CN109063351B - Cable-stayed bridge cable force calculation method under influence of adjusting sleeve - Google Patents

Cable-stayed bridge cable force calculation method under influence of adjusting sleeve Download PDF

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CN109063351B
CN109063351B CN201810908311.6A CN201810908311A CN109063351B CN 109063351 B CN109063351 B CN 109063351B CN 201810908311 A CN201810908311 A CN 201810908311A CN 109063351 B CN109063351 B CN 109063351B
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adjusting sleeve
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CN109063351A (en
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张开银
吴倩赟
吕雷
姚璐
吴飞
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Wuhan University of Technology WUT
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Abstract

The invention discloses a cable force calculation method of a cable-stayed bridge under the influence of an adjusting sleeve, which is used for calculating the cable force of a flexible cable, wherein the flexible cable is provided with the adjusting sleeve, the outer ends of the flexible cable and the adjusting sleeve are respectively provided with a hinged anchor, the flexible cable is fixedly connected with the adjusting sleeve, the hinged anchors are hinged with a bridge body, the adjusting sleeve is a rigid pull rod, and the calculation method comprises the following steps: calculating a displacement function; deformation coordination; and solving the cable force. The invention has the advantages that: according to the method, the influence of the adjusting sleeve is considered in a calculation formula, so that the calculation accuracy is obviously improved, and the superposition process of the sine function and the linear vibration shape is simplified through deformation coordination processing.

Description

Cable-stayed bridge cable force calculation method under influence of adjusting sleeve
Technical Field
The invention relates to the technical field of bridge engineering, in particular to a calculation method of cable force of a cable-stayed bridge under the influence of an adjusting sleeve.
Background
The cable force adjustment of the stay cable is one of key technologies of the cable-stayed bridge, and the main girder and the stay cable reach ideal stress states by adjusting the internal force of the main girder through the stay cable.
At present, the cable force detection is widely adopted to measure and estimate the cable force by a vibration method, namely, the cable force is estimated by testing the natural vibration frequency of the cable. For a inhaul cable with a longer length, the influence of the adjusting sleeve is almost negligible, and the inhaul cable can be regarded as a flexible inhaul cable, and the result obtained by calculation through the existing calculation formula is reliable. However, for the inhaul cable with shorter length, the influence caused by the difference between the rigidity of the adjusting sleeve and the mass of the adjusting sleeve in unit length and the flexible cable section is more remarkable, if the difference is ignored, larger errors and even errors are brought to the test result, and engineering application cannot be met, so that the influence of the adjusting sleeve on the vibration characteristic must be counted into a calculation formula, and the rigid pull rod can be regarded as.
Disclosure of Invention
The invention aims to provide a cable-stayed bridge cable force calculation method under the influence of an adjusting sleeve, which has higher calculation precision, thereby improving the detection accuracy and the bridge safety.
In order to achieve the above purpose, the invention provides a cable force calculation method of a cable-stayed bridge under the influence of an adjusting sleeve, which is used for calculating the cable force of a flexible cable, wherein the flexible cable is provided with the adjusting sleeve, the outer ends of the flexible cable and the adjusting sleeve are respectively provided with a hinged anchor, the flexible cable is fixedly connected with the adjusting sleeve, the hinged anchors are hinged with a bridge body, the adjusting sleeve is a rigid pull rod, and the calculation method comprises the following steps:
step 1: calculating a displacement function;
step 2: deformation coordination;
step 3: and solving the cable force.
Further, the step 1 further includes the following steps:
step 1.1: and obtaining a vibration pattern diagram of the flexible inhaul cable under the action of the unilateral adjusting sleeve by using calculation mode analysis:
step 1.2: the vibration shape function of the general inhaul cable is regarded as a sine function, the vibration shape of the flexible inhaul cable is changed under the action of the adjusting sleeve, the flexible inhaul cable part is a superposition function of the sine function and the linear function, and the adjusting sleeve part is the linear function, so that the displacement function of the flexible inhaul cable part is obtained;
step 1.3: a linear function is superimposed on the displacement function of the flexible cable portion to derive a vibration shape function and a linear function of the adjustment sleeve portion.
Further, the step 3 further includes the following steps:
step 3.1: calculating kinetic energy and potential energy of the flexible inhaul cable;
step 3.2: calculating kinetic energy and potential energy of the adjusting sleeve;
step 3.3: calculating the total kinetic energy and the total potential energy of the inhaul cable system;
step 3.4: an expression of the cable force T is calculated.
Further, in the step 1.2, a displacement function of the flexible cable portion is:
Figure SMS_1
（1）
wherein: phi (x) is the cable vibration form functionA number;
Figure SMS_2
after the vibration damper is symmetrically arranged for the cable, the natural frequency of the nth order vibration;
Figure SMS_3
the initial phase of the vibration of the inhaul cable is obtained.
Further, in the step 1.3, a vibration shape function of the flexible cable portion and a linear function of the adjusting sleeve portion are respectively:
vibration shape function of flexible cable part:
Figure SMS_4
（2）
wherein: a. b is a constant to be determined;
the linear function of the adjustment sleeve portion is:
Figure SMS_5
（3）
wherein: k. c is a pending constant.
Further, in the step 2, the specific steps of deformation coordination are as follows:
the adjusting flexible inhaul cable and the adjusting sleeve are arranged on
Figure SMS_6
The process is as follows:
the displacement is equal to
Figure SMS_7
) Then:
Figure SMS_8
Figure SMS_9
i.e.
Figure SMS_10
；
Its slope is equal to that of%
Figure SMS_11
) Then:
Figure SMS_12
=
Figure SMS_13
Figure SMS_14
i.e.
Figure SMS_15
Obtaining:
Figure SMS_16
Figure SMS_17
Figure SMS_18
。
further, in the step 3.1, the steps of calculating the kinetic energy and the potential energy of the flexible inhaul cable are as follows:
kinetic energy T of the flexible inhaul cable 1 The method comprises the following steps:
Figure SMS_19
Figure SMS_20
（4）
Figure SMS_21
=
Figure SMS_22
=
Figure SMS_23
；
potential energy V of the flexible inhaul cable 1 The method comprises the following steps:
Figure SMS_24
Figure SMS_25
（5）
Figure SMS_26
=
Figure SMS_27
=
Figure SMS_28
。
further, in the step 3.2, the kinetic energy and potential energy calculation step of the adjusting sleeve is as follows:
the kinetic energy T of the regulating sleeve 2 The method comprises the following steps:
Figure SMS_29
（6）
=
Figure SMS_30
potential energy V of the adjusting sleeve 2 The method comprises the following steps:
Figure SMS_31
（7）。
further, in the step 3.3, the steps of calculating kinetic energy and potential energy of the cable system are as follows:
total kinetic energy E of the guy system k The method comprises the following steps:
Figure SMS_32
Figure SMS_33
+
Figure SMS_34
（8）
total potential energy E of the guy cable system p The method comprises the following steps:
Figure SMS_35
Figure SMS_36
（9）。
further, in the step 3.4, the calculating the expression of the cable force T includes:
according to the law of conservation of energy, there are
Figure SMS_37
（10）
Calculated kinetic energy is that
Figure SMS_38
Maximum is reached, thus it can be deduced that the potential energy is +.>
Figure SMS_39
Maximum is reached according to the above conclusion +.>
Figure SMS_40
And (3) after simplification, obtaining:
Figure SMS_41
Figure SMS_42
+
Figure SMS_43
（11）
Figure SMS_44
=
Figure SMS_45
（12）
substituting the kinetic and potential energy maxima into equation (10), reduced to an equation for a, where a is required to be a non-0 solution, and thus the expression of the cable force T can be obtained:
Figure SMS_46
{/>
Figure SMS_47
+
Figure SMS_48
-/>
Figure SMS_49
}/>
Figure SMS_50
。
the invention has the advantages that: according to the method, the influence of the adjusting sleeve is considered in a calculation formula, so that the calculation accuracy is obviously improved, and the superposition process of the sine function and the linear vibration shape is simplified through deformation coordination processing.
Drawings
FIG. 1 is a schematic diagram of a cable system;
fig. 2 is a diagram of the vibration pattern of the flexible cable under the action of the single-side adjusting sleeve.
In the figure: flexible guy cable 1, adjusting sleeve 2, articulated anchor 3.
Detailed Description
The invention is described in further detail below with reference to the attached drawings and to specific embodiments:
the method for calculating the cable force of the cable-stayed bridge under the influence of the adjusting sleeve shown in fig. 1-2 is used for calculating the cable force of the flexible cable 1, the adjusting sleeve 2 is arranged on the flexible cable 1, the outer ends of the flexible cable 1 and the adjusting sleeve 2 are respectively provided with a hinged anchor 3, the flexible cable 1 is fixedly connected with the adjusting sleeve 2, the hinged anchors 3 are hinged with the bridge body, the adjusting sleeve 2 is a rigid pull rod, and the calculating method comprises the following steps:
step 1: calculating a displacement function;
step 1.1: the vibration pattern diagram of the flexible inhaul cable 1 under the action of the unilateral adjusting and adjusting sleeve 2 is obtained by using calculation mode analysis, and the result is shown in fig. 2:
step 1.2: the vibration shape function of the general inhaul cable is regarded as a sine function, the vibration shape of the flexible inhaul cable 1 is changed under the action of the adjusting sleeve 2, the flexible inhaul cable 1 is a superposition function of the sine function and the linear function, and the adjusting sleeve 2 is a linear function, so that the displacement function of the flexible inhaul cable 1 is obtained;
in the step 1.2, the displacement function of the flexible inhaul cable 1 part is as follows:
Figure SMS_51
（1）
wherein: phi (x) is a inhaul cable vibration shape function;
Figure SMS_52
after the vibration damper is symmetrically arranged for the cable, the natural frequency of the nth order vibration;
Figure SMS_53
the initial phase of the vibration of the inhaul cable is obtained.
Step 1.3: a linear function is superimposed on the displacement function of the flexible cable 1 portion to derive its mode shape function and the linear function of the adjustment sleeve 2 portion.
In the step 1.3, the vibration shape function of the flexible inhaul cable 1 part and the linear function of the adjusting sleeve 2 part are respectively:
vibration shape function of flexible cable 1 part:
Figure SMS_54
（2）
wherein: a. b is a constant to be determined;
the linear function of the adjusting sleeve 2 part is:
Figure SMS_55
（3）
wherein: k. c is a pending constant.
Step 2: deformation coordination;
in the step 2, the specific steps of deformation coordination are as follows:
the adjusting flexible inhaul cable 1 and the adjusting sleeve 2 are arranged on the main body
Figure SMS_56
The process is as follows:
the displacement is equal to
Figure SMS_57
) Then:
Figure SMS_58
Figure SMS_59
i.e.
Figure SMS_60
；
Its slope is equal to that of%
Figure SMS_61
) Then:
Figure SMS_62
=
Figure SMS_63
Figure SMS_64
i.e.
Figure SMS_65
Obtaining:
Figure SMS_66
Figure SMS_67
Figure SMS_68
。
step 3: solving the cable force:
step 3.1: calculating kinetic energy and potential energy of the flexible inhaul cable 1;
in the step 3.1, the steps of calculating the kinetic energy and potential energy of the flexible inhaul cable 1 are as follows:
kinetic energy T of the flexible inhaul cable 1 1 The method comprises the following steps:
Figure SMS_69
Figure SMS_70
（4）
Figure SMS_71
=
Figure SMS_72
=
Figure SMS_73
；
potential energy V of flexible inhaul cable 1 1 The method comprises the following steps:
Figure SMS_74
Figure SMS_75
（5）
Figure SMS_76
=
Figure SMS_77
=
Figure SMS_78
。
step 3.2: calculating kinetic energy and potential energy of the adjusting sleeve 2;
in the step 3.2, the kinetic energy and potential energy calculation steps of the adjusting sleeve 2 are as follows:
the kinetic energy T of the regulating sleeve 2 2 The method comprises the following steps:
Figure SMS_79
（6）
=
Figure SMS_80
potential energy V of the adjusting sleeve 2 2 The method comprises the following steps:
Figure SMS_81
（7）。
step 3.3: calculating the total kinetic energy and the total potential energy of the inhaul cable system;
in the step 3.3, the steps of calculating the kinetic energy and potential energy of the inhaul cable system are as follows:
total kinetic energy E of the guy system k The method comprises the following steps:
Figure SMS_82
Figure SMS_83
+
Figure SMS_84
（8）
total potential energy E of the guy cable system p The method comprises the following steps:
Figure SMS_85
Figure SMS_86
（9）。
step 3.4: calculating an expression of the cable force T:
in the step 3.4, the calculating step of the expression for calculating the cable force T is as follows:
according to the law of conservation of energy, there are
Figure SMS_87
（10）
Calculated kinetic energy is that
Figure SMS_88
Maximum is reached, thus it can be deduced that the potential energy is +.>
Figure SMS_89
Maximum is reached according to the above conclusion +.>
Figure SMS_90
And (3) after simplification, obtaining:
Figure SMS_91
Figure SMS_92
+
Figure SMS_93
（11）
Figure SMS_94
=
Figure SMS_95
（12）
substituting the kinetic and potential energy maxima into equation (10), reduced to an equation for a, where a is required to be a non-0 solution, and thus the expression of the cable force T can be obtained:
Figure SMS_96
{/>
Figure SMS_97
+
Figure SMS_98
-/>
Figure SMS_99
}/>
Figure SMS_100
。
finally, it should be noted that the above embodiments are merely representative examples of the present invention. Obviously, the invention is not limited to the above-described embodiments, but many variations are possible. Any simple modification, equivalent variation and modification of the above embodiments according to the technical substance of the present invention should be considered to be within the scope of the present invention.

Claims (5)

1. The utility model provides a cable-stay bridge cable force calculation method under adjusting sleeve influences for calculate the cable force of flexible cable (1), be equipped with adjusting sleeve (2) on flexible cable (1), the outer end of flexible cable (1), adjusting sleeve (2) all is equipped with articulated anchor (3), rigid coupling between flexible cable (1) and adjusting sleeve (2), articulated anchor (3) are articulated with the bridge body, adjusting sleeve (2) are rigid pull rod, its characterized in that:
the calculation method comprises the following steps:
step 1: calculating a displacement function;
step 2: deformation coordination;
step 3: solving the cable force;
the step 1 further comprises the following steps:
step 1.1: obtaining a vibration pattern of the flexible inhaul cable (1) under the action of the single-side adjusting sleeve (2) by using calculation mode analysis:
step 1.2: the vibration shape function of the general inhaul cable is regarded as a sine function, the vibration shape of the flexible inhaul cable (1) is changed under the action of the adjusting sleeve (2), the flexible inhaul cable (1) is a superposition function of the sine function and the linear function, and the adjusting sleeve (2) is a linear function, so that the displacement function of the flexible inhaul cable (1) is obtained;
step 1.3: superposing a linear function in the displacement function of the flexible inhaul cable (1) part so as to obtain the vibration shape function and the linear function of the adjusting sleeve (2) part;
the step 3 further comprises the following steps:
step 3.1: calculating kinetic energy and potential energy of the flexible inhaul cable (1);
step 3.2: calculating kinetic energy and potential energy of the adjusting sleeve (2);
step 3.3: calculating the total kinetic energy and the total potential energy of the inhaul cable system;
step 3.4: calculating an expression of the cable force T;
in the step 1.2, the displacement function of the flexible inhaul cable (1) part is as follows:
Figure QLYQS_1
（1）
wherein: phi (x) is a inhaul cable vibration shape function;
Figure QLYQS_2
after the vibration damper is symmetrically arranged for the cable, the natural frequency of the nth order vibration; />
Figure QLYQS_3
The initial phase of the vibration of the inhaul cable;
in the step 1.3, the vibration shape function of the flexible inhaul cable (1) part and the linear function of the adjusting sleeve (2) part are respectively as follows:
vibration shape function of flexible cable (1) part:
Figure QLYQS_4
（2）
wherein: a. b is a constant to be determined;
the linear function of the adjusting sleeve (2) part is:
Figure QLYQS_5
（3）
wherein: k. c is a constant to be determined;
in the step 2, the specific steps of deformation coordination are as follows:
the flexible inhaul cable (1) and the adjusting sleeve (2) are arranged on
Figure QLYQS_6
The process is as follows:
the displacement is equal to
Figure QLYQS_7
) Then:
Figure QLYQS_8
Figure QLYQS_9
i.e.
Figure QLYQS_10
；
Its slope is equal to that of%
Figure QLYQS_11
) Then:
Figure QLYQS_12
=
Figure QLYQS_13
Figure QLYQS_14
i.e.
Figure QLYQS_15
Obtaining:
Figure QLYQS_16
Figure QLYQS_17
Figure QLYQS_18
。
2. the method for calculating the cable force of the cable-stayed bridge under the influence of the adjusting sleeve according to claim 1, wherein the method comprises the following steps: in the step 3.1, the kinetic energy and potential energy calculation steps of the flexible inhaul cable (1) are as follows:
kinetic energy T of the flexible inhaul cable (1) 1 The method comprises the following steps:
Figure QLYQS_19
Figure QLYQS_20
（4）
Figure QLYQS_21
=
Figure QLYQS_22
=
Figure QLYQS_23
；
potential energy V of the flexible inhaul cable (1) 1 The method comprises the following steps:
Figure QLYQS_24
Figure QLYQS_25
（5）
Figure QLYQS_26
=
Figure QLYQS_27
=
Figure QLYQS_28
。
3. the method for calculating the cable force of the cable-stayed bridge under the influence of the adjusting sleeve according to claim 1, wherein the method comprises the following steps: in the step 3.2, the kinetic energy and potential energy calculation steps of the adjusting sleeve (2) are as follows:
the kinetic energy T of the regulating sleeve (2) 2 The method comprises the following steps:
Figure QLYQS_29
（6）
=
Figure QLYQS_30
potential energy V of the adjusting sleeve (2) 2 The method comprises the following steps:
Figure QLYQS_31
（7）。
4. the method for calculating the cable force of the cable-stayed bridge under the influence of the adjusting sleeve according to claim 2, wherein the method comprises the following steps: in the step 3.3, the steps of calculating the kinetic energy and potential energy of the inhaul cable system are as follows:
total kinetic energy E of the guy system k The method comprises the following steps:
Figure QLYQS_32
Figure QLYQS_33
+
Figure QLYQS_34
（8）
total potential energy E of the guy cable system p The method comprises the following steps:
Figure QLYQS_35
Figure QLYQS_36
（9）。
5. a method for calculating the cable force of a cable-stayed bridge under the influence of an adjusting sleeve according to claim 3, wherein: in the step 3.4, the calculating step of the expression for calculating the cable force T is as follows:
according to the law of conservation of energy, there are
Figure QLYQS_37
（10）
Calculated kinetic energy is that
Figure QLYQS_38
Maximum is reached, thus it can be deduced that the potential energy is +.>
Figure QLYQS_39
Maximum is reached according to the above conclusion +.>
Figure QLYQS_40
And (3) after simplification, obtaining:
Figure QLYQS_41
Figure QLYQS_42
+
Figure QLYQS_43
（11）
Figure QLYQS_44
=
Figure QLYQS_45
（12）
substituting the kinetic and potential energy maxima into equation (10), reduced to an equation for a, where a is required to be a non-0 solution, and thus the expression of the cable force T can be obtained:
Figure QLYQS_46
{/>
Figure QLYQS_47
+
Figure QLYQS_48
-/>
Figure QLYQS_49
}/>
Figure QLYQS_50
。
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