CN117057100A - Be applied to assembled ribbed steel pipe concrete column foot intensity, rigidity calculation model - Google Patents
Be applied to assembled ribbed steel pipe concrete column foot intensity, rigidity calculation model Download PDFInfo
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Abstract
The method is applied to an assembled ribbed steel tube concrete column base strength and rigidity calculation model, and column base nodes are simplified into different components according to different eccentricities; deriving that the bending moment resistance of the foot joint of the ribbed steel tube concrete column is expressed as a function of the load eccentricity e; the unequal ratio is regarded as an infinite equal ratio loading process, and the output quantity of the equivalent compression T-shaped piece and the equivalent tension T-shaped piece corresponding to each applied moment value is calculated according to each applied moment value; the minimum value obtained by deduction is the bending resistance bearing capacity of the column base connecting node. All the components are simulated by using spring units or rigid rods, linearity or non-linearity is given to the spring units, the spring units or the rigid rods are assembled into a mechanical model of an integral structure by series-parallel combination, and a calculation model of the initial rigidity of the column base node of the node type is obtained. The influence of the rib plates on the column compressive resistance and the rotation center is considered, the corner deformation caused by bending of the steel column is considered, and the mechanical property of the column foot is accurate.
Description
Technical Field
The application relates to the technical field of constructional engineering, in particular to a calculation model for strength and rigidity of an assembled ribbed steel tube concrete column base.
Background
The construction of China mainly uses site construction, the traditional production mode has low industrialization degree, coarser design and construction, unstable quality of building products, low construction efficiency, large labor force demand, large material consumption and construction waste, large resource and energy consumption, and can not meet the sustainable development construction requirements of energy conservation and environmental protection. Along with the acceleration of the progress of building industrialization and residence industrialization in China, the trend of the residence industrialization is becoming obvious, and the building production mode is undergoing a revolution, namely, the construction of novel fabricated buildings is gradually expanded, and the application of novel fabricated reinforced concrete structures is becoming one of the current research hotspots. The column foot node is used as a key part for connecting the upper main body structure and the lower foundation, and the mechanical property of the column foot directly influences the mechanical property of the whole frame, so that the accurate definition of the bending resistance of the column foot is particularly important.
The traditional node design method has obvious defects in evaluating the mechanical response of the novel fabricated concrete filled steel tube column foot node. The method is mainly characterized in that the bending resistance bearing capacity prediction is too conservative, and when the axial pressure is relatively large, the deviation between the calculated result and the actual test result is relatively large. On the basis, the influence of rib plates on the column compressive resistance and the rotation center needs to be reasonably considered, and a plurality of rows of anchor bolts exist on the tension side so as to solve the problems in the prior art.
Disclosure of Invention
The application aims to provide a calculation model for the strength and rigidity of an assembled ribbed steel tube concrete column base, which considers the influence of rib plates on the column compressive resistance and the rotation center, considers the corner deformation caused by bending of a steel column, and provides a solving formula for the column base node bearing capacity and the bending rigidity under the condition that a plurality of rows of anchor bolts exist on the tension side, so as to solve the problem that the traditional node design method is inaccurate in evaluating the mechanical response of a novel assembled ribbed steel tube concrete column base node.
In order to achieve the purpose of the application, the following technical scheme is adopted.
A calculation model for the strength and the rigidity of an assembled ribbed steel tube concrete column base comprises the following steps:
step one: the toe nodes are simplified to different components according to the eccentricity.
Step two: deducing a node type TypeA with only one row of anchor bolts on the tension side and column base nodes with multiple rows of anchor bolts TypeB on the tension side under the action of equal proportion loading according to the balance conditions of force and bending moment; to obtain the bending moment resistance (M) of the ribbed steel tube concrete column base node j，Rd ) Represented as a function of the load eccentricity e.
Step three: considering the unequal ratio as an infinite number of equal ratio loading processes, for each applied moment value (M sd ) And calculating the output quantity of the equivalent compression T-shaped piece and the equivalent tension T-shaped piece corresponding to each applied moment value.
Step four: determining the relative mechanical properties-strength of each component while characterizing each component; for each test piece, M values corresponding to the different damage forms are respectively provided, wherein the M values comprise anchor bolt damage, bottom plate buckling and column wing source buckling; by comparison of M corresponding to different forms of destruction j，Rd And obtaining a minimum value which is the bending resistance bearing capacity of the column base connecting node.
Step five: all the components are modeled with spring units or rigid rods, and linear or nonlinear constructs are assigned to the spring units, calculating the spring rate k16 representing the anchor rods and the flexural floor spring rate k15, and the spring rate k13 representing the compressed concrete.
Step six: the spring units or the rigid rods are assembled into a mechanical model of an integral structure in a series-parallel connection manner, so that the integral mechanical property of the structure is obtained; deriving initial rigidity of a column base node of a node type TypeA with a row of anchor bolts on the tension side and a column base node of a column base node type with a plurality of rows of anchor bolts on the tension side; and obtaining a calculation model of the initial rigidity of the ribbed concrete filled steel tube column base node.
Step seven: and obtaining an initial rigidity calculation model of the connection node taking the bending corner deformation of the steel column into consideration by using the transverse force and transverse displacement response recorded by experiments.
When the eccentricity is smaller, the column foot node is simplified into a left equivalent compression T-shaped piece and a right equivalent compression T-shaped piece, and when the eccentricity is larger, the column foot node is simplified into an equivalent compression T-shaped piece and an equivalent tension T-shaped piece; considering the response of ribbed steel tube concrete column foot joints under the action of buckling, the equivalent compression T-shaped piece mainly comprises compression of a concrete foundation and compression of a column flange, and the equivalent tension T-shaped piece mainly comprises end plate buckling and anchor bolt tension.
For a toe connection node under small eccentricity conditions, each of which applies a moment value (M sd ) The function with respect to the load eccentricity e is expressed as:
e < zcr at small eccentricities:
wherein M is sd Applying a moment value to the column base; n (N) sd Pressure applied to the column shoe; f (F) cl Is stressed by the left pressed T-shaped piece; f (F) cr Is stressed by the right side compression tee.
Since the loading is equal-proportion, the M eccentricity remains unchanged during loading, and
f in the formula cl，Rd Is a T-shaped part pressed on the left sideCompressive strength; f (F) cr，Rd The compressive strength value of the right-side compression T-shaped piece; z is Z cl 、Z cr The force combining points from the center of the section of the column to the left compression T-shaped piece and the right compression T-shaped piece are respectively; the resultant force point of the pressed T-shaped piece is set as the rib edge by combining the numerical value and the test result.
For the column foot connection node under the working condition of large eccentricity, a row of node type TypeA of the anchor bolts exists on the tension side, a plurality of rows of column foot nodes of the anchor bolt type TypeB exist on the tension side, each of the column foot nodes applies a moment value (M j，Rd ) The function with respect to the load eccentricity e is expressed as: column foot node for TypeA type anchor arrangement:
e > zcr at large eccentricity
Due to the equal proportion loading, the M-eccentricity remains unchanged during loading, and can be obtained:
the same applies to the toe node of the TypeB type anchor bolt arrangement (assuming the floor is a rigid body):
F cl，Rd the compression strength of the T-shaped part pressed on the left side is the compression strength of the T-shaped part pressed on the left side; f (F) cr，Rd The compressive strength value of the right-side compression T-shaped piece; f (F) tl，Rd Tensile strength value of the left tensile T-shaped piece; fi is the tension at the i-th row of bolts; zi is the distance from the ith row of bolts to the combining force point of the left pressed T-shaped piece; z is Z 0 The distance from the left tension T-shaped piece to the point of combining force of the left compression T-shaped piece; f (F) tl，Rd，eq Is the tensile strength value of the equivalent pressed T-shaped piece; z is Z eq Is an equivalent moment arm; z is Z cr 、Z tl The distance from the center of the section of the column to the resultant force point of the left pressed T-shaped piece, the resultant force point of the right pressed T-shaped piece and the resultant force point of the left pulled T-shaped piece are respectively; z is Z ， t =Z eq -Z c Wherein the arm length Z (z=z cr +Z tl) The influence of the end plate connection of the ribbed rib plate on the position of the rotation center is considered, the combination value and the test result show that the stiffening rib shows an inclined supporting effect, the rotation center of the node changes along with the rotation of the node, and the combination value and the test result set the rotation center as the edge of the rib plate.
Considering the unequal ratio as an infinite equal ratio loading process, the output of the equivalent compression T-piece and the equivalent tension T-piece corresponding to each applied moment value is expressed as:
small eccentricity e<z cr ：
E when large eccentric>z cr ：
Determining the relative mechanical properties-strength of each component, the ultimate strength of an equivalent tensile T-piece can be expressed by the following relationship:
when prying force exists:
when no prying force is present:
the connecting node has a prying force if the following formula is satisfied:
wherein L is b For the length of the anchor bolt, provision is made according to the European Specification:
the design value of the bending moment bearing capacity of the bottom plate connection is equal to the standard value of the bending moment bearing capacity divided by the safety coefficient gamma M0 ：
Wherein F is t，Rd The design value of the tensile bearing capacity of the anchor bolt is equal to the standard tensile value divided by the safety coefficient gamma M2 ：
Wherein: f (f) ub The tensile strength of the anchor rod is the tensile strength; n is n b The number of the anchor bolts at the tension side; gamma ray M2 Equal to 1.25; db is the diameter of the anchor bolt; tg, tp, tw and tn are respectively the mortar layer thickness, the bottom plate thickness, the end plate height and the nut height; as is the cross-sectional area of the anchor bolt; m is M pl，1，Rd Is the plastic bending moment value of the base plate corresponding to the type 1 damage form; m is M pl，2，Rd Plastic bending moment value of the base plate corresponding to the type 2 damage form; e is the elastic modulus of the steel; m is the distance from the plastic hinge to the axis of the anchor bolt; n is the distance from the prying force to the axis of the anchor bolt; e, e w =d w 4; dw is the nut diameter of the bolt; fy is the yield strength of the bottom plate;is the effective length of the tension T-shaped flange; gamma ray M0 Equal to 1;
calculation of the bearing capacity of the equivalent compression T-shaped part, wherein the calculation comprises F controlled by the compression of the concrete foundation cl,rd And Fcr, rd, which is pressure controlled by the column flange; the strength values Fcl, rd, fcr, rd (concrete crush, column bulge) controlled by the compression side assembly failure are given by the load carrying capacity of the compression side assembly—the smaller value between the concrete compression resistance and the column section compression resistance:
in practice, the column section is resistant to bending load M due to the presence of stiffening ribs b，Rd The column section bending bearing capacity M is larger than that of the connection node of the non-stiffening end plate c，Rd . When the column flange is pressed, the influence of the stiffening rib on the column body pressure resistance is considered, and the plastic hinge is positioned at the height of the stiffening rib plate by combining the test and the finite element result, so that the corresponding calculation formula of the pressure resistance bearing value of the ribbed steel tube concrete section is obtained as follows:
wherein: f (f) jd B, compressive stress of the foundation concrete below the end plate eff And l eff Is the effective width and length of the T-shaped part on the pressed side, b eff And l eff Are all functions of equivalent width c, c being equal to 1.25 times t p ；h c Is the height of the section of the column, t cf Is the thickness of the column flange; h is the section distance from the loading point to the column bottom, h 1 The height of the rib plate is set; m is M c，Rd The bending resistance bearing capacity of the section of the concrete-filled steel tube under the action of the axial compression load (N) is calculated by utilizing the bending resistance bearing capacity of the section of the opposite concrete-filled steel tube under the action of the axial compression by utilizing x-track, wherein the steel tube and the core concrete structure are defined by utilizing auxiliary material property tests, the ideal elastoplasticity and the three-fold line are respectively adopted for simulation aiming at the constitutive curve of the steel tube, the bending resistance bearing value of the corresponding section of the concrete-filled steel tube under the action of the axial compression is obtained, and the calculated bending resistance bearing capacity of the column foot connecting node is compared with the test value and analyzed.
The flexural rigidity k15 of the base plate is calculated as follows:
when prying force exists:
when no prying force is present:
k 16 tensile stiffness of the anchor bolt:
when prying force exists:
when no prying force is present:
K t，l stiffness for the tension side assembly (anchor in tension and floor in bending):
for the compression region, the compression rigidity Kc is equal to the rigidity coefficient k13, and k13 is taken as the compression rigidity of the basic concrete:
wherein E and E c The elastic modulus of steel and concrete respectively; b eff And l eff Expressed as effective width and effective length, b, respectively, of an equivalent stressed T-piece eff And l eff Are all functions of the relationship equivalent width c, with reference to the preamble c being equal to 1.25 times t p 。
Column foot node for TypeA type anchor arrangement:
column base corner:
column shoe rotational stiffness:
the above formula is combined to obtain:
toe node for TypeB type anchor arrangement:
column base corner:
column shoe rotational stiffness:
the equivalent rigidity coefficient k is obtained according to the balance of force and bending moment eq And corresponding equivalent moment arm Z eq The calculation formula is as follows:
δ ti the ith row of bolts are vertically deformed; k (k) ti Tensile stiffness at the ith row of bolts; delta eq Equivalent vertical deformation; z is Z i The distance from the ith row of bolts to the combining point of the left pressed T-shaped piece is set; e is the elastic modulus; z is Z c 、Z t The distance from the center of the section of the column to the resultant force point of the right pressed T-shaped piece and the resultant force point of the left pulled T-shaped piece are respectively; z is Z ， t =Z eq -Z c Wherein the arm length Z (z=z cr +Z tl ) Considering the influence of the end plate connection of the ribbed rib plate on the position of the rotation center, combining the numerical value and the test result, the stiffening rib shows an inclined supporting effect, and the node rotatesThe dynamic center changes along with the rotation of the node, and the rotation center is taken as the center of the column taking flange when the rigidity of the node is calculated by combining the numerical value and the test result.
According to the recorded transverse force V and transverse displacement response, in the initial loading stage, the influence of the axial force on the bending moment is not considered, and the corresponding bending moment-node rotation angle response is converted through the following equation; obtaining the bending rigidity K of the connecting node through conversion as follows;
L columm distance from the lateral force application point to the bottom plate; e (E) column Modulus of elasticity; i column Moment of inertia of the column cross section; θ is the toe node angle; θ column Corner deformation caused by bending of the steel column; θ base Corner deformation caused by bending of the steel column is not considered; k (k) column Flexural rigidity of the steel ball.
The method is applied to an assembled ribbed concrete filled steel tube column base strength and rigidity calculation model, and column base nodes are simplified into different components according to different eccentricities. Under the action of equal proportion loading, the bending moment resistance (M) of the foot node of the ribbed steel tube concrete column with the node type TypeA with only one row of anchor bolts on the tension side and the multi-row anchor bolt type TypeB on the tension side is obtained j，Rd ) And (5) calculating a formula. The unequal ratio is regarded as an infinite equal ratio loading process, and the output quantity of the equivalent compression T-shaped piece and the equivalent tension T-shaped piece corresponding to each applied moment value is calculated for each applied moment value (Msd). In characterizing each component, the relative mechanical properties-strength-of the individual components are determined. For each test piece, M values corresponding to the different damage forms are respectively provided, and the obtained minimum value is the bending resistance bearing capacity of the column base connecting node. All the components are simulated by using spring units or rigid rods, linear or nonlinear structures are endowed to the spring units, the spring units or the rigid rods are assembled into a mechanical model of an integral structure by series-parallel combination, and the calculation of the initial rigidity of the column foot nodes with the tension side values of the node type TypeA with one row of anchor bolts and the tension side with multiple rows of anchor bolts TypeB is obtainedA formula; the influence of the rib plates on the column compressive resistance and the rotation center is considered, the corner deformation caused by bending of the steel column is considered, and the provided solving formula for the column foot node bearing capacity and the bending rigidity under the condition that multiple rows of anchor bolts exist on the tension side is accurate in mechanical response of evaluating the novel fabricated steel tube concrete column foot node.
Drawings
FIG. 1 is a schematic view of a node type TypeA with a row of anchors on the tension side;
FIG. 2 is a schematic view of a node type TypeB with multiple rows of anchors on the tension side;
under the action of equal proportion loading, deriving column base nodes of a node type TypeA with only one row of anchor bolts on the tension side and a node type TypeB with multiple rows of anchor bolts on the tension side according to the balance conditions of force and bending moment.
Detailed Description
In order to make the technical scheme and advantages of the application clearer, the technical scheme applied to the fabricated ribbed concrete filled steel tube column base strength and rigidity calculation model is clearly and completely described below by combining the embodiment and the attached drawings.
Example 1
The assembling ribbed steel pipe concrete column base strength and rigidity calculation model comprises the following steps of;
step one: the toe nodes are simplified to different components according to the eccentricity. When the eccentricity is smaller, the column foot node is simplified into a left equivalent compression T-shaped piece and a right equivalent compression T-shaped piece, and when the eccentricity is larger, the column foot node is simplified into an equivalent compression T-shaped piece and an equivalent tension T-shaped piece. Considering the response of ribbed steel tube concrete column foot joints under the action of buckling, the equivalent compression T-shaped piece mainly comprises compression of a concrete foundation and compression of a column flange, and the equivalent tension T-shaped piece mainly comprises end plate buckling and anchor bolt tension.
Step two: under the action of equal proportion loading, deducing the node type TypeA with only one row of anchor bolts on the tension side and the column base node with a plurality of rows of anchor bolts TypeB on the tension side according to the balance conditions of force and bending moment. To obtain the bending moment resistance (M) of the ribbed steel tube concrete column base node j，Rd ) Expressed as load deflectionFunction of the heart e.
E < zcr at small eccentricities:
wherein M is sd Applying a moment value to the column base; n (N) sd Pressure applied to the column shoe; f (F) cl Is stressed by the left pressed T-shaped piece; f (F) cr Is stressed by the right side compression tee. F (F) cl，Rd The compression strength of the T-shaped part pressed on the left side is the compression strength of the T-shaped part pressed on the left side; f (F) cr，Rd The compressive strength value of the right-side compression T-shaped piece; z is Z cl 、Z cr The force combining points from the center of the section of the column to the left compression T-shaped piece and the right compression T-shaped piece are respectively; the resultant force point of the pressed T-shaped piece is set as the rib edge by combining the numerical value and the test result.
For the column foot connection node under the working condition of large eccentricity, a row of node type TypeA of the anchor bolts exists on the tension side, a plurality of rows of column foot nodes of the anchor bolt type TypeB exist on the tension side, each of the column foot nodes applies a moment value (M j，Rd ) The function with respect to the load eccentricity e is expressed as: column foot node for TypeA type anchor arrangement:
e > zcr at large eccentricity
Due to the equal proportional loading, during loading, the M-eccentricity remains unchanged, which is obtainable according to the above formula:
the same applies to the toe node of the TypeB type anchor bolt arrangement (assuming the floor is a rigid body):
F cl，Rd the compression strength of the T-shaped part pressed on the left side is the compression strength of the T-shaped part pressed on the left side; f (F) cr，Rd The compressive strength value of the right-side compression T-shaped piece; f (F) tl，Rd Tensile strength value of the left tensile T-shaped piece; fi is the tension at the i-th row of bolts; zi is the distance from the ith row of bolts to the combining force point of the left pressed T-shaped piece; z is Z 0 The distance from the left tension T-shaped piece to the point of combining force of the left compression T-shaped piece; f (F) tl，Rd，eq Is the tensile strength value of the equivalent pressed T-shaped piece; z is Z eq Is an equivalent moment arm; z is Z cr 、Z tl The distance from the center of the section of the column to the resultant force point of the left pressed T-shaped piece, the resultant force point of the right pressed T-shaped piece and the resultant force point of the left pulled T-shaped piece are respectively; arm length Z (z=z) cr +Z tl) The rotation center is at the edge of the rib plate.
Step three: considering the unequal ratio as an infinite number of equal ratio loading processes, for each applied moment value (M base ) The eccentricity corresponding thereto is calculated for distinguishing small eccentricity from large eccentricity. And calculating the output quantity of the equivalent compression T-shaped piece and the equivalent tension T-shaped piece corresponding to each applied moment value according to the difference of the large eccentricity and the small eccentricity.
The output of the equivalent compression and tension tee for each applied moment value is expressed as:
small eccentricity e<z cr ：
E when large eccentric>z cr ：
Step four: in characterizing each component, the relative mechanical properties-strength-of the individual components are determined. For each test piece, the different failure modes respectively have M values corresponding to the failure modes, including anchor bolt failure, buckling of the bottom plate and buckling of the column wing source. By passing throughContrast M corresponding to different failure modes j，Rd And obtaining a minimum value which is the bending resistance bearing capacity of the column base connecting node. The ultimate strength of an equivalent tension tee can be expressed by the following relationship:
when prying force exists:
when no prying force is present:
calculation of the bearing capacity of the equivalent compression T-shaped part, wherein the calculation comprises F controlled by the compression of the concrete foundation cl,Rd And F controlled by column flange compression cr,Rd . Intensity value F controlled by failure of the pressure side assembly cl，Rd 、F cr，Rd (concrete crush, column bulge) is given by the load carrying capacity of the compression side assembly—the smaller value between the concrete compression resistance and the column section compression resistance:
in practice, the column section is resistant to bending load M due to the presence of stiffening ribs b，Rd The column section bending bearing capacity M is larger than that of the connection node of the non-stiffening end plate c，Rd . When the column flange is pressed, the influence of the stiffening rib on the column body pressure resistance is considered, and the plastic hinge is positioned at the height of the stiffening rib plate by combining the test and the finite element result, so that the corresponding calculation formula of the pressure resistance bearing value of the ribbed steel tube concrete section is obtained as follows:
wherein: fjd is the end plate lower foundation concrete compressive stress, beff and leff are the effective width and length of the compression side T-piece, beff and leff are both functions of the equivalent width c, c is equal to 1.25 tp;hc is column section height, tcf is column flange thickness; h is the distance from the loading point to the column bottom section, and h1 is the rib plate height; m is M c，Rd The bending resistance bearing capacity of the section of the concrete-filled steel tube under the action of the axial compression load (N) is calculated by utilizing the bending resistance bearing capacity of the section of the opposite concrete-filled steel tube under the action of the axial compression by utilizing x-track, wherein the steel tube and the core concrete structure are defined by utilizing auxiliary material property tests, the ideal elastoplasticity and the three-fold line are respectively adopted for simulation aiming at the constitutive curve of the steel tube, the bending resistance bearing value of the corresponding section of the concrete-filled steel tube under the action of the axial compression is obtained, and the calculated bending resistance bearing capacity of the column foot connecting node is compared with the test value and analyzed.
Step five: all the components are modeled with spring units or rigid rods, and linear or nonlinear constructs are assigned to the spring units, calculating the spring rate k16 representing the anchor rods and the flexural floor spring rate k15, and the spring rate k13 representing the compressed concrete.
k15 is the flexural rigidity of the base plate:
when prying force exists:
when no prying force is present:
k16 is the tensile stiffness of the anchor:
when prying force exists:
when no prying force is present:
K t，l stiffness for the tension side assembly (anchor in tension and floor in bending):
for the compression region, the compression rigidity Kc is equal to the rigidity coefficient k13, and k13 is taken as the compression rigidity of the basic concrete:
wherein E and Ec are the elastic moduli of steel and concrete, respectively. beff and leff are expressed as the effective width and effective length, respectively, of an equivalent stressed tee, and are each a function of the relative equivalent width c, referenced above c equal to 1.25 times tp.
Step six: the spring units or the rigid rods are assembled into a mechanical model of an integral structure in a series-parallel connection mode, and then the integral mechanical property of the structure is obtained. The initial rigidity of the column base node is deduced for the node type TypeA with a row of anchors on the tension side and the column base node type with a plurality of rows of anchors on the tension side. And obtaining a calculation formula of the initial rigidity of the ribbed concrete filled steel tube column base node. Column foot node for TypeA type anchor arrangement:
column base corner:
column shoe rotational stiffness:
the above formula is combined to obtain:
toe node for TypeB type anchor arrangement:
column base corner:
column shoe rotational stiffness:
the equivalent rigidity coefficient k is obtained according to the balance of force and bending moment eq And corresponding equivalent moment arm Z eq The calculation formula is as follows:
δ ti the ith row of bolts are vertically deformed; k (k) ti Tensile stiffness at the ith row of bolts; delta eq Equivalent vertical deformation; z is Z i The distance from the ith row of bolts to the combining point of the left pressed T-shaped piece is set; e is the elastic modulus; z is Z c 、Z t The distance from the center of the section of the column to the resultant force point of the right pressed T-shaped piece and the resultant force point of the left pulled T-shaped piece are respectively; z is Z ， t =Z eq -Z c Wherein the arm length Z (z=z cr +Z tl ) The influence of the end plate connection of the ribbed rib plate on the position of the rotation center is considered, the combination of the numerical value and the test result shows that the stiffening rib has an inclined support function, the rotation center of the node changes along with the rotation of the node, and the rotation center is taken as the center of the column taking flange when the rigidity of the node is calculated by the combination of the numerical value and the test result.
Step seven: and obtaining an initial rigidity calculation model of the connection node taking the bending corner deformation of the steel column into consideration by using the transverse force V and the transverse displacement response recorded by experiments. By recording the transverse force and transverse displacement response, the initial rigidity and the bending rigidity K of the connecting node are obtained through conversion without considering the influence of the axial force on the bending moment at the initial stage of loading.
L columm Distance from the lateral force application point to the bottom plate; e (E) column Modulus of elasticity; i column Moment of inertia of the column cross section; θ is the toe node angle; θ column Corner deformation caused by bending of the steel column; θ base Corner deformation caused by bending of the steel column is not considered; k (k) column Flexural rigidity of the steel ball.
The above description is not intended to limit the application to the particular embodiments disclosed, but to limit the application to the particular embodiments disclosed, as many variations, modifications, additions and substitutions are possible, without departing from the scope of the application as disclosed in the accompanying claims.
Claims (8)
1. The calculation model for the strength and the rigidity of the assembled ribbed steel tube concrete column base is characterized by comprising the following steps:
step one: simplifying the column base nodes into different components according to different eccentricities;
step two: deducing a node type TypeA with only one row of anchor bolts on the tension side and column base nodes with multiple rows of anchor bolts TypeB on the tension side under the action of equal proportion loading according to the balance conditions of force and bending moment; to obtain the bending moment resistance (M) of the ribbed steel tube concrete column base node j，Rd ) Expressed as a function of load eccentricity e;
step three: considering the unequal ratio as an infinite number of equal ratio loading processes, for each applied moment value (M sd ) Calculating output quantities of the equivalent compression T-shaped piece and the equivalent tension T-shaped piece corresponding to each applied moment value;
step four: determining the relative mechanical properties-strength of each component while characterizing each component; for each ofThe test pieces are respectively provided with M values corresponding to the different damage forms, including anchor bolt damage, bottom plate buckling and column wing source buckling; by comparison of M corresponding to different forms of destruction j，Rd The value, the minimum value obtained is the bending resistance bearing capacity of the column base connecting node;
step five: all the components are simulated by using spring units or rigid rods, linear or nonlinear structures are given to the spring units, and the spring stiffness k16 representing the anchor rods and the spring stiffness k15 of the bent bottom plate and the spring stiffness k13 representing the compressed concrete are calculated;
step six: the spring units or the rigid rods are assembled into a mechanical model of an integral structure in a series-parallel connection manner, so that the integral mechanical property of the structure is obtained; deriving initial rigidity of a column base node of a node type TypeA with a row of anchor bolts on the tension side and a column base node of a column base node type with a plurality of rows of anchor bolts on the tension side; obtaining a calculation model of the initial rigidity of the ribbed concrete filled steel tube column base node;
step seven: and obtaining an initial rigidity calculation model of the connection node taking the bending corner deformation of the steel column into consideration by using the transverse force and transverse displacement response recorded by experiments.
2. The fabricated ribbed concrete-filled steel tube column base strength and rigidity calculation model of claim 1, wherein: when the eccentricity is smaller, the column foot node is simplified into a left equivalent compression T-shaped piece and a right equivalent compression T-shaped piece, and when the eccentricity is larger, the column foot node is simplified into an equivalent compression T-shaped piece and an equivalent tension T-shaped piece; considering the response of ribbed steel tube concrete column foot joints under the action of buckling, the equivalent compression T-shaped piece mainly comprises compression of a concrete foundation and compression of a column flange, and the equivalent tension T-shaped piece mainly comprises end plate buckling and anchor bolt tension.
3. The fabricated ribbed concrete-filled steel tube column base strength and rigidity calculation model of claim 2, wherein: for a toe connection node under small eccentricity conditions, each of which applies a moment value (M sd ) The function with respect to the load eccentricity e is expressed as:
small eccentricity e<zcr：
Wherein M is sd Applying a moment value to the column base; n (N) sd Pressure applied to the column shoe; f (F) cl Is stressed by the left pressed T-shaped piece; f (F) cr Is stressed by the right-side compression T-piece;
since the loading is equal-proportion, the M eccentricity remains unchanged during loading, and
f in the formula cl，Rd The compression strength of the T-shaped part pressed on the left side is the compression strength of the T-shaped part pressed on the left side; f (F) cr，Rd The compressive strength value of the right-side compression T-shaped piece; z is Z cl 、Z cr The force combining points from the center of the section of the column to the left compression T-shaped piece and the right compression T-shaped piece are respectively; setting the resultant force point of the pressed T-shaped piece as the rib plate edge by combining the numerical value and the test result;
for the column foot connection node under the working condition of large eccentricity, a row of node type TypeA of the anchor bolts exists on the tension side, a plurality of rows of column foot nodes of the anchor bolt type TypeB exist on the tension side, each of the column foot nodes applies a moment value (M j，Rd ) The function with respect to the load eccentricity e is expressed as: column foot node for TypeA type anchor arrangement:
e > zcr at large eccentricity
Due to the equal proportional loading, the M-eccentricity remains unchanged during loading, and thus is available:
the same applies to the toe node of the TypeB type anchor bolt arrangement (assuming the floor is a rigid body):
F cl，Rd the compression strength of the T-shaped part pressed on the left side is the compression strength of the T-shaped part pressed on the left side; f (F) cr，Rd The compressive strength value of the right-side compression T-shaped piece; f (F) tl，Rd Tensile strength value of the left tensile T-shaped piece; fi is the tension at the i-th row of bolts; zi is the distance from the ith row of bolts to the combining force point of the left pressed T-shaped piece; z is Z 0 The distance from the left tension T-shaped piece to the point of combining force of the left compression T-shaped piece; f (F) tl，Rd，eq Is the tensile strength value of the equivalent pressed T-shaped piece; z is Z eq Is an equivalent moment arm; z is Z cr 、Z tl The distance from the center of the section of the column to the resultant force point of the left pressed T-shaped piece, the resultant force point of the right pressed T-shaped piece and the resultant force point of the left pulled T-shaped piece are respectively; wherein the arm length Z (z=z cr +Z tl) The influence of the end plate connection of the ribbed rib plate on the position of the rotation center is considered, the combination value and the test result show that the stiffening rib shows an inclined supporting effect, the rotation center of the node changes along with the rotation of the node, and the combination value and the test result set the rotation center as the edge of the rib plate.
4. A fabricated ribbed concrete filled steel tube column base strength, stiffness calculation model as defined in claim 3, wherein: considering the unequal ratio as an infinite equal ratio loading process, the output of the equivalent compression T-piece and the equivalent tension T-piece corresponding to each applied moment value is expressed as:
small eccentricity e<z cr ：
E when large eccentric>z cr ：
。
5. The fabricated ribbed concrete-filled steel tube column base strength and rigidity calculation model of claim 4, wherein: determining the relative mechanical properties-strength of each component, the ultimate strength of an equivalent tensile T-piece can be expressed by the following relationship:
when prying force exists:
when no prying force is present:
the connecting node has a prying force if the following formula is satisfied:
wherein L is b For the length of the anchor bolt, provision is made according to the European Specification:
the design value of the bending moment bearing capacity of the bottom plate connection is equal to the standard value of the bending moment bearing capacity divided by the safety coefficient gamma M0 ：
Wherein F is t，Rd The design value of the tensile bearing capacity of the anchor bolt is equal to the standard tensile value divided by the safety coefficient gamma M2 ：
Wherein: f (f) ub The tensile strength of the anchor rod is the tensile strength; n is n b The number of the anchor bolts at the tension side; gamma ray M2 Equal to 1.25; db is the diameter of the anchor bolt; tg, tp, tw and tn are respectively the mortar layer thickness, the bottom plate thickness, the end plate height and the nut height; as is the cross-sectional area of the anchor bolt; m is M pl，1，Rd Is the plastic bending moment value of the base plate corresponding to the type 1 damage form; m is M pl，2，Rd Plastic bending moment value of the base plate corresponding to the type 2 damage form; e is the elastic modulus of the steel; m is the distance from the plastic hinge to the axis of the anchor bolt; n is the distance from the prying force to the axis of the anchor bolt; e, e w =d w 4; dw is the nut diameter of the bolt; fy is the yield strength of the bottom plate;is the effective length of the tension T-shaped flange; gamma ray M0 Equal to 1;
calculation of the bearing capacity of the equivalent compression T-shaped part, wherein the calculation comprises F controlled by the compression of the concrete foundation cl,Rd And F controlled by column flange compression cr,Rd The method comprises the steps of carrying out a first treatment on the surface of the Intensity value F controlled by failure of the pressure side assembly cl，Rd 、F cr，Rd (concrete crush, column bulge) is given by the load carrying capacity of the compression side assembly—the smaller value between the concrete compression resistance and the column section compression resistance:
in practice, the column section is resistant to bending load M due to the presence of stiffening ribs b，Rd The column section bending bearing capacity M is larger than that of the connection node of the non-stiffening end plate c，Rd The method comprises the steps of carrying out a first treatment on the surface of the When the column flange is pressed, considering the influence of the stiffening rib on the column body pressure resistance, combining the test and the finite element result to obtain that the plastic hinge is positioned at the height of the stiffening rib plate, and obtaining the corresponding ribbed steel tube concrete section pressure-resistant bearingThe value calculation formula is as follows:
wherein: f (f) jd B, compressive stress of the foundation concrete below the end plate eff And l eff Is the effective width and length of the T-shaped part on the pressed side, b eff And l eff Are all functions of equivalent width c, c being equal to 1.25 times t p ；h c Is the height of the section of the column, t cf Is the thickness of the column flange; h is the section distance from the loading point to the column bottom, h 1 The height of the rib plate is set; m is M c，Rd The bending resistance bearing capacity of the section of the concrete-filled steel tube under the action of the axial compression load (N) is calculated by utilizing the bending resistance bearing capacity of the section of the opposite concrete-filled steel tube under the action of the axial compression by utilizing x-track, wherein the steel tube and the core concrete structure are defined by utilizing auxiliary material property tests, the ideal elastoplasticity and the three-fold line are respectively adopted for simulation aiming at the constitutive curve of the steel tube, the bending resistance bearing value of the corresponding section of the concrete-filled steel tube under the action of the axial compression is obtained, and the calculated bending resistance bearing capacity of the column foot connecting node is compared with the test value and analyzed.
6. The fabricated ribbed concrete-filled steel tube column base strength and rigidity calculation model of claim 5, wherein: the flexural rigidity k15 of the base plate is calculated as follows:
when prying force exists:
when no prying force is present:
k 16 tensile stiffness of the anchor bolt:
when prying force exists:
when no prying force is present:
K t，l stiffness for the tension side assembly (anchor in tension and floor in bending):
for the compression region, the compression rigidity Kc is equal to the rigidity coefficient k13, and k13 is taken as the compression rigidity of the basic concrete:
wherein E and E c The elastic modulus of steel and concrete respectively; b eff And l eff Expressed as effective width and effective length, b, respectively, of an equivalent stressed T-piece eff And l eff Are all functions of the relationship equivalent width c, with reference to the preamble c being equal to 1.25 times t p 。
7. The fabricated ribbed concrete-filled steel tube column base strength and rigidity calculation model of claim 6, wherein: column foot node for TypeA type anchor arrangement:
column base corner:
column shoe rotational stiffness:
the above formula is combined to obtain:
toe node for TypeB type anchor arrangement:
column base corner:
column shoe rotational stiffness:
the equivalent rigidity coefficient k is obtained according to the balance of force and bending moment eq And corresponding equivalent moment arm Z eq The calculation formula is as follows:
δ ti the ith row of bolts are vertically deformed; k (k) ti Tensile stiffness at the ith row of bolts; delta eq Equivalent vertical deformation; z is Z i The distance from the ith row of bolts to the combining point of the left pressed T-shaped piece is set; e is an elastic dieAn amount of; z is Z c 、Z t The distance from the center of the section of the column to the resultant force point of the right pressed T-shaped piece and the resultant force point of the left pulled T-shaped piece are respectively; z is Z ， t =Z eq -Z c Wherein the arm length Z (z=z cr +Z tl ) The influence of the end plate connection of the ribbed rib plate on the position of the rotation center is considered, the combination of the numerical value and the test result shows that the stiffening rib has an inclined support function, the rotation center of the node changes along with the rotation of the node, and the rotation center is taken as the center of the column taking flange when the rigidity of the node is calculated by the combination of the numerical value and the test result.
8. The fabricated ribbed concrete-filled steel tube column base strength and rigidity calculation model of claim 7, wherein: according to the recorded transverse force V and transverse displacement response, in the initial loading stage, the influence of the axial force on the bending moment is not considered, and the corresponding bending moment-node rotation angle response is converted through the following equation; obtaining the bending rigidity K of the connecting node through conversion as follows;
L columm distance from the lateral force application point to the bottom plate; e (E) column Modulus of elasticity; i column Moment of inertia of the column cross section; θ is the toe node angle; θ column Corner deformation caused by bending of the steel column; θ base Corner deformation caused by bending of the steel column is not considered; k (k) column Flexural rigidity of the steel ball.
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| CN117947959A (en) * | 2024-03-27 | 2024-04-30 | 东海县建设工程质量检测中心 | Efficient auxiliary installation equipment for assembled building and supporting control method thereof |
| CN117947959B (en) * | 2024-03-27 | 2024-05-28 | 东海县建设工程质量检测中心 | Efficient auxiliary installation equipment for assembled building and supporting control method thereof |
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