CN111797531B - Hinge support tower deviation calculation method for three-span cable hoisting system with tower pressing cable - Google Patents
Hinge support tower deviation calculation method for three-span cable hoisting system with tower pressing cable Download PDFInfo
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Abstract
The invention discloses a method for calculating the deflection of a hinged tower of a three-span cable hoisting system with a tower pressing cable; the method is characterized in that; the left tower and the right tower are simultaneously subjected to external force, and the implementation steps are as follows: step 1, calculating horizontal elastic rigidity of a left side span, a middle span and a right side span pressing tower cable according to an equivalent elastic modulus theory, and respectively recording as K 1 、K 2 、K 3 The method comprises the steps of carrying out a first treatment on the surface of the Step 2, calculating the deviation of the left tower and the right tower when Zuo Da is acted by external force; step 3, calculating the deviation of the left tower and the right tower when the right tower is acted by external force; step 4, calculating unbalanced external force Q of the left tower and the right tower H1 And Q H2 The tower is deviated under the combined action. The invention perfects the calculation theory and method of the deflection of the cable hoisting tower, the calculation method is simple and clear, and in the initial stage of the tower pressing cable design of the three-span cable hoisting system, a great amount of modeling work is avoided, and the calculation time is greatly reduced.
Description
Technical Field
The invention relates to the field of cable hoisting construction of large-span arch bridges, in particular to a method for calculating the deflection of a hinged tower of a three-span cable hoisting system provided with a tower pressing cable.
Background
In the construction process of cable lifting of a large-span arch bridge, a tower pressing cable is an important part in a cable lifting system, when a flexible cable tower is subjected to unbalanced external force, the tower pressing cable can be tensioned and loosened, and the unbalanced external force applied to the cable tower in the cable lifting system is balanced by generating tension difference, so that the displacement of the tower top is reduced, and the purpose of controlling the deflection of the tower is achieved. In practical engineering application, systematic research on deflection calculation of a cable hoisting system tower with a tower pressing rope under the action of external force is generally lacking, tower deflection simulation is generally carried out by adopting finite element analysis software, modeling workload is huge, and the number of tower pressing ropes and initial tension are generally required to be adjusted repeatedly to achieve an ideal state, so that calculation time is long, and calculation process is complicated.
Disclosure of Invention
Therefore, in order to solve the defects, the invention provides a method for calculating the deflection of the hinged tower of the three-span cable hoisting system with the tower pressing rope; the invention perfects the calculation theory and method of the deflection of the cable hoisting tower, the calculation method is simple and clear, and in the initial stage of the tower pressing cable design of the three-span cable hoisting system, a great amount of modeling work is avoided, and the calculation time is greatly reduced.
The invention is realized in such a way, and constructs a method for calculating the deflection of the hinged tower of the three-span cable hoisting system with the tower pressing cable, which is characterized in that; the left tower and the right tower are simultaneously subjected to external force, and the implementation steps are as follows:
step 1, calculating horizontal elastic rigidity of a left side span, a middle span and a right side span pressing tower cable according to an equivalent elastic modulus theory, and respectively recording as K 1 、K 2 、K 3 ；
Step 2, calculating the deviation of the left tower and the right tower when Zuo Da is acted by external force;
(1) According to the calculation in the step 1, the horizontal elastic rigidity of the left side pressure tower cable of the left tower is K 1 K is considered in the horizontal elastic rigidity of the left tower and right side pressure tower cable 2 、K 3 Defining a K Z Represents the horizontal overall rigidity of the tower cable at the right side of the left tower, K Z The calculation formula is as follows:
(2) Calculate Zuo Da the external force Q H1 Left tower deflection delta under action Z1 The calculation formula is as follows:
(3) When the left tower is subjected to external force, the right tower deflects in the same direction as the left tower, and the right tower deflects delta Y1 The calculation formula is as follows:
step 3, calculating the deviation of the left tower and the right tower when the right tower is acted by external force;
(1) According to the calculation in the step 1, the horizontal elastic rigidity of the right tower cable at the right side pressure of the right tower is K 3 K is considered in the horizontal elastic rigidity of the left side pressure tower cable of the right tower 1 、K 2 Defining a K Y Represents the horizontal overall rigidity of the left side pressure tower cable of the right tower, K Y The calculation formula is as follows:
(2) Calculate the external force Q of the right tower H2 Right tower offset delta under action Y2 The calculation formula is as follows:
(3) When the right tower is subjected to external force, the left tower deflects in the same direction as the right tower, and the left tower deflects delta Z2 The calculation formula is as follows:
step 4, calculating unbalanced external force Q of the left tower and the right tower H1 And Q H2 The tower is deviated under the combined action;
left tower offset delta Z The calculation formula is as follows:
δ Z ＝δ Z1 +δ Z2
right tower offset delta Y The calculation formula is as follows:
δ Y ＝δ Y1 +δ Y2 。
the invention has the following advantages: 1. the offset calculation of the hinged tower of the three-span cable hoisting system with the tower pressing cable is realized, and a large amount of modeling work is avoided; 2. the calculation time for the deflection of the hinged tower of the three-span cable hoisting system with the tower pressing cable is greatly shortened.
Drawings
FIG. 1 is a schematic diagram of a tower offset calculation parameter;
fig. 2 is a schematic diagram of an example.
Detailed Description
The following detailed description of the present invention will provide clear and complete description of the technical solutions of embodiments of the present invention, with reference to fig. 1-2, and it is apparent that the described embodiments are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The invention provides a method for calculating the deflection of a hinged tower of a three-span cable hoisting system of a pressure tower cable through improvement; the invention perfects the calculation theory and method of the deflection of the cable hoisting tower, the calculation method is simple and clear, and in the initial stage of the tower pressing cable design of the three-span cable hoisting system, a great amount of modeling work is avoided, and the calculation time is greatly reduced.
The application conditions are as follows: the initial tension of the tower pressing rope is 15.4% greater than the designed breaking tension.
The calculation method of the invention is based on the equivalent elastic modulus theory, namely:
1. the equivalent elastic modulus of the rope is calculated as follows:
wherein E, A, W, L, T is the elastic modulus of the rope, the stress-free cross-sectional area of the rope, the dead weight of the rope per linear meter, the horizontal projection length of the rope and the initial tension of the rope end respectively.
2. The calculation formula of the horizontal elastic rigidity of the cable is as follows:
3. horizontal external force Q of cable at cable end H The calculation formula of the pivot horizontal displacement delta under the action is as follows:
the invention takes the case that the left tower and the right tower are simultaneously subjected to external force as an example, and the realization steps are as follows:
step 1, calculating horizontal elastic rigidity of a left side span, a middle span and a right side span pressing tower cable according to an equivalent elastic modulus theory, and respectively recording as K 1 、K 2 、K 3 ；
Step 2, calculating the deviation of the left tower and the right tower when Zuo Da is acted by external force;
(1) According to the calculation in the step 1, the horizontal elastic rigidity of the left side pressure tower cable of the left tower is K 1 K is considered in the horizontal elastic rigidity of the left tower and right side pressure tower cable 2 、K 3 Defining a K Z Represents the horizontal overall rigidity of the tower cable at the right side of the left tower, K Z The calculation formula is as follows:
(2) Calculate Zuo Da the external force Q H1 Left tower deflection delta under action Z1 The calculation formula is as follows:
(3) When the left tower is subjected to external force, the right tower deflects in the same direction as the left tower, and the right tower deflects delta Y1 The calculation formula is as follows:
step 3, calculating the deviation of the left tower and the right tower when the right tower is acted by external force;
(1) According to the calculation in the step 1, the horizontal elastic rigidity of the right tower cable at the right side pressure of the right tower is K 3 K is considered in the horizontal elastic rigidity of the left side pressure tower cable of the right tower 1 、K 2 Defining a K Y Represents the horizontal overall rigidity of the left side pressure tower cable of the right tower, K Y The calculation formula is as follows:
(2) Calculate the external force Q of the right tower H2 Right tower offset delta under action Y2 The calculation formula is as follows:
(3) When the right tower is subjected to external force, the left tower deflects in the same direction as the right tower, and the left tower deflects delta Z2 The calculation formula is as follows:
step 4, calculating unbalanced external force Q of the left tower and the right tower H1 And Q H2 The tower is deviated under the combined action;
left tower offset delta Z The calculation formula is as follows:
δ Z ＝δ Z1 +δ Z2
right tower offset delta Y The calculation formula is as follows:
δ Y ＝δ Y1 +δ Y2 。
this patent has following advantage and beneficial effect:
1. the offset calculation of the hinged tower of the three-span cable hoisting system with the tower pressing cable is realized, and a large amount of modeling work is avoided; 2. the calculation time for the deflection of the hinged tower of the three-span cable hoisting system with the tower pressing cable is greatly shortened.
Taking a three-span cable hoisting system with a tower pressing cable as an example, the main tower bottom adopts a hinged structure form, and the three-span tower pressing cable adopts 10 steel strands, and has the design parameters as follows: l (L) 1 ＝200m，h 1 ＝-100m，L 2 ＝400m，h 2 ＝0，L 3 ＝300m，h 3 ＝-120m，W＝1.01kg/m，E＝195e 5 Mpa，A＝140mm 2 ，Q H1 ＝20t，Q H2 =30t (pointing positive in mid-span). The calculation results of different cable initial tension values are compared with the calculation results of finite element software by adopting the calculation method disclosed by the invention, and the comparison results are shown in the following table:
comparison table of calculation results
According to comparison, when the initial tension of the middle span tower cable is larger than 30t, the maximum error between the calculated result of the calculating method and the calculated result of the finite element software is only 2cm, the calculated error is smaller, and at the moment, the initial tension of the middle span tower cable is about 15.4% of the designed breaking force. Therefore, when the initial tension of the tower pressing rope is larger than the designed breaking force by 15.4%, the calculation method disclosed by the invention has higher calculation precision, and meets the requirements of cable hoisting design and construction.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims (1)
1. A method for calculating the deflection of a hinged tower of a three-span cable hoisting system with a tower pressing cable is characterized in that; the left tower and the right tower are simultaneously subjected to external force, and the implementation steps are as follows:
step 1, calculating horizontal elastic rigidity of a left side span, a middle span and a right side span pressing tower cable according to an equivalent elastic modulus theory, and respectively recording as K 1 、K 2 、K 3 ；
Step 2, calculating the deviation of the left tower and the right tower when Zuo Da is acted by external force;
(1) According to the calculation in the step 1, the horizontal elastic rigidity of the left side pressure tower cable of the left tower is K 1 K is considered in the horizontal elastic rigidity of the left tower and right side pressure tower cable 2 、K 3 Defining a K Z Represents the horizontal overall rigidity of the tower cable at the right side of the left tower, K Z The calculation formula is as follows:
(2) Calculate Zuo Da the external force Q H1 Left tower deflection delta under action Z1 The calculation formula is as follows:
(3) When the left tower is subjected to external force, the right tower deflects in the same direction as the left tower, and the right tower deflects delta Y1 The calculation formula is as follows:
step 3, calculating the deviation of the left tower and the right tower when the right tower is acted by external force;
(1) According to the calculation in the step 1, the horizontal elastic rigidity of the right tower cable at the right side pressure of the right tower is K 3 K is considered in the horizontal elastic rigidity of the left side pressure tower cable of the right tower 1 、K 2 Defining a K Y Represents the horizontal overall rigidity of the left side pressure tower cable of the right tower, K Y The calculation formula is as follows:
(2) Calculate the external force Q of the right tower H2 Right tower offset delta under action Y2 The calculation formula is as follows:
(3) When the right tower is subjected to external force, the left tower deflects in the same direction as the right tower, and the left tower deflects delta Z2 The calculation formula is as follows:
step 4, calculating unbalanced external force Q of the left tower and the right tower H1 And Q H2 The tower is deviated under the combined action;
left tower offset delta Z The calculation formula is as follows:
δ Z ＝δ Z1 +δ Z2
right tower offset delta Y The calculation formula is as follows:
δ Y ＝δ Y1 +δ Y2 。
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