 (40)
Yield:
wherein k is the slope of the hardened section of the tendon，k＝(fpu-fpy)/(εpu-εpy)
b. Stress of post-tensioned rib
Unyielding: sigmap24＝σcon2-σlI2+Ep(Δεpc24+εpc23) (42)
Yield:
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 delta phi can be obtained through calculation4. 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 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 (3)
1. The utility model provides a post-tensioned has prestressing concrete composite beam that co-stretches that bonds, includes that precast concrete component, superimposed layer (2), top indulge muscle (1), bottom indulge muscle (6) and stirrup (7) the upper portion of precast concrete component of superimposed beam is provided with superimposed layer (2), muscle (1) are indulged in the top and bottom set up respectively in the top and the bottom of superimposed beam to muscle (1) and bottom, muscle (1) are located in superimposed layer (2) are indulged in the top, stirrup (7) set up in inside and parcel of superimposed beam muscle (1) are indulged in the top and bottom indulge muscle (6), its characterized in that: the middle part of the superposed beam is provided with two layers of tie bars (8), the lower end of each layer of the tie bars (8) is provided with a waist bar (3), a plurality of pre-tensioned prestressed bars (5) and reserved channels are also arranged in a concrete prefabricated part positioned at the lower part of the superposed beam, a plurality of post-tensioned adhesive prestressed bars (4) are also arranged at the lower part of the superposed beam, and the post-tensioned adhesive prestressed bars (4) are arranged in the reserved channels; the post-tensioned bonded prestressed concrete composite beam is characterized in that two ends of the post-tensioned bonded prestressed tendon (4) extend out of the composite beam, two ends of the post-tensioned bonded prestressed concrete composite beam are respectively and fixedly provided with an anchorage device (10) and a clamp (9), and the design method of the post-tensioned bonded co-tensioned prestressed concrete composite beam comprises the following steps: the construction and the use stress conditions of the post-tensioned and bonded co-tensioned prestressed concrete composite beam are divided into the following stages:
(a) determining the cross-sectional dimensions b, h1，h2
For the post-tensioned bonded co-tensioned prestressed concrete superposed beam, the height h of the post-tensioned bonded co-tensioned prestressed concrete superposed beam before and after superposition is determined1And 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) estimating the area A of the precast beam with bonding and post-tensioning bonding ribsp1And Ap2
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 with bonding and bonding ribs is estimatedp1And Ap2；
According to the structure type and the control requirement of the normal section crack, the prestress of the pre-tensioned adhesive prestressed tendon and the post-tensioned adhesive prestressed tendon is calculated according to the following formula, and the larger value of the result is taken
Pretensioned with cohesive pre-stress
Post-tensioned with cohesive pre-stress
Or
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]Respectively taking the tensile limit reference specifications of the concrete under the load standard combination and the load quasi-permanent combination; w1And W2Elastic resisting moments of tension edges of the sections of the components of the precast beam and the superposed composite beam respectively; a. the01And A2Respectively the section areas of the components of the precast beam and the superposed composite beam after the pore channel is deducted; e.g. of the type01And e02The eccentricity of the center of the prestressed tendon relative to the precast beam and the superposed composite beam is respectively; 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 tendonspe1And Npe2Estimating the area A of the pre-tensioned bonded and post-tensioned bonded tendonsp1And Ap2The estimation is performed as follows:
wherein σcon1And σcon2Tension control stress for pretensioned bonded and post-tensioned bonded tendons；σl，tot1And σl，tot2Predicting all prestress losses of pre-tensioned prestressed tendons with bonding and post-tensioned prestressed tendons with bonding;
(c) determining the area A of non-prestressed tendons designed for bondings
From the area A of the tendonp1And Ap2Degree of prestress λ, minimum reinforcement ratio ρminAnd the construction requirement determines the area A of the non-prestressed tendons；
As≥ρminbh2And is and
wherein, lambda is the prestress degree; f. ofpyThe tensile strength of the pre-tensioned prestressed tendon is larger than that of the post-tensioned prestressed tendon; 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 pre-tensioned and post-tensioned with bond prestress losses sigmal1And σl2
(e) Checking calculation of reinforcement limit value of post-tensioned bonded co-tensioned prestressed concrete composite beam
(f) Pretensioning method for applying prestress to precast beam
Stress of concrete at any point
In the formula, A01The area of the cross section of the converted cross section of the precast beam after deducting the area of the bonded prestressed tendon; i is01The calculated section inertia moment of the precast beam after deducting the area of the bonded prestressed tendon is obtained; e.g. of the type01The distance from the center of the acting force of the pretensioned rib to the centroid of the converted section; y is1The distance from the stress position of the concrete to the centroid of the converted section is calculated;
wherein the concrete stress at the edge of the tension area of the section is calculated by checking:
in the formula (I), the compound is shown in the specification,
compressive stress of concrete at the bottom of the precast beam, fcThe compressive strength of concrete is shown;
and calculating the stress sigma of the prestressed tendon after the pretensioned prestressed tendon is releasedp11Comprises the following steps:
σp11＝σcon1-σlI1-αEpσpc1
in the formula, alphaEpThe ratio of the elastic modulus of the prestressed tendons to the elastic modulus of the precast beam concrete; sigmalI1The loss of the pretensioned prestressed tendons before the pretensioned prestressed tendons are relaxed; sigmapc1After the I-th batch of prestress loss occurs, the normal stress of the concrete with the combined action of the prestress ribs;
stress sigma of ordinary steel bars1＝αEsσsc1
In the formula, alphaEsThe ratio of the elastic modulus of the common steel bar to the elastic modulus of the precast beam concrete; sigmasc1The normal stress of the concrete acting on the combination of the prestressed tendons after the I-th batch of prestressed losses occurs;
(g) calculating the primary stress of the prestressed precast beam
(h) Prestress applied to laminated beam by calculating post-tensioning method
(i) And calculating the integral stress of the post-tensioned and bonded co-tensioned prestressed concrete composite beam.
2. The post-tensioned bonded co-tensioned prestressed concrete composite beam as claimed in claim 1, wherein the stirrups (7) within a range of twice the beam height at both sides of the position where said post-tensioned bonded prestressed tendons (4) pass through the composite layer are required to be doubly densely arranged.
3. A construction method of the post-tensioned bonded co-tensioned prestressed concrete composite girder as recited in claim 1, comprising the steps of:
a. arranging common steel bars, common prestressed tendons and bonded prestressed tendons in advance before pouring the prefabricated part;
b. tensioning common prestressed tendons on the pedestal;
c. pouring, maintaining and forming, transporting, hoisting in place on site, and pouring a superposed layer;
d. stretching the pre-buried bonded prestressed tendons when the curing of the laminated layer reaches the standard and the requirement of stretching secondary prestress is met;
e. after tensioning meets the requirements, grouting the pore passages;
f. the grouting material in the pore canal is slowly solidified, and finally, a completely bonded state is achieved.
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| CN102852276A (en) * | 2012-08-15 | 2013-01-02 | 杨众 | Large-tonnage prestressed superposed crane beam and construction method |
| CN105735469A (en) * | 2016-02-23 | 2016-07-06 | 同济大学 | Partially-bonded precast prestressed concrete frame structure |
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| CN102852276A (en) * | 2012-08-15 | 2013-01-02 | 杨众 | Large-tonnage prestressed superposed crane beam and construction method |
| CN105735469A (en) * | 2016-02-23 | 2016-07-06 | 同济大学 | Partially-bonded precast prestressed concrete frame structure |
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