CN104899377A - Suspension bridge cable force optimization method - Google Patents

Abstract

The invention provides a cable force optimization method, belongs to the technical field of bridge engineering, relates to suspension bridges, and specifically relates to suspension bridge cable force optimization. According to the method, based on the constant-load rigidity, an influence matrix of a suspension bridge structure is formed, and an ideal cable force for the suspension bridge is obtained via iteration analysis. According to the suspension bridge cable force optimization method, the concept is clear, and the convergence speed is fast.

Description

A kind of suspension bridge cable force optimality method

Technical field

The invention belongs to technical field of bridge engineering, relate to suspension bridge, be related specifically to suspension bridge cable force optimality.

Background technology

Suspension bridge has stronger geometrical non-linearity, and Cable system cannot be shaped under unstress state, and only under load and Suo Li effect, funicular system configuration could be stablized, and meets balance equation.The finally stable configuration of funicular system is that the ideal under corresponding load is linear, desirable linearly correspond to desirable Suo Li, i.e. the process of this process of " looking for shape " i.e. cable force optimality.

A lot of scholar launches research to suspension bridge cable force optimality or " looking for shape ".Method conventional at present has non-linear cable elements method and multistage bar unit process of iteration.Non-linear cable elements method is based on catenary elements, and main push-towing rope subdivision is catenary elements by cable element stiffness matrix of having derived.Multistage bar unit process of iteration is the Bar element of multistage by main push-towing rope subdivision, by successive ignition, converges on net result.

Yang Jun etc. apply influence matrix method and calculate self-anchored suspension bridge work progress stretching force in " the self-anchored suspension bridge construction stretching power based on influence matrix method is determined " literary composition, and Wang Zhanguo etc. apply influence matrix method adjustment self-anchored suspension bridge suspender force in " the influence matrix method that self-anchored suspension bridge suspender force is optimized " literary composition.The two does not all consider load initial stiffness when forming influence matrix, and significantly non-linear, speed of convergence is slow.

Summary of the invention

The invention provides a kind of suspension bridge cable force optimality method, this method clear concept, fast convergence rate.

Technical scheme of the present invention is:

A kind of suspension bridge cable force optimality method, step is as follows:

1st step, sets up finite element model, the dead load of definition suspension bridge and Suo Li variable load; Wherein dead load comprises dead load W ₁, secondary dead load W ₂with Initial cable force C ₀; Suo Li variable load is adjustable Suo Li C _v.

2nd step, calculates the reacting value A of Suspension bridge structure under dead load _d;

3rd step, calculates at dead load and adjustable Suo Li C _vi, i=1,2 ..., the reacting value A of the lower Suspension bridge structure of n effect _d+vi;

4th step, passes through A _vi=A _d+vi-A _d, obtain the Suo Li C in adjustment _vi, i=1,2 ..., the reacting value of the lower Suspension bridge structure of n effect;

5th step, repeats above-mentioned steps, obtains influence matrix [A]=[A _v1a _v2... A _vn].

6th step, linearly structure, calculates Suo Li, X by [A] X=D ₁=[A] ^-1(D-D ₀) C _v, wherein, D is object vector, D ₀=A _d, i.e. the reacting value of suspension bridge under dead load, C _vit is adjustable rope force vector;

7th step, by X ₁bring finite element model into, calculate suspension bridge at dead load and X ₁structural response D under effect ₁;

8th step, by influence matrix, calculates new rope force vector X ₂=X ₁+ [A] ^-1(D-D ₁) C _v;

9th step, by X ₂bring finite element model into, calculate suspension bridge at dead load and X ₂structural response D under effect ₂;

10th step, repeats second step ~ the 4th step, until || D-D _i|| < ε, obtains final desirable Suo Li X.

Beneficial effect of the present invention: the method, on the basis of dead load rigidity, defines the influence matrix of Suspension bridge structure, afterwards by iterative analysis, obtains the desirable Suo Li of suspension bridge.The invention provides a kind of suspension bridge cable force optimality method, this method clear concept, fast convergence rate.

Accompanying drawing explanation

Fig. 1 is the inventive method process flow diagram.

Fig. 2 is certain suspension bridge.

In figure: 1 main push-towing rope; 2 suspension rods; 3 girders.

Embodiment

The specific embodiment of the present invention is described in detail below in conjunction with technical scheme and accompanying drawing.

In suspended-cable structure, there are 4 sections of main push-towing ropes, 3 suspension rods.Girder and main push-towing rope span are 20m.The area of section of main push-towing rope is 1.398 × 10 ^-2m ², the area of section of suspension rod is 8.84 × 10 ^-3m ², the two bending resistance moment of inertia is 0, does not bear moment of flexure.Main push-towing rope and suspension rod adopt high-strength parallel steel wire, and elasticity modulus of materials is 1.9 × 10 ⁵mPa.The area of section of girder is 0.84m ², bending resistance moment of inertia is 5.488 × 10 ^-3m ⁴, adopt Q345 steel, elasticity modulus of materials is 2.1 × 10 ⁵mPa.At girder effect evenly load 20KN/m.

Main push-towing rope and suspension rod Initial cable force C are set ₀=100KN, main push-towing rope cable adjustable power is 10000KN, and suspension rod cable adjustable power is 1000KN.So influence matrix is

After 4 take turns iteration || D-D ₄|| <0.01, optimum results

X ₄＝[-6386.26,3579.63,3568.88,-6385.14,34855.19,141.06,34849.18] ^T。

Claims (1)

1. a suspension bridge cable force optimality method, is characterized in that, step is as follows:

1st step, sets up finite element model, the dead load of definition suspension bridge and Suo Li variable load; Wherein dead load comprises dead load W ₁, secondary dead load W ₂with Initial cable force C ₀; Suo Li variable load is adjustable Suo Li C _v;

2nd step, calculates the reacting value A of Suspension bridge structure under dead load _d;

3rd step, calculates at dead load and adjustable Suo Li C _vi, i=1,2 ..., the reacting value A of the lower Suspension bridge structure of n effect _d+vi;

4th step, passes through A _vi=A _d+vi-A _d, obtain the Suo Li C in adjustment _vi, i=1,2 ..., the reacting value of the lower Suspension bridge structure of n effect;

5th step, repeats above-mentioned steps, obtains influence matrix [A]=[A _v1a _v2... A _vn];

6th step, linearly structure, calculates Suo Li, X by [A] X=D ₁=[A] ^-1(D-D ₀) C _v, wherein, D is object vector, D ₀=A _d, i.e. the reacting value of suspension bridge under dead load, C _vit is adjustable rope force vector;

7th step, by X ₁bring finite element model into, calculate suspension bridge at dead load and X ₁structural response D under effect ₁;

8th step, by influence matrix, calculates new rope force vector X ₂=X ₁+ [A] ^-1(D-D ₁) C _v;

9th step, by X ₂bring finite element model into, calculate suspension bridge at dead load and X ₂structural response D under effect ₂;

10th step, repeats second step ~ the 4th step, until || D-D _i|| < ε, obtains final desirable Suo Li X.