Method for calculating horizontal displacement of lifted structure under action of horizontal force during lifting construction

Abstract

The invention provides a method for calculating the horizontal displacement of a lifted structure under the action of horizontal force during lifting construction. The method comprises the steps that a target structure is lifted through n vertical lifting ropes; establishing a rectangular coordinate system, obtaining lifting point data, and obtaining a horizontal force acting on the target structure and an acting point coordinate; calculating the gravity of the target structure and the gravity center of the target structure; a gravity center coordinate system is formed, the next series of data of the gravity center coordinate system are calculated and calculated, and finally the displacement (ux, uy) of the target structure is obtained through calculation and compared with a limit value. According to the method, under the conditions that the ratio of the horizontal load to the vertical load is small (not larger than 15%), the horizontal rigidity of the lifted structure is relatively large, and the pulling force of the lifting rope is obtained through vertical analysis, the horizontal displacement of the lifted structure, the horizontal component force of the lifting rope, the vertical rotating angle and the like are calculated, and complex geometric nonlinear finite element analysis is avoided.

Description

Technical Field

[0001] The present application relates to the technical field of structural construction, and in particular to a method for calculating the horizontal displacement of a lifted structure under the action of a horizontal force during lifting construction. Background Art

[0002] When the lifting method is used to lift the structure, the action of horizontal loads such as wind load will cause horizontal displacement of the structure and vertical rotation angle of the lifting rope. Excessive horizontal displacement may cause collision between the lifted structure and the existing structure and the lifting device. Excessive vertical rotation angle of the lifting rope (generally exceeding 8.5º or 0.15 radians) will cause abnormal operation of the lifting cylinder. The horizontal component of the rope tension caused by this angle can resist the action of horizontal external loads.

[0003] Usually, lifting calculations require the use of professional finite element software. To consider the horizontal component of the rope tension, it is necessary to consider geometric nonlinearity, that is, to establish an equilibrium equation based on the deformed structure. Therefore, the calculation is very complicated. In some cases, such as when the length of the rope far exceeds the scale of the lifted structure, the calculation may be difficult to converge or the result may be abnormal, and the correct result cannot be obtained.

[0004] Therefore, there is an urgent need for a method to calculate the horizontal displacement of the lifted structure under the action of horizontal force during lifting construction to avoid complex geometric nonlinear finite element analysis. Summary of the invention

[0005] In order to overcome the defects of the above-mentioned related technologies, the present application provides a method for calculating the horizontal displacement of a lifted structure under the action of a horizontal force during lifting construction, which can avoid complex geometric nonlinear finite element analysis.

[0006] The present application provides a method for calculating the horizontal displacement of a lifted structure under the action of a horizontal force during lifting construction, comprising the following steps:

[0007] The target structure is lifted by using n vertical lifting ropes, where n is a positive integer (n≥3), and the lifting ropes are initially arranged in a vertical direction;

[0008] Establish a rectangular coordinate system (x o , y o , z o ), the z of the rectangular coordinate system o The axis is in the vertical direction, the lifting point of each suspension rope is numbered, and the lifting point data is obtained, including: rope length H i , lifting point horizontal coordinate (x i o , y i o ), vertical tension T at the lifting point i , T i>0; Get the horizontal force acting on the target structure (W x ,W y ) and the coordinates of the point of action (x w o , y w o );

[0009] The gravity G of the target structure is calculated based on the following formula:

[0010] ,

[0011] The center of gravity (x) of the target structure is calculated based on the following formula G o ,y G o ):

[0012] ,

[0013] ,

[0014] The origin of the rectangular coordinate system is translated to the center of gravity of the target structure to form a center of gravity coordinate system (x, y, z). The coordinates of the lifting point in the center of gravity coordinate system (x) are calculated based on the following formula: i , y i ) and polar radius r i :

[0015] ,

[0016] ,

[0017] ,

[0018] The coordinates of the horizontal force action point of the lifting point in the center of gravity coordinate system (x w ,y w ):

[0019] ,

[0020] ,

[0021] Based on the following formula, calculate the horizontal torque T generated by the horizontal force on the center of gravity position of the target structure in the center of gravity coordinate system w :

[0022] ,

[0023] Based on the following formula, calculate the horizontal stiffness γ of each suspension rope: Hi , the linear density of the cable moment about the x-axis γ Mxi, the linear density of the cable moment about the y-axis γ Myi 、Linear density of the polar moment of inertia of the cable γ ρi :

[0024] ,

[0025] ,

[0026] ,

[0027] ,

[0028] The total horizontal stiffness γ is calculated based on the following formula: H , the total cable moment density about the x-axis γ Mx , the total cable moment density about the y-axis γ My 、Linear density of the polar moment of inertia of the cable γ ρ :

[0029] ,

[0030] ,

[0031] ,

[0032] ,

[0033] Based on the following formula, the equivalent cable force T of the target lifting structure is calculated. e , Equivalent total cable moment M affected by horizontal force e :

[0034] ,

[0035] ,

[0036] Based on the following formula, the horizontal displacement of the target structure (r x , r y ) and the rotation angle α:

[0037] ,

[0038] ,

[0039] ,

[0040] Based on the following formula, the horizontal displacement (u xi , u yi ) and horizontal component (F xi , F yi ):

[0041] ,

[0042] ,

[0043] ,

[0044] ,

[0045] Get the coordinates (x, y) of the point on the target structure that needs to be checked for horizontal collision in the center of gravity coordinate system, and calculate the displacement (u x , u y ), and compare with the limit value:

[0046] ,

[0047] .

[0048] Compared with the prior art, the advantages of this application are:

[0049] This application provides a case where the ratio of horizontal load to vertical load is small (no more than 15%) and the horizontal stiffness of the lifted structure is relatively large. Under the premise that the rope tension has been obtained through vertical analysis, the horizontal displacement of the lifted structure, the horizontal component of the rope and the vertical rotation angle are calculated, thereby avoiding complex geometric nonlinear finite element analysis. DETAILED DESCRIPTION

[0050] Example embodiments will now be described more fully. However, example embodiments can be implemented in a variety of forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided so that this application will be more comprehensive and complete and fully convey the concepts of the example embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0051] The embodiments of the present application are exemplary and do not necessarily include all the steps. For example, some steps can be decomposed, while some steps can be combined or partially combined. Therefore, the actual execution order may change according to the actual situation.

[0052] The present application provides a method for calculating the horizontal displacement of a lifted structure under the action of a horizontal force during lifting construction, comprising the following steps:

[0053] The target structure is lifted by using n vertical lifting ropes, where n is a positive integer (n≥3), and the lifting ropes are initially arranged in a vertical direction;

[0054] Establish a rectangular coordinate system (x o , yo , z o ), the z of the rectangular coordinate system o The axis is in the vertical direction, the lifting point of each suspension rope is numbered, and the lifting point data is obtained, including: rope length H i , lifting point horizontal coordinate (x i o , y i o ), vertical tension T at the lifting point i , T i >0; Get the horizontal force acting on the target structure (W x ,W y ) and the coordinates of the point of action (x w o , y w o );

[0055] The gravity G of the target structure is calculated based on the following formula:

[0056] ,

[0057] The center of gravity (x) of the target structure is calculated based on the following formula G o ,y G o ):

[0058] ,

[0059] ,

[0060] The origin of the rectangular coordinate system is translated to the center of gravity of the target structure to form a center of gravity coordinate system (x, y, z). The coordinates of the lifting point in the center of gravity coordinate system (x) are calculated based on the following formula: i , y i ) and polar radius r i :

[0061] ,

[0062] ,

[0063] ,

[0064] The coordinates of the horizontal force action point of the lifting point in the center of gravity coordinate system (x w ,y w ):

[0065] ,

[0066] ,

[0067] Based on the following formula, calculate the horizontal torque T generated by the horizontal force on the center of gravity position of the target structure in the center of gravity coordinate system w :

[0068] ,

[0069] Based on the following formula, calculate the horizontal stiffness γ of each suspension rope: Hi , the linear density of the cable moment about the x-axis γ Mxi , the linear density of the cable moment about the y-axis γ Myi 、Linear density of the polar moment of inertia of the cable γ ρi :

[0070] ,

[0071] ,

[0072] ,

[0073] ,

[0074] The total horizontal stiffness γ is calculated based on the following formula: H , the total cable moment density about the x-axis γ Mx , the total cable moment density about the y-axis γ My 、Linear density of the polar moment of inertia of the cable γ ρ :

[0075] ,

[0076] ,

[0077] ,

[0078] ,

[0079] Based on the following formula, the equivalent cable force T of the target lifting structure is calculated. e , Equivalent total cable moment M affected by horizontal force e :

[0080] ,

[0081] ,

[0082] Based on the following formula, the horizontal displacement of the target structure (r x , r y ) and the rotation angle α:

[0083] ,

[0084] ,

[0085] ,

[0086] Based on the following formula, the horizontal displacement (u xi , u yi ) and horizontal component (F xi , F yi ):

[0087] ,

[0088] ,

[0089] ,

[0090] ,

[0091] Get the coordinates (x, y) of the point on the target structure that needs to be checked for horizontal collision in the barycentric coordinate system, and calculate the displacement (u x , u y ):

[0092] ,

[0093] .

[0094] Furthermore, the displacement of the target structure (u x , u y ) is compared with a limit value.

[0095] Furthermore, when the lengths of the suspension ropes are different, the target structure will twist even if the torque is 0; if the resultant force of the horizontal load is 0 but the torque is not 0, the structure will also move horizontally. When the lengths of the suspension ropes are the same, the displacement and torsion angle of the structure are no longer coupled, the direction of the translation displacement is exactly the same as the direction of the horizontal load, and the magnitude is proportional, with a flexibility of H / G; the torsion angle depends entirely on the magnitude of the torque.

[0096] In summary, a method for calculating the horizontal displacement of a lifted structure under the action of a horizontal force during lifting construction is used in the present application. There is no need to use complex finite element analysis software that considers geometric nonlinearity for analysis. The method has low requirements for calculation personnel and is easy to implement. At the same time, the concept is clear and the structure has very good accuracy.

[0097] The above are merely a number of specific implementations of a method for calculating the horizontal displacement of a lifted structure under the action of a horizontal force during lifting construction in the present application. Each implementation can be implemented independently or in combination, and the present application is not limited thereto.

Claims

1. A method for calculating the horizontal displacement of a structure being lifted under the action of a horizontal force during lifting construction, characterized in that: The steps include: The target structure is lifted by using n vertical lifting ropes, where n is a positive integer (n≥3), and the lifting ropes are initially arranged in a vertical direction; Establish a rectangular coordinate system (x o , y o , z o ), the z of the rectangular coordinate system o The axis is in the vertical direction, the lifting point of each suspension rope is numbered, and the lifting point data is obtained, including: rope length H i , lifting point horizontal coordinate (x i o , y i o ), vertical tension T at the lifting point i , T i >0; Get the horizontal force acting on the target structure (W x ,W y ) and the coordinates of the point of action (x w o , y w o ); The gravity G of the target structure is calculated based on the following formula: ， The center of gravity (x) of the target structure is calculated based on the following formula G o ,y G o ): ， ， The origin of the rectangular coordinate system is translated to the center of gravity of the target structure to form a center of gravity coordinate system (x, y, z). The coordinates of the lifting point in the center of gravity coordinate system (x i , y i ) and polar radius r i : ， ， ， The coordinates of the horizontal force action point of the lifting point in the center of gravity coordinate system (x w ,y w ): ， ， Based on the following formula, calculate the horizontal torque T generated by the horizontal force on the center of gravity position of the target structure in the center of gravity coordinate system w : ， Based on the following formula, calculate the horizontal stiffness γ of each suspension rope: Hi , the linear density of the cable moment about the x-axis γ Mxi , the linear density of the cable moment about the y-axis γ Myi 、Linear density of the polar moment of inertia of the cable γ ρi : ， ， ， ， The total horizontal stiffness γ is calculated based on the following formula: H , the total cable moment linear density γ about the x-axis Mx , the total cable moment density about the y-axis γ My 、Linear density of the polar moment of inertia of the cable γ ρ : ， ， ， ， Based on the following formula, the equivalent cable force T of the target lifting structure is calculated. e , Equivalent total cable moment M affected by horizontal force e : ， ， Based on the following formula, the horizontal displacement of the target structure (r x , r y ) and the rotation angle α: ， ， ， Based on the following formula, the horizontal displacement (u xi , u yi ) and horizontal component (F xi , F yi ): ， ， ， ， Get the coordinates (x, y) of the point on the target structure that needs to be checked for horizontal collision in the barycentric coordinate system, and calculate the displacement (u x , u y ), and compare with the limit value: ， 。

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