Behaviour of composite frames with castellated steel beams at elevated temperatures

Abstract

The behaviour of composite frames with castellated steel beams at elevated temperatures is investigated, and the results obtained were compared with the companion results of simply supported composite castellated steel beams. Overall, it is aimed to investigate the effect of axial and rotational restraining of the steel beam via rigid connections with protected steel columns at elevated temperatures. A previously reported finite element model for the analysis of composite beams in fire was extended to perform the nonlinear analyses of composite frames at elevated temperatures. The finite element model has accounted for the frame geometries and boundary conditions, nonlinear material properties of steel, concrete, profiled steel sheeting, longitudinal and lateral reinforcement bars as well as shear connection behaviour at ambient and elevated temperatures. The thermal properties at the steel beam top flange/profiled steel sheeting and profiled steel sheeting/concrete elements interfaces were considered in the thermal heat transfer analysis that allowed the temperatures to be accurately predicted in the composite slab during fire exposure. The comparison of composite frames and composite beams behaviour has shown that if the columns were sufficiently protected and the connection maintained its rigidity during fire exposure, such that it can restrain the composite beam thermal expansions, this would result in considerable reduction in fire resistances of the composite frames compared with that of simply supported composite beams. This is attributed to the premature failure at elevated temperatures due to local buckling at the bottom flange of the steel beams in the frame connections. Furthermore, the variables that influence the fire resistance and behaviour of the composite frames comprising different load ratios during fire, different fire curves, presence of web openings and different steel grades were investigated by parametric studies. It is shown that the strength of steel and the fire scenarios have a considerable effect on the time–displacement behaviour and fire resistances of the composite frames.

Keywords

castellated composite frames elevated temperatures profiled steel sheeting restrained unprotected

Introduction

Structural performance of composite beams in multistorey steel frame buildings at elevated temperatures has been extensively investigated experimentally and numerically. The early investigations were reported by Bentley et al. (1995a, 1995b), Najjar and Burgess (1996), Lennon (1996), O’Connor and Martin (1998), Bailey et al. (1999), Bailey and Moore (2000a, 1995b), Huang et al. (2000), Elghazouli et al. (2000), Elghazouli and Izzuddin (2001), Huang et al. (2002, 2003a, 2003b), Lamont et al. (2004) and by other researchers. The investigations have described the whole building behaviour and structural fire design of steel-framed structures based on real fire conditions as well as full-scale fire tests. In addition, the behaviour of individual composite beams and composite beams in single-storey buildings under fire conditions was investigated by Zhao and Kruppa (1997) and Wald et al. (2006), respectively. Furthermore, finite element models were developed highlighting the structural performance of cellular steel beams at ambient temperatures by Durif et al. (2014) and at elevated temperatures by Wang et al. (2014, 2015). Finally finite element models were developed for composite cellular steel beams under fire conditions mainly by Nadjai et al. (2007), Vassart et al. (2010) and Bihina et al. (2013). Extensive review on fire tests has been recently presented by Bisby et al. (2013). The aforementioned literature review has shown that, to date, investigations detailing the behaviour of restrained composite beams under fire conditions are rarely found in the literature. In addition, there is no study reported in the literature that highlighted nonlinear three-dimensional (3D) finite element modelling of composite frames with castellated steel beams including shear stud exposed to different fire conditions, hence leading to the current investigation. Looking at a whole building, the behaviour of a heated composite beam under fire conditions is affected by the adjacent cool structural members. The cool structural elements would act as a restraint to thermal expansion. Hence, when a whole building is exposed to fire, it is important to investigate the restraint condition. However, studying retrained structural elements under fire conditions requires special care to apply restraining actions and to maintain these actions during fire tests. Therefore, only limited investigations were found in the literature that investigated the behaviour of restrained composite frames, which is also addressed in this study.

The nonlinear behaviour of a fire test subject to high restraint was investigated by Huang et al. (2001). The study introduced the application of VULCAN software for the analysis of steel-framed buildings in fire. It was showed that when composite beams are subjected to severe fire conditions such that the steel beam temperatures exceed 400°C, the shear connection is lost and the slab separates from the steel beam and only contributes to the thermal curvature of the composite beam. It was also showed that the VULCAN simulates the behaviour of a composite steel-framed building by an assembly of finite beam–column, spring, shear connector and slab elements. The beam–columns are represented by two-noded line elements. The shear connection is represented by link elements. Liu et al. (2002) investigated the behaviour of axially restrained steel beams in fire. The study presented an experimental programme conducted at the University of Manchester. The experimental programme comprised 20 fire tests on steel frames with the two types of beam-to-column connections. The load ratios during fire ranged from 0.3 to 0.7. The bottom flange temperature–mid-span deflection and bottom flange temperature–hogging moment relationships and failure modes were observed in the fire tests. The main failure mode observed in the tests was local buckling at the bottom flange of the steel beams. Yin and Wang (2004) presented a finite element analysis using ABAQUS software highlighting the large deflection behaviour of steel beams with different elastic axial and rotational restraints. The S4R shell elements available in the ABAQUS element library were used to simulate the steel beams. The boundary conditions investigated comprised fully axially restrained beams with lateral restraints, laterally restrained beams with different levels of axial restraint and laterally and axially restrained beams with different levels of rotational restraint. The study has shown that axial restraints result in catenary action for the steel beam provided that the restraining structure is able to sustain the catenary forces applied to the beams. Wong (2005) presented an analytical method for evaluating the failure temperature for steel beams in fire in multistorey buildings. The study showed that the limiting temperature of restrained steel beams exposed to fire may be reduced by 50%. The axial restraints were simulated using spring elements with variable stiffness. It was also shown that the limiting temperatures may increase if the beam is allowed to deflect up to 1/20 the effective beam length. Li et al. (2007) presented analytical study highlighting the nonlinear behaviour of restrained steel beams at elevated temperatures. The analytical method was based on the axis arc-length and section rotation. The method was used to analyse an elastic restrained steel beam heated under different load ratios and having different axial restraint stiffness. Li and Guo (2008) presented an experimental investigation on two axially restrained steel beams in fire during heating and cooling phases. It was showed that axially restrained steel beams could perform better in fire compared with isolated steel beams provided that axial restraining force can be maintained during fire exposure. It was also shown that after the fire exposure, a larger tension force was produced in the restrained steel beams by contraction as the temperature decreased. In addition, local buckling at the bottom flange of the beams near the ends was observed in the fire tests. Santiago et al. (2008) presented a numerical study highlighting the structural performance of a beam-to-column assembly under fire. A parametric study on sub-frame assemblies was performed, which showed the behaviour of the sub-frame assemblies is dependent on the joint characteristics and the degree of force redistribution that occurred as the fire progressed. Dai et al. (2010) presented a numerical study on restrained steel beam–column assemblies having different joints. The failure modes of weld fracture and bolt thread stripping were not simulated because they were not included in the ABAQUS models. It was shown that generally good agreement was achieved between the experimental and numerical results. Sun et al. (2012) investigated progressive collapse mechanisms of braced two-dimensional steel-framed structures at elevated temperatures. The study showed the pull-in of columns was one of the main factors which generated progressive collapse. It was also shown that stronger vertical bracing systems redistributed load from a buckled column to its surrounding structural members.

Detailed finite element modelling of composite beams with web openings and profiled steel sheeting at ambient and elevated temperatures was rarely found in the literature due to the complexity in modelling shear connection and the lack of information reported in the literature, the contribution of the concrete slab to the local bending caused by the shear forces in the sections above and below the openings, the so-called Vierendeel action, partial shear connection, web buckling (WB) and web yielding (WY) at the opening regions, nonlinear material behaviour of the composite beam components as well as interaction of moment and shear at the openings at ambient and elevated temperatures. This complicated structural behaviour was recently addressed by nonlinear finite element analyses presented by Ellobody and Young (2015a, 2015b). In the studies, the behaviour of simply supported beams with profiled steel sheeting oriented transversely to the steel beams and with large stiffened and unstiffened web openings was addressed at ambient temperature. In addition, the behaviour of simply supported composite beams with castellated steel beams and profiled steel sheeting was modelled and verified at elevated temperatures. The study at elevated temperatures used a nonlinear 3D finite element approach for the analysis of different structures under fire conditions as detailed by Ellobody and Bailey (2008, 2009, 2011), Ellobody and Young (2010) and Ellobody (2013). In these investigations, uncoupled thermal heat transfer and structural–thermal analyses were performed to determine the temperature distributions within the structural members at elevated temperatures, time–displacement relationships, failure modes and fire resistances. This nonlinear finite element approach was extended in this study to investigate the structural performance of composite frames with castellated steel beams and with profiled steel sheeting exposed to different fire conditions.

The main objective of this study is to extend the finite element approach detailed by Ellobody and Bailey (2008, 2009, 2011), Ellobody and Young (2010, 2011) and Ellobody (2013) to study the structural performance of composite frames with castellated and noncastellated steel beams with profiled steel sheeting under fire conditions. The extended models have carefully considered the frame geometries and boundary conditions, nonlinear material properties of steel, concrete, profiled steel sheeting, longitudinal and lateral reinforcement bars as well as shear connection behaviour at ambient and elevated temperatures. The software ABAQUS (2013) was used to perform the finite element analyses. The time–temperature relationships, deformed shapes at failure, time–vertical displacement relationships, failure modes and fire resistances of the composite frames were evaluated by the extended finite element models and compared against the companion simply supported composite beams with castellated steel beams previously reported by Ellobody and Young (2015b), with detail discussions and critical analyses presented.

Finite element modelling of simply supported composite beams with castellated and noncastellated steel beams at elevated temperatures

Figure 1 shows the finite element mesh and general layout of the simply supported composite castellated steel beam modelled in Ellobody and Young (2015b) at elevated temperatures. The finite element modelling approach, detailed by Ellobody and Bailey (2008, 2009, 2011), Ellobody and Young (2010) and Ellobody (2013), was used to analyse the composite beams investigated by Wald et al. (2010). The details of the finite element model (Figure 1) verification and validation were previously reported in Ellobody and Young (2015b). A combination of 3D solid elements (C3D8 and C3D6) available in ABAQUS (2013) element library were used to model the composite beam components, comprising the steel beam, concrete slab and profiled steel sheeting. A fine mesh was used in the models, see Figure 1, to accurately represent the buckling behaviour in the web of the castellated steel beams. The finite element model simulated the thermal behaviour of composite castellated steel beams during a well-known full-scale fire test conducted on an administrative building in Mokrsko by Wald et al. (2010), commonly known as the ‘Mokrsko fire test’. The steel beams were castellated, as shown as in Figure 1, which was also known as the ‘Angelina beams’ in Wald et al. (2010). The simply supported castellated beams investigated in Ellobody and Young (2015b) had an effective length of 9 m and were cut from an IPE 270 with an overall depth of 395 mm and conformed to steel grade S235 in EC3 (2005). The composite slab (Figure 1) had an effective width of 2 m. The concrete slab had an average density of 2340 kg/m³ and an average compressive cylindrical strength of 32.5 MPa. The composite castellated beams were subjected to fire from underneath under a static load during fire of 5.6 kN/m², with a load ratio of 0.26. The load ratio is defined in this study as the applied load during fire divided by the nominal (unfactored) design load carried by the composite beams at ambient temperature that is determined based on the design rules specified in EC4 (2004). The fire curves in the building Wald et al. (2010) were lower than that of the specified fire curve given in EC1 (2002); therefore, the experimental fire curves were used in simulating the simply supported composite beams as detailed in Ellobody and Young (2015b). The reinforcements used in the concrete slab were located at mid-slab height above the sheeting and comprised a mesh of 5-mm diameter spaced longitudinally and laterally at 100-mm spacing. The headed stud shear connectors used in the tests were 19-mm diameter × 100-mm height.

Figure 1.

Finite element mesh and general layout of the composite castellated steel beam used in the fire test and modelled in Ellobody and Young (2015b).

A thermal 3D finite element analysis was performed for all the simply supported composite castellated and noncastellated steel beams investigated in Ellobody and Young (2015b) using the heat transfer analysis detailed in ABAQUS (2013). The temperature distribution in the composite beams was predicted based on the measured time–temperature curves in the full-scale fire test detailed in Wald et al. (2010) as well as based on the standard (ST) fire curve given in the EC1 (2002). A constant convective coefficient (α_c) of 25 W/m² K was assumed for the exposed surface and 9 W/m² K was assumed for the unexposed surface. The radiative heat flux was calculated using an emissivity (e) value of 0.7. The same convective coefficients and concrete emissivity value were previously used, with reasonable accuracy, as detailed by Ellobody and Bailey (2008, 2009, 2011), Ellobody and Young (2010) and Ellobody (2013). The concrete was modelled using the damaged plasticity model implemented in the ABAQUS (2013). The stress–strain–temperature curves for concrete under compression and tension were based on the reduction factors given in EC4 (2005) as detailed in Ellobody (2011, 2012). The specific heat and thermal conductivity of concrete were calculated according to EC2 (2004) with the measured moisture content considered in the calculation of the specific heat of concrete. The stress–strain curves for the structural steel and reinforcement bars at elevated temperatures were calculated based on the reduction factors given in the EC4 (2005). The specific heat, thermal conductivity and thermal expansion of the structural steel and reinforcement bars were also calculated according to EC4 (2005). Thermal expansion coefficients for concrete with different aggregates were based on linear thermal expansion coefficients as recommended by Klieger and Lamond (1994). To ensure an accurate heat transfer across the steel beam–profiled steel sheeting and profiled steel sheeting–concrete slab interfaces, gap elements were used in the thermal heat transfer analysis and the thermal properties at the interfaces were included in the heat transfer analysis. The thermal properties at the interface comprised gap heat conductance, gap heat generation, gap radiation and friction change at elevated temperatures.

Following the heat transfer analysis, a structural–thermal analysis was performed in two steps for the composite castellated and noncastellated steel beams investigated by Ellobody and Young (2006). In the first step, the composite beams were subjected to the static load at ambient temperature. In the second step, the composite beams were heated using the temperatures predicted from the heat transfer analysis, with the static load remaining constant at all time. The temperatures were applied using the *TEMPERATURE option available in ABAQUS (2013). Since the thermal heat transfer analysis considered the heat at the interfaces among the composite beam components, the temperatures predicted at the element nodes were correctly represented. Therefore, the concrete slab was rigidly connected to the profiled steel sheeting in direction 3-3, as shown in Figure 1, to ensure the transfer of vertical loads from the upper surface of the concrete slab to the supporting steel beams. The shear connection was also carefully represented to allow the transfer of vertical loads from the composite slab to the supporting steel beams, via rigid spring elements, as well as to allow movement at the steel sheeting–top flange surface interface depending on the stiffness of headed shear stud connectors used via spring elements with variable stiffness. The shear stud connector stiffness was evaluated from previous studies by the authors (2006) and reduced with time gradually based on the reduction factors given in Zhao and Kruppa (1997).

Finite element modelling of composite frames with castellated steel beams

Figure 2 shows the finite element mesh and general layout of the finite element model used to analyse the composite frames with castellated steel beams investigated in this study. In the context of this study, the composite frames are defined as steel frames having reinforced concrete slab with profiled steel sheeting. The model is an extension to the finite element model of simply supported composite beams with castellated steel beams, which was previously reported in Ellobody and Young (2015b). The finite element modelling of the castellated steel beam, profiled steel sheeting, reinforced concrete slab, reinforcement bars and shear connections was identical to that of the simply supported beam. The profiled steel sheeting used in the simply supported composite beams investigated in Ellobody and Young (2015b) and in the composite frames investigated in this study had the dimensions shown in Figure 3. The only extensions to the finite element model previously verified and validated in Ellobody and Young (2015b) were the steel columns and beam–column connections. The steel columns were protected HEB 180 columns, which were identical to that used in the fire test in Wald et al. (2010). The beam–column connections at both beam ends were assumed as protected rigid connections via eight high-strength bolts connecting top and bottom steel beam flanges with columns. The steel columns were modelled using a fine mesh of C3D8 solid elements available in ABAQUS (2013) element library. The protected high-strength bolts were modelled using MPC connections, which apply pin-ended constraints at the position of each bolt. MPCs are multi-point constraints provided in ABAQUS (2013) element library to allow for constraints to be imposed between different degrees of freedom of the model. The MPCs can be quite linear, nonlinear and nonhomogeneous. The beam–column connections represented actual axial and rotational restraints, which were similar to that used in practice for the fire test in Wald et al. (2010). The column ends were connected to rigid steel plates representing lower bearing base plates and were modelled using C3D8 solid elements. The rigid bearing base plates were restrained, in directions 1-1 and 3-3 (Figure 2), at four points representing the anchor bolts used in the fire test in Wald et al. (2010) and simulating hinged supports. The composite frame was prevented to displace laterally in direction 2-2 at the lower bearing base plates as well as beam–column top and bottom connections (see Figure 2) simulating lateral bracings, which is identical to that used in practice in the fire test in Wald et al. (2010).

Figure 2.

Finite element mesh and general layout of the composite frame with castellated steel beam investigated in this study.

Figure 3.

Details of the profiled steel sheeting used in this study.

A thermal heat transfer analysis was performed for all the composite frames investigated in this study using the time–temperature curves measured in the test detailed in Wald et al. (2010), the ST fire curve specified in EC1 (2002) and different natural fire curves. The temperatures were predicted from the thermal analysis at different locations in the composite frames. The locations are shown in Figure 4 and comprised the bottom flange hot surface (HS), the mid-concrete slab surface (MS) and top concrete slab surface (TS). Figure 5 shows an example for the temperature contours, plotted by ABAQUS (2013), for the composite frame with castellated steel beam heated using the experimental fire curve detailed in Wald et al. (2010) at the end of fire exposure. The experimental time–temperature curve was predicted at composite beam AS2 in Wald et al. (2010). The temperatures in the castellated steel beam cross section of the composite frame were also predicted and compared against the experimental temperatures. Generally, it can be seen that good agreement has been achieved between the experimental and numerical results at all locations, which gives confidence that the heat in the composite frames is closely representing the actual heat in the fire test. Figure 6 plots the time–temperature curves obtained experimentally and numerically at the bottom flange HS, the MS and the TS as shown in Figure 4. It can be seen that both the experimental and numerical results showed that the bottom flange (HS) reached around 936°C at 59 min of fire exposure as predicted from the finite element analysis compared with 941°C at 58 min observed in the test. It can also be seen that the TS reached a temperature of 81.4°C as predicted from the finite element analysis compared with 87.9°C observed in the test.

Figure 4.

Locations of predicted time–temperature curves in the composite frames with castellated steel beams.

Figure 5.

Temperature contours at the end of fire exposure predicted numerically for the composite frame with castellated steel beam.

Figure 6.

Time–temperature relationships obtained experimentally and numerically on the perforated steel beam for the composite frame with castellated beam AS2.

In the thermal heat transfer analysis, a thermal–structural analysis was performed for all the composite frames investigated in this study. The deformed shapes at failure, fire resistances, time–displacement relationships and failure modes were predicted from the finite element analysis. Figure 7 shows the deformed and undeformed shapes predicted numerically for the composite frame with castellated steel beam AS2 at the end of fire exposure. The principal stresses in direction 1-1 (Figure 7) were also plotted in the figure. Similar to the predicted failure mode for the simply supported beam with castellated steel beam reported in Ellobody and Young (2015b), a combined bottom flange buckling (BFB), WB and pullout (PO) of headed stud shear connector failure due to the loss of shear connection at failure was predicted numerically for the composite frame investigated in this study. However, interestingly, it can be seen that the failure was originated by local buckling of the bottom flange at the end connection with the protected steel column (LB). This is attributed to the axial and rotational restraints provided by the columns via rigid connections. The restraints limited the composite beam thermal expansions resulting in internal compressive stresses in the bottom flange at the end connection. The time–mid-span vertical displacements were also plotted for the composite beam with castellated steel beam AS2 reported in Ellobody and Young (2015b) and the companion composite frame investigated in this study for the purpose of comparison, as shown in Figure 8. It can be seen that failure was predicted numerically for the simply supported composite castellated steel beam at 48.8 min compared with 40.4 min for the companion composite frame. A reduction of 17.2% in the fire resistance was observed due to restrained thermal expansion in the composite frame. The maximum mid-beam span deflection predicted numerically for the simply supported beam was 342.1 mm at failure, while that observed in the composite frame was 70.8 mm. A reduction of 79.3% in the mid-beam span deflections was observed due to restrained thermal expansion in the composite frame.

Figure 7.

Deformed shape (enlarged three times) and stress contours at failure predicted numerically for the composite frame with castellated steel beam.

Figure 8.

Comparison of time–mid-span deflection relationships obtained numerically for the composite beam AS2 and the composite frame with beam AS2.

Parametric study and discussions

Tables 1 and 2 summarise the main parameters investigated in the parametric study, material properties and dimensions of the composite frames with castellated and noncastellated steel beams, respectively. The finite element model shown in Figure 2 was used to perform an extensive parametric study comprising 54 composite frames with castellated and noncastellated steel beams. The main parameters investigated in the parametric study were different fire curves, different load ratios during fire and different steel strengths. The fire curves investigated were the ST fire curve given in EC1 (2002), and two long cool fires (LC1 and LC2) previously used in the studies by Ellobody and Bailey (2008, 2009, 2011), Ellobody and Young (2010) and Ellobody (2013) to represent steel-framed structures with unprotected composite steel beams. The LC1 fire curve reaches 800°C at 97.5 min and cools at 540 min, while LC2 reaches 740°C at 83 min and cools at 363.7 min. The three fire curves used in this study were plotted, as shown in Figure 9. The load ratios investigated were 0.3, 0.4 and 0.5, and the load ratio is defined as the applied load during fire divided by the nominal (unfactored) design strength of the composite beam at ambient temperature determined based on EC4 (2004). The yield stresses and ultimate strengths of the steel investigated were (275 and 430 MPa), (460 and 690 MPa) and (690 and 760 MPa), respectively. The composite frames investigated at elevated temperatures were divided into 18 groups (G1–G18), with each group containing three composite frames denoted CFR and heated under load ratios of 0.3, 0.4 and 0.5. Groups G1–G9 had composite frames with castellated steel beams similar to that in the fire test detailed in Wald et al. (2010), while groups G10–G18 had the companion composite frames, to that in G1–G9, with noncastellated steel beams. Composite frames in groups G1, G4 and G7 were heated using the ST fire curve. Composite frames in groups G2, G5 and G8 were heated using the LC1 fire curve. Composite frames in groups G3, G6 and G9 were heated using the LC2 fire curve. Composite frames in groups G1–G3, G4–G6 and G7–G9 had yield stresses (f_y) and ultimate strengths (f_u) of the steel (275 and 430 MPa), (460 and 690 MPa) and (690 and 760 MPa), respectively. All the composite castellated and noncastellated steel frames had the steel beam and concrete slab dimensions as those in the fire test detailed in Wald et al. (2010). Furthermore, the headed shear stud connector, and the transverse and longitudinal reinforcement bars were identical to that used in the fire test. In addition, all the composite frames investigated had concrete slab cylinder strength (f_c) of 32.5 MPa, which is also identical to the fire test.

Table 1.

Composite frames with castellated steel beams investigated in the parametric study and having profiled steel sheeting oriented transversely to the steel beam.

Group	Composite frame	Fire curve	Load ratio	Beam web	Composite frame		Concrete	Steel beam
					L_eff (mm)	B_eff (mm)	f_c (MPa)	f_y (MPa)	f_u (MPa)
	CFR1	ST	0.3	Castellated	9000	2000	32.5	275	430
G1	CFR2	ST	0.4	Castellated	9000	2000	32.5	275	430
	CFR3	ST	0.5	Castellated	9000	2000	32.5	275	430
	CFR4	LC1	0.3	Castellated	9000	2000	32.5	275	430
G2	CFR5	LC1	0.4	Castellated	9000	2000	32.5	275	430
	CFR6	LC1	0.5	Castellated	9000	2000	32.5	275	430
	CFR7	LC2	0.3	Castellated	9000	2000	32.5	275	430
G3	CFR8	LC2	0.4	Castellated	9000	2000	32.5	275	430
	CFR9	LC2	0.5	Castellated	9000	2000	32.5	275	430
	CFR10	ST	0.3	Castellated	9000	2000	32.5	460	530
G4	CFR11	ST	0.4	Castellated	9000	2000	32.5	460	530
	CFR12	ST	0.5	Castellated	9000	2000	32.5	460	530
	CFR13	LC1	0.3	Castellated	9000	2000	32.5	460	530
G5	CFR14	LC1	0.4	Castellated	9000	2000	32.5	460	530
	CFR15	LC1	0.5	Castellated	9000	2000	32.5	460	530
	CFR16	LC2	0.3	Castellated	9000	2000	32.5	460	530
G6	CFR17	LC2	0.4	Castellated	9000	2000	32.5	460	530
	CFR18	LC2	0.5	Castellated	9000	2000	32.5	460	530
	CFR19	ST	0.3	Castellated	9000	2000	32.5	690	760
G7	CFR20	ST	0.4	Castellated	9000	2000	32.5	690	760
	CFR21	ST	0.5	Castellated	9000	2000	32.5	690	760
	CFR22	LC1	0.3	Castellated	9000	2000	32.5	690	760
G8	CFR23	LC1	0.4	Castellated	9000	2000	32.5	690	760
	CFR24	LC1	0.5	Castellated	9000	2000	32.5	690	760
	CFR25	LC2	0.3	Castellated	9000	2000	32.5	690	760
G9	CFR26	LC2	0.4	Castellated	9000	2000	32.5	690	760
	CFR27	LC2	0.5	Castellated	9000	2000	32.5	690	760

ST: standard; LC: long cool fire.

Table 2.

Composite frames with noncastellated steel beams investigated in the parametric study and having profiled steel sheeting oriented transversely to the steel beam.

Group	Composite frame	Fire curve	Load ratio	Beam web	Composite frame		Concrete	Steel beam
					L_eff (mm)	B_eff (mm)	f_c (MPa)	f_y (MPa)	f_u (MPa)
	CFR28	ST	0.3	Noncastellated	9000	2000	32.5	275	430
G10	CFR29	ST	0.4	Noncastellated	9000	2000	32.5	275	430
	CFR30	ST	0.5	Noncastellated	9000	2000	32.5	275	430
	CFR31	LC1	0.3	Noncastellated	9000	2000	32.5	275	430
G11	CFR32	LC1	0.4	Noncastellated	9000	2000	32.5	275	430
	CFR33	LC1	0.5	Noncastellated	9000	2000	32.5	275	430
	CFR34	LC2	0.3	Noncastellated	9000	2000	32.5	275	430
G12	CFR35	LC2	0.4	Noncastellated	9000	2000	32.5	275	430
	CFR36	LC2	0.5	Noncastellated	9000	2000	32.5	275	430
	CFR37	ST	0.3	Noncastellated	9000	2000	32.5	460	530
G13	CFR38	ST	0.4	Noncastellated	9000	2000	32.5	460	530
	CFR39	ST	0.5	Noncastellated	9000	2000	32.5	460	530
	CFR40	LC1	0.3	Noncastellated	9000	2000	32.5	460	530
G14	CFR41	LC1	0.4	Noncastellated	9000	2000	32.5	460	530
	CFR42	LC1	0.5	Noncastellated	9000	2000	32.5	460	530
	CFR43	LC2	0.3	Noncastellated	9000	2000	32.5	460	530
G15	CFR44	LC2	0.4	Noncastellated	9000	2000	32.5	460	530
	CFR45	LC2	0.5	Noncastellated	9000	2000	32.5	460	530
	CFR46	ST	0.3	Noncastellated	9000	2000	32.5	690	760
G16	CFR47	ST	0.4	Noncastellated	9000	2000	32.5	690	760
	CFR48	ST	0.5	Noncastellated	9000	2000	32.5	690	760
	CFR49	LC1	0.3	Noncastellated	9000	2000	32.5	690	760
G17	CFR50	LC1	0.4	Noncastellated	9000	2000	32.5	690	760
	CFR51	LC1	0.5	Noncastellated	9000	2000	32.5	690	760
	CFR52	LC2	0.3	Noncastellated	9000	2000	32.5	690	760
G18	CFR53	LC2	0.4	Noncastellated	9000	2000	32.5	690	760
	CFR54	LC2	0.5	Noncastellated	9000	2000	32.5	690	760

ST: standard; LC: long cool fire.

Figure 9.

Different fire curves used in the parametric study.

A thermal heat transfer analysis was performed for all the composite frames with castellated and noncastellated steel beams investigated in the parametric study and heated using the ST, LC1 and LC2 fire curves. Figure 10 shows the time–temperature curves plotted for the composite frames with castellated steel beams in groups G1–G3. It should be noted that the thermal analysis was performed for the ST fire curve up to 65 min since failure of the composite frame was expected during that period. On the other hand, the thermal analysis was performed for the whole fire duration for the composite frames heated using the LC curves. The time–temperature curves were predicted from the thermal analysis and plotted at mid-composite frame span at the bottom flange HS (HS in Figure 4), at the MS (MS in Figure 4) and at the TS (TS in Figure 4). Following the thermal heat transfer analysis, a structural–thermal analysis was conducted for all the composite frames with castellated and noncastellated steel beams investigated in the parametric study. The fire resistances, maximum mid-span deflections, failure modes and time–vertical displacement relationships were predicted from the finite element analysis. Tables 3 and 4 summarise the finite element results for composite frames with castellated steel beams (groups G1–G9) and noncastellated steel beams (groups G10–G18) steel beams, respectively.

Figure 10.

Time–temperature relationships of the composite frames with castellated steel beams in groups G1–G3 and heated using different fire curves.

Table 3.

Comparison of composite castellated frame and simply supported composite castellated beam behaviour under fire conditions as predicted from finite element analysis.

Group	Composite frame	Composite frame			Simply supported composite beam			Frame/beam
		Fire resistance (min.)	Max. deflection (mm)	FM	Fire resistance (min.)	Max. deflection (mm)	FM	Fire resistance
	CFR1	14.5	−100.3	FM 1+LB	27.0	−558.1	FM 1	0.54
G1	CFR2	13.4	−123.0	FM 1+LB	20.0	−590.1	FM 1	0.67
	CFR3	12.7	−148.3	FM 1+LB	17.3	−657.2	FM 1	0.73
	CFR4	37.1	−92.5	FM 1+LB	81.2	−524.0	FM 1	0.46
G2	CFR5	28.9	−114.3	FM 1+LB	60.2	−612.8	FM 1	0.48
	CFR6	25.0	−140.0	FM 1+LB	47.9	−661.9	FM 1	0.52
	CFR7	42.1	−92.6	FM 1+LB	363.7	−452.4	–	–
G3	CFR8	33.8	−112.9	FM 1+LB	64.8	−614.1	FM 1	0.52
	CFR9	29.3	−138.4	FM 1+LB	52.0	−664.0	FM 1	0.56
	CFR10	14.7	−91.5	FM 1+LB	28.2	−296.8	FM 1	0.52
G4	CFR11	13.7	−104.9	FM 1+LB	25.8	−504.2	FM 1	0.53
	CFR12	13.2	−118.8	FM 1+LB	18.6	−560.8	FM 1	0.71
	CFR13	42.7	−83.6	FM 1+LB	80.1	−359.9	FM 1	0.53
G5	CFR14	33.7	−97.0	FM 1+LB	77.2	−516.3	FM 1	0.44
	CFR15	27.9	−111.8	FM 1+LB	54.4	−571.7	FM 1	0.51
	CFR16	47.5	−85.1	FM 1+LB	363.7	−341.8	–	–
G6	CFR17	39.2	−97.3	FM 1+LB	363.7	−487.4	–	–
	CFR18	33.1	−111.9	FM 1+LB	59.0	−573.2	FM 1	0.56
	CFR19	16.9	−99.4	FM 2+LB	26.9	−246.5	FM 2	0.63
G7	CFR20	15.7	−115.9	FM 2+LB	26.8	−363.3	FM 2	0.59
	CFR21	14.9	−129.8	FM 2+LB	25.8	−489.0	FM 2	0.58
	CFR22	53.5	−95.0	FM 2+LB	81.2	−249.3	FM 2	0.66
G8	CFR23	46.6	−110.0	FM 2+LB	81.2	−375.5	FM 2	0.57
	CFR24	40.2	−122.0	FM 2+LB	77.3	−522.6	FM 2	0.52
	CFR25	57.7	−96.6	FM 2+LB	363.7	−269.9	–	–
G9	CFR26	50.6	−108.7	FM 2+LB	363.7	−386.8	–	–
	CFR27	44.6	−122.1	FM 2+LB	363.7	−505.2	–	–
Mean	–	–	–	–	–	–	–	0.56
COV	–	–	–	–	–	–	–	0.139

FM: failure mode; COV: coefficient of variation; TFB: top flange buckling; BFB: bottom flange buckling; BFY: bottom flange yielding; WB: web buckling; WY: web yielding; PO: pullout; CC: concrete crushing.

FM 1: TFB+BFB+BFY+WB+WY+PO.

FM 2: TFB+BFB+BFY+WB+WY+PO+CC.

Table 4.

Comparison of composite noncastellated frame and simply supported composite noncastellated beam behaviour under fire conditions as predicted from finite element analysis.

Group	Composite frame	Composite frame			Simply supported composite beam			Frame/beam
		Fire resistance (min.)	Max. deflection (mm)	FM	Fire resistance (min.)	Max. deflection (mm)	FM	Fire resistance
	CFR28	14.1	−78.6	FM 3+LB	26.6	−403.9	FM 3	0.53
G10	CFR29	13.2	−99.7	FM 3+LB	20.2	−457.3	FM 3	0.65
	CFR30	12.7	−121.7	FM 3+LB	17.3	−527.9	FM 3	0.73
	CFR31	37.8	−66.9	FM 3+LB	79.6	−410.4	FM 3	0.47
G11	CFR32	29.2	−85.5	FM 3+LB	61.0	−453.2	FM 3	0.48
	CFR33	25.3	−104.0	FM 3+LB	48.1	−506.6	FM 3	0.53
	CFR34	42.2	−66.0	FM 3+LB	363.7	−320.4	–	–
G12	CFR35	34.4	−83.1	FM 3+LB	66.1	−452.9	FM 3	0.52
	CFR36	29.7	−101.7	FM 3+LB	52.2	−508.1	FM 3	0.57
	CFR37	14.5	−69.6	FM 4+LB	26.8	−257.2	FM 4	0.54
G13	CFR38	13.6	−80.0	FM 4+LB	25.6	−410.6	FM 4	0.53
	CFR39	13.0	−90.3	FM 4+LB	18.7	−445.5	FM 4	0.70
	CFR40	43.2	−59.2	FM 4+LB	80.5	−243.5	FM 4	0.54
G14	CFR41	33.7	−70.0	FM 4+LB	76.2	−366.3	FM 4	0.44
	CFR42	28.0	−83.0	FM 4+LB	54.8	−437.3	FM 4	0.51
	CFR43	47.4	−59.1	FM 4+LB	363.7	−231.3	–	–
G15	CFR44	39.2	−69.4	FM 4+LB	363.7	−347.7	–	–
	CFR45	33.2	−82.0	FM 4+LB	59.4	−437.4	FM 4	0.56
	CFR46	16.8	−71.7	FM 4+LB	26.8	−136.3	FM 4	0.63
G16	CFR47	15.6	−83.8	FM 4+LB	26.8	−244.3	FM 4	0.58
	CFR48	14.8	−94.8	FM 4+LB	23.4	−365.3	FM 4	0.63
	CFR49	54.7	−63.4	FM 4+LB	76.2	−199.5	FM 4	0.72
G17	CFR50	47.2	−73.7	FM 4+LB	76.2	−282.4	FM 4	0.62
	CFR51	40.9	−84.4	FM 4+LB	76.2	−367.7	FM 4	0.54
	CFR52	59.9	−64.5	FM 4+LB	363.7	−188.6	–	–
G18	CFR53	51.2	−73.6	FM 4+LB	363.7	−267.1	–	–
	CFR54	45.2	−84.0	FM 4+LB	363.7	−351.0	–	–
Mean	–	–	–	–	–	–	–	0.57
COV	–	–	–	–	–	–	–	0.140

FM: failure mode; COV: coefficient of variation; WY: web yielding; WB: web buckling; PO: pullout; CC: concrete crushing.

FM 3: WY+WB+PO.

FM 4: WY+WB+PO+CC.

In Table 3, it can be seen that the composite frames with unprotected castellated steel beams heated using the ST fire curves failed between 12.7 and 16.9 min, which is below 30 min fire resistance, depending on the load ratio during fire. Similar conclusions could be drawn for the composite frames with unprotected noncastellated beams heated using the ST fire curve, as shown in Table 4. It can also be seen that the composite frames with castellated steel beams heated using LC1 fire curve failed between 25.0 and 53.5 min depending on the load ratio, while the composite frames with castellated steel beams heated using LC2 fire curve failed between 29.3 and 57.7 min depending on the load ratio. It can also be seen that the higher the load ratio during fire, the higher the maximum mid-span vertical displacement and the lower fire resistance. In addition, it is also shown that the steel strength has a considerable effect on the maximum deflections and fire resistances. High-strength steels have higher yield and ultimate stresses compared with normal strength steels, which limits the deformations of the steel beams at elevated temperatures and delays the occurrence of local buckling around the web openings. As an example, looking at G3 and G9 in Table 3, it can be seen that fire resistances of composite frames heated using LC2 fire curve have increased by 37%–52% due to the increase in steel yield stress from 275 to 690 MPa. Furthermore, looking at Tables 3 and 4, it can be noted that although the fire resistances of the composite frames with noncastellated steel beams were not clearly affected compared with the companion composite frames with castellated steel beams, the vertical mid-span deflections were reduced considerably. The span-to-maximum deflection ratios of the composite frames with castellated steel beams ranged from 60 to 107, while that of the companion composite frames with noncastellated steel beams ranged from 74 to 152.

Eight failure modes were identified for the composite frames with castellated and noncastellated steel beams in the parametric study, as shown in Tables 3 and 4. The failure modes comprised local buckling of bottom flanges at end connections (LB), top flange buckling (TFB), BFB, bottom flange yielding (BFY), WB, WY, PO of heads stud shear connectors and concrete crushing (CC) at the top concrete fibres. The composite frames with castellated steel beams in groups G1–G6 failed by a combined (TFB+BFB+BFY+WB+WY+PO)+LB failure mode, and this combined failure mode is called ‘FM 1+LB’ in the context of this article. The remaining composite frames with castellated steel beams in groups G7–G9 failed by a combined (TFB+BFB+BFY+WB+WY+PO+CC)+LB failure mode, and this is called ‘FM 2+LB’ in the context of this article. Furthermore, the composite frames with noncastellated steel beams in groups G10–G12 failed by a combined (WY+WB+PO)+LB failure mode, and this is called ‘FM 3+LB’ in the context of this article. Finally, the composite frames with noncastellated steel beams in groups G13–G18 failed by a combined (WY+WB+PO+CC)+LB failure mode, and this is called ‘FM 4+LB’ in the context of this article. It should be noted that WY and WB failure modes occurred in the composite frames with castellated beams at the web opening regions, while in composite frames with noncastellated steel beams occurred mainly at the end connections. It should also be noted that PO failure mode was predicted by observing the end slip between the composite slab and the steel beam. Furthermore, the CC failure mode occurred in composite frames for higher steel strengths.

The time–mid-span deflection relationships of all the composite frames with castellated and noncastellated steel beams investigated in the parametric study were predicted from the finite element analyses. Figures 11 to 16 show examples for the composite frames with castellated steel beams in groups G1–G9. Figure 11 plots the time–mid-span deflection relationships of the composite frames with castellated steel beams in groups G1–G3 heated using different fire curves, under different load ratios and having a steel yield stress of 275 MPa. Once again, it can be seen that the higher the load ratio, the higher the vertical displacement and the lower fire resistance. Similar conclusions can be drawn from Figures 12 and 13 that plot the time–mid-span deflection relationships for the composite frames having steel yield stresses of 460 and 690 MPa, respectively. The time–mid-span deflection relationships of the composite frames with castellated steel beams in groups (G1, G4 and G7) having different steel beam strengths heated under different load ratios and heated using ST fire curve are plotted as shown in Figure 14. Looking at Figure 14, it can be seen that the mid-span deflections are decreased and the fire resistances are increased as the steel strength is increased from 275 to 460 MPa. However, interestingly, the mid-span deflections are increased and the fire resistances are increased as the steel strength is increased from 460 to 690 MPa. This is attributed to the change in failure mode as the strength is increased from 460 to 690 MPa. The change in failure mode is clearly observed by the presence of CC as shown in Table 3. Similar conclusions can be drawn from Figures 15 and 16 that plot the time–mid-span deflection relationships for the composite frames in (G2, G5 and G8) and (G3, G6 and G9) heated using LC1 and LC2 fire curves, respectively.

Figure 11.

Time–mid-span deflection relationships of the composite frames with castellated steel beams in groups G1–G3 heated using different fire curves, under different load ratios and having a steel yield stress of 275 MPa.

Figure 12.

Time–mid-span deflection relationships of the composite frames with castellated steel beams in groups G4–G6 heated using different fire curves, under different load ratios and having a steel yield stress of 460 MPa.

Figure 13.

Time–mid-span deflection relationships of the composite frames with castellated steel beams in groups G7–G9 heated using different fire curves, under different load ratios and having a steel yield stress of 690 MPa.

Figure 14.

Time–mid-span deflection relationships of the composite frames with castellated steel beams in groups (G1, G4 and G7) having different steel beam strengths, heated under different load ratios and heated using ST fire curve.

Figure 15.

Time–mid-span deflection relationships of the composite frames with castellated steel beams in groups (G2, G5 and G8) having different steel beam strengths, heated under different load ratios and heated using LC1 fire curve.

Figure 16.

Time–mid-span deflection relationships of the composite frames with castellated steel beams in groups (G3, G6 and G9) having different steel beam strengths, heated under different load ratios and heated using LC2 fire curve.

Comparison of composite frames and simply supported composite beams

The results obtained from the finite element analyses performed in this study on composite frames with castellated and noncastellated were compared with the companion results of simply supported composite beams detailed in Ellobody and Young (2015b) as summarised in Tables 3 and 4. It can be seen that the restraints to thermal expansion of the steel beam provided by the protected steel columns and rigid frame connections resulted in considerable reductions in the fire resistances of the composite frames. This is attributed to the premature failure due to local buckling of the bottom steel beam flange at the end connections with the columns as shown in Figure 7 and summarised in Tables 3 and 4. It should be noted that restraint to tensile action permits the development of catenary action which has been shown to be beneficial in some cases where heated parts of the buildings are surrounded by unheated (cool) parts. The cool parts permit the development of the catenary action. Since the studied composite frames were continuously heated from underneath, restraints to thermal expansion of the castellated steel beams resulted in considerable reductions in the fire resistance of the composite frames. The reduction in the fire resistance is attributed to the premature failure mainly by local buckling of the bottom flange at the end connections. The mean values of the fire resistances of the composite frames to that of the simply supported composite beams with castellated and noncastellated steel beams are 0.56 and 0.57 with the corresponding coefficients of variation of 0.139 and 0.14, respectively, as shown in Tables 3 and 4. It can also be seen that the composite frames CFR7, CFR16, CFR17, CFR25, CFR26, CFR27, CFR34, CFR43, CFR44, CFR52, CFR53 and CFR54 did not survive the natural fires compared with the companion simply supported composite beams. It should be noted that the fire resistances of these composite frames were not included in the mean and coefficient of variation values.

The time–mid-span deflection relationships obtained from the finite element analyses performed in this study on composite frames with castellated and noncastellated were also compared with the companion relationships of simply supported composite beams detailed in Ellobody and Young (2015b), with examples shown in Figures 17 to 19. The figures plotted the relationships of the composite frames and simply supported beams with castellated steel beams in groups G1–G3, respectively, heated under different load ratios, having a steel yield stress of 275 MPa and heated using ST, LC1 and LC2 fire curves, respectively. Looking at the figures, it can be seen that the premature failure due to local buckling (Figure 7) limited the vertical displacements and fire resistances of the composite frames compared with the companion simply supported composite beams.

Figure 17.

Comparison of time–mid-span deflection relationships of the composite frames and simply supported beams with castellated steel beams in group G1 heated under different load ratios, having a steel yield stress of 275 MPa and heated using ST fire curve.

Figure 18.

Comparison of time–mid-span deflection relationships of the composite frames and simply supported beams with castellated steel beams in group G2 heated under different load ratios, having a steel yield stress of 275 MPa and heated using LC1 fire curve.

Figure 19.

Comparison of time–mid-span deflection relationships of the composite frames and simply supported beams with castellated steel beams in group G3 heated under different load ratios, having a steel yield stress of 275 MPa and heated using LC2 fire curve.

Conclusion

Nonlinear analysis of composite frames with castellated and noncastellated steel beams having profiled steel sheeting under fire conditions has been performed and reported in this article. 3D nonlinear finite element models were extended by adopting a previously reported nonlinear finite element approach for the analysis of unprotected composite beams exposed to fire. The finite element models have carefully considered the frame geometries and boundary conditions as well as the nonlinear material properties of steel, concrete, profiled steel sheeting, longitudinal and lateral reinforcement bars. In addition, the shear connection behaviour at ambient and elevated temperatures has been carefully incorporated in the finite element models. Furthermore, the thermal properties at the steel beam section/profiled steel sheeting and profiled steel sheeting/concrete elements interfaces were carefully inserted in the thermal heat transfer analysis. The time–temperature relationships, deformed shapes at failure, time–vertical displacement relationships, failure modes and fire resistances of the composite frames were evaluated by the finite element analysis. The comparison of composite frame and composite beam behaviour has shown that if the columns were sufficiently protected and the connection maintained its rigidity during fire exposure such that it can restrain the composite beam thermal expansions, this would result in considerable reduction in fire resistances of the composite frames compared with that of simply supported composite beams. This is attributed to premature failure at elevated temperatures due to local buckling at the bottom flange of the steel beam in the frame connections.

Parametric studies were performed to investigate the effects on the behaviour and fire resistances of composite frames with castellated and noncastellated steel beams due to different load ratios during fire, different fire curves, presence of web openings and different steel strengths. It has been shown that the composite frames with unprotected castellated steel beams heated using the ST fire curves failed between 13 and 17 min, depending on the load ratio during fire. On the other hand, the composite frames heated using the natural fire curves failed between 25 and 58 min depending on the load ratio. It can also be seen that the higher the load ratio during fire, the higher the maximum mid-span vertical displacement and the lower fire resistance. In addition, it has been shown that although the fire resistances of the composite frames with noncastellated steel beams were not clearly affected compared with the companion composite frames with castellated steel beams, the vertical mid-span deflections were reduced considerably. The span-to-maximum deflection ratios of the composite frames with castellated steel beams ranged from 60 to 107, while that of the companion composite frames with noncastellated steel beams ranged from 74 to 152. Furthermore, the results of the parametric studies have shown that the strength of steel beam and the fire scenarios have a considerable effect on the time–displacement behaviour and fire resistances of the composite frames.

Footnotes

Appendix 1 Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The research work described in this paper was supported by a grant from the University of Hong Kong under the seed funding program for basic research.

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