CN113569344B - Mechanical model based on pulling and hanging unloading method scaffold and solving method thereof - Google Patents

Mechanical model based on pulling and hanging unloading method scaffold and solving method thereof Download PDF

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CN113569344B
CN113569344B CN202110583144.4A CN202110583144A CN113569344B CN 113569344 B CN113569344 B CN 113569344B CN 202110583144 A CN202110583144 A CN 202110583144A CN 113569344 B CN113569344 B CN 113569344B
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scaffold
section
force
wire rope
vertical
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CN113569344A (en
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卢德辉
邵泉
苏建华
张厚美
周岳峰
吴瑞卿
王龙
倪毅
凌文轩
戴仲文
程瀛
李敏健
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Guangzhou Construction Industrial Research Institute Co ltd
Guangzhou Jianshe Bay District Zhizao Technology Co ltd
Guangzhou Yijian Construction Group Co ltd
Guangzhou Construction Co Ltd
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Guangzhou Construction Industrial Research Institute Co ltd
Guangzhou Jianshe Bay District Zhizao Technology Co ltd
Guangzhou Yijian Construction Group Co ltd
Guangzhou Construction Co Ltd
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    • G06F30/10—Geometric CAD
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces
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Abstract

The invention belongs to the technical field of engineering stress calculation, and provides a mechanical model based on a scaffold by a pulling and lifting unloading method and a solving method thereof, which mainly comprise a single upright model formed on the basis of an inner upright or an outer upright of the scaffold, wherein the single upright model comprises: k is a radical of1、G1、k2、G2、k3、G3…kn、Gn、kn+1And k is1And G1… k betweennAnd GnAre correspondingly connected with ks1、ks2…ksn；k1Vertical stiffness of the scaffolding at the base segment; k is a radical ofs2…ksnThe vertical rigidity of the unloading steel wire rope at the corresponding section of the corresponding scaffold; g1…GnRespectively equivalent concentrated vertical loads at the n-th section of the upright rod of the 1 st section …; k is a radical of2、…kn+1Respectively, 1 st segment … nth segment vertical rod. The invention can effectively improve the unloading of the pulling craneThe force calculation accuracy and the calculation convenience of the scaffold under the law.

Description

Mechanical model based on pulling and hanging unloading method scaffold and solving method thereof
Technical Field
The invention belongs to the technical field of engineering stress calculation, and particularly relates to a mechanical model based on a pulling and lifting unloading method scaffold and a solving method thereof.
Background
In the building construction process, steel pipe scaffolds are often erected on the periphery of a building so as to achieve the purposes of providing an operation surface for building outer wall construction, safely enclosing high-altitude operation, passing workers up and down, transporting tools and the like. Along with economic technology's development, the building is higher and higher, and the scaffold puts up and also higher and higher, and the axial force that scaffold bottom steel pipe received is very big, leads to the bottom steel pipe of scaffold under many situations can't satisfy the requirement when the stability is checked and calculated. In the prior art, in order to reduce the axial force borne by the steel pipe at the bottom of the scaffold, a sectional lapping method, a steel pipe section increasing method and a steel wire rope pulling and hanging unloading method are commonly adopted, and compared with the former two methods, the steel wire rope pulling and hanging unloading method has the advantages of economy and high efficiency, and is widely applied to actual engineering.
At present, an unloading empirical coefficient method is usually adopted for calculating the unloading force of the steel wire rope pulling crane, if the steel wire rope bears the load of 80 percent (unloading coefficient) of the corresponding scaffold section, and the rest 20 percent of the load is transmitted downwards. A large number of finite element calculation researches show that unloading coefficients are influenced by a large number of factors, discreteness and errors are large, direct value taking is difficult to achieve through experience, and the calculation results are often inaccurate, so that potential safety hazards exist in actual construction and use of the scaffold.
Disclosure of Invention
In order to overcome the defects in the prior art, the invention aims to provide a mechanical model based on a scaffold adopting a pulling and lifting unloading method and a solving method thereof, so as to effectively improve the stress calculation accuracy and calculation convenience of the scaffold adopting the pulling and lifting unloading method.
The technical scheme adopted by the invention for solving the technical problems is as follows:
the utility model provides a mechanical model based on draw and hang off-load method scaffold frame, includes the single pole setting model that forms on the basis of the interior pole setting of scaffold frame or outer pole setting, single pole setting model includes that it arranges the setting in order to be the straight line form from bottom to top:
k1、G1、k2、G2、k3、G3……kn、Gn、kn+1and k is1And G1K is2And G2… … k betweennAnd GnAre correspondingly connected with ks1、ks2……ksn(ii) a Wherein the content of the first and second substances,
k1vertical stiffness of the scaffolding at the base segment;
ks2、ks3……ksnunloading the vertical rigidity of the steel wire rope for the corresponding section of the corresponding scaffold;
G1、G2……Gnequivalent concentrated vertical loads at the upright of the nth section are respectively the 1 st section and the 2 nd section;
k2、k3……kn+1equivalent springs at the upright rods of the 1 st section and the 2 nd section.
Preferably, the scaffold comprises a floor type scaffold and an overhanging type steel scaffold.
Preferably, the scaffold is a floor scaffold, in which case k is1Vertical stiffness, k, of natural foundations1To construct the spring rate, there is ks1＝0。
Preferably, the scaffold is an overhanging section steel scaffold, in which case k is1The vertical rigidity of the vertical rod at the position of the cantilever profile steel is realized.
A method for solving a mechanical model based on a scaffold adopting a pulling and lifting unloading method is suitable for the mechanical model based on the scaffold adopting the pulling and lifting unloading method, and comprises the following steps:
s10, calculating by taking a single scaffold as a segment unit, calculating the stress condition of an object under the single vertical rod model by a segmented gradual loading solution, and when the number of the scaffold is n and the number of the unloading steel wire ropes is n, respectively calculating the steel wire rope counter-force, the bottom support rod counter-force and the vertical rod axial force corresponding to the x-th section of scaffold as follows:
reaction force of the wire rope:
Figure GDA0003597792930000021
bottom support bar counter-force:
Figure GDA0003597792930000022
pole setting axial force: n is a radical ofx＝Rsx+Rqx，
Base reaction force: rf＝N1；
S20, constructing a matrix expression to calculate the final stress of the object under the single vertical rod model, wherein the matrix expression comprises the following steps:
reaction force of the wire rope:
[Rs]＝[Ms]·[G](formula 1)
Bottom support bar counter-force:
[Rq]＝[Mq]·[G](formula 2)
Pole setting axial force:
[N]＝[Rs]+[Rq](formula 3)
Wherein the content of the first and second substances,
[Rs]＝[Rs1,Rs2,Rs3,…,Rsn]，
[Rq]＝[Rq1,Rq2,Rq3,…,Rqn]，
[N]＝[N1,N2,N3,…,Nn]，
[G]＝[G1,G2,G3,…,Gn]，
Figure GDA0003597792930000023
Figure GDA0003597792930000031
in the formula (I), the compound is shown in the specification,
Figure GDA0003597792930000032
En、An、Lnthe elastic modulus, the section area and the length of the nth section of scaffold steel pipe are respectively set;
Esn、Asn、Lsn、θnthe elastic modulus, the section area, the length and the horizontal included angle of the nth section of steel wire rope are respectively obtained.
Further, step S10 includes calculation of the base segment to determine k1、ks1When being the overhanging shaped steel scaffold, there is the formula of calculating:
ks1＝EA/L·sin2θ1
where E, A, L is the modulus of elasticity, the cross-sectional area and the calculated length, θ, of the steel cord, respectively1Is the included angle between the unloading steel wire rope and the horizontal reference line.
Further, step S10 includes the step of comparing G1The calculation at the segment, based on vertical force balance, exists:
reaction force of the wire rope:
Figure GDA0003597792930000033
bottom support bar counter-force:
Figure GDA0003597792930000034
wherein k isq1＝k1。
Further, step S10 includes the step of comparing G2The calculation at the segment, based on vertical force balance, exists:
reaction force of the wire rope:
Figure GDA0003597792930000035
bottom support bar counter-force:
Figure GDA0003597792930000036
wherein k isq2＝(ks1+kq1)·k2/(k2+ks1+kq1)；
Reaction force of the wire rope:
Figure GDA0003597792930000037
bottom support bar counter-force:
Figure GDA0003597792930000038
wherein k isq1＝k1。
Further, step S10 includes the step of comparing GnThe calculation at the segment, based on vertical force balance, exists:
reaction force of the wire rope:
Figure GDA0003597792930000039
counter-force of bottom support rod
Figure GDA00035977929300000310
Wherein k isqn＝(ks(n-1)+kq(n-1))·kn/(kn+ks(n-1)+kq(n-1))；
Reaction force of the wire rope:
Figure GDA00035977929300000311
bottom support bar counter-force:
Figure GDA00035977929300000312
compared with the prior art, the invention has the beneficial effects that:
according to the scheme, the scaffold is divided into a plurality of sections according to the structural characteristics of the scaffold and the number of unloading steel wire ropes, and then a mechanical model based on the scaffold adopting a pulling and lifting unloading method is provided based on the engineering mechanical assumption of an equivalent spring, an equivalent concentrated load, a rigid rod and a rigid base, so that the mechanical solution of the scaffold is closer to the actual condition, and the accuracy of numerical values in actual calculation is effectively improved. Meanwhile, through the derivation of a mechanical theory, a solving method of the single upright rod model is provided, and a matrix expression is carried out on a solving formula, so that three calculation formulas of the counter force of the steel wire rope, the counter force of the bottom support rod and the axial force of each section of upright rod are provided. The scheme has the characteristics of reasonable and reliable mechanical model, simple and clear calculation formula and strong applicability, overcomes the defect of unreliability existing in the traditional technology adopting an empirical coefficient method, and can quickly and accurately obtain theoretical accurate solutions of relevant numerical parameters of the scaffold, the unloading steel wire rope and the like through a manual calculation or programming mode.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.
Figure 1 is a schematic view of a single pole model of the present invention.
Fig. 2 is a schematic view of a single vertical rod model in the case of the two-section scaffold of the present invention.
FIG. 3 shows the present invention G1The stress structure of the segment is shown schematically.
FIG. 4 shows the present invention G2The stress structure of the segment is shown schematically.
FIG. 5 shows the present invention GnThe stress structure of the segment is shown schematically.
Detailed Description
So that the manner in which the above recited objects, features and advantages of the present invention can be understood in detail, a more particular description of the invention, briefly summarized above, may be had by reference to the embodiments thereof which are illustrated in the appended drawings. In addition, the embodiments and features of the embodiments of the present application may be combined with each other without conflict. In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, and the embodiments described are merely some, but not all embodiments of the invention. All other embodiments, which can be obtained by a person skilled in the art without any inventive step based on the embodiments of the present invention, are within the scope of the present invention.
Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. The terminology used herein in the description of the invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention.
Example 1
As shown in fig. 1-5, the present embodiment provides a mechanical model based on a scaffold by a pulling, hoisting and unloading method, including a single-upright model formed based on an inner upright or an outer upright of the scaffold, where the single-upright model includes a plurality of models sequentially arranged in a straight line from bottom to top:
k1、G1、k2、G2、k3、G3……kn、Gn、kn+1and k is1And G1K is2And G2… … k betweennAnd GnAre correspondingly connected with ks1、ks2……ksn(ii) a As shown in fig. 1, in which,
k1vertical stiffness of the scaffolding at the base section;
ks2、ks3……ksnunloading the vertical rigidity of the steel wire rope for the corresponding section of the corresponding scaffold;
G1、G2……Gnequivalent concentrated vertical loads at the upright of the nth section are respectively the 1 st section and the 2 nd section;
k2、k3……kn+1equivalent springs at the upright rods of the 1 st section and the 2 nd section.
In traditional building engineering, scaffold form commonly used mainly is console mode scaffold frame and overhanging type shaped steel scaffold frame for the steel pipe cross-section of putting up the scaffold frame generally adopts the diameter to be 48.3mm, and thickness is the thin-walled cold-formed steel pipe of 3.6mm, and the connection form commonly used then has fastener formula and dish knot formula. The single vertical rod model in the scheme is suitable for both the floor type scaffold and the overhanging type steel scaffold.
And to scaffold structure's biography power mode, mainly divide into vertical load transmission and horizontal load transmission two kinds, specific transmission mode is:
vertical load transfer: constant and live loads → scaffold boards → horizontal crossbars → inner and outer vertical rods → ground or cantilever section steel;
horizontal load transfer: wind load → dense mesh type safety net → outer side vertical cross rod → horizontal cross rod → wall connecting piece → main structure.
In the scheme, a single scaffold is selected as a segment calculation unit, one end of an unloading steel wire rope is connected with a main body structure, the other end of the unloading steel wire rope is connected with the scaffold, and when the scaffold is stressed in work, the steel wire rope is pulled to provide an upward pulling force to share the vertical load of the scaffold with a scaffold foundation.
And the atress condition of comparing inside and outside pole setting can know, the atress mode of inside and outside pole setting is unanimous basically, and the main difference lies in: (1) the included angle between the unloading steel wire rope and the horizontal line is different; (2) because the outer vertical rod is provided with the handrail, the foot blocking plate and the safety net, the load factors need to be considered when calculating the load of the outer vertical rod; (3) when the scaffold is in an overhanging type steel type, the bottom rigidity values of the inner upright post and the outer upright post are different. Therefore, the inner vertical rod and the outer vertical rod can be calculated by adopting the single vertical rod model, and only the values of a plurality of parameters are different. On the basis, based on engineering mechanics assumptions such as an equivalent spring, an equivalent concentrated load, a rigid rod and a rigid base, a single-vertical-rod mechanical model of the two-section scaffold is provided, as shown in fig. 2.
Two-section type scaffold single vertical rod mechanical model parameter description:
k1: when the scaffold is in floor type, k1Vertical stiffness for natural foundation; when overhanging section steel scaffold, k1The vertical rigidity of the upright rod at the position of the cantilever section steel is realized;
ks1: when the scaffold is in floor type, ks1For constructing the spring rate, value ks10; overhanging type steel footWhen setting up the hand, ks1The vertical rigidity of the unloading steel wire rope at the section steel is measured;
ks2: the vertical stiffness of the unloading steel wire rope;
G1、G2: equivalent concentrated vertical loads of the first section of vertical rod and the second section of vertical rod are respectively;
k2、k3: the equivalent springs of the first section of single vertical rod and the second section of single vertical rod are respectively.
In addition, the embodiment also provides a method for solving the mechanical model based on the scaffold by the pulling and hanging unloading method, which is suitable for the mechanical model based on the scaffold by the pulling and hanging unloading method, and mainly includes the following steps:
s10, calculating by taking a single scaffold as a segment unit, and calculating the stress condition of an object under a single upright model by a segmented gradual loading solution; including at the base section, G1At the segment, G2At the segment to GnComputation at the segment.
S12, calculating the basic section to determine k1、ks1Value of (a), k when floor scaffold1For vertical stiffness of the natural foundation, it can be calculated to take a large value, e.g. 1020(ii) a When the scaffold is an overhanging section steel scaffold, k1The vertical rigidity of the vertical rod at the overhanging section steel can be obtained by calculating the material and the arrangement parameters of the overhanging section steel. When for encorbelmenting shaped steel scaffold, there is the formula of calculating:
ks1＝EA/L·sin2θ1
where E, A, L is the modulus of elasticity, the cross-sectional area and the calculated length, θ, of the steel cord, respectively1Is the included angle between the unloading steel wire rope and the horizontal reference line.
S14. pair G1When calculating at the segment, based on the vertical force balance, as shown in fig. 3, there are:
reaction force of the wire rope:
Figure GDA0003597792930000061
bottom support bar counter-force:
Figure GDA0003597792930000062
wherein k isq1＝k1。
S16. pair G2When calculating at the segment, based on the vertical force balance, as shown in fig. 4, there are:
reaction force of the wire rope:
Figure GDA0003597792930000063
bottom support bar counter-force:
Figure GDA0003597792930000064
wherein k isq2＝(ks1+kq1)·k2/(k2+ks1+kq1)；
Reaction force of the steel wire rope:
Figure GDA0003597792930000065
bottom sprag pole counter-force:
Figure GDA0003597792930000066
wherein k isq1＝k1。
S18. pair GnWhen calculating at the segment, based on the vertical force balance, as shown in fig. 5, there are:
reaction force of the wire rope:
Figure GDA0003597792930000067
counter-force of bottom support rod
Figure GDA0003597792930000068
Wherein k isqn＝(ks(n-1)+kq(n-1))·kn/(kn+ks(n-1)+kq(n-1))；
Reaction force of the wire rope:
Figure GDA0003597792930000069
bottom support bar counter-force:
Figure GDA00035977929300000610
at this moment, when the scaffold is n sections, when off-load wire rope number is n, then wire rope counter-force, bottom sprag pole counter-force and the pole setting axle power that the x section scaffold corresponds are respectively:
reaction force of the wire rope:
Figure GDA0003597792930000071
bottom support bar counter-force:
Figure GDA0003597792930000072
pole setting axial force: n is a radical ofx＝Rsx+Rqx，
Base reaction force: rf＝N1。
S20, constructing a matrix expression to calculate the final stress of the object under the single vertical rod model, wherein the matrix expression comprises the following steps:
reaction force of the steel wire rope:
[Rs]＝[Ms]·[G](formula 1)
Bottom support bar counter-force:
[Rq]＝[Mq]·[G](formula 2)
Pole setting axial force:
[N]＝[Rs]+[Rq](formula 3)
Wherein the content of the first and second substances,
[Rs]＝[Rs1,Rs2,Rs3,…,Rsn]，
[Rq]＝[Rq1,Rq2,Rq3,…,Rqn]，
[N]＝[N1,N2,N3,…,Nn]，
[G]＝[G1,G2,G3,…,Gn]，
Figure GDA0003597792930000073
Figure GDA0003597792930000074
in the formula (I), the compound is shown in the specification,
Figure GDA0003597792930000075
En、An、Lnthe elastic modulus, the section area and the length of the nth section of scaffold steel pipe are respectively set;
Esn、Asn、Lsn、θnthe elastic modulus, the section area, the length and the horizontal included angle of the nth section of steel wire rope are respectively obtained.
In order to facilitate further understanding of the present solution, a specific application example is also provided in this embodiment:
when the known building engineering is constructed by adopting floor type double-row outer scaffolds, the height of the scaffold is 50m, the distance between the scaffold and a building is 200mm, the longitudinal distance between upright rods is 1.5m, the transverse distance between the upright rods is 0.8m, and the step distance between cross rods is 1.8 m; the dead weight standard value of the scaffold board is 0.1kN/m2, the dead weight of the railing and the foot baffle board is 0.17kN/m, the dead weight of the dense mesh type safety net is 0.01kN/m2, and the live load of the scaffold surface is 3 kN/m; the scaffold live load is 2 layers calculated, the constant load component coefficient is 1.3, the live load component coefficient is 1.5, the section of the steel pipe is phi 48x3mm, the elastic modulus E of the steel pipe is 206GPa, and the section area A of the steel pipe is 4.24cm 2; 2 pulling and hanging unloading steel wire ropes are adopted, and the height of a hanging point on each pulling and hanging unloading steel wire rope is as follows: [19.67,36.33]m, height of a lower lifting point for unloading by pulling and lifting: [16.67,33.33]m, the number of scaffold sections n is 3, the section height h is [16.67,16.67]m, the diameter d of the steel wire rope is 20.00mm, and the section area A of the steel wire rope is 3.14cm2The elastic modulus E of the steel wire rope is 100 GPa.
1. If the maximum stress of the steel wire rope, the maximum axial pressure of the steel pipe and the axial pressure of the base are required; according to the known data, the design values of the constant load and the live load of the inner upright rod and the outer upright rod can be calculated:
design value of constant load of outer vertical rod: nd — 1 — 19.991 kN;
design value of constant load of inner vertical rod: nd — 2 — 9.726 kN;
design value of live load of outer vertical rod: nl _1 ═ 4.860 kN;
design value of live load of inner vertical rod: nl _2 is 4.860 kN.
2. For the base segment: setting a large value k for foundation rigidity of floor type scaffold1＝1020At this time ks10; the most unfavorable situation is considered, and the unloading section live load is loaded on the topmost section.
3. Based on the single vertical rod model, the relevant calculation process of the outer vertical rod is obtained:
the load of each unloading section is as follows: [G] [6.66,6.66,11.52] kN
The vertical stiffness of each unloading steel wire rope is as follows: [ ks ] ═ EA/L ^ sin theta 2 ^ 0,8941,8941] kN · m
The vertical rigidity of each sectional upright rod is as follows: [k] EA/L [1020,5242,5242,5242] kN.m
The equivalent vertical rigidity of each subsection lower frame body is as follows: [ kq ] ═ EA/L ═ 1020,5242,3827] kN · m
The unloading coefficient of each steel wire rope section is as follows: [ α ] ═ ks/(ks + kq) [0.0,0.63,0.7]
The unloading coefficient of each section is as follows: [ β ] ═ kq/(ks + kq) ([ 1.0,0.37,0.3]
Constructing an equivalent vertical stiffness matrix of each segmented lower frame body:
Figure GDA0003597792930000081
constructing a vertical rigidity matrix of each unloading steel wire rope:
Figure GDA0003597792930000082
the vertical counter-force of each steel wire rope is as follows: [ Rs ] ═ Ms ] ═ G ] ═ 0.0,6.38,8.07] kN
The vertical counter-force of each subsection lower part frame body is as follows: [ Rq ] ═ Mq ] ═ G ] ═ 10.4,3.74,3.45] kN
The vertical rod axial force of each section is as follows: [ N ] ═ Rq ] + [ Rs ] ═ 10.4,10.12,11.52] kN
Thus, the following results were obtained:
total vertical load of the scaffold: g _ sum + Nl _ sum (G) 24.85kN
Sum of vertical counter forces of the steel wire ropes: rs _ sum (Rs) 14.45kN
Maximum reaction force of the steel wire rope: tsmax (Rs/sin theta) 8.51kN
Maximum axial force of the vertical rod of the scaffold: nmax (n) 11.52kN
Axial force of the bottommost section of the scaffold upright rod: nbtm 10.40kN
The reaction force of the substrate (section steel) is as follows: rf＝10.40kN
4. Based on the single vertical rod model, the related calculation process of the inner vertical rod is obtained:
the load of each unloading section is as follows: [G] [3.24,3.24,8.1] kN
The vertical stiffness of each unloading steel wire rope is as follows: [ ks ] ═ EA/L ^ sin theta 2 ^ 0,10402,10402] kN · m
The vertical rigidity of each sectional upright rod is as follows: [k] EA/L [1020,5242,5242,5242] kN.m
The equivalent vertical rigidity of each subsection lower frame body is as follows: [ kq ] ═ EA/L ═ 1020,5242,3926] kN · m
The unloading coefficient of each steel wire rope section is as follows: [ α ] ═ ks/(ks + kq) [ (0.0, 0.665,0.726 ]) ]
The unloading coefficient of each section is as follows: [ β ] ═ kq/(ks + kq) ([ 1.0,0.335,0.274 ]) ]
Constructing an equivalent vertical rigidity matrix of each segmented lower frame body:
Figure GDA0003597792930000091
constructing a vertical rigidity matrix of each unloading steel wire rope:
Figure GDA0003597792930000092
the vertical counter-force of each steel wire rope is as follows: [ Rs ] ═ Ms ] ═ G ] ═ 0.0,3.63,5.88] kN
The vertical counter-force of each subsection lower part frame body is as follows: [ Rq ] ═ Mq ] × [ G ] ═ 5.07,1.83,2.22] kN
The axial force of each sectional upright rod is as follows: [ N ] ═ Rq ] + [ Rs ] ═ 5.07,5.46,8.1] kN
Thus, the following results were obtained:
total vertical load of the scaffold: g _ sum + Nl _ sum (G) 14.59kN
Sum of vertical counter forces of the steel wire ropes: rs _ sum (Rs) 9.51kN
Maximum reaction force of the steel wire rope: tsmax (Rs/sin theta) 5.90kN
Maximum axial force of the upright rod of the scaffold: nmax (n) 8.10kN
Axial force of the bottommost section of the scaffold upright rod: nbtm 5.07kN
The reaction force of the substrate (section steel) is as follows: r isf＝5.07kN
5. And (3) sorting the calculation results of the inner upright rod and the outer upright rod to obtain:
maximum value Nmax _1 of external vertical rod axial force is 11.52kN
Maximum value Nmax _2 of axial force of inner vertical rod is 8.10kN
Maximum axial force Nbtm — 1 of the bottom outer leg of 10.40kN
Maximum axial force Nbtm _2 of bottom inner vertical rod is 5.07kN
Maximum external vertical rod steel wire rope tension Ts _1 is 8.51kN
Maximum steel wire rope tension Ts _2 of inner vertical rod is 5.90kN
Therefore, the mechanical model of the scheme is more reasonable and reliable, the calculation formula is simple and clear, the applicability is higher, the defect of unreliability existing in the traditional technology adopting the empirical coefficient method is effectively overcome, and the related solution values of the scaffold and the pulling and hanging unloading steel wire rope can be quickly and accurately obtained through a manual calculation or programming mode.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the present invention in any way, so that any modification, equivalent change and modification made to the above embodiment according to the technical spirit of the present invention are within the scope of the technical solution of the present invention.

Claims (8)

1. A method for solving a mechanical model of a scaffold based on a pulling and lifting unloading method is characterized by comprising the following steps:
s10, calculating by taking a single scaffold as a segment unit, wherein the single scaffold comprises a single vertical rod model formed on the basis of an inner vertical rod or an outer vertical rod of the scaffold, and the stress condition of an object under the single vertical rod model is calculated by a segmented gradual loading solution, and the single vertical rod model comprises a plurality of single vertical rod models which are sequentially arranged in a linear shape from bottom to top:
k1、G1、k2、G2、k3、G3……kn、Gn、kn+1and k is1And G1K is2And G2… … k betweennAnd GnAre correspondingly connected with ks1、ks2……ksn(ii) a Wherein, the first and the second end of the pipe are connected with each other,
k1for the vertical stiffness, k, of the scaffolding at the foundation sections1The rigidity of a spring or the vertical rigidity of an unloading steel wire rope at the section steel is constructed;
ks2、ks3……ksnunloading the vertical rigidity of the steel wire rope for the corresponding section of the corresponding scaffold;
G1、G2……Gnequivalent concentrated vertical loads at the vertical rod of the nth section are respectively a 1 st section and a 2 nd section;
k2、k3……kn+1equivalent springs at the upright rods of the 1 st section and the 2 nd section are respectively;
when the scaffold is n sections, when off-load wire rope number is n, then wire rope counter-force, bottom sprag pole counter-force and the pole setting axle power that the x section scaffold corresponds are respectively:
reaction force of the wire rope:
Figure FDA0003597792920000011
bottom support bar counter-force:
Figure FDA0003597792920000012
pole setting axial force: n is a radical ofx＝Rsx+Rqx，
Base reaction force: rf＝N1；
In the formula (I), the compound is shown in the specification,
Figure FDA0003597792920000013
the counter force of the steel wire rope at the corresponding section of the corresponding scaffold is obtained;
Figure FDA0003597792920000014
the counter force of the bottom supporting rod at the corresponding section of the corresponding scaffold is obtained;
s20, constructing a matrix expression to calculate the final stress of the object under the single vertical rod model, wherein the matrix expression comprises the following steps:
reaction force of the steel wire rope:
[Rs]＝[Ms]·[G](formula 1)
Bottom support bar counter-force:
[Rq]＝[Mq]·[G](formula 2)
Pole setting axial force:
[N]＝[Rs]+[Rq](formula 3)
Wherein the content of the first and second substances,
[Rs]＝[Rs1，Rs2，Rs3，...，Rsn]，
[Rq]＝[Rq1，Rq2，Rq3，...，Rqn]，
[N]＝[N1，N2，N3，...，Nn]，
[G]＝[G1，G2，G3，...，Gn]，
Figure FDA0003597792920000021
Figure FDA0003597792920000022
in the formula (I), the compound is shown in the specification,
Figure FDA0003597792920000023
En、An、Lnthe elastic modulus, the section area and the length of the nth section of scaffold steel pipe are respectively set;
Esn、Asn、Lsn、θnthe elastic modulus, the section area, the length and the horizontal included angle of the nth section of steel wire rope are respectively obtained.
2. The method for solving the mechanical model of the scaffold based on the pulling and hoisting unloading method according to claim 1, wherein the step S10 comprises the calculation of the basic segment to determine k1、ks1When being the overhanging shaped steel scaffold, there is the formula of calculating:
ks1＝EA/L·sin2θ1
where E, A, L is the modulus of elasticity, the cross-sectional area and the calculated length, θ, of the steel cord, respectively1Is the included angle between the unloading steel wire rope and the horizontal reference line.
3. The method for solving the mechanical model of the scaffold based on the pulling and hoisting unloading method according to claim 1, wherein the step S10 comprises the step of solving the G1The calculation at the segment, based on vertical force balance, exists:
reaction force of the wire rope:
Figure FDA0003597792920000024
bottom supportBrace bar counter force:
Figure FDA0003597792920000025
wherein k isq1＝k1。
4. The method for solving the mechanical model of the scaffold based on the pulling and hoisting unloading method according to claim 1, wherein the step S10 comprises the step of solving the G2The calculation at the segment, based on vertical force balance, exists:
reaction force of the wire rope:
Figure FDA0003597792920000026
bottom support bar counter-force:
Figure FDA0003597792920000027
wherein k isq2＝(ks1+kq1)·k2/(k2+ks1+kq1)；
Reaction force of the wire rope:
Figure FDA0003597792920000031
bottom support bar counter-force:
Figure FDA0003597792920000032
wherein k isq1＝k1。
5. The method for solving the mechanical model of the scaffold based on the pulling and hoisting unloading method according to claim 1, wherein the step S10 comprises the step of solving the GnThe calculation at the segment, based on vertical force balance, exists:
reaction force of the wire rope:
Figure FDA0003597792920000033
counter-force of bottom support rod
Figure FDA0003597792920000034
Wherein k isqn＝(ks(n-1)+kq(n-1))·kn/(kn+ks(n-1)+kq(n-1))；
Reaction force of the wire rope:
Figure FDA0003597792920000035
bottom support bar counter-force:
Figure FDA0003597792920000036
6. the method for solving the mechanical model of the scaffold based on the pulling and lifting unloading method according to claim 1, wherein the scaffold comprises a floor scaffold and an overhanging steel scaffold.
7. The method for solving the mechanical model of the scaffold based on the pulling and lifting unloading method according to claim 6, wherein the scaffold is a floor scaffold, and k is the k at the time1For the vertical stiffness of the natural foundation, there is ks1＝0。
8. The method for solving the mechanical model of the scaffold based on the pulling and hoisting unloading method according to claim 6, wherein the scaffold is an overhanging type steel scaffold, and k is the k at the time1Is the vertical rigidity of the vertical rod at the overhanging section steel, ks1The vertical rigidity of the unloading steel wire rope at the section steel is obtained.
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