CN109868935B - Post-tensioned bonded prestressed concrete composite beam and design and construction method thereof - Google Patents
Post-tensioned bonded 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 prestressed concrete composite beam and a construction method thereof. Compared with the traditional superposed beam, the post-tensioned adhesive prestress technology is adopted, the characteristics of high prefabricated assembly degree, convenient construction and the like of the lower superposed structure are inherited, and the anti-cracking and anti-bending performance of the component can be improved. Because the post-tensioned prestressing tendons can apply post-tensioned prestressing force after the integral construction and the post-tensioned unbonded prestressing tendons have better corrosion resistance, the post-tensioned unbonded prestressing tendons are particularly suitable for structures with high performance requirements on deformation control, bearing capacity, weather resistance, large span, heavy load and the like, and can embody the superiority of an 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 prestressed concrete composite beam with post-tensioning bonding and a construction method thereof, which is a novel prestressed member adopting bonding prestressed bars. The laminated structure combines two traditional structures of a laminated structure and a bonded prestressed structure, introduces a special innovative design and construction technology of prestress, completely inherits the good construction performance of the laminated structure and the bonded prestressed structure, and can make up for the defects of low bearing capacity of the laminated structure and insufficient mechanical performance of the pure bonded structure.
In order to achieve the purpose, the invention adopts the following scheme:
a post-tensioned bonded prestressed concrete composite beam is provided with a composite layer 2 on the upper part of the composite beam, and a concrete prefabricated part is arranged on the lower part of the composite layer 2; a layer of top longitudinal ribs 1 is arranged at the top of the superposed beam, and a layer of bottom longitudinal ribs 5 is arranged at the bottom of the superposed beam; still have a plurality of stirrups 6, stirrups 6 set up in inside and the parcel of composite beam muscle 1 is indulged at the top and muscle 5 is indulged to the bottom the middle part of composite beam is provided with tie bar 7, is close to the lower extreme of tie bar 7 is provided with kidney muscle 3 the composite beam lower part still is equipped with a plurality of post-tensioned and has bonding prestressing tendons 4, be provided with the reservation pore in the precast concrete component, the post-tensioned has bonding prestressing tendons 4 to set up in the reservation pore, the post-tensioned has bonding prestressing tendons 4's both ends to pass the laminating layer 2 of composite beam stretches out outside the composite beam, its both ends are fixed respectively and are provided with ground tackle 9 and anchor clamps 8, the tip of laminating layer 2 still is equipped with post-cast district 10.
Furthermore, the stirrups 6 which are positioned at two sides of the position where the post-tensioned adhesive prestressed tendon 4 passes through the superposed layer and are within the range of twice the beam height are arranged in a double-dense mode.
Furthermore, 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.
Furthermore, the post-tensioned bonded prestressed tendons 4 are arranged into 2-5 pieces and are arranged between the lower part of the tie bar 7 and the upper part of the bottom longitudinal bar 5.
The invention also provides a design method of the post-tensioned and bonded prestressed concrete composite beam, which comprises the following stages according to the construction and use stress conditions of the post-tensioned and bonded prestressed concrete composite beam:
(a) determining the cross-sectional dimensions b, h1，h2
(b) Estimating the area A of the post-tensioned bonding ribp2
(c) Determining the area A of non-prestressed tendons designed for bondings
(d) Calculating the post-tensioning cohesive pre-stress loss sigmal1And σl2
(e) Checking calculation of reinforcement limit value of post-tensioned bonded 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 prestressed concrete composite beam with the bond after tensioning.
The invention also provides a construction method of the prestressed concrete composite beam with post-tensioning bonding, which comprises the following steps:
a. arranging common steel bars and bonded 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 bonded prestressed tendons when the maintenance of the laminated layer reaches the standard and the requirement of the stretching prestress is met;
d. the binding material in the binding prestressed tendon slowly produces binding force with the time lapse, and finally reaches a complete binding state to form the post-tensioned binding prestressed concrete superposed beam.
Compared with the traditional prestressed composite beam, the prestressed concrete composite beam with the post-tensioning bonding 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 post-tensioned prestressed tendon adopts the form of the bonded prestressed tendon, the tendon can be separated from the corrosive medium to a great extent by virtue of the outer sheath of the tendon and the filled bonding material, and the deformation capability of the sheath and the bonding material is better under the general condition, so that the requirement of no rupture under high strain can be met, and the weather resistance of the component is ensured.
(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 prestressed concrete composite beam post-tensioned with adhesive
FIG. 2 is a front view of a prestressed concrete composite beam with a post-tensioned adhesive bond (without a post-cast zone)
FIG. 3 is a front view of a prestressed concrete composite beam with a post-tensioned adhesive bond (with a post-cast zone)
FIG. 4 is a schematic view of a post-tensioned bonded prestressed concrete composite beam node (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 simplified diagram of calculation of precast beam cracking
FIG. 11 is a schematic diagram of calculation of post-tensioning prestress applied to 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 figure includes: 1-top longitudinal bar, 2-laminated layer, 3-waist bar, 4-post-tensioned binding prestressed bar, 5-bottom longitudinal bar, 6-stirrup, 7-tie bar, 8-clamp, 9-anchor, 10 post-pouring area, 11 column, 12-concrete, 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 prestressed concrete composite beam with adhesive is provided, the composite beam is applied with adhesive prestress by a post-tensioning method, a layer of top longitudinal ribs 1 is arranged at the top of the composite beam, a layer of bottom longitudinal ribs 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 waist rib 3 is arranged at the lower end of each layer of tie bars 7, a plurality of adhesive prestressed ribs 4 are arranged at the lower part of the composite beam, a hoop rib 6 is arranged at the periphery of the composite beam, two ends of the post-tensioned adhesive 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 adhesive prestressed concrete composite beam, and a post-cast area 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 bonded prestressed concrete composite beam, a node diagram of the combination of two composite beams and a column 11 can be seen.
The post-tensioned bonded prestressed concrete superposed beam is characterized by that it adopts post-tensioning method to apply bonded prestress to the superposed beam so as to make the member meet the requirements of bearing capacity and service performance of every stage.
The post-tensioned adhesive prestressed tendons 4 can adopt a linear or curvilinear arrangement mode according to the actual stress condition of the component 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, and the post-tensioned adhesive tendons 4 are allowed to cross the laminated surface and extend into the laminated layer 2.
As shown in fig. 6, which is a schematic view of a post-tensioned and slowly-bonded tendon, a plurality of edge wires 14 are arranged outside a core wire 13, a grouting material 15 is coated outside the edge wires, and a sheath 16 is arranged on the outermost layer.
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 10. 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 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 bonded 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, a prestressed concrete composite beam with adhesive is formed.
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 following explains the calculation method for the expansion design of the post-tensioned prestressed concrete composite beam according to four stages and a limit reinforcing bar value. The calculation flow is shown in fig. 5.
1. Determining the cross-sectional dimensions b, h1，h2
For the prestressed concrete composite beam with the post-tensioned adhesive, 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 pre-estimated precast beam with bonding ribs in post-tensioningp2
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 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 concretep2。
According to the structure type and the control requirement of the normal section crack, the prestress of the post-tensioned bonding prestressed tendon can be calculated according to the following formula, and the larger value of the result is taken.
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 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 beam is the area of the cross section of the component of the superposed beam with the pore channel removed; 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 prestressed tendonsp2Can be estimated as follows
3. 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 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 design value of the tensile strength of the post-tensioned adhesive 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. Post-tensioning with cohesive pre-stress loss sigmal2
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 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 prestressed concrete composite beam with the post-tensioned bond, 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＝Tc2lA+Ts2lB (5)
In the formula, Tc2、Ts2Respectively showing the resultant force of the concrete, the ordinary steel bar and the prestressed bar in the tension area, lA、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 table:
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 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′) (9)
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.
8. Integral stress analysis and checking calculation for post-tensioned bonded 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.
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
Unyielding: sigmap24＝σcon2-σlI2+Ep(Δεpc24+εpc23)(30)
Yield:
if the normal reinforcement is arranged, the common steel bar can yield, so the stress of the common steel bar can be considered as the yield stress fy.
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 equal to 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 (3)
1. A post-tensioned bonded prestressed concrete composite beam is provided with a composite layer (2) on the upper part of the composite beam, and a concrete prefabricated part is arranged on the lower part of the composite layer (2); a layer of top longitudinal ribs (1) is arranged at the top of the superposed beam, and a layer of bottom longitudinal ribs (5) is arranged at the bottom of the superposed beam; still have a plurality of stirrups (6), stirrup (6) set up in inside and the parcel of composite beam muscle (1) is indulged at the top and muscle (5) is indulged to the bottom the middle part of composite beam is provided with drawknot muscle (7), is close to the lower extreme of drawknot muscle (7) is provided with waist muscle (3), its characterized in that: the lower part of the superposed beam is also provided with a plurality of post-tensioned bonded prestressed tendons (4), a reserved hole channel is arranged in the concrete prefabricated part, the post-tensioned bonded prestressed tendons (4) are arranged in the reserved hole channel, two ends of the post-tensioned bonded prestressed tendons (4) penetrate through the superposed layer (2) of the superposed beam and extend out of the superposed beam, two ends of the post-tensioned bonded prestressed tendons (4) are respectively and fixedly provided with an anchorage device (9) and a clamp (8), the end part of the superposed layer (2) is also provided with a post-pouring area (10), and the design method of the post-tensioned bonded prestressed concrete superposed beam is as follows: the construction and the using stress conditions of the prestressed concrete composite beam with the post-tensioned adhesive are divided into the following stages:
(a) determining the cross-sectional dimensions b, h1，h2
Determining the height h of the post-tensioned and bonded 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) estimating the area A of the post-tensioned bonding ribp2
Determining the total area of prestressed reinforcing bars according to the bonding design and the requirement of normal use limit state and crack control, and making prestressed concrete according to the uncracked stateCalculating; under the conditions of construction and use and under the action of design load and prestress, the area A with bonding ribs is estimatedp2；
According to the structure type and the control requirement of the normal section crack, the prestress of the post-tensioned bonding prestressed tendon is calculated according to the following formula, and the larger value of the result is taken,
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; w2Elastic resisting moment of tension edge of member section of the superposed composite beam; a. the2The cross section areas of the components of the precast beam and the superposed composite beam are obtained after the pore channels are deducted; e.g. of the type02The eccentricity of the center of the prestressed tendon relative to the precast beam and the superposed composite 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 prestressed tendonsp2The estimation is performed as follows:
wherein σcon2Controlling the stress for post-tensioning the bonded prestressed tendon; sigmal，tot2To estimate post-tensionAll the prestressing force loss of the bonded prestressed tendons;
(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, lambda is the prestress degree; f. ofpyThe design value of the tensile strength of the post-tensioned adhesive 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 the post-tensioning cohesive pre-stress loss sigmal2
(e) Checking calculation of reinforcement limit value of post-tensioned bonded prestressed concrete composite beam
The boundary reinforcement is divided into boundary reinforcement of 'proper reinforcement' and 'excessive reinforcement' and boundary reinforcement of 'proper reinforcement' and 'few reinforcement' for checking calculation;
the height of the relative compression zone of the reinforcement boundary of the 'adaptive reinforcement' and the 'extra reinforcement' can be divided into two parts to represent:
in the above formula,. DELTA.xnThe height difference between the compression areas of the superposed beams and the precast beams is obtained under the reinforcement boundary state of the 'suitable reinforcement' and the 'extra reinforcement'; Δ xn4The height of the compression zone of the composite beam; h isp1The distance between the center of gravity of the prestressed tendon and the top of the superposed beam is calculated; xib1And xib2Are respectively Δ xnAnd Δ xn4And hp1Ratio according to the deformationThe coordination relationship may be calculated according to the following equation:
in the formula, xn2The height of the concrete in the tension area of the precast beam in the first stage stress state is determined; epsiloncuIs the ultimate compressive strain of the concrete; epsilonpc12The strain of the concrete at the gravity center position of the prestressed tendon; h is1p1The distance from the center of gravity of the prestressed tendon to the top of the precast beam; h is the total height of the composite beam; delta epsilonpc14The strain increment of the concrete at the center of gravity of the prestressed tendon is obtained according to the deformation coordination condition,
εp12is the strain of the tendon;
the height xi of the compression zone of the rib fitting and extra rib boundary can be obtained by combining the above formulasb；
When the boundary reinforcement calculation of the 'suitable reinforcement' and the 'less reinforcement' is carried out, the calculation method of the minimum reinforcement ratio of the composite beam is as follows:
in the formula (f)tThe tensile strength of concrete; f. ofyThe yield strength of common steel bars; h is0Is the effective height of the superposed forming rear beam; h is01Is the effective height of the precast beam;
(f) calculating the primary stress of the prestressed precast beam
(g) Prestress applied to laminated beam by calculating post-tensioning method
The calculation of the post-tensioning method for applying prestress to the laminated beam requires separate discussion on whether the primary stressed beam cracks, wherein the primary stressed beam cracks needs to be checked whether the cracks are closed or not,
if a load force M1Does not cause cracking of the concrete, i.e. M1＜Mcr1，Mcr1The stress level of the cross section is smaller for the anti-cracking strength of the precast beam, the stress condition of the cross section is considered in an elastic state, and the stress variable 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; 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 primary stress cracking is carried out, the two conditions are divided according to whether the concrete in the compression area of the precast beam is decompressed or not, and 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 for estimation, and the method comprises the following steps:
calculating the area of the converted section
An2＝bh-Dtxn2+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 prestressed concrete composite beam with the bond after tensioning.
2. The post-tensioned bonded prestressed concrete composite beam according to claim 1, characterized in that the stirrups (6) 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 doubly densely arranged.
3. A construction method of the post-tensioned bonded prestressed concrete composite girder according to claim 1, comprising the steps of:
a. arranging common steel bars and bonded 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 bonded prestressed tendons when the maintenance of the laminated layer reaches the standard and the requirement of the stretching prestress is met;
d. the binding material in the binding prestressed tendon slowly produces binding force with the time lapse, and finally reaches a complete binding state to form the post-tensioned binding prestressed concrete superposed beam.
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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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