CN102968557A - Method for valuing construction period wind load of ultra-large cooling tower - Google Patents

Abstract

The invention relates to a method for valuing the construction period wind load of an ultra-large cooling tower. The method is characterized by comprising the following steps of: (1) establishing a structural design reference period, a time interval relation among different time intervals in the structural design reference period, a construction period, and a reliability relation among different time intervals of the construction period respectively by taking a reliability theory as a theoretical foundation with a time interval analysis method of structural reliability to form a time interval relation expression and a reliability relation expression; (2) resolving the relation expressions in the step (1) to obtain the proportion of a construction period wind load standard value to a design reference period wind load standard value; and (3) resolving a construction period wind load factor according to the proportion in the step (2). The valuing standard problem of the construction period design wind load of a tower is researched on the premise of the same reliability in the construction period of a cooling tower and the design reference period by taking the basic theory of a structural reliability design as a foundation, the determination of the design wind load in the construction period of the cooling tower is facilitated, and the method plays a role in deciding the stability and manufacturing cost of the cooling tower in the construction period.

Description

A kind of ultra-large type cooling tower construction phase wind load obtaining value method

Technical field

The present invention relates to the ultra-large type cooling tower, especially a kind of ultra-large type cooling tower construction phase wind load obtaining value method.The technical field of buildings that belongs to the nuclear power station of electric system.

Background technology

The ultra-large type cooling tower is to adopt crucial construction of structures in the nuclear power station of secondary circulation cooling system.There is no in the world at present the construction experience of nuclear power station cooling tower.Cognitive according to existing industry, the cooling tower of 1000MW rank nuclear power station, tower height generally need to reach more than the 200m, more than the zero rice diameter 180m.So other construction of level is built, and is one of structures of nuclear power station monomer solid amount maximum.Therefore the safety of structure of ultra-large type cooling tower has vital impact to the nuclear safety of whole nuclear power station.

The tower cylinder of reinforced concrete hyperbolic curve cooling tower is the thin-wall case structure, and is very responsive to wind action.Wind load belongs to variable action.In the design specifications of the industries such as railway, highway, harbour, water conservancy and hydropower, although the variable action design standards to the construction time has all been done clear and definite regulation, but in related specifications and clause explanation thereof, all do not provide the concrete derivation of determining construction time variable action design standards.Except this, the correlation theory research of structure construction phase variable action also is still waiting to strengthen.

Determining of cooling tower construction phase designed wind load has decisive meaning to stability and the cost of construction time cooling tower.The cooling tower tube construction phase, relatively its design reference period was shorter, as the wind load design standards of taking design reference period carries out the checking computations of cooling tower construction operating mode, required obviously too high.When the concrete intensity of construction time barrel and elastic modulus are in the rise period, adopt this standard may significantly increase the quantities of barrel, cause the unnecessary increase of construction investment, particularly for the ultra-large type cooling tower, the value research of construction time wind load has prior meaning.In addition, the structural design of China's cooling tower belongs to building engineering at present, carries out structural design according to building structure RELIABILITY DESIGN unified standard and corresponding rules, standard thereof.But the designed wind load standard of reinforced concrete hyperbolic curve cooling tower tube construction phase does not clearly provide in the relevant specification of construction work industry, and this vacancy is also demanded urgently filling up.

Therefore, must further investigate the problems of value of cooling tower tube construction phase designed wind load.

At present, the value of domestic cooling tower construction phase designed wind load is consistent with design reference period, the wind load value of construction time and cooling tower is not built up final operating mode and distinguishes.

The present invention proposes ultra-large type cooling tower construction phase wind load obtaining value method first.

Summary of the invention

Purpose of the present invention is to provide a kind of ultra-large type cooling tower construction phase wind load obtaining value method.

Purpose of the present invention can reach by taking following technical scheme:

A kind of ultra-large type cooling tower construction phase wind load obtaining value method is characterized in that:

1) take Reliability Theory as theoretical foundation, utilize the period analytical approach of structural reliability set up respectively the structural design base period and therebetween the period relation of day part and construction time and during the fiduciary level relation of each time period, form day part relational expression and fiduciary level relational expression;

2) solution procedure 1) described relational expression, obtain construction time characteristi cvalue o fwindload and design reference period characteristi cvalue o fwindload ratio;

3) according to step 2) described ratio finds the solution the construction time wind load factor.

The present invention is take the basic theories of structural reliability design as the basis, has identical fiduciary level as prerequisite in cooling tower tube construction phase and design reference period, and the value typical problem of tower tube construction phase designed wind load is studied.According to the characteristics of the steady binomial random process model of wind load, utilize the period analytical approach of structural reliability to set up respectively structural design base period and the therebetween relation of day part and construction time and therebetween the fiduciary level relation of day part.Start with from the structure reactance of construction time and design reference period is proportional, requirement according to partial safety factor method for designing in the standard, obtain the same proportional conclusion of construction time characteristi cvalue o fwindload and design reference period characteristi cvalue o fwindload, and obtain accordingly the construction time wind load factor.

Purpose of the present invention can also reach by taking following technical scheme:

1) the structural design base period and therebetween the relation between the fiduciary level on the day part represent with following expression formula:

The form that the power function of structure all adopts structure reactance to compare with load effect, establish the power function of structure in arbitrary τ and be:

Zi＝Ri-Si＝R-Si，i＝1，2，...，n， (1)

Wherein R is the structure reactance function, and Si is the load effect function;

The failure probability pfe of each period and reliability index β e are:

p _fe＝Φ(-β _e)＝P(Z _i≤0) (2)

Structural failure Probability p f and reliability index β are:

$p_f=\mathrm{\Φ}(-\mathrm{\β})=P(\underset{i=1}{\overset{n}{U}}{Z}_i\≤0)=1-P(\underset{i=1}{\overset{n}{I}}{Z}_i>0)---\left(3\right)$

Perhaps be:

p _f＝Φ(-β)≈1-Φ _n(β _e，ρ) (4)

In the expression formula (4), Φ n represents n dimension Standard Normal Distribution; β e is that element all is the n dimension reliability index vector of β e; ρ is n rank related coefficient square formations, and its nondiagonal element is ρ e.ρ e is Zi and the Zj (related coefficient of i ≠ j).

Further, if the equal Normal Distribution of R and S, the average μ R of R, standard deviation is σ R; The average of Se is μ S, and standard deviation is σ S, then

${\mathrm{\β}}_e=\frac{{\mathrm{\μ}}_R-{\mathrm{\μ}}_S}{\sqrt{{\mathrm{\σ}}_R^2+{\mathrm{\σ}}_S^2}}---\left(1\right)$

A perhaps β e through type mistake! Do not find Reference source.With the formula mistake! Do not find Reference source.Obtain.

Further, consider that R and Si or Sj are separate, (related coefficient of i ≠ j) is for Zi and Zj

${\mathrm{\ρ}}_e=\frac{\mathrm{cov}(Z_i,Z_j)}{{\mathrm{\σ}}_{Z_i}{\mathrm{\σ}}_{Z_j}}=\frac{\mathrm{cov}(R-S_i,R-S_j)}{{\mathrm{\σ}}_{R-S_i}{\mathrm{\σ}}_{R-S_j}}=\frac{{\mathrm{\σ}}_R^2}{{\mathrm{\σ}}_R^2+{\mathrm{\σ}}_S^2}---\left(2\right)$

Further, if R and S are Non-normal Variable, the cumulative distribution function of R is FR (R), and probability density function is fR (R); The cumulative distribution function of Se is FS (S), and probability density function is fS (S); Utilize the JC method to carry out the equivalent normalize of variable, establish with the corresponding equivalent normalize of R variable is R ' for this reason, and its average is μ _{R '}, standard deviation is σ _{R '}With the corresponding equivalent normalize of S variable be S ', its average is μ _{S '}, standard deviation is σ _{S '}An if power function mistake! Do not find Reference source.Designcheck point be (r ^*, s ^*), according to the equivalent normalize condition of JC method,

μ _R′＝r ^*-Φ ^-1[FR(r ^*)]σ _R′，

μ _S′＝r ^*-Φ ^-1[F _S(s ^*)]σ _S′，

In the formula,

Expression standard normal probability density function; So, have

${\mathrm{\β}}_e=\frac{{\mathrm{\μ}}_{R^{\′}}-{\mathrm{\μ}}_{S^{\′}}}{\sqrt{{\mathrm{\σ}}_{R^{\′}}^2+{\mathrm{\σ}}_{S^{\′}}^2}}---\left(5\right)$

${\mathrm{\ρ}}_e=\frac{{\mathrm{\σ}}_{R^{\′}}^2}{{\mathrm{\σ}}_{R^{\′}}^2+{\mathrm{\σ}}_{S^{\′}}^2}---\left(6\right)$

2) the structure construction phase and during relation between the fiduciary level on the period represented by following expression formula:

If Tc inner structure reliability index is β c, failure probability is pf, c; τ c inner structure reliability index is β e, and c, failure probability are pfe, c, and corresponding structure reactance is Rc, and following expression is namely arranged:

Z _i，c＝R _c-S _i＝R _c-S _e＝Z _e， _c， i＝1，2，K，n _c (7)

p _fe，c＝Φ(-β _e，c)＝P(Z _i，c≤0)＝P(Z _e，c≤0) (8)

$p_{f,c}=\mathrm{\Φ}(-{\mathrm{\β}}_c)=P(\underset{i=1}{\overset{n_c}{U}}{Z}_{i,c}\≤0)=1-P(\underset{i=1}{\overset{n_c}{I}}{Z}_{i,c}>0)=1-{\mathrm{\Φ}}_{c_c}({\mathrm{\β}}_{e,c},{\mathrm{\ρ}}_c)---\left(9\right)$

β e wherein, c is that element all is β e, the n dimension reliability index vector of c; ρ c is n rank related coefficient square formations, and its nondiagonal element is ρ e, c.

Further, for construction time Tc and the wherein processing of the relation between the fiduciary level of period τ c, adopt structural design base period and the relational expression mistake between the fiduciary level on the day part therebetween! Do not find Reference source.～formula mistake! Do not find Reference source.If, Rc and S Normal Distribution, the average of Rc is Standard deviation is Then

${\mathrm{\β}}_{e,c}=\frac{{\mathrm{\μ}}_{R_c}-{\mathrm{\μ}}_S}{\sqrt{{\mathrm{\σ}}_{R_c}^2+{\mathrm{\σ}}_S^2}}---\left(10\right)$

${\mathrm{\ρ}}_{e,c}=\frac{{\mathrm{\σ}}_{R_c}^2}{{\mathrm{\σ}}_{R_c}^2+{\mathrm{\σ}}_S^2}---\left(11\right)$

If Rc and S are Non-normal Variables, the cumulative distribution function of Rc is

Probability density function is

Can utilize the JC method to carry out the equivalent normalize of variable, establish with the corresponding equivalent normalize of Rc variable is R ' for this reason _c, its average is

Standard deviation is

If power function Zi, the designcheck point of c=Rc-Se are (rc ^*, s ^*), the equivalent normalize condition according to the JC method obtains expression formula

${\mathrm{\μ}}_{R_c^{\′}}=r_c^{*}-{\mathrm{\Φ}}^{-1}\left[F_R\left(r_c^{*}\right)\right]{\mathrm{\σ}}_{R_c^{\′}},$

The equivalent normalize condition of S is pressed expression formula (8), so, obtain expression formula

${\mathrm{\β}}_{e,c}=\frac{{\mathrm{\μ}}_{R_c^{\′}}-{\mathrm{\μ}}_{S^{\′}}}{\sqrt{{\mathrm{\σ}}_{R_c^{\′}}^2+{\mathrm{\σ}}_{S^{\′}}^2}}---\left(13\right)$

${\mathrm{\ρ}}_{e,c}=\frac{{\mathrm{\σ}}_{R_c^{\′}}^2}{{\mathrm{\σ}}_{R_c^{\′}}^2+{\mathrm{\σ}}_{S^{\′}}^2}---\left(14\right)$

3) relation between construction time and the design reference period characteristic value of variable action is represented by following expression formula:

Construction time structure reactance Rc is the function of design reference period structure reactance R, and expression formula is

R _c＝kR (15)

Wherein k is scale-up factor, is the construction time structure reactance factor.

Further, if the equal Normal Distribution of R and S, with formula (15) substitution formula (14) and formula (15),

${\mathrm{\β}}_{e,c}=\frac{k{\mathrm{\μ}}_R-{\mathrm{\μ}}_S}{\sqrt{k^2{\mathrm{\σ}}_R^2+{\mathrm{\σ}}_S^2}}---\left(16\right)$

${\mathrm{\ρ}}_{e,c}=\frac{k^2{\mathrm{\σ}}_R^2}{k^2{\mathrm{\σ}}_R^2+{\mathrm{\σ}}_S^2}---\left(17\right)$

If R and S are Non-normal Variables, will through corresponding parameter in the parameter substitution formula (16) after the equivalent normalize of JC method and the formula (17), get

${\mathrm{\β}}_{e,c}=\frac{k{\mathrm{\μ}}_{R_c^{\′}}-{\mathrm{\μ}}_{S^{\′}}}{\sqrt{k^2{\mathrm{\σ}}_{R_c^{\′}}^2+{\mathrm{\σ}}_{S^{\′}}^2}}---\left(18\right)$

${\mathrm{\ρ}}_{e,c}=\frac{k^2{\mathrm{\σ}}_{R_c^{\′}}^2}{k^2{\mathrm{\σ}}_{R_c^{\′}}^2+{\mathrm{\σ}}_{S^{\′}}^2}---\left(19\right)$

Further, the design load of establishing structure reactance R and action effect S is respectively Rd, Sd, and standard value is respectively Rk, Sk, and partial safety factor is respectively γ R, γ S, requires γ 0Sd≤Rd during the ultimate limit states design, when being in ultimate limit state is

γ ₀S _d＝R _d，γ0γ _SS _k＝R _k/γ _R (20)

Wherein

γ _R＝R _k/R _d＝R _k/r ^*＝(μ _R-α _Rσ _R)/r ^* (21)

γ _S＝S _d/S _k＝s ^*/S _k＝s ^*/(μ _S+α _Sσ _S) (22)

The desirable α R=of fraction during fraction coefficient 95% α S=1.645.

Further, the standard value of establishing required drag Rc of structure construction phase is Rck, and the standard value of action effect is Sck, presses equally the ultimate limit states design, namely requires γ 0Scd≤Rcd, when being in ultimate limit state is

γ ₀S _cd＝R _cd，γ ₀γ _SS _ck＝R _ck/γ _R (23)

By formula (15), formula (20) and formula (23),

S _ck＝kS _k (24)

According to the structural design standard, the design load Sd of combination of load effect gets the least favorable value among the following combination and determines:

Combination by the variable load effect control

$S_d={\mathrm{\γ}}_G{S}_{\mathrm{Gk}}+{\mathrm{\γ}}_{Q_1}{S}_{Q_{1}k}+\underset{i=2}{\mathrm{\Σ}}{\mathrm{\γ}}_{Q_i}{\mathrm{\ψ}}_{\mathrm{ci}}{S}_{Q_{i}k}---\left(25\right)$

Combination by the permanent load effect control

$S_d={\mathrm{\γ}}_G{S}_{\mathrm{Gk}}+\underset{i=1}{\mathrm{\Σ}}{\mathrm{\γ}}_{\mathrm{Qi}}{\mathrm{\ψ}}_{\mathrm{ci}}{S}_{Q_{i}k}---\left(26\right)$

In the formula, γ G is the dead load partial safety factor;

With

Be the 1st and i variable load partial safety factor; SGk is the characteristic value of load effect;

Be the 1st variable load standard value effect, this effect is greater than other any one variable load standard value effects;

Be i variable load standard value effect; ψ ci is the combined value coefficient of i variable load.

Further, the situation for the construction time has following expression

$S_{\mathrm{cd}}={\mathrm{\γ}}_G{S}_{\mathrm{Gk}}+{\mathrm{\γ}}_{Q_1}{S}_{Q_1\mathrm{ck}}+\underset{i=2}{\mathrm{\Σ}}{\mathrm{\γ}}_{Q_i}{\mathrm{\ψ}}_{\mathrm{ci}}{S}_{Q_i\mathrm{ck}}---\left(27\right)$

$S_{\mathrm{cd}}={\mathrm{\γ}}_G{S}_{\mathrm{Gk}}+\underset{i=1}{\mathrm{\Σ}}{\mathrm{\γ}}_{\mathrm{Qi}}{\mathrm{\ψ}}_{\mathrm{ci}}{S}_{Q_i\mathrm{ck}}---\left(28\right)$

Consider first separately certain just like

Or The characteristic value of variable action effect, and with Q1 as wind load W, make that other characteristic value of action effects are 0 in formula (25)～formula (28), recycling formula (24) can get

$S_{W_{\mathrm{ck}}}=k{S}_{W_k}---\left(29\right)$

When structure was carried out theoretical analysis, action effect S and effect Q generally adopted linear relationship, i.e. S=CQ, and C is coefficient.If the front then has thinking that the coefficient of action effect of different times is constant at this moment

W _ck＝kW _k (30)

4) construction time variable action factor k's finds the solution

Find the solution construction time variable action factor k according to following steps:

(1) gets initial value n=50, β=β c=2.7～4.2, γ S=1.4, γ R=1.1～1.4, μ S=1.Given a certain nc.

(2) initial value of supposition μ R, σ R and σ S, for example 5,0.5,0.5.

(3) separate the formula mistake! Do not find Reference source.With the formula mistake! Do not find Reference source., get β e, σ _{R '}, σ _{S '}, r ^*And s ^*Utilize the designcheck point method, wherein μ _{R '}And σ _{R '}Calculate μ with formula (7) _{S '}And σ _{S '}Calculate with formula (8).

(4) calculate ρ e, utilize formula (10).

(5) form system of equations, utilize the formula mistake! Do not find Reference source., formula (21) and formula (22).Solution μ R, σ R and σ S.

(6) calculate k, utilize formula (13), formula (18) and formula (19).

When not being the integral multiple in 1 year for construction time Tc, k calculates with following way:

(1) calculate first Tc integer year correspondence k, meter is made k1.

(2) regard remaining fate of Tc as new nc, T got into 365 days, and γ R is identical when calculating k1, calculates k, is denoted as k2.

(3)k＝k1 k2。

About the formula mistake! Do not find Reference source.The calculating of middle n dimension normal distyribution function Φ n (β e, ρ), when n=1, Φ n (β e, ρ)=Φ (β e); When n=2, can utilize following formula to calculate: [3]

Wherein

When n＞3, can utilize following formula: [3]

When R and S Normal Distribution, probability density function and the cumulative distribution function of normal random variable X are respectively

When the R obeys logarithm normal distribution, it is that Gumbel distributes that S obeys the distribution of extreme value I type, and probability density function and the cumulative distribution function of lognormal variable R are respectively $f_R\left(r\right)=\frac{1}{\sqrt{2\mathrm{\π}}\mathrm{\ζr}}\exp [-\frac{{(\ln r-\mathrm{\ξ})}^2}{2{\mathrm{\ζ}}^2}],$ r＞0 (36) $F_R\left(r\right)=\mathrm{\Φ}\left(\frac{\ln r-\mathrm{\ξ}}{\mathrm{\ζ}}\right),$ r＞0 (37)

Parameter wherein

$\mathrm{\ξ}={\mathrm{\μ}}_{\ln R}=\ln \frac{{\mathrm{\μ}}_R}{\sqrt{1+{\mathrm{\δ}}_R^2}},$ $\mathrm{\ζ}={\mathrm{\σ}}_{\ln R}=\sqrt{\ln (1+{\mathrm{\δ}}_R^2)}---\left(38\right)$

Probability density function and the cumulative distribution function of extreme value I type variable S are respectively

f _s(s)＝αexp{-α(s-u)-exp[-α(s-u)]} (39)

F _S(s)＝exp{-exp[-α(s-u)]} (40)

Wherein

$\mathrm{\α}=\frac{\mathrm{\π}}{\sqrt{6}}\frac{1}{{\mathrm{\σ}}_S},$ $u={\mathrm{\μ}}_S-\frac{\mathrm{\γ}}{\mathrm{\α}}={\mathrm{\μ}}_S-\frac{0.5772156649...}{\mathrm{\α}}---\left(41\right)$

The present invention has following outstanding beneficial effect:

1, the present invention relates to the numerical analysis method of complete ultra-large type cooling tower construction phase wind load value, comprise finding the solution of relation between fiduciary level relation, construction time and the design reference period characteristic value of variable action of cooling tower structure construction time and day part thereof and the wind load factor.The wind load value of construction time and cooling tower are built up final operating mode distinguish, can reduce construction investment, particularly for the ultra-large type cooling tower, determine that the value of construction time wind load can be reducingd the construction costs greatly.In addition, can according to method of the present invention, work up the designed wind load standard of reinforced concrete hyperbolic curve cooling tower tube construction phase at the relevant specification of construction work industry.

2, the present invention is take the basic theories of structural reliability design as the basis, in cooling tower tube construction phase and design reference period, has identical fiduciary level as prerequisite, value typical problem to tower tube construction phase designed wind load is studied, be conducive to determining of cooling tower construction phase designed wind load, stability and the cost of construction time cooling tower had decisive meaning.

Embodiment

The ultra-large type cooling tower construction phase wind load obtaining value method that present embodiment relates to comprises the steps:

1) sets up the steady binomial random process model of wind load;

2) according to the characteristics of the steady binomial random process model of wind load, utilize the period analytical approach of structural reliability to set up respectively structural design base period and the relation of day part therebetween, reach the fiduciary level relation of day part therebetween with the construction time, form day part relational expression and fiduciary level relational expression;

3) start with according to the structure reactance of construction time and design reference period is proportional, by solution procedure 2) in relational expression, obtain construction time characteristi cvalue o fwindload and design reference period characteristi cvalue o fwindload ratio;

4) according to step 3) obtain construction time characteristi cvalue o fwindload and the same proportional conclusion of design reference period characteristi cvalue o fwindload, obtain accordingly the construction time wind load factor.

In the present embodiment:

1) the structural design base period and therebetween the relation between the fiduciary level on the day part represent with following expression formula:

According to action effect, every change direct action time length structurally, design reference period T is divided into n period τ that equates, or think that action effect evenly changes n=T/ τ time in design reference period T, in each period τ, action effect S is stochastic variable, and upper Si of different period and Sj (probability distribution of i ≠ j) is identical, action effect amplitude stochastic variable on the different period τ is separate, and with whether to occur load on the period irrelevant;

The form that the power function of structure all adopts structure reactance to compare with load effect is Zi=Ri-Si=R-Si so can establish the power function of structure in arbitrary τ, i=1,2 ..., n, wherein R is the structure reactance function, and Si is the load effect function, and they are separate, when being linear relationship between load and the load effect, upper load effect Si of different periods and Sj, wherein i ≠ j, independent identically distributed, equivalent stochastic variable Se on the available period τ represents, Zi=R-Se, therefore

Z _i＝R-S _i＝R-S _e，i＝1，2，K，n (1)

The failure probability pfe of each period and reliability index β e are

p _fe＝Φ(-β _e)＝P(Z _i≤0) (2)

Wherein Φ represents Standard Normal Distribution;

Like this, be exactly the failure event of n period series connection system in the failure event of T inner structure, i.e. structural failure Probability p f and reliability index β are

$p_f=\mathrm{\Φ}(-\mathrm{\β})=P(\underset{i=1}{\overset{n}{U}}{Z}_i\≤0)=1-P(\underset{i=1}{\overset{n}{I}}{Z}_i>0)---\left(3\right)$

The computing method of cascade system failure probability have bound method and direct calculation method [3], and the latter's calculating formula is

p _f＝Φ(-β)≈1-Φ _n(β _e，ρ) (4)

Wherein Φ n represents n dimension Standard Normal Distribution; β e is that element all is the n dimension reliability index vector of β e; ρ is n rank related coefficient square formations, and its nondiagonal element is ρ e.ρ e is Zi and the Zj (related coefficient of i ≠ j).

If the equal Normal Distribution of R and S, the average μ R of R, standard deviation is σ R; The average of Se is μ S, and standard deviation is σ S, then

${\mathrm{\β}}_e=\frac{{\mathrm{\μ}}_R-{\mathrm{\μ}}_S}{\sqrt{{\mathrm{\σ}}_R^2+{\mathrm{\σ}}_S^2}}---\left(42\right)$

β e also could unify the through type mistake! Do not find Reference source.With the formula mistake! Do not find Reference source.Obtain.Consider that again R and Si or Sj are separate, (related coefficient of i ≠ j) is for Zi and Zj

${\mathrm{\ρ}}_e=\frac{\mathrm{cov}(Z_i,Z_j)}{{\mathrm{\σ}}_{Z_i}{\mathrm{\σ}}_{Z_j}}=\frac{\mathrm{cov}(R-S_i,R-S_j)}{{\mathrm{\σ}}_{R-S_i}{\mathrm{\σ}}_{R-S_j}}=\frac{{\mathrm{\σ}}_R^2}{{\mathrm{\σ}}_R^2+{\mathrm{\σ}}_S^2}---\left(43\right)$

If R and S are Non-normal Variables, the cumulative distribution function of R is FR (R), and probability density function is fR (R); The cumulative distribution function of Se is FS (S), and probability density function is fS (S).Can utilize the JC method to carry out the equivalent normalize of variable.Establish with the corresponding equivalent normalize of R variable is R ' for this reason, and its average is μ _{R '}, standard deviation is σ _{R '}With the corresponding equivalent normalize of S variable be S ', its average is μ _{S '}, standard deviation is σ _{S '}An if power function mistake! Do not find Reference source.Designcheck point be (r ^*, s ^*), according to the equivalent normalize condition [3] of JC method,

μ _R′＝r ^*-Φ ^-1[F _R(r ^*)]σ _R′，

μ _S′＝r ^*-Φ ^-1[F _S(s ^*)]σ _S′，

In the formula,

Expression standard normal probability density function.So, have

${\mathrm{\β}}_e=\frac{{\mathrm{\μ}}_{R^{\′}}-{\mathrm{\μ}}_{S^{\′}}}{\sqrt{{\mathrm{\σ}}_{R^{\′}}^2+{\mathrm{\σ}}_{S^{\′}}^2}}---\left(46\right)$

${\mathrm{\ρ}}_e=\frac{{\mathrm{\σ}}_{R^{\′}}^2}{{\mathrm{\σ}}_{R^{\′}}^2+{\mathrm{\σ}}_{S^{\′}}^2}---\left(47\right)$

Known that by formula (44) and formula (45) compare formula (42) and formula (43), formula (46) and formula (47) have more generality.

2) the structure construction phase and during relation between the fiduciary level on the period represented by following expression formula:

Suppose in the effect of structure construction phase and effect thereof identical in the characteristic of construction time and design reference period.The action effect of supposing again structure can be processed into steady binomial stochastic process, i.e. supposition: (1) is according to the every change direct action of action effect time length structurally, design reference period Tc is divided into nc period τ that equates, or thinks that the interior action effect of Tc evenly changes nc=Tc/ τ c time.(2) in each period τ c, action effect S is stochastic variable, and upper Si of different period and Sj (probability distribution of i ≠ j) is identical.(3) the action effect amplitude stochastic variable on the different period τ c is separate, and with whether to occur load on the period irrelevant.

Design reference period is the time parameter of selecting for the value of determining variable action etc.Shorter when the construction time, as less than 1 year, it is just improper for the variable action that has such as wind load (year maximum wind pressure) then Tc to be analogous to T.Therefore, the effect of structure construction phase and effect thereof being used as steady binomial stochastic process processes approximation is arranged.

If Tc inner structure reliability index is β c, failure probability is pf, c; τ c inner structure reliability index is β e, and c, failure probability are pfe, c, and corresponding structure reactance is Rc, and following expression is namely arranged:

Z _i，c＝R _c-S _i＝R _c-S _e＝Z _e，c， i＝1，2，K，n _c (48)

p _fe， _c＝Φ(-β _e，c)＝P(Z _i，c≤0)＝P(Z _e，c≤0) (49)

$p_{f,c}=\mathrm{\Φ}(-{\mathrm{\β}}_c)=P(\underset{i=1}{\overset{n_c}{U}}{Z}_{i,c}\≤0)=1-P(\underset{i=1}{\overset{n_c}{I}}{Z}_{i,c}>0)=1-{\mathrm{\Φ}}_{c_c}({\mathrm{\β}}_{e,c},{\mathrm{\ρ}}_c)---\left(50\right)$

β e wherein, c is that element all is β e, the n dimension reliability index vector of c; ρ c is n rank related coefficient square formations, and its nondiagonal element is ρ e, c.

It may be noted that for construction time Tc and the wherein processing of the relation between the fiduciary level of period τ c, be equivalent to the formula mistake! Do not find Reference source.～formula mistake! Do not find Reference source.If Rc and the equal Normal Distribution of S, the average of Rc is

Standard deviation is

Then

${\mathrm{\β}}_{e,c}=\frac{{\mathrm{\μ}}_{R_c}-{\mathrm{\μ}}_S}{\sqrt{{\mathrm{\σ}}_{R_c}^2+{\mathrm{\σ}}_S^2}}---\left(51\right)$

${\mathrm{\ρ}}_{e,c}=\frac{{\mathrm{\σ}}_{R_c}^2}{{\mathrm{\σ}}_{R_c}^2+{\mathrm{\σ}}_S^2}---\left(52\right)$

If Rc and S are Non-normal Variables, the cumulative distribution function of Rc is

Probability density function is

Can utilize the JC method to carry out the equivalent normalize of variable.Establish with the corresponding equivalent normalize of Rc variable is R ' for this reason _c, its average is

Standard deviation is

If power function Zi, the designcheck point of c=Rc-Se are (rc ^*, s ^*), according to the equivalent normalize condition [3] of JC method,

${\mathrm{\μ}}_{R_c^{\′}}=r_c^{*}-{\mathrm{\Φ}}^{-1}\left[F_R\left(r_c^{*}\right)\right]{\mathrm{\σ}}_{R_c^{\′}},$

The equivalent normalize conditional (45) of S stands good.So, have

${\mathrm{\β}}_{e,c}=\frac{{\mathrm{\μ}}_{R_c^{\′}}-{\mathrm{\μ}}_{S^{\′}}}{\sqrt{{\mathrm{\σ}}_{R_c^{\′}}^2+{\mathrm{\σ}}_{S^{\′}}^2}}---\left(54\right)$

${\mathrm{\ρ}}_{e,c}=\frac{{\mathrm{\σ}}_{R_c^{\′}}^2}{{\mathrm{\σ}}_{R_c^{\′}}^2+{\mathrm{\σ}}_{S^{\′}}^2}---\left(55\right)$

3) relation between construction time and the design reference period characteristic value of variable action is represented by following expression formula:

Construction time structure reactance Rc is the function of design reference period structure reactance R, and this function always can come match with polynomial expression, and when R=0 Rc=0 should be arranged, thus in the polynomial expression without constant term.Wherein simple and practical with proportionate relationship, namely

R _c＝kR (56)

Wherein k is scale-up factor, can be called the construction time structure reactance factor.

If the equal Normal Distribution of R and S, with formula (15) substitution formula (51) and formula (52),

${\mathrm{\β}}_{e,c}=\frac{k{\mathrm{\μ}}_R-{\mathrm{\μ}}_S}{\sqrt{k^2{\mathrm{\σ}}_R^2+{\mathrm{\σ}}_S^2}}---\left(57\right)$

${\mathrm{\ρ}}_{e,c}=\frac{k^2{\mathrm{\σ}}_R^2}{k^2{\mathrm{\σ}}_R^2+{\mathrm{\σ}}_S^2}---\left(58\right)$

If R and S are Non-normal Variables, will through corresponding parameter in the parameter substitution formula (16) after the equivalent normalize of JC method and the formula (17), get

${\mathrm{\β}}_{e,c}=\frac{k{\mathrm{\μ}}_{R_c^{\′}}-{\mathrm{\μ}}_{S^{\′}}}{\sqrt{k^2{\mathrm{\σ}}_{R_c^{\′}}^2+{\mathrm{\σ}}_{S^{\′}}^2}}---\left(59\right)$

${\mathrm{\ρ}}_{e,c}=\frac{k^2{\mathrm{\σ}}_{R_c^{\′}}^2}{k^2{\mathrm{\σ}}_{R_c^{\′}}^2+{\mathrm{\σ}}_{S^{\′}}^2}---\left(60\right)$

If the design load of structure reactance R and action effect S is respectively Rd, Sd, standard value is respectively Rk, Sk, and partial safety factor is respectively γ R, γ S, requires γ 0Sd≤Rd[4 during the ultimate limit states design], when just being in ultimate limit state be

γ ₀S _d＝R _d，γ ₀γ _SS _k＝R _k/γ _R (61)

Wherein

γ _R＝R _k/R _d＝R _k/r ^*＝(μ _R-α _Rσ _R)/r ^* (62)

γ _S＝S _d/S _k＝s ^*/S _k＝s ^*/(μ _S+α _Sσ _S) (63)

And the desirable α R=of the fraction α S=1.645 during fraction coefficient 95%.

If the standard value of required drag Rc of structure construction phase is Rck, the standard value of action effect is Sck, presses equally the ultimate limit states design, namely requires γ 0Scd≤Rcd, when just being in ultimate limit state is

γ ₀S _cd＝R _cd，γ ₀γ _SS _ck＝ _Rck/γ _R (64)

By formula (15), formula (20) and formula (23),

S _ck＝kS _k (65)

Structural design standard [4] regulation, the design load Sd of combination of load effect should get the least favorable value among following combination

Determine:

(1) by the combination of variable load effect control

$S_d={\mathrm{\γ}}_G{S}_{\mathrm{Gk}}+{\mathrm{\γ}}_{Q_1}{S}_{Q_{1}k}+\underset{i=2}{\mathrm{\Σ}}{\mathrm{\γ}}_{Q_i}{\mathrm{\ψ}}_{\mathrm{ci}}{S}_{Q_{i}k}---\left(66\right)$

(2) by the combination of permanent load effect control

$S_d={\mathrm{\γ}}_G{S}_{\mathrm{Gk}}+\underset{i=1}{\mathrm{\Σ}}{\mathrm{\γ}}_{\mathrm{Qi}}{\mathrm{\ψ}}_{\mathrm{ci}}{S}_{Q_{i}k}---\left(67\right)$

In the formula, γ G is the dead load partial safety factor; With

Be the 1st and i variable load partial safety factor; SGk is the characteristic value of load effect; Be the 1st variable load standard value effect, this effect is greater than other any one variable load standard value effects; Be i variable load standard value effect; ψ ci is the combined value coefficient of i variable load.

Situation for the construction time has

$S_{\mathrm{cd}}={\mathrm{\γ}}_G{S}_{\mathrm{Gk}}+{\mathrm{\γ}}_{Q_1}{S}_{Q_1\mathrm{ck}}+\underset{i=2}{\mathrm{\Σ}}{\mathrm{\γ}}_{Q_i}{\mathrm{\ψ}}_{\mathrm{ci}}{S}_{Q_i\mathrm{ck}}---\left(68\right)$

$S_{\mathrm{cd}}={\mathrm{\γ}}_G{S}_{\mathrm{Gk}}+\underset{i=1}{\mathrm{\Σ}}{\mathrm{\γ}}_{\mathrm{Qi}}{\mathrm{\ψ}}_{\mathrm{ci}}{S}_{Q_i\mathrm{ck}}---\left(69\right)$

Consider first separately certain just like

Or

The characteristic value of variable action effect, and with Q1 as wind load W, make that other characteristic value of action effects are 0 in formula (25)～formula (28), recycling formula (24) can get

$S_{W_{\mathrm{ck}}}=k{S}_{W_k}---\left(70\right)$

When structure was carried out theoretical analysis, action effect S and effect Q generally adopted linear relationship, i.e. S=CQ, and C is coefficient.If the front then has thinking that the coefficient of action effect of different times is constant at this moment

W _ck＝kW _k (71)

Therefore, by formula (15) and formula (24) as can be known, according to the designing requirement of existing standard, structure should be identical at the ratio of the ratio of the drag standard value of construction time and design reference period and action effect value.Again according to formula (30), when effect and effect thereof were linear, also the ratio with variable action such as characteristi cvalue o fwindload was identical.This ratio k is hereinafter referred to as the construction time variable action factor.

4) construction time variable action factor k's finds the solution

According to above analysis, can find the solution k according to following steps:

(1) gets initial value n=50, β=β c=2.7～4.2, γ S=1.4, γ R=1.1～1.4, μ S=1.Given a certain nc.

(2) initial value of supposition μ R, σ R and σ S, for example 5,0.5,0.5.

(3) separate the formula mistake! Do not find Reference source.With the formula mistake! Do not find Reference source., get β e, σ _{R '}, σ _{S '}, r ^*And s ^*Utilize the designcheck point method, wherein μ _{R '}And σ _{R '}Calculate μ with formula (44) _{S '}And σ _{S '}Calculate with formula (45).

(4) calculate ρ e, utilize formula (47).

(5) form system of equations, utilize the formula mistake! Do not find Reference source., formula (21) and formula (22).Solution μ R, σ R and σ S.

(6) calculate k, utilize formula (50), formula (18) and formula (19).

When not being the integral multiple in 1 year for construction time Tc, k can calculate with following way:

(1) calculate first Tc integer year correspondence k, meter is made k1.

(2) regard remaining fate of Tc as new nc, T got into 365 days, and γ R is identical when calculating k1, calculates k, is denoted as k2.

(3)k＝k1 k2。

About the formula mistake! Do not find Reference source.The calculating of middle n dimension normal distyribution function Φ n (β e, ρ), when n=1, Φ n (β e, ρ)=Φ (β e); When n=2, can utilize following formula to calculate: [3]

Wherein

When n＞3, can utilize following formula: [3]

The simplest situation is the equal Normal Distribution of R and S.Probability density function and the cumulative distribution function of normal random variable X are respectively

More realistic is R obeys logarithm normal distribution [1], and S obeys extreme value I type distribution (Gumbel distribution) [4].Probability density function and the cumulative distribution function of lognormal variable R are respectively $f_R\left(r\right)=\frac{1}{\sqrt{2\mathrm{\π}}\mathrm{\ζr}}\exp [-\frac{{(\ln r-\mathrm{\ξ})}^2}{2{\mathrm{\ζ}}^2}],$ r＞0 (77) $F_R\left(r\right)=\mathrm{\Φ}\left(\frac{\ln r-\mathrm{\ξ}}{\mathrm{\ζ}}\right),$ r＞0 (78)

Parameter wherein

$\mathrm{\ξ}={\mathrm{\μ}}_{\ln R}=\ln \frac{{\mathrm{\μ}}_R}{\sqrt{1+{\mathrm{\δ}}_R^2}},$ $\mathrm{\ζ}={\mathrm{\σ}}_{\ln R}=\sqrt{\ln (1+{\mathrm{\δ}}_R^2)}---\left(79\right)$

Probability density function and the cumulative distribution function of extreme value I type variable S are respectively

f _s(s)＝αexp{-α(s-u)-exp[-α(s-u)]} (80)

F _s(s)＝exp{-exp[-α(s-u)]} (81)

Wherein

$\mathrm{\α}=\frac{\mathrm{\π}}{\sqrt{6}}\frac{1}{{\mathrm{\σ}}_S},$ $u={\mathrm{\μ}}_S-\frac{\mathrm{\γ}}{\mathrm{\α}}={\mathrm{\μ}}_S-\frac{0.5772156649...}{\mathrm{\α}}---\left(82\right)$

This paper is with the platform of MATLAB software as the above algorithm of realization.Form and solving equation group function:

5) result of calculation of construction time variable action factor k

According to " engineering structure reliability design unified standard ", design reference period T is 50 years, and 2 grades of the reliability index beta structure safe classes of structural-load-carrying capacity ultimate limit state design, destruction type are that ductile fracture gets 3.2.According to " industrial circulating water Cooling Design standard ", " loading code for design of building structures ", generally get the partial safety factor γ S=1.40 of load and effect thereof.Partial safety factor for resistance γ R is regulation not, and according to Related domestic documents to the analysis of ordinary reinforced concrete structure under the stresses such as uniaxial force, eccentric force, flexure, Shear, 1.10≤γ R≤1.40.1.30≤γ R≤1.39 when the member axial compression, 1.10≤γ R≤1.40 when eccentric compression, Shear, 1.10≤γ R≤1.15 when axial tension, eccentric tension, flexure.Structure is identical with the level of reliability of design reference period in the construction time.Accordingly, just can utilize this paper program to calculate variable action or wind load factor k under different partial safety factor for resistance γ R and the construction time Tc.

R, S obeyed the wind load factor k of the ultimate limit states design of different distributions when table 1 and table 2 had provided respectively β=β c=3.2.As expected, k increases with the increase of Tc, reduces with the increase of γ R.

Wind load factor k (β=β c=3.2) when table 1R and the equal Normal Distribution of S

Wind load factor k (β=β c=3.2) when table 2R obeys logarithm normal distribution, S obey the distribution of extreme value I type

According to the loading characteristic of cooling tower, get γ R=1.15, to β=β c=3.2, calculate the k value of Tc＜1 year, and associative list 1, table 2 result, the calculated value by k provides recommendation, respectively shown in table 3, table 4.Can find out that k reduces gradually with the amplitude of variation of Tc.

Wind load factor k (β=β c=3.2, γ R=1.15) when table 3R and the equal Normal Distribution of S

Wind load factor k (β=β c=3.2, γ R=1.15) when table 4R obeys logarithm normal distribution, S obey the distribution of extreme value I type

In structural reliability problem, to only have when structural failure Probability p f 〉=0.001 (or reliability index β≤3.0902), the result of calculation of pf is just insensitive to the distribution form of variable.The β of the problems referred to above=3.2, so be necessary in the research of cooling tower wind load value, to consider the actual distribution form of R and S, and R obeys logarithm normal distribution, S are obeyed extreme value I type and are distributed more realisticly than the equal Normal Distribution of R, S, therefore have reason to think that the result of table 2, table 4 is more reasonable.

Use for convenient, utilize this paper program to calculate more k value, put the result of table 4 in order merger, as shown in table 5.

Table 5 cooling tower tube construction phase wind load factor k (β=β c=3.2, γ R=1.15)

Claims (5)

1. ultra-large type cooling tower construction phase wind load obtaining value method is characterized in that:

1) take Reliability Theory as theoretical foundation, utilize the period analytical approach of structural reliability set up respectively the structural design base period and therebetween the period relation of day part and construction time and during the fiduciary level relation of each time period, form day part relational expression and fiduciary level relational expression;

2) solution procedure 1) described relational expression, obtain construction time characteristi cvalue o fwindload and design reference period characteristi cvalue o fwindload ratio;

3) according to step 2) described ratio finds the solution the construction time wind load factor.

2. a kind of ultra-large type cooling tower construction phase wind load obtaining value method according to claim 1 is characterized in that: the structural design base period and therebetween the relation between the fiduciary level on the day part represent with following expression formula:

1) the structure function function expression is: Zi=Ri-Si=R-Si, and i=1,2 ..., n,

Wherein R is the structure reactance function, and Si is the load effect function;

2) the failure probability pfe of each period and reliability index β e expression formula are: p _Fe=Φ (β _e)=P (Z _i≤ 0)

3) structural failure Probability p f and reliability index β expression formula are:

Perhaps structural failure Probability p f and reliability index β expression formula are: p _f=Φ (β) ≈ 1-Φ _n(β _e, ρ)

In the expression formula, Φ n represents n dimension Standard Normal Distribution; β e is that element all is the n dimension reliability index vector of β e; ρ is n rank related coefficient square formations, and its nondiagonal element is ρ e.ρ e is Zi and the Zj (related coefficient of i ≠ j).

3. a kind of ultra-large type cooling tower construction phase wind load obtaining value method according to claim 1 is characterized in that: the structure construction phase and during relation between the fiduciary level on the period represented by following expression formula:

1) establishing Tc inner structure reliability index is β c, and failure probability is pf, c; τ c inner structure reliability index is β e, and c, failure probability are pfe, c, and corresponding structure reactance is Rc, and following expression is namely arranged:

Z _i，c＝R _c-S _i＝R _c-S _e＝Z _e，c， i＝1，2，K，n _c

p _fe，c＝Φ(-β _e，c)＝P(Z _i，c≤0)＝P(Z _e，c≤0)

β e wherein, c is that element all is β e, the n dimension reliability index vector of c; ρ c is n rank related coefficient square formations, and its nondiagonal element is ρ e, c.

2) for construction time Tc and the wherein processing of the relation between the fiduciary level of period τ c, if Rc and S Normal Distribution, the average of Rc is

Standard deviation is

Then

3) if Rc and S are Non-normal Variables, the cumulative distribution function of Rc is

Probability density function is

Can utilize the JC method to carry out the equivalent normalize of variable, establish with the corresponding equivalent normalize of Rc variable is R ' for this reason _c, its average is

Standard deviation is

If power function Zi, the designcheck point of c=Rc-Se are (rc ^*, s ^*), the equivalent normalize condition according to the JC method obtains expression formula

。

4. a kind of ultra-large type cooling tower construction phase wind load obtaining value method according to claim 1, it is characterized in that: the relation between construction time and the design reference period characteristic value of variable action is represented by following expression formula:

1) construction time structure reactance Rc is the function of design reference period structure reactance R, and expression formula is R _c=kR wherein k is scale-up factor, is the construction time structure reactance factor;

2) if the equal Normal Distribution of R and S obtains following expression

3) if R and S are Non-normal Variables, will be through the parameter substitution 2 after the equivalent normalize of JC method) in various in corresponding parameter, obtain following expression

The design load of 4) establishing structure reactance R and action effect S is respectively Rd, Sd, and standard value is respectively Rk, Sk, and partial safety factor is respectively γ R, γ S, requires γ 0Sd≤Rd during the ultimate limit states design, when being in ultimate limit state is

γ ₀S _d＝R _d，γ ₀γ _SS _k＝R _k/γ _R

γ wherein _R=R _k/ R _d=R _k/ r ^*=(μ _R-α _Rσ _R)/r ^*(1), γ _S=S _d/ S _k=s ^*/ S _k=s ^*/ (μ _S+ α _Sβ _S)

Fraction during fraction coefficient 95% is got α R=α S=1.645;

The standard value of 5) establishing required drag Rc of structure construction phase is Rck, and the standard value of action effect is Sck, presses equally the ultimate limit states design, namely requires γ 0Scd≤Rcd, when being in ultimate limit state is

γ ₀S _cd＝R _cd，γ ₀γ _SS _ck＝R _ck/γ _R；

6) according to the structural design standard, the design load Sd of combination of load effect gets the least favorable value among the following combination and determines:

Combination by the variable load effect control

Combination by the permanent load effect control

In the formula, γ G is the dead load partial safety factor;

With

Be the 1st and i variable load partial safety factor; SGk is the characteristic value of load effect;

Be the 1st variable load standard value effect, this effect is greater than other any one variable load standard value effects;

Be i variable load standard value effect; ψ ci is the combined value coefficient of i variable load;

7) for the situation of construction time, following expression is arranged

Consider first separately certain just like

Or

The characteristic value of variable action effect, and with Q1 as wind load W, make the formula mistake! Do not find Reference source.～formula mistake! Do not find Reference source.In other characteristic value of action effects be 0, recycling formula mistake! Do not find Reference source., can get

When structure was carried out theoretical analysis, action effect S and effect Q generally adopted linear relationship, i.e. S=CQ, and C is coefficient.If then there is W the front to thinking that the coefficient of action effect of different times is constant at this moment _Ck=kW _k

5. a kind of ultra-large type cooling tower construction phase wind load obtaining value method according to claim 1, it is characterized in that: the construction time solution procedure of variable action factor k is as follows:

1) find the solution construction time variable action factor k according to following steps:

(1) gets initial value n=50, β=β c=2.7～4.2, γ S=1.4, γ R=1.1～1.4, μ S=1; Given a certain nc;

(2) initial value of supposition μ R, σ R and σ S, for example 5,0.5,0.5;

(3) utilize the designcheck point method, the solution formula gets β e, σ _{R '}, σ _{S '}, r ^*And s ^*

(4) calculate ρ e;

(5) form system of equations, and solutions must μ R, σ R and σ S;

(6) calculate k;

When not being the integral multiple in 1 year for construction time Tc 2), k calculates with following way:

(1) calculate first Tc integer year correspondence k, meter is made k1;

(2) regard remaining fate of Tc as new nc, T got into 365 days, and γ R is identical when calculating k1, calculates k, is denoted as k2;

(3)k＝k1 k2；

3) about the calculating of n dimension normal distyribution function Φ n (β e, ρ) in the formula, when n=1, Φ n (β e, ρ)=Φ (β e); When n=2, can utilize following formula to calculate:

Wherein

When n＞3, can utilize following formula:

4) when R and S Normal Distribution, probability density function and the cumulative distribution function of normal random variable X are respectively

5) when the R obeys logarithm normal distribution, it is that Gumbel distributes that S obeys the distribution of extreme value I type, and probability density function and the cumulative distribution function of lognormal variable R are respectively

R＞0

R＞0

Parameter wherein

Probability density function and the cumulative distribution function of extreme value I type variable S are respectively

f _S(s)＝exp{-α(s-u)-exp[-α(s-u)]}

F _S(s)＝exp{-exp[-α(s-u)]}

Wherein