THEORETICAL & APPLIED MECHANICS LETTERS 4, 034006 (2014)
Study on mechanical characteristics and safety evaluation method of steel frame structure after fire Qiang Sun,1, a) Congcong Guan,1, 2 Dingtang Wang1 1) College
of Civil Engineering, Anhui Jianzhu University, Hefei 230601, China Construction 4th Engineering Bureau 6th Corp Limited, Hefei 230011, China (Received 26 September 2013; revised 19 March 2014; accepted 22 April 2014) 2) China
Abstract Mechanical characterization of steel frame structure after fire are analyzed based on fire dynamics, heat transfer theory, structural mechanics, and finite element theory. We study the temperature characteristics and mechanical properties of steel frame structure under different fire locations and propose a safety evaluation method. We also analyze damage level of main frame components, maximum temperature of fire, thermal characteristics of frame components, firing duration, etc. to provide useful information for fire resistance design of the steel frame structure and post-disaster safety evaluation. c 2014 The Chinese Society of Theoretical and Applied Mechanics. [doi:10.1063/2.1403406] Keywords fire, steel frame, mechanical characteristics, safety level, safety evaluation
Safety evaluation and reinforcement in the reinforced concrete structure and steel structure are widely applied nowadays. However, it lacks of systematic research. Only site visit combining with technical data in related references and surface damage level of material are considered in currently safety evaluation. Appraisal conclusion depends largely on the evaluator’s experience, and such kind of evaluation does not match the modern design theory and detection technology. Few researches1–9 can be found on how to systematically evaluate the safety level of steel frame structure after fire. This study proposes a safety evaluation method for steel frame structure and provides some guidance information for fire resistance design and safety assessment post-disaster. Temperature field of steel frame in the building is normally assumed to has a uniform or linear distribution in the thermal analysis. However, temperature distributions of frame components can be quite different under elevated temperature in a fire. In this paper, thermal analysis of a plane frame is performed using ANSYS software and the standard time-temperature curve (ISO-834 Curve) selected for the fire modeling. At elevated temperature, failure criterion of steel frame’s bearing capacity can be analyzed from two aspects: local damage of frame component and general failure of steel frame. Steel frame structure is deemed to have failed when one of the following criteria, divided into these two aspects, is exceeded.10,11 Criterion I Deforming rate of frame component exceeds dδ / dt l 2 /(15h) (component loses its stability bearing capacity). Criterion II Deformation of frame component exceeds δ l/20 (component loses its stability bearing capacity). Here δ is maximum deflection of component, l is length of component, h is a) Corresponding
author. Email:
[email protected].
Theor. Appl. Mech. Lett. 4, 034006 (2014)
034006-2 Q. Sun, C. C. Guan, D. T. Wang
15.3 m
height of component’s cross section, and t is time of combustion. Criterion III Integral deformation of steel frame exceeds δ /h 1/30 (structure loses its general stability). Here δ is inter-story drift and l is height of the overall framework. In this work, a plane frame fixed on the ground and having 4 layers and 3 spans (as shown in Fig. 1) is studied, and its height is 15.3 m and has a column spacing of 6 m. Lateral supports are provided to all columns of the frame on both left side and right side. Concentrated load is assumed to be imposed on the top of column, and the outside load and inside load of lateral column are 80 and 160 kN. A uniform load of 27 kN/m is imposed to all beams. Beam and column all have an I-shaped cross-section and their sizes are listed in Table 1.
Mode 1
Mode 2
6m
6m
6m
Fig. 1. Schematic of steel frame model under fire. Table 1. Beam and column size of steel frame. High/mm
Wide/mm
Flange/mm
Beam
600
300
20
Web/mm 12
Column
500
360
20
14
The fire is supposed to happen in a fireproof compartment (Mode 1 or Mode 2 as shown in Fig. 1) and the fire duration is 15 min. In both modes, beam and column are heated directly except the top flange of beam and outside edge of column. We also assume the fireproof compartment is capable to prevent the fire spreading to other rooms, even without the coating effects of steel frame surface. Temperature and displacement of the plane frame are analyzed using ANSYS software based on the engineering condition described above (Mode 1 and Mode 2 in Fig. 1). Figure 2 shows that displacement in X direction at the beginning (t = 0, so-call static displacement) is small and in the safe range. With heating growing, steel component gradually loses its strength and lateral displacement becomes larger and larger with plastic hinge coming out and rapid dropping of lateral rigidity. Comparing to other parts of beam and column, displacements of beam-column joints in X direction (Fig. 3) show great different thermal characteristics due to the temperature variation. This makes beam-column joints the weakness of steel frame. Static displacement of beam-column joint in Y direction (as shown in Fig. 4) is also small and in the safe range. When the heating grows, stiffness and bearing capacity of steel component decrease gradually and deflection becomes larger and larger. Figure 5 shows that deforming rate of beam is low before 600 s. Due to the continuous
Displacement/cm
0 Middle-span of fire beam
-1 -2
Middle of fire column
-3
Roof of fire column roof
-4 0
200
Displacement/cm
034006-3 Study on mechanical characteristics and safety evaluation method
8
Middle of fire column
0
Roof of fire column
-8 -16
Middle-span of fire beam
-24
400 600 Time/s
800
0
1000
Fig. 2. Displacement in X direction in Mode 1.
200
400 600 Time/s
800
1000
Fig. 3. Displacement in Y direction in Mode 1.
Displacement/cm
Middle-span of fire beam -0.8 -1.6
Middle of fire column
-2.4 Left beam-column node unfired Fire beam-column node -3.2 0 200 400 600 Time/s
Displacement/cm
0 0
-1.6
Middle of fire column Roof of fire column
-3.2 Middle-span of fire beam -4.8 -6.4
800
1000
Fig. 4. Displacement in X direction in Mode 2.
0
200
400 600 Time/s
800
1000
Fig. 5. Displacement in Y direction in Mode 2.
accumulation of plasticity and loss of bearing capacity, deforming rate increases more and more quickly after 600 s, showing as rapid development of deflection. The following facts can be concluded from comparisons between Mode 1 and Mode 2, as shown in Figs. 6 and 7. (1) It seems influences to the steel frame and the frame components under different fire locations are basically same. With increasing temperature, plasticity of the steel frame constantly increases and finally causes frame’s destruction. (2) Plasticity development in Mode 1 is faster than that in Mode 2. Before 400 s, changing rates of deflection in Mode 1 and Mode 2 are almost equal and the plasticity deformation has not obviously shown up yet. After 400 s, plastic deformation occurs and the changing rate in Mode 1 is faster than Mode 2. 200 150
25 Mode 1 Mode 2
Deflection/mm
Deflection/mm
250
100 50 0 0
200
400 600 Time/s
800
1000
Fig. 6. Deflection of beam under different fire locations.
Mode 1 Mode 2
20 15 10 5 0
0
200
400 600 Time/s
800
1000
Fig. 7. Displacement of column in X direction under different fire locations.
Above analysis techniques can be used to evaluate the safety level of steel frame. The proposed safety evaluation method includes the following factors and procedures: site visit and accounting on the number of comburent,12 calculation of fire load density13 and the duration time,11
Theor. Appl. Mech. Lett. 4, 034006 (2014)
034006-4 Q. Sun, C. C. Guan, D. T. Wang Site visit and accounting on the number of comburent
Calculation of fire load density
Calculation of the duration time
Estimate of the fire temperature
Thermal analysis of steel frame under thermo-mechanical loads
Safety evaluation
Fig. 8. Safety evaluation method and procedure of fire steel frame.
estimate of the fire temperature,14 thermal analysis of steel frame under thermo-mechanical loads, and safety evaluation of steel frame, as shown in Fig. 9. Analysis of an instance project of ordinary steel framing residential building is given below. The fire source is located in the master bedroom and the whole structure is not destroyed. Onsite survey shows that the building compartment is 4.2 m (width) × 6.0 m (length) with a height of 3.3 m, and the sizes of beam and column are listed in Table 1. The fire is caused by a burning cigarette ending in the rubbish bin. There are some wooden furniture, textiles (mainly cotton), plastic decoration, carpet, paper, leather clothing, etc., in the compartment. Doors and windows are all closed when burning, and the fuel is not completely burned. The amount of the fuel in the analysis can be found in Table 2. Table 2. Amount of the fuel in the compartment. Wood furniture Cotton textile Plastic decorative Carpet Paper Leather goods Else Weight mc /kg
300
36
14
32
9
3
13
Combustion value Hc /(MJ·kg−1 )
19
20
35
19
17
19
16
Fire load density can be obtained by formula (2) in the Ref. 13 as QL = ∑ mc × Hc = 7 936 MJ, qki = (∑ mc Hc )/Af = 314.9 MJ/m2 . Here QL is fire load, qki is fire load density in the compartment, mc is gross mass of combustible material, Hc is available heating value of combustible material, and Af is gross floor area of the compartment. The rate of heat release is assumed to be a medium speed, since doors and windows are all closed. The fire type constant α is 0.011 27 according to Ref. 11, so we have the release rate of heat Q = α t 2 = 0.011 27t 2 , QL = Qt = 0.011 27t 3 , and the fire duration t = (QL /α )1/3 = 596.9 s. Duration time of the fire is regarded as 600 s based on the above calculation, and we build a model for thermal analysis. For simplicity, the fire is assumed to happen in a single compartment and the fire does not spread to other rooms. A plane frame is modeled for the thermal analysis with solid element and the ISO-834 Curve, and the surface of component is assumed to have no protection. Then we can get the temperature distribution of the plane frame as shown in Fig. 9. From Fig. 9 we can see that, after 600 s the maximum temperatures of fire beam and fire column flank edge reach 710◦ C and 480◦ C. This temperature distribution is loaded to the plane frame model for thermal analysis. Results obtained from thermal analysis under thermo-mechanical loads are shown in Figs. 10–12. Based on above calculation, we can then obtain the failure criteria for frame component. Criterion I of fire column is dδ / dt l 2 /(15h) = 3 3002 /(15 × 500) = 24.2 mm/min, Criterion I of fire beam is dδ / dt l 2 /(15h) = 4 2002 /(15 × 600) = 32.67 mm/min, and Criterion II of fire column (beam) is δ l/20 = 3 300 (4 200) /20 = 165 (210) mm.
034006-5 Study on mechanical characteristics and safety evaluation method NODAL SOLUTION STEP=15 SUB=3 TIME=900 TEMP (AVG) RSYS=0 SMN=20.394 SMX=710.684
Y X
Z 20.394
173.792
327.19
480.588
633.985
Fig. 9. Temperature (◦ C) distribution of the plane frame. (a)
(b)
NODAL SOLUTION STEP=11 SUB=3 TIME=600 TEMP (AVG) RSYS=0 DMX=0.30882 SMN=-0.030809 SMX=0.003884
Y Z
NODAL SOLUTION STEP=11 SUB=3 TIME=600 TEMP (AVG) RSYS=0 DMX=0.30882 SMN=-0.030809 SMX=0.003884
Y X
-30.809 -23.099 -15.390 -7.680
0.289
Τ10-3
Z
X
-25.300 -19.028 -12.756 -6.485
0.213
Τ10-3
Fig. 10. Displacements (mm) of beam-column joint in (a) X direction and (b) Y direction at 600 s
As shown in Fig. 11, deforming rate of the top of fire column is −5.31 mm/min at 900 s, which does not exceed Criterion I of fire column and satisfies the safety requirement. Deformation rate of the middle of fire beam is 39.12 mm/min at about 840 s, and reaches 92.11 mm/min at 900 s, which has exceeded the failure criterion. The deformation is 225.1 mm at 900 s. To sum up, the frame beam does not meet the safety conditions, namely the frame beam will quickly damage because of the deformation has reached the limiting condition. To further evaluate the safety level, we can calculate the interlayer displacement δ h/30 = 3 300/30 = 110 mm. The maximum displacement between the layers is 38 mm as shown in Fig. 12, and it meets the safety conditions. Our analysis shows that neither the steel frame nor the fire column exceeds the criterion, and they are safe. Fire beam has reached its stability bearing capacity limit and it is not safe anymore, and a reinforcement or repair or replacement of components is required. 0 Middle of fire beam (deflection) Top of fire column (lateral displacement)
120
240
360
480
600
720
840
Time/s
Fig. 11. Deforming rate in the middle of fire beam and on the top of fire column.
Displacement/m
Deforming rate/ (mm.min-1)
100 80 60 40 20 0 -20
Layer 2
-0.8 -1.6 -2.4
Layer 1
-3.2 -4.0
0
200
400 600 Time/s
800
1000
Fig. 12. Displacement in X direction versus time of Layer 1 and Layer 2.
034006-6 Q. Sun, C. C. Guan, D. T. Wang
Theor. Appl. Mech. Lett. 4, 034006 (2014)
Based on the analysis of a plane frame, the following conclusions are obtained. (1) Temperature of beam-column joints changes quickly, and its distribution is quite uneven. Non-uniform temperature stress is easy to arise in this condition and redistribution of internal force occurs. This leads to plastic changes or local damage. The beam-column joints are safety vulnerabilities of steel frame. (2) Thermal effect becomes more obvious when temperature increases. Rigidity of fire beam decreases, and deflection becomes higher. Deforming rate is low before 600 s, and becomes higher after 600 s because of the plasticity development and the loss of unceasing accumulation capacity. Then the deflection increases rapidly and the steel frame gradually loses its bearing capacity. (3) Influences to the steel frame and frame components under different firing positions are different. Difference is still small in the elastic phase. However, in the plastic phase, deflection of firing side-span changes more quickly than that of firing middle-span, and it causes a larger displacement to steel column. That means side-span firing is danger than middle-span firing. (4) Analysis of an instance project is given to illustrate the proposed safety evaluation method. Our study can facilitate a better reference for fire resistance design of the steel frame structure and post-disaster safety evaluation. This work was supported by the National Basic Research Program of China (2012CB719703) and University of Anhui Provincial Natural Science Fund Project (J2013A068). 1. S. X. Sun, W. Gao. Architecture Comprehensive Fire Protection Design. Tianjin Science and Technology Translation Publishing Company, Tianjin (1994) (in Chinese). 2. GB50045. The Code for Fire Protection Design of Tall Buildings. China Planning Press, Beijing (2005) (in Chinese). 3. Y. Q. Zheng, Y. F. Yang, H. L. Han. Using ANSYS to analyze the temperature field of steel and concrete composite column. Industrial Construction 36, 74–77 (2006) (in Chinese). 4. Q. G. Li, P. J. Wang, S. C. Jiang. Non-linear finite element analysis of axially restrained steel beams at elevated temperatures in a fire. Journal of Constructional Steel Research 63, 1175–1183 (2007). 5. M. Knobloch, M. Fontana. Strain-based approach to local buckling of steel sections subjected to fire. Journal of Constructional Steel Research 62, 44–67 (2006). 6. Z. M. Lu, B. Q. Hu, J. A. Lu. Fire safety gray relational evaluation for existing buildings. Journal of Wuhan University 5, 62–66 (2004). 7. Y. M. Tian, M. Liu. Comprehensive probability fuzzy evaluation of fire risk for high-rise buildings. China Safety Science Journal 9, 99–103 (2004). 8. L. Gardner, N. R. Baddoo. Fire testing and design of stainless steel structures. Journal of Constructional Steel Research 62, 532–543 (2006). 9. P. S. e Valdir. Determination of the steel fire protection material thickness by an analytical process a simple derivation. Engineering Structures 27, 2036–2043 (2005). 10. GB50017. Code for Design of Steel Structures. China Planning Press, Beijing (2003) (in Chinese). 11. Q. G. Li. Fire Resistance Design of Steel Structure and Steel — Concrete Composite Structure. China Building Industry Press, Beijing (2006) (in Chinese). 12. W. C. Fan, Q. A. Wang. Fire Learning Introductory Tutorial. China University of Science and Technology Press, Hefei (1995) (in Chinese). 13. L. Wu, Y. P. Cheng, L. Li. Research on dormitory fire load of college students. Fire Science and Technology 6, 83–85 (2010) (in Chinese). 14. J. F. Chen. Research on fire temperature estimation method of steel structure. Building Science 5, 67–70 (2010) (in Chinese).
