CN111027157B

CN111027157B - Design method of flexible support system of double-limb combined cross-section bending column of dust remover box body

Info

Publication number: CN111027157B
Application number: CN201911323362.3A
Authority: CN
Inventors: 王登峰; 赵婧同
Original assignee: Jiangnan University
Current assignee: Jiangnan University
Priority date: 2019-12-20
Filing date: 2019-12-20
Publication date: 2021-11-02
Anticipated expiration: 2039-12-20
Also published as: CN111027157A

Abstract

The invention discloses a design method of a flexible support system of a double-limb combined cross-section bending column of a dust remover box body, belonging to the technical field of structural engineering. The invention provides a design method of a flexible support system of a bending column with a double-limb combined section of a box body of a dust remover, which can be used for designing the flexible support system consisting of a support rod and a connecting rod, is reliable and reasonable in design and has extremely high application prospect in the aspect of designing the flexible support system of the bending column with the double-limb combined section of the box body of the dust remover.

Description

Design method of flexible support system of double-limb combined cross-section bending column of dust remover box body

Technical Field

The invention relates to a design method of a flexible support system of a double-limb combined cross-section bending column of a dust remover box body, belonging to the technical field of structural engineering.

Background

The dust remover is an important environment-friendly device which is widely applied to industries such as electric power, metallurgy, chemical industry, building materials and the like and is used for eliminating smoke dust. The capture and collection of the smoke dust particles are all completed in the box body of the dust remover, so the box body is one of the most important process parts of the dust remover. The enclosure structure of the medium and large dust collector box bodies generally adopts a stiffening wallboard-H-shaped section upright post structure system or a stiffening wallboard-rectangular pipe section upright post structure system.

In order to ensure the tightness, the wall plate in the stiffening wall plate-H-shaped section upright post structure system or the stiffening wall plate-rectangular pipe section upright post structure system is continuously welded and connected with one side of the upright post. When the wallboard in the box receives the horizontal load that negative pressure and wind load formed, the horizontal load that acts on the wallboard can transmit and distribute to the stand for the stand bears the horizontal distribution load, and simultaneously, axial pressure is born at the stand top, therefore, the stand in the wallboard-H shape cross-section stand structural system of putting more energy into or the wallboard-rectangular pipe cross-section stand structural system of putting more energy into is actually a buckling component, i.e. the buckling post.

Due to the process requirements in the aspect of discharge distance and the design consideration in the aspects of strength and stability when bearing larger load, the upright columns in the stiffening wallboard-H-shaped section upright column structure system or the stiffening wallboard-rectangular tube section upright column structure system of some dust collectors can be designed into a wider section, namely a double-limb combined section is adopted. Two single-limb bending columns with double-limb combined sections are connected at the neutral axis position by adopting a stiffening connecting wallboard with an angle steel stiffening rib. In order to reduce the slenderness ratio of the single-limb bending column in the double-limb combined section column and improve the rigidity of the double-limb combined section column, a support rod (usually a hot-rolled circular steel tube) perpendicular to the direction of the box body wall plate and the connecting wall plate between two limbs is arranged on the whole double-limb combined section column to provide transverse support for the two single-limb bending columns.

In order to provide support in a transverse load action plane for two single-limb bending columns at the same time, the arrangement modes of the support rods are mainly two, one is a conventional support mode that the support rods are directly welded on the two single-limb bending columns in the double-limb combined section column (if the support rods are H-shaped section single-limb bending columns, the support rods directly act on the flange middle points of the single-limb bending columns), and in the support mode, the support rods independently form a support system, namely the conventional flexible support system of the double-limb combined section bending columns of the dust remover box body; the other type is a special flexible supporting system which is characterized in that connecting rods (usually hot rolled channel steel) are connected between single-limb bending columns, a support rod does not directly act on the single-limb bending columns but is supported at the middle point of the connecting rods between the two single-limb bending columns, the support rod is indirectly connected with the middle point of the connecting rods to form a supporting mode of translational restraint in the direction vertical to the wall plate of the two single-limb bending columns, and in the supporting mode, the support rod and the connecting rods jointly form a supporting system, namely the special flexible supporting system of the double-limb combined section bending column of the dust remover box body.

At present, when a stiffening wallboard-H-shaped section upright column structure system or a stiffening wallboard-rectangular pipe section upright column structure system of a dust remover box body is designed, in order to ensure the integral stability of the structure and the reliability and effectiveness of a supporting system, the flexible supporting system of the double-limb combined section bending column needs to be structurally designed. However, in the prior art, only a design method for a conventional axial compression column flexible support system (see the reference in the specification of steel structure stability design manual (the third edition)) exists, and a design method for a bending column special flexible support system does not exist, which greatly increases the actual design and manufacturing difficulty of the special flexible support system. Therefore, a design method of a special flexible support system of the double-limb combined cross-section bending column is urgently needed to be developed.

Disclosure of Invention

[ problem ] to

The invention aims to provide a structural design method of a flexible support system of a double-limb combined cross-section bending column of a dust remover box body.

[ solution ]

In order to solve the technical problem, the invention provides a design method of a flexible support system of a double-limb combined cross-section bending column of a box body of a dust remover, which comprises the following steps:

the method comprises the following steps: designing a double-limb combined section bending column of a flexible supporting system according to requirements, and preliminarily trying to set the preset sectional area value of a middle support rod in the flexible supporting system to be A₁The preset value of the minimum turning radius of the cross section is i₁(ii) a Determining the total height L of the upright column, the height L of the support column and the length L of the middle support rod of the double-limb combined section bending column of the flexible support system₁The value of (d); calculating the initial supporting rigidity gamma of the flexible supporting system according to the preset value and the numerical value₀；

Initial support stiffness γ₀Calculated according to the following formula:

where ζ is a coefficient in which the nonlinear influence of the decrease in the rigidity of the flexible support system with the increase in the supporting force is taken into consideration, and E is the structural steel elastic modulus, and the above formula is calculated such that E is 2.06 × 10⁵N/mm²；

The flexible supporting system is made of Q235 steel or Q345 steel, and the middle supporting rod is a type a section or a type b section of the axial compression member;

when the material of the flexible supporting system is Q235 steel and the middle support rod is a class a section of the axial center compression member, a coefficient zeta considering the nonlinear influence that the rigidity of the flexible supporting system is reduced along with the increase of the supporting force satisfies the following formula:

when the material of the flexible supporting system is Q235 steel and the middle support rod is a b-type section of the axial center compression member, a coefficient zeta considering the nonlinear influence that the rigidity of the flexible supporting system is reduced along with the increase of the supporting force satisfies the following formula:

when the material of the flexible supporting system is Q345 steel and the middle support rod is a class a section of the axial center compression member, a coefficient zeta considering the nonlinear influence that the rigidity of the flexible supporting system is reduced along with the increase of the supporting force satisfies the following formula:

when the material of the flexible supporting system is Q345 steel and the middle support rod is a b-type section of the axial compression member, a coefficient zeta considering the nonlinear influence that the rigidity of the flexible supporting system is reduced along with the increase of the supporting force satisfies the following formula:

in the formula, λ₁The length-to-thickness ratio of the middle support rod is obtained;

length-thin ratio lambda of middle stay bar₁Satisfies the following formula:

λ₁＝l₁/i₁；

among the above values, the sectional area of the middle stay bar is preset value A₁In mm unit²Length of middle stay bar l₁The unit of (1) is mm, the unit of the preset value i of the minimum turning radius of the cross section of the strut is mm, and the unit of the elastic modulus E of the material is N/mm²Initial support stiffness γ₀The unit of (A) is N/mm;

step two: determining an axial pressure design value N borne by the top of a double-limb combined cross-section bending column of a flexible supporting system to be designed, transversely and uniformly distributing load design values q borne by a span, and calculating to obtain the maximum supporting force F of the single-limb bending column according to the axial pressure N, the transversely and uniformly distributed load q, the linear rigidity K of the single-limb bending column, the height l of a supporting column, the supporting rigidity gamma of the flexible supporting system and the number N of middle supports;

when n is 1, the maximum supporting force F satisfies the following formula:

F＝γΔ_AB；

in the formula,. DELTA._ABThe deflection of the single-limb bending column at the middle supporting position is obtained by taking gamma as gamma in the formula during initial calculation₀Taking the section specification of the middle supporting rod and the section specification of the connecting rod after determining

Deflection delta of single-limb bending column at middle support_ABSatisfies the following formula:

wherein C and S are flexural rigidity coefficient of single-limb bending column, M_FBAThe bending moment at the fixed end of the single-limb bending column segment is hinged at one end and fixedly connected at one end, K is the linear rigidity of the single-limb bending column, and L is L/2;

in the above numerical values, the unit of the height l of the support column is mm, the unit of the axial pressure N is N, the unit of the transversely uniformly distributed load q is N/mm, and the deflection delta of the single-limb bending column at the middle support part_ABThe unit of (3) is mm, the unit of the linear rigidity K of the single-limb bending column is N.mm, and the unit of the supporting rigidity gamma is N/mm;

when n is 2, the maximum supporting force F satisfies the following formula:

F＝γΔ_AB；

in the formula,. DELTA._ABThe deflection of the single-limb bending column at the middle L/3 and 2L/3 column heights is obtained by taking gamma as gamma in the formula during initial calculation₀Taking the section specification of the middle supporting rod and the section specification of the connecting rod after determining

Middle L/3 and 2L/3 column height displacement delta_ABSatisfies the following formula:

wherein C and S are flexural rigidity coefficient of single-limb bending column, M_FBAFor bending the fixed end bending moment of a column segment for a single limb with one hinged end and one fixed end, M_FBCThe fixed end bending moment of the bending component is fixedly connected with the two ends, K is the linear rigidity of the single-limb bending column, and L is equal to L/3;

in the numerical values, the unit of the height L of the support columns is mm, the unit of the axial pressure N is N, the unit of the transversely uniformly distributed load q is N/mm, and the deflection delta of the single-limb bending column at the middle L/3 and 2L/3 column heights_ABThe unit of (3) is mm, the unit of the linear rigidity K of the single-limb bending column is N.mm, and the unit of the supporting rigidity gamma is N/mm;

when n is 3, the maximum supporting force F satisfies the following formula:

F＝γΔ_AC；

in the formula,. DELTA._ACFor the mid-span deflection of the single-limb bending column, the formula is that gamma is taken as gamma in the initial calculation₀Taking the section specification of the middle supporting rod and the section specification of the connecting rod after determining

Mid-span deflection delta of single-limb bending column_ACSatisfies the following formula:

Δ_AC＝Δ_AB+Δ_BC；

in the formula, c₁₁＝K(C+S)，c₁₂＝－γl/2，c₁₃＝N－γl/2－2K(C+S)/l，c₂₁＝KC，c₂₂＝3γl/2－N，c₂₃＝γl/2－K(C+S)/l，c₃₁＝K(2C²－S²)/C，c₃₂＝K(S²－C²)/(Cl)，c₃₃＝－K(C+S)/l，d₁＝－ql²/2，d₂＝3ql²/2－M_FBC，d₃＝－M_FBC－M_FBA；θ_AFor bending the column corner, theta, at the column top for a single limb_BFor single limb bending column corner, delta, at quarter column height_ABAnd Δ_ACRespectively the deflection of one fourth of the single-limb bending column and the deflection of one half of the column height (because of symmetry, the column corner at the column top of the single-limb bending column is equal to the column corner at the column bottom of the single-limb bending column, the column corner at the column height of one fourth of the single-limb bending column is equal to the column corner at the column height of three fourth of the single-limb bending column, the deflection of the bending column at the column height of one fourth of the single-limb bending column is equal to the deflection of the bending column at the column height of three fourth of the single-limb bending column), delta_BCThe deflection of the high part of the column is increased relative to the deflection of the high part of the column, C and S are the bending rigidity coefficient of the single-limb bending column, M_FBAFor bending the fixed end bending moment of a column segment for a single limb with one hinged end and one fixed end, M_FBCThe fixed end bending moment of the bending component is fixedly connected with the two ends, K is the linear rigidity of the single-limb bending column, and L is equal to L/4;

in the above numerical values, the unit of the height l of the column between the supports is mm, the unit of the axial pressure N is N, the unit of the transversely uniformly distributed load q is N/mm, and the deflection value delta of each item of the column is_AC、Δ_ABAnd Δ_BCThe unit of (3) is mm, the unit of the linear rigidity K of the single-limb bending column is N.mm, and the unit of the supporting rigidity gamma is N/mm;

when n is 4, the maximum supporting force F satisfies the following formula:

F＝γΔ_AC；

in the formula,. DELTA._ACThe deflection of the single-limb bending column at the 2L/5 and 3L/5 column heights is obtained by taking gamma as gamma in the formula during initial calculation₀Taking the section specification of the middle supporting rod and the section specification of the connecting rod after determining

2L/5 and 3L/5 column height parts of single-limb bending columnDeflection delta_ACSatisfies the following formula:

Δ_AC＝Δ_AB+Δ_BC；

Δ_AB＝(Cθ_A+Sθ_B)l/(C+S)；

Δ_BC＝l[(2C－S)θ_C+Sθ_B]/(C+S)；

in the formula, a₁₁＝K(S－C)，a₁₂＝2K(C－S)，a₁₃＝2K(S－C)，a₂₁＝K(S²－C²)+(Nl－2γl²)C，a₂₂＝K(C²－S²)+(Nl－3γl²)S，a₂₃＝γl²(S－2C)，a₃₁＝－Cγl²，a₃₂＝K(C²－S²)+(Nl－2γl²)S，a₃₃＝3K(S²－C²)+(Nl－γl²)(2C－S)，b₁＝－M_FBA－M_FBC，b₂＝－(C+S)(M_FBA+2ql²)，b₃＝－(C+S)ql²；θ_AFor bending the column corner, theta, at the column top for a single limb_BThe column corner theta at the height of one fifth of the column is formed by pressing a single limb_CThe column corner, delta, at two fifths of the height of the column for single limb bending_ABThe deflection of the bending column at the height of one fifth of the bending column of the single limb (because of symmetry, the column corner at the top of the bending column of the single limb is equal to the column corner at the bottom of the bending column of the single limb, the column corner at the height of one fifth of the bending column of the single limb is equal to the column corner at the height of four fifth of the bending column of the single limb, the column corner at the height of two fifth of the bending column of the single limb is equal to the column corner at the height of three fifth of the bending column of the single limb, the deflection of the bending column at the height of one fifth of the bending column of the single limb is equal to the deflection of the bending column at the height of four fifth of the bending column of the single limb), delta_BCThe deflection of the single-limb bending column at the height of two fifths of the column is increased compared with the deflection of the single-limb bending column at the height of one fifths of the column, and C and S are bending rigidity coefficients of the single-limb bending column，M_FBAFor bending the fixed end bending moment of a column segment for a single limb with one hinged end and one fixed end, M_FBCThe fixed end bending moment of the single-limb bending column segment is fixedly connected with two ends, K is the linear rigidity of the single-limb bending column, and L is L/5;

in the above numerical values, the unit of the height l of the column between the supports is mm, the unit of the axial pressure N is N, the unit of the transversely uniformly distributed load q is N/mm, and the deflection value delta of each item of the column is_AC、Δ_ABAnd Δ_BCIn units of mm, the displacement delta at the column heights of the middle L/5 and 4L/5_ABThe unit of (3) is mm, the unit of the linear rigidity K of the single-limb bending column is N.mm, and the unit of the supporting rigidity gamma is N/mm;

when n is greater than 4, calculating the maximum supporting force F according to the condition that n is 4;

wherein, the bending rigidity coefficient C of the single-limb bending column meets the following formula:

the bending rigidity coefficient S of the single-limb bending column meets the following formula:

in the formula, k is a calculation coefficient;

the calculation coefficient k satisfies the following formula:

fixed end bending moment M of single-limb bending column segment with one hinged end and one fixed end_FBAThe following formula is satisfied such that the pole segments are positive for clockwise rotation and negative for counterclockwise rotation:

two ends fixed single limb bending column segmentFixed end bending moment M_FBCThe following formula is satisfied such that the pole segments are positive for clockwise rotation and negative for counterclockwise rotation:

the linear rigidity K of the single-limb bending column meets the following formula:

K＝EI_c/l；

in the formula I_cThe bending moment of inertia of the section of the single-limb bending column around the bending axis of the single-limb bending column is E, and the elasticity modulus of structural steel is E;

the single-limb bending column is biaxial symmetric hot-rolled section steel or a welded combined section component;

when the single-limb bending column is hot-rolled section steel, the section inertia moment I of the single-limb bending column around the bending axis thereof_cCan be obtained by directly inquiring a profile steel table;

when the single-limb bending column is a welding combined section component, if the single-limb bending column is a welding H-shaped section, the section inertia moment I of the single-limb bending column around the bending axis thereof_cSatisfies the following formula:

wherein H is the total height of the welded H-shaped section, B is the width of the welded H-shaped section, t₁For welding webs of H-section, t₂The thickness of the flange of the H-shaped section;

if the single-limb bending column is the section of the welded rectangular pipe, the section inertia moment I of the single-limb bending column around the bending axis thereof_cSatisfies the following formula:

in the formula, a₁For welding the length of the cross-section of rectangular tubes parallel to the bending axis, a₂For welding the length of the rectangular tube cross-section perpendicular to the bending axis, t' is the weldConnecting the wall thickness of the section of the rectangular pipe;

if the single-limb bending column is the section of the welded circular tube, the section inertia moment I of the single-limb bending column around the bending axis thereof_cSatisfies the following formula:

I_c＝π[D⁴-(D-2t″)⁴]/64

in the formula, D is the outer diameter of the section of the welding circular tube, and t' is the wall thickness of the section of the welding circular tube;

of the above numerical values, M_FBAHas the unit of N.mm, M_FBCHas a unit of N.mm, and the section inertia moment I of the single-limb bending column around the bending axis thereof_cIn mm unit⁴；

Step three: requires the flexural integral stability of the connecting rod to calculate the stress sigma_cr2Not exceeding the design value f of the strength of the connecting rod steel₂Calculating the stress sigma from the flexural global stability of the connecting rod_cr2Calculating to obtain the section modulus W of the connecting rod around the bending axis₂A lower limit value of (d); tangential supporting rigidity gamma provided by flexible supporting system to single-limb upright post_TIs more than or equal to the lower limit value gamma of the supporting rigidity requirement of the flexible supporting system on the single-limb upright post_crTangential support stiffness γ to the single-limb column provided by the flexible support system_TCalculating to obtain the inertia moment I of the section of the connecting rod around the bending axis of the connecting rod₂A lower limit value of (d); according to the section modulus W of the connecting rod about its bending axis₂And the section moment of inertia I₂The section specification of the connecting rod is preliminarily determined by inquiring a profile steel table;

section modulus W of connecting rod around bending axis thereof₂Satisfies the following formula:

in the formula I₂As the length of the connecting rod,

the above formula is taken in the preliminary calculation for the overall stability factor when the connecting rod is used as a flexural member

f₂Determining according to the steel product trade mark of the steel product used by the connecting rod and the design standard of the steel structure;

tangential support stiffness gamma provided by flexible support system to single-limb upright column_TSatisfies the following formula:

wherein eta is the ratio of the bending flexibility of the connecting rod to the axial compression flexibility of the middle stay bar, F_EIs the euler critical force of the middle stay bar;

euler critical force F of middle stay_ESatisfies the following formula:

F_E＝π²EA₁/λ₁ ²；

moment of inertia I of the cross-section of the connecting rod about its bending axis₂And the ratio eta of the bending flexibility of the connecting rod to the axial flexibility of the middle support rod meets the following formula:

of the above values, the link length l₂In mm, the second moment of inertia of the section of the connecting rod about its axis of bending I₂In mm unit⁴Section modulus W of connecting rod around bending axis thereof₂In mm unit³Tangential support stiffness gamma provided by the flexible support system to the single-limb upright_THas the unit of N/mm, and the lower limit value gamma of the supporting rigidity requirement of the flexible supporting system on the single-limb upright post_crHas a unit of N/mm, a unit of N is the maximum supporting force F, and the Euler critical force F of the middle supporting rod_EThe unit of (a) is N;

step four: obtaining the section modulus W of the connecting rod around the bending axis according to the section specification of the connecting rod preliminarily determined in the step three₂And the section moment of inertia I₂The actual value of (c); according to the section inertia of the connecting rod around the bending axis preliminarily determined in the third stepMoment of sex I₂Calculating the actual values to obtain the ratio eta of the bending flexibility of the connecting rod to the axial flexibility of the middle support rod and the actual support rigidity gamma provided by the flexible support system to the single-limb upright post; substituting the actual support stiffness gamma provided by the flexible support system for the single-limb upright column into the second step to recalculate to obtain the maximum support force F; substituting the recalculated maximum supporting force F into the step three to recalculate the flexural integral stability calculation stress sigma of the connecting rod by checking_cr2And the tangential supporting rigidity gamma provided by the flexible supporting system to the single-limb upright post_TWhether the requirement is met or not, and checking the axial pressure integral stable bearing capacity F of the middle supporting rod according to the maximum supporting force F obtained by recalculation_crWhether the requirement is met, wherein the stress sigma is calculated by calculating the flexural integral stability of the connecting rod_cr2Overall stability factor when the connecting rod is used as a flexural member

The integral stability coefficient of the bent member in the steel structure design standard is determined according to the section specification of the connecting rod; calculating stress sigma if the whole of the connecting rod is bent stably_cr2If the requirement is not met, the connecting rod with a larger section needs to be replaced, and the section modulus W of the connecting rod with the larger section around the bending axis of the connecting rod with the larger section is used₂' Replacing original design connecting rod section modulus W₂If the flexible support system provides tangential support stiffness gamma to the single-limb upright column_TAnd the bearing capacity F of the middle support rod for stabilizing the whole axle pressure_crIf one of the two does not meet the requirement, the middle stay bar with a larger cross section needs to be replaced so as to increase the cross section determination value A of the middle stay bar in the rear flexible supporting system₁' Preset value of cross-sectional area of middle stay bar in alternative flexible supporting system A₁To increase the minimum turning radius i of the section of the rear middle strut₁' Preset value of radius of gyration of section in place of middle stay i₁And repeating the first step to the fourth step until the stress sigma of the whole bending stability of the connecting rod is calculated_cr2The tangential supporting rigidity gamma provided by the flexible supporting system to the single-limb upright column_TAnd the bearing capacity F of the middle support rod for stabilizing the whole axle pressure_crAll meet the requirements;

the actual support stiffness gamma provided by the flexible support system to the single-limb upright column satisfies the following formula:

stress sigma is calculated by integral stability of bending of connecting rod_cr2The requirements to be met are as follows:

the ratio eta of the bending flexibility of the connecting rod to the axial flexibility of the middle support rod meets the following formula:

tangential support stiffness gamma provided by flexible support system to single-limb upright column_TThe requirements to be met are as follows:

bearing capacity F of middle stay bar for integrally stabilizing axial compression_crThe requirements to be met are as follows:

2F≤F_cr；＝

bearing capacity F of middle stay bar for integrally stabilizing axial compression_crSatisfies the following formula:

in the formula (I), the compound is shown in the specification,

the axial compression integral stability coefficient of the middle stay bar is determined according to the slenderness ratio lambda of the middle stay bar₁And the section classification of the axial compression steel member is determined according to the Steel Structure design Standard f₁Steel material for supporting rod at middle partThe strength design value is determined according to the steel structure design standard according to the steel product grade of the steel used for the middle stay bar;

among the above values, the design value f of the strength of the steel material of the middle stay bar₁Has a unit of N/mm²And the bearing capacity F of the middle support rod is integrally stabilized by axial compression_crThe unit of (d) is N.

In one embodiment of the invention, the double-limb combined-section bending column comprises two single-limb bending columns, a connecting wallboard welded between the two single-limb bending columns, and a stiffening rib welded on the connecting wallboard and vertical to the two single-limb bending columns; the flexible supporting system of the double-limb combined cross-section bending column comprises a connecting rod and a middle supporting rod; the connecting rod is welded between the two single-limb bending columns and is positioned on the connecting line of the centroids of the sections of the two single-limb bending columns; the middle stay bar is perpendicular to the connecting wall plate and welded at one half of the connecting rod in the length direction.

In one embodiment of the invention, the single-limb bending column is a biaxial symmetric steel member, and H-shaped cross-section and rectangular pipe cross-section steel members are more adopted in the engineering.

In one embodiment of the present invention, when the single-limb bending column is an H-shaped section steel member, the connecting wall plate is welded between the webs of the two single-limb bending columns, and the connecting rod is welded between the webs of the two single-limb bending columns.

In one embodiment of the invention, the connecting rod is a symmetrical section steel member.

In one embodiment of the present invention, the link is a channel steel, a rectangular tube-section steel member, or an H-section steel member.

In an embodiment of the present invention, when the connecting rod is a channel, the connecting rod includes a channel flange and a channel web, the opening of the connecting rod faces downward (toward the column bottom), the channel flange is parallel to the connecting wall plate, the channel web is perpendicular to the connecting wall plate, and the middle brace is welded to the channel flange.

In one embodiment of the invention, the middle stay is a steel member having a biaxial symmetric section.

In one embodiment of the present invention, the middle stay is a circular-tube-section steel member, a rectangular-tube-section steel member, or an H-section steel member.

In one embodiment of the present invention, the cross section of the middle stay is a cross section of the middle stay perpendicular to the Y axis.

In one embodiment of the invention, the total height of the upright column is the total height of the single-limb bending column.

In one embodiment of the invention, the inter-strut height refers to the spacing between the middle struts, i.e. the lateral strut spacing of the single-limb bending strut.

In one embodiment of the invention, a single limb with one end hinged and one end fixed bends the fixed end bending moment of the column section to make the clockwise rotation of the column section positive and the counterclockwise rotation of the column section negative.

In one embodiment of the invention, the span is the distance between adjacent support points of the members.

In one embodiment of the invention, when n ≧ 1, the middle supports are equally spaced.

The invention also provides application of the design method in designing the flexible support system of the double-limb combined section bending column.

In one embodiment of the invention, the flexible supporting system of the double-limb combined-section bending column bears the combined action of transversely uniform load and axial pressure of the column top.

In one embodiment of the invention, the flexible supporting system of the double-limb combined cross-section bending column is a flexible supporting system of a double-limb combined cross-section bending column of a dust remover box body.

[ advantageous effects ]

The invention provides a design method of a flexible support system of a bending column with a double-limb combined section of a box body of a dust remover, which can be used for designing the flexible support system consisting of a support rod and a connecting rod, is reliable and reasonable in design and has extremely high application prospect in the aspect of designing the flexible support system of the bending column with the double-limb combined section of the box body of the dust remover.

Drawings

FIG. 1 is a schematic view of a three-dimensional model of a stiffened wall panel-column structure system of a dust collector box body envelope.

Fig. 2 is a schematic front view of a flexible supporting system of a double-limb combined cross-section bending column of a dust remover box body.

FIG. 3 is a schematic top view of a flexible support system of a double-limb combined cross-section press bending column of a dust remover box body.

In fig. 1-3, 1 is a single-limb bending column, 2 is a box body wallboard, 3 is a box body wallboard stiffening rib, 4 is a flexible supporting system, 5 is a connecting rod, 6 is a middle supporting rod, 7 is a front flange of a single-limb upright column with an H-shaped cross section, 8 is a rear flange of the single-limb upright column with the H-shaped cross section, 9 is a web of the single-limb upright column with the H-shaped cross section, 10 is a connecting wallboard between two limbs, 11 is an angle steel stiffening rib on the connecting wallboard, 12 is a flange of a channel steel connecting rod, and 13 is a web of the channel steel connecting rod.

FIG. 4 is a schematic view of a press bending column with a center support.

Figure 5 is a schematic diagram of a press bending column calculation with four mid-supports.

FIG. 6 is a graph showing the relationship between the supporting force and the supporting rigidity (with four middle supports) under different parameters.

Fig. 7 shows the deformation of a central strut with an initial defect under axial force.

Fig. 8 is a schematic of the deformation at the support point.

FIG. 9 is a graph of the value of 2/(2+ ζ) versus the value of ψ.

FIG. 10 is a plot of maximum deflection Δ at the support point versus the value of η.

Fig. 11 is a graph of maximum support force F versus η at the support point.

Detailed Description

The invention will be further elucidated with reference to the embodiments and the drawings.

The calculations for studying the two-limb combination cross-section buckling columns in the following examples are assumed to be: the two ends of the bending column are restrained by the simple supports, the top of the column is stressed by axial pressure N, and the midspan is stressed by transversely and uniformly distributed loads q. In the following examples, it is considered that the central struts are equally spaced, assuming equal column lengths l and equal linear stiffnesses between the support points, K-EI_cL is calculated as follows. Due to current engineering design not consideringPlasticity development, elasticity calculations are used in the examples below. Since the response of the press bending member is non-linear, influenced by the load path, the following example assumes in the calculation that the laterally uniform load on the press bending column increases in proportion to the concentrated pressure at the top of the column in synchronism with the increase in the load.

The first step is calculation of the supporting force borne by the double-limb combined section bending column:

a simplified calculation diagram of the buckling column with a middle brace is shown in figure 4, considering the symmetry of the structure and the load, and the turning angle theta of the point B_B＝0，θ_A＝－θ_C；

M_AB＝K[Cθ_A+Sθ_B－(C+S)Δ_AB/l]＝0；

M_BA＝K[Cθ_B+Sθ_A－(C+S)Δ_AB/l]+M_FBA＝K(S－C)θ_A+M_FBA；

Wherein C and S are bending rigidity coefficients of the single-limb bending column,

M_FBAthe fixed end bending moment of the single-limb bending column segment with one end hinged (point A in the figure) and one end fixedly connected (point B in the figure) is calculated:

(the bending moment is positive to rotate the column section clockwise and negative to rotate the column section counter-clockwise).

The bending moment balance condition of the AB section is as follows:

M_BA+NΔ_AB+F_Al－ql²/2＝0；

from the horizontal force balance conditions:

F_A＝ql－F_B/2；

the conditions of coordination of the deformation at the support can be derived:

F_B＝γΔ_AB；

wherein gamma is the axial deformation rigidity of the middle support rod;

the calculation formula is arranged to obtain:

a simplified calculation diagram of the buckling column with four middle support rods is shown in FIG. 5, considering the symmetry of the structure and the load, theta_D＝－θ_C；

For point A, there are:

M_AB＝K[Cθ_A+Sθ_B－(C+S)Δ_AB/l]＝0；

∴Cθ_A+Sθ_B＝(C+S)Δ_AB/l；

for point B:

M_BA＝K[Cθ_B+Sθ_A－(C+S)Δ_AB/l]+M_FBA；

M_BC＝K[Cθ_B+Sθ_C－(C+S)Δ_BC/l]+M_FBC；

M_BA+M_BC＝0；

in the formula, MFBC is fixed end bending moment with two ends fixedly connected with a single limb bending column segment,

for point C:

M_CB＝K[Cθ_C+Sθ_B－(C+S)Δ_BC/l]+M_FCB；

M_CD＝K(Cθ_C－Sθ_C)+M_FCD；

∵M_CB+M _CD0, and M_FCB＝－M_FCD；

∴(2C－S)θ_C+Sθ_B＝(C+S)Δ_BC/l；

The bending moment balance condition of the AB section is as follows:

M_BA+NΔ_AB+F_Al－ql²/2＝0；

in the formula, F_A＝5ql/2－F_B－F_C，F_B＝γΔ_AB，F_C＝γ(Δ_AB+Δ_BC)；

The bending moment balance condition of the BC section is obtained as follows:

M_CB+M_BC+NΔ_BC+(3ql/2－F_C)l－ql²/2＝0；

after the above calculation formulas are arranged, the value of theta can be obtained_A、θ_BAnd theta_CExpressed in the form:

in the formula, a₁₁＝K(S－C)，a₁₂＝2K(C－S)，a₁₃＝2K(S－C)，a₂₁＝K(S²－C²)+(Nl－2γl²)C，a₂₂＝K(C²－S²)+(Nl－3γl²)S，a₂₃＝γl²(S－2C)，a₃₁＝－Cγl²，a₃₂＝K(C²－S²)+(Nl－2γl²)S，a₃₃＝3K(S²－C²)+(Nl－γl²)(2C－S)，b₁＝－M_FBA－M_FBC，b₂＝－(C+S)(M_FBA+2ql²)，b₃＝－(C+S)ql²。

Solved to theta_A、θ_BAnd theta_CThen, the delta can be obtained_ABAnd Δ_BCAnd then obtaining the supporting force at each supporting point:

F_B＝γΔ_AB，F_C＝γ(Δ_AB+Δ_BC)；

can be solved by the same method to have two middle partsThe deflection of the bending column at the supporting point when the supporting rod is propped is shown as the following formula, and the supporting force is F_B＝γΔ_AB；

The deflection value of the bending column at the supporting point when three equidistant middle supporting rods exist can be obtained by solving the following linear equation set:

in the formula, c₁₁＝K(C+S)，c₁₂＝－γl/2，c₁₃＝N－γl/2－2K(C+S)/l，c₂₁＝KC，c₂₂＝3γl/2－N，c₂₃＝γl/2－K(C+S)/l，c₃₁＝K(2C²－S²)/C，c₃₂＝K(S²－C²)/(Cl)，c₃₃＝－K(C+S)/l，d₁＝－ql²/2，d₂＝3ql²/2－M_FBC，d₃＝－M_FBC－M_FBA；

In the formula, theta_BIs the column angle at L/4 column height, Delta_ABAnd Δ_AC＝(Δ_AB+Δ_BC) The bending column deflection at L/4 and L/2 respectively.

In order to verify the correctness of the analytical solution, the analytical method and the finite element method proposed herein are respectively adopted for several embodiments to solve the bending column bending value at the supporting point. The finite element solution is carried out by adopting an ANSYS program, a single-limb bending column is simulated by adopting a BEAM188 BEAM unit, a strut is simulated by adopting a COMBIN14 spring unit, the geometric nonlinear effect is considered, the structural steel adopts an elastic body, and the elastic modulus E is 2.06 multiplied by 10⁵MPa。

Example 1:

the height L of the upright post of the dust remover box body is 16460 mm; the number n of the supports in the middle of the upright is 1; the height l of the support column is 8230mm, and the section inertia moment I of the single-limb bending column_cIs 1.14X 10⁸mm⁴Branch and branchThe support rigidity gamma is 91391N/mm; the axial pressure N was 314000N, the lateral load q was 37.31N/mm, and the buckling column deflection values at the support points calculated using the first step analytical solution and the nonlinear finite element solution are shown in table 1.

Example 2 to example 4:

examples 2 to 4 with respect to example 1, only the number n of supports in the middle of the column was changed, and the specific structural parameters and the bending column deflection values at the support points calculated by the analytic solution of the first step and the nonlinear finite element solution are shown in table 1.

Example 5:

the height L of the upright post of the dust remover box body is 18000 mm; the number n of the supports in the middle of the upright is 1; the height l of the support column is 9000mm, and the section inertia moment I of the single-limb bending column_cIs 1.31X 10⁸mm⁴The supporting rigidity gamma is 120709N/mm; the axial pressure N was 462300N, the lateral load q was 42.64N/mm, and the buckling column deflection values at the support points calculated using the first step analytical solution and the nonlinear finite element solution are shown in table 1.

Example 6 to example 7:

examples 6 to 7 with respect to example 5, only the number n of supports in the middle of the column was changed, and the specific construction parameters and the bending column deflection values at the support points calculated by the analytic solution of the first step and the nonlinear finite element solution are shown in table 1.

Example 8:

example 8 only the bending column section moment of inertia I was changed from example 4_cIs 9.74 multiplied by 10⁷mm⁴. The specific construction parameters and the bending values of the buckling column at the supporting points calculated by the analytic solution of the first step and the nonlinear finite element solution are shown in table 1.

Example 9:

example 9 only the strut stiffness γ was changed to 73113N/mm relative to example 4. The specific construction parameters and the bending values of the buckling column at the supporting points calculated by the analytic solution of the first step and the nonlinear finite element solution are shown in table 1.

Example 10:

example 10 only the loading was changed relative to example 4: n was 471000N and the transverse load q was 55.97N/mm. The specific construction parameters and the bending values of the buckling column at the supporting points calculated by the analytic solution of the first step and the nonlinear finite element solution are shown in table 1.

TABLE 1 comparison of bending values of a bending column at a support point calculated by the method of the present invention and a finite element method

Note: delta_AC＝Δ_AB+Δ_BC。

The comparison of the calculation results shows that the maximum deviation of the analytic solution and the nonlinear finite element solution is 1.6%, and the analytic solution is accurate and reliable. When the single-limb buckling column height, the single-limb buckling column section moment of inertia, the middle support rod rigidity and the load are unchanged through examining comparative examples 1 to 4 and examples 5 to 7, the calculation result shows that the larger the number of middle supports, the smaller the deflection at the support point and the smaller the required support force. The more the number of supports is, the more the calculation result tends to be equal, therefore, when the number of middle support rods exceeds 4, the supporting force can be calculated by 4 middle support rods in a biased manner. Considering comparative example 4 and example 8, when the total height of the upright post, the rigidity of the middle support rod, the support number and the load are not changed, the linear rigidity of the single-limb bending column is reduced (actually, the bending rigidity of the upright post is weakened), the maximum bending value at each support point is increased, and the maximum support force is increased. The relationship curve of the maximum supporting force and the supporting rigidity when the K, l, N and q values are different is shown in figure 6. Examining the curves of comparative example 4, example 9 and fig. 6, the support stiffness was increased, the deflection value at the support point was significantly decreased, and the support force was increased to a small extent. This shows that the influence of the stiffness of the middle stay bar on the supporting force is small when the linear stiffness of the single-limb bending column, the height of the single-limb bending column and the supporting number and load are unchanged.

The second step is that the support rigidity of the flexible support system formed by the middle support rod and the connecting rod of the double-limb combined section bending column is calculated:

considering the initial deflection and the manufacturing and installation deviation of the middle stay bar under the action of the dead weight, the initial deformation of the middle stay bar is as follows:

in the formula, w₀The initial deflection of the middle stay bar is shown, and xi is the axial distance from any point on the stay bar to the far end (the end far away from the connecting rod) of the stay bar;

after receiving the strut force of 2F, the deformation is shown in fig. 7 as follows:

in the formula, A_mTo take into account the amplification factor of the second order effect,

F_Eis the euler critical force of the middle stay bar;

the axial deformation of the strut caused by bending is:

considering the bending deformation of the intermediate connecting rod, for the single-limb upright post, the deformation at the supporting action point is as shown in the attached figure 8, the two limbs are connected by the steel plate, because the steel plate is thin, the bending rigidity of the plate is safe, and the deformation at the supporting point is as follows:

for the middle stay bar, taking the initial deflection under the action of self weight and the manufacturing and mounting deviation into consideration₀＝l₁/500：

The secant stiffness γ of the support system is:

the rigidity of the support system decreases with increasing support force due to the consideration of the initial geometrical defects of the struts, and is non-linear, such that psi is F/F_E；

Eta is the ratio of the bending flexibility of the connecting rod to the axial flexibility of the middle support rod; while

Then there are:

when the supporting force is calculated in the first step, the calculation derivation of the bending column bending value and the supporting force at the middle supporting point is based on the constant stiffness, the stiffness of the actual supporting system changes along with the increase of the load, so that an accurate solution can be obtained only by setting an initial stiffness value and then carrying out iterative calculation, the process is complex, and the method is not easy to apply in engineering, so that a simple and convenient method for determining the initial supporting stiffness which is deviated from safety is derived in the following.

Middle stay bar slenderness ratio lambda of bending column in dust remover₁Generally controlled between 90 and 150, and the supporting force born by the middle supporting rod is 2F or less and F or less_cr(F_crTo stabilize the bearing capacity for the axial compression of the strut), thus:

middle part of dust removerThe stay bar is generally made of Q235 or Q345 steel and corresponds to a type a or b section of a pressed component of a shaft center in the Steel Structure design Standard; for the stay rod with selected steel type and section type, the upper limit psi of psi value_maxOnly with λ₁Is related to

The method can be used for representing the reduction of the rigidity of the support system caused by the action of the axial force of the stay bar; when η is 0, i.e. the influence of the connecting rod on the rigidity is not considered, the relation curve of the value 2/(2+ zeta) and the value psi is shown in the attached figure 9, and it can be seen that as the stress of the middle stay rod is increased, the rigidity reduction amplitude is increased, and λ is increased₁The larger the rigidity reduction amplitude caused by the stress of the middle support rod is, the larger the rigidity reduction amplitude is; when in engineering design, the stress 2F of the stay bar is generally controlled to be 0.5F_cr～F_crSo that the psi value is 0.5 psi_max～ψ_max(ii) a Considering that the supporting force F is slightly increased as the initially set F value is decreased and γ is increased, the supporting system design conservatively takes 2F to 0.5F_crI.e. psi 0.5 psi_maxThe gamma value of the time is used as the rigidity of the supporting system, and the deformation of the supporting point and the calculation of the supporting force are carried out; when psi is 0.5 psi for different steel type and section type stay bar_max，λ₁The numerical fitting of the least square method is carried out on the zeta value when the support force is 90-150, so that the zeta value used in the calculation of the initial support force can be calculated according to a fixed formula, the initial support rigidity can be obtained simply and conveniently according to the construction of a support system, and the specific process is as follows:

q235 steel is selected for manufacturing, a middle support rod (such as a hot-rolled seamless steel pipe) of a type a section of the axial compression member in the steel structure design standard can be calculated according to the following formula:

q235 steel is selected for manufacturing, a middle stay bar (such as a welded straight seam circular tube, a hot rolled H-shaped steel, a welded or rolled rectangular tube) of a b-type section of an axial compression member in the steel structure design standard can be calculated according to the following formula:

q345 steel is selected for manufacturing, the middle support rod of the a-type section of the axial compression member in the steel structure design standard is classified as the center, and zeta can be calculated according to the following formula:

q345 steel is selected for manufacturing, the middle support rod of the b-type section of the axial compression member in the steel structure design standard is classified as the center, and zeta can be calculated according to the following formula:

when the number n of the equal-spacing middle supporting rods is more than or equal to 3, the column deflection value and the supporting force of each supporting point are unequal, so that the rigidity of each supporting system is different; for the bending column with four unequal-rigidity supports, the displacement at the supporting point can be calculated according to the method of the first step, and only 6 coefficients in the calculation method of the bending column with four middle supporting rods need to be modified:

a₂₁＝K(S²－C²)+(Nl－γ_Bl²－γ_Cl²)C，a₂₂＝K(C²－S²)+(Nl－γ_Bl²－2γ_Cl²)S，a₂₃＝γ_Cl²(S－2C)，a₃₁＝－Cγ_Cl²，a₃₂＝K(C²－S²)+(Nl－2γ_Cl²)S，a₃₃＝3K(S²－C²)+(Nl－γl²)(2C－S)；

in the formula, gamma_BSupport stiffness at column heights of L/5 and 4L/5, gamma_CThe support rigidity at the height of the column is 2L/5 and 3L/5.

For the stand column, the support structure and the load condition commonly used in the dust collector, the following examples were calculated by the above analytical method according to the equal support stiffness and the unequal stiffness, respectively.

Example 11:

the height L of the upright post of the dust remover box body is 16460 mm; the height l of the support column is 3292mm, and the section inertia moment I of the single-limb bending column_cIs 1.14X 10⁸mm⁴(ii) a Support stiffness gamma at L/5 and 4L/5 column heights_BIs 91391N/mm, gamma_CTake 0.5 gamma_B(ii) a The axial pressure N was 1226000N, the lateral load q was 20.36N/mm, and the equivalent and unequal support force ratios were obtained by the second analytical solution shown in Table 2.

Example 12:

example 12 only gamma is compared to example 11_CIs changed into 2 gamma_BTable 2 shows the specific structural parameters and the equivalent and non-equivalent support force ratio of the analytic solution support stiffness of the second step.

Example 13:

the height L of the upright post of the dust remover box body is 15000 mm; the height l of the support column is 3000mm, and the section inertia moment I of the single-limb bending column_cIs 0.98X 10⁸mm⁴(ii) a Support stiffness gamma at L/5 and 4L/5 column heights_B67911N/mm, gamma_CTake 0.5 gamma_B(ii) a The axial pressure N was 981000N, the lateral load q was 18.66N/mm, and the equivalent and unequal support force ratios were supported using the analytical solution of the second step, as shown in Table 2.

Example 14:

example 14 comparing example 13 with only γ_CIs changed into 2 gamma_BTable 2 shows the specific structural parameters and the equivalent and non-equivalent support force ratio of the analytic solution support stiffness of the second step.

Example 15:

the height L of the upright post of the dust remover box body is 18000 mm; the height l of the support column is 3600mm, and the section inertia moment I of the single-limb bending column_cIs 1.31X 10⁸mm⁴(ii) a Support stiffness gamma at L/5 and 4L/5 column heights_BIs 120709N/mm, gamma_CTake 0.5 gamma_B(ii) a The axial pressure N is 1471000N, the transverse load q is 25.73N/mm, and the support stiffness is equal by the analytic solution of the second stepThe pair of unequal support forces is shown in table 2.

Example 16:

example 16 only gamma is compared to example 15_CIs changed into 2 gamma_BTable 2 shows the specific structural parameters and the equivalent and non-equivalent support force ratio of the analytic solution support stiffness of the second step.

TABLE 2 comparison of equal and unequal support forces for equal support stiffness (four supports arranged at equal intervals)

Comparison of the results shows that the gamma values for the examples 11 to 16 in the table are calculated as unequal support stiffness_CRespectively taking 0.5 gamma_BAnd 2 gamma_BThe relative deviation is 4.0% at the maximum, as compared with the support force calculated as the support rigidity is equal, and the deviation decreases as the average value of the support rigidity increases. The middle support rods in the dust remover are identical in structure, and only the support rods are unequal in stress, which causes the difference of support rigidity. When lambda is₁150F (the most flexible case of the strut), the strut is stressed by 2F from 0.5F_crIncrease to F_crDuring the process, the reduction amplitude of the rigidity of the supporting system is not more than 22 percent, namely the maximum variation range of the supporting rigidity ratio in the dust remover is as follows: gamma is not less than 0.78_C/γ_BLess than or equal to 1.28 and less than or equal to 0.5 and less than or equal to gamma in the embodiment_C/γ_BThe variation range is less than or equal to 2; and the initial rigidity (rigidity when the stay bar is not stressed) of the support system in the actual structure is larger, so that the deviation of a calculation result caused by unequal rigidity due to unequal stress of each support point is less than 4.0 percent, the deviation can be ignored, and the column deflection and the support force of each support point can be calculated according to the condition that the support rigidity is equal.

When the support is supported at the middle point of the connecting rod between the two single-limb bending columns, the bending deformation of the connecting rod can increase the flexibility of the support system,

additional compliance caused by the linkage can be characterized. When there are four supports, the relation between the deflection and eta value at the maximum bearing point under forceThe system curve is shown in figure 10, and the deflection basically linearly increases along with the eta value. The relation curve of the supporting force at the maximum supporting point and the eta value is shown in the attached drawing 11, eta is increased, the rigidity gamma of the supporting system is reduced, and the reduction amplitude of the supporting force is small. Therefore, for the supporting system structure commonly used in engineering, the supporting force is less influenced by the support flexibility caused by the middle point of the connecting rod supported between the two limbs of the upright post.

Example 17: design method of flexible support system of double-limb combined cross-section bending column of dust remover box body

The method comprises the following steps:

Initial support stiffness γ₀Calculated according to the following formula:

length-thin ratio lambda of middle stay bar₁Satisfies the following formula:

λ₁＝l₁/i₁；

when n is 1, the maximum supporting force F satisfies the following formula:

F＝γΔ_AB；

when n is 2, the maximum supporting force F satisfies the following formula:

F＝γΔ_AB；

when n is 3, the maximum supporting force F satisfies the following formula:

F＝γΔ_AC；

Δ_AC＝Δ_AB+Δ_BC；

when n is 4, the maximum supporting force F satisfies the following formula:

F＝γΔ_AC；

Deflection delta of 2L/5 and 3L/5 column height of single-limb bending column_ACSatisfies the following formula:

Δ_AC＝Δ_AB+Δ_BC；

Δ_AB＝(Cθ_A+Sθ_B)l/(C+S)；

Δ_BC＝l[(2C－S)θ_C+Sθ_B]/(C+S)；

in the formula, a₁₁＝K(S－C)，a₁₂＝2K(C－S)，a₁₃＝2K(S－C)，a₂₁＝K(S²－C²)+(Nl－2γl²)C，a₂₂＝K(C²－S²)+(Nl－3γl²)S，a₂₃＝γl²(S－2C)，a₃₁＝－Cγl²，a₃₂＝K(C²－S²)+(Nl－2γl²)S，a₃₃＝3K(S²－C²)+(Nl－γl²)(2C－S)，b₁＝－M_FBA－M_FBC，b₂＝－(C+S)(M_FBA+2ql²)，b₃＝－(C+S)ql²；θ_AFor bending the column corner, theta, at the column top for a single limb_BThe column corner theta at the height of one fifth of the column is formed by pressing a single limb_CThe column corner, delta, at two fifths of the height of the column for single limb bending_ABThe deflection of the bending column at the height of one fifth of the bending column of the single limb (due to symmetry, the column corner at the top of the bending column of the single limb is equal to the column corner at the bottom of the bending column of the single limb, the column corner at the height of one fifth of the bending column of the single limb is equal to the column corner at the height of four fifth of the bending column of the single limb, the column corner at the height of two fifth of the bending column of the single limb is equal to the column corner at the height of three fifth of the bending column of the single limb, and the deflection of the bending column at the height of one fifth of the bending column of the single limb is equal to the deflection of the bending column at the height of four fifth of the bending column of the single limbBending column deflection) of Δ_BCThe deflection of the single-limb bending column at the height of two fifths of the column is increased compared with the deflection at the height of one fifths of the column, C and S are bending rigidity coefficients of the single-limb bending column, M_FBAFor bending the fixed end bending moment of a column segment for a single limb with one hinged end and one fixed end, M_FBCThe fixed end bending moment of the single-limb bending column segment is fixedly connected with two ends, K is the linear rigidity of the single-limb bending column, and L is L/5;

in the formula, k is a calculation coefficient;

the calculation coefficient k satisfies the following formula:

fixed end bending moment M with two ends fixedly connected with single-limb bending column segment_FBCThe following formula is satisfied such that the pole segments are positive for clockwise rotation and negative for counterclockwise rotation:

K＝EI_c/l；

in the formula, a₁For welding the length of the cross-section of rectangular tubes parallel to the bending axis, a₂The length of the side of the section of the welded rectangular tube, which is perpendicular to the bending axis side, is t ', and the thickness of the section of the welded rectangular tube is t';

I_c＝π[D⁴-(D-2t″)⁴]/64

in the formula I₂As the length of the connecting rod,

euler critical force F of middle stay_ESatisfies the following formula:

F_E＝π²EA₁/λ₁ ²；

step four: according to the connecting rod section preliminarily determined in the third stepThe specification yields the section modulus W of the connecting rod around its bending axis₂And the section moment of inertia I₂The actual value of (c); according to the third step, the section inertia moment I of the connecting rod around the bending axis is preliminarily determined₂Calculating the actual values to obtain the ratio eta of the bending flexibility of the connecting rod to the axial flexibility of the middle support rod and the actual support rigidity gamma provided by the flexible support system to the single-limb upright post; substituting the actual support stiffness gamma provided by the flexible support system for the single-limb upright column into the second step to recalculate to obtain the maximum support force F; substituting the recalculated maximum supporting force F into the step three to recalculate the flexural integral stability calculation stress sigma of the connecting rod by checking_cr2And the tangential supporting rigidity gamma provided by the flexible supporting system to the single-limb upright post_TWhether the requirement is met or not, and checking the axial pressure integral stable bearing capacity F of the middle supporting rod according to the maximum supporting force F obtained by recalculation_crWhether the requirement is met, wherein the stress sigma is calculated by calculating the flexural integral stability of the connecting rod_cr2Overall stability factor when the connecting rod is used as a flexural member

The integral stability coefficient of the bent member in the steel structure design standard is determined according to the section specification of the connecting rod; calculating stress sigma if the whole of the connecting rod is bent stably_cr2If the requirement is not met, the connecting rod with a larger section needs to be replaced, and the section modulus W of the connecting rod with the larger section around the bending axis of the connecting rod with the larger section is used₂' Replacing original design connecting rod section modulus W₂If the flexible support system provides tangential support stiffness gamma to the single-limb upright column_TAnd the bearing capacity F of the middle support rod for stabilizing the whole axle pressure_crIf one of the two does not meet the requirement, the middle stay bar with a larger cross section needs to be replaced so as to increase the cross section determination value A of the middle stay bar in the rear flexible supporting system₁' Preset value of cross-sectional area of middle stay bar in alternative flexible supporting system A₁To increase the minimum turning radius i of the section of the rear middle strut₁' Preset value of radius of gyration of section in place of middle stay i₁And repeating the first step to the fourth step until the stress sigma of the whole bending stability of the connecting rod is calculated_cr2The flexible supporting system is provided for the single-limb upright postTangential support stiffness γ of_TAnd the bearing capacity F of the middle support rod for stabilizing the whole axle pressure_crAll meet the requirements;

2F≤F_cr；＝

in the formula (I), the compound is shown in the specification,

is an axial compression whole of a middle support rodStability factor according to the slenderness ratio lambda of the middle strut₁And the section classification of the axial compression steel member is determined according to the Steel Structure design Standard f₁Determining the design value of the strength of the steel of the middle stay bar according to the steel grade of the steel used for the middle stay bar and the design standard of a steel structure;

Example 18: design of flexible support system of double-limb combined cross-section bending column of dust remover box body

According to the method of the embodiment 17, a flexible supporting system which is derived from a double-limb combined section bending column in a box body structure of the dust remover, which is subjected to transversely uniformly distributed load and column top shaft pressure in actual engineering and consists of a supporting rod and a connecting rod is designed, and the structural size of the double-limb combined section bending column is as follows: the total height L of the upright column is 16460mm, the height L of the support middle column is 3292mm, the number n of the middle support rods of the bending column is 4, and the linear rigidity K of the upright column is 7.13 multiplied by 10⁹N · mm, designed value of axial pressure at the top of the column N is 1226kN, designed value of transversely uniformly distributed load q in midspan q is 20.36N/mm, and length l of the stay bar₁9050mm, link length l₂＝1120mm。

The method comprises the following steps: preliminarily designed middle support rod made of Q235 steel

The straight slit steel pipe is a b-type axial compression bar section, and f is 215N/mm²，λ ₁120 according to formula

Calculating a coefficient ζ which takes into account a nonlinear influence that the rigidity of the support system decreases with an increase in the support force to be 0.108; cross-sectional area A of middle stay bar₁＝4015mm²Minimum radius of gyration i of cross section₁75.3mm, strut section moment of inertia I₁＝22787400mm⁴According to the formula

Calculating to obtain initial support rigidity gamma₀＝21677N/mm；

Step two: the L of the double-limb combined section bending column is 16460mm, L is 3292mm, K is 7.13X 10⁹Nmm, N1226 kN, q 20.36N/mm, and let the support rigidity γ be γ₀According to the formula

Calculating to obtain the maximum supporting force F of the single-limb upright column which is 69990N when four (N is 4) equidistant middle supporting rods exist;

step three: designing the connecting rod according to the maximum supporting force F, wherein the length l of the connecting rod₂1120mm, hot rolled channel steel commonly used in engineering is selected as a connecting rod, and the connecting rod can be selected during primary design

Stability of connecting rod according to

Designing to obtain the net section modulus W of the connecting rod₂≥202555mm³(ii) a According to the Euler critical force of the middle stay bar

And

the ratio eta of the bending flexibility of the connecting rod to the axial flexibility of the middle support rod is calculated to be less than or equal to 65.69 and substituted into

It can be seen that the moment of inertia I of the connecting rod about its bending axis₂≥395337mm⁴Therefore, the connecting rod is made of 22a channel steel W₂＝218000mm³，I₂＝23940000mm⁴；

Step four: the moment of inertia I of the selected 22a channel steel₂Re-substitution

Eta is calculated to be 1.085 from

ψ＝F/F_ECalculated zeta 0.089, and substituted

Obtaining the actual supporting rigidity gamma of the supporting system which is 28793N/mm; according to the parameters and formula of the designed brace rod and connecting rod

The maximum supporting force F of the single-limb stand column is calculated again to be 71.196kN, and the hot-rolled channel steel connecting rod is used as a flexural member

The values were calculated according to "steel structure design Standard":

wherein h, b and t are the total height of the section of the channel steel, the width of a flange and the average thickness, the unit is mm, the selected 22a channel steel is checked to obtain h which is 220mm, b which is 77mm and t which is 11.5 mm;

obtained by

Then, according to the design standard of steel structure, the corresponding calculation is obtained according to the following formula

Value substitution

The value:

is calculated to

And calculating corresponding according to the above formula

Value substitution

Value, the overall stability factor of the connecting rod as a flexural member can be obtained

According to

And

is calculated to obtain

The overall stability checking calculation of the connecting rod meets the requirement; according to

Calculating to obtain gamma_T＝28359N/mm≥γ_cr1347N/mm, the tangent rigidity of the whole supporting system meets the requirement; 2F according to

Calculating to obtain the stress of the middle stay bar

And the checking calculation of the whole stability of the stay bar is satisfied. Determining the design middle brace rod as

The straight slit steel pipe and the connecting rod are 22a channel steel, can meet the requirements of the overall bending stability of the connecting rod, the tangential rigidity of a supporting system and the overall axial compression stability of the stay bar, and are composed of the stay bar and a connecting rod groupThe flexible supporting system has reasonable design.

Although the present invention has been described with reference to the preferred embodiments, it should be understood that various changes and modifications can be made therein by those skilled in the art without departing from the spirit and scope of the invention as defined in the appended claims.

Claims

1. A design method of a flexible supporting system of a double-limb combined cross-section bending column is characterized by comprising the following steps:

Initial support stiffness γ₀Calculated according to the following formula:

Among the above values, the sectional area of the middle stay bar is preset value A₁In mm unit²Length of middle stay bar l₁In mm, the preset value i of the minimum turning radius of the cross section of the strut₁In mm, and the modulus of elasticity E of the material in N/mm²Initial support stiffness γ₀The unit of (A) is N/mm;

the maximum supporting force F satisfies the following formula:

F＝γΔ_max；

in the formula,. DELTA._maxThe deflection of the single-limb bending column at the support position closest to the midspan is obtained by taking delta when the number n of supports is less than or equal to 2_max＝Δ_ABWhen the number of supports n is greater than 2, take Delta_max＝Δ_ACIn the formula, when the initial calculation is carried out, the value of gamma is equal to gamma₀；

Step three: requires the flexural integral stability of the connecting rod to calculate the stress sigma_cr2Not exceeding the design value f of the strength of the connecting rod steel₂Calculating the stress sigma from the flexural global stability of the connecting rod_cr2Calculating to obtain the section modulus W of the connecting rod₂A lower limit value of (d); tangential supporting rigidity gamma provided by flexible supporting system to single-limb upright post_TIs more than or equal to the lower limit value gamma of the supporting rigidity requirement of the flexible supporting system on the single-limb upright post_crTangential support stiffness γ to the single-limb column provided by the flexible support system_TCalculating to obtain the section inertia moment I of the connecting rod₂A lower limit value of (d); according to the section modulus W of the connecting rod about its bending axis₂And the section moment of inertia I of the connecting rod about its bending axis₂Preliminarily determining the section specification of the connecting rod according to the lower limit value;

in the formula I₂As the length of the connecting rod,

when connecting-rods as flexural membersOverall stability factor, the above formula being taken during preliminary calculation

f₂Determining according to the grade of the steel material used by the connecting rod;

euler critical force F of middle stay_ESatisfies the following formula:

F_E＝π²EA₁/λ₁ ²；

length-thin ratio lambda of middle stay bar₁Satisfies the following formula:

λ₁＝l₁/i₁；

of the above values, the link length l₂In mm, the second moment of inertia of the section of the connecting rod about its axis of bending I₂In mm unit⁴Section modulus W of connecting rod around bending axis thereof₂In mm unit³Tangential support stiffness gamma provided by the flexible support system to the single-limb upright_THas the unit of N/mm, and the lower limit value gamma of the supporting rigidity requirement of the flexible supporting system on the single-limb upright post_crUnit of (2)Is N/mm, the unit of the maximum supporting force F is N, and the Euler critical force F of the middle supporting rod_EThe unit of (a) is N;

step four: obtaining the section modulus W of the connecting rod around the bending axis according to the section specification of the connecting rod preliminarily determined in the step three₂And the section moment of inertia I₂The actual value of (c); according to the third step, the section inertia moment I of the connecting rod around the bending axis is preliminarily determined₂Calculating the actual values to obtain the ratio eta of the bending flexibility of the connecting rod to the axial flexibility of the middle support rod and the actual support rigidity gamma provided by the flexible support system to the single-limb upright post; substituting the actual support stiffness gamma provided by the flexible support system for the single-limb upright column into the second step to recalculate to obtain the maximum support force F; substituting the recalculated maximum supporting force F into the step three to recalculate the flexural integral stability calculation stress sigma of the connecting rod by checking_cr2And the tangential supporting rigidity gamma provided by the flexible supporting system to the single-limb upright post_TWhether the requirement is met or not, and checking the axial pressure integral stable bearing capacity F of the middle supporting rod according to the maximum supporting force F obtained by recalculation_crWhether the requirement is met, wherein the stress sigma is calculated by calculating the flexural integral stability of the connecting rod_cr2Overall stability factor when the connecting rod is used as a flexural member

The connecting rod is determined according to the section specification of the connecting rod; calculating stress sigma if the whole of the connecting rod is bent stably_cr2If the requirement is not met, the connecting rod with a larger section needs to be replaced, and the section modulus W of the connecting rod with the larger section around the bending axis of the connecting rod with the larger section is used₂' Replacing original design connecting rod section modulus W₂If the flexible support system provides tangential support stiffness gamma to the single-limb upright column_TAnd the bearing capacity F of the middle support rod for stabilizing the whole axle pressure_crIf one of the two does not meet the requirement, the middle stay bar with a larger cross section needs to be replaced so as to increase the cross section determination value A of the middle stay bar in the rear flexible supporting system₁' Preset value of cross-sectional area of middle stay bar in alternative flexible supporting system A₁To increase the minimum turning radius i of the section of the rear middle strut₁' Preset value of radius of gyration of section in place of middle stay i₁And is combined withRepeating the first step to the fourth step until the stress sigma is calculated stably on the whole of the connecting rod in bending_cr2The tangential supporting rigidity gamma provided by the flexible supporting system to the single-limb upright column_TAnd the bearing capacity F of the middle support rod for stabilizing the whole axle pressure_crAll meet the requirements;

2F≤F_cr；

in the formula (I), the compound is shown in the specification,

the axial compression integral stability coefficient of the middle stay bar is determined according to the slenderness ratio lambda of the middle stay bar₁And its section classification determination, f₁Determining a design value of the strength of the steel of the middle stay bar according to the grade of the steel used for the middle stay bar;

2. The design method of a double-limb combined-section bending column flexible supporting system according to claim 1, wherein the material of the flexible supporting system is Q235 steel or Q345 steel, and the middle supporting rod is an integrally stable class a section or a class b section of an axial compression steel member.

3. The method for designing a flexible supporting system of a bending column with a combined double limb section as claimed in claim 2, wherein when the material of the flexible supporting system is Q235 steel and the middle supporting rod is a class a section of the axial compression member, a coefficient ζ considering a nonlinear influence of the flexible supporting system, in which the rigidity decreases with the increase of the supporting force, satisfies the following formula:

4. the design method of a flexible supporting system of a double-limb combined-section bending column as claimed in claim 1, wherein when n is 1, the maximum supporting force F satisfies the following formula:

F＝γΔ_AB；

wherein C and S are flexural rigidity coefficient of single-limb bending column, M_FBAIs a single limb bending column with one end hinged and the other end fixedly connectedThe fixed end bending moment of the segment, K is the linear rigidity of the single-limb bending column, and L is L/2;

when n is 2, the maximum supporting force F satisfies the following formula:

F＝γΔ_AB；

in the formula,. DELTA._ABThe deflection of the single-limb bending column at the column height of L/3 and 2L/3 is obtained by taking gamma as gamma in the formula during initial calculation₀Taking the section specification of the middle supporting rod and the section specification of the connecting rod after determining

Single-limb bending column deflection delta at L/3 and 2L/3 column height_ABSatisfies the following formula:

in the numerical values, the unit of the height L of the support columns is mm, the unit of the axial pressure N is N, the unit of the transversely uniformly distributed load q is N/mm, and the deflection delta of the single-limb bending column at the column heights of L/3 and 2L/3 is L/3_ABThe unit of (3) is mm, the unit of the linear rigidity K of the single-limb bending column is N.mm, and the unit of the supporting rigidity gamma is N/mm;

when n is 3, the maximum supporting force F satisfies the following formula:

F＝γΔ_AC；

in the formula,. DELTA._ACFor the mid-span deflection of the single-limb bending column, the formula is that gamma is taken as the initial calculationγ₀Taking the section specification of the middle supporting rod and the section specification of the connecting rod after determining

Δ_AC＝Δ_AB+Δ_BC；

in the formula, c₁₁＝K(C+S)，c₁₂＝－γl/2，c₁₃＝N－γl/2－2K(C+S)/l，c₂₁＝KC，c₂₂＝3γl/2－N，c₂₃＝γl/2－K(C+S)/l，c₃₁＝K(2C²－S²)/C，c₃₂＝K(S²－C²)/(Cl)，c₃₃＝－K(C+S)/l，d₁＝－ql²/2，d₂＝3ql²/2－M_FBC，d₃＝－M_FBC－M_FBA；θ_AFor bending the column corner, theta, at the column top for a single limb_BFor single limb bending column corner, delta, at quarter column height_ABAnd Δ_ACDeflection, delta, at the height of one quarter and one half of the column, respectively, of a single-limb bending column_BCThe deflection of the high part of the column is increased relative to the deflection of the high part of the column, C and S are the bending rigidity coefficient of the single-limb bending column, M_FBAFor bending the fixed end bending moment of a column segment for a single limb with one hinged end and one fixed end, M_FBCThe fixed end bending moment of the bending component is fixedly connected with the two ends, K is the linear rigidity of the single-limb bending column, and L is equal to L/4;

when n is 4, the maximum supporting force F satisfies the following formula:

F＝γΔ_AC；

Deflection delta at the column height of 2L/5 and 3L/5 in the middle of the column_ACSatisfies the following formula:

Δ_AC＝Δ_AB+Δ_BC；

Δ_AB＝(Cθ_A+Sθ_B)l/(C+S)；

Δ_BC＝l[(2C－S)θ_C+Sθ_B]/(C+S)；

in the formula, a₁₁＝K(S－C)，a₁₂＝2K(C－S)，a₁₃＝2K(S－C)，a₂₁＝K(S²－C²)+(Nl－2γl²)C，a₂₂＝K(C²－S²)+(Nl－3γl²)S，a₂₃＝γl²(S－2C)，a₃₁＝－Cγl²，a₃₂＝K(C²－S²)+(Nl－2γl²)S，a₃₃＝3K(S²－C²)+(Nl－γl²)(2C－S)，b₁＝－M_FBA－M_FBC，b₂＝－(C+S)(M_FBA+2ql²)，b₃＝－(C+S)ql²；θ_AFor bending the column corner, theta, at the column top for a single limb_BThe column corner theta at the height of one fifth of the column is formed by pressing a single limb_CThe column corner, delta, at two fifths of the height of the column for single limb bending_ABThe deflection of the bending column at the height of one fifth of the bending column of a single limb_BCThe deflection of the single-limb bending column at the height of two fifths of the column is increased compared with the deflection at the height of one fifths of the column, C and S are bending rigidity coefficients of the single-limb bending column, M_FBAFor bending the fixed end bending moment of a column segment for a single limb with one hinged end and one fixed end, M_FBCThe fixed end bending moment of the single-limb bending column segment is fixedly connected with two ends, K is the linear rigidity of the single-limb bending column, and L is L/5;

when n >4, the maximum supporting force F is calculated when n is 4.

5. The design method of a flexible supporting system of a double-limb combined section bending column as claimed in claim 4, wherein the bending rigidity coefficient C of the single-limb bending column satisfies the following formula:

in the formula, k is a calculation coefficient;

the calculation coefficient k satisfies the following formula:

fixed end bending moment M of single-limb bending column segment with one hinged end and one fixed end_FBAThe following formula is satisfied such that the rod segment rotates clockwise to positive and counterclockwiseThe direction rotation is negative:

K＝EI_c/l；

I_c＝π[D⁴-(D-2t″)⁴]/64

of the above numerical values, M_FBAHas the unit of N.mm, M_FBCHas a unit of N.mm, and the section inertia moment I of the single-limb bending column around the bending axis thereof_cIn mm unit⁴。

6. The design method of a flexible supporting system of a double-limb combined-section bending column according to any one of claims 1 to 5, wherein the double-limb combined-section bending column comprises two single-limb bending columns, a connecting wall plate welded between the two single-limb bending columns, and stiffening ribs welded on the connecting wall plate and perpendicular to the two single-limb bending columns; the flexible supporting system of the double-limb combined cross-section bending column comprises a connecting rod and a middle supporting rod; the connecting rod is welded between the two single-limb bending columns and is positioned on the connecting line of the centroids of the sections of the two single-limb bending columns; the middle stay bar is perpendicular to the connecting wall plate and welded at one half of the connecting rod in the length direction.

7. The method for designing a flexible supporting system of a double-limb combined-section buckling column as claimed in any one of claims 1 to 5, wherein the section of the middle supporting rod is a section of the middle supporting rod perpendicular to the Y axis.

8. A design method of a double-limb combined-section bending column flexible supporting system according to any one of claims 1 to 5, wherein the middle support rod is a biaxial symmetric section steel member.

9. A design method of a double-limb combined-section bending column flexible supporting system according to any one of claims 1 to 5, wherein the connecting rod is a symmetrical-section steel member.

10. Use of the design method of any one of claims 1 to 5 for designing a flexible support system for a dual limb combined cross-section buckling column.