Cover page Tite: Coapse Mechanisms of Composite Sab Panes in Fire Authors: Anthony Abu Verotiana Ramanitrarivo Ian Burgess
ABSTRACT The identification of tensie membrane action as a sustainabe, high-capacity oad-bearing mechanism of composite foors under fire conditions has ed to the deveopment of a number of simpified design soutions, because of the unsuitabiity of finite eement anaysis for routine design. Prominent amongst these is the Baiey-BRE method, which predicts composite sab capacity by cacuating the enhancement of its traditiona yied-ine oad capacity due to tensie membrane action. This method assumes that the two-way bending sab pane, composed internay of parae unprotected composite beams, is supported on edges which resist vertica defection. In practice, the protected composite beams which simuate this vertica edge support in fire defect under the combination of heating and oad, and this oss of vertica support induces singe-curvature bending, which eads to an eventua structura faiure by foding of the sab pane. A simpe foding mechanism, which considers the contributions of the interna unprotected beams and the protected edge beams, has been deveoped for isoated sab panes. In the current study the mechanism has been extended to incude the reinforcement in the sab as we as its continuity across the protected edge beams. Structura faiure of the pane depends on the appied oads, the reative beam sizes, their ocations within the buiding, their arrangement in the sab pane considered, the ocation of the sab pane and the severity of fire exposure. These factors are considered in deveoping a number of coapse mechanisms as an additiona check within the Baiey-BRE design method. Comparisons are made with the finite eement software Vucan and other acceptance criteria. Anthony Abu PhD, Lecturer, Department of Civi and Natura Resources Engineering, University of Canterbury, Private Bag 4800, Christchurch 840, New Zeaand Verotiana Ramanitrarivo, Structura Designer, MDCI Concept Industry, 53-55 Rue du Capitaine Guynemer, 92400 Courbevoie, Paris, France Ian Burgess PhD, Professor, Department of Civi and Structura Engineering, University of Sheffied, Sir Frederick Mappin Buiding, Mappin Street, Sheffied S 3JD, United Kingdom
INTRODUCTION Recent advances in structura fire engineering have paved the way for innovation and an increased use of performance-based design, especiay in steeframed buidings. Research and observations of structura behaviour under fire conditions over the past 20 years have shown that oad redistribution and arge defections of parts of the structure at the Fire Limit State are essentia to the surviva of the entire structure. Both accidenta fires and tests on fu-scae buidings have shown that designing composite foors for tensie membrane action yieds considerabe savings in protection costs, and structura stabiity is maintained by taking advantage of this rea buiding behaviour in fire []. Tensie membrane action is a mechanism that produces increased oad-bearing capacity in thin sabs undergoing arge vertica dispacements, in which radia tension in the centra area of a sab induces an equiibrating periphera ring of compression. The conditions necessary for the effective use of this mechanism are two-way bending of the sab and vertica support aong a of its edges. Due to its sef-equiibrating nature, horizonta edge restraint is not required to mobiise tensie membrane action. To optimise composite foors to take advantage of this higher oad capacity in structura fire engineering design, a composite foor is divided into severa fireresisting rectanguar zones of ow aspect ratio, caed sab panes, each usuay comprising a set of parae adjacent unprotected composite beams in the interior of the pane, with edges which primariy resist vertica defection [2]. This vertica support is usuay provided by protected composite beams aong a four edges, and the panes are generay set out to aign with the coumn gridines, as shown in Figure. Unprotected beams (a) Rectanguar Sab Pane Protected beams (b) Square Sab Panes Figure : Rectanguar and square sab panes In fire the unprotected beams ose strength and stiffness rapidy, and their oads are then borne by the concrete sab, which undergoes two-way bending and increases its resistance as its defections increase. At arge defections and high temperatures, the sab pane s capacity is dependent on the tensie strength of the reinforcement, provided sufficient vertica support is avaiabe at the sab pane boundary. The benefits of incorporating tensie membrane action into fire engineering design have inspired the deveopment of severa software packages to hep quantify sab capacities in fire. Whoe-structure behaviour in fire can be modeed in a threedimensiona framework with sophisticated finite eement software (such as Vucan [3], TNO DIANA, ABAQUS and SAFIR) which incorporates geometri and materia noninearity properties of structures. Athough these simuations provide
usefu information on compete oad-deformation and stress deveopment at eevated temperatures, they can be very costy processes; simper methods [2, 4-6] are often preferred for routine design. Prominent among these simpified approaches is the Baiey-BRE Method. It treats sab panes as isoated, because the arge hogging moments which may be generated at the edges at arge defections are assumed to fai the sab reinforcement over the edge beams, eiminating any continuity with adjacent panes. The method anayses the panes on the assumption that the protected edge beams offer sufficient vertica restraint throughout the fire exposure. The imiting condition is the formation of a centra through-depth tensie crack across the short span of the sab, which constitutes a faiure of the integrity of compartmentation rather than a rea structura stabiity faiure. However, a combination of the redistributed appied oads and ong-term therma exposure can cause significant defections of some of the edge beams, resuting in the oss of the sustained doube-curvature, which may ead to a oca structura coapse. Finite eement investigations of composite sab systems have confirmed this, and a simpe foding mechanism has been proposed for isoated panes [7]. This paper extends the proposa to cover reinforcement, sab continuity, and to examine other potentia coapse mechanisms which coud be incorporated into the Baiey-BRE method to make it more robust. COLLAPSE MECHANISMS Structura coapse of a sab can be modeed using pastic foding mechanisms which aow coapse without generating membrane forces in the sab. is not a unified concept. It requires work-baance cacuations for a range of faiure modes, seecting the one which occurs first; this depends on the ayout of the sab and its support conditions. After postuating a faiure mode, the agebraic expressions for externa and interna work done are derived, and equating these unearths the appropriate coapse oad. In fire, the oad intensity is invariant at the Fire Limit State oading. However, the resistance of each structura component varies as its therma exposure changes. For a sab pane, the overa resistance depends on the reative temperatures of its components; the sab, its reinforcement, and the protected and unprotected beams. In addition, continuity woud increase the pane s capacity due to the hogging moments generated across the edge beams not invoved in foding. The deveopment therefore cacuates the reduced interna work done due to the therma exposure at each time step, and then compares it with the constant externa work done for a given defection. The point at which the interna work done ceases to exceed the externa work done defines faiure of the pane, and hence the faiure time. Figure 2 presents a summary of the mechanisms discussed in this paper:. Coapse Mechanism is for the isoated sab pane case. 2. Coapse Mechanism 2 foows the principes of the isoated pane, but incudes continuity across two opposite sides of the sab pane. Athough
uncommon, this type of faiure occurs in arge compartments, such as open-pan offices, where the fire can cover very arge areas. 3. Coapse Mechanism 3 is appropriate to sab panes at the edge of a buiding, subjected to fires which are oca to that compartment. 4. Coapse Mechanism 4 woud cover a simiar fire exposure scenario, but resuting in a different response of the sab pane, due to its ocation and the reative sizes of its beams. 2 4 3 Protected secondary beams Unprotected secondary beams Protected primary beams Fod ines Pastic hinges L 2 Figure 2: Proposed Coapse mechanisms These simpified mechanisms have been verified with Vucan [3], and checked against the Baiey-BRE Limit and the conventiona span/20 defection imit. The design data for the exampe case are: dead oad = 4.33kN/m 2 ; ive oad = 5.0kN/m 2 ; trapezoida decking profie with a trough depth of 60mm; overa sab thickness of 30mm, and a concrete cube strength of 40N/mm 2. The foor beams were designed to BS5950 Parts 3 and 8, and the edge beams were protected to reach a maximum temperature of 550 C at 60min Standard Fire exposure. Two sab pane sizes (9m x 9m and 2m x 9m, with properties isted in Tabe ) were used for the verification. Intermediate secondary beams were spaced at 3m. Tabe : Sab pane design data Sab Pane Size Beam Type Beam Section Load Ratio Temperature at 60 minutes Span (m) 9m x 9m Intermediate 305 x 27 x 48 UB 0.47 940 C 9 Secondary 356 x 7 x 67 UB 0.442 550 C 9 Primary 533 x 20 x 0 UB 0.446 548 C 9 2m x 9m Intermediate 457 x 52 x 67 UB 0.470 94 C 9 Secondary 406 x 78 x 67 UB 0.443 548 C 9 Secondary 2 533 x 20 x 0 UB 0469 550 C 9 Primary 60 x 305 x 79 UB 0.47 547 C 2
Vertica defection [mm] In the equations that foow, the foowing notation is used: L ength of primary beam ength of secondary beam w appied foor oad at the fire imit state w eff effective width of composite beam δ maximum defection of the sab (or beams) θ beam or sab rotation M pp pastic moment capacity of the protected primary beam at time t M ps pastic moment capacity of the protected secondary beam at time t M u pastic moment capacity of the unprotected beam at time t m + sagging moment capacity of the sab m - hogging moment capacity of the sab n number of intermediate unprotected beams in the sab pane Coapse Mechanism (see Figure 2) 0-200 Reative faiure times A252-400 span/20 A393-600 -800 BRE Limit A93-000 0 5 30 45 60 75 90 Time [min] Figure 3: Coapse mechanism - comparisons Foding across secondary beams: wl 8 2 M ps 4nM u 4m L n w 0 eff () Foding across primary beams: wl 8 4 0 2 M pp m (2) L L In the equations above, the pastic capacities of the composite beams incude the contribution of the reinforcement in the sab which forms the upper fange. The term (L-(n+)w eff ) therefore accounts for the parts of the reinforced concrete sab which do not form parts of the effective upper fange widths.
Vertica defection [mm] Figure 3 shows a snapshot from the Vucan anaysis of the singe-curvature foding of the isoated 9m x 9m sab pane. Foowing from the previous study [7] the anaysis was conducted with 3 mesh sizes A93, A252 and A393 (93, 252 and 393 mm 2 /m in each direction, respectivey). It is observed that the mesh size infuences the faiure time a feature which is picked up by the improved proposa. The 4 vertica ines in the pot signify the faiure times without reinforcement (73min), with A93 (75min), A252 (76min) and A393 (77min) respectivey from eft to right. Coapse Mechanism 2 (see Figure 2) Faiure across secondary beams: wl 8 2 M ps 4nM u 4m L n w 4m L 0 eff (3) 0-200 -400 span/20 Defection of protected secondary beam Faiure Time -600-800 BRE Limit Defection of centre Faiure across primary beams: -000 0 5 30 45 60 75 90 Figure 4: Coapse Mechanism 2 - comparisons m m 0 Time [min] wl 8 4 2 M pp (4) L L Assumptions made in the determination of hogging moments due to the reinforcement are:. The rebar breaks prematurey (the Baiey assumption), which resuts in either isoated sab panes or a free-edge condition. 2. The net compressive force acts at the centroid of the connection (possiby the beam centroid if primary and secondary beams have the same crosssection). For the anayses discussed here it is assumed that the net compression is at the centroid of the unprotected stee I-beam. 3. The bottom fange of the secondary beam contacts the web of the primary beam.
Vertica defection [mm] A verification of Coapse Mechanism 2 is shown in Figure 4. The Vucan anaysis on the eft is of two bays of 9m x 9m sab panes, with continuity across one edge of primary beams. This simuates a fire in a arge compartment in the outer bays of a buiding. The graph on the right shows defections of the centre of the 9m x 9m sab pane and the protected secondary beam between the two panes. It is observed that, due to the redistribution of oads that takes pace, couped with therma exposure, the protected beam defection runs away, resuting in another singe-curvature faiure. The proposed coapse mechanism is seen to give a good approximation of the faiure time (82min) of the muti-bay mode. Coapse Mechanism 3 (see Figure 2) Faiure of protected secondary beam: 4M ps 4nM u 4m wl 3 4m L 2m m 0-400 L L n w eff 0 Defection of protected secondary beam span/20 (5) -800-200 BRE Limit Defection of -600 centre Predicted Faiure Time -2000 0 30 60 90 20 50 80 20 240 Time [min] Faiure of protected primary beam: Figure 5: Coapse Mechanism 3 - comparisons 4M wl 3 m pp 4 m L m L n w eff m L L 0 (6) A comparison of defections of the 2m x 9m Vucan mode and the imiting defections is shown in Figure 5. Reative to the span/20 criterion, the sab pane fais at about 25min, whie the Baiey-BRE imit suggests the pane can adequatey survive a 20min exposure to the standard fire. However, the defection-time pot
shows no cear sign of faiure unti about 50min into the fire when the defections of the centres of both the pane and the edge beam acceerate. The proposed coapse mechanism gives a very conservative prediction. In the derivations so far, the fod ines have been perpendicuar to the orientation of either the faiing secondary or primary beams. In this particuar case, they are at an ange, and coud especiay infuence the capacities of the unprotected beams. The Vucan modes show a twisting of the unprotected beams at the pastic hinges; the next update of these coapse mechanisms wi expore the possibiity of incorporating this in the method to improve predictions. Coapse Mechanism 4 (see Figure 2) Coapse Mechanism 4 is proposed to predict the faiure of corner panes. The aim is to determine the infuence of different support conditions and beam sizes on sab pane faiure. The suggested faiure mechanism is shown in Figure 2. However, comparisons using the numerica modes has shown faiure modes simiar to those of isoated sab panes, foding in singe-curvature directy across secondary beams, regardess of the support conditions at the edges of the pane. More investigation wi be carried out to ascertain this and evauate how aspect ratios infuence this behaviour. CONCLUSION A number of coapse mechanisms have been proposed for incusion into the Baiey-BRE Method to act as an extra check against structura coapse, as distinct from the compartment integrity faiure on which the existing method is based. Two of the proposas, for isoated panes and for arge compartments, give accurate predictions, but those for edge panes and panes in the corner of a buiding require improvement. In the study, the effects of coumns were not considered. The presence of coumns wi provide some axia restraint to the beams and the sab panes as a whoe. Depending on the oads on the beams attached to the coumns and the coumns themseves, couped with fire severity, the beams coud fai, puing the coumns inwards which coud potentiay fai due to p-δ effects. This is however a subject for future research. REFERENCES. Newman, G. M., Robinson, J. T. and Baiey, C. G., Fire Safe Design: A New Approach to Muti-Storey Stee-Framed Buidings, Second Edition, SCI Pubication P288, The Stee Construction Institute, UK, 2006 2. Baiey, C. G., Design of Stee Structures with Composite Sabs at the Fire Limit State, Fina Report No. 845, prepared for DETR and SCI, The Buiding Research Estabishment, Garston, UK. 2000 3. Huang, Z., Burgess I. W. and Pank R. J., Modeing membrane action of concrete sabs in composite sabs in fire. I: Theoretica Deveopment, ASCE Journa of Structura Engineering, 29 (8), 2003, p093-02
4. Cameron, N. J. K. and Usmani, A. S. (2005a) New design method to determine the membrane capacity of ateray restrained composite foor sabs in fire; Part : Theory and method, The Structura Engineer 83 (9), 28-33 5. Omer, E., Izzudin, B. A. and Eghazoui, A. Y. (2006), Faiure assessment of simpy supported foor sabs under eevated temperature Structura Engineering Internationa 6 (2), 48-55 6. Li, G. Q., Guo, S. X. and Zhou, H. S. (2007) Modeing of membrane action in foor sabs subjected to fire, Engineering Structures 29, 880-887 7. Abu A. K., Burgess I. W. and Pank R. J. (2008). Effects of edge support and reinforcement ratios on sab pane faiure in fire, Proceedings of the 5 th Structures in Fire Conference, Singapore, 380-39