CN103207205A - Method for computing stagnation temperature of flexural steel member - Google Patents

Abstract

The invention relates to a practical fire resisting design method of a construction steel structure, and particularly relates to a method for computing stagnation temperature of a flexural steel member. According to the method provided by the invention, aiming at different stability coefficients and load ratios, the stagnation temperature of the flexural steel member can be directly taken through checking a table; and the reduction in the steel product strength at a high temperature is determined according to a great quantity of test data, and the stability coefficient of the flexural steel member at the high temperature is directly taken through checking the table. According to the method provided by the invention, the stagnation temperature of the flexural steel member is given out through a form mode, and the complicated numerical calculation process is avoided; and the invention provides a convenient and reliable steel structure fire resisting design method.

Description

Be subjected to the critical temperature computing method of curved steel member

Technical field

The present invention relates to the practical anti-fiery method for designing of construction steel structure, relate to the curved steel member estimation of Critical Temperature method that is subjected to especially.

Background technology

Steel construction is because of advantage such as its lightweight, high-strength, easy construction and material be capable of circulation, in China's skyscraper, obtained widespread use, but steel are not fire-resistant, when fire temperature reaches 600 ° of C and spends, steel will be lost most of intensity, cause the destruction of steel construction, cause great loss for human lives and properties.Stipulate the fire protection requirement of steel construction among " construction steel structure fireproofing technique standard " CECS200:2006 by " fire endurance " concept, and be defined in generally speaking, can only carry out the checking computations of anti-fiery ultimate limit state to each member of structure, satisfy the anti-fiery designing requirement of member.Anti-fiery ultimate limit state is defined as under the fire condition, state when bearing of component equates with the combined effect that the effect of adding (comprising load and temperature action) produces, for flexural member, reach anti-fiery ultimate limit state should satisfy produce enough plastic hinges and become changeable mechanism, general loss is stable or reach and be unsuitable for the distortion that continues to carry.The anti-fiery designing requirement of steel structure member should be satisfied one of following requirement: (1) in the structure fire resistance limit time of regulation, the combined effect that bearing of component should not produce less than various effects; (2) under various combination of load effect, the fire resistance period of member should be less than the fire endurance of the member of stipulating; (3) critical temperature of member should not be lower than the maximum temperature at the fire resistance period inner member.Critical temperature is defined as the temperature on the member section when member reaches anti-fiery ultimate limit state, and this definition supposition fire evenly distributes along length and the cross section of member.

The anti-fiery design of steel structure member at present can be adopted carrying force method or critical temperature method.The carrying force method preestablishes internal temperature and the corresponding internal force of member under the fire endurance that requires of fireproof coating thickness by calculating, carry out the anti-fiery ultimate limit state checking computations of member, and the applicability of repeated authentication flameproof protection layer thickness.The critical temperature rule is calculated the critical temperature of member according to member and load type, according to critical temperature and the fire endurance calculating member fire-resistant protection layer thickness of member.Critical temperature method clear concept calculates easyly, is widely used in the Fire-resistance of Steel Structures design.Existing patent of invention " design and selection method of the steel frame structure fire-resistant protection " (patent No.: 200610161954.6) proposed to determine integrally-built critical temperature by the upper bound method of plastic limit analysis; this critical temperature is based on different destruction structures; pass through iterative computation; process is loaded down with trivial details, and calculated amount is bigger.

Summary of the invention

The object of the invention is to overcome the deficiencies in the prior art, proposes a kind of curved steel member estimation of Critical Temperature method that is subjected to.

The technical scheme that the present invention provides is:

A kind of critical temperature computing method that are subjected to curved steel member is characterized in that this method comprises the steps:

Step 1: the temperature when the steel member reaches anti-fiery ultimate limit state is defined as critical temperature, form under the normal temperature of stipulating in (being under the high temperature) steel bearing of component ultimate limit state checking computations employing and the existing Code for design of steel structures under the described critical temperature, described critical temperature ultimate limit state is characterized by:

$\frac{M}{j_{\mathrm{bT}}W}=f_{\mathrm{yT}}---\left(1\right)$

M in the formula---the moment of flexure that member is suffered;

j _BT---the monolithic stability coefficient of flexural member under the high temperature;

The gross cross-sectional modulus of W---member;

f _YT---the yield strength of steel under the high temperature.

Step 2: determine the yield strength of steel under the high temperature, the yield strength of steel is calculated by following formula under the high temperature:

f _yT=h _Tf _y=h _Tg _Rf （2）

H in the formula _T---the strength reduction factor of steel under the high temperature;

f _y---the yield strength of steel under the normal temperature;

g _R---the resistance coefficient of steel, the approximate g that gets _R=1.1;

F---the Intensity Design value of steel under the normal temperature is taken by " Code for design of steel structures " GB50017:2003.

Step 3: the Critical Bending Moment of flexural member is write as M _CrT=j _BTWf _YT

（6ａ）

Step 4: according to the physical dimension of steel member, (" Code for design of steel structures " GB50017:2003) checks in the stability factor j under the member normal temperature by existing Code for design of steel structures _b, the ratio that defines the monolithic stability coefficient under flexural member high temperature and the normal temperature again is parameter a _B=j _BT/ j _b, based on this, the stability factor j of high temperature lower member _BTCan be according to the stability factor j under the normal temperature _b, parameter a _B=j _BT/ j _bLogical conversion obtains.

Step 5: (6a) is rewritten as with formula $M_{\mathrm{crT}}=j_{\mathrm{bT}}^{\′}W{f}_{\mathrm{yT}}---\left(9a\right)$

Step 6: (9 a) substitution formulas (1) obtain with formula (2), formula $\frac{M}{j_b^{\′}\mathrm{Wf}}=\frac{j_{\mathrm{bT}}^{\′}}{j_b^{\′}}{h}_T{g}_R---\left(10\right)$

H in the formula _TBe the strength reduction factor of steel under the high temperature, g _RBe the resistance coefficient of steel, j ' _BTStability factor for flexural member under the high temperature.

Step 7: defining above-mentioned formula (10) left side item is the loading ratio R of flexural member, namely obtains

$R=\frac{M}{j_b^{\′}\mathrm{Wf}}---\left(11\right)$

Step 8: by formula (10) and (11), adopt numerical evaluation, try to achieve the critical temperature T of member _d

Further optimize, described step 4, in order to consider steel plasticity to stable influence, thus make correction greater than 0.6 the time when stability factor, namely by described standard according to the big I of the stability factor stability factor j ' of definite revised normal temperature and high temperature lower member respectively _bAnd j ' _BT, formula specific as follows:

$j_b^{\′}=\left\{\begin{array}{cc}{j}_b& j_b\≤0.6\\ 1.07-\frac{0.282}{j_b}\≤1.0& j_b>0.6\end{array}\right.---\left(8a\right)$

$j_{\mathrm{bT}}^{\′}=\left\{\begin{array}{cc}{a}_b{j}_{\mathrm{bT}}& a_b{j}_b\≤0.6\\ 1.07-\frac{0.282}{a_b{j}_{\mathrm{bT}}}\≤1.0& a_b{j}_b>0.6\end{array}\right.---\left(8b\right)$

Thus, the stability factor j of high temperature lower member _BTCan be according to the stability factor j under the normal temperature _b1 directly take by tabling look-up.Described table 1 is as follows:

Be subjected to the stability factor parameter a of curved steel member under table 1 high temperature _B

Further specify, the invention has the advantages that, the critical temperature T of member described in the step 8 _dCan also be according to loading ratio R and stability factor j ' _b2 directly take by tabling look-up, described table 2 is:

Table 2 is subjected to the critical temperature T of curved steel member _d(° C)

Further specify, determine the strength reduction factor h of steel under the high temperature by great number tested data _T

The present invention calculates easy, can be directly used in Fire-resistance of Steel Structures design checking computations, also can be member fire-resistant protection layer thickness determine the necessary parameter foundation is provided, have important and practical meanings.

Description of drawings

Fig. 1: the geometric model that is subjected to curved steel member.

Fig. 2: be subjected to curved steel member estimation of Critical Temperature sketch.

Embodiment

Below in conjunction with drawings and Examples technical solution of the present invention is described further.

Embodiment 1(theoretical foundation)

Under the fire, along with the rising of steel construction internal temperature, the bearing capacity of steel construction will descend, and when the bearing capacity of structure dropped to the combined effect that produces with the effect of adding (comprising temperature action) and equates, then structure reached anti-fiery ultimate limit state.Under the high temperature steel bearing of component ultimate limit state checking computations can adopt with existing Code for design of steel structures in similar forms under the normal temperature stipulated, when the cross section did not have weakening, generally by monolithic stability control, its ultimate limit state can be expressed from the next the bearing capacity of flexural member:

$\frac{M}{j_{\mathrm{bT}}W}=f_{\mathrm{yT}}---\left(1\right)$

M in the formula---the moment of flexure that member is suffered;

---the monolithic stability coefficient of flexural member under the high temperature;

The gross cross-sectional modulus of W---member;

f _YT---the yield strength of steel under the high temperature.

Temperature when the steel member reaches anti-fiery ultimate limit state is defined as critical temperature, and the calculating that the present invention proposes is subjected to the method for curved steel member critical temperature, and concrete derivation is as follows:

(1) determines the yield strength of steel under the high temperature

The yield strength of steel can be calculated by following formula under the high temperature:

f _yT=h _Tf _y=h _Tg _Rf （2）

H in the formula _T---the strength reduction factor of steel under the high temperature;

f _y---the yield strength of steel under the normal temperature;

g _R---the resistance coefficient of steel, the approximate g that gets _R=1.1;

F---the Intensity Design value of steel under the normal temperature is taken by " Code for design of steel structures " GB50017:2003.

Tongji University has carried out the comparatively high temperature wood property test of system to 16M n steel and SM41 steel, consider " the blue shortness effect " of general structural steel and adopt bigger apparent strain to determine that its high-temperature yield strength, the present invention adopt following formula to calculate the elevated temperature strength reduction coefficient of general structural steel:

h _T=f _yT/f _y=1.0 　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　20°Ｃ≤Ｔ≤300°Ｃ 　　　　　　　　（3ａ）

h _T=f _yT/f _y=1.24×10 ^-8T ³-2.096×10 ^-5T ²+9.228×10 ^-3T-0.2168 　　300°Ｃ＜Ｔ＜800°　Ｃ 　　　　　　（3ｂ）

h _T=f _yT/f _y=0.5-T/2000 　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　800°Ｃ≤Ｔ≤1000°Ｃ　 　　　　　（3ｃ）

T is the temperature of steel in the formula.

(2) determine the stability factor of flexural member under the high temperature

The ultimate bearing capacity that calculates flexural member under the high temperature can adopt with normal temperature under same supposition and computing method, its computation model is as shown in Figure 1.When the cross section does not have weakening, controlled by monolithic stability by curved steel bearing of component.According to theory of elasticity, the Critical Bending Moment around strong single shaft (or twin shaft) the symmetrical section steel member of being bent commonly used is expressed from the next:

$M_{\mathrm{crT}}=C_1\frac{p^2{E}_T{I}_y}{l^2}[C_{2}a+C_{3}b+\sqrt{{(C_{2}a+C_{3}b)}^2+\frac{I_w}{I_y}(1+\frac{G_T{I}_t{l}^2}{p^2{E}_T{I}_w})}]b_b---\left(4\right)$

M in the formula _CrT---the Critical Bending Moment of flexural member under the high temperature;

C ₁, C ₂, C ₃---the coefficient relevant with load;

b _b---the equivalent bending moment coefficient of member monolithic stability;

B---the parameter relevant with the member section shape;

A---the lateral load application point is to the distance at section shear center;

I _y---member section is around the moment of inertia of weak axle y axle;

I _ω---the fan moment of inertia of member section;

I _τ---the torsional moment of inertia of member section;

The span of l---member;

E _T---the elastic modulus under the high temperature;

G _T---the modulus of shearing under the high temperature.

The present invention adopts the steel elastic modulus E under the following formula calculating high temperature _T:

$E_T=\frac{7T-4780}{6T-4760}E$ 20°Ｃ≤Ｔ≤600°Ｃ 　　　　　　（5ａ）

$E_T=\frac{1000-T}{6T-2800}E$ 600°Ｃ＜Ｔ≤1000°　 Ｃ　　　（5ｂ）

Modulus of shearing under the high temperature can be calculated by mechanics of materials constitutive relation, i.e. G _T=E _T/ 2(1+ ν), ν is the Poisson's Ratio of steel, does not vary with temperature.The Critical Bending Moment of flexural member can be write as again

M _crT=j _bTWf _yT （6ａ）

M _cr=j _bWf _y （6ｂ）

The ratio of the monolithic stability coefficient under definition flexural member high temperature and the normal temperature is parameter a _B, namely

$a_b=\frac{j_{\mathrm{bT}}}{j_b}=\frac{M_{\mathrm{crT}}{f}_y}{M_{\mathrm{cr}}{f}_{\mathrm{yT}}}=\frac{M_{\mathrm{crT}}}{M_{\mathrm{cr}}{h}_T}---\left(7\right)$

Work as E _TAnd G _TWhen being taken as elastic modulus under the member normal temperature and modulus of shearing, can obtain flexural member Critical Bending Moment M at normal temperatures _CrCan calculate a of all kinds of section structural members by formula (7) and formula (3)～(5) _BCalculate and design a among the present invention for convenient _BCan directly take by table 1 disclosed by the invention.

Current Chinese code of practice " Code for design of steel structures " GB50017:2003 has stipulated the stable checking computations of flexural member under the normal temperature, and the stable checking computations of flexural member can be adopted identical regulation under the high temperature, and expression formula is seen formula (8a) and (8b).

$j_b^{\′}=\left\{\begin{array}{cc}{j}_b& j_b\≤0.6\\ 1.07-\frac{0.282}{j_b}\≤1.0& j_b>0.6\end{array}\right.---\left(8a\right)$

$j_{\mathrm{bT}}^{\′}=\left\{\begin{array}{cc}{a}_b{j}_{\mathrm{bT}}& a_b{j}_b\≤0.6\\ 1.07-\frac{0.282}{a_b{j}_{\mathrm{bT}}}\≤1.0& a_b{j}_b>0.6\end{array}\right.---\left(8b\right)$

Formula (6) can be rewritten as

$M_{\mathrm{crT}}=j_{\mathrm{bT}}^{\′}W{f}_{\mathrm{yT}}---\left(9a\right)$

$M_{\mathrm{cr}}=j_b^{\′}W{f}_y---\left(9b\right)$

(3) determine the critical temperature of axis compression member

With formula (2) and (9) substitution formula (1),

$\frac{M}{j_b^{\′}\mathrm{Wf}}=\frac{j_{\mathrm{bT}}^{\′}}{j_b^{\′}}{h}_T{g}_R---\left(10\right)$

Definition (10) left side item is the loading ratio R of flexural member, namely

$R=\frac{M}{j_b^{\′}\mathrm{Wf}}---\left(11\right)$

The stability factor j ' of known flexural member then _bWith loading ratio R, can be tried to achieve the critical temperature T of member by formula (10) and (11) _dBecause formula (10) is a transcendental equation, finds the solution inconvenience.For this reason, adopt numerical evaluation, obtain different loading ratio R and stability factor j ' _bThe critical temperature T of following flexural member _d, see disclosed table 2 among the present invention, calculate and design with convenient.

Embodiment 2(concrete example)

Be subjected to curved steel member estimation of Critical Temperature method as shown in Figure 2, concrete steps are as follows:

(1) physical dimension and the moment M of known steel member in the general Steel Structural Design, according to physical dimension such as cross sectional moment of inertia I, section modulus W, slenderness ratio l etc. can be checked in the stability factor j of flexural member under the normal temperature by " Code for design of steel structures " GB50017:2003.

(2) according to moment M, section modulus W and steel strength design load f, can calculate the loading ratio R=M/jWf of member.

(3) according to loading ratio R, can calculate the critical temperature T that is subjected to curved steel member by formula (10) and (11) _dUse for convenient, according to loading ratio R and stability factor j, T _dCan table look-up and 2 directly take.

For a better understanding of the present invention, provide following calculated examples.

Knownly be subjected to curved girder steel basic condition: grade of steel Q235; Member span 5m, no lateral support; The cross section specification is I36b.The effect of beam top flange has along strong axial evenly load q=30kN/m, and beam section is around the section modulus W=920.8cm of strong axle ³, the monolithic stability coefficient j ' of normal temperature underbeam _b=0.73.Determine the critical temperature of this girder steel.

Calculation procedure is as follows:

Separate: (1) is got by above-mentioned: the suffered moment of flexure of girder steel $M=\frac{1}{8}{\mathrm{ql}}^2=\frac{1}{8}\×30\×{10}^3\×5^2=93.75\mathrm{kN}\·m.$

(2) the Intensity Design value f of steel Q235 can check in f=215N/mm by above standard ²Can calculate the loading ratio of girder steel according to moment of flexure value, section modulus and Intensity Design value:

$R=\frac{M}{j_b^{\′}\mathrm{Wf}}=\frac{93.75\×{10}^3}{0.73\×920.8\×{10}^{-6}\×215\×{10}^6}=0.649$

(3) according to member monolithic stability coefficient and loading ratio, can be checked in the critical temperature T of girder steel by table 2 _d=556.2 ° of C.

Claims (4)

1. critical temperature computing method that are subjected to curved steel member is characterized in that this method comprises the steps:

Step 1: the temperature when the steel member reaches anti-fiery ultimate limit state is defined as critical temperature, form under the normal temperature of stipulating in (being under the high temperature) steel bearing of component ultimate limit state checking computations employing and the existing Code for design of steel structures under the described critical temperature, described critical temperature ultimate limit state is characterized by:

$\frac{M}{j_{\mathrm{bT}}W}=f_{\mathrm{yT}}---\left(1\right)$

M in the formula---the moment of flexure that member is suffered;

j _BT---the monolithic stability coefficient of flexural member under the high temperature;

The gross cross-sectional modulus of W---member;

f _YT---the yield strength of steel under the high temperature;

Step 2: determine the yield strength of steel under the high temperature, the yield strength of steel is calculated by following formula under the high temperature:

f _yT＝h _Tf _y＝h _Tg _Rf (2)

H in the formula _T---the strength reduction factor of steel under the high temperature;

f _y---the yield strength of steel under the normal temperature;

g _R---the resistance coefficient of steel, the approximate g that gets _R=1.1;

F---the Intensity Design value of steel under the normal temperature is taken by " Code for design of steel structures " GB50017:2003.

Step 3: the Critical Bending Moment of flexural member is write as

M _crT＝j _bTWf _yT (6a)

Step 4: according to the physical dimension of steel member, (" Code for design of steel structures " GB50017:2003) checks in the stability factor j under the member normal temperature by existing Code for design of steel structures _b, the ratio that defines the monolithic stability coefficient under flexural member high temperature and the normal temperature again is parameter ab=j _BT/ j _b, based on this, the stability factor j of high temperature lower member _BTCan be according to the stability factor j under the normal temperature _b, parameter ab=j _BT/ j _bObtain by conversion;

Step 5: (6a) is rewritten as with formula

M _crT＝j′ _bTWf _yT (9a)

Step 6: with formula (2), formula (9a) substitution formula (1), obtain

$\frac{M}{j_b^{\′}\mathrm{Wf}}=\frac{j_{\mathrm{bT}}^{\′}}{j_b^{\′}}{h}_T{g}_R---\left(10\right)$

H in the formula _TBe the strength reduction factor of steel under the high temperature, g _RBe the resistance coefficient of steel, j ' _BTStability factor for flexural member under the high temperature.

Step 7: defining above-mentioned formula (10) left side item is the loading ratio R of flexural member, namely obtains

$R=\frac{M}{j_b^{\′}\mathrm{Wf}}---\left(11\right)$

Step 8: by formula (10) and (11), adopt numerical evaluation, try to achieve the critical temperature T of member _d

2. the method for claim 1, it is characterized in that, described step 4, in order to consider that steel plasticity is to stable influence, so when stability factor is made correction greater than 0.6 the time, namely determine the stability factor j ' of revised normal temperature and high temperature lower member respectively according to the size of stability factor by described standard _bAnd j ' _BT, specific as follows:

$j_b^{\′}=\left\{\begin{array}{cc}{j}_b& j_b\≤0.6\\ 1.07-\frac{0.282}{j_b}\≤1.0& j_b>0.6\end{array}\right.---\left(8a\right)$

$j_{\mathrm{bT}}^{\′}=\left\{\begin{array}{cc}{a}_b{j}_{\mathrm{bT}}& a_b{j}_b\≤0.6\\ 1.07-\frac{0.282}{a_b{j}_{\mathrm{bT}}}\≤1.0& a_b{j}_b>0.6\end{array}\right.---\left(8b\right)$

So, the stability factor j of high temperature lower member _BTAccording to the stability factor j under the normal temperature _b1 directly take by tabling look-up, described table 1 is as follows:

Be subjected to the stability factor parameter ab of curved steel member under table 1 high temperature

3. the method for claim 1 is characterized in that, the critical temperature T of member described in the step 8 _dIn addition according to loading ratio R and stability factor j ' _b2 directly take by tabling look-up, described table 2 is:

Table 2 is subjected to the critical temperature T of curved steel member _d(℃)

4. the method for claim 1 is characterized in that, determines the strength reduction factor h of steel under the high temperature by great number tested data _T

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