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 PDFInfo
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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
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:
wherein: phi (x) is the cable vibration form functionA number;after the vibration damper is symmetrically arranged for the cable, the natural frequency of the nth order vibration;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:
wherein: a. b is a constant to be determined;
the linear function of the adjustment sleeve portion is:
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 onThe process is as follows:
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:
potential energy V of the flexible inhaul cable 1 The method comprises the following steps:
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:
potential energy V of the adjusting sleeve 2 The method comprises the following steps:
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:
total potential energy E of the guy cable system p The method comprises the following steps:
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
Calculated kinetic energy is thatMaximum is reached, thus it can be deduced that the potential energy is +.>Maximum is reached according to the above conclusion +.>And (3) after simplification, obtaining:
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:
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:
wherein: phi (x) is a inhaul cable vibration shape function;after the vibration damper is symmetrically arranged for the cable, the natural frequency of the nth order vibration;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:
wherein: a. b is a constant to be determined;
the linear function of the adjusting sleeve 2 part is:
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 bodyThe process is as follows:
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:
potential energy V of flexible inhaul cable 1 1 The method comprises the following steps:
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:
potential energy V of the adjusting sleeve 2 2 The method comprises the following steps:
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:
total potential energy E of the guy cable system p The method comprises the following steps:
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
Calculated kinetic energy is thatMaximum is reached, thus it can be deduced that the potential energy is +.>Maximum is reached according to the above conclusion +.>And (3) after simplification, obtaining:
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:
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:
wherein: phi (x) is a inhaul cable vibration shape function;after the vibration damper is symmetrically arranged for the cable, the natural frequency of the nth order vibration; />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:
wherein: a. b is a constant to be determined;
the linear function of the adjusting sleeve (2) part is:
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 onThe process is as follows:
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:
potential energy V of the flexible inhaul cable (1) 1 The method comprises the following steps:
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:
potential energy V of the adjusting sleeve (2) 2 The method comprises the following steps:
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:
total potential energy E of the guy cable system p The method comprises the following steps:
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
Calculated kinetic energy is thatMaximum is reached, thus it can be deduced that the potential energy is +.>Maximum is reached according to the above conclusion +.>And (3) after simplification, obtaining:
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:
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