CN113203394B - Online monitoring and intelligent early warning method for inclination angle of tower equipment - Google Patents

Online monitoring and intelligent early warning method for inclination angle of tower equipment Download PDF

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CN113203394B
CN113203394B CN202110333753.4A CN202110333753A CN113203394B CN 113203394 B CN113203394 B CN 113203394B CN 202110333753 A CN202110333753 A CN 202110333753A CN 113203394 B CN113203394 B CN 113203394B
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tower
inclination angle
tower body
wall thickness
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CN113203394A (en
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业成
张伯君
文耀华
于敬利
崔强
方学锋
姜君
雒相垚
周丹
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Nanjing Boiler & Pressure Vessel Supervision And Inspection Institute
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    • G01C9/00—Measuring inclination, e.g. by clinometers, by levels
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Abstract

An on-line monitoring and intelligent early warning method for the inclination angle of tower equipment features that the allowable inclination angle of each curved section of tower body under wind load is obtained based on the allowable stress of materialθ i ]Measuring the measured values of the inclinometers by arranging them on the top of the tower and on the designed critical sections of the tower installation (α i1,β i1) And further calculating the actual inclination angle value of each section relative to the plumb direction by 360 degreesθ i The actual tilt angle valueθ i Allowable inclination angle with respect to the corresponding cross sectionθ i ]Comparing and judging if the actual inclination angle of each sectionθ i All below its allowable tilt angleθ i ]It is judged as safe, otherwise, one or more than one appearsθ i Out of allowable tilt angleθ i ]And if the situation is not safe, the system automatically screens and records the position and the inclination angle value of the overrun dangerous section, and simultaneously sends out an early warning signal.

Description

Online monitoring and intelligent early warning method for inclination angle of tower equipment
Technical Field
The invention relates to a safety monitoring and early warning method for tower equipment, belongs to the field of safety production, and particularly relates to an online monitoring and intelligent risk early warning method for an inclination angle of slender tower equipment.
Background
The tower equipment is important mass transfer equipment in chemical and petrochemical industries, and the consumed steel and the cost in the whole set of process equipment account for very high, some even nearly 50%. In order to improve economic benefits and reduce production cost, tower equipment is developed in the direction of large scale and large height-diameter ratio H/D (H is tower height, mm; D is tower outer diameter, mm). The tower equipment with a large height-diameter ratio is easy to generate large-amplitude bending deformation under the action of combined wind bending moment taking wind load as a main factor, so that larger axial section stress is caused. If the deflection deformation of the tower body exceeds the allowable value, the stability and the safety of the process can be seriously influenced, and safety problems such as local stress concentration of the tower body, cracking of welding seams of dangerous sections, even fracture and overturn of the tower body and the like can be caused.
The tower body has various structural forms of equal diameter and equal wall thickness, equal diameter and unequal wall thickness and unequal diameter and unequal wall thickness along the height direction. The dangerous sections of the tower body needing stress checking comprise a skirt shell cross section on the upper surface of a basic ring plate, a shell cross section at the maximum opening of a skirt, a skirt and shell welded joint cross section, a tower shell cross section at a variable-section junction of unequal-diameter towers, a tower shell cross section at a variable-wall-thickness junction of equal-diameter towers (namely, a bottom cross section of a tower section with the same thickness), a section where a lower seal head tangent of the tower is located, a bottom cross section of a skirt transition section and the like. According to the mechanics of materials, the deflection (or the inclination angle) of the tower top is generated by the common contribution of the deflection deformation of each section of the tower body, all dangerous sections of the tower body cannot be accurately positioned only by monitoring one magnitude value of the deflection (or the inclination angle) of the tower top, and even if the deflection (or the inclination angle) of the tower top is within the range of the design control value, the situation that a certain section of weak tower section approaches or exceeds the safe allowable strength can occur.
Regarding the control of the deflection deformation of the tower equipment, the control value of the deflection of the tower top with the tower tray is set between H/500 and H/100 by various engineering companies and design units at home and abroad, and the control value of the deflection of the tower top with the filler can be properly relaxed. Deflection and inclination are two basic quantities for measuring bending deformation of the tower body, and the two quantities can be mutually converted to a certain extent. The tower container calculation in the current standard only gives an analytical calculation formula of the deflection of the tower top under the action of wind load, does not give calculation formulas of the inclination angle of the tower top, the deflection of any section and the inclination angle, and does not clearly specify the allowable deflection or the allowable inclination angle of tower equipment. Patent CN201811228155.5 provides a method for calculating deflection of the top of a variable cross-section tower container under the action of lateral force. Regarding the monitoring of the tilt deformation, the related patent technology utilizes a three-dimensional laser scanning technology, a GNSS technology, and the like to perform tilt monitoring on an object. The related patent only uses the deflection of the tower top as a monitoring object and uses a displacement sensor for monitoring.
In summary, the safety precaution research on the deflection and inclination of the tower equipment in the existing technology has certain limitations: (1) for tower equipment with a variable cross-section structure, when a tower body is subjected to flexural deformation, the prior art cannot meet the requirement of effective and safe identification and early warning on a variable cross-section dangerous cross section; (2) the measured tower top deflection value is a displacement amount, a fixed datum point needs to be referred, the measurement deviation is not easy to obtain directly, and the measurement deviation is large; (3) the data acquisition and processing cycle of the three-dimensional laser scanning and GNSS technology is long, the change of the object form can not be monitored in real time, the positioning requirement is high, the detection cost is high, and the method is generally only used for periodic inspection and is not suitable for real-time online monitoring and early warning of tower equipment. Therefore, it is necessary to research an online monitoring and intelligent early warning method for the inclination angle of the tower equipment.
Disclosure of Invention
In order to solve the problem that effective and safe identification and early warning on various dangerous sections of a tower body cannot be realized when the tower equipment inclines in the prior art, the invention aims to provide the tower equipment inclination angle on-line monitoring and intelligent early warning method.
In order to solve the problems, the invention adopts the technical scheme that:
an on-line monitoring and intelligent early warning method for the inclination angle of tower equipment is based on the safety condition of allowable material strength to obtain the allowable inclination angle [ theta ] of each cross section of tower body after bending under wind loadi]The measured values (alpha) of the inclinometers are measured by arranging the inclinometers on the top of the tower and on the designed dangerous sections of the tower equipment1i,β1i) And sending the data to the early warning platform in a wireless communication mode. The early warning platform automatically calculates to obtain the actual inclination angle value theta of each sectioniThe actual tilt angle value thetaiAllowable inclination angle [ theta ] with respect to corresponding cross-sectioni]Comparing and judging if the actual inclination angle theta of each sectioniAll below its allowable inclination angle [ theta ]i]Then it is judged as safe, otherwise one or more theta appeariOut of allowable inclination angle [ theta ]i]And if the situation is not safe, the platform intelligently screens and records the position and the inclination angle value of the overrun dangerous section, and simultaneously sends out an early warning signal.
Specifically, the tower equipment inclination angle online safety monitoring and intelligent early warning method comprises the following steps:
analyzing the structural type of a tower body of tower equipment, and finding out various dangerous variable cross sections of the tower body according to design conditions, wherein the number of the dangerous variable cross sections is N;
secondly, calculating the allowable inclination angle [ theta ] of each dangerous variable cross section according to the formula (22)i]Wherein (i ═ 1,2,3, …, N)
Figure BDA0002996457980000041
Thirdly, respectively installing and positioning 1 inclinometer on each dangerous variable cross section;
fourthly, the early warning platform obtains the value (alpha) of the inclinometer in real time in a wireless communication modei,βi) The actual inclination angle value theta of each dangerous section is automatically obtained by the formula (27)iWherein (i ═ 1,2,3, …, N);
Figure BDA0002996457980000042
fifthly, intelligently judging the condition of safety early warning, and automatically setting the allowable inclination angle [ theta ] of the second step by the early warning platformi]With the actual value of inclination theta of the fourth stepiMaking a comparison if all thetai≤[θi](i is 1,2,3, …, N), the tower body is judged to be in a safe state; if one or more theta occursi>[θi]If the tower body is in a non-safety state, the platform sends out an alarm signal in time.
Allowable inclination angle derivation for tower equipment
Specifically, according to the design standard of the tower type container, tower equipment can be simplified into cantilever beams, and the stress of the tower body is analyzed by utilizing the calculation of a virtual beam method (conjugate beam method) of material mechanics.
According to the mechanics of materials, the maximum positive stress σ occurs at the outer surface on the section with the largest bending momentmaxThe deflection Y and the inclination angle θ are two basic quantities for measuring bending deformation, namely:
Figure BDA0002996457980000043
for tower equipment with equal diameter and equal wall thickness
As shown in fig. 1, the center a of the tower at the top end is the origin, the central axis of the tower before deformation is the X-axis, and the X is downward. On a cross section with coordinate x, the wind load concentration is:
Figure BDA0002996457980000051
the wind bending moment caused by the wind load on the section with coordinate x is:
Figure BDA0002996457980000052
the dip angle equation is obtained from the approximate differential equation of the material mechanics deflection line:
Figure BDA0002996457980000053
combining the formula (3) and the formula (4), the tilt angle equation is obtained by integrating the formula (4) under the boundary conditions x being H and θ (H) being 0:
Figure BDA0002996457980000054
equal diameter equal wall thickness tower equipment, the biggest moment of flexure takes place at the stiff end of tower, and top of the tower department inclination is:
Figure BDA0002996457980000055
loading equal diameter windt＝P0ftFormula (6) is taken in, and is converted by combining formula (1):
Figure BDA0002996457980000056
the upper type
Figure BDA0002996457980000057
With reference to formula (1), the tower top inclination angle due to wind load is determined by taking formula (7) into formula (6):
Figure BDA0002996457980000058
combining the formula (1) and the formula (8), obtaining the tower top allowable inclination angle of the equal-diameter equal-wall thickness tower equipment:
Figure BDA0002996457980000061
for tower equipment with equal diameter and unequal wall thickness
As shown in FIG. 2, for tower equipment with equal diameter and unequal wall thickness, the center A of the top end of the tower is taken as the origin, the central axis of the tower before deformation is taken as the X axis, and the X axis faces downwards. On a cross section with the coordinate x, the wind load concentration is obtained by equation (2), and the wind bending moment calculation is obtained by equation (3).
The bending deformation of the tower-type container with equal diameter and unequal wall thickness is solved by using a piecewise rigidization method, and the section inclination angle theta of any node iiThe section rotation angles generated at the node i when each segment at the lower side of the node i is independently deformed are respectively thetai1、θi2、……、θiN. When the upper sections of the nodes i are independently deformed, the sections of the nodes i cannot be displaced, so that the superposition principle includes:
Figure BDA0002996457980000062
as can be seen from FIG. 2, the resultant force F generated by all wind loads of the tower section above the node iiSum and resultant moment Mi：
Figure BDA0002996457980000063
According to the calculation formula (6) of the inclination angle of the equal-diameter equal-wall thickness tower equipment, the rotation angle theta generated on the i section due to the i-th section wind load is calculatediPAnd deflection YiPRespectively as follows:
Figure BDA0002996457980000064
therefore, there is a corner θ generated at the i-section when the i-section is deformed aloneiiComprises the following steps:
Figure BDA0002996457980000071
in the formula:
Figure BDA0002996457980000072
further, the following is obtained:
Figure BDA0002996457980000073
the corner theta generated on the section i when any j section at the lower side of the node i +1 is independently deformedijComprises the following steps:
Figure BDA0002996457980000074
from the equation (10), the cross-sectional rotation angle θ of the node i is obtainediThe calculation formula is as follows:
Figure BDA0002996457980000075
the maximum bending moment of the ith section is M at the (i + 1) th sectionimax
Figure BDA0002996457980000076
By combining formula (1), the following can be calculated:
Figure BDA0002996457980000077
loading equal diameter windt＝P0ftCarry-in (19), and further convert to:
Figure BDA0002996457980000081
and (3) bringing the formula (20) into the formula (17), and calculating the upper limit condition of each section inclination angle value of the tower equipment with equal diameter and unequal wall thickness by calculation:
Figure BDA0002996457980000082
combining the formula (1) and the formula (21), obtaining the allowable inclination angle of each section of the tower equipment with the equal diameter and unequal wall thickness:
Figure BDA0002996457980000083
in the formula, the expression of the coefficient K is,
Figure BDA0002996457980000084
according to the third step of the invention, the inclinometers are sequentially arranged at the variable cross section positions on the tower body from the top to the bottom of the tower equipment, and the position numbers and corresponding inclination angle measured values of the inclinometers are as follows:
Figure BDA0002996457980000085
the chosen two-axis inclinometer itself defines the x-axis and y-axis, as shown in fig. 3, and its output signals α and β are the angles of deflection of the inclinometer about the x-axis and y-axis, respectively, when placed horizontally. Acceleration sensor output signal gx、gyAnd the angles α, β can be given by the following formula:
Figure BDA0002996457980000091
in the formula, gx，gyRespectively representing the component outputs of the gravity acceleration on an x axis and a y axis, and g is the gravity acceleration.
According to fig. 4, the output of the inclinometer is deflected by deflection angles α and β about the x and y axes, and γ represents the actual deflection angle of the inclinometer. OA is a normal unit vector of the inclinometer, OB is a projection of OA on an XOZ plane, OD is a projection of OA on a YOZ plane, and a quadrangle ABCD is a rectangle, according to the projection relation:
Figure BDA0002996457980000092
the actual tilt angle γ of the inclinometer with respect to the plumb line is then:
Figure BDA0002996457980000093
obtaining the actual inclination angle theta of the ith section on the tower body according to the formula (26)iAnd the measured value alphaiAnd betaiThe relationship of (1) is:
Figure BDA0002996457980000094
in the formula: alpha is alphaiAnd betaiThe i-th section is measured by an inclinometer with the number i on the o-xy horizontal plane, and the measured values of the angles of deflection around the x-axis and the y-axis are obtained.
Compared with the prior art, the invention has the following advantages:
1. the method can carry out real-time monitoring and intelligent early warning on the inclination angles of each dangerous section and each weak tower section of the tower body, and guarantee the safety of the tower equipment structure in the whole life cycle.
2. Compared with a displacement method for monitoring the deflection value of the tower top, the method for monitoring the inclination of the tower body by using the inclinometer is easy to realize, the inclinometer does not need to refer to a fixed datum point, the measuring point arrangement is flexible, the measured data deviation is extremely small, the monitored data is transmitted in a wireless mode in real time, and the method is suitable for monitoring the deflection deformation of high-rise tower equipment on line.
Therefore, the invention integrates the allowable material safety condition of the tower equipment and the appropriate inclination angle monitoring method, and provides the inclination angle monitoring and intelligent early warning method for the tower equipment. The method is based on the allowable strength safety limiting condition of the material mechanics principle, deduces the allowable inclination calculation formula of each section by solving the inclination calculation formula of each section of the tower equipment, adopts the early warning platform to monitor the inclination value of each dangerous section and compares the inclination value with the allowable inclination value, can effectively identify and monitor each dangerous section and weak tower section of the tower body, and can carry out online monitoring and intelligent early warning on the safety state of the tower equipment structure.
Drawings
FIG. 1 is a schematic diagram of a calculation of bending deformation of a tower with equal diameter and unequal wall thickness;
FIG. 2 is a schematic diagram of a calculation of bending deformation of a tower with equal diameter and unequal wall thickness;
FIG. 3 is a schematic diagram of a horizontally disposed inclinometer measurement;
FIG. 4 is a computational model of an inclinometer;
description of the symbols
Pt: wind load per unit length of the top of the tower, N/mm;
P0: wind load of unit length at 10m height from the ground, N/mm;
ft: the wind pressure height change coefficient can be obtained by checking the 10 wind pressure change coefficient in the standard NB/T47041-;
h: the total height of the tower body is mm;
Hi: i-th section of tower body with unequal wall thickness
I: the tower body with the same diameter and the same wall thickness has the section moment of inertia;
Ii: i-th section inertia moment of tower body with unequal wall thickness
D: an effective outer diameter of the tower body;
w: the bending-resistant section coefficient of the tower body with the same diameter and the same wall thickness;
Wi: the bending-resistant section coefficient of the ith section of the tower body with unequal wall thickness;
σmax: the maximum normal stress occurs at the outer surface of the section with the maximum bending moment;
[ sigma ]: the allowable stress of the material at the design temperature of the tower equipment can be selected according to the GB 150 specification, or 65% of the yield strength at the design temperature.
Detailed Description
The embodiment of the invention only takes the wind-borne bending moment of tower equipment in a self-supporting mode with equal diameter and equal wall thickness and a self-supporting mode with equal diameter and unequal wall thickness as an example, and demonstrates the implementation steps and the core idea of the method. For tower equipment with unequal diameters and unequal wall thicknesses, different mounting and supporting modes, influence by other loads and the like, the method can also be used for obtaining a relation between the allowable inclination angle and the allowable strength so as to obtain the safety monitoring condition.
According to the design standard of the tower type container, tower equipment can be simplified into cantilever beams, and the stress of the tower body is analyzed by utilizing the calculation of a virtual beam method (conjugate beam method) of material mechanics.
According to the mechanics of materials, the maximum positive stress σ occurs at the outer surface on the section with the largest bending momentmaxThe deflection Y and the inclination angle θ are two basic quantities for measuring bending deformation, namely:
Figure BDA0002996457980000121
example 1 for a column apparatus of equal diameter and equal wall thickness
As shown in fig. 1, the center a of the tower at the top end is the origin, the central axis of the tower before deformation is the X-axis, and the X is downward. On a cross section with coordinate x, the wind load concentration is:
Figure BDA0002996457980000122
the wind bending moment caused by the wind load on the section with coordinate x is:
Figure BDA0002996457980000123
the dip angle equation is obtained from the approximate differential equation of the material mechanics deflection line:
Figure BDA0002996457980000124
combining the formula (3) and the formula (4), the tilt angle equation is obtained by integrating the formula (4) under the boundary conditions x being H and θ (H) being 0:
Figure BDA0002996457980000125
equal diameter equal wall thickness tower equipment, the biggest moment of flexure takes place at the stiff end of tower, and top of the tower department inclination is:
Figure BDA0002996457980000126
loading equal diameter windt＝P0ftFormula (6) is taken in, and is converted by combining formula (1):
Figure BDA0002996457980000131
the upper type
Figure BDA0002996457980000132
With reference to formula (1), the tower top inclination angle due to wind load is determined by taking formula (7) into formula (6):
Figure BDA0002996457980000133
combining the formula (1) and the formula (8), obtaining the tower top allowable inclination angle of the equal-diameter equal-wall thickness tower equipment:
Figure BDA0002996457980000134
example 2 for equal diameter, unequal wall thickness tower apparatus
As shown in FIG. 2, for tower equipment with equal diameter and unequal wall thickness, the center A of the top end of the tower is taken as the origin, the central axis of the tower before deformation is taken as the X axis, and the X axis faces downwards. On a cross section with the coordinate x, the wind load concentration is obtained by equation (2), and the wind bending moment calculation is obtained by equation (3).
The bending deformation of the tower-type container with equal diameter and unequal wall thickness is solved by using a piecewise rigidization method, and the section inclination angle theta of any node iiAt the node i when each segment under the node i deforms independentlyThe section angles of rotation produced by point i are each thetai1、θi2、……、θiN. When the upper sections of the nodes i are independently deformed, the sections of the nodes i cannot be displaced, so that the superposition principle includes:
Figure BDA0002996457980000135
as can be seen from FIG. 2, the resultant force F generated by all wind loads of the tower section above the node iiSum and resultant moment Mi：
Figure BDA0002996457980000136
According to the calculation formula (6) of the inclination angle of the equal-diameter equal-wall thickness tower equipment, the rotation angle theta generated on the i section due to the i-th section wind load is calculatediPAnd deflection YiPRespectively as follows:
Figure BDA0002996457980000141
therefore, there is a corner θ generated at the i-section when the i-section is deformed aloneiiComprises the following steps:
Figure BDA0002996457980000142
in the formula:
Figure BDA0002996457980000143
further, the following is obtained:
Figure BDA0002996457980000144
the corner theta generated on the section i when any j section at the lower side of the node i +1 is independently deformedijComprises the following steps:
Figure BDA0002996457980000145
from the equation (10), the cross-sectional rotation angle θ of the node i is obtainediThe calculation formula is as follows:
Figure BDA0002996457980000146
the maximum bending moment of the ith section is M at the (i + 1) th sectionimax
Figure BDA0002996457980000147
By combining formula (1), the following can be calculated:
Figure BDA0002996457980000151
loading equal diameter windt＝P0ftAn introduction (18) and further converts:
Figure BDA0002996457980000152
and (3) bringing the formula (20) into the formula (17), and calculating the upper limit condition of each section inclination angle value of the tower equipment with equal diameter and unequal wall thickness by calculation:
Figure BDA0002996457980000153
combining the formula (1) and the formula (21), obtaining the allowable inclination angle of each section of the tower equipment with the equal diameter and unequal wall thickness:
Figure BDA0002996457980000154
in the formula, the expression of the coefficient K is,
Figure BDA0002996457980000155
example 3 inclinometer monitoring Tilt calculation
In the third step of the invention, the inclinometers are sequentially arranged at the variable cross section positions on the tower body from the top to the bottom of the tower equipment, and the position numbers and the corresponding inclination angle measured values of the inclinometers are as follows:
Figure BDA0002996457980000156
Figure BDA0002996457980000161
the chosen two-axis inclinometer itself defines the x-axis and y-axis, as shown in fig. 3, and its output signals α and β are the angles of deflection of the inclinometer about the x-axis and y-axis, respectively, when placed horizontally. Acceleration sensor output signal gx、gyAnd the angles α, β can be given by the following formula:
Figure BDA0002996457980000162
in the formula, gx，gyRespectively representing the component outputs of the gravity acceleration on an x axis and a y axis, and g is the gravity acceleration.
According to fig. 4, the output of the inclinometer is deflected by deflection angles α and β about the x and y axes, and γ represents the actual deflection angle of the inclinometer. OA is a normal unit vector of the inclinometer, OB is a projection of OA on an XOZ plane, OD is a projection of OA on a YOZ plane, and a quadrangle ABCD is a rectangle, according to the projection relation:
Figure BDA0002996457980000163
the actual tilt angle γ of the inclinometer with respect to the plumb line is then:
Figure BDA0002996457980000164
obtaining the actual inclination angle theta of the ith section on the tower body according to the formula (26)iAnd the measured value alphaiAnd betaiThe relationship of (1) is:
Figure BDA0002996457980000165
in the formula: alpha is alphaiAnd betaiThe i-th section is measured by an inclinometer with the number i on the o-xy horizontal plane, and the measured values of the angles of deflection around the x-axis and the y-axis are obtained.
The above description is only an example of the present invention and is not intended to limit the scope of the present invention, and all methods described in the present specification or other related fields directly or indirectly can be used in the present invention.

Claims (1)

1. The tower equipment inclination angle on-line monitoring and intelligent early warning method is characterized by comprising the following steps:
analyzing the structural type of a tower body of tower equipment, and finding out various dangerous variable cross sections of the tower body according to design conditions, wherein the number of the dangerous variable cross sections is N;
second, calculating the allowable inclination angle [ theta ] of each dangerous variable cross sectioni]Wherein (i ═ 1,2,3, …, N);
for a column device with equal diameter and equal wall thickness, the allowable inclination angle of the column top is as follows:
Figure FDA0003456277730000011
the allowable inclination angles of all sections of the tower equipment with the equal diameter and unequal wall thickness are as follows:
Figure FDA0003456277730000012
in the formula, the expression of the coefficient K is,
Figure FDA0003456277730000013
thirdly, respectively installing and positioning 1 inclinometer on each dangerous variable cross section;
fourthly, reading the measured value (alpha) of the deflection of each inclinometer on the horizontal plane o-xy around the x axis and the y axisi,βi) Further, the actual inclination angle theta of each dangerous variable cross section relative to the plumb direction is calculated and obtainediWherein (i ═ 1,2,3, …, N);
by means of an inclinometer i measurement (alpha) mounted on the i-th section of the toweri,βi) The actual inclination angle value of each dangerous section relative to the plumb direction is thetai：
Figure FDA0003456277730000014
In the formula: alpha is alphaiAnd betaiMeasuring the deflection angle of the ith section on an o-xy horizontal plane and around an x axis and a y axis by an inclinometer with the serial number of i;
fifthly, judging the condition of safety early warning, and determining the allowable inclination angle [ theta ] of the second stepi]With the actual value of inclination theta of the fourth stepiMaking a comparison if all thetai≤[θi](i is 1,2,3, …, N), the tower body is judged to be in a safe state; if one or more than one theta occursi>[θi]If the tower body is judged to be in a non-safety state, an early warning signal is sent out;
the symbols involved in the above formula are illustrated below:
Pt: wind load per unit length of the top of the tower, N/mm;
P0: wind load of unit length at 10m height from the ground, N/mm;
ft: the wind pressure height change coefficient can be obtained by checking the 10 wind pressure change coefficient in the standard NB/T47041-;
h: the total height of the tower body is mm;
hi: i-th section of tower body with unequal wall thickness
I: the tower body with the same diameter and the same wall thickness has the section moment of inertia;
ii: i-th section inertia moment of tower body with unequal wall thickness
D: an effective outer diameter of the tower body;
w: the bending-resistant section coefficient of the tower body with the same diameter and the same wall thickness;
and Wi: the bending-resistant section coefficient of the ith section of the tower body with unequal wall thickness;
σmax: the maximum normal stress occurs at the outer surface of the section with the maximum bending moment;
[ sigma ]: the allowable stress of the material at the design temperature of the tower equipment can be selected according to the GB 150 specification, or 65% of the yield strength at the design temperature.
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