CN109446742B - Multi-body dynamic simulation method for pipe grabbing machine of pipe processing equipment of semi-submersible drilling platform - Google Patents

Abstract

The multi-body dynamic simulation method for the pipe grabbing machine of the pipe processing equipment of the semi-submersible drilling platform comprises the following steps: establishing a three-dimensional entity model in three-dimensional design software; step two: importing the three-dimensional entity model into ADAMS software; step three: establishing a multi-rigid-body dynamics simulation model in ADAMS software; step four: establishing a multi-flexible-body dynamic simulation model in ADAMS software; step five: loading wind load; step six: performing multi-rigid body and flexible body dynamics simulation and acquiring corresponding output data and curves; the method simulates the dynamic characteristics of the deepwater semi-submersible drilling platform when the pipe processing equipment grabs the pipe machine under the action of wind waves, can improve the analysis and calculation precision, and provides technical support for the design and optimization of the pipe machine.

Description

Multi-body dynamics simulation method of pipe handling equipment for pipe handling equipment on semi-submersible drilling platforms

technical field

The invention relates to the technical field of offshore oil equipment, in particular to a multi-body dynamics simulation method for a pipe grabber of a semi-submersible drilling platform pipe processing equipment.

Background technique

During the drilling operation, the semi-submersible drilling platform adopts various measures such as heave compensation device, anti-rolling device and dynamic positioning system to maintain the position of the platform on the sea surface before drilling operations can be carried out. Roll, heave, sway and other movements. Pipe grabber is one of the large-scale pipe handling equipments operating on the platform. It is used to pick up and hoist pipe strings such as drill pipes and casings on the platform yard and place them on the power catwalk, and then use the subsequent pipe arranging machines, etc. Equipped to realize automatic drilling operations. Pipe handling equipment The pipe grabbing machine bears a large and complex load during operation, and its light weight should also be considered in the design under the condition of guaranteed strength. The traditional static strength design based on experience cannot accurately grasp the dynamic characteristics of the equipment during operation. Considering the movement of the platform foundation under the influence of wind and waves, it is more difficult to carry out accurate multi-body dynamic analysis of the equipment, which increases the difficulty of equipment design.

SUMMARY OF THE INVENTION

In order to overcome the design difficulties of pipe handling equipment and avoid major accidents such as damage due to insufficient strength of the designed equipment during operation, the purpose of the present invention is to provide a multi-body dynamics simulation of pipe handling equipment for pipe handling equipment on a semi-submersible drilling platform. The method has the characteristics of high dynamic simulation accuracy, simplicity and speed.

In order to achieve the above object, the technical scheme of the present invention is:

The multi-body dynamics simulation method for the pipe grabber of the pipe handling equipment on the semi-submersible drilling platform includes the following steps:

Step 1: Build a 3D solid model with 3D design software;

Step 2: Import the 3D solid model into the ADAMS software;

Step 3: Establish a multi-rigid body dynamics simulation model in ADAMS software, add kinematic pair constraints and driving constraints between adjacent components, and add driving constraints on the corresponding kinematic pairs according to the actual driving type and position requirements. The working parameters set the motion function of each drive constraint;

Step 4: Establish a multi-flexible body dynamics simulation model in ADAMS software;

Step 5: Wind load loading;

Step 6: Perform multi-rigid and flexible-body dynamics simulation and obtain corresponding output data and curves; obtain corresponding output data and curves through the ADAMS post-processing module. After the dynamic simulation of the model, the flexible body components are invalidated, the rigid body components in their original positions are restored, the multi-rigid body components are simulated, and the analysis and comparison of the multi-flex and multi-rigid body model simulations are carried out.

The second step is specifically:

Import the three-dimensional solid model into the ADAMS software, set the dimensions, adjust the position and angle of the model, set the name, material parameters, and appearance color of each component; establish a simulation that can simulate the motion of the semi-submersible drilling platform under the action of waves Platform, in the inertial coordinate system, under the influence of wind and waves, the motion that can occur on the deepwater semi-submersible drilling platform includes the rotational degrees of freedom of roll, yaw, and pitch around the three coordinate axes of x, y, and z, and the rotational degrees of freedom along the x, y, and z axes. , y, z three coordinate axes, the translational degrees of freedom of surge, heave, and sway, and the combination of several motions; in order to simulate these motions, a motion component and a motion pair are established at the bottom of the platform to simulate the The response of the platform under the influence of ocean waves, due to the small yaw motion, has little impact, so this motion simulation is not performed. The method is as follows:

A pitch rotation pair 13 is established between the pitch base 1 and the roll member 2, and a rotational drive is established on this rotation pair, and a motion function is set to simulate the rolling of the platform under the action of ocean waves;

A roll rotation pair 14 is established between the roll member 2 and the heave member 3, and a rotational drive is established on this rotation pair, and a motion function is set to simulate the pitch of the platform under the action of ocean waves;

A heave moving pair 10 is established between the heave member 3 and the heave member 4, and a mobile drive is established on this, and a motion function is set to simulate the heave motion of the platform under the action of ocean waves;

A surging moving pair 8 is established between the surging and swaying member 4 and the fixed base 5, and a mobile drive is established on this movement, and a motion function is set to simulate the surging motion of the platform under the action of ocean waves;

At the same time, a swaying moving pair 15 is established between the swaying and swaying member 4 and the fixed base 5, and a moving drive is established on the moving pair, and a motion function is set to simulate the swaying motion of the platform under the action of ocean waves ;

At the same time, a fixed pair a 6, a fixed pair b 7, a fixed pair c 9, a fixed pair d 11, and a fixed pair e 12 are respectively established between the above components. When the influence of ocean waves does not need to be considered, the above fixed pair is set to be active. , the rest of the kinematic pairs and drives above are all set to fail; when one or more of the working conditions need to be simulated, first set the fixed pairs between the corresponding components to fail, and then activate the corresponding kinematic pairs and drives to make When it is activated, it can simulate the rolling, pitch, heave, surge, and sway of the platform under the action of waves, or the superposition of several conditions according to the actual situation.

In the step 3, the kinematic pair constraints and driving constraints between adjacent components are added, as follows:

Add kinematic pairs in the pipe grabbing machine as follows: between the column and the rotating bracket, between the rotating bracket and the main arm, between the main arm and the folding arm, between the rotating bracket and the main arm cylinder, between the main arm and the main arm cylinder rod , Add a rotating pair between the main arm and the hydraulic cylinder barrel of the folding arm, and between the folding arm and the hydraulic cylinder rod of the folding arm; respectively add a moving pair between the main arm and the hydraulic cylinder rod of the main arm, and between the main arm and the hydraulic cylinder barrel of the folding arm;

The drive constraints are added to the pipe grabbing machine as follows: add a rotational drive to the rotating pair between the column and the rotating bracket, and set the angular displacement drive function according to the actual working conditions; between the main arm and the main arm hydraulic cylinder rod, the main arm and the folding Displacement drives are added to the moving pairs between the arm cylinders respectively, and the displacement drive function is set according to the actual working conditions; the local coordinate MARKER is established at the key position of the component, and the load type is added to the MARKER point of the corresponding component according to the actual working condition. The direction of the load, the load function;

Add a measurement function to the MARKER point of the component to be analyzed to measure the motion parameters or mechanical parameters of the point during the simulation process. The motion parameters include displacement, velocity, and acceleration, and the mechanical parameters include force and torque. Complete the establishment of a multi-rigid body simulation model, As the basis for the establishment of the multi-flexible body model, a multi-rigid body simulation model of the pipe grabber is established.

Described step 4, specific steps are as follows:

(1) Generate MNF modal files for the components in the multi-rigid body model respectively;

For the components in the above mechanisms that need to be converted into flexible bodies, save the 3D solid model of the component in SAT and other formats in the 3D solid modeling software respectively;

Import the above files into the finite element analysis software, adjust the scale of the model, and set the elastic modulus, density, and meshing type of the material;

Perform finite element mesh division, and convert the meshed model into an MNF format file after the division is completed;

(2) Import the MNF file in ADAMS, adjust the direction and position of the flexible body component, completely coincide with the rigid body component that needs to be replaced, make the original rigid body component effective, and create a massless fiction at the component connected with the flexible body component The same kinematic pair constraint and driving constraint as the multi-rigid body model are added between the virtual component and the connected component; and the vertical direction is loaded at the end of the folding arm according to the actual lifting load of the pipe grabber. The loading method is the same as that of the multi-rigid body model, and the establishment of the multi-flex body model is completed.

The fifth step is specifically: the wind pressure is represented by ω. The wind pressure ω is related to the wind speed v, and the wind pressure ω is calculated according to the Bernoulli equation in fluid mechanics:

where: ω—wind pressure per unit area, kN/m ² ; ρ—air density, t/m ³ ; γ—air gravity per unit volume, kN/m ³ ; g—gravity acceleration, m/ s ² ; v——wind speed, m/s;

According to the working wind speed, the wind pressure can be obtained by substituting the above formula. On the main wind-loaded components of multi-rigid and multi-flexible bodies, the total wind load of the component is calculated by the product of the wind pressure and the windward area of the component, and then multiple marker MARKER points are evenly distributed on the component. On the MARKER point, according to the wind load direction, the equivalent load is equally divided into the load, so as to be equivalent to the total wind load on the component.

The invention simulates the dynamic characteristics of the deepwater semi-submersible drilling platform when the pipe grabber works under the action of wind and waves, can improve the analysis and calculation accuracy, and provides technical support for the design and optimization of the pipe grabber.

Description of drawings

Fig. 1 is a schematic flow chart of a multi-body dynamics simulation method for a pipe grabber of a deepwater semi-submersible drilling platform pipe processing equipment according to the present invention.

Figure 2 is a schematic diagram of the movement of the pipe grabber mechanism.

Figure 3 Three-dimensional view of the pipe grabber assembly.

Figure 4 An ocean platform with 6 degrees of freedom.

Figure 5 simulates the restraint and drive of the platform under the action of wind and waves, Figure 5a is the front view; Figure 5b is the left side view.

Detailed ways

The present invention will be described in further detail below with reference to the accompanying drawings and specific embodiments.

As shown in Figure 1, a multi-body dynamics simulation method for a pipe grabber of a deepwater semi-submersible drilling platform pipe processing equipment of the present invention includes the following steps:

Step 1: Build a 3D solid model in the 3D design software. As shown in Figure 2, it is a schematic diagram of the movement of the pipe grabber mechanism of the drilling platform pipe handling equipment, which mainly includes the column 1-1, the rotating bracket 1-2, the main arm 1-3, Folding arm 1-4, telescopic rod, main arm hydraulic cylinder barrel 1-5, main arm hydraulic cylinder rod 1-6, folding arm hydraulic cylinder barrel 1-7, folding arm hydraulic cylinder rod 8 components. In the 3D design software (such as Pro/E, Solid Edge, etc.), the 3D entity is drawn according to the actual structure to improve the simulation accuracy. As shown in Figure 3, it is a three-dimensional drawing of the simulation assembly of the established pipe grabbing machine.

Step 2: Import the 3D solid model into the ADAMS software, set the dimensions, adjust the position and angle of the model, and set the names, material parameters, and appearance colors for each component; establish a model capable of simulating the generation of semi-submersible drilling platforms under the action of ocean waves The motion simulation platform is shown in Figure 4. In the inertial coordinate system, under the influence of wind and waves, the motion that can occur on the deep-water semi-submersible drilling platform includes rolling, yaw, and longitudinal movements around the three coordinate axes of x, y, and z. The rotational degrees of freedom of the shake and the translational degrees of freedom of the surge, heave, and sway along the three axes of x, y, and z, and combinations of several motions. As shown in Figure 5 and combined with Figure 3, in order to simulate these kinds of motions, a motion component and a motion pair are established at the bottom of the platform respectively to simulate the response of the platform under the influence of waves. Due to the small yaw motion, the influence is small. , do not do this motion simulation, the method is as follows:

A pitch rotation pair 13 is established between the pitch base 1 and the roll member 2, and a rotational drive is established on the rotation pair, and a motion function is set to simulate the rolling of the platform under the action of ocean waves.

A roll rotation pair 14 is established between the roll member 2 and the heave member 3, and a rotational drive is established on the rotation pair, and a motion function is set for simulating the pitch of the platform under the action of ocean waves.

A heave movement pair 10 is established between the heave member 3 and the heave member 4, and a movement drive is established thereon, and a motion function is set for simulating the heave movement of the platform under the action of ocean waves.

A surge moving pair 8 is established between the surge and sway member 4 and the fixed base 5, and a moving drive is established on this movement, and a motion function is set for simulating the surge motion of the platform under the action of ocean waves.

At the same time, a swaying moving pair 15 is established between the swaying and swaying member 4 and the fixed base 5, and a moving drive is established on the moving pair, and a motion function is set to simulate the swaying motion of the platform under the action of ocean waves .

At the same time, a fixed pair a 6, a fixed pair b 7, a fixed pair c 9, a fixed pair d 11, and a fixed pair e 12 are respectively established between the above components. When the influence of ocean waves does not need to be considered, the above fixed pair is set to be active. , the rest of the above kinematic pairs and drives are all set invalid. When it is necessary to simulate one or more of these working conditions, first set the fixed pair between the corresponding components to be invalid, and then activate the corresponding kinematic pair and drive to make them in an active state, so that the simulation under the action of ocean waves can be performed respectively. One of several working conditions of platform roll, pitch, heave, surge, and sway or the superposition of several conditions according to the actual situation.

Step 3: Establish a multi-rigid body dynamic simulation model in ADAMS software, and add kinematic pair constraints and driving constraints between adjacent components. According to the actual driving type and position requirements, add driving constraints to the corresponding kinematic pairs, and set the motion function of each driving constraint according to the actual working parameters; combined with Figure 2, the specific method in Figure 3 is as follows:

Add kinematic pairs in the pipe grabbing machine as follows: between the column and the rotating bracket, between the rotating bracket and the main arm, between the main arm and the folding arm, between the rotating bracket and the main arm cylinder, between the main arm and the main arm cylinder rod , Between the main arm and the hydraulic cylinder barrel of the folding arm, and between the folding arm and the hydraulic cylinder rod of the folding arm, respectively add a rotating pair; add a moving pair between the main arm and the hydraulic cylinder rod of the main arm, and between the main arm and the hydraulic cylinder barrel of the folding arm.

The drive constraints are added to the pipe grabbing machine as follows: add a rotational drive to the rotating pair between the column and the rotating bracket, and set the angular displacement drive function according to the actual working conditions; between the main arm and the main arm hydraulic cylinder rod, the main arm and the folding Displacement drives are respectively added to the moving pairs between the arm cylinders, and the displacement drive functions are set according to the actual working conditions.

Establish a local coordinate MARKER at the key position of the component, add the load type to the MARKER point of the corresponding component according to the actual working conditions, set the direction of the load, and the load function;

Add a measurement function to the MARKER point of the component to be analyzed to measure the motion parameters (displacement, velocity, acceleration, etc.) or mechanical parameters (force, moment) of the point during the simulation process, and complete the establishment of a multi-rigid body simulation model. The basis for soft body modeling.

Step 4: Establish a multi-flexible body dynamics simulation model in ADAMS software, the steps are as follows:

1) Generate MNF modal files from the components in the multi-rigid body model respectively;

For the components in the above mechanisms that need to be converted into flexible bodies, save the 3D solid model of the component in SAT and other formats in the 3D solid modeling software respectively;

Import the above files into finite element analysis software (such as ANSYS), adjust the model scale, and set the material elastic modulus, density, and mesh division type;

Perform finite element mesh division, and after the division is completed, convert the meshed model into an MNF format file (modal file).

2) Import the MNF file in ADAMS, adjust the direction and position of the flexible body component, completely coincide with the rigid body component that needs to be replaced, make the original rigid body component effective, and create a massless virtual component at the component connected to the flexible body component , and is fixed with the flexible body component, and the same kinematic pair constraints and driving constraints as the multi-rigid body model are added between the virtual component and the connected components. And according to the actual lifting load of the pipe grabber, the vertical working load is loaded at the end of the folding arm. The loading method is the same as that of the multi-rigid body model, and the multi-flexible body model is established.

Step 5: Loading of wind loads:

The calculation of wind load can be carried out according to the load code of building structures in my country. When the wind moves forward at a certain speed and encounters an obstacle, it will generate pressure on the obstacle, which is wind pressure. For engineering structure design calculations, the magnitude of the wind effect is best expressed directly by wind pressure. The higher the wind speed, the higher the wind pressure. Wind pressure is represented by ω. The wind pressure ω is related to the wind speed v, and the wind pressure ω is calculated according to the Bernoulli equation in fluid mechanics:

where: ω—wind pressure per unit area, kN/m ² ; ρ—air density, t/m ³ ; γ—air gravity per unit volume, kN/m ³ ; g—gravity acceleration, m/ s ² ; v——wind speed, m/s.

According to the working wind speed, the wind pressure can be obtained by substituting the above formula. On the main wind-loaded components of multi-rigid and multi-flexible bodies, the total wind load of the component is calculated by the product of the wind pressure and the windward area of the component, and then multiple marker MARKER points are evenly distributed on the component. On the MARKER point, according to the wind load direction, the equivalent load is equally divided into the load, so as to be equivalent to the total wind load on the component.

When performing multi-rigid body dynamics simulation, activate all multi-rigid body models and invalidate multi-flex body models; when performing multi-flex body dynamics simulation, activate all multi-flex body models and invalidate multi-rigid body models.

Step 6: Perform multi-rigid and flexible body dynamics simulation and obtain corresponding output data and curves, and obtain corresponding output data and curves through the ADAMS post-processing module. In order to facilitate the comparison of multi-rigid and multi-flexible body simulation models, after the dynamic simulation of the multi-flexible body model, each flexible body component is invalidated, the rigid body components in their original positions are restored, and the multi-rigid body components are simulated to perform multi-flex and multi-body components. Analytical comparison of rigid body model simulations.

The above describes the specific embodiments of the present invention, but those skilled in the art should understand that these are only examples, and various changes or modifications can be made to this embodiment without departing from the principle and essence of the present invention. The scope of protection is limited only by the appended claims.

Claims (2)

1. The multi-body dynamic simulation method for the pipe grabbing machine of the pipe processing equipment of the semi-submersible drilling platform is characterized by comprising the following steps of:

the method comprises the following steps: establishing a three-dimensional entity model in three-dimensional design software;

step two: importing the three-dimensional entity model into ADAMS software; the method specifically comprises the following steps:

importing the three-dimensional entity model into ADAMS software, setting dimensions, adjusting the position and angle of the model, and setting names, material parameters and appearance colors for each component; establishing a simulation platform capable of simulating the motion of the semi-submersible drilling platform under the action of sea waves, wherein in an inertial coordinate system, under the influence of wind waves, the motion which can be generated by the deepwater semi-submersible drilling platform comprises the rotational freedom of rolling, yawing and pitching around three coordinate axes of x, y and z, the translational freedom of pitching, heaving and swaying along the three coordinate axes of x, y and z, and the combination of several motions; in order to simulate the motions, a motion component and a motion pair are respectively established at the bottom of the platform and used for simulating the response of the platform under the influence of sea waves, and because the yawing motion is small, the influence is little, the motion simulation is not carried out, and the method comprises the following steps:

a pitching revolute pair (13) is established between the pitching base (1) and the rolling component (2), and a rotary drive is established on the revolute pair, and a motion function is set for simulating the rolling of the platform under the action of sea waves;

a rolling rotation pair (14) is established between the rolling component (2) and the heaving component (3), and a rotation drive is established on the rotation pair, and a motion function is set for simulating the pitching of the platform under the action of sea waves;

a heave moving pair (10) is established between the heave member (3) and the surging and surging member (4), and a moving drive is established on the heave moving pair, and a motion function is set for simulating the heave motion of the platform under the action of sea waves;

a surging moving pair (8) is established between the surging and surging component (4) and the fixed base (5), and a moving drive is established on the movement, and a motion function is set for simulating the surging motion of the platform under the action of sea waves;

meanwhile, a swaying moving pair (15) is established between the surging swaying component (4) and the fixed base (5), and a moving drive is established on the moving pair, and a motion function is set for simulating the swaying motion of the platform under the action of sea waves;

meanwhile, a fixed pair a (6), a fixed pair b (7), a fixed pair c (9), a fixed pair d (11) and a fixed pair e (12) are respectively established among the components, when the influence of sea waves is not considered, the fixed pairs are set to be in an activated state, and all the rest kinematic pairs and the drives are set to be invalid; when one or more working conditions need to be simulated, the fixed pair between the corresponding components is set to be invalid, then the corresponding kinematic pair and the drive are activated to be in an activated state, and then the rolling, pitching, heaving, pitching and rolling of the platform under the action of sea waves can be simulated respectively or the superposition of the working conditions under the actual condition is realized;

step three: establishing a multi-rigid-body dynamics simulation model in ADAMS software, adding kinematic pair constraints and driving constraints between adjacent components, adding driving constraints on corresponding kinematic pairs according to actual driving types and position requirements, and setting motion functions of the driving constraints according to actual working parameters;

in the third step, kinematic pair constraint and driving constraint between adjacent components are added, specifically as follows:

the pipe grabbing machine is added with the following kinematic pairs: adding revolute pairs between the upright column and the rotary support, between the rotary support and the main arm, between the main arm and the folding arm, between the rotary support and the main arm hydraulic cylinder barrel, between the main arm and the main arm hydraulic cylinder rod, between the main arm and the folding arm hydraulic cylinder barrel, and between the folding arm and the folding arm hydraulic cylinder rod respectively; moving pairs are respectively added between the main arm and the main arm hydraulic cylinder rod and between the main arm and the folding arm hydraulic cylinder barrel;

the driving constraints added in the pipe grabbing machine are as follows: adding a rotation drive on a revolute pair between the upright post and the rotary support, and setting an angular displacement drive function according to actual working conditions; respectively adding displacement drive to the sliding pairs between the main arm and the main arm hydraulic cylinder rod and between the main arm and the folding arm hydraulic cylinder barrel, and setting a displacement drive function according to actual working conditions; establishing local coordinates MARKER at key positions of the components, adding load types on MARKER points of the corresponding components according to actual working conditions, and setting load directions and load functions;

adding a measurement function to a MARKER point of a component to be analyzed to measure a motion parameter or a mechanical parameter of the point in a simulation process, wherein the motion parameter comprises displacement, speed and acceleration, the mechanical parameter comprises force and moment, the establishment of a multi-rigid-body simulation model is completed, and the multi-rigid-body simulation model is established as a basis for the establishment of a multi-flexible-body model;

step four: establishing a multi-flexible-body dynamic simulation model in ADAMS software; the method comprises the following specific steps:

(1) Respectively generating MNF modal files for components in the multi-rigid-body model;

for the component needing to be converted into the flexible body in the mechanism, respectively storing the three-dimensional solid model of the component in an SAT format in three-dimensional solid modeling software;

importing the files into finite element analysis software, adjusting the model proportion, and setting the elastic modulus, the density and the grid division type of the material;

carrying out finite element meshing, and converting a meshed model into an MNF format file after the meshing is finished;

(2) Introducing an MNF file into ADAMS, adjusting the direction and position of the flexible member, completely overlapping the flexible member with a rigid member to be replaced, actually replacing the original rigid member, establishing a virtual member without mass at the position where the flexible member is connected with the flexible member, fixing the virtual member with the flexible member, and adding kinematic pair constraint and driving constraint which are the same as those of a multi-rigid model between the virtual member and the connected member; loading a working load in the vertical direction at the tail end of the folding arm according to the actual hoisting load of the pipe grabbing machine, wherein the loading method is the same as that of a multi-rigid-body model, and the multi-flexible-body model is built;

step five: loading wind load;

step six: performing multi-rigid body and flexible body dynamics simulation and acquiring corresponding output data and curves; and acquiring corresponding output data and curves through an ADAMS post-processing module, and after the dynamic simulation of the multi-flexible-body model, invalidating each flexible-body component, recovering the rigid-body component at the original position, simulating the multi-rigid-body components, and analyzing and comparing the simulation of the multi-flexible-body and multi-rigid-body models in order to compare the multi-rigid-body and multi-flexible-body simulation models.

2. The multi-body dynamic simulation method of the pipe grabbing machine of the semi-submersible drilling platform pipe handling equipment according to claim 1, wherein the fifth step is specifically as follows:

wind pressure is represented by omega; the wind pressure omega is related to the wind speed v, and the wind pressure omega is calculated according to the Bernoulli equation in hydrodynamics:

in the formula: omega-wind pressure per unit area, kN/m ² (ii) a Rho-air density, t/m ³ (ii) a Gamma-air gravity per unit volume, kN/m ³ (ii) a g-acceleration of gravity, m/s ² (ii) a v-wind speed, m/s;

according to the working wind speed, substituting the formula into the formula to obtain the wind pressure; on the main wind load bearing member of multiple rigid bodies and multiple flexible bodies, the total wind load of the member is calculated through the product of the wind pressure and the windward area of the member, then a plurality of marked MARKER points are uniformly distributed and established on the member, and the load is equally loaded on each MARKER point according to the wind load direction so as to be equivalent to the total wind load of the member.

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