CN103279588A - Method for calculating fatigue stress of steel bridge deck slab under combined action of vehicle load and temperature - Google Patents

Abstract

The invention discloses a method for calculating the fatigue stress of a steel bridge deck slab under the combined action of a vehicle load and the temperature. The method includes the following steps: building a steel bridge deck slab-pavement layer integrated fatigue analysis model under the combined action of the vehicle load and the temperature, selecting a single standard fatigue vehicle, loading the integrated fatigue analysis model to the fatigue vehicle, calculating fatigue stress time history curves of welding details under predetermined working conditions, on the basis of the curve, building an analysis model for calculating the fatigue stress time history of the welding details under any working condition, and determining the fatigue stress time history of the welding details under the combined action of the vehicle load and the temperature. The calculation method can achieve simulation of the fatigue stress time history of the steel bridge deck slab during any time period, the simulating result can accurately reflect the change rule of the fatigue stress of the steel bridge deck slab in a real operation state, and the method fills the gap that no appropriate method for calculating the fatigue stress of the steel bridge deck slab under the combined action of the vehicle load and the temperature exists in the prior art.

Description

Steel bridge deck Fatigue stress calculation method under vehicular load and the temperature acting in conjunction

Technical field

The invention belongs to analysis of fatigue and the design field of striding cable carrying bogie girder construction steel bridge deck greatly, be specifically related to the steel bridge deck Fatigue stress calculation method under a kind of vehicular load and the temperature acting in conjunction.

Background technology

The influence factor of steel bridge deck fatigue behaviour has the residing environment of bridge structure and extraneous load action, wherein vehicular load is as major influence factors, in the research field of steel bridge deck fatigue problem, paid close attention to, for example woods is daily waits the people to set up fatigue criterion vehicle model in all parts of the country based on actual measurement vehicular load data, and the car load car weight, the axle that have obtained the fatigue criterion auto model on this basis by analysis weigh parameters such as partition coefficient, axial length, wheelbase distribution to steel bridge deck fatigue damage and Fatigue Life rule; In addition, studies show that environment temperature also can exert an influence to the fatigue behaviour of steel bridge deck, its influence comes from asphalt mixture surfacing and has temperature sensitivity, layer variation of temperature of mating formation changed the elastic modulus of the layer of mating formation, and then changed the transmission pressure of vehicular load in the layer of mating formation, thereby remote effect the fatigue behaviour of steel bridge deck.Yet Chinese scholars is devoted to solve the fatigue problem of steel bridge deck under the vehicular load continuous action always at present, and ignores the influence of temperature action; Simultaneously, the research of most of steel bridge deck fatigue problem only is confined in the finite time length, and the fatigue damage of considering steel bridge deck is a constantly process of accumulation, and the tired result of calculation in the finite time length is difficult to satisfy analysis and requires.

Therefore, need a kind of new vehicular load and the steel bridge deck Fatigue stress calculation method under the temperature acting in conjunction to address the above problem.

Summary of the invention

Goal of the invention: the present invention is directed to the defective that the fatigue problem of steel bridge deck under the vehicular load continuous action in the prior art do not considered the influence of temperature action, the method for the steel bridge deck Fatigue stress calculation under a kind of vehicular load and the temperature acting in conjunction is provided.

Technical scheme: for solving the problems of the technologies described above, the steel bridge deck Fatigue stress calculation method under vehicular load of the present invention and the temperature acting in conjunction adopts following technical scheme:

Steel bridge deck Fatigue stress calculation method under a kind of vehicular load and the temperature acting in conjunction may further comprise the steps:

1), sets up steel bridge deck under vehicular load and the temperature acting in conjunction-integrated analysis of fatigue model of layer of mating formation;

2), choose single fatigue criterion car, load on the described steel bridge deck-integrated analysis of fatigue model of layer of mating formation that step 1) is set up, calculate the fatigue stress time-history curves of welding details under the predetermined operating mode, set up the analytical model that welding details fatigue stress time-histories is calculated under arbitrary operating mode on this basis;

3), choose k fatigue criterion car and carry out stochastic simulation, wherein, the initial moment t of each fatigue criterion car on time shaft determined in k 〉=2 _{1, m}, the finish time t _{2, m}And at time period [t _{1, m}, t _{2, m}] interior speed of operation v _m, m=1 wherein ..., k;

4), the temperature value to asphalt mixture surfacing carries out stochastic simulation, determining step 3) time period [t _{1, m}, t _{2, m}] the interior corresponding layer temperature value T that mat formation;

5), with time period [t _{1, m}, t _{2, m}] interior speed of operation v _mAnd layer temperature value T substitution step 2 of mating formation) analytical model, calculate corresponding fatigue stress value of each time period in each moment, and with the fatigue stress value linear superposition of different time sections synchronization, determine the welding details fatigue stress time-histories under vehicular load and the temperature acting in conjunction.

Further, the described steel bridge deck of the step 1)-integrated analysis of fatigue model of layer of mating formation obtains by the following method:

Based on the ANSYS finite element analysis software, set up the steel bridge deck-integrated analysis of fatigue model of layer of mating formation under vehicular load and the temperature acting in conjunction:

1. the steel bridge deck part is made up of top board and vertical rib, adopts shell unit to simulate;

2. asphalt mixture surfacing adopts the solid element simulation, wherein for the simulation of asphalt mixture surfacing elastic modulus, utilizes the elastic modulus E of asphalt mixture surfacing and the correlativity of mating formation between layer temperature T, and the employing following formula is represented:

E＝1.2×10 ^{0.01693(20-T)+3}。

Further, the direction across bridge size of steel bridge deck is got 6 U-shaped ribs, gets 5 diaphragm plate spacings to size along bridge, and the surrounding bound constrained is modeled as hinged support, and it is 1.88 * 10 that middle diaphragm plate is modeled as the rigidity size to the boundary constraint of steel bridge deck ⁷The vertical spring of N/m supports.

Further, step 2) chooses single fatigue criterion car in, load on the described steel bridge deck-integrated analysis of fatigue model of layer of mating formation that step 1) is set up, calculate the fatigue stress time-history curves of welding details under the predetermined operating mode, set up the analytical model that welding details fatigue stress time-histories is calculated under arbitrary operating mode on this basis, specifically may further comprise the steps:

(a) get single fatigue criterion car Load Model, with speed of operation v ₀Cross the integrated analysis of fatigue model that step 1) is set up along the track center line, be divided into the different design condition of n kind according to the difference of asphalt mixture surfacing temperature T, calculate the fatigue stress time-history curves S of steel bridge deck welding details ₁(t)～S _n(t), be expressed as S (t)={ S with set ₁(t) ..., S _n(t) }, wherein t is the time, S _r(t) be fatigue stress time-history curves under the r kind design condition, r=1 ..., n;

(b) according to the n bar fatigue stress time-history curves S (t) of welding details, choose it at t ₀Fatigue stress value S (t constantly ₀) and corresponding asphalt mixture surfacing temperature value T, draw S (t ₀)-T scatter diagram also utilizes least square method to carry out the match of quadratic polynomial function, sets up S (t ₀)-T correlation model S (t ₀, T), can obtain t accordingly ₀Arbitrary fatigue stress value of mating formation during layer temperature T constantly travels through constantly all of S (t) according to the method and can obtain arbitrary moment t, arbitrary fatigue stress value of mating formation during layer temperature T, with function S (t, T) expression;

(c) (t, time variable t T) multiply by scale-up factor v/v to function S ₀, with function S (vt/v ₀, T) expression can obtain independent variable v, t, the T welding details fatigue stress value when set-point, wherein function S (tv/v accordingly ₀, T) can be used as the analytical model that welding details fatigue stress time-histories is calculated.

Further, step (a) the medium pitch layer temperature T of mating formation is divided into-10 ℃, 0 ℃, 10 ℃, 20 ℃, 30 ℃, 40 ℃, 50 ℃ and 60 ℃ of eight kinds of different situations.

Further, speed of operation v described in the step (a) ₀=60km/h.

Further, determine the initial moment t of each fatigue criterion car on time shaft in the step 3) _{1, m}, the finish time t _{2, m}And at time period [t _{1, m}, t _{2, m}] interior speed of operation v _m, specifically may further comprise the steps:

(a1), settle the standard the probability density statistical model f (s) of the vehicular gap s of tired car and speed of operation v and g (v):

Probability density statistical model f (s) obeys logarithm normal distribution of the following distance s of fatigue criterion garage with equation expression is:

$f\left(s\right)=\frac{1}{\mathrm{s\γ}\sqrt{2\mathrm{\π}}}{e}^{\frac{{(\ln s-\mathrm{\η})}^2}{2{\mathrm{\γ}}^2}}$

In the formula, η, γ are parameter to be estimated, and utilize the lognormal distribution function in the Matlab statistical tool case, vehicular gap is gathered sample carry out the probability density statistical characteristic analysis, determine η, γ estimates of parameters,

The fatigue criterion car travel speed of a motor vehicle v probability density statistical model g (v) adopt following formula to express:

g(v)＝f(s)p(t _p)

$p\left(t_p\right)=\frac{1}{\mathrm{\ρ}}{e}^{-\frac{t_p}{\mathrm{\ρ}}}$

In the formula, t _pBe the used time of last axletree of certain fatigue criterion car through extremely back fatigue criterion car first axletree process of observation station observation station, p (t _p) be time t _pThe probability density statistical model, obeys index distribution, wherein ρ is p (t _p) parameter to be estimated, utilize the exponential distribution function in the Matlab statistical tool case, to time t _pThe collection sample carry out the probability density statistical characteristic analysis, determine the ρ estimates of parameters;

(b1), to probability density statistical model f (s) and g (v) carry out the Monte Carlo sampling, determine vehicular gap s and speed of operation v sample sequence S and the V on time shaft:

Utilize implicit expression Monte Carlo sampling formula, the probability density statistical model f (s) of the following distance s of fatigue criterion garage carried out even random sampling, obtain the sample sequence S of the following distance s of fatigue criterion garage:

F(S)＝F(S _a)+[F(S _b)-F(S _a)]·rand(0,1)

In the formula, S _a, S _bBe respectively the bound of sample sequence S; F (S), F (S _a), F (S _b) be respectively f (s) interval (∞, S], (∞, S _a], (∞, S _b] on integrated value; [F (S _b)-F (S _a)] rand (0,1) is at interval (0, F (S _b)-F (S _a)] on even random sampling, wherein k-1 is the capacity of sample sequence S;

Utilize implicit expression Monte Carlo sampling formula, to the fatigue criterion car travel speed of a motor vehicle v probability density statistical model g (v) carry out even random sampling, obtain the travel sample sequence V of speed of a motor vehicle v of fatigue criterion car:

F(V)＝F(V _a)+[F(V _b)-F(V _a)]·rand(0,1)

In the formula, V _a, V _bBe respectively the bound of sample sequence V; F (V), F (V _a), F (V _b) be respectively f (v) interval (∞, V], (∞, V _a], (∞, V _b] on integrated value; [F (V _b)-F (V _a)] rand (0,1) is at interval (0, F (V _b)-F (V _a)] on even random sampling, wherein k is the capacity of sample sequence V;

(c1) based on sample sequence S and V, k fatigue criterion car carried out stochastic simulation: each wheelbase sum of a phantom order fatigue criterion car is l ₁, the suitable bridge of integrated analysis model is l to length ₂, if at t _{1, m}Constantly, m fatigue criterion car first axletree is with speed of operation v _m(being positioned at the m row of sample sequence V) sails integrated analysis model, then elapsed-time standards l into ₁/ v _mAfter, last axle of m fatigue criterion car can be through observation station, after this latency period △ t again _m(△ t _m=S _m/ v _M+1, S _mBe positioned at the m row of sample sequence S) after, m+1 fatigue criterion car first axletree can be with speed of operation v _M+1Sail the integrated analysis model into, analyze accordingly and can obtain the finish time t of m fatigue criterion car on time shaft _{2, m}=t _{1, m}+ l _1/vm+ l ₂/ v _m, m+1 the initial moment t of fatigue criterion car on time shaft _{1, m+1}=t _{1, m}+ l ₁/ v _m+ △ t _mAnd the like, just can determine the initial moment t of k fatigue criterion car on time shaft according to sampled sequence _{1, m}With the t finish time _{2, m}(m=1 ..., k), and at time period [t _{1, m}, t _{2, m}] interior speed of operation v _m

Analog result can accurately reflect the steel bridge deck fatigue stress Changing Pattern under the actual operation state: 1. when the probability density statistical model to stochastic variable s, v carries out the Monte Carlo sampling, control the finish time t of last fatigue criterion car on time shaft by adjusting sampling number k-1, k _{2, k}, can realize the steel bridge deck fatigue stress time-histories simulation in arbitrary time span; 2. the probability density statistical model of stochastic variable s, v, the T probability density statistical property that is based on the actual measurement sample obtains, so its analog sample sequence also has the probability density statistical nature of actual measurement sample.

Further, in the step 5) with time period [t _{1, m}, t _{2, m}] interior speed of operation v _mAnd layer temperature value T substitution step 2 of mating formation) analytical model, calculate corresponding fatigue stress value of each time period in each moment, and with the fatigue stress value linear superposition of different time sections synchronization, determine the welding details fatigue stress time-histories under vehicular load and the temperature acting in conjunction, specifically may further comprise the steps:

(a2), based on step 3) and step 4), according to m time period [t _{1, m}, t _{2, m}] middle t _mThe speed of operation v that the moment is corresponding _m(t _m) and layer temperature value T (t that mat formation _m), make t=t _m-t _{1, m}, v=v _m(t _m), T=T (t _m), substitution step 2) analytical model, determine m fatigue criterion car t on time shaft _mFatigue stress value is constantly determined the fatigue stress time-histories of k fatigue criterion car on time shaft to the moment traversal of all time periods;

(b2), with the fatigue stress value linear superposition of fatigue stress time-histories synchronization on time shaft of k fatigue criterion car, obtain the simulated series of fatigue stress value on time shaft, thereby determine the steel bridge deck fatigue stress time-histories under vehicular load and the temperature acting in conjunction.

Beneficial effect: the steel bridge deck Fatigue stress calculation method under vehicular load of the present invention and the temperature acting in conjunction, can realize the steel bridge deck fatigue stress time-histories simulation in arbitrary time span, the fatigue stress time-histories that obtains based on the analog sample sequence can accurately reflect the steel bridge deck fatigue stress Changing Pattern under the actual operation state.These computing method have been filled up the blank that does not have steel bridge deck Fatigue stress calculation method under suitable vehicular load and the temperature acting in conjunction in the prior art, can obtain extensive promotion and application.

Description of drawings

Fig. 1 raises the bridge cable-stayed bridge steel bridge deck-layer integrated analysis model of mating formation for embodiment of the invention profit;

Fig. 2 is the front view of embodiment of the invention fatigue criterion car Load Model;

Fig. 3 is the vertical view of embodiment of the invention fatigue criterion car Load Model;

Fig. 4 is that the one-sided wheel load of the embodiment of the invention is monitored the position along bridge to layout and fatigue stress;

Fig. 5 is that the one-sided wheel load direction across bridge of the embodiment of the invention is arranged and fatigue stress monitoring position;

The fatigue stress time-histories of measuring point A when Fig. 6 mats formation layer temperature for embodiment of the invention difference;

The fatigue stress time-histories of measuring point B when Fig. 7 mats formation layer temperature for embodiment of the invention difference;

Fig. 8 is the S (t of embodiment of the invention measuring point A, B ₀)-T correlation model scatter diagram and estimation curve;

Fig. 9 is embodiment of the invention analytical model S (vt/60, T) the fatigue stress time-histories when v, the given value of T;

Figure 10 is the probability density statistical property of embodiment of the invention stochastic variable s analog sample;

Figure 11 is the probability density statistical property of embodiment of the invention stochastic variable t analog sample;

Figure 12 is embodiment of the invention temperature simulation sample T _YearTime-histories sequence after the adjustment;

Figure 13 is embodiment of the invention temperature simulation sample T _YearThe probability density statistical property;

Figure 14 is steel bridge deck fatigue stress time-histories under embodiment of the invention vehicular load and the temperature acting in conjunction.

Embodiment

Below in conjunction with the drawings and specific embodiments, further illustrate the present invention, should understand these embodiment only is used for explanation the present invention and is not used in and limits the scope of the invention, after having read the present invention, those skilled in the art all fall within the application's claims institute restricted portion to the modification of the various equivalent form of values of the present invention.

Steel bridge deck Fatigue stress calculation method under vehicular load of the present invention and the temperature acting in conjunction, these computing method comprise the steps:

Step 1) is set up the steel bridge deck-integrated analysis of fatigue model of layer of mating formation under vehicular load and the temperature acting in conjunction:

Based on the ANSYS finite element analysis software, according to design drawing and the data of striding cable carrying bogie girder construction system greatly, set up the steel bridge deck-integrated analysis of fatigue model of layer of mating formation under vehicular load and the temperature acting in conjunction.1. wherein the steel bridge deck part is made up of top board and vertical rib, adopt shell unit to simulate, the direction across bridge size of steel bridge deck is got 6 U-shaped ribs, get 5 diaphragm plate spacings along bridge to size, the surrounding bound constrained is modeled as hinged support, and it is 1.88 * 10 that middle diaphragm plate is modeled as the rigidity size to the boundary constraint of steel bridge deck ⁷The vertical spring of N/m supports; 2. asphalt mixture surfacing adopts the solid element simulation, wherein for the simulation of asphalt mixture surfacing elastic modulus, utilizes the elastic modulus E of asphalt mixture surfacing and the correlativity of mating formation between layer temperature T, and employing formula (1) is represented:

E＝1.2×10 ^{0.01693(20-T)+3} （1）

Step 2) chooses single fatigue criterion car, load on the integrated analysis of fatigue model that step 1) is set up, calculate specific operation (given speed of operation v and layer temperature T of mating formation) the fatigue stress time-history curves of welding details down, set up the analytical model that welding details fatigue stress time-histories is calculated under arbitrary operating mode on this basis:

(a) get single fatigue criterion car Load Model, cross the integrated analysis of fatigue model that step 10) is set up with speed of operation v=60km/h along the track center line, difference according to asphalt mixture surfacing temperature T (10 ℃, 0 ℃, 10 ℃, 20 ℃, 30 ℃, 40 ℃, 50 ℃, 60 ℃) is divided into eight kinds of design conditions, calculates the fatigue stress time-history curves S of steel bridge deck welding details ₁(t)～S ₈(t), be expressed as S (t)={ S with set ₁(t) ..., S ₈(t) }, wherein t is the time, S _r(t) be fatigue stress time-history curves under the r kind design condition, r=1 ..., 8;

(b) according to eight fatigue stress time-history curves S (t) of welding details, choose it at t ₀Fatigue stress value S (t constantly ₀) and corresponding asphalt mixture surfacing temperature value T, draw S (t ₀)-T scatter diagram also utilizes least square method to carry out the match of quadratic polynomial function, sets up S (t ₀)-T correlation model S (t ₀, T), can obtain t accordingly ₀Arbitrary fatigue stress value of mating formation during layer temperature T constantly travels through constantly all of S (t) according to the method and can obtain arbitrary moment t, arbitrary fatigue stress value of mating formation during layer temperature T, with function S (t, T) expression;

(c) to function S (t, T) time variable t multiply by scale-up factor v/60, with function S (vt/60, T) expression, can obtain independent variable v, t, the T welding details fatigue stress value when set-point accordingly, wherein (tv/60 T) can be used as the analytical model that welding details fatigue stress time-histories is calculated to function S;

Step 3) is chosen k(k 〉=2) a fatigue criterion car carries out stochastic simulation, determines the initial moment t of each fatigue criterion car on time shaft _{1, m}With the t finish time _{2, m}(m=1 ..., k), and at time period [t _{1, m}, t _{2, m}] interior speed of operation v _m:

(a1) settle the standard the probability density statistical model f (s) of the vehicular gap s of tired car and speed of operation v and g (v):

Probability density statistical model f (s) obeys logarithm normal distribution of the following distance s of fatigue criterion garage with equation expression is:

$f\left(s\right)=\frac{1}{\mathrm{s\γ}\sqrt{2\mathrm{\π}}}{e}^{\frac{{(\ln s-\mathrm{\η})}^2}{2{\mathrm{\γ}}^2}}---\left(2\right)$

In the formula, η, γ are parameter to be estimated, and utilize the lognormal distribution function in the Matlab statistical tool case, vehicular gap is gathered sample carry out the probability density statistical characteristic analysis, determine η, γ estimates of parameters.The fatigue criterion car travel speed of a motor vehicle v probability density statistical model g (v) adopt following formula to express:

g(v)＝f(s)p(t _p) （3a）

$p\left(t_p\right)=\frac{1}{\mathrm{\ρ}}{e}^{-\frac{t_p}{\mathrm{\ρ}}}---\left(3b\right)$

In the formula, t _pBe the used time of last axletree of certain fatigue criterion car through extremely back fatigue criterion car first axletree process of observation station observation station, p (t _p) be time t _pThe probability density statistical model, obeys index distribution, wherein ρ is p (t _p) parameter to be estimated, utilize the exponential distribution function in the Matlab statistical tool case, to time t _pThe collection sample carry out the probability density statistical characteristic analysis, determine the ρ estimates of parameters;

(b1) to probability density statistical model f (s) and g (v) carry out the Monte Carlo sampling, determine vehicular gap s and speed of operation v sample sequence S and the V on time shaft:

Utilize implicit expression Monte Carlo sampling formula (4), the probability density statistical model f (s) of formula (2) carried out even random sampling, obtain the sample sequence S of the following distance s of fatigue criterion garage:

F(S)＝F(S _a)+[F(S _b)-F(S _a)]·rand(0,1) （4）

In the formula (4), S _a, S _bBe respectively the bound of sample sequence S, be taken as 13.2m and 1000m respectively; F (S), F (S _a), F (S _b) be respectively f (s) interval (∞, S], (∞, S _a], (∞, S _b] on integrated value, utilize integral function order vpa in the Matlab mathematical software (int (f (s) ,-∞, S)), vpa (int (f (s) ,-∞, S _a)), vpa (int (f (s) ,-∞, S _b)) obtain; [F (S _b)-F (S _a)] rand (0,1) is at interval (0, F (S _b)-F (S _a)] on even random sampling, utilize the sampling function order (F (S in the Matlab mathematical software _b)-F (S _a)) * rand (1, k-1) obtain, wherein k-1 is the capacity of sample sequence S;

Utilize implicit expression Monte Carlo sampling formula (5), to the probability density statistical model g of formula (3a) (v) carry out even random sampling, obtain the travel sample sequence V of speed of a motor vehicle v of fatigue criterion car:

F(V)＝F(V _a)+[F(V _b)-F(V _a)]·rand(0,1) （5）

In the formula (5), V _a, V _bBe respectively the bound of sample sequence V, be taken as 13.8m/s and 30.6m/s respectively; F (V), F (V _a), F (V _b) be respectively f (v) interval (∞, V], (∞, V _a], (∞, V _b] on integrated value, utilize integral function order vpa in the Matlab mathematical software (int (f (v) ,-∞, V)), vpa (int (f (v) ,-∞, V _a)), vpa (int (f (v) ,-∞, V _b)) obtain; [F (V _b)-F (V _a)] rand (0,1) is at interval (0, F (V _b)-F (V _a)] on even random sampling, utilize the sampling function order (F (V in the Matlab mathematical software _b)-F (V _a)) * rand (1, realize that k) wherein k is the capacity of sample sequence V;

(c1) based on sample sequence S and V, k fatigue criterion car carried out stochastic simulation:

Each wheelbase sum of a phantom order fatigue criterion car is l ₁, the suitable bridge of integrated analysis model is l to length ₂, if at t _{1, m}Constantly, m fatigue criterion car first axletree is with speed of operation v _m(being positioned at the m row of sample sequence V) sails integrated analysis model, then elapsed-time standards l into ₁/ v _mAfter, last axle of m fatigue criterion car can be through observation station, after this latency period △ t again _m(△ t _m=S _m/ v _M+1, S _mBe positioned at the m row of sample sequence S) after, m+1 fatigue criterion car first axletree can be with speed of operation v _M+1Sail the integrated analysis model into, analyze accordingly and can obtain the finish time t of m fatigue criterion car on time shaft _{2, m}=t _{1, m}+ l ₁/ v _m+ l ₂/ v _m, m+1 the initial moment t of fatigue criterion car on time shaft _{1, m+1}=t _{1, m}+ l ₁/ v _m+ △ t _mAnd the like, just can determine the initial moment t of k fatigue criterion car on time shaft according to sampled sequence _{1, m}With the t finish time _{2, m}(m=1 ..., k), and at time period [t _{1, m}, t _{2, m}] interior speed of operation v _m

Step 4) is carried out stochastic simulation to the temperature value of asphalt mixture surfacing, determining step 3) each time period [t _{1, m}, t _{2, m}] the interior corresponding layer temperature value T that mat formation:

With reference to relevant patent, application number: 201110195454.5, publication number: 102393877A, name is called: the analogy method of a kind of bridge structure steel case Liang Suijiwenduchang, to time period [t _1,1, t _{2, k}] in layer temperature value T that mat formation carry out stochastic simulation, and therefrom filter out each time period [t of step 3) _{1, m}, t _{2, m}] the interior corresponding layer temperature value T that mat formation;

Step 5) is with each time period [t _{1, m}, t _{2, m}] interior speed of operation v _mAnd layer temperature value T substitution step 2 of mating formation) analytical model, calculate corresponding fatigue stress value of each time period in each moment, and with the fatigue stress value linear superposition of different time sections synchronization, determine the welding details fatigue stress time-histories under vehicular load and the temperature acting in conjunction:

(a2) based on step 3) and step 4), according to m time period [t _{1, m}, t _{2, m}] middle t _mThe speed of operation v that the moment is corresponding _m(t _m) and layer temperature value T (t that mat formation _m), make t=t _m-t _{1, m}, v=v _m(t _m), T=T (t _m), substitution step 2) fatigue load effect analysis model S (tv/60 T), determines m fatigue criterion car t on time shaft _mFatigue stress value is constantly determined the fatigue stress time-histories of k fatigue criterion car on time shaft to the moment traversal of all time periods;

(b2) with the fatigue stress value linear superposition of fatigue stress time-histories synchronization on time shaft of k fatigue criterion car, obtain the simulated series of fatigue stress value on time shaft, thereby determine the steel bridge deck fatigue stress time-histories under vehicular load and the temperature acting in conjunction;

Embodiment:

Raising the Fatigue stress calculation analysis of bridge north branch of a river cable-stayed bridge steel bridge deck under vehicular load and temperature acting in conjunction with profit below is example, and specific implementation process of the present invention is described:

(1) profit of setting up according to step 1) is raised the steel bridge deck of bridge north branch of a river cable-stayed bridge-mat formation layer integrated analysis model as shown in Figure 1, and establishment step 2 on this basis) steel bridge deck welding details fatigue stress time-histories is calculated under arbitrary operating mode analytical model:

1. tired car and load mode settle the standard: step 2) used fatigue criterion car Load Model as shown in Figures 2 and 3, the both sides wheel load of considering the same axle of fatigue criterion car is independent of each other to the result of calculation of fatigue stress, adopt one-sided wheel load load mode, load position and fatigue stress monitoring position respectively as shown in Figure 4 and Figure 5, wherein measuring point A is top board-vertical rib welding details monitoring position among Fig. 5, and measuring point B is vertical rib butt joint welding details monitoring position;

2. according to step 2) in (a) step load, obtain eight fatigue stress time-history curves S of two classes welding details ₁(t)～S ₈(t), the part curve is respectively shown in Fig. 6,7; Further according to step 2) in (b) step set up two classes welding details S (t)-T correlation model S (t, T), with the quadratic polynomial function representation be S (t, T)=a (t) T ²+ b (t) T+c (t), wherein a (t), b (t), c (t) are parameter to be estimated, adopt least square method and quadratic nonlinearity homing method can determine estimates of parameters, table 1 has provided correlation model S (t, S (t)-T scatter diagram and estimation curve when the T) estimates of parameters when moment t part value, Fig. 8 have further provided t=0.768s constantly;

3. based on (c) among the correlation model S (t, T), according to step 2) step determine the analytical model S that welding details fatigue stress time-histories is calculated under arbitrary operating mode (vt/60, T), with the quadratic polynomial function representation be S (vt/60, T)=a (vt/60) T ²+ b (vt/60) T+c (vt/60), Fig. 9 have provided analytical model S (vt/60, T) the fatigue stress time-histories of top board-vertical rib welding details when independent variable v, T part value (v=50km/h, 70km/h, 90km/h, 110km/h, T=10 ℃);

Table 1

(2) choose 4,000,000 fatigue criterion cars and simulate at time shaft, time span is about 1 year.Based on step 3) (a1) probability density statistical model f (s) and the p (t in step _p), to vehicular gap s and time t _pThe collection sample carry out the probability density statistical characteristic analysis, obtain the lognormal distribution that f (s) obeys η=2.2451, γ=1.3497, p (t _p) obey the exponential distribution of ρ=0.0436; Further according to step 3) (b1) step probability density statistical model f (s) and the g that determines (v) carried out the Monte Carlo sampling, determine vehicular gap s and speed of operation v sample sequence S and the V on time shaft, the probability density statistical property of S and V as shown in Figure 10 and Figure 11, as can be seen with probability density statistical model f (s) and p (t _p) the estimation curve match result good; Based on sample sequence S and V, according to the stochastic simulation of step 3) (c1) one step process realization to 4,000,000 fatigue criterion cars, determine the initial moment t of each fatigue criterion car on time shaft _{1, m}With the t finish time _{2, m}(m=1 ..., k), and at time period [t _{1, m}, t _{2, m}] interior speed of operation v _m

(3) with reference to relevant patent, application number: 201110195454.5, publication number: 102393877A, name is called: the analogy method of a kind of bridge structure steel case Liang Suijiwenduchang, asphalt mixture surfacing temperature value to 1 year carries out stochastic simulation, determining step 3) each time period [t _{1, m}, t _{2, m}] the interior corresponding layer temperature value T that mat formation:

1. determine maximal value and the minimum value of 1 year temperature simulation sample: when being basic with 10min apart from the temperature simulation sample T that generates 1 year _Year, analog sample T wherein _YearTemperature value number N=144 * 365=52560.If T _YearMaximal value and minimum value use T respectively _{Year, max}T _{Year, min}Expression, then T _{Year, max}And T _{Year, min}Surmount Probability p _Max, p _MinBe 1/N, utilize following formula can try to achieve T _{Year, max}And T _{Year, min}:

$p_{\max }=1-Q\left(T_{\mathrm{year},\max }\right)=1-{\∫}_{-\∞}^{T_{\mathrm{year},\max }}q\left(T\right)\mathrm{dT}---\left(6a\right)$

$p_{\min }=Q\left(T_{\mathrm{year},\min }\right)={\∫}_{-\∞}^{T_{\mathrm{year},\min }}q\left(T\right)\mathrm{dT}---\left(6b\right)$

In the formula, Q (T) is the probability cumulative distribution function of temperature T, and q (T) is the probability density function of temperature T, and wherein q (T) obeys the weighted sum of n normal distribution, adopts following formula to be expressed as:

$q\left(T\right)=\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_j\&CenterDot;\left[\frac{1}{{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA00003025040400012.png,HDA00003025040400022.png"\; state="\{\{state\}\}">j</figure-callout>}}\sqrt{2\mathrm{\&pi;}}}{e}^{\frac{-{(T-{\mathrm{\&mu;}}_j)}^2}{2{\mathrm{\&sigma;}}_j^2}}\right]---\left(7\right)$

In the formula, α _jBe weight, and The average of expression normal distyribution function, σ _jThe variance of expression normal distyribution function, n is 〉=2 integer, j is integer, and j=1,2 ..., n, α _j, μ _jAnd σ _jBe parameter to be estimated; Get n=2 and the collection sample of layer temperature of mating formation is carried out the probability density statistical characteristic analysis, it is as shown in table 2 to obtain estimates of parameters, further calculates T according to formula (7), (8) _{Year, max}=51.3 ℃, T _{Year, max}=-9.8 ℃, the interval of hence one can see that temperature simulation sample is [9.8 ℃, 51.3 ℃].

Table 2

Parameter to be estimated	α 1	μ 1	σ 1	α 2	μ 2	σ 2
							Estimated value	0.28	5.63	5.52	0.72	25.66	9.13

2. in the interval of temperature simulation sample, sample: utilize probability density function q (T) in the interval of temperature simulation sample [9.8 ℃, 51.3 ℃], to sample, determine the temperature value of temperature simulation sample in a year.Calculated T _YearMaximum of T _{Year, max}=51.3 ℃, minimum value T _{Year, max}=-9.8 ℃, then the sampling of the residue in interval (9.8 ℃, 51.3 ℃) number is N-2.Temperature range (9.8 ℃, 51.3 ℃) uniformly-spaced is divided into 100 sub-ranges, and then the increment Delta T in each sub-range is 0.61 ℃, and the scope in i sub-range is [(i-1) * 0.61-9.8, i * 0.61-9.8], i=1 wherein, and 2 ..., 100.If the number of the temperature value in each sub-range is N _i, N then _iFor:

In the formula,

Expression rounds downwards.Because formula (8) rounds downwards, cause the temperature samples number of actual generation to be less than the sample number of requirement, its difference DELTA N is:

$\mathrm{\&Delta;N}=(n-2)-\underset{i=1}{\overset{100}{\mathrm{\&Sigma;}}}{N}_i---\left(9\right)$

Unnecessary temperature samples number is assigned randomly in 100 sub-ranges, if the unnecessary sample number of i sub-range distribution is Δ N _i, the number of the final temperature value in i sub-range then

For:

${\stackrel{\&OverBar;}{N}}_i=N_i+\mathrm{\&Delta;}{N}_i---\left(10\right)$

Temperature samples number according to i sub-range

Generate equally distributed random number rand between [0,1]

Then the temperature samples sequence in i sub-range is:

$(i-1)\&times;0.61-9.8+0.61\&times;\mathrm{rand}({\stackrel{\&OverBar;}{N}}_i,\mathrm{0,1})---\left(11\right)$

Each sub-range traveled through to generate the temperature simulation sample sequence T that satisfies the destination probability density function _Year

3. the temperature simulation sample is carried out the adjustment of seasonal variations feature: to the 2. temperature simulation sample sequence T that obtain of step _YearRearrange, make it have day variation characteristic and the annual seasons variation characteristic round the clock of observed temperature sample.At first the year according to the observed temperature sample changes feature from T _YearIn select a moon crest maximal value, month crest minimum value, month trough maximal value, month trough minimum value (T _{Max, peak}, T _{Min, peak}, T _{Max, trough}, T _{Min, trough}), on this basis from T _YearIn select 2 suitable temperature values as certain day crest value T of 1 day _PeakWith day trough value T _Trough, make T _Peak, T _TroughIn the month at this 1 day place, satisfy T _{Min, peak}＜T _Peak＜T _{Max, peak}, T _{Min, trough}＜T _Trough＜T _{Max, trough}, 365 days traversals are just obtained the day crest value T in 1 year _PeakWith day trough value T _Trough, and then according to day crest value T _PeakWith day trough value T _TroughDetermine the ideal sinusoidal curve that degree/day changes.Utilize nonlinear least square method from T _YearChoose and the immediate sample of certain moment ideal value, the temperature simulation sample sequence T after just can obtaining adjusting _Year, as shown in figure 12, the temperature simulation sample sequence T after adjusting as can be seen _YearThe year that reflects observed temperature changes and the diurnal variation rule.Figure 13 has further provided temperature simulation sample sequence T _YearProbability density statistical property comparison diagram with the observed temperature sample, can find both probability density curve (Probability Density Function, be called for short PDF) identical substantially, illustrate that the temperature simulation sample can accurately reflect the probability density statistical property of surveying sample;

(4) based on step 5), determine the steel bridge deck fatigue stress time-histories under vehicular load and the temperature acting in conjunction:

1. according to m time period [t _{1, m}, t _{2, m}] middle t _mThe speed of operation v that the moment is corresponding _m(t _m) and layer temperature value T (t that mat formation _m), make t=t _m-t _{1, m}, v=v _m(t _m), T=T (t _m), substitution step 2) fatigue load effect analysis model S (tv/60 T), determines m fatigue criterion car t on time shaft _mFatigue stress value is constantly determined the fatigue stress time-histories of 4,000,000 fatigue criterion cars on time shaft to the moment traversal of all time periods;

2. with the fatigue stress value linear superposition of fatigue stress time-histories synchronization on time shaft of 4,000,000 fatigue criterion cars, obtain the simulated series of fatigue stress value on time shaft, thereby determine the steel bridge deck fatigue stress time-histories under vehicular load and the temperature acting in conjunction, as shown in figure 14.

Claims (8)

1. the steel bridge deck Fatigue stress calculation method under a vehicular load and the temperature acting in conjunction is characterized in that, may further comprise the steps:

1), sets up steel bridge deck under vehicular load and the temperature acting in conjunction-integrated analysis of fatigue model of layer of mating formation;

2), choose single fatigue criterion car, load on the described steel bridge deck-integrated analysis of fatigue model of layer of mating formation that step 1) is set up, calculate the fatigue stress time-history curves of welding details under the predetermined operating mode, set up the analytical model that welding details fatigue stress time-histories is calculated under arbitrary operating mode on this basis;

3), choose k fatigue criterion car and carry out stochastic simulation, wherein, the initial moment t of each fatigue criterion car on time shaft determined in k 〉=2 _{1, m}, the finish time t _{2, m}And at time period [t _{1, m}, t _{2, m}] interior speed of operation v _m, m=1 wherein ..., k;

4), the temperature value to asphalt mixture surfacing carries out stochastic simulation, determining step 3) time period [t _{1, m}, t _{2, m}] the interior corresponding layer temperature value T that mat formation;

5), with time period [t _{1, m}, t _{2, m}] interior speed of operation v _mAnd layer temperature value T substitution step 2 of mating formation) analytical model, calculate corresponding fatigue stress value of each time period in each moment, and with the fatigue stress value linear superposition of different time sections synchronization, determine the welding details fatigue stress time-histories under vehicular load and the temperature acting in conjunction.

2. the steel bridge deck Fatigue stress calculation method under vehicular load as claimed in claim 1 and the temperature acting in conjunction is characterized in that, the described steel bridge deck of the step 1)-integrated analysis of fatigue model of layer of mating formation obtains by the following method:

Based on the ANSYS finite element analysis software, set up the steel bridge deck-integrated analysis of fatigue model of layer of mating formation under vehicular load and the temperature acting in conjunction:

1. the steel bridge deck part is made up of top board and vertical rib, adopts shell unit to simulate;

2. asphalt mixture surfacing adopts the solid element simulation, wherein for the simulation of asphalt mixture surfacing elastic modulus, utilizes the elastic modulus E of asphalt mixture surfacing and the correlativity of mating formation between layer temperature T, and the employing following formula is represented:

E＝1.2×10 ^{0.01693(20-T)+3}。

3. the steel bridge deck Fatigue stress calculation method under vehicular load as claimed in claim 2 and the temperature acting in conjunction, it is characterized in that, the direction across bridge size of steel bridge deck is got 6 U-shaped ribs, get 5 diaphragm plate spacings along bridge to size, the surrounding bound constrained is modeled as hinged support, and it is 1.88 * 10 that middle diaphragm plate is modeled as the rigidity size to the boundary constraint of steel bridge deck ⁷The vertical spring of N/m supports.

4. the steel bridge deck Fatigue stress calculation method under vehicular load as claimed in claim 1 and the temperature acting in conjunction, it is characterized in that, step 2) chooses single fatigue criterion car in, load on the described steel bridge deck-integrated analysis of fatigue model of layer of mating formation that step 1) is set up, calculate the fatigue stress time-history curves of welding details under the predetermined operating mode, set up the analytical model that welding details fatigue stress time-histories is calculated under arbitrary operating mode on this basis, specifically may further comprise the steps:

(a) get single fatigue criterion car Load Model, with speed of operation v ₀Cross the integrated analysis of fatigue model that step 1) is set up along the track center line, be divided into the different design condition of n kind according to the difference of asphalt mixture surfacing temperature T, calculate the fatigue stress time-history curves S of steel bridge deck welding details ₁(t)～S _n(t), be expressed as S (t)={ S with set ₁(t) ..., S _n(t) }, wherein t is the time, S _r(t) be fatigue stress time-history curves under the r kind design condition, r=1 ..., n;

(b) according to the n bar fatigue stress time-history curves S (t) of welding details, choose it at t ₀Fatigue stress value S (t constantly ₀) and corresponding asphalt mixture surfacing temperature value T, draw S (t ₀)-T scatter diagram also utilizes least square method to carry out the match of quadratic polynomial function, sets up S (t ₀)-T correlation model S (t ₀, T), can obtain t accordingly ₀Arbitrary fatigue stress value of mating formation during layer temperature T constantly travels through constantly all of S (t) according to the method and can obtain arbitrary moment t, arbitrary fatigue stress value of mating formation during layer temperature T, with function S (t, T) expression;

(c) (t, time variable t T) multiply by scale-up factor v/v to function S ₀, with function S (vt/v ₀, T) expression can obtain independent variable v, t, the T welding details fatigue stress value when set-point, wherein function S (tv/v accordingly ₀, T) can be used as the analytical model that welding details fatigue stress time-histories is calculated.

5. the steel bridge deck Fatigue stress calculation method under vehicular load as claimed in claim 4 and the temperature acting in conjunction, it is characterized in that step (a) the medium pitch layer temperature T of mating formation is divided into-10 ℃, 0 ℃, 10 ℃, 20 ℃, 30 ℃, 40 ℃, 50 ℃ and 60 ℃ of eight kinds of different situations.

6. the steel bridge deck Fatigue stress calculation method under vehicular load as claimed in claim 4 and the temperature acting in conjunction is characterized in that, speed of operation v described in the step (a) ₀=60km/h.

7. the steel bridge deck Fatigue stress calculation method under vehicular load as claimed in claim 1 and the temperature acting in conjunction is characterized in that, determines the initial moment t of each fatigue criterion car on time shaft in the step 3) _{1, m}, the finish time t _{2, m}And at time period [t _{1, m}, t _{2, m}] interior speed of operation v _m, specifically may further comprise the steps:

(a1), settle the standard the probability density statistical model f (s) of the vehicular gap s of tired car and speed of operation v and g (v):

Probability density statistical model f (s) obeys logarithm normal distribution of the following distance s of fatigue criterion garage with equation expression is:

$f\left(s\right)=\frac{1}{\mathrm{s\&gamma;}\sqrt{2\mathrm{\&pi;}}}{e}^{\frac{{(\ln s-\mathrm{\&eta;})}^2}{2{\mathrm{\&gamma;}}^2}}$

In the formula, η, γ are parameter to be estimated, and utilize the lognormal distribution function in the Matlab statistical tool case, vehicular gap is gathered sample carry out the probability density statistical characteristic analysis, determine η, γ estimates of parameters,

The fatigue criterion car travel speed of a motor vehicle v probability density statistical model g (v) adopt following formula to express:

g(v)＝f(s)p(t _p)

$p\left(t_p\right)=\frac{1}{\mathrm{\&rho;}}{e}^{-\frac{t_p}{\mathrm{\&rho;}}}$

In the formula, t _pBe the used time of last axletree of certain fatigue criterion car through extremely back fatigue criterion car first axletree process of observation station observation station, p (t _p) be time t _pThe probability density statistical model, obeys index distribution, wherein ρ is p (t _p) parameter to be estimated, utilize the exponential distribution function in the Matlab statistical tool case, to time t _pThe collection sample carry out the probability density statistical characteristic analysis, determine the ρ estimates of parameters;

(b1), to probability density statistical model f (s) and g (v) carry out the Monte Carlo sampling, determine vehicular gap s and speed of operation v sample sequence S and the V on time shaft:

Utilize implicit expression Monte Carlo sampling formula, the probability density statistical model f (s) of the following distance s of fatigue criterion garage carried out even random sampling, obtain the sample sequence S of the following distance s of fatigue criterion garage:

F(S)＝F(S _a)+[F(S _b)-F(S _a)]·rand(0,1)

In the formula, S _a, S _bBe respectively the bound of sample sequence S; F (S), F (S _a), F (S _b) be respectively f (s) interval (∞, S], (∞, S _a], (∞, S _b] on integrated value; [F (S _b)-F (S _a)] rand (0,1) is at interval (0, F (S _b)-F (S _a)] on even random sampling, wherein k-1 is the capacity of sample sequence S;

Utilize implicit expression Monte Carlo sampling formula, to the fatigue criterion car travel speed of a motor vehicle v probability density statistical model g (v) carry out even random sampling, obtain the travel sample sequence V of speed of a motor vehicle v of fatigue criterion car:

F(V)＝F(V _a)+[F(V _b)-F(V _a)]·rand(0,1)

In the formula, V _a, V _bBe respectively the bound of sample sequence V; F (V), F (V _a), F (V _b) be respectively f (v) interval (∞, V], (∞, V _a], (∞, V _b] on integrated value; [F (V _b)-F (V _a)] rand (0,1) is at interval (0, F (V _b)-F (V _a)] on even random sampling, wherein k is the capacity of sample sequence V;

(c1) based on sample sequence S and V, k fatigue criterion car carried out stochastic simulation: each wheelbase sum of a phantom order fatigue criterion car is l ₁, the suitable bridge of integrated analysis model is l to length ₂, if at t _{1, m}Constantly, m fatigue criterion car first axletree is with speed of operation v _m(being positioned at the m row of sample sequence V) sails integrated analysis model, then elapsed-time standards l into ₁/ v _mAfter, last axle of m fatigue criterion car can be through observation station, after this latency period △ t again _m(△ t _m=S _m/ v _M+1, S _mBe positioned at the m row of sample sequence S) after, m+1 fatigue criterion car first axletree can be with speed of operation v _M+1Sail the integrated analysis model into, analyze accordingly and can obtain the finish time t of m fatigue criterion car on time shaft _{2, m}=t _{1, m}+ l ₁/ v _m+ l ₂/ v _m, m+1 the initial moment t of fatigue criterion car on time shaft _{1, m+1}=t _{1, m}+ l ₁/ v _m+ △ t _mAnd the like, just can determine the initial moment t of k fatigue criterion car on time shaft according to sampled sequence _{1, m}With the t finish time _{2, m}(m=1 ..., k), and at time period [t _{1, m}, t _{2, m}] interior speed of operation v _m

8. the steel bridge deck Fatigue stress calculation method under vehicular load as claimed in claim 1 and the temperature acting in conjunction is characterized in that, in the step 5) with time period [t _{1, m}, t _{2, m}] interior speed of operation v _mAnd layer temperature value T substitution step 2 of mating formation) analytical model, calculate corresponding fatigue stress value of each time period in each moment, and with the fatigue stress value linear superposition of different time sections synchronization, determine the welding details fatigue stress time-histories under vehicular load and the temperature acting in conjunction, specifically may further comprise the steps:

(a2), based on step 3) and step 4), according to m time period [t _{1, m}, t _{2, m}] middle t _mThe speed of operation v that the moment is corresponding _m(t _m) and layer temperature value T (t that mat formation _m), make t=t _m-t _{1, m}, v=v _m(t _m), T=T (t _m), substitution step 2) analytical model, determine m fatigue criterion car t on time shaft _mFatigue stress value is constantly determined the fatigue stress time-histories of k fatigue criterion car on time shaft to the moment traversal of all time periods;

(b2), with the fatigue stress value linear superposition of fatigue stress time-histories synchronization on time shaft of k fatigue criterion car, obtain the simulated series of fatigue stress value on time shaft, thereby determine the steel bridge deck fatigue stress time-histories under vehicular load and the temperature acting in conjunction.

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