- Email: [email protected]
Vibration control by damped braces of fire-damaged steel structures subjected to wind and seismic loads
Soil Dynamics and Earthquake Engineering 83 (2016) 53–58
Contents lists available at ScienceDirect
Soil Dynamics and Earthquake Engineering journal homepage: www.elsevier.com/locate/soildyn
Vibration control by damped braces of fire-damaged steel structures subjected to wind and seismic loads Fabio Mazza n, Marco Fiore Dipartimento di Ingegneria Civile, Università della Calabria, Via P. Bucci, Rende, 87036 Cosenza, Italy
art ic l e i nf o
a b s t r a c t
Article history: Received 1 January 2016 Received in revised form 4 January 2016 Accepted 5 January 2016
The aim of the present work is to evaluate the effectiveness of viscoelastic-damped braces (VEDBs) to improve the wind and earthquake responses of fire-damaged steel framed buildings, where a significant reduction of stiffness and strength properties of the structural elements following exposure to fire is highlighted. To this end, a ten-storey steel office building, designed for a low-risk zone under the former Italian seismic code and in line with Eurocodes 1 and 3, is considered as test structure. The dynamic response of the test structure in a no fire situation is compared with what would happen in the event of three fire scenarios, on the assumption that the fire compartment with a uniform temperature is confined to the area of the first (i.e. F1), fifth (i.e. F5) and tenth (i.e. F10) level, with the parametric temperature–time fire curve evaluated in line with Eurocode 1. Two retrofitting structural solutions are examined to upgrade the fire damaged test structures, by inserting diagonal steel braces with or without viscoelastic dampers. Frame members are idealized by a bilinear model, which allows the simulation of the nonlinear behavior under seismic loads, while an elastic linear law is considered for diagonal braces. Finally, viscoelastic dampers are idealized by means of a frequency-dependent model. & 2016 Elsevier Ltd. All rights reserved.
Keywords: Fire-damaged and fire-retrofitted steel structures Viscoelastic damped braces Wind and seismic loads
1. Introduction In the assessment of fire damage to existing structures there is a high degree of uncertainty about the residual load capacity [1]. During fire, steel frame members of earthquake-damaged structures experience loss of load capacity and stiffness, due to hightemperature induced degradation in strength and Young's modulus of elasticity [2]. This behavior can induce geometrical and mechanical fire damage despite the fact that steel recovers much of its initial strength and stiffness after cooling. The main purpose of the present work is to evaluate the effectiveness of the passive energy dissipation devices, attached to the framed structure via a bracing system, for the fire retrofitting of medium-rise steel buildings later subjected to wind and seismic loads. Damped braces available in the literature differ according to the features of the supplementary damping devices [3]. Attention is focused on viscoelastic dampers (VEDs) which are displacement- and velocity-dependent, so ensuring a restoring force and the activation for vibrations of small amplitude [4]. A ten-storey steel office framed building, which was originally designed for a low-risk zone under the former Italian seismic code [5] and in line with the Eurocodes 1 [6] and 3 [7], is considered as n
Corresponding author. E-mail addresses: [email protected] (F. Mazza), fi[email protected] (M. Fiore). http://dx.doi.org/10.1016/j.soildyn.2016.01.003 0267-7261/& 2016 Elsevier Ltd. All rights reserved.
test structure. A numerical fire investigation is preliminarily carried out in the event of three fire scenarios, on the assumption that the fire compartment with a uniform temperature is confined to the area of the first (i.e. F1), fifth (i.e. F5) and tenth (i.e. F10) level. The residual load capacity of the structural members after fire is evaluated considering the reduction factors of stiffness and strength proposed by EC3 [7], at the maximum temperature of the fire compartment (i.e. T ¼600 °C) evaluated by the EC1 time– temperature natural curves corresponding to the design fire load. For each fire scenario, two retrofitting structural solutions are examined to upgrade the test structure damaged by fire: additional diagonal braces; VEDs supported by the additional diagonal braces.
2. Test structure and modeling of the fire A ten-storey office building with a symmetric plan (Fig. 1a), constituted of moment resisting steel frames (Fig. 1b) and steelconcrete composite deck with horizontal bracing, is assumed as test structure [2]. Three fire scenarios are also reported in Fig. 1b, assuming the fire compartment (Fig. 1a) confined to the area of the first (i.e. F1), fifth (i.e. F5) and tenth (i.e. F10) level, where a uniform temperature is considered as fire condition before wind or earthquake.
54
F. Mazza, M. Fiore / Soil Dynamics and Earthquake Engineering 83 (2016) 53–58
Fig. 1. Test structure (units in m). (a) Plan and fire compartment. (b) Elevation and fire scenarios. Table 1 Fire parameters in the EC1 time–temperature curves. T (°C)
600
First level
Upper levels
qf,d (MJ/m2)
b (J/m2 s1/2 K)
t max (h)
qf,d (MJ/m2)
b (J/m2 s1/2 K)
t max (h)
186.21
1671
0.10
198.11
1696
0.10
Fig. 2. Flexural stiffness of columns exposed to fire.
The EC1 parametric fire curve is used in the present study to simulate the time–temperature evolution during an actual fire [6], on the assumption that the fire load of the compartment is completely burnt out. Fire parameters in the EC1 time–temperature curves of the first and upper levels are reported in Table 1: i.e. T, maximum temperature; qf,d, design fire load corresponding to the surface area of the floor; b, thermal absorptivity of surrounding surfaces of the compartment; t max , time when the maximum temperature in the heating phase happens.
3. Fire effects and retrofitting of the test structure The fire-damage effects on the residual capacity of the test structure are evaluated on the basis of the temperature distribution in the frame members, considering the EC1 time–temperature
natural curve of the fire compartment. In accordance with the high thermal conductivity of steel and the thinness of the cross-sections, the assumption of a uniform temperature distribution of T¼ 600 °C is admissible after 60 min for the F1 and F5 fire scenarios and after 45 min for the F10 fire scenario. Then, the residual load capacity of the structural members after fire is evaluated considering the reduction factors of effective yield strength and Young's modulus of elasticity of the steel proposed by EC3. In Fig. 2, flexural stiffness of columns is reported along the building height, assuming a direct correspondence between the examined level (i.e. HE450B, HE300B and HE200B) and the fire compartment (i.e. F1, F5 and F10). In particular, major (i.e. EIy) and minor (i.e. EIz) axes of bending are examined. Note that a decrease in stiffness of about 69% is obtained in comparison with the no-fire condition. Plastic domains between axial load (N) and bending moment (M) of columns are shown in Fig. 3 along the major axis of bending. Fire compartments at the first (i.e. F1), fifth (i.e. F5) and tenth (i.e. F10) levels are compared with the no-fire condition at the ambient temperature T ¼20 °C. Moreover, the N–M domain is obtained in line with EC3, simply by replacing the plastic axial load under uniform compression with the buckling load. A marked narrowing of the N–M domain of about 59% is observed. Further details on the fire damage of girders can be found in [2]. For the purpose of retrofitting the fire-damaged structure, from a low- up to a high-risk seismic zone, and controlling the windinduced vibrations, two structural solutions are examined for each fire scenario: the insertion of diagonal braces at the level where the fire compartment is hypothesized only (AB structure, with “Added Braces”); the insertion of VEDs supported by the additional
F. Mazza, M. Fiore / Soil Dynamics and Earthquake Engineering 83 (2016) 53–58
55
Fig. 3. Plastic N–M domains of columns along major bending axis. (a) Undamaged section. (b) Fire-damaged section.
Fig. 4. Damped Added Braces (DAB) test structure. (a) Plan and fire compartment. (b) Elevation and fire scenarios.
diagonal braces (DAB structure, with “Damped Added Braces”). Damped added braces with stiffness properties able to restore the corresponding initial values at that level, in the no fire condition, are placed in the perimeter frames along both in-plan principal directions (Fig. 4). The main properties of the VEDs are summarized in Table 2, hypothesizing the bracing system much stiffer than the VED which is supported (i.e. KDB ffiK 0D and K ″DB ffi K ″D ). More specifically, for each fire scenario, distribution laws of horizontal storage (KDB,h) and loss (K ″DB;h ) stiffness of the DAB structure are evaluated along the in-plan directions X and Y, given that KDB ¼ KB and K ″DB ¼ 0 in case of the AB structure. Further details can be found in [2,8].
4. Numerical results A computer code for a step-by-step time-domain analysis of framed structures equipped with either braces or VEDBs and subjected to wind or seismic loads is adopted [9]. To account for the inelastic deformation due to the seismic loads, the frame members are idealized by a lumped plasticity model constituted of two components, one elastic-perfectly plastic and the other simply elastic, assuming a hardening ratio of 2%. Sophisticated models are available to describe the brace hysteretic response [10]. In the present work, the response of the additional diagonal braces in the AB structure is simulated by an elastic linear force-displacement law, assuming that the braces collapse when their buckling load is
Table 2 Properties of the VEDBs (units in kN/m). Fire scenario
F1 F5 F10
In-plane X direction
In-plane Y direction
KDB,h ffiK 0D;h
K ″DB;h ffi K ″D;h
KDB,h ffi K 0D;h
K ″DB;h ffi K ″D;h
1.02E05 5.39E04 1.35E04
1.41E05 7.46E04 1.87E04
2.79E04 3.55E04 8.52E03
4.32E04 5.50E04 1.32E04
reached. An elastic-linear law, in tension and compression, is considered for the additional bracing systems supporting the VEDs (i.e. the DAB structure), providing that yielding and buckling be prevented. Moreover, the nonlinear response of the VEDs is simulated by a six-element generalized model, which is a combination of the classical Kelvin and Maxwell models [2,8]. Wind loads are schematized by means of pressure at the floor levels evaluated in line with the equivalent wind spectrum technique [11]. The instantaneous wind velocity for the return period Tr ¼50 years is considered. With regard to the seismic loads, two set of three artificial motions are generated with the computer code SIMQKE [12], for the serviceability (i.e. operational, OP: PGAOP ¼0.124 g) and ultimate (i.e. life-safety, LS: PGALS ¼0.396 g) limit states provided by the current Italian seismic code (NTC08, [13]) in case of high-risk seismic zone and medium subsoil class.
56
F. Mazza, M. Fiore / Soil Dynamics and Earthquake Engineering 83 (2016) 53–58
Fig. 5. Maximum floor displacement for three fire scenarios: wind loads along Y direction.
Fig. 6. Maximum storey drift for three fire scenarios: wind (a,b,c) and seismic (d,e,f) loads along Y direction.
The results are obtained as an average of those separately obtained for each set of three accelerograms. At first, maximum values of floor displacement (umax) under wind loads for Tr ¼50 years are plotted in Fig. 5 along the frame height, comparing steel structures in no-fire condition with fire damaged structures before (i.e. Fi structures, i ¼1,5,10) and after (i.e. AB.Fi and DAB.Fi structures, i¼1,5,10) retrofitting. Three fire scenarios are examined on the assumption that the fire compartment is confined to the area of the first (i.e. F1 scenario, Fig. 5a), fifth (i.e. F5 scenario, Fig. 5b) and tenth (i.e. F10 scenario, Fig. 5c)
levels. A black line reports the deformability limit imposed by EC3 [7] on the top displacement (i.e. 1/500 of the building height). Only results in the weakest (Y) direction of the building plan are reported. As can be observed in Fig. 5a, the maximum top displacement of the fire-damaged F1 structure has exceeded the deformability threshold imposed by EC3. The results also show that the AB.Fi and DAB.Fi structures (i¼1, 5, 10) are both effective in controlling the horizontal displacements. Curves similar to the previous ones are plotted in Fig. 6, where the maximum storey drift (Δmax/h) along the in-plan Y direction is
F. Mazza, M. Fiore / Soil Dynamics and Earthquake Engineering 83 (2016) 53–58
57
Fig. 7. Maximum floor acceleration (a,b,c) and axial force in the columns (d,e,f) for three fire scenarios: wind and seismic loads along X and Y directions, respectively.
compared under wind (Figs. 6a–c) and seismic (Figs. 6d–f) loads, the latter corresponding to the operational limit state (PGAOP ¼0.124 g). A black line also plots the serviceability limit imposed by EC3 with regard to the storey drift (i.e. 1/300 of the storey height) and the analogous damage limitation requirement imposed by NTC08 (i.e. 1/200 of the storey height). Note that the amplification in the structural response of the fire-damaged structures is localized to the level where the fire compartment is hypothesized only, exceeding the deformability (EC3) and damage (NTC08) thresholds, with the exception of the F10 structure under wind loads (Fig. 6c). As can be observed, the fire-retrofitted structures can obtain values of Δmax /h lower than the EC3 (Figs. 6a–c) and NTC08 (Figs. 6d–f) thresholds. The insertion of VEDBs (DAB.Fi structures) is most favorable for all fire scenarios. It is worth noting that a PGA value lower than that considered for the OP limit state (PGAOP ¼0.124 g) can be reached by adopting the AB structure for all three fire scenarios (Figs. 6d–f), because added braces are supposed to collapse when their buckling load is reached. With regard to the control of the maximum floor acceleration (amax) under wind loads, which is expressed as percentage of the gravity acceleration g, results obtained in the stiff direction of the building plan (i.e. the X direction) are plotted in Figs. 7a–c, comparing wind responses of the original, fire-damaged and fireretrofitted structures for three fire scenarios. For the fire damaged structure note that the number of levels where the ISO discomfort threshold [14] is exceeded and the annoyance range is reached decreases when the fire compartment is assumed at the upper levels. The AB structure is not satisfactory to control the maximum floor acceleration in the case of F1 fire scenario (Fig. 7a). On the other hand, the increased damping capacity due to the VEDBs
makes the DAB solution preferable with regard to the control of acceleration, obtaining values of amax lower than the annoyance range in the event of fire at the first (i.e. F1 scenario, Fig. 7a) and fifth (i.e. F5 scenario, Fig. 7b) level. Finally, maximum axial force in the columns under the LS ground motions are shown in Figs. 7d–f along the in-plan Y direction. A black solid line reports the buckling threshold (i.e. Nb,Rd) imposed by EC3 in the no-fire condition, while a dashed black line represents the reduced buckling load of the fire compartment (i.e. Nb,Rd,600 °C). A marked reduction of the buckling load is observed for the three fire scenarios, thereby limiting the maximum peak ground acceleration achievable when the fire compartment is localized on the lower levels (Figs. 7d–f); moreover, fire compartment at the top level (i.e. the F10 scenario in Fig. 7f) does not significantly affect the attainment of the PGA value corresponding to the LS limit state (i.e. PGALS ¼0.396 g). The results for seismic loads also show that the DAB structure is effective in controlling the maximum axial force in the columns, which proves to be well within the buckling threshold imposed by EC3 and often comparable to that corresponding to the no-fire condition. However, a lower level of PGA can be reached by adopting the AB structure for all three fire scenarios.
5. Conclusions For the purpose of retrofitting a fire-damaged steel framed structure from a low up to a high-risk seismic zone and controlling the vibrations under wind loads, additional steel braces acting alone or in combination with VEDs are considered. Amplification in the structural response of the fire-damaged structures is
58
F. Mazza, M. Fiore / Soil Dynamics and Earthquake Engineering 83 (2016) 53–58
localized to the level where the fire compartment concerned, where the deformability (EC3) and damage (NTC08) thresholds are exceeded. The AB.Fi and DAB.Fi structures are both effective in controlling the horizontal floor displacement of the fire-damaged structures under wind loads. The AB.Fi structures prove to be on the whole unsatisfactory under seismic loads, highlighting a PGA value lower than that considered for the OP limit state, because added braces are supposed to collapse when their buckling load is reached. The insertion of VEDBs (i.e. DAB.Fi structures) is the most favorable for all fire scenarios. On the other hand, the increased damping capacity due to the VEDBs makes the DAB.Fi structures preferable to the AB.Fi ones with regard to the control of floor acceleration, obtaining values below the annoyance range in the F1 and F5 fire scenarios. Finally, a marked reduction of the buckling load is found for the three fire scenarios under the LS ground motions but the DAB.Fi structures are effective in controlling the maximum axial force in the columns, which proves to be well within the buckling threshold imposed by EC3 and oftencomparable to that corresponding to the no-fire condition. Moreover, a lower level of peak ground acceleration at the LS limit state can be reached adopting the AB structure for all fire scenarios.
References [1] Della Corte G, Landolfo R, Mazzolani FM. Post-earthquake fire resistance of moment resisting steel frames. Fire Saf J 2003;38:593–612.
[2] Mazza F. Wind and earthquake dynamic responses of fire exposed steel framed structures. Soil Dyn Eng Struct Dyn 2015;78:218–29. [3] Christopoulos C, Filiatrault A. Principles of passive supplemental damping and seismic isolation. Italy: IUSS Press, Istituto Universitario di Studi Superiori di Pavia; 2006. [4] Christopoulos C, Montgomery M. Viscoelastic coupling dampers (VCDs) for enhanced wind and seismic performance of high-rise buildings. Earthq Eng Struct Dyn 2013;42:2217–33. [5] Italian Ministry of Public Works (DM96). Norme tecniche per le costruzioni in zone sismiche e relative istruzioni, D.M. 16-01-1996 and C.M. 10-04-1997, n. 65/AA.GG. [6] Eurocode 1. Actions on structures – Part 1-2: General actions, actions on structures exposed to fire. C. E. N., European Committee for Standardization; October 2004. [7] Eurocode 3. Design of steel structures – Part 1-1: General rules and rules for buildings. Part 1-2: General rules, structural fire design. C. E. N., European Committee for Standardization; December 2005. [8] Mazza F. A. Vulcano, Control of the along-wind response of steel framed buildings by using viscoelastic or friction dampers. Wind Structures 2007;10 (3):233–47. [9] Mazza F. A. Vulcano, Nonlinear dynamic response of r.c. framed structures subjected to near-fault ground motions. Bull Earthq Eng 2010;8:1331–50. [10] D'Aniello M, La Manna Ambrosino G, Portioli F, Landolfo R. Modelling aspects of the seismic response of steel concentric braced frames. Steel Compos Struct Int J 2013;15(5):539–66. [11] Solari G. Equivalent wind spectrum technique: theory and applications. J Struct Eng 1998;114:1303–23. [12] Gasparini D, Vanmarcke E. Simulated earthquake motions compatible with prescribed response spectra. USA: Massachusetts Institute of Technology, Dept. of Civil Eng.; 1976. p. 7. [13] Italian Ministry of Infrastructures (NTC08). Nuove norme tecniche per le costruzioni, D.M.14-01-2008. [14] ISO/TC 98/SC 3 International Standard Organization. Wind loads on structures, Berlin, Germany; 1990.
Contents lists available at ScienceDirect
Soil Dynamics and Earthquake Engineering journal homepage: www.elsevier.com/locate/soildyn
Vibration control by damped braces of fire-damaged steel structures subjected to wind and seismic loads Fabio Mazza n, Marco Fiore Dipartimento di Ingegneria Civile, Università della Calabria, Via P. Bucci, Rende, 87036 Cosenza, Italy
art ic l e i nf o
a b s t r a c t
Article history: Received 1 January 2016 Received in revised form 4 January 2016 Accepted 5 January 2016
The aim of the present work is to evaluate the effectiveness of viscoelastic-damped braces (VEDBs) to improve the wind and earthquake responses of fire-damaged steel framed buildings, where a significant reduction of stiffness and strength properties of the structural elements following exposure to fire is highlighted. To this end, a ten-storey steel office building, designed for a low-risk zone under the former Italian seismic code and in line with Eurocodes 1 and 3, is considered as test structure. The dynamic response of the test structure in a no fire situation is compared with what would happen in the event of three fire scenarios, on the assumption that the fire compartment with a uniform temperature is confined to the area of the first (i.e. F1), fifth (i.e. F5) and tenth (i.e. F10) level, with the parametric temperature–time fire curve evaluated in line with Eurocode 1. Two retrofitting structural solutions are examined to upgrade the fire damaged test structures, by inserting diagonal steel braces with or without viscoelastic dampers. Frame members are idealized by a bilinear model, which allows the simulation of the nonlinear behavior under seismic loads, while an elastic linear law is considered for diagonal braces. Finally, viscoelastic dampers are idealized by means of a frequency-dependent model. & 2016 Elsevier Ltd. All rights reserved.
Keywords: Fire-damaged and fire-retrofitted steel structures Viscoelastic damped braces Wind and seismic loads
1. Introduction In the assessment of fire damage to existing structures there is a high degree of uncertainty about the residual load capacity [1]. During fire, steel frame members of earthquake-damaged structures experience loss of load capacity and stiffness, due to hightemperature induced degradation in strength and Young's modulus of elasticity [2]. This behavior can induce geometrical and mechanical fire damage despite the fact that steel recovers much of its initial strength and stiffness after cooling. The main purpose of the present work is to evaluate the effectiveness of the passive energy dissipation devices, attached to the framed structure via a bracing system, for the fire retrofitting of medium-rise steel buildings later subjected to wind and seismic loads. Damped braces available in the literature differ according to the features of the supplementary damping devices [3]. Attention is focused on viscoelastic dampers (VEDs) which are displacement- and velocity-dependent, so ensuring a restoring force and the activation for vibrations of small amplitude [4]. A ten-storey steel office framed building, which was originally designed for a low-risk zone under the former Italian seismic code [5] and in line with the Eurocodes 1 [6] and 3 [7], is considered as n
Corresponding author. E-mail addresses: [email protected] (F. Mazza), fi[email protected] (M. Fiore). http://dx.doi.org/10.1016/j.soildyn.2016.01.003 0267-7261/& 2016 Elsevier Ltd. All rights reserved.
test structure. A numerical fire investigation is preliminarily carried out in the event of three fire scenarios, on the assumption that the fire compartment with a uniform temperature is confined to the area of the first (i.e. F1), fifth (i.e. F5) and tenth (i.e. F10) level. The residual load capacity of the structural members after fire is evaluated considering the reduction factors of stiffness and strength proposed by EC3 [7], at the maximum temperature of the fire compartment (i.e. T ¼600 °C) evaluated by the EC1 time– temperature natural curves corresponding to the design fire load. For each fire scenario, two retrofitting structural solutions are examined to upgrade the test structure damaged by fire: additional diagonal braces; VEDs supported by the additional diagonal braces.
2. Test structure and modeling of the fire A ten-storey office building with a symmetric plan (Fig. 1a), constituted of moment resisting steel frames (Fig. 1b) and steelconcrete composite deck with horizontal bracing, is assumed as test structure [2]. Three fire scenarios are also reported in Fig. 1b, assuming the fire compartment (Fig. 1a) confined to the area of the first (i.e. F1), fifth (i.e. F5) and tenth (i.e. F10) level, where a uniform temperature is considered as fire condition before wind or earthquake.
54
F. Mazza, M. Fiore / Soil Dynamics and Earthquake Engineering 83 (2016) 53–58
Fig. 1. Test structure (units in m). (a) Plan and fire compartment. (b) Elevation and fire scenarios. Table 1 Fire parameters in the EC1 time–temperature curves. T (°C)
600
First level
Upper levels
qf,d (MJ/m2)
b (J/m2 s1/2 K)
t max (h)
qf,d (MJ/m2)
b (J/m2 s1/2 K)
t max (h)
186.21
1671
0.10
198.11
1696
0.10
Fig. 2. Flexural stiffness of columns exposed to fire.
The EC1 parametric fire curve is used in the present study to simulate the time–temperature evolution during an actual fire [6], on the assumption that the fire load of the compartment is completely burnt out. Fire parameters in the EC1 time–temperature curves of the first and upper levels are reported in Table 1: i.e. T, maximum temperature; qf,d, design fire load corresponding to the surface area of the floor; b, thermal absorptivity of surrounding surfaces of the compartment; t max , time when the maximum temperature in the heating phase happens.
3. Fire effects and retrofitting of the test structure The fire-damage effects on the residual capacity of the test structure are evaluated on the basis of the temperature distribution in the frame members, considering the EC1 time–temperature
natural curve of the fire compartment. In accordance with the high thermal conductivity of steel and the thinness of the cross-sections, the assumption of a uniform temperature distribution of T¼ 600 °C is admissible after 60 min for the F1 and F5 fire scenarios and after 45 min for the F10 fire scenario. Then, the residual load capacity of the structural members after fire is evaluated considering the reduction factors of effective yield strength and Young's modulus of elasticity of the steel proposed by EC3. In Fig. 2, flexural stiffness of columns is reported along the building height, assuming a direct correspondence between the examined level (i.e. HE450B, HE300B and HE200B) and the fire compartment (i.e. F1, F5 and F10). In particular, major (i.e. EIy) and minor (i.e. EIz) axes of bending are examined. Note that a decrease in stiffness of about 69% is obtained in comparison with the no-fire condition. Plastic domains between axial load (N) and bending moment (M) of columns are shown in Fig. 3 along the major axis of bending. Fire compartments at the first (i.e. F1), fifth (i.e. F5) and tenth (i.e. F10) levels are compared with the no-fire condition at the ambient temperature T ¼20 °C. Moreover, the N–M domain is obtained in line with EC3, simply by replacing the plastic axial load under uniform compression with the buckling load. A marked narrowing of the N–M domain of about 59% is observed. Further details on the fire damage of girders can be found in [2]. For the purpose of retrofitting the fire-damaged structure, from a low- up to a high-risk seismic zone, and controlling the windinduced vibrations, two structural solutions are examined for each fire scenario: the insertion of diagonal braces at the level where the fire compartment is hypothesized only (AB structure, with “Added Braces”); the insertion of VEDs supported by the additional
F. Mazza, M. Fiore / Soil Dynamics and Earthquake Engineering 83 (2016) 53–58
55
Fig. 3. Plastic N–M domains of columns along major bending axis. (a) Undamaged section. (b) Fire-damaged section.
Fig. 4. Damped Added Braces (DAB) test structure. (a) Plan and fire compartment. (b) Elevation and fire scenarios.
diagonal braces (DAB structure, with “Damped Added Braces”). Damped added braces with stiffness properties able to restore the corresponding initial values at that level, in the no fire condition, are placed in the perimeter frames along both in-plan principal directions (Fig. 4). The main properties of the VEDs are summarized in Table 2, hypothesizing the bracing system much stiffer than the VED which is supported (i.e. KDB ffiK 0D and K ″DB ffi K ″D ). More specifically, for each fire scenario, distribution laws of horizontal storage (KDB,h) and loss (K ″DB;h ) stiffness of the DAB structure are evaluated along the in-plan directions X and Y, given that KDB ¼ KB and K ″DB ¼ 0 in case of the AB structure. Further details can be found in [2,8].
4. Numerical results A computer code for a step-by-step time-domain analysis of framed structures equipped with either braces or VEDBs and subjected to wind or seismic loads is adopted [9]. To account for the inelastic deformation due to the seismic loads, the frame members are idealized by a lumped plasticity model constituted of two components, one elastic-perfectly plastic and the other simply elastic, assuming a hardening ratio of 2%. Sophisticated models are available to describe the brace hysteretic response [10]. In the present work, the response of the additional diagonal braces in the AB structure is simulated by an elastic linear force-displacement law, assuming that the braces collapse when their buckling load is
Table 2 Properties of the VEDBs (units in kN/m). Fire scenario
F1 F5 F10
In-plane X direction
In-plane Y direction
KDB,h ffiK 0D;h
K ″DB;h ffi K ″D;h
KDB,h ffi K 0D;h
K ″DB;h ffi K ″D;h
1.02E05 5.39E04 1.35E04
1.41E05 7.46E04 1.87E04
2.79E04 3.55E04 8.52E03
4.32E04 5.50E04 1.32E04
reached. An elastic-linear law, in tension and compression, is considered for the additional bracing systems supporting the VEDs (i.e. the DAB structure), providing that yielding and buckling be prevented. Moreover, the nonlinear response of the VEDs is simulated by a six-element generalized model, which is a combination of the classical Kelvin and Maxwell models [2,8]. Wind loads are schematized by means of pressure at the floor levels evaluated in line with the equivalent wind spectrum technique [11]. The instantaneous wind velocity for the return period Tr ¼50 years is considered. With regard to the seismic loads, two set of three artificial motions are generated with the computer code SIMQKE [12], for the serviceability (i.e. operational, OP: PGAOP ¼0.124 g) and ultimate (i.e. life-safety, LS: PGALS ¼0.396 g) limit states provided by the current Italian seismic code (NTC08, [13]) in case of high-risk seismic zone and medium subsoil class.
56
F. Mazza, M. Fiore / Soil Dynamics and Earthquake Engineering 83 (2016) 53–58
Fig. 5. Maximum floor displacement for three fire scenarios: wind loads along Y direction.
Fig. 6. Maximum storey drift for three fire scenarios: wind (a,b,c) and seismic (d,e,f) loads along Y direction.
The results are obtained as an average of those separately obtained for each set of three accelerograms. At first, maximum values of floor displacement (umax) under wind loads for Tr ¼50 years are plotted in Fig. 5 along the frame height, comparing steel structures in no-fire condition with fire damaged structures before (i.e. Fi structures, i ¼1,5,10) and after (i.e. AB.Fi and DAB.Fi structures, i¼1,5,10) retrofitting. Three fire scenarios are examined on the assumption that the fire compartment is confined to the area of the first (i.e. F1 scenario, Fig. 5a), fifth (i.e. F5 scenario, Fig. 5b) and tenth (i.e. F10 scenario, Fig. 5c)
levels. A black line reports the deformability limit imposed by EC3 [7] on the top displacement (i.e. 1/500 of the building height). Only results in the weakest (Y) direction of the building plan are reported. As can be observed in Fig. 5a, the maximum top displacement of the fire-damaged F1 structure has exceeded the deformability threshold imposed by EC3. The results also show that the AB.Fi and DAB.Fi structures (i¼1, 5, 10) are both effective in controlling the horizontal displacements. Curves similar to the previous ones are plotted in Fig. 6, where the maximum storey drift (Δmax/h) along the in-plan Y direction is
F. Mazza, M. Fiore / Soil Dynamics and Earthquake Engineering 83 (2016) 53–58
57
Fig. 7. Maximum floor acceleration (a,b,c) and axial force in the columns (d,e,f) for three fire scenarios: wind and seismic loads along X and Y directions, respectively.
compared under wind (Figs. 6a–c) and seismic (Figs. 6d–f) loads, the latter corresponding to the operational limit state (PGAOP ¼0.124 g). A black line also plots the serviceability limit imposed by EC3 with regard to the storey drift (i.e. 1/300 of the storey height) and the analogous damage limitation requirement imposed by NTC08 (i.e. 1/200 of the storey height). Note that the amplification in the structural response of the fire-damaged structures is localized to the level where the fire compartment is hypothesized only, exceeding the deformability (EC3) and damage (NTC08) thresholds, with the exception of the F10 structure under wind loads (Fig. 6c). As can be observed, the fire-retrofitted structures can obtain values of Δmax /h lower than the EC3 (Figs. 6a–c) and NTC08 (Figs. 6d–f) thresholds. The insertion of VEDBs (DAB.Fi structures) is most favorable for all fire scenarios. It is worth noting that a PGA value lower than that considered for the OP limit state (PGAOP ¼0.124 g) can be reached by adopting the AB structure for all three fire scenarios (Figs. 6d–f), because added braces are supposed to collapse when their buckling load is reached. With regard to the control of the maximum floor acceleration (amax) under wind loads, which is expressed as percentage of the gravity acceleration g, results obtained in the stiff direction of the building plan (i.e. the X direction) are plotted in Figs. 7a–c, comparing wind responses of the original, fire-damaged and fireretrofitted structures for three fire scenarios. For the fire damaged structure note that the number of levels where the ISO discomfort threshold [14] is exceeded and the annoyance range is reached decreases when the fire compartment is assumed at the upper levels. The AB structure is not satisfactory to control the maximum floor acceleration in the case of F1 fire scenario (Fig. 7a). On the other hand, the increased damping capacity due to the VEDBs
makes the DAB solution preferable with regard to the control of acceleration, obtaining values of amax lower than the annoyance range in the event of fire at the first (i.e. F1 scenario, Fig. 7a) and fifth (i.e. F5 scenario, Fig. 7b) level. Finally, maximum axial force in the columns under the LS ground motions are shown in Figs. 7d–f along the in-plan Y direction. A black solid line reports the buckling threshold (i.e. Nb,Rd) imposed by EC3 in the no-fire condition, while a dashed black line represents the reduced buckling load of the fire compartment (i.e. Nb,Rd,600 °C). A marked reduction of the buckling load is observed for the three fire scenarios, thereby limiting the maximum peak ground acceleration achievable when the fire compartment is localized on the lower levels (Figs. 7d–f); moreover, fire compartment at the top level (i.e. the F10 scenario in Fig. 7f) does not significantly affect the attainment of the PGA value corresponding to the LS limit state (i.e. PGALS ¼0.396 g). The results for seismic loads also show that the DAB structure is effective in controlling the maximum axial force in the columns, which proves to be well within the buckling threshold imposed by EC3 and often comparable to that corresponding to the no-fire condition. However, a lower level of PGA can be reached by adopting the AB structure for all three fire scenarios.
5. Conclusions For the purpose of retrofitting a fire-damaged steel framed structure from a low up to a high-risk seismic zone and controlling the vibrations under wind loads, additional steel braces acting alone or in combination with VEDs are considered. Amplification in the structural response of the fire-damaged structures is
58
F. Mazza, M. Fiore / Soil Dynamics and Earthquake Engineering 83 (2016) 53–58
localized to the level where the fire compartment concerned, where the deformability (EC3) and damage (NTC08) thresholds are exceeded. The AB.Fi and DAB.Fi structures are both effective in controlling the horizontal floor displacement of the fire-damaged structures under wind loads. The AB.Fi structures prove to be on the whole unsatisfactory under seismic loads, highlighting a PGA value lower than that considered for the OP limit state, because added braces are supposed to collapse when their buckling load is reached. The insertion of VEDBs (i.e. DAB.Fi structures) is the most favorable for all fire scenarios. On the other hand, the increased damping capacity due to the VEDBs makes the DAB.Fi structures preferable to the AB.Fi ones with regard to the control of floor acceleration, obtaining values below the annoyance range in the F1 and F5 fire scenarios. Finally, a marked reduction of the buckling load is found for the three fire scenarios under the LS ground motions but the DAB.Fi structures are effective in controlling the maximum axial force in the columns, which proves to be well within the buckling threshold imposed by EC3 and oftencomparable to that corresponding to the no-fire condition. Moreover, a lower level of peak ground acceleration at the LS limit state can be reached adopting the AB structure for all fire scenarios.
References [1] Della Corte G, Landolfo R, Mazzolani FM. Post-earthquake fire resistance of moment resisting steel frames. Fire Saf J 2003;38:593–612.
[2] Mazza F. Wind and earthquake dynamic responses of fire exposed steel framed structures. Soil Dyn Eng Struct Dyn 2015;78:218–29. [3] Christopoulos C, Filiatrault A. Principles of passive supplemental damping and seismic isolation. Italy: IUSS Press, Istituto Universitario di Studi Superiori di Pavia; 2006. [4] Christopoulos C, Montgomery M. Viscoelastic coupling dampers (VCDs) for enhanced wind and seismic performance of high-rise buildings. Earthq Eng Struct Dyn 2013;42:2217–33. [5] Italian Ministry of Public Works (DM96). Norme tecniche per le costruzioni in zone sismiche e relative istruzioni, D.M. 16-01-1996 and C.M. 10-04-1997, n. 65/AA.GG. [6] Eurocode 1. Actions on structures – Part 1-2: General actions, actions on structures exposed to fire. C. E. N., European Committee for Standardization; October 2004. [7] Eurocode 3. Design of steel structures – Part 1-1: General rules and rules for buildings. Part 1-2: General rules, structural fire design. C. E. N., European Committee for Standardization; December 2005. [8] Mazza F. A. Vulcano, Control of the along-wind response of steel framed buildings by using viscoelastic or friction dampers. Wind Structures 2007;10 (3):233–47. [9] Mazza F. A. Vulcano, Nonlinear dynamic response of r.c. framed structures subjected to near-fault ground motions. Bull Earthq Eng 2010;8:1331–50. [10] D'Aniello M, La Manna Ambrosino G, Portioli F, Landolfo R. Modelling aspects of the seismic response of steel concentric braced frames. Steel Compos Struct Int J 2013;15(5):539–66. [11] Solari G. Equivalent wind spectrum technique: theory and applications. J Struct Eng 1998;114:1303–23. [12] Gasparini D, Vanmarcke E. Simulated earthquake motions compatible with prescribed response spectra. USA: Massachusetts Institute of Technology, Dept. of Civil Eng.; 1976. p. 7. [13] Italian Ministry of Infrastructures (NTC08). Nuove norme tecniche per le costruzioni, D.M.14-01-2008. [14] ISO/TC 98/SC 3 International Standard Organization. Wind loads on structures, Berlin, Germany; 1990.