CN1995570A - Steel frame structure fire-resistant protection design and selection method - Google Patents

Steel frame structure fire-resistant protection design and selection method Download PDF

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CN1995570A
CN1995570A CN 200610161954 CN200610161954A CN1995570A CN 1995570 A CN1995570 A CN 1995570A CN 200610161954 CN200610161954 CN 200610161954 CN 200610161954 A CN200610161954 A CN 200610161954A CN 1995570 A CN1995570 A CN 1995570A
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temperature
steel
steel frame
rod member
critical
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张荣钢
张宏涛
王晓纯
张素枝
郑建华
徐秉业
高建岭
白玉星
徐彤
李园
刘刚锋
颜聪枝
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North China University of Technology
China Huanqiu Engineering Co Ltd
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North China University of Technology
China Huanqiu Engineering Co Ltd
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Abstract

The invention provides a design selecting method for fire protection with steel frame structure, comprising following procedures that (1) according to plastic limit analysis theory, the total number N of basic failure mechanism of planar structure or spatial structure of steel frame structure is determined; (2) the object function eta, which is the ratio of internal work and external work added on basic failure mechanism in plastic limit state, is determined; (3) the minimum of eta is obtained by optimal analysis treatment and relative failure mechanism is found, according to the principle of plastic limit analysis theory relative critical temperature is the minimum value of all possible failure mechanisms in steel frame; (4) according to the variance of temperature, critical temperature of steel frame relative to the minimum value of object function eta is determined by iterative method and critical temperatures of every bars in steel frame are calculated whether the iterative result is coincidence with regular iterative convergence criterion or not; (5) critical temperatures of every bars in steel frame compare with temperature eigenvalue, which is achieved when fire happens, so as to determine if the steel frame is protected. The method makes structure calculation simple, effective and it is applied in engineering design.

Description

The design and selection method of steel frame structure fire-resistant protection
Technical field
The preventive works that the present invention relates to prevent and reduce natural disasters in the building structure field design, and relate to a kind of design and selection method of steel frame structure fire-resistant protection especially.
Background technology
The normal steel framed structure that adopts in building structure; if the temperature that steel framed structure may reach under the fire condition is less than 200 ℃; then do not need the steel framed structure mineral wool is protected; but when surpassing 200 ℃, the temperature that may reach when steel framed structure then need protect; because though the temperature of steel still keeps certain intensity during in 200 ℃≤T≤600 ℃; but intensity reduces, and the intensity of steel is 30% under the normal temperature situation in the time of 600 ℃, and the intensity of steel is 0 during to 900 ℃.For this reason, generally, anti-fiery coating of the part or all of coating of steel framed structure or encased steel reinforced concrete are imposed protection by calculating.
At present for the design and selection method of the flameproof protection of steel framed structure; what usually adopt in structure design is that " prescribing method " of clause formula carries out, and determines corresponding protection scope and thickness according to the fire resistance rating of building or purposes and fire endurance time that is:.Mainly there are the following problems for the flameproof protection of " prescribing method " design steel framed structure: do not consider that 1. the steel temperature surpasses the intensity more than 200 ℃.2. for the different same a kind of form of structure of building occupancy, do not consider different, the stress ratio of external load variation, fringe conditions and sectional dimension that structure is suffered and all multifactor influences such as various operating modes of structure stand under load; 3. cause anti-fire safety degree deficiency sometimes, can cause bigger waste sometimes again is that precision is not high.
For the another kind of advanced method of the design alternative of the anti-flameproof protection of steel framed structure is to guarantee that structure finishes the performance method for designing of function.That is: according to the fire load size and the possible fire sight that act on the steel framed structure, adopt the mechanical function feature of heat conducting basic principle and high temperature of fire case structure, calculate the anti-fire prevention of definite steel frame and the method for protection quantitatively.The performance method for designing has overcome the shortcoming of " prescribing method " fully, and analysis mainly contains two kinds of methods for steel frame structure fire-resistant: the lower limit method of FEM (finite element) calculation and the upper bound method of plastic limit analysis.Finite Element be owing to considering that material nonlinearity and geometrical non-linearity under the high temperature have been subjected to a lot of scholars' favor, but because specificity that its is handled problems and modeling, amount of calculation are bigger, cause difficulty in the engineering design and use.Upper bound method based on classic plastic Theory of Limit Analysis (Plastic limit analysis theory) can directly calculate the ultimate bearing capacity of all kinds of engineering structuress under ratio loads, not only easy to use and effectively simple, be to solve the anti-fire of steel frame to analyze efficient ways.
Summary of the invention:
In order scientifically to determine the guard method of steel frame; patent steel frame structure fire-resistant of the present invention and guard method; considered that steel are above the guard method of the intensity more than 200 ℃ to various basic steel frame constructions; proposed to determine integrally-built critical-temperature by the upper bound method of plastic limit analysis, overcome lower limit method calculation of complex in the past loaded down with trivial details, be difficult to the deficiency that restrains and use.Satisfying under the required precision prerequisite that engineering uses, make structural calculation become simply, effective, be suitable for using in the engineering design.By calculating anti-fiery coating of the part or all of coating of steel framed structure or external wrapping concrete are imposed protection.
The invention provides a kind of design and selection method of steel frame structure fire-resistant protection, comprise the steps:
(1) determines the plane structure of steel framed structure or the basic destruction sum N of mechanism of space structures according to plasticity and limit analysis theory, and set the initial temperature of each rod member of steel framed structure;
(2) determine object function η, destroy the ratio of internal work with the external work of mechanism's superposition when η is the plastic limit state substantially, and satisfy following formula:
η = Σ n = 1 N X n W in Σ n = 1 N X n W en ( X n ≥ 0 )
If destroying the internal force plastic work done of the n of mechanism substantially is W In, W InRelevant with the plastic limit bending moment and the destruction mechanism rod member corner in steel framed structure control cross section under temperature and this temperature, corresponding external work is W En, W EnWith act on structure boundary on the broad sense external load and to destroy the rate of displacement of mechanism relevant, N is an above-mentioned basic destruction mechanism sum, X nBe the basic corner multiplying factor of destroying mechanism;
(3) η and variable X 1 in the above-mentioned formula, X2 ..., the relation of Xn is followed successively by non-linear relation one time, optimizes and analyzes affiliated nonlinear problem, by optimizing X nMake the plastic hinge of superposition mechanism disappear, make internal work reduce, thereby obtain the minimum of η, it is found to destroy mechanism accordingly, is minimum value in all possible destruction of the steel frame mechanism according to the critical-temperature of this mechanism's correspondence of plasticity and limit analysis theory principle;
(4) adopt iterative method to determine the critical temperature value of steel frame of the minimum value correspondence of object function η: the temperature increment of setting each rod member of described steel framed structure is dt, next step temperature increment becomes (η-1) dt, η wherein is a previous step iteration gained, carries out iteration optimization and calculates;
(5) set tole for allowing precision, dt1 adds up for all member temperature variable quantity absolute values, the iteration convergence criterion adopt abs (dt1)<tole or | η-1|<tole when iterative computation satisfies one of above-mentioned two iteration convergence criterions, calculates the critical-temperature of each rod member of steel frame;
The temperature profile value that corresponding rod member can reach during (6) with the critical-temperature of each rod member of steel frame of calculating and fire burning compares, to determine whether and need protect steel frame.
Preferably, described permission precision tole value is 0.01.
Described internal force plastic work done W InWith the length of the yield strength of the cross section type of steel frame, cross section parameter, steel and beam, post direct relation is arranged, external work is W EnRelevant with the type and the fringe conditions of external load, steel frame on acting on steel framed structure.
Steel frame is protected employing partly or entirely anti-fiery coating of coating or external wrapping concrete.
Described steel framed structure is one of single span single-store frame, twin spans single-store frame, single span double-layer frame, three layers of framework of single span, five kinds of structures of two-way single span individual layer space frame.
Described steel framed structure is plane steel framed structure or spatial steel-frame structure, when being the spatial steel-frame structure, it destroys determining by space structures being decomposed into the plane structure of twocouese of mechanism's number substantially, finds out the basic destruction mechanism number that basic destruction structure number is superposed to space structures respectively by plane structure again.
Described temperature profile value adopts English, U.S. general calculation formula is tried to achieve or obtain according to " construction steel structure fireproofing technique standard " CECS200:2006.
Described optimization is analyzed nonlinear problem and is adopted accurate newton's method to be optimized calculating.
Described space structures is decomposed into plane structure after, determine corresponding beam mechanism, layer mechanism and joint mechanism, and further determine basic the destructions mechanism number of corresponding each mechanism, obtain the basic total N of mechanism that destroys by adding up.
The temperature profile value that corresponding rod member can reach when the critical-temperature of each rod member of steel frame that calculates is burnt greater than fire; whether checking computations rod member strength of stability meets the demands; when meeting the demands; steel framed structure safety; do not need to do the flame retardant coating protection; when not meeting the demands, to structure division or all do flame retardant coating protection, or enlarging section is not done topping according to result of calculation.
Description of drawings:
Five kinds of citation forms of Fig. 1 steel framed structure;
Fig. 2 determines framework critical temperature Tc (i) computer block diagram
The computing block diagram of the protection domain of steel frame when Fig. 3 determines fire
Fig. 4 space structures is decomposed into plane structure calculation diagram and beam mechanism map
Fig. 5 space structures is decomposed into the layer mechanism map of plane structure
Fig. 6 single span three layer construction calculation diagram
One of Fig. 7 single span three layer construction protection domain figure
Two of Fig. 8 single span three layer construction protection domain figure
Three of Fig. 9 single span three layer construction protection domain figure
Four of Figure 10 single span three layer construction protection domain figure
Figure 11 twin spans single layer structure calculation diagram
Figure 12 twin spans single layer structure protection domain figure
The two-way single span individual layer of Figure 13 space steel frame calculation diagram
The two-way single span individual layer of Figure 14 space steel frame protection domain figure
For understanding the present invention better, the invention will be further described below in conjunction with the drawings and specific embodiments.
The specific embodiment:
As shown in Figure 1, be the citation form that steel framed structure adopts usually: 1. single span single-store frame; 2. twin spans single-store frame; 3. single span double-layer frame; 4. three layers of framework of single span; 5. two-way single span individual layer space frame;
Five kinds of forms of above-mentioned steel frame are the basic structure in industry and the civilian construction, and according to the difference of building occupancy, load is also different.May be equipment supporter and piping lane in industrial premises, the device, also may be dwelling house, office building and the market etc. of the corresponding number of plies and span.Analyze for petrochemical industry compound steel framework piping lane etc. among the embodiment, different according to variation that acts on load structurally and structural section size, the steel frame protection scheme that calculates when one deck has burning things which may cause a fire disaster is also different.
Steel framed structure adopts anti-fiery coating of partly or entirely coating or external wrapping concrete to impose protection.Citation form for above-mentioned steel framed structure; under the temperature that structure is born when fringe conditions, structure stand under load and the various operating mode of steel elevated temperature strength, structure, fire when considering the situation of external load, fire and all multifactor conditions such as fire endurance time of structure, the upper bound method that adopts plastic limit analysis is by calculating the protection domain of determining the steel frame citation form.
Under the general fire condition, along with the increase of external load, the reduction of temperature rising back steel yield strength, the enhancing of structure boundary constraint etc., the critical-temperature of steel frame presents the trend of reduction.Adopt the upper bound method of plasticity and limit analysis theory to connect by interior external work and above-mentioned factor, the internal force plastic work done of steel frame destruction mechanism was when basic principle was intensification
W i=∑M uj(t)·θ j (1)
In the formula, M UjThe plastic limit bending moment in steel framed structure control cross section when (t) being temperature t, θ jBe the corresponding mechanism's rod member corner that destroys;
The external work of structure is expressed as follows:
Figure A20061016195400081
In the formula, P iFor acting on the broad sense external load on the structure boundary,
Figure A20061016195400082
Be the corresponding rate of displacement of destroying mechanism.
According to the critical destruction equation of steel frame Upper bound analysis
W i=W e (3)
In the formula, W iDestroy whole internal works of mechanism accordingly for steel frame; W eDestroy whole external works of mechanism accordingly for steel frame.
Order η = W i W e , then η is critical failure load multiplier, represents that structure is in critical collapse state when η=1, and η>1 expression structure is not destroyed, and η<1 expression structure is destroyed.
At internal force plastic work done W iBe in the formula (1), M Uj(t) with example in cross section type, the cross section parameter (being the parameter in (2) in the example, (3)) of steel frame direct relation is arranged, usually cross section type and sectional dimension parameter is different, the plastic limit bending moment of rod member is also different, the sectional dimension parameter is bigger, the plastic limit bending moment value is higher, finally the structure critical temperature value of the destruction mechanism correspondence of seeking out by optimum theory is also higher, otherwise still; Influence M UjThe yield strength of steel when another key factor (t) is temperature t, usually yield strength reduces with the rising of structure temperature, equally, low then its critical-temperature of the yield strength of structure also reduces, controlling (5)-(11) of counting by the material yield Strength Changes in example determines, concrete numerical value can draw by the performance test under the material at high temperature, and what China selected for use at present is that the strain of European ECCS standard is 0.5% o'clock a numerical value.
External work W in structure eIn, P iReflected that basic parameter in the example (12) acts on structural external load and operating mode,
Figure A20061016195400084
Be the rate of displacement of corresponding destruction mechanism, its fringe conditions with the type of steelframe and structure is relevant, promptly definite by basic parameter (4) in the dimensional parameters example of basic parameter (1) in the example and structure,
Figure A20061016195400085
The size of value depends on the situation of displacement field possible in the Theory of Limit Analysis.Usually it is bigger to act on structural external load size bigger and structure, and the critical temperature value of structural deterioration is lower.
The fire endurance time that another key factor that influences the structure critical-temperature is a structure, its rate of heat release Q during by fire reflects, and the rate of heat release Q of fire is determined by tabling look-up or calculating by related specifications according to the type and the scale of fire.Usually the structure fire resistance limit time that requires is longer, and the critical-temperature of structure is lower.
Critical temperature Tc (i) when determining the steel frame fire, concrete technical application scheme is:
At first, determine the basic destruction mechanism that structure is possible according to plasticity and limit analysis theory.For general plane steel framed structure, can determine the basic mechanism that destroys by existing method in the plasticity and limit analysis theory; For the spatial steel-frame structure, the application has proposed space structures is decomposed into the plane structure of twocouese, finds out the method that the basic structure number is superposed to the basic system number of space structures respectively by plane structure again.
The concrete grammar that space structures is decomposed into the plane structure of twocouese is: with the two-way single span individual layer spatial steel-frame of Figure 13, successively along 1 of yz plane, 4 of 3 rod members, xz plane, 6 of 5 rod members and yz plane, 8 rod members, expand into the plane structure sketch of Fig. 4, the beam mechanism that determines according to plasticity and limit analysis theory as shown in Figure 4, destroying mechanism's number substantially is 2; The layer mechanism that determines as shown in Figure 5, destroying mechanism's number substantially is 3; The joint mechanism of determining as shown in Figure 5, destroying mechanism's number substantially is 4.In like manner, along 1,6 rod member on xy plane, 2,7 rod members on xz plane and 3,8 rod members on xy plane, expand into plane structure successively, definite beam, layer and joint mechanism number are respectively 0,3 and 4.Addition is counted by the mechanism of the plane structure of two dimensional development amount to 16, be the destruction mechanism number of two-way single span individual layer spatial steel-frame.
Then, use plasticity and limit analysis theory and Non-Linear Programming optimum theory and determine object function η, the different basic ratios that destroy internal work with the external work of mechanism's superposition of structure when η is the plastic limit state, the expression formula of the η that the application proposes is (4), by optimize calculating the destruction mechanism of searching internal work minimum in institute might mechanism, the internal force plastic work done of supposing to destroy substantially the n of mechanism is W In, corresponding external work is W En, destroy mechanism substantially and add up to N.X nBe the basic corner multiplying factor of destroying mechanism.The criterion of optimizing is: by optimizing X nMake the plastic hinge of superposition mechanism disappear, make internal work reduce, thereby obtain the minimum of η, it is found to destroy mechanism accordingly, is minimum value in all possible destruction of the steel frame mechanism according to the critical-temperature of this mechanism's correspondence of plasticity and limit analysis theory principle.
η = Σ n = 1 N X n W in Σ n = 1 N X n W en ( X n ≥ 0 ) - - - ( 4 )
According to the expression formula (4) of object function η, η and variable X 1, X2 ..., the relation of Xn is followed successively by non-linear relation one time, for optimizing the nonlinear programming problem of analyzing, adopts the accurate newton's of FORTRAN establishment method source program to be optimized calculating on mathematics.
At last, determine the critical-temperature of structure according to the critical temperature value of the steel frame of the minimum value correspondence of object function η by adopting iterative method for determining.For the influence of considering the material nonlinearity curve of steel in the fire temperature field, promptly with the reduction curve of fire temperature rising steel strength value.According to actual conditions, when fire took place, the temperature of every member was evenly to increase in time.Therefore temperature increment dt that can every member given in advance, in Practical Calculation, the η that utilizes the previous step iteration to obtain, next step temperature increment become (η-1) dt, reenter to optimize to find the solution again, and have improved computational efficiency and precision.Dt1 adds up for all member temperature variable quantity absolute values, and the iteration convergence criterion in the program can be used | and η-1|<tole or abs (dt1)<tole judges.Allow non-linear the finding the solution of precision finally to determine integrally-built critical temperature Tc (i) by iteration with being provided with, wherein i is corresponding each bar piece number in the overall structure, and tole generally is taken as 0.01 for allowing precision.
Above-mentioned definite critical-temperature computer software is realized block diagram as shown in Figure 2.General computational process is: the length of steel frame type and beam column, the sectional dimension of rod member, the reduction along with variation of temperature steel yield strength, the size of effect external load, the initial temperature of rod member etc. are set at master data, promptly comprise every basic parameter of structure and determine the basic required information of mechanism of destroying, the input master data, caller is optimized to analyze and obtains load multiplier η=eta1, eta1=1 has exact solution when calculating for simple structure, can directly draw the critical-temperature of structure; Calculate for labyrinth, general eta1 then needs to try to achieve η=eta1 by optimizing iteration greater than 1, judges in the structure when all temperature variations of each member all satisfy abs (the dt1)<TOLE condition of convergence, calculates the critical temperature Tc (i) of structure.Otherwise carry out the optimization iterative of η=eta1 again, repeat the aforementioned calculation process up to satisfying the critical temperature Tc (i) that the condition of convergence obtains structure.
The temperature profile value Tm (i) that rod member can reach when next determining the fire burning
When fire took place, along with continuing of time t, the temperature that steel framed structure reached constantly increased.Different according to fire sight and rod member position, the available correlation formula of temperature profile value Tm (i) of each rod member is calculated.In the fire endurance time range that structure reaches, as the critical temperature Tc (i) of the fruit structure Tm (i) greater than corresponding rod member, then structure is safe, otherwise is in unsafe condition.
Characteristic value Tm (i) when the design formulas of countries such as employing English, U.S. is determined the fire burning:
The height of continuous flame: l c = 0.08 Q 2 5 - - - ( 6 )
Column of flame temperature: T p-T 0=880 work as Z < 0.08 Q 2 5 - - - ( 7 )
T p - T 0 = 70 ( Q 2 5 Z ) When 0.08 Q 2 5 < Z < 0.2 Q 2 5 - - - ( 8 )
T p - T 0 = 23.6 ( Q 2 5 Z ) 5 3 When Z > 0.2 Q 2 5 - - - ( 9 )
L in the formula c---the height of flame, m;
Q---stablize the rate of heat release of burning things which may cause a fire disaster, kW;
T p---the average temperature (column of flame temperature) of burning things which may cause a fire disaster height Z place plume, ℃;
T 0---environment temperature all round, ℃;
Z---burning things which may cause a fire disaster height Z, m;
Or method is determined among employing " construction steel structure fireproofing technique standard " CECS200:2006.Calculate: the maximum temperature Tm of member (℃):
Relatively above both temperature values, i.e. Tc (i) and Tm (i), the computing block diagram of the protection domain of steel frame is seen Fig. 3 when determining fire.
Rate of heat release Q according to fire; adopt thermokinetics basic principle and existing formula to determine the temperature T m (i) of rod member in the steel frame; the critical temperature Tc (i) of rod member compares with the temperature T m (i) of rod member in the steel framed structure that aforementioned calculation is gone out; when Tc (i) 〉=Tm (i); after the strength of stability requirement is satisfied in checking computations to rod member; corresponding rod member can not done flameproof protection in the steel frame, otherwise need do flameproof protection or strengthen the double counting of bar cross section size till meeting the demands.
Utilize said method to determine the anti-fireproof protection scheme of steel frame, consequently steel framed structure need not to do protection, steel framed structure partly need do protection and steel framed structure all need be protected three kinds.
With existing resist technology difference: temperature surpasses the intensity that 200 ℃ of situations are considered steel during 1. for the steel framed structure fire, calculate to determine the critical temperature Tc (i) of structure by theory, and guarantee temperature T m (i) that structure fire reality can reach critical temperature Tc (i) less than structure; 2. adopt the upper bound method of plasticity and limit analysis theory, the destruction mechanism of searching internal work minimum in institute might mechanism is calculated in the optimization of ratio η by interior external work, all multifactor influences such as fringe conditions of the different and structure of the variation of non-linear, the external load that structure is born of variations in temperature material and operating mode, sectional dimension when considering fire; 3. by calculating the diversity and the flexibility of protection domain and the protection scheme of having determined steel frame quantitatively.
[beneficial effect]
The advantage of the steel frame structure fire-resistant protection method that the application provides is: adopt advanced theory; worked out computer software; can scientifically quantitatively calculate the protection domain of steel frame; design with respect to present steel frame " prescribing method "; only determine the method for fire endurance time and protection domain, obtained anti-fire safety of structure and economic doulbe-sides' victory according to fire resistance rating and purposes.
For understanding the present invention better, provide following calculated examples.
(1) three layers of framework of single span are example
● example 1: the span of certain petrochemical industry single span compound steel framework is 12m, one, two, three layers floor height is respectively 5m, 3m, 3m, and the horizontal loading that bears is 100kN, and the vertical load that bears is 200kN, beam section is HN700 * 300, and column section is HM588 * 300.The hot burst size Q that burning things which may cause a fire disaster bears at the ground steel frame during fire is 36MW.Show as Fig. 6, determine the guard method of steel frame.
Calculation procedure is as follows:
1. the calculation procedure basic parameter of determining the appropriate size and structure:
(1) steelframe type ip1=4, temperature variations ip2=1, ip3=ip4=ip5=ip6=0;
(2) cross section type: 2; (1 expression square-section, 2 expression i shaped cross sections)
(3) cross section parameter:
I shape: cbb=0.3m; Chb=0.7m; Tb1=0.024m; Tb2=0.0013m; Cbc=0.3m; Chc=0.588m; Tc1=0.002m; Tc2=0.012m;
(4) length of beam, post: 1=12m; H1=3m; H2=3m; H3=5m;
(5) material yield intensity varies with temperature to control and counts: MST=6;
(6) material yield intensity and corresponding temperature first point: the CMS (1,1)=205000; CMS (1,2)=0;
(7) material yield intensity and corresponding temperature second point: the CMS (2,1)=159000; CMS (2,2)=300;
(8) material yield intensity and corresponding temperature are thirdly: CMS (3,1)=100000; CMS (3,2)=500;
(9) material yield intensity and corresponding temperature the 4th point: CMS (3,1)=25000; CMS (3,2)=700;
(10) material yield intensity and corresponding temperature the 5th point: CMS (3,1)=12000; CMS (3,2)=800;
(11) material yield intensity and corresponding temperature the 6th point: CMS (3,1)=2000; CMS (3,2)=1000;
(12) size of active force:
PV1=200KN;PV2=200KN;PV3=200KN;
PH1=100KN;PH2=100KN;PH3=100KN;
2. safeguard measure when determining to calculate: unprotect;
3. determine rod member initial temperature t (i):
t(1)=200℃;t(2)=150℃;t(3)=100℃;
t(4)=100℃;t(5)=150℃;t(6)=200℃;
t(7)=100℃;t(8)=150℃;t(9)=200℃;
4. determine rod member temperature variations it (i):
it(1)=1;it(2)=1;it(3)=1;it(4)=1;it(5)=1;
it(6)=1;it(7)=1;it(8)=1;it(9)=1;
[annotate: it (i)=0 expression is temperature-resistant; It (i)>0 represents variations in temperature, if it (1)=it (3)>0 expression 1 changes identical with 3 member temperature.]
5. the calculation procedure that calls establishment carries out critical-temperature and calculates;
6. program calculates the critical temperature Tc (i) of rod member:
Tc(1)=573.0120℃;Tc(2)=523.0118℃;Tc(3)=473.0118℃;
Tc(4)=473.0118℃;Tc(5)=523.0118℃;Tc(6)=573.0120℃;
Tc(7)=473.0118℃;Tc(8)=523.0118℃;Tc(9)=573.0120℃;
7. the temperature profile value Tm (i) that reaches when the rod member fire burns:
Characteristic value when the design formulas of countries such as employing English, U.S. is determined the fire burning:
Calculate: the maximum temperature Tm of member (℃):
One deck Tm=900 ℃; Two layers Tm=602 ℃; Three layers Tm=443 ℃;
8. preliminary conclusion:
Tc (one deck)=573.0120 ℃<Tm (one deck)=900 ℃
Tc (two layers)=523.0118 ℃<Tm (two layers)=602 ℃
Tc (three layers)=473.0118 ℃>Tm (three layers)=443 ℃
The critical-temperature of calculating by program and the comparison of member maximum temperature, steel framed structure one deck and two layers all are in unsafe condition.So take safeguard measure as follows: can take to structure one deck or one deck, two layers or one deck, two layers, three layers this three kinds of safeguard measures.Be calculated as follows.
9. carrying out safeguard measure calculates: one deck protection;
10. the calculation procedure that calls establishment carries out critical-temperature and calculates;
11. program calculates the critical temperature Tc (i) of rod member:
Tc(1)=200.0000℃;Tc(2)=661.2?581℃;Tc(3)=611.2579℃;
Tc(4)=611.2579℃;Tc(5)=661.2581℃;Tc(6)=200.0000℃;
Tc(7)=611.2579℃;Tc(8)=661.2581℃;Tc(9)=200.0000℃;
12. final conclusion:
Tc (two layers)=661.2581 ℃>Tm (two layers)=602 ℃
Tc (three layers)=611.2579 ℃>Tm (three layers)=443 ℃
The critical-temperature of calculating by program and the comparison of member maximum temperature: steel framed structure one deck, two layers and three layers all are in a safe condition.So the guard method of steel frame is: structure one deck is protected, seen Fig. 7.Coating fireproof paint or external wrapping concrete guarantee that the fire endurance time of steel frame is 90 minutes.
● example 2: the span of certain petrochemical industry single span compound steel framework is 12m, one, two, three layers floor height is respectively 5m, 3m, 3m, and the horizontal loading that bears is 300kN, and the vertical load that bears is 100kN, beam section is HN700 * 300, and column section is HM588 * 300.The hot burst size Q that burning things which may cause a fire disaster bears at the ground steel frame during fire is 36MW.Show as Fig. 6, determine the guard method of steel frame.
Calculation procedure 1-7 is with example 1.
8. preliminary conclusion 1:
Tc (one deck)=397.0286 ℃<Tm (one deck)=900 ℃
Tc (two layers)=347.0287 ℃<Tm (two layers)=602 ℃
Tc (three layers)=297.0286 ℃<Tm (three layers)=443 ℃
The critical-temperature of calculating by program and the comparison of member maximum temperature, steel framed structure one deck, two layers and three layers all are in unsafe condition.So take safeguard measure as follows: can take to structure one deck or one deck, two layers or one deck, two layers, three layers this three kinds of safeguard measures.Be calculated as follows:
9. carrying out safeguard measure calculates: one deck protection;
10. the calculation procedure that calls establishment carries out critical-temperature and calculates;
11. program calculates the critical temperature Tc (i) of rod member:
Tc(1)=200.0000℃;Tc(2)=534.0538℃;Tc(3)=484.0537℃;
Tc(4)=484.0537℃;Tc(5)=534.0538℃;Tc(6)=200.0000℃;
Tc(7)=484.0537℃;Tc(8)=534.0538℃;Tc(9)=200.0000℃;
12. preliminary conclusion 2:
Tc (two layers)=534.0538 ℃<Tm (two layers)=602 ℃
Tc (three layers)=484.0537 ℃>Tm (three layers)=443 ℃
The critical-temperature of calculating by program and the comparison of member maximum temperature: steel framed structure still is in unsafe condition for two layers.So the guard method of steel frame is: can take safeguard measure to structure one deck, two layers.Be calculated as follows:
13. carrying out safeguard measure calculates: one, two layers of protection;
Carry out critical-temperature calculating 14. call the calculation procedure of establishment;
15. program calculates the critical temperature Tc (i) of rod member:
Tc(1)=200.0000℃;Tc(2)=150.0000℃;Tc(3)=654.3721℃;
Tc(4)=654.3721℃;Tc(5)=150.0000℃;Tc(6)=200.0000℃;
Tc(7)=654.3721℃;Tc(8)=150.0000℃;Tc(9)=200.0000℃;
16. final conclusion:
Tc (three layers)=654.3721 ℃>Tm (three layers)=443 ℃
The critical-temperature of calculating by program and the comparison of member maximum temperature: steel framed structure one deck, two layers and three layers all are in a safe condition.So the guard method of steel frame is: structure one deck and two layers are protected, seen Fig. 8.Coating fireproof paint or external wrapping concrete guarantee that the fire endurance time of steel frame is 90 minutes.
For this petrochemical production device single span compound steel framework piping lane, according to fire situation may take place, according to the requirement of foreign vendor, in the equal mineral wool protection of all steel work of fire and explosive hazard district scope.On the other hand, press the clause method of domestic petroleum chemical industry standard, steel frame piping lane only one deck structure must be done flameproof protection.And the guard method that the above-mentioned steel frame science that adopts the application to provide is calculated; the protection domain of comparing steel frame with foreign method can reduce 35%; saved construction investment, the protection domain of comparing steel frame with the domestic bar syntax has increased by 30%, has guaranteed the anti-fire safety degree of structure.This is owing to domesticly do not consider the design method of the external load and the fringe conditions of structure based on component test, to the anti-fire safety degree deficiency of above-mentioned concrete Project design.
● example 3: the span of certain petrochemical industry single span compound steel framework is 12m, one, two, three layer floor height branch
Wei 5m, 3m, 3m, the horizontal loading that bears is 200kN, the vertical load that bears is 100kN, beam section is HN346 * 174, column section is HM588 * 300.The hot burst size Q that burning things which may cause a fire disaster bears at the ground steel frame during fire is 36MW.Show as Fig. 6, determine the guard method of steel frame.
Calculation procedure 1-7 is with example 1.
8. preliminary conclusion 1:
Tc (one deck)=204.8698 ℃<Tm (one deck)=900 ℃
Tc (two layers)=154.8698 ℃<Tm (two layers)=602 ℃
Tc (three layers)=104.8698 ℃<Tm (three layers)=443 ℃
The critical-temperature of calculating by program and the comparison of member maximum temperature, steel framed structure one deck, two layers and three layers all are in unsafe condition.So take safeguard measure as follows: can take to structure one deck or one deck, two layers or one deck, two layers, three layers this three kinds of safeguard measures.Be calculated as follows:
9. carrying out safeguard measure calculates: one deck protection;
10. the calculation procedure that calls establishment carries out critical-temperature and calculates;
11. program calculates the critical temperature Tc (i) of rod member:
Tc(1)=200.0000℃;Tc(2)=150.3711℃;Tc(3)=100.3711℃;
Tc(4)=100.3711℃;Tc(5)=150.3711℃;Tc(6)=200.0000℃;
Tc(7)=100.3711℃;Tc(8)=150.3711℃;Tc(9)=200.0000℃;
12. preliminary conclusion 2:
Tc (two layers)=150.3711 ℃<Tm (two layers)=602 ℃
Tc (three layers)=100.3711 ℃<Tm (three layers)=443 ℃
The critical-temperature of calculating by program and the comparison of member maximum temperature: steel framed structure still is in unsafe condition for two layers, three layers.So the guard method of steel frame is: can take safeguard measure to structure one deck, two layers.Be calculated as follows:
13. carrying out safeguard measure calculates: one, two layers of protection;
Carry out critical-temperature calculating 14. call the calculation procedure of establishment;
15. program calculates the critical temperature Tc (i) of rod member:
Tc(1)=200.0000℃;Tc(2)=150.0000℃;Tc(3)=102.8963℃;
Tc(4)=102.8963℃;Tc(5)=150.0000℃;Tc(6)=200.0000℃;
Tc(7)=102.8963℃;Tc(8)=150.0000℃;Tc(9)=200.0000℃;
16. final conclusion:
Tc (three layers)=102.8963 ℃<Tm (three layers)=443 ℃
The critical-temperature of calculating by program and the comparison of member maximum temperature: steel framed structure still is in unsafe condition for three layers.So the guard method of steel frame is: structure one deck, two layers and three layers are protected, seen Fig. 9.Coating fireproof paint or external wrapping concrete guarantee that the fire endurance time of steel frame is 90 minutes.
● example 4: the span of certain civilian single span compound steel framework is 12m, one, two, three layers floor height is respectively 3m, 3m, 3m, the horizontal loading that bears is 300kN, the vertical load that bears is 100kN, beam section is HN396 * 199, and column section is HM588 * 300, and one deck is for opening wide spacious space, burning things which may cause a fire disaster is 10MW at the hot burst size Q that two layers of ground steel frame bear during fire, referring to Fig. 6.Determine the guard method of steel frame.
Calculation procedure is as follows:
1. the calculation procedure basic parameter of determining the appropriate size and structure:
(1) steelframe type ip1=4, temperature variations ip2=1, ip3=i p4=ip5=ip6=0;
(2) cross section type: 2; (1 expression square-section, 2 expression i shaped cross sections)
(3) cross section parameter:
I shape: cbb=0.199m; Chb=0.396m; Tb1=0.011m; Tb2=0.007m; Cbc=0.3m; Chc=0.588m; Tc1=0.002m; Tc2=0.012m;
(4) length of beam, post: 1=12m; H1=3m; H2=3m; H3=3m;
(5) material yield intensity varies with temperature to control and counts: MST=6;
(6) material yield intensity and corresponding temperature first point: the CMS (1,1)=205000; CMS (1,2)=0;
(7) material yield intensity and corresponding temperature second point: the CMS (2,1)=159000; CMS (2,2)=300;
(8) material yield intensity and corresponding temperature are thirdly: CMS (3,1)=100000; CMS (3,2)=500;
(9) material yield intensity and corresponding temperature the 4th point: CMS (3,1)=25000; CMS (3,2)=700;
(10) material yield intensity and corresponding temperature the 5th point: CMS (3,1)=12000; CMS (3,2)=800;
(11) material yield intensity and corresponding temperature the 6th point: CMS (3,1)=2000; CMS (3,2)=1000; (12) size of active force:
PV1=100KN;PV2=100KN;PV3=100KN;
PH1=300KN;PH2=300KN;PH3=300KN;
2. safeguard measure when determining to calculate: unprotect;
3. determine rod member initial temperature t (i):
t(1)=20℃;t(2)=20℃;t(3)=20℃;
t(4)=20℃;t(5)=20℃;t(6)=20℃;
t(7)=20℃;t(8)=20℃;t(9)=20℃;
4. determine rod member temperature variations it (i):
it(1)=0;it(2)=1;it(3)=1;it(4)=1;it(5)=1;
it(6)=0;it(7)=1;it(8)=1;it(9)=0;
[annotate: it (i)=0 expression is temperature-resistant; It (i)>0 represents variations in temperature, if it (1)=it (3)>0 expression 1 changes identical with 3 member temperature.]
5. the calculation procedure that calls establishment carries out critical-temperature and calculates;
6. program calculates the critical temperature Tc (i) of rod member:
Tc(1)=20℃;Tc(2)=429.35?77℃;Tc(3)=429.3577℃;
Tc(4)=429.3577℃;Tc(5)=429.35?77℃;Tc(6)=20℃;
Tc(7)=429.3577℃;Tc(8)=429.35?77℃;Tc(9)=20℃;
7. the temperature profile value Tm (i) that reaches when the rod member fire burns:
Characteristic value when the design formulas of countries such as employing English, U.S. is determined the fire burning:
Calculate: the maximum temperature Tm of member (℃):
One deck Tm=20 ℃; Two layers Tm=485 ℃; Three layers Tm=302 ℃;
8. preliminary conclusion:
Tc (two layers)=429.35 77 ℃<Tm (two layers)=485 ℃
Tc (three layers)=429.35 77 ℃>Tm (three layers)=302 ℃
The critical-temperature of calculating by program and the comparison of member maximum temperature, steel framed structure is in unsafe condition for two layers.So take safeguard measure as follows: can take to two layers on structure or two layers, three layers this two kinds of safeguard measures.Be calculated as follows:
9. carrying out safeguard measure calculates: second layer protection;
10. the calculation procedure that calls establishment carries out critical-temperature and calculates;
11. program calculates the critical temperature Tc (i) of rod member:
Tc(1)=20℃;Tc(2)=20℃;Tc(3)=457.0719℃;
Tc(4)=457.0719℃;Tc(5)=20℃;Tc(6)=20℃;
Tc(7)=457.0719℃;Tc(8)=20℃;Tc(9)=20℃;
12. final conclusion:
Tc (three layers)=457.0719 ℃>Tm (three layers)=302 ℃
The critical-temperature of calculating by program and the comparison of member maximum temperature: steel framed structure one deck, two layers and three layers all are in a safe condition.So the guard method of steel frame is: the structure second layer is protected, seen Figure 10.Coating fireproof paint or external wrapping concrete guarantee that the fire endurance time of steel frame is 90 minutes.
(2) twin spans single-store frame
● example 1: the span of certain petrochemical industry twin spans individual layer steel frame is 12m, and the horizontal loading that floor height is 3m, bear is 500kN, and the vertical load that bears is 200kN, and beam section is HN700 * 300, and column section is HM588 * 300.Burning things which may cause a fire disaster is 3.535MW at the hot burst size Q that the ground steel frame bears during fire, sees Figure 11.Determine the guard method of steel frame.
Calculation procedure 1-5 is with example 1.
6. program calculates the critical temperature Tc (i) of rod member:
Tc(1)=583℃;Tc(2)=583℃;Tc(3)=583℃;
Tc(4)=583℃;Tc(5)=583℃;
7. the temperature profile value Tm (i) that reaches when the rod member fire burns:
Adopt the design formulas of example 1 to calculate: the maximum temperature Tm of member (℃) Tm=600 ℃
8. preliminary conclusion:
Tc=583℃<Tm=600℃
The critical-temperature of calculating by program and the comparison of member maximum temperature, steel framed structure is in unsafe condition.So take safeguard measure as follows: pillar is carried out flameproof protection.Be calculated as follows:
9. carrying out safeguard measure calculates: the post protection;
10. the calculation procedure that calls establishment carries out critical-temperature and calculates;
Wherein: it (1)=0; It (2)=1; It (3)=0; It (4)=1; It (5)=0;
[annotate: it (i)=0 expression is temperature-resistant; It (i)>0 represents variations in temperature, if it (1)=it (3)>0 expression 1 changes identical with 3 member temperature.
11. program calculates the critical temperature Tc (i) of rod member:
Tc(1)=200℃;Tc(2)=612℃;Tc(3)=200℃;
Tc(4)=612℃;Tc(5)=200℃;
12. final conclusion:
Tc=612℃>Tm=600℃
The critical-temperature of calculating by program and the comparison of member maximum temperature: steel framed structure is in a safe condition.So the guard method of steel frame is: pillar is protected, seen Figure 12.Coating fireproof paint or external wrapping concrete guarantee that the fire endurance time of steel frame is 90 minutes.
(4) space one deck framework
● example 1: the span of the steel frame of certain petrochemical industry space one deck fastening is 12m, and floor height is 3m, and the horizontal loading that bears is 50kN, and the vertical load that bears is 100kN, and beam section is HN700 * 300, and column section is HM588 * 300.Burning things which may cause a fire disaster is 36MW at the hot burst size Q that the ground steel frame bears during fire, as Figure 13.Determine the guard method of steel frame.
Calculation procedure is as follows:
1. the calculation procedure basic parameter of determining the appropriate size and structure:
(1) steelframe type ip1=31, temperature variations ip2=1, ip3=ip4=ip5=ip6=0;
(2) cross section type: 2; (1 expression square-section, 2 expression i shaped cross sections)
(3) cross section parameter:
I shape: cbb=0.3m; Chb=0.7m; Tb1=0.024m; Tb2=0.0013m; Cbc=0.3m; Chc=0.588m; Tc1=0.002m; Tc2=0.012m;
(4) length of beam, post: C11=12m; C12=12m; CH1=3m;
(5) material yield intensity varies with temperature to control and counts: MST=6;
(6) material yield intensity and corresponding temperature first point: the CMS (1,1)=205000; CMS (1,2)=0;
(7) material yield intensity and corresponding temperature second point: the CMS (2,1)=159000; CMS (2,2)=300;
(8) material yield intensity and corresponding temperature are thirdly: CMS (3,1)=100000; CMS (3,2)=500;
(9) material yield intensity and corresponding temperature the 4th point: CMS (3,1)=25000; CMS (3,2)=700;
(10) material yield intensity and corresponding temperature the 5th point: CMS (3,1)=12000; CMS (3,2)=800;
(11) material yield intensity and corresponding temperature the 6th point: CMS (3,1)=2000; CMS (3,2)=1000;
(12) size of active force:
Px1=50KN;Px2=50KN;Py1=100KN;Py2=100KN;
Pz1=50KN;Pz2=50KN;
2. safeguard measure when determining to calculate: unprotect;
3. determine rod member initial temperature t (i):
t(1)=200℃;t(2)=200℃;t(3)=200℃;
t(4)=200℃;t(5)=200℃;t(6)=200℃;
t(7)=200℃;t(8)=200℃;
4. determine rod member temperature variations it (i):
it(1)=1;it(2)=1;it(3)=1;it(4)=1;it(5)=1;it(6)=1;
it(7)=1;it(8)=1;
[annotate: it (i)=0 expression is temperature-resistant; It (i)>0 represents variations in temperature, if it (1)=it (3)>0 expression 1 changes identical with 3 member temperature.]
5. the calculation procedure that calls establishment carries out critical-temperature and calculates;
6. program calculates the critical temperature Tc (i) of rod member:
Tc(1)=592.2399℃;Tc(2)=592.2399℃;Tc(3)=592.2399℃;
Tc(4)=592.2399℃;Tc(5)=592.2399℃;Tc(6)=592.2399℃;
Tc(7)=592.2399℃;Tc(8)=592.2399℃;
7. the temperature profile value Tm (i) that reaches when the rod member fire burns:
Characteristic value when the design formulas of countries such as employing English, U.S. is determined the fire burning:
Calculate: the maximum temperature Tm of member (℃):
Tm=900;
8. preliminary conclusion:
Tc(i)=592.2399℃<Tm=900℃(i=1…8)
The critical-temperature of calculating by program and the comparison of member maximum temperature, steel framed structure is in unsafe condition.So take safeguard measure as follows: can take only coupled columns protection, only beam protection, beam column all be protected this three kinds of safeguard measures.Be respectively calculated as follows:
9. carrying out safeguard measure calculates:
9.1, guard column only
9.1.1, the calculation procedure that calls establishment carries out critical-temperature and calculates;
9.1.2, program calculates the critical temperature Tc (i) of beam column spare:
Tc(2)=592.2399℃<Tm=900℃;
Tc(4)=592.2399℃<Tm=900℃;
Tc(5)=592.2399℃<Tm=900℃;
Tc(7)=592.2399℃<Tm=900℃;
When only coupled columns protection was described, structure still was in unsafe condition.
9.2, only protect beam
9.2.1, the calculation procedure that calls establishment carries out critical-temperature and calculates;
9.2.2, program calculates the critical temperature Tc (i) of mast spare:
Tc(1)=592.2399℃<Tm=900℃;
Tc(3)=592.2399℃<Tm=900℃;
Tc(6)=592.2399℃<Tm=900℃;
Tc(8)=592.2399℃<Tm=900℃;
Illustrate that structure still is in unsafe condition when only beam being protected.
10. final conclusion:
The critical-temperature of calculating by program and the comparison of member maximum temperature, the guard method of this steel frame is: structure one deck beam column is all protected, seen Figure 14.Coating fireproof paint or external wrapping concrete guarantee that the fire endurance time of steel frame is 90 minutes.

Claims (12)

1, a kind of design and selection method of steel frame structure fire-resistant protection comprises the steps:
(1) determines the plane structure of steel framed structure or the basic destruction sum N of mechanism of space structures according to plasticity and limit analysis theory, and set the initial temperature of each rod member of steel framed structure;
(2) determine object function η, destroy the ratio of internal work with the external work of mechanism's superposition when η is the plastic limit state substantially, and satisfy following formula:
&eta; = &Sigma; n = 1 N X n W in &Sigma; n = 1 N X n W en ( X n &GreaterEqual; 0 )
If destroying the internal force plastic work done of the n of mechanism substantially is W In, W InRelevant with the plastic limit bending moment and the destruction mechanism rod member corner in steel framed structure control cross section under temperature, this temperature, corresponding external work is W En, W EnWith act on structure boundary on the broad sense external load and to destroy the rate of displacement of mechanism relevant, N is an above-mentioned basic destruction mechanism sum, X nBe the basic corner multiplying factor of destroying mechanism;
(3) η and variable X 1 in the above-mentioned formula, X2 ..., the relation of Xn is followed successively by non-linear relation one time, optimizes and analyzes described nonlinear problem, by optimizing X nMake the plastic hinge of superposition mechanism disappear, make internal work reduce, thereby obtain the minimum of η, it is found to destroy mechanism accordingly, is minimum value in all possible destruction of the steel frame mechanism according to the critical-temperature of this mechanism's correspondence of plasticity and limit analysis theory principle;
(4) adopt iterative method to determine the critical temperature value of steel frame of the minimum value correspondence of object function η: the temperature increment of setting each rod member of described steel framed structure is dt, next step temperature increment becomes (η-1) dt, η wherein is a previous step iteration gained, carries out iteration optimization and calculates;
(5) set tole for allowing precision, dt1 adds up for all member temperature variable quantity absolute values, the iteration convergence criterion adopt abs (dt1)<tole or | η-1|<tole when iterative computation satisfies one of above-mentioned two iteration convergence criterions, calculates the critical-temperature of each rod member of steel frame;
The temperature profile value that corresponding rod member can reach during (6) with the critical-temperature of each rod member of steel frame of calculating and fire burning compares, to determine whether and need protect steel frame.
2, the method for claim 1, described permission precision tole value is 0.01.
3, method as claimed in claim 1 or 2, described internal force plastic work done W InDirect relation is arranged, external work W with the length of the yield strength of the cross section type of steel frame, cross section parameter, steel and beam, post EnRelevant with the type and the fringe conditions of external load, steel frame on acting on steel framed structure.
4, method as claimed in claim 3 is protected employing partly or entirely anti-fiery coating of coating or external wrapping concrete to steel frame.
5, method as claimed in claim 4, steel framed structure wherein are one of single span single-store frame, twin spans single-store frame, single span double-layer frame, three layers of framework of single span, five kinds of structures of two-way single span individual layer space frame.
6, method as claimed in claim 5, described steel framed structure is plane steel framed structure or spatial steel-frame structure, when being the spatial steel-frame structure, it destroys determining by space structures being decomposed into the plane structure of twocouese of mechanism's number substantially, finds out the basic destruction mechanism number that basic destruction structure number is superposed to space structures respectively by plane structure again.
7, method as claimed in claim 6, described temperature profile value adopts English, U.S. general calculation formula is tried to achieve or obtain according to " construction steel structure fireproofing technique standard " CECS200:2006.
8, method as claimed in claim 3, described optimization are analyzed nonlinear problem and are adopted accurate newton's method to be optimized calculating.
9, method as claimed in claim 6, space structures is decomposed into plane structure after, determine corresponding beam mechanism, layer mechanism and joint mechanism, and further determine basic the destructions mechanism number of corresponding each mechanism, obtain the basic total N of mechanism that destroys by adding up.
10, method as claimed in claim 3; the temperature profile value that corresponding rod member can reach when the critical-temperature of each rod member of steel frame that calculates is burnt greater than fire; whether checking computations rod member strength of stability meets the demands; when meeting the demands; steel framed structure safety does not need to do the flame retardant coating protection, when not meeting the demands; to structure division or all do flame retardant coating protection, or enlarging section is not done topping according to result of calculation.
11, method as claimed in claim 10 is protected employing partly or entirely anti-fiery coating of coating or encased steel reinforced concrete to steel frame.
12, method as claimed in claim 9; the temperature profile value that corresponding rod member can reach when the critical-temperature of each rod member of steel frame that calculates is burnt greater than fire; whether checking computations rod member strength of stability meets the demands; when meeting the demands; steel framed structure safety does not need to do the flame retardant coating protection, when not meeting the demands; to structure division or all do flame retardant coating protection, or enlarging section is not done topping according to result of calculation.
CN 200610161954 2006-12-11 2006-12-11 Steel frame structure fire-resistant protection design and selection method Pending CN1995570A (en)

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Cited By (7)

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Publication number Priority date Publication date Assignee Title
CN101799843A (en) * 2010-03-12 2010-08-11 哈尔滨工业大学深圳研究生院 Fireproof performance evaluation method of concrete member of water-injection hollow steel pipe and application
CN103207206A (en) * 2013-04-03 2013-07-17 同济大学 Stagnation temperature computing method of bending steel members
CN103207205A (en) * 2013-04-03 2013-07-17 同济大学 Method for computing stagnation temperature of flexural steel member
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CN103235871A (en) * 2013-04-03 2013-08-07 同济大学 Method for calculating critical temperature of axial compression steel components
CN109299540A (en) * 2018-09-25 2019-02-01 重庆大学 Plane frame structure Static Non-linear Analyisis based on rigid body criterion
CN116956395A (en) * 2023-05-06 2023-10-27 杭州铁木辛柯建筑结构设计事务所有限公司 Design method of fireproof protection layer of rectangular steel tube concrete column by critical temperature method

Cited By (10)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101799843A (en) * 2010-03-12 2010-08-11 哈尔滨工业大学深圳研究生院 Fireproof performance evaluation method of concrete member of water-injection hollow steel pipe and application
CN101799843B (en) * 2010-03-12 2012-09-26 哈尔滨工业大学深圳研究生院 Fireproof performance evaluation method of concrete member of water-injection hollow steel pipe and application
CN103226654A (en) * 2013-03-29 2013-07-31 浙江大学 Heliostat field simulation method for CSP (concentrating solar power)
CN103226654B (en) * 2013-03-29 2015-12-09 浙江大学 A kind of solar energy thermal-power-generating heliostat field analogy method
CN103207206A (en) * 2013-04-03 2013-07-17 同济大学 Stagnation temperature computing method of bending steel members
CN103207205A (en) * 2013-04-03 2013-07-17 同济大学 Method for computing stagnation temperature of flexural steel member
CN103235871A (en) * 2013-04-03 2013-08-07 同济大学 Method for calculating critical temperature of axial compression steel components
CN109299540A (en) * 2018-09-25 2019-02-01 重庆大学 Plane frame structure Static Non-linear Analyisis based on rigid body criterion
CN116956395A (en) * 2023-05-06 2023-10-27 杭州铁木辛柯建筑结构设计事务所有限公司 Design method of fireproof protection layer of rectangular steel tube concrete column by critical temperature method
CN116956395B (en) * 2023-05-06 2024-06-11 杭州铁木辛柯建筑结构设计事务所有限公司 Design method of fireproof protection layer of rectangular steel tube concrete column by critical temperature method

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