CN109098216B - Method for calculating bending resistance bearing capacity of normal section of circular-section fender post after local breakage - Google Patents

Method for calculating bending resistance bearing capacity of normal section of circular-section fender post after local breakage Download PDF

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CN109098216B
CN109098216B CN201810989266.1A CN201810989266A CN109098216B CN 109098216 B CN109098216 B CN 109098216B CN 201810989266 A CN201810989266 A CN 201810989266A CN 109098216 B CN109098216 B CN 109098216B
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fender post
circular
bearing capacity
bending resistance
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CN109098216A (en
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雷明锋
刘瑶
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Central South University
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    • E—FIXED CONSTRUCTIONS
    • E02—HYDRAULIC ENGINEERING; FOUNDATIONS; SOIL SHIFTING
    • E02D—FOUNDATIONS; EXCAVATIONS; EMBANKMENTS; UNDERGROUND OR UNDERWATER STRUCTURES
    • E02D33/00—Testing foundations or foundation structures
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Abstract

The invention discloses a method for calculating the bending resistance bearing capacity of a normal section of a circular-section fender post after local breakage, which comprises the following steps: step one, dispersing the guard piles uniformlyThe distributed steel bars are equivalent to a continuous steel ring with equal thickness, and the thickness t of the equivalent steel ring is obtained by calculations(ii) a Step two, establishing a section concrete compressive stress resultant force DcTension and compression resultant force D of cross-section steel barsAccording to the balance equation, the height coefficient ξ of the pressed section area of the circular section fender post after the partial breakage is obtained, and step three, the bending resistance bearing capacity M of the residual section of the circular section fender post after the partial breakage is calculatedcAnd the bending resistance bearing capacity M of the reinforcing steel barsFinally, the bending resistance bearing capacity M of the normal section of the circular section fender post after the local breakage is obtainedpu：Mpu＝Mc+Ms. The method has clear thought and reliable result, can be used for the safety analysis of the structure of the circular-section fender post after the partial breakage in the actual engineering, provides direct reference for the safety evaluation and further treatment method of the foundation pit under similar conditions, and improves the engineering safety coefficient.

Description

Method for calculating bending resistance bearing capacity of normal section of circular-section fender post after local breakage
Technical Field
The invention relates to a method for calculating the bending resistance of a normal section of a circular-section reinforced concrete fender post, in particular to a method for calculating the bending resistance and the bearing capacity of the normal section of the circular-section fender post after local breakage.
Background
The fender pile and inner support structure system is a commonly used support mode for the current open-cut deep foundation pit, and a circular-section cast-in-situ bored pile is used as a main fender pile type.
In the actual construction process, the pile-forming verticality deviation often appears under the influence of stratum conditions, drilling equipment and the like, and even the pile-forming verticality deviation invades the limit of a main structure. At the moment, in order to ensure the size requirement of the main structure, the guard piles intruding into the boundary of the main structure must be chiseled, and even the stressed reinforcing steel bars in the piles are cut off, so that the bearing capacity of the guard piles is reduced, and the integral instability and overturning of the foundation pit guard structure can be caused in serious cases.
Therefore, in order to ensure the construction safety, it is necessary to calculate and analyze the bearing capacity of the broken circular-section enclosure pile, so as to determine the weakening condition of the bearing capacity of the pile after the local breaking, and evaluate the overall safety of the enclosure structure.
At present, a method for calculating the bending resistance bearing capacity of the normal section of a complete circular-section fender post is clearly specified, but a method for clearly calculating the bending resistance bearing capacity of the normal section of the circular-section fender post after the circular-section fender post is partially broken is not specified, so that potential safety hazards exist.
Disclosure of Invention
The invention aims to provide a method for calculating the bending resistance bearing capacity of the normal section of the circular-section fender post after the partial breakage, which has clear thought and reliable result, can be used for the safety analysis of the structure of the circular-section fender post after the partial breakage in the actual engineering, provides direct reference for the safety evaluation and further treatment method of the foundation pit under similar conditions, and improves the engineering safety coefficient.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows:
a method for calculating the bending resistance and bearing capacity of a normal section of a circular-section fender post after local breakage is characterized by comprising the following steps of:
step one, the reinforcing steel bars which are dispersedly and uniformly distributed in the fender post are equivalent to a continuous steel ring with equal thickness, and the thickness t of the equivalent steel ring is obtained through calculations；
Step two, establishing a section concrete compressive stress resultant force DcTension and compression resultant force D of cross-section steel barsAccording to the balance equation, the height coefficient ξ of the cross section compression area after the circular cross section fender post is partially broken is obtained;
step three, calculating the bending resistance bearing capacity M of the residual section of the circular-section fender post after the partial breakagecAnd the bending resistance bearing capacity M of the reinforcing steel barsFinally, the bending resistance bearing capacity M of the normal section of the circular section fender post after the local breakage is obtainedpu：Mpu＝Mc+Ms。
Further, in the step one, the thickness t of the equivalent steel ringsThe calculation formula is as follows:
Figure BDA0001780404720000021
wherein A iss0The sum of the cross-sectional areas r of all longitudinal reinforcements of the complete circular-section fender postsIs a complete circular sectionAnd the centers of all longitudinal steel bar centroids of the pile protectors are located on the radius of the circumference.
Further, in the second step, DcAnd DsThe equation of equilibrium of (a) is calculated as: dc＝DsWherein:
Dc＝α1fc(θh-sinθhcosθh)r2；
Figure BDA0001780404720000031
Figure BDA0001780404720000032
Figure BDA0001780404720000033
Figure BDA0001780404720000034
Figure BDA0001780404720000035
x0＝r-ξ(2r-d)；
ξ＝xc/(2r-d)；
in the formula, α1Is a constant coefficient, fcFor concrete compressive strength, r is the radius of the fender post, θhPosition x of neutral axis after local breaking of fender posthHalf of the corresponding central angle, fsFor the tensile strength of the longitudinal reinforcement, As0The cross-sectional area of all longitudinal steel bars of the complete circular cross-section fender post is the sum,
Figure BDA0001780404720000036
for breaking the corresponding half of the central angle, theta, of the fender postsIs half of the central angle theta corresponding to the tensile yield position of the steel barsIs half of the central angle, x, corresponding to the yielding position of the steel bar under pressure0Is a cross sectionThe distance between the mandrel and the actual neutral axis, d is the broken radial thickness of the guard post,ufor ultimate compressive strain of concrete, EsIs the modulus of elasticity, f, of the longitudinal reinforcements' is the longitudinal bar compressive strength, xcAnd the actual compression zone height of the residual section under the limit load condition after the pile body is broken.
Preferably, in the second step, the ξ is obtained by a binary search solution.
In a preferable mode, in the third step,
Figure BDA0001780404720000041
Figure BDA0001780404720000042
preferably, α is the concrete strength rating of no more than C5011.0 is selected, and when the concrete strength grade is C80, α1Taking 0.94, when the concrete strength grade is between C50 and C80, determining α between 1.0 and 0.94 according to a linear interpolation method1The value of (c).
Compared with the prior art, the invention has the beneficial effects that: theoretical derivation is carried out based on the assumption of a flat section and equivalent steel ring treatment of longitudinal stressed steel bars, the bending resistance bearing capacity of the front section of the fender post after the partial breaking is obtained according to the dichotomy principle, the defect that the bending resistance bearing capacity of the front section of the fender post after the partial breaking cannot be calculated at present is overcome, the method can be used for safety analysis of the structure of the fender post with the circular section after the partial breaking in actual engineering, direct reference is provided for foundation pit safety evaluation and further treatment under similar conditions, and the engineering safety coefficient is improved.
Drawings
FIG. 1 is a flow chart of the present invention.
Fig. 2 is a schematic diagram of the calculation of equivalent steel ring of the circular-section fender post steel bar of the invention.
Fig. 3 is a schematic parameter diagram related to calculation of the bending resistance bearing capacity of the front section of the fender post after the fender post is partially broken.
Detailed Description
The invention is further described with reference to the following figures and detailed description.
As shown in fig. 1, one embodiment of the present invention includes the steps of:
step one, collecting basic data and data of a fender post with a circular cross section, equating the discrete and evenly distributed steel bars (shown as figure 2 (a)) in the fender post to be a continuous steel ring with equal thickness (shown as figure 2 (b)), and calculating to obtain the thickness t of the equivalent steel rings：
Figure BDA0001780404720000056
Wherein A iss0The sum of the cross-sectional areas r of all longitudinal reinforcements of the complete circular-section fender postsThe radius of the circumference of the complete circular section fender post where all longitudinal steel bar centroids are located.
Step two, as shown in fig. 3, establishing the compressive stress resultant force D of the section concretecTension and compression resultant force D of cross-section steel barsThe equilibrium equation of (c): dc＝DsWherein:
Dc＝α1fc(θh-sinθhcosθh)r2；
Figure BDA0001780404720000051
Figure BDA0001780404720000052
Figure BDA0001780404720000053
Figure BDA0001780404720000054
Figure BDA0001780404720000055
x0＝r-ξ(2r-d)；
ξ＝xc/(2r-d)；
in the formula (I), the compound is shown in the specification,
α1for constant coefficient, when the concrete strength grade does not exceed C50, α11.0 is selected, and when the concrete strength grade is C80, α1Taking 0.94, when the concrete strength grade is between C50 and C80, determining α between 1.0 and 0.94 according to a linear interpolation method1The value of (c).
fcFor concrete compressive strength, r is the radius of the fender post, θhPosition x of neutral axis after local breaking of fender posthHalf of the corresponding central angle, fsFor the tensile strength of the longitudinal reinforcement, As0The cross-sectional area of all longitudinal steel bars of the complete circular cross-section fender post is the sum,
Figure BDA0001780404720000061
for breaking the corresponding half of the central angle, theta, of the fender postsIs half of the central angle theta corresponding to the tensile yield position of the steel barsIs half of the central angle, x, corresponding to the yielding position of the steel bar under pressure0The distance between the section-shaped mandrel and the actual neutral axis, d is the broken radial thickness of the fender post,uin order to limit the compressive strain of the concrete,utake 0.0033, EsIs the modulus of elasticity, f, of the longitudinal reinforcements' is the longitudinal bar compressive strength, xcAnd the actual compression zone height of the residual section under the limit load condition after the pile body is broken.
Then, the method for obtaining the height coefficient ξ of the cross-section compression zone after the circular cross-section fender post is partially broken according to the balance equation is a dichotomy search solution, and the specific solution process of ξ is as follows:
define function F (ξ):
Figure BDA0001780404720000062
find the reasonable interval [ a, b ] of ξ where the root is]Satisfies F (a) < 0, and F (b) > 0.
① F [ (a + b)/2] ═ 0, then (a + b)/2 is the root sought;
② if F [ (a + b)/2] < 0, there is zero point in the interval [ (a + b)/2, b ], assign (a + b)/2 to a, continue using the key function value from ① to judge;
③ if F [ (a + b)/2] > 0, there is a zero point in the interval [ a, (a + b)/2], assigning (a + b)/2 to b, and continuing to use the key function value judgment from ①;
④ when the interval is less than the required accuracy, the iterative process is ended, taking the average (a + b)/2 of this interval as the root to be found.
Step three, calculating the bending resistance bearing capacity M of the residual section of the circular-section fender post after the partial breakagecAnd the bending resistance bearing capacity M of the reinforcing steel bars(taking distance to the neutral axis), and finally obtaining the bending resistance bearing capacity M of the normal section after the part of the circular section fender pile is brokenpu：Mpu＝Mc+Ms，
Wherein the content of the first and second substances,
Figure BDA0001780404720000071
Figure BDA0001780404720000072
while the present invention has been described with reference to the embodiments shown in the drawings, the present invention is not limited to the embodiments, which are illustrative and not restrictive, and it will be apparent to those skilled in the art that various changes and modifications can be made therein without departing from the spirit and scope of the invention as defined in the appended claims.

Claims (5)

1. A method for calculating the bending resistance and bearing capacity of a normal section of a circular-section fender post after local breakage is characterized by comprising the following steps:
step one, the reinforcing steel bars which are dispersedly and uniformly distributed in the fender post are equivalent to a continuous steel ring with equal thickness, and the thickness t of the equivalent steel ring is obtained through calculations；
Step two, establishing a section concrete compressive stress resultant force DcTension and compression resultant force D of cross-section steel barsAccording to the balance equation, the height coefficient ξ of the cross section compression area after the circular cross section fender post is partially broken is obtained;
in the second step, DcAnd DsThe equation of equilibrium of (a) is calculated as: dc＝DsWherein:
Dc＝α1fc(θh-sinθhcosθh)r2；
Figure FDA0002396689820000011
Figure FDA0002396689820000012
Figure FDA0002396689820000013
Figure FDA0002396689820000014
Figure FDA0002396689820000015
x0＝r-ξ(2r-d)；
ξ＝xc/(2r-d)；
in the formula, α1Is a constant coefficient, fcFor concrete compressive strength, r is the radius of the fender post, θhPosition x of neutral axis after local breaking of fender posthHalf of the corresponding central angle, fsFor the tensile strength of the longitudinal reinforcement, As0The cross-sectional area of all longitudinal steel bars of the complete circular cross-section fender post is the sum,
Figure FDA0002396689820000016
for breaking the corresponding half of the central angle, theta, of the fender postsIs half of a central angle theta 'corresponding to a tensile yielding position of the reinforcing steel bar'sIs half, x of the central angle corresponding to the yielding position of the steel bar under pressure0The distance between the section-shaped mandrel and the actual neutral axis, d is the broken radial thickness of the fender post,ufor ultimate compressive strain of concrete, EsIs the modulus of elasticity, f, of the longitudinal reinforcements' is the longitudinal bar compressive strength, xcThe actual compression area height of the residual section under the condition of ultimate load after the pile body is broken;
step three, calculating the bending resistance bearing capacity M of the residual section of the circular-section fender post after the partial breakagecAnd the bending resistance bearing capacity M of the reinforcing steel barsFinally, the bending resistance bearing capacity M of the normal section of the circular section fender post after the local breakage is obtainedpu：Mpu＝Mc+Ms。
2. The method for calculating the bending resistance and bearing capacity of the circular-section fender post after being partially broken off according to claim 1, wherein in the first step, the thickness t of the equivalent steel ringsThe calculation formula is as follows:
Figure FDA0002396689820000021
wherein A iss0The sum of the cross-sectional areas r of all longitudinal reinforcements of the complete circular-section fender postsThe radius of the circumference of the complete circular section fender post where all longitudinal steel bar centroids are located.
3. The method for calculating the bending resistance and the bearing capacity of the positive section of the circular-section fender post after the partial breakage of the circular-section fender post according to claim 1, wherein in the second step, the calculation method of ξ is a dichotomy search solution.
4. The method for calculating the bending resistance and bearing capacity of the circular-section fender post after the partial breakage is carried out according to claim 1, wherein in the third step,
Figure FDA0002396689820000022
Figure FDA0002396689820000031
5. the method for calculating the bending resistance and bearing capacity of the circular-section fender post after being partially broken off according to claim 1, wherein α is set when the strength grade of concrete does not exceed C5011.0 is selected, and when the concrete strength grade is C80, α1Taking 0.94, when the concrete strength grade is between C50 and C80, determining α between 1.0 and 0.94 according to a linear interpolation method1The value of (c).
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