CN119004597A - Full-process analysis method for bending capacity of transverse joint of prefabricated comprehensive pipe rack - Google Patents
Full-process analysis method for bending capacity of transverse joint of prefabricated comprehensive pipe rack Download PDFInfo
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Abstract
The invention provides a whole process analysis method for bending capacity of a transverse joint of a prefabricated comprehensive pipe rack, which comprises the following steps: acquiring basic data; respectively carrying out stress analysis on a decompression stage, an initial opening stage and a full opening stage of the transverse joint of the prefabricated comprehensive pipe rack based on basic data to obtain a stress analysis result; determining condition information of a damage stage of the transverse joint of the prefabricated comprehensive pipe rack based on a stress analysis result; and drawing a result curve based on the stress analysis result, and assisting a designer in joint design. The invention avoids testing pipe gallery joints of each type and size in the design stage to determine joint calculation parameters, saves precious time and resources, improves the design work efficiency, generates obvious economic benefit and is suitable for popularization and use.
Description
Technical Field
The invention relates to the technical field of application of prefabricated underground comprehensive pipe racks, in particular to a full-process analysis method for bending capacity of transverse joints of a prefabricated comprehensive pipe rack.
Background
As a modern and industrialized city construction mode, the prefabricated comprehensive pipe rack has remarkable advantages and wide application prospect in the aspects of construction efficiency, engineering quality, low environmental impact, cost saving, promotion of industrialized development and the like. The upper and lower block groove type prefabricated assembled pipe gallery has wide application in the multi-cabin large-section comprehensive pipe gallery due to the advantages of the upper and lower block groove type prefabricated assembled pipe gallery in the aspect of reducing the size and the weight of components. The transverse joint is a key part of the upper and lower block groove type prefabricated assembled pipe gallery, and the performance of the transverse joint directly influences the bearing capacity and the deformation capacity of the whole pipe gallery.
The bending capability of the transverse joint is influenced by a plurality of factors such as joint structure, assembly mode, prestress, limit value of joint opening amount, water-stop rubber deformation performance and the like, and the technical specification of urban comprehensive pipe gallery engineering GB50838-2015 considers that the bending performance of the transverse joint can be truly reflected by determining the rotation rigidity of the transverse joint through experiments. However, in actual engineering design, the rotational stiffness of the joint also changes due to the difference in cross-sectional dimensions of the pipe rack, the earth covering conditions, the joint structure, the prestress and the like, and the problem that the actual conditions are restricted exists in the design after each joint is subjected to a model test or a full-scale test.
At present, students at home and abroad develop certain theoretical research and engineering test work aiming at the stress performance of the prefabricated assembled utility tunnel joint. Chen Zhijiang and the like establish a prefabricated prestressed comprehensive pipe gallery joint design calculation method considering the joint splice deformation form, the prestress rib elongation and the influence of the elastic modulus of a water-swelling rubber strip based on the joint internal force balance and deformation coordination conditions by taking the prefabricated prestressed comprehensive pipe gallery engineering of the Shanghai world Expo park in 2010 as a background, but the formula is complex and the equation needs to be solved in a combined way. Wu Jianqiu et al analyzed the bending stiffness of pipe lane joints in different assembly modes by using a stiffness analysis method and finite element numerical simulation. Wang Pengyu and the like, according to internal force balance and deformation coordination conditions, a transverse joint of a high-strength bolt is arranged on the inner side, a mechanical model representing the joint section from stress to damage and a corresponding theoretical analysis expression are established, and a two-stage bending stiffness value method of the pipe gallery transverse joint is provided. Chen Haiyong, and the like, deducing a theoretical calculation formula of the nonlinear rotation rigidity of the joint of the block type prefabricated comprehensive pipe rack joint connected by bolts in 4 different stress stages. Tan Lin and the like carry out numerical analysis on the stress of the transverse joint of the pipe gallery of the upper and lower segmented sections, an equivalent model of the transverse joint is established, bending stiffness and shear stiffness parameters of the joint are obtained, and a pipe gallery beam-spring simplified model considering the transverse joint is established by means of spring unit simulation. And the peri-static and the like are used for obtaining the conclusion that the deformation resistance of the joint can be effectively enhanced and the pressure-eliminating bending moment of the joint can be improved by improving the prestress of the joint through bending test research and finite element nonlinear numerical analysis of the prefabricated assembled pipe gallery socket joint, but the bending bearing capacity of the joint is kept unchanged.
In summary, the research results on the bending capability of the prefabricated pipe rack transverse joint still remain in the theoretical research stage, and an efficient method for analyzing the bending capability of the prefabricated pipe rack transverse joint in the whole process is not yet available, so as to assist a designer in joint design.
Disclosure of Invention
The invention aims to determine the rotational rigidity of the prefabricated pipe gallery joint through a calculation means under the condition that the pipe gallery joint test is not carried out in the stage of designing the prefabricated pipe gallery, and provide a basis for the calculation of the internal force of the pipe gallery and the calculation of the joint deformation. The whole process of bending capacity of the pipe gallery transverse joint is described by a material mechanics method of stress balance and deformation coordination of the pipe gallery transverse joint aiming at the upper and lower segmented groove type prefabricated assembled pipe gallery transverse joint, and a mathematical calculation formula of a full-stage load-internal force-deformation process of decompression, initial opening, complete opening and damage of the joint is established, so that a bending moment-opening amount curve, a bending moment-corner curve, a rotation stiffness-opening amount curve, a rotation stiffness-corner curve and the like of the joint can be directly calculated in a design stage, and the design problem of the prefabricated pipe gallery transverse joint is solved.
The embodiment of the invention provides a whole process analysis method for the bending capacity of a transverse joint of a prefabricated comprehensive pipe rack, which comprises the following steps:
Acquiring basic data;
Respectively carrying out stress analysis on a decompression stage, an initial opening stage and a full opening stage of the transverse joint of the prefabricated comprehensive pipe rack based on basic data to obtain a stress analysis result;
determining condition information of a damage stage of the transverse joint of the prefabricated comprehensive pipe rack based on a stress analysis result;
And drawing a result curve based on the stress analysis result, and assisting a designer in joint design.
Optionally, the base data includes at least: the cross section size of the transverse joint of the prefabricated pipe gallery, concrete material parameters, prestressed rib area, tensioning control stress coefficient and prestress loss.
Optionally, the step of performing stress analysis on the decompression phase of the prefabricated utility tunnel lateral joint based on the base data includes:
based on basic data, calculating effective compressive stress in a decompression stage of the transverse joint of the prefabricated comprehensive pipe rack, critical bending moment of the full-section compression state and maximum compressive stress of the edge of the concrete in the corresponding joint compression zone by the following formula:
σc1＝2σce
Wherein, sigma ce: effective compressive stress of the joint concrete when uniformly pressed; n k0: the axial force standard value of the joint; sigma pe: the initial effective stress of the prestressed tendons; a p: the area of the prestressed tendons; b: the longitudinal length of the joint; h: the height of the joint cross section; sigma c1: maximum compressive stress of the concrete edge of the joint compression zone corresponding to M k1;
M k1: critical bending moment in full section compression.
Optionally, the step of performing a stress analysis on the initial opening phase of the prefabricated utility tunnel lateral joint based on the base data includes:
based on basic data, calculating the stress distribution of joint concrete, the effective total stress of the prestressed tendons, the external bending moment, the joint expansion amount, the joint rotation angle and the joint rotation rigidity in the initial expansion stage of the transverse joint of the prefabricated comprehensive pipe gallery by the following formula:
Wherein, sigma c: the maximum compressive stress of the concrete edge of the joint compression area at the stage; n k0: the axial force standard value of the joint; sigma pe: the initial effective stress of the prestressed tendons; alpha E: the ratio of the elastic modulus of the prestressed tendon to the elastic modulus of the concrete; a p: the area of the prestressed tendons; b: the longitudinal length of the joint; h: the height of the joint cross section; y: length of the zero stress region of the joint; sigma p: the effective total stress of the prestressed tendons; sigma ce: effective compressive stress of the joint concrete when uniformly pressed; m k: an external bending moment; Δ y: the opening amount of the outer edge of the joint; θ y: a joint moving corner; η: the height coefficient is influenced by the compression deformation of the concrete in the pressed area, and the value range is 0-1.0; h 0: the total calculated height of the upper and lower joint pipe racks; e c: modulus of elasticity of the concrete; k Ry: joint rotational stiffness.
Optionally, the step of performing a stress analysis of the fully open phase of the prefabricated utility tunnel lateral joint based on the base data includes:
based on basic data, calculating the stress distribution of joint concrete, the effective total stress of the prestressed tendons, the external bending moment, the joint expansion amount, the joint rotation angle and the joint rotation rigidity in the complete expansion stage of the transverse joint of the prefabricated comprehensive pipe gallery by the following formula:
Wherein, sigma c: the maximum compressive stress of the concrete edge of the joint compression area at the stage; n k0: the axial force standard value of the joint; sigma pe: the initial effective stress of the prestressed tendons; alpha E: the ratio of the elastic modulus of the prestressed tendon to the elastic modulus of the concrete; a p: the area of the prestressed tendons; b: the longitudinal length of the joint; h: the height of the joint cross section; y: length of the zero stress region of the joint; sigma p: the effective total stress of the prestressed tendons; sigma ce: effective compressive stress of the joint concrete when uniformly pressed; m k: an external bending moment; Δ y: the opening amount of the outer edge of the joint; θ y: the joint rotation angle; η: the height coefficient is influenced by the compression deformation of the concrete in the pressed area, and the value range is 0-1.0; h 0: the total calculated height of the upper and lower joint pipe racks; e c: modulus of elasticity of the concrete; k Ry: joint rotational stiffness.
Optionally, the step of determining the condition information of the failure stage of the prefabricated utility tunnel lateral joint based on the stress analysis result includes:
When the concrete compressive stress of the joint compressive edge in the stress analysis result exceeds a concrete compressive strength design value or the stress of the prestressed tendons in the stress analysis result exceeds a strength design value, judging that the transverse joint of the prefabricated comprehensive pipe gallery is damaged, and taking the corresponding bending moment as a damage bending moment value.
Optionally, the achievement profile includes at least: bending moment-opening amount curve, bending moment-rotation angle curve, rotation stiffness-opening amount curve, and rotation stiffness-rotation angle curve.
Optionally, the step of assisting the designer in designing the joint includes:
And outputting and displaying the stress analysis result and the result curve to a designer.
The invention has the following beneficial effects:
the bending moment-opening amount curve, bending moment-corner curve, rotation rigidity-opening amount curve and rotation rigidity-corner curve of the joint can be calculated by using the calculation method for the pipe gallery transverse joints with different sizes and prestress, the whole process of load-internal force-deformation of the prefabricated pipe gallery transverse joint under the action of external bending moment load is comprehensively reflected, and basis is provided for calculation of internal force of the pipe gallery and calculation of joint deformation. In the design stage, the pipe gallery joint of each type and size is prevented from being tested to determine joint calculation parameters, precious time and resources are saved, the design work efficiency is improved, obvious economic benefits are generated, and the method is suitable for popularization and use.
Additional features and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. The objectives and other advantages of the invention will be realized and attained by the structure particularly pointed out in the written description and claims thereof as well as the appended drawings.
The technical scheme of the invention is further described in detail through the drawings and the embodiments.
Drawings
The accompanying drawings are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate the invention and together with the embodiments of the invention, serve to explain the invention. In the drawings:
FIG. 1 is a schematic flow chart of the present invention;
FIG. 2 is a three-dimensional schematic view of a prefabricated utility tunnel lateral joint of the present invention;
FIG. 3 is a schematic illustration of a prefabricated utility tunnel lateral joint bending moment-splay amount curve;
FIG. 4 is a schematic illustration of a prefabricated utility tunnel lateral joint bending moment-angle curve;
FIG. 5 is a graphical representation of the rotational stiffness versus amount of expansion of a prefabricated utility tunnel lateral joint;
FIG. 6 is a schematic view of a prefabricated utility tunnel lateral joint rotational stiffness versus rotational angle curve.
Detailed Description
The preferred embodiments of the present invention will be described below with reference to the accompanying drawings, it being understood that the preferred embodiments described herein are for illustration and explanation of the present invention only, and are not intended to limit the present invention.
The embodiment of the invention provides a whole process analysis method for bending capacity of a transverse joint of a prefabricated comprehensive pipe rack, which is shown in fig. 1 and comprises the following steps:
Acquiring basic data;
Respectively carrying out stress analysis on a decompression stage, an initial opening stage and a full opening stage of the transverse joint of the prefabricated comprehensive pipe rack based on basic data to obtain a stress analysis result;
determining condition information of a damage stage of the transverse joint of the prefabricated comprehensive pipe rack based on a stress analysis result;
And drawing a result curve based on the stress analysis result, and assisting a designer in joint design.
The basic data at least comprises: the cross section size of the transverse joint of the prefabricated pipe gallery, concrete material parameters, prestressed rib area, tensioning control stress coefficient and prestress loss.
Based on basic data, the step of carrying out stress analysis on the decompression stage of the transverse joint of the prefabricated comprehensive pipe rack comprises the following steps:
based on basic data, calculating effective compressive stress in a decompression stage of the transverse joint of the prefabricated comprehensive pipe rack, critical bending moment of the full-section compression state and maximum compressive stress of the edge of the concrete in the corresponding joint compression zone by the following formula:
σc1＝2σce
Wherein, sigma ce: effective compressive stress of the joint concrete when uniformly pressed; n k0: the axial force standard value of the joint; sigma pe: the initial effective stress of the prestressed tendons; a p: the area of the prestressed tendons; b: the longitudinal length of the joint; h: the height of the joint cross section; sigma c1: maximum compressive stress of the concrete edge of the joint compression zone corresponding to M k1;
M k1: critical bending moment in full section compression.
Based on basic data, the step of carrying out stress analysis on the initial opening stage of the transverse joint of the prefabricated comprehensive pipe rack comprises the following steps:
based on basic data, calculating the stress distribution of joint concrete, the effective total stress of the prestressed tendons, the external bending moment, the joint expansion amount, the joint rotation angle and the joint rotation rigidity in the initial expansion stage of the transverse joint of the prefabricated comprehensive pipe gallery by the following formula:
Wherein, sigma c: the maximum compressive stress of the concrete edge of the joint compression area at the stage; n k0: the axial force standard value of the joint; sigma pe: the initial effective stress of the prestressed tendons; alpha E: the ratio of the elastic modulus of the prestressed tendon to the elastic modulus of the concrete; a p: the area of the prestressed tendons; b: the longitudinal length of the joint; h: the height of the joint cross section; y: length of the zero stress region of the joint; sigma p: the effective total stress of the prestressed tendons; sigma ce: effective compressive stress of the joint concrete when uniformly pressed; m k: an external bending moment; Δ y: the opening amount of the outer edge of the joint; θ y: a joint moving corner; η: the height coefficient is influenced by the compression deformation of the concrete in the pressed area, and the value range is 0-1.0; h 0: the total calculated height of the upper and lower joint pipe racks; e c: modulus of elasticity of the concrete; k Ry: joint rotational stiffness.
Based on basic data, the step of carrying out stress analysis on the fully opened stage of the transverse joint of the prefabricated comprehensive pipe rack comprises the following steps:
based on basic data, calculating the stress distribution of joint concrete, the effective total stress of the prestressed tendons, the external bending moment, the joint expansion amount, the joint rotation angle and the joint rotation rigidity in the complete expansion stage of the transverse joint of the prefabricated comprehensive pipe gallery by the following formula:
Wherein, sigma c: the maximum compressive stress of the concrete edge of the joint compression area at the stage; n k0: the axial force standard value of the joint; sigma pe: the initial effective stress of the prestressed tendons; alpha E: the ratio of the elastic modulus of the prestressed tendon to the elastic modulus of the concrete; a p: the area of the prestressed tendons; b: the longitudinal length of the joint; h: the height of the joint cross section; y: length of the zero stress region of the joint; sigma p: the effective total stress of the prestressed tendons; sigma ce: effective compressive stress of the joint concrete when uniformly pressed; m k: an external bending moment; Δ y: the opening amount of the outer edge of the joint; θ y: the joint rotation angle; η: the height coefficient is influenced by the compression deformation of the concrete in the pressed area, and the value range is 0-1.0; h 0: the total calculated height of the upper and lower joint pipe racks; e c: modulus of elasticity of the concrete; k Ry: joint rotational stiffness.
Based on the stress analysis result, the step of determining the condition information of the damage stage of the transverse joint of the prefabricated comprehensive pipe rack comprises the following steps:
When the concrete compressive stress of the joint compressive edge in the stress analysis result exceeds a concrete compressive strength design value or the stress of the prestressed tendons in the stress analysis result exceeds a strength design value, judging that the transverse joint of the prefabricated comprehensive pipe gallery is damaged, and taking the corresponding bending moment as a damage bending moment value.
The achievement curve at least comprises: bending moment-opening amount curve, bending moment-rotation angle curve, rotation stiffness-opening amount curve, and rotation stiffness-rotation angle curve.
The steps of assisting the designer in designing the joint include:
And outputting and displaying the stress analysis result and the result curve to a designer.
Example 1
Referring to fig. 1, a calculation method for whole process analysis of bending capability of a transverse joint of a prefabricated comprehensive pipe rack includes the following steps:
step A, basic data and parameters take values, wherein the basic data and parameters comprise: the cross section size of the transverse joint of the prefabricated pipe gallery, concrete material parameters, prestressed rib area, tension control stress coefficient, prestress loss and the like;
And B, calculating stress of the transverse joint of the prefabricated pipe gallery in a decompression stage. This stage is characterized in that as the external bending moment load to which the joint is subjected increases gradually from 0, the joint enters an eccentric compression full-section compression state from a uniform compression full-section compression state, and no zero stress region is present in the joint. And C, substituting the parameters determined in the step A into a joint stress calculation mathematical formula in the decompression stage, and calculating the effective compressive stress (also called effective interface stress) of the joint concrete when the joint is uniformly compressed, the critical bending moment in the full-section compression state and the maximum compressive stress of the edge of the concrete in the corresponding joint compression area. At this stage the joint opening angle is zero.
And C, calculating the stress of the transverse joint of the prefabricated pipe gallery in the initial opening stage. This stage is characterized by the fact that as the external bending moment continues to increase, the joint develops a zero stress zone and produces an amount of splay, but the length of the zero stress zone does not span the location of the tendon. According to the mathematical formula of the step, the stress distribution of the joint concrete, the effective total stress of the prestressed tendons, the external bending moment, the opening amount of the joint, the joint rotation angle and the joint rotation rigidity of the joint at the stage are calculated.
And D, calculating the stress of the transverse joint of the prefabricated pipe gallery in the fully-opened stage. This stage is characterized by the fact that as the external bending moment continues to increase, the length of the zero stress zone of the joint spans the tendon location. According to the mathematical formula of the step, the stress distribution of the joint concrete, the effective total stress of the prestressed tendons, the external bending moment, the opening amount of the joint, the joint rotation angle and the joint rotation rigidity of the joint at the stage are calculated.
And E, judging the damage stage of the transverse joint of the prefabricated pipe gallery. The stage is characterized in that along with the continuous increase of the external bending moment, the concrete compressive stress of the pressed edge of the joint calculated according to the step C or the step D exceeds the designed compressive strength value of the concrete or the stress of the prestressed tendons exceeds the designed strength value of the prestressed tendons, and the joint is judged to be damaged at the moment, and the corresponding bending moment is the damage bending moment value.
Step F, completing the calculation of the steps through a computer program, and synchronously drawing a result curve: bending moment-opening amount curve, bending moment-rotation angle curve, rotation stiffness-opening amount curve, rotation stiffness-rotation angle curve, and the like.
In the embodiment of the present invention, in the step B, the effective compressive stress of the joint concrete when being uniformly compressed, the critical bending moment in the full-section compression state, and the maximum compressive stress of the edge of the concrete in the corresponding joint compression zone may be calculated according to the formula:
σc1＝2σce
Wherein, sigma ce: effective compressive stress of the joint concrete when uniformly pressed; n k0: the axial force standard value of the joint; sigma pe: the initial effective stress of the prestressed tendons; a p: the area of the prestressed tendons; b: the longitudinal length of the joint; h: the height of the joint cross section; sigma c1: maximum compressive stress of the concrete edge of the joint compression zone corresponding to M k1;
M k1: critical bending moment in full section compression.
In the embodiment of the present invention, in the step C, the stress distribution of the joint concrete, the effective total stress of the tendon, the external bending moment, the joint opening amount, the joint rotation angle, and the joint rotational stiffness may be calculated according to the formula:
Wherein, sigma c: the maximum compressive stress of the concrete edge of the joint compression area at the stage; n k0: the axial force standard value of the joint; sigma pe: the initial effective stress of the prestressed tendons; alpha E: the ratio of the elastic modulus of the prestressed tendon to the elastic modulus of the concrete; a p: the area of the prestressed tendons; b: the longitudinal length of the joint; h: the height of the joint cross section; y: length of the zero stress region of the joint; sigma p: the effective total stress of the prestressed tendons; sigma ce: effective compressive stress of the joint concrete when uniformly pressed; m k: an external bending moment; Δ y: the opening amount of the outer edge of the joint; θ y: the joint rotation angle; η: the height coefficient is influenced by the compression deformation of the concrete in the pressed area, and the value range is 0-1.0; h 0: the total calculated height of the upper and lower joint pipe racks; e c: modulus of elasticity of the concrete; k Ry: joint rotational stiffness.
In the embodiment of the present invention, in the step D, the stress distribution of the joint concrete, the effective total stress of the tendon, the external bending moment, the joint opening amount, the joint rotation angle, and the joint rotational stiffness may be calculated according to the formula:
Wherein, sigma c: the maximum compressive stress of the concrete edge of the joint compression area at the stage; n k0: the axial force standard value of the joint; sigma pe: the initial effective stress of the prestressed tendons; alpha E: the ratio of the elastic modulus of the prestressed tendon to the elastic modulus of the concrete; a p: the area of the prestressed tendons; b: the longitudinal length of the joint; h: the height of the joint cross section; y: length of the zero stress region of the joint; sigma p: the effective total stress of the prestressed tendons; sigma ce: effective compressive stress of the joint concrete when uniformly pressed; m k: an external bending moment; Δ y: the opening amount of the outer edge of the joint; θ y: the joint rotation angle; η: the height coefficient is influenced by the compression deformation of the concrete in the pressed area, and the value range is 0-1.0; h 0: the total calculated height of the upper and lower joint pipe racks; e c: modulus of elasticity of the concrete; k Ry: joint rotational stiffness.
Example two
Please participate in fig. 3-6, a calculation method for the whole process analysis of the bending capability of the transverse joint of the prefabricated comprehensive pipe rack includes the following steps:
Step A, basic data and parameters take values, wherein the basic data and parameters comprise: the cross section size of the transverse joint of the prefabricated pipe gallery, concrete material parameters, prestressed rib area, tensioning control stress and prestress loss.
The height H 0 =4.2 m is calculated for the upper and lower segmented groove type prefabricated assembled pipe gallery with the prestressed reinforcement arranged in the middle, the cross section height h=400 mm of the transverse joint, the longitudinal length b=2.4 m of the single component, the concrete is C40, the prestressed reinforcement is 4 phi 22PC steel bars, the ultimate strength standard value 1230MPa of the prestressed reinforcement, the strength design value 1080MPa of the prestressed reinforcement, the tension control stress coefficient is 0.70, the prestress loss is 80MPa, the standard value N k0 = 280.8kN of the axial force born by the joint, and the initial effective stress sigma pe =0.70×1230-80=781 MPa of the prestressed reinforcement.
And B, calculating stress of the transverse joint of the prefabricated pipe gallery in a decompression stage. And obtaining the effective compressive stress of the joint concrete when uniformly pressed, the critical bending moment of the full-section pressed state and the corresponding maximum compressive stress of the edge of the joint pressed region concrete according to the following formula.
σc1＝2σce＝3.059MPa
Wherein, sigma ce: effective compressive stress of the joint concrete when uniformly pressed; n k0: the axial force standard value of the joint; sigma pe: the initial effective stress of the prestressed tendons; a p: the area of the prestressed tendons; b: the longitudinal length of the joint; h: the height of the joint cross section; sigma c1: maximum compressive stress of the concrete edge of the joint compression zone corresponding to M k1;
M k1: critical bending moment in full section compression.
And C, calculating the stress of the transverse joint of the prefabricated pipe gallery in the initial opening stage. And C, further calculating the stress distribution of the joint concrete, the effective total stress of the prestressed tendons, the external bending moment, the joint opening amount, the joint rotation angle and the joint rotation rigidity in the initial opening stage according to the calculation parameters and the results of the steps A-B, wherein the calculation can be performed according to the following formula:
Wherein, sigma c: the maximum compressive stress of the concrete edge of the joint compression area at the stage; n k0: the axial force standard value of the joint; sigma pe: the initial effective stress of the prestressed tendons; alpha E: the ratio of the elastic modulus of the prestressed tendon to the elastic modulus of the concrete; a p: the area of the prestressed tendons; b: the longitudinal length of the joint; h: the height of the joint cross section; y: length of the zero stress region of the joint; sigma p: the effective total stress of the prestressed tendons; sigma ce: effective compressive stress of the joint concrete when uniformly pressed; m k: an external bending moment; Δ y: the opening amount of the outer edge of the joint; θ y: the joint rotation angle; η: the concrete compression deformation of the pressed area affects the height coefficient, and the second eta of the embodiment takes a value of 0.5; h 0: the total calculated height of the upper and lower joint pipe racks; e c: modulus of elasticity of the concrete; k Ry: joint rotational stiffness.
In the second embodiment, the analysis results (partial results) of the whole process of load-internal force-deformation at the initial opening stage of the joint in table 1 are shown in the following table:
And D, calculating the stress of the transverse joint of the prefabricated pipe gallery in the fully-opened stage. And C, further calculating the stress distribution of the joint concrete, the effective total stress of the prestressed tendons, the external bending moment, the joint opening amount, the joint rotation angle and the joint rotation rigidity in the complete opening stage according to the calculation parameters and the results of the steps A to C, wherein the calculation can be performed according to the following formula:
Wherein, sigma c: the maximum compressive stress of the concrete edge of the joint compression area at the stage; n k0: the axial force standard value of the joint; sigma pe: the initial effective stress of the prestressed tendons; alpha E: the ratio of the elastic modulus of the prestressed tendon to the elastic modulus of the concrete; a p: the area of the prestressed tendons; b: the longitudinal length of the joint; h: the height of the joint cross section; y: length of the zero stress region of the joint; sigma p: the effective total stress of the prestressed tendons; sigma ce: effective compressive stress of the joint concrete when uniformly pressed; m k: an external bending moment; Δ y: the opening amount of the outer edge of the joint; θ y: the joint rotation angle; η: the concrete compression deformation of the pressed area affects the height coefficient, and the second eta of the embodiment takes a value of 0.5; h 0: the total calculated height of the upper and lower joint pipe racks; e c: modulus of elasticity of the concrete; k Ry: joint rotational stiffness.
In the second embodiment, the results (partial results) of the load-internal force-deformation overall process analysis at the fully opened stage of the joint in table 2 are shown in the following table:
And E, judging the damage stage of the transverse joint of the prefabricated pipe gallery. In the second step D of the embodiment, when the length y=330 mm of the zero stress area of the joint, the maximum compressive stress of the concrete edge of the pressed area
And sigma c＝19.69MPa＞fc = 19.1MPa, the effective total stress sigma p＝825.7MPa＜fpy = 1080MPa of the prestressed tendons, and the maximum compressive stress of the edges of the concrete exceeds the strength design value of the prestressed tendons although the effective total stress of the prestressed tendons does not exceed the strength design value of the prestressed tendons, so that joint damage is judged, and the joint damage corresponds to the upper-stage damage bending moment value M k = 277.3 kn.m.
Step F, the computer program completes the calculation of the steps and synchronously draws a result curve: bending moment-opening amount curve, bending moment-turning angle curve, rotational stiffness-opening amount curve, rotational stiffness-turning angle curve, as shown in fig. 3 to 6.
As apparent from the calculation result table and the curve, along with the increase of the external bending moment born by the transverse joint of the prefabricated pipe gallery, the opening amount and the rotation angle of the joint are gradually increased, the rotation rigidity of the joint is gradually reduced, and the change rule reflected by the curve accords with engineering practice. Further, as the joint is subjected to bending load to yield and break, the joint rotational stiffness remains substantially within a low magnitude level. Furthermore, according to the technical Specification of urban Utility tunnel engineering GB 50838-2015, the limit value of the joint opening amount is 2mm, the corresponding bending moment value is 250 kN.m, and the corresponding joint rotation rigidity is directly found out from the result curveTherefore, the method effectively solves the problems of internal force calculation and joint deformation calculation of the pipe gallery, and has very obvious effect.
It will be apparent to those skilled in the art that various modifications and variations can be made to the present invention without departing from the spirit or scope of the invention. Thus, it is intended that the present invention also include such modifications and alterations insofar as they come within the scope of the appended claims or the equivalents thereof.
Claims (8)
1. The whole process analysis method for the bending capacity of the transverse joint of the prefabricated comprehensive pipe rack is characterized by comprising the following steps of:
Acquiring basic data;
Respectively carrying out stress analysis on a decompression stage, an initial opening stage and a full opening stage of the transverse joint of the prefabricated comprehensive pipe rack based on basic data to obtain a stress analysis result;
determining condition information of a damage stage of the transverse joint of the prefabricated comprehensive pipe rack based on a stress analysis result;
And drawing a result curve based on the stress analysis result, and assisting a designer in joint design.
2. The method for analyzing the bending capacity of the transverse joint of the prefabricated comprehensive pipe rack in the whole process according to claim 1, wherein the basic data at least comprises: the cross section size of the transverse joint of the prefabricated pipe gallery, concrete material parameters, prestressed rib area, tensioning control stress coefficient and prestress loss.
3. The method for analyzing the bending capacity of the transverse joint of the prefabricated utility tunnel in the whole process according to claim 2, wherein the step of carrying out stress analysis on the decompression phase of the transverse joint of the prefabricated utility tunnel based on basic data comprises the following steps:
based on basic data, calculating effective compressive stress in a decompression stage of the transverse joint of the prefabricated comprehensive pipe rack, critical bending moment of the full-section compression state and maximum compressive stress of the edge of the concrete in the corresponding joint compression zone by the following formula:
σc1＝2σce
Wherein, sigma ce: effective compressive stress of the joint concrete when uniformly pressed; n k0: the axial force standard value of the joint; sigma pe: the initial effective stress of the prestressed tendons; a p: the area of the prestressed tendons; b: the longitudinal length of the joint; h: the height of the joint cross section; sigma c1: maximum compressive stress of the concrete edge of the joint compression zone corresponding to M k1;
M k1: critical bending moment in full section compression.
4. The method for analyzing the bending capacity of the transverse joint of the prefabricated utility tunnel in the whole process according to claim 2, wherein the step of analyzing the stress of the initial opening stage of the transverse joint of the prefabricated utility tunnel based on the basic data comprises the steps of:
based on basic data, calculating the stress distribution of joint concrete, the effective total stress of the prestressed tendons, the external bending moment, the joint expansion amount, the joint rotation angle and the joint rotation rigidity in the initial expansion stage of the transverse joint of the prefabricated comprehensive pipe gallery by the following formula:
Wherein, sigma c: the maximum compressive stress of the concrete edge of the joint compression area at the stage; n k0: the axial force standard value of the joint; sigma pe: the initial effective stress of the prestressed tendons; alpha E: the ratio of the elastic modulus of the prestressed tendon to the elastic modulus of the concrete; a p: the area of the prestressed tendons; b: the longitudinal length of the joint; h: the height of the joint cross section; y: length of the zero stress region of the joint; sigma p: the effective total stress of the prestressed tendons; sigma ce: effective compressive stress of the joint concrete when uniformly pressed; m k: an external bending moment; Δ y: the opening amount of the outer edge of the joint; θ y: a joint moving corner; η: the height coefficient is influenced by the compression deformation of the concrete in the pressed area, and the value range is 0-1.0; h 0: the total calculated height of the upper and lower joint pipe racks; e c: modulus of elasticity of the concrete; k Ry: joint rotational stiffness.
5. The method for analyzing the bending capacity of the transverse joint of the prefabricated utility tunnel in the whole process according to claim 2, wherein the step of analyzing the stress of the fully opened stage of the transverse joint of the prefabricated utility tunnel based on the basic data comprises the steps of:
based on basic data, calculating the stress distribution of joint concrete, the effective total stress of the prestressed tendons, the external bending moment, the joint expansion amount, the joint rotation angle and the joint rotation rigidity in the complete expansion stage of the transverse joint of the prefabricated comprehensive pipe gallery by the following formula:
Wherein, sigma c: the maximum compressive stress of the concrete edge of the joint compression area at the stage; n k0: the axial force standard value of the joint; sigma pe: the initial effective stress of the prestressed tendons; alpha E: the ratio of the elastic modulus of the prestressed tendon to the elastic modulus of the concrete; a p: the area of the prestressed tendons; b: the longitudinal length of the joint; h: the height of the joint cross section; y: length of the zero stress region of the joint; sigma p: the effective total stress of the prestressed tendons; sigma ce: effective compressive stress of the joint concrete when uniformly pressed; m k: an external bending moment; Δ y: the opening amount of the outer edge of the joint; θ y: the joint rotation angle; η: the height coefficient is influenced by the compression deformation of the concrete in the pressed area, and the value range is 0-1.0; h 0: the total calculated height of the upper and lower joint pipe racks; e c: modulus of elasticity of the concrete; k Ry: joint rotational stiffness.
6. The method for analyzing the bending capacity of the transverse joint of the prefabricated utility tunnel according to claim 1, wherein the step of determining the condition information of the breaking stage of the transverse joint of the prefabricated utility tunnel based on the result of the stress analysis comprises the steps of:
When the concrete compressive stress of the joint compressive edge in the stress analysis result exceeds a concrete compressive strength design value or the stress of the prestressed tendons in the stress analysis result exceeds a strength design value, judging that the transverse joint of the prefabricated comprehensive pipe gallery is damaged, and taking the corresponding bending moment as a damage bending moment value.
7. The method for analyzing the bending capacity of the transverse joint of the prefabricated comprehensive pipe rack in the whole process according to claim 1, wherein the achievement curve at least comprises: bending moment-opening amount curve, bending moment-rotation angle curve, rotation stiffness-opening amount curve, and rotation stiffness-rotation angle curve.
8. The method for analyzing the bending capacity of the transverse joint of the prefabricated utility tunnel in the whole process according to claim 1, wherein the step of assisting the designer in designing the joint comprises the steps of:
And outputting and displaying the stress analysis result and the result curve to a designer.
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