CN109063351A - A kind of cord force of cable-stayed bridge calculation method under the influence of adjusting sleeve - Google Patents
A kind of cord force of cable-stayed bridge calculation method under the influence of adjusting sleeve Download PDFInfo
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Abstract
The invention discloses the cord force of cable-stayed bridge calculation methods under the influence of a kind of adjusting sleeve, for calculating the Suo Li of flexible cable, the flexible cable, which is equipped with, adjusts sleeve, the flexible cable, the outer end for adjusting sleeve are equipped with articulated anchor, it is affixed between the flexible cable and adjusting sleeve, the articulated anchor and pontic are hinged, and the adjusting sleeve is push-and-pull rod, and the calculation method includes the following steps: to calculate displacement function;Compatibility of deformation;Solve Suo Li.The present invention has the advantages that it, which passes through, takes into account calculation formula for the influence for adjusting sleeve, it will be apparent that improve computational accuracy, handled by compatibility of deformation, simplify SIN function and linear vibration shape additive process.
Description
Technical field
The present invention relates to technical field of bridge engineering, refer specifically to a kind of cord force of cable-stayed bridge calculating side adjusted under the influence of sleeve
Method.
Background technique
The adjusting of Cable power is one of key technology of cable-stayed bridge, is adjusted by drag-line to beam stress, makes girder
Reach ideal stress with drag-line.
What Suo Li detection at present was widely used is that Cable power is estimated in vibratory drilling method survey, that is, passes through test drag-line eigentone
To estimate Cable power.Drag-line longer for length, the influence for adjusting sleeve almost can be ignored, that is, can be considered flexible
It is reliable to calculate acquired results with existing calculation formula for drag-line.But the drag-line shorter for length, adjust the rigidity of sleeve
And its influence caused by difference of the linear mass with flexible cable section, if ignoring this difference, can give test than more prominent
As a result biggish error even mistake is brought, engineer application is not able to satisfy, so must be adjusting sleeve to the shadow of vibration characteristics
Sound is included in calculation formula, that is, can be considered push-and-pull rod.
Summary of the invention
Present invention aim to provide it is a kind of adjusting sleeve under the influence of cord force of cable-stayed bridge calculation method, have more
High computational accuracy, to improve the accuracy of detection and the safety of bridge.
To achieve the above object, the cord force of cable-stayed bridge calculation method under the influence of a kind of adjusting sleeve designed by the present invention,
For calculating the Suo Li of flexible cable, the flexible cable, which is equipped with, adjusts sleeve, the flexible cable, the outer end for adjusting sleeve
It is equipped with articulated anchor, affixed between the flexible cable and adjusting sleeve, the articulated anchor and pontic are hinged, the adjusting sleeve
For push-and-pull rod, the calculation method includes the following steps:
Step 1: calculating displacement function;
Step 2: compatibility of deformation;
Step 3: solving Suo Li.
Further, the step 1 further includes following steps:
Step 1.1: flexible cable is obtained in the unilateral vibration shape figure adjusted under sleeve effect using computational modal analysis:
Step 1.2: the shaping function of general drag-line is accordingly to be regarded as SIN function, under the action of adjusting sleeve, flexible cable
Vibration shape changed, flexible cable part is the superpositing function of SIN function and linear function, and adjusts sleeve part and is divided into
Linear function, to obtain the displacement function of flexible cable part;
Step 1.3: a linear function is superimposed in the displacement function of flexible cable part, to obtain its shaping function
With the linear function for adjusting sleeve part.
Further, the step 3 further includes following steps:
Step 3.1: calculating the kinetic energy and potential energy of flexible cable;
Step 3.2: calculating the kinetic energy and potential energy for adjusting sleeve;
Step 3.3: calculating cable systems total kinetic energy and total potential energy;
Step 3.4: calculating the expression formula of Suo Li T.
Further, in the step 1.2, the displacement function of the displacement function of the flexible cable part are as follows:
In formula: φ (x) is drag-line shaping function;ωnAfter being symmetrically installed damper for rope, the intrinsic frequency of n-th order vibration;For inhaul cable vibration initial phase.
Further, in the step 1.3, the shaping function of the flexible cable part and the linear of sleeve part is adjusted
Function is respectively as follows:
The shaping function of flexible cable part:
In formula: a, b are undetermined constant;
Adjust the linear function of sleeve part are as follows:
y2(x)=k2x+c (3)
In formula: k, c are undetermined constant.
Further, in the step 2, the specific steps of the denaturation coordination are as follows:
The adjusting flexible cable and adjusting sleeve are in x=l1Place:
It is displaced equal (y1=y2), then:
y2(x)=k2l1-k2(l1+l2)=- k2l2
I.e.
Equal (the y ' of its slope1=y '2), then:
y′2=k2
I.e.
:
Further, in the step 3.1, the kinetic energy and potential energy of the flexible cable calculate step are as follows: the flexibility
The kinetic energy T of drag-line1Are as follows:
The potential energy V of the flexible cable1Are as follows:
Further, in the step 3.2, the kinetic energy for adjusting sleeve and potential energy calculate step are as follows: the adjusting set
The kinetic energy T of cylinder2Are as follows:
The potential energy V for adjusting sleeve2Are as follows:
V2=0 (7).
Further, in the step 3.3, the kinetic energy and potential energy of the cable systems calculate step are as follows: the drag-line
The total kinetic energy E of systemkAre as follows:
The total kinetic energy E of the cable systemspAre as follows:
Further, in the step 3.4, the expression formula for calculating Suo Li T calculates step are as follows:
According to law of conservation of energy, have
Ek+Ep=constant=Ek max=Ep max (10)
It is computed, kinetic energy existsWhen reach maximum, thus can push away, potential energy existsWhen reach maximum, by above-mentioned conclusion Ek maxAnd Ep maxAfter abbreviation:
Kinetic energy maximum value and potential energy maximum value are substituted into formula (10), is an equation about a after abbreviation, requires a at this time
For non-zero solution, this makes it possible to obtain the expression formulas of Suo Li T:
The present invention has the advantages that it, which passes through, takes into account calculation formula for the influence for adjusting sleeve, it will be apparent that improve meter
Precision is calculated, is handled by compatibility of deformation, SIN function and linear vibration shape additive process are simplified.
Detailed description of the invention
Fig. 1 is the structural schematic diagram of cable systems;
Fig. 2 is flexible cable in the unilateral vibration shape figure adjusted under sleeve effect.
In figure: flexible cable 1 adjusts sleeve 2, articulated anchor 3.
Specific embodiment
The present invention is described in further detail in the following with reference to the drawings and specific embodiments:
A kind of cord force of cable-stayed bridge calculation method adjusted under the influence of sleeve as shown in Fig. 1~2, for calculating flexible cable
1 Suo Li, the flexible cable 1, which is equipped with, adjusts sleeve 2, and the flexible cable 1, the outer end for adjusting sleeve 2 are equipped with hingedly
Anchor 3, affixed between the flexible cable 1 and adjusting sleeve 2, the articulated anchor 3 and pontic are hinged, and the adjusting sleeve 2 is rigid
Property pull rod, the calculation method include the following steps:
Step 1: calculating displacement function;
Step 1.1: obtaining flexible cable 1 in the unilateral vibration shape adjusted under sleeve 2 acts on using computational modal analysis
Figure, result such as Fig. 2:
Step 1.2: the shaping function of general drag-line is accordingly to be regarded as SIN function, under the action of adjusting sleeve 2, flexible cable
1 vibration shape is changed, and 1 part of flexible cable is the superpositing function of SIN function and linear function, and adjusts 2 part of sleeve
For linear function, to obtain the displacement function of 1 part of flexible cable;
In the step 1.2, the displacement function of the displacement function of 1 part of flexible cable are as follows:
In formula: φ (x) is drag-line shaping function;ωnAfter being symmetrically installed damper for rope, the intrinsic frequency of n-th order vibration;For inhaul cable vibration initial phase.
Step 1.3: a linear function is superimposed in the displacement function of 1 part of flexible cable, to obtain its shape letter that shakes
Number and the linear function for adjusting 2 part of sleeve.
In the step 1.3, the shaping function of 1 part of flexible cable and the linear function point for adjusting 2 part of sleeve
Not are as follows:
The shaping function of 1 part of flexible cable:
In formula: a, b are undetermined constant;
Adjust the linear function of 2 part of sleeve are as follows:
y2(x)=k2x+c (3)
In formula: k, c are undetermined constant.
Step 2: compatibility of deformation;
In the step 2, the specific steps of the denaturation coordination are as follows:
The adjusting flexible cable 1 and adjusting sleeve 2 are in x=l1Place:
It is displaced equal (y1=y2), then:
y2(x)=k2l1-k2(l1+l2)=- k2l2
I.e.
Equal (the y ' of its slope1=y '2), then:
y′2=k2
I.e.
:
Step 3: solve Suo Li:
Step 3.1: calculating the kinetic energy and potential energy of flexible cable 1;
In the step 3.1, the kinetic energy and potential energy of the flexible cable 1 calculate step are as follows:
The kinetic energy T of the flexible cable 11Are as follows:
The potential energy V of the flexible cable 11Are as follows:
Step 3.2: calculating the kinetic energy and potential energy for adjusting sleeve 2;
In the step 3.2, the kinetic energy for adjusting sleeve 2 and potential energy calculate step are as follows:
The kinetic energy T for adjusting sleeve 22Are as follows:
The potential energy V for adjusting sleeve 22Are as follows:
V2=0 (7).
Step 3.3: calculating cable systems total kinetic energy and total potential energy;
In the step 3.3, the kinetic energy and potential energy of the cable systems calculate step are as follows:
The total kinetic energy E of the cable systemskAre as follows:
The total kinetic energy E of the cable systemspAre as follows:
Step 3.4: calculate the expression formula of Suo Li T:
In the step 3.4, the expression formula for calculating Suo Li T calculates step are as follows:
According to law of conservation of energy, have
Ek+Ep=constant=Ek max=Ep max (10)
It is computed, kinetic energy existsWhen reach maximum, thus can push away, potential energy existsWhen reach maximum, by above-mentioned conclusion Ek maxAnd Ep maxAfter abbreviation:
Kinetic energy maximum value and potential energy maximum value are substituted into formula (10), is an equation about a after abbreviation, requires a at this time
For non-zero solution, this makes it possible to obtain the expression formulas of Suo Li T:
Finally it is pointed out that above embodiments are only the more representational examples of the present invention.It is clear that the invention is not restricted to
Above-described embodiment, acceptable there are many deformations.Any letter made to the above embodiment according to the technical essence of the invention
Single modification, equivalent variations and modification, are considered as belonging to the scope of protection of the present invention.
Claims (10)
1. a kind of cord force of cable-stayed bridge calculation method adjusted under the influence of sleeve, described soft for calculating the Suo Li of flexible cable (1)
Property drag-line (1) be equipped with adjust sleeve (2), the flexible cable (1), adjust sleeve (2) outer end be equipped with articulated anchor (3),
Affixed between the flexible cable (1) and adjusting sleeve (2), the articulated anchor (3) and pontic are hinged, the adjusting sleeve (3)
For push-and-pull rod, it is characterised in that:
The calculation method includes the following steps:
Step 1: calculating displacement function;
Step 2: compatibility of deformation;
Step 3: solving Suo Li.
2. a kind of cord force of cable-stayed bridge calculation method adjusted under the influence of sleeve according to claim 1, it is characterised in that: institute
Stating step 1 further includes following steps:
Step 1.1: obtaining flexible cable (1) in the unilateral vibration shape adjusted under sleeve (2) effect using computational modal analysis
Figure:
Step 1.2: the shaping function of general drag-line is accordingly to be regarded as SIN function, under the action of adjusting sleeve (2), flexible cable
(1) vibration shape is changed, and flexible cable (1) is partially the superpositing function of SIN function and linear function, and adjusts sleeve
It (2) is partially linear function, to obtain the displacement function of flexible cable (1) part;
Step 1.3: a linear function is superimposed in the displacement function of flexible cable (1) part, to obtain its shaping function
With the linear function for adjusting sleeve (2) part.
3. a kind of cord force of cable-stayed bridge calculation method adjusted under the influence of sleeve according to claim 2, it is characterised in that: institute
Stating step 3 further includes following steps:
Step 3.1: calculating the kinetic energy and potential energy of flexible cable (1);
Step 3.2: calculating the kinetic energy and potential energy for adjusting sleeve (2);
Step 3.3: calculating cable systems total kinetic energy and total potential energy;
Step 3.4: calculating the expression formula of Suo Li T.
4. a kind of cord force of cable-stayed bridge calculation method adjusted under the influence of sleeve according to claim 3, it is characterised in that: institute
It states in step 1.2, the displacement function of the displacement function of flexible cable (1) part are as follows:
In formula: φ (x) is drag-line shaping function;ωnAfter being symmetrically installed damper for rope, the intrinsic frequency of n-th order vibration;For
Inhaul cable vibration initial phase.
5. a kind of cord force of cable-stayed bridge calculation method adjusted under the influence of sleeve according to claim 4, it is characterised in that: institute
It states in step 1.3, the shaping function of flexible cable (1) part and the linear function for adjusting sleeve (2) part are respectively as follows:
The shaping function of flexible cable (1) part:
In formula: a, b are undetermined constant;
Adjust the linear function of sleeve (2) part are as follows:
y2(x)=k2x+c (3)
In formula: k, c are undetermined constant.
6. a kind of cord force of cable-stayed bridge calculation method adjusted under the influence of sleeve according to claim 5, it is characterised in that: institute
It states in step 2, the specific steps that the denaturation is coordinated are as follows:
The adjusting flexible cable (1) and adjusting sleeve (2) are in x=l1Place:
It is displaced equal (y1=y2), then:
y2(x)=k2l1-k2(l1+l2)=- k2l2
I.e.
Equal (the y ' of its slope1=y '2), then:
y′2=k2
I.e.
:
7. the cord force of cable-stayed bridge calculation method under the influence of a kind of adjusting sleeve described according to claim 1~any one of 6,
It is characterized by: the kinetic energy and potential energy of the flexible cable (1) calculate step in the step 3.1 are as follows:
The kinetic energy T of the flexible cable (1)1Are as follows:
The potential energy V of the flexible cable (1)1Are as follows:
8. a kind of cord force of cable-stayed bridge calculation method adjusted under the influence of sleeve according to claim 6, it is characterised in that: institute
It states in step 3.2, the kinetic energy for adjusting sleeve (2) and potential energy calculate step are as follows:
The kinetic energy T for adjusting sleeve (2)2Are as follows:
The potential energy V for adjusting sleeve (2)2Are as follows:
V2=0 (7).
9. a kind of cord force of cable-stayed bridge calculation method adjusted under the influence of sleeve according to claim 7, it is characterised in that: institute
It states in step 3.3, the kinetic energy and potential energy of the cable systems calculate step are as follows:
The total kinetic energy E of the cable systemskAre as follows:
The total kinetic energy E of the cable systemspAre as follows:
10. a kind of cord force of cable-stayed bridge calculation method adjusted under the influence of sleeve according to claim 8, it is characterised in that:
In the step 3.4, the expression formula for calculating Suo Li T calculates step are as follows:
According to law of conservation of energy, have
Ek+Ep=constant=Ek max=Ep max (10)
It is computed, kinetic energy existsWhen reach maximum, thus can push away, potential energy exists
When reach maximum, by above-mentioned conclusion Ek maxAnd Ep maxAfter abbreviation:
Kinetic energy maximum value and potential energy maximum value are substituted into formula (10), are an equation about a after abbreviation, it is non-zero for requiring a at this time
Solution, this makes it possible to obtain the expression formulas of Suo Li T:
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