Simplified Design Procedure for RC Ribbed Slabs in Fire Based on Experimental and Numerical Thermal Analysis

Abstract

Ribbed slabs are a solution for increasing the bending capacity while reducing the total concrete consumption and the dead weight compared to conventional reinforced concrete slabs. The EN 1992-1.2 standard contains a tabulated method (TM) for the fire design of these structures, which suggests combinations of cross-sectional dimensions and concrete cover thickness to determine the fire resistance. Using a finite element (FE) model solved with Abaqus software, a transient thermal analysis of these slabs was performed, correlating the results with the standardized TM. Cross-sections with different concrete widths and concrete covers were numerically tested to define a new TM based on the same criteria proposed by the EN. To validate the FE models, the results were compared with the experimental data of two full-scale specimens of ribbed slabs. It was found that the current TM is not consistent in all cases, and the concrete cover needs to be improved by between 20 and 50%. A fire design of ribbed slabs based on EN 1992-1.2 shows that the reinforcement is heated beyond its critical temperature, but the flange thickness can be reduced. A new tabular procedure is proposed based on the critical temperature of the reinforcement, the concrete cross-section, and the thermal insulation criteria.

1. Introduction

According to Huang et al. [1] and Yardim et al. [2], 40–60% of the total dead load of the structure is accounted for by the slabs. To improve the performance of conventional slabs and reduce total concrete consumption and dead load, small beams are often used as reinforced ribs of the reinforced concrete (RC) slabs, resulting in ribbed slabs (RS). There are several types of RS, which differ in the geometry and arrangement of the ribs [3]. RS are also an excellent solution to reduce the number of columns in very tall RC buildings [4,5], emphasizing the environmental aspect of RS [6], which reduce the environmental impact of concrete consumption in buildings. RS are formed by longitudinal and sometimes also by transverse ribs. It is a solution with a large cross-sectional inertia and a small total area, making it suitable for large spans. Longitudinal and transverse ribs form a multiple-rib arrangement, with the longitudinal ribs forming the main bending resistance [7]. The transverse ribs can be considered as discrete shear connectors along the length of the slabs, reducing the shear resistance of the longitudinal ribs and improving bending resistance.

Several studies have attempted to optimize rib geometries to increase their mechanical efficiency while reducing total concrete consumption [3,8,9,10]. The use of alternative materials to improve the mechanical properties, such as ultra-high-strength concrete (UHSC) or high-strength steel, was proposed to improve the reduction in the cross-sectional area [11,12,13]. Most of the experimental studies focused on analyses at room temperature without taking into account the effect of fire. The papers focused on flexural behavior in lightweight ribbed slabs [1], precast ribbed sandwich slabs [7], steel–UHPC composite slabs [14], prestressed concrete composite slabs [15], fiber RC ribbed slabs [16], and lightweight concrete ribbed slabs [17]. The same can be seen for the numerical research [6,18,19,20,21]. However, the intended reduction in cross-sectional area increases their thermal field and makes them more susceptible to fire. Recent building collapses, such as the Notre Dame Cathedral in Paris (France), the Wilton Paes de Almeida building in São Paulo (Brazil), and the World Trade Center in New York (USA), have heightened concerns about the effects of high temperatures on structures. However, it is clear that the study of RS in fires has hardly been discussed, suggesting that it has received little attention from researchers. In fact, recent research on RC slabs (in general) in fires has not focused on the ribbed slabs (e.g., ref. [21] focused on thermal-damaged FRP-RC slabs, ref. [22] on FRP reinforced concrete slabs, ref. [23] on cross-laminated timber slabs, ref. [24] on two-way restrained and unrestrained precast concrete composite slabs, ref. [25] on CFRP-strengthened RC slabs, refs. [26,27] on GFRP reinforced concrete slabs, ref. [28] on lightweight and normal RC slabs, refs. [29,30] on hollow-core slabs, ref. [31] on steel decking slabs, ref. [32] on polyurethane foam slabs).

The lack of research on reinforced concrete ribbed slabs in the case of fire motivated this research.

High temperatures lead to physical, chemical, and mechanical changes in building materials. This research focuses on mechanics. In the case of steel reinforcement, fib Bulletin No. 38 [33] proposes 500 °C as the critical temperature (due to the limit of mechanical damage). For concrete, there are divergences. Some studies [33] assume a critical temperature of 500 °C from a mechanical point of view, but authors such as Qiao et al. [34] and Khoury [35] suggest temperatures in the range of 250 to 500 °C because of the possibility of spalling, while Tenchev and Purnell [36] suggest 300 °C for the same reason. According to fib Bulletin No. 38 [33], this is a critical temperature at the unexposed surface. This temperature is, on average, 140 °C or 180 °C at local peaks of the slab and is referred to as the thermal insulation criterion.

Wang et al. [37] investigated the load-bearing behavior of RC ribbed slabs under different fire conditions, including the influence of factors such as fire scenario, reinforcement ratio, and steel rebar arrangement. According to the authors, different failure modes, such as punching or bending, were more likely to occur in continuous RC slabs exposed to a traveling fire than in uniform fires. The degree of reinforcement, the arrangement of the reinforcement, and the slab thickness had a greater influence on the residual load-bearing capacity of fire-damaged continuous slabs than the direction of fire spread and the time delay. According to the authors, the failure criterion of l/50 deflection can be used to determine the residual capacity of fire-damaged continuous slabs with a lower span-to-thickness ratio, regardless of the fire scenario.

The structural performance of RC ribbed slabs under different fire exposure conditions depends on the level of mechanical load applied, as described by Sidnei et al. [38]. As highlighted by the authors, the maximum temperature on the heating surface of the RC ribbed slab was 944.33 °C; critical stresses of over 30 MPa were observed in the longitudinal ribs of the slab, and the fire resistance limits of the slab were determined to be 57 min, 51 min, and 43.9 min at 50%, 70%, and 100% of the maximum load, respectively. However, in its tabular procedure, EN 1992-1.2 does not consider the level of load as a decisive factor for the fire design of these structures, which highlights a contradiction.

The study proposed by Qader et al. [39] investigates the behavior of reinforced concrete cantilever slabs exposed to elevated temperatures and different cooling regimes. According to the authors, visual observations may not accurately reflect the damage that occurs in RC slabs under high-temperature conditions. The cracking behavior of concrete slabs was highly dependent on the temperature to which they were exposed, and cracking was random and unpredictable. The residual flexural stiffness and failure criteria of RC slabs were strongly influenced by the cooling method used, with the heating and cooling processes leading to a reduction in the flexural stiffness of the material.

The paper presented by Qin et al. [40] provides an overview of the damage assessment of reinforced concrete structures exposed to fire and discusses mitigation measures. As described by the authors, the severity of fire damage to reinforced concrete structures depends on the intensity and duration of the fire. The most common causes of fire damage to reinforced concrete structures are electrical problems, faulty fire alarm systems, lack of fire extinguishing equipment, and obstructions at emergency exits. This review paper summarizes the results of previous surveys and case studies on fire damage to reinforced concrete structures.

EN 1992-1.2 [37] in cooperation with EN 1992-1.1 [41] proposes a tabular method for designing RC ribbed slabs in fire based on critical temperatures. The EN 1992-1.2 [37] is based on DIN 4102-4 [42], which states that the tabulated data are based on experimental laboratory tests. After an extensive literature review, the origin of the tabular method proposed in the German standard cannot be clearly established. In this sense, there is a lack of knowledge. There are no studies focusing on the analysis of the tabular method proposed in the standard, and there is a lack of experimental studies aiming at the validation of FE numerical models. The present study aims to fill this gap by analyzing and discussing the tabular procedure proposed by the standard finite element thermal models. To validate the FEA models, two full-scale specimens were built and tested according to ISO 834 [39]. Experimental results are used to validate the FEA thermal models. The results made it possible to critically analyze the tabular method proposed in EN 1992-1.2 standard in an unprecedented way. This investigation has shown that the standard tabular method needs to be revised and can sometimes be unsafe. A new tabular method was proposed.

2. Methods

2.1. Experimental Research

2.1.1. Specimens

Two nominally identical full-scale specimens or ribbed slabs named S1 and S2 were built with rectangular plan dimensions of 3600 mm × 4600 mm. The cross-section is shown in Figure 1. The experimental setup is shown in Figure 2a,b.

Cross-section and flexural reinforcement were designed, not taking the effect of fire into consideration, according to [40]. The specimen was loaded with thick steel washers placed in a rigid frame (auxiliary frame loading), producing gravitational loads of 2.5 (S1) and 3.0 kN/m² (S2). This is a conventional load in the quasi-permanent combination used in the design of residential buildings under exceptional load [41]. The load was assumed to be constant throughout the test. The washers are mounted on top of the slab with pistons that move in response to the deflection of the slab (Figure 2a), keeping the load on the slab surface constant.

Figure 2b shows the structural drawing of the slab. N1 to N4 to N5 and N6 are the positive (tension) and the negative (compression) rebars, respectively. L is their length, and S is the spacing between rebars. The slabs had a size of 3600 × 4600 mm. N1 and N2 had a diameter of Ø 8 mm; N3 and N4 had a diameter of Ø 8 mm, while N5 and N6 had a diameter of Ø 5 mm. The thickness of the concrete cover was c = 30 mm.

For more information on the experimental test, see Bolina et al. [42] research, which used the same slab prototypes.

2.1.2. Materials

A Portland Brazilian cement classified as Type III according to ASTM C 150 [43] was used to build the specimens. The gravel was dacite with plagioclase (Gravel 1) and quartz base (Gravel 2). Natural quartz and industrialized dacite sand were used in the concrete mixture. Figure 3 shows their particle size distribution, and

Table 1. Concrete mix.

Material	Mixing Ratio (kg/m3)	Mixing Ratio
Cement	440	1.00
Gravel 1	400	0.91
Gravel 2	320	0.73
Industrialized Sand	320	0.73
Natural Sand	960	2.18
Water	200 ± 20	0.45 ± 0.05

shows the concrete mix. The compressive strength of the concrete at 540 days was 22.3 MPa, and at 28 days, it was 17.8 MPa. The tests were performed according to ASTM C39 [44].

Tension rebars were Ø 8 and Ø 10 mm in diameter. All specimens were constructed with welded steel mesh with a cross-sectional area of 92 mm²/m, made by square grids with rebars of Ø 5 mm in diameter and 15 cm spacing in both directions. The rebars had a nominal tensile yield strength of fy = 500 MPa, while the steel mesh had a nominal tensile yield strength of fy = 600 MPa.

2.1.3. Instrumentation

The cross-sectional temperatures of the specimen were measured at both the top flange and the rib. The temperature control points at the flange were named STf (slab temperature flange) and at the web (rib) STw (slab temperature web). Type K thermocouples (Ø 1.65 mm) were placed in cross-sectional layers: four for alignment STf (named Tf20, Tf35, Tf50, and Tf65 at 20, 35, 50, and 65 mm from the top specimen surface, respectively) and six for STw (Tw50, Tw80, Tw110, Tw140, Tw170, and Tw200 at 50, 80, 110, 140, 170, and 200 mm from the top surface, respectively), according to Figure 1. Thermal insulation (Ti) was measured on the unexposed surface. The criterion was defined based on the average temperature of 4 points (Ti1–Ti4). These analyses were based on the standard BS 476-20 [45].

2.1.4. Furnace Temperature

Figure 4a shows the horizontal furnace with a ribbed slab specimen during the experimental fire tests. The furnace has 8 gas burners that are set to apply the ISO 834 [39] time–temperature heating curve. Figure 4b shows the temperature during the test and the upper and lower limits of variability of ISO 834. These fire tests were conducted in the Fire Safety Laboratory of Unisinos University, in Brazil (itt Performance). The full-scale fire test was made according to ASTM E 119 [46] and BS EN 1363-1 [47].

2.2. Numerical Research

Calibration, Validation, and Extrapolations

A numerical model was set with the aim of investigating its efficacy in simulating the experimental results and obtaining further information after possible validation through extrapolation of the results. The boundary conditions are shown in Figure 5a. To reduce the time consumption, only the region of a rib was numerically tested, placing adiabatic vertical surfaces at the vertical boundaries of the model. On their bottom surface, the ISO 834 [39] heating was applied assuming thermal convection (heat transfer α = 25 W/m²·K) and radiation (thermal emissivity Ɛ = 0.70 [37]). On the top surface (unexposed surface), a room temperature of 25 °C was considered. The FE model was developed in ABAQUS [48] software (https://www.3ds.com/products/simulia/abaqus, accessed on 1 May 2025). The steel reinforcement was modeled as a truss with a 2-node link (DCC1D2) and the concrete as a 3D solid with an 8-node linear isoparametrics (DC3D8) finite element. A mesh-sensitive analysis was performed, and the element size was 0.5 mm for the DCC1D2 and 0.5 × 0.5 × 0.5 mm for the DC3D8, showing a good match with the experimental results proposed in this research.

The mesh size was selected using the full-scale testing data. A total of four mesh sizes were investigated, and the mesh size was determined by taking the largest difference between the experimental and numerical data to be around 10%. The 0.5 mm mesh size produced the best results and took the shortest time to resolve. The total number of elements was 4990. Figure 6 shows the mesh analysis, while Figure 7 shows the cross-section mesh details. The mesh sensitivity analysis in Figure 6 uses two control points as examples: the temperature in the reinforcements in the ribs with C = 20 mm (see Figure 6a) and the temperature in the reinforcements in the flange with C′ = 20 mm (see Figure 6b).

The thermal conductivity and density of the concrete were determined according to [37] and validated by the fire tests. The thermal conductivity and specific heat of the steel were also taken from [37]. Reinforcements were considered to have a density of 7850 kg/m³. The FE model was validated in accordance with the experimental results.

The thermal field analysis of the ribbed slabs was obtained, assuming various cross-sectional characteristics. The width (bw) and height (hw) of the rib and the thickness of the flange (hf) were considered as variable parameters in this research (Figure 5b). These cross-sectional dimensions (

Table 2. Dimensions of the cross section: study of the geometry of the ribs.

Slab Nomenclature	Cross-Section Dimensions (mm)
	${\mathbf{b}}_{\mathbf{w}}$	${\mathbf{h}}_{\mathbf{w}}$	${\mathbf{h}}_{\mathbf{f}}$	C
study of the geometry of the ribs
80 × 300 × 100	80	300	100	10 to 40
100 × 300 × 100	100	300	100	10 to 50
120 × 300 × 100	120	300	100	10 to 60
160 × 300 × 100	160	300	100	10 to 80
190 × 300 × 100	190	300	100	10 to 90
220 × 300 × 100	220	300	100	10 to 90
250 × 300 × 100	250	300	100	10 to 90
260 × 300 × 100	260	300	100	10 to 90
300 × 300 × 100	300	300	100	10 to 90
350 × 300 × 100	350	300	100	10 to 90
410 × 300 × 100	410	300	100	10 to 90
500 × 300 × 100	500	300	100	10 to 90
study of the geometry of the flange
100 × 300 × 80	100	300	80	5 to 40
100 × 300 × 90	100	300	90	5 to 45
100 × 300 × 100	100	300	100	5 to 50
100 × 300 × 110	100	300	110	5 to 55
100 × 300 × 120	100	300	120	5 to 60
100 × 300 × 130	100	300	130	5 to 65
100 × 300 × 140	100	300	140	5 to 70
100 × 300 × 150	100	300	150	5 to 75
100 × 300 × 160	100	300	160	5 to 80
100 × 300 × 170	100	300	170	5 to 85
100 × 300 × 175	100	300	175	5 to 85

) were selected in accordance with the EN 1992-1-2 [37] tabulated procedure. It should be noted that some of these dimensions are unusual but are in accordance with the standardized TM. As shown in Figure 5b, C and C′ are the concrete cover thicknesses (i.e., the distance between the axis of the reinforcements and the cross-section surface) in relation to the reinforcements placed in the ribs and flange, respectively.

In the case of the ribs, the “e” and “i” reinforcements are placed at the ends (corners) and possibly in the intermediate position (between the two “e” reinforcements), respectively. If an intermediate rebar is present in the rib (“i” reinforcement), its temperature can be significantly lower with respect to the more exposed “e” rebars. The distance between the “i” and “e” reinforcements is defined as “x”.

Table 2 shows the geometric parameters of the cross-sections used in the FE study. They aimed to determine the influence of the ribs or the flange on the results of the thermal field. In the case of reinforcements placed in the ribs, C values of 10 mm each were tested, with the minimum C = 10 mm (may represent some existing slabs built according to old standards or subjected to errors in the positioning of the rebars) and the maximum being the geometrical capacity of the rib width. Regarding the flange, C′ = 5 mm is assumed as the minimum and the limit of the neutral axis (i.e., around 0.5 × h_f) as the maximum thickness dimension.

2.3. Checking the Current Tables in EN 1992-1.2

In order to compare the results of the FE model with the TM of EN 1992-1.2 [37] for simply supported slabs, the cross-sections of Table 2 were related to standardized tables. The limit temperature of the reinforcement and the thermal insulation requirements were both assumed to be critical in these comparisons.

A temperature of 500 °C was considered critical for the reinforcement. This criterion was defined according to the fib Bulletin No. 38 [33]. In the case of thermal insulation, the limit temperature in the unexposed surface was assumed to be 180 °C [33]. This temperature was measured in the smallest thickness of the flange (hf thickness).

In order to compare the experimental and numerical cross-section results obtained in this study with those of the tabulated method proposed in EN 1992-1.2 [37], it was assumed that these slabs were designed with only two longitudinal reinforcements in the ribs (the reinforcement named as “e” in Figure 4b), thus neglecting the presence of intermediate rebars. When these lateral rebars reach the critical temperature of 500 °C, the Fire Resistance Rating (FRR) of the slab is calculated.

However, it is known that intermediate rebars in the ribs (named “i” in Figure 5b) have greater thermal protection than the corner reinforcements (“e”). In this sense, an alternative tabular method was integrated to consider the influence of these steel rebars on the structural capacity of ribbed slabs in the fire.

3. Results

3.1. Numerical Model Validation

The experimental (exp) results are presented with the corresponding validation of the numerical (num) in Figure 6. The cross-section dimensions of the experimental prototype (Figure 1) were implemented into the FE model. Appendix A also describes the divergences between experimental (exp.) values and numerical (num) data in more detail (see

Table A1. Temperature of concrete layers of experimental (Exp) and numerical (Num) results and the respective variation (Δ).

Concrete Point		ISO 834 Time (min)
		0	30	60	90	120
Tw50	Exp (°C)	25.0	46.3	93.4	101.0	108.3
	Num (°C)	25.0	43.2	86.7	108.0	128.7
	Δ (%)	0.0	6.7	7.2	6.4	15.8
Tw80	Exp (°C)	25.0	82.0	100.7	128.4	202.6
	Num (°C)	25.0	60.0	105.2	123.3	223.9
	Δ (%)	0.0	26.8	4.3	3.9	9.5
Tw110	Exp (°C)	25.0	99.4	114.3	213.0	335.8
	Num (°C)	25.0	78.1	114.9	233.7	409.3
	Δ (%)	0.0	21.4	0.5	8.8	17.9
Tw140	Exp (°C)	25.0	100.3	153.4	301.8	448.7
	Num (°C)	25.0	85.0	119.3	326.0	507.7
	Δ (%)	0.0	15.3	22.2	7.4	11.6
Tw170	Exp (°C)	25.0	99.9	264.8	438.0	583.2
	Num (°C)	25.0	93.9	260.0	432.3	607.2
	Δ (%)	0.0	6.0	1.8	1.3	3.9
Tw200	Exp (°C)	25.0	99.8	389.5	587.4	722.8
	Num (°C)	25.0	127.0	405.3	619.5	769.1
	Δ (%)	0.0	21.4	3.8	5.1	6.0
Tf20	Exp (°C)	25.0	95.5	136.6	212.8	287.6
	Num (°C)	25.0	69.8	153.1	237.8	296.3
	Δ (%)	0.0	26.9	10.7	10.5	2.9
Tf35	Exp (°C)	25.0	121.1	198.9	311.0	403.5
	Num (°C)	25.0	115.9	241.3	340.8	409.7
	Δ (%)	0.0	4.3	17.6	8.7	1.5
Tf50	Exp (°C)	25.0	183.5	336.3	463.4	564.7
	Num (°C)	25.0	216.7	375.2	485.2	561.8
	Δ (%)	0.0	15.3	10.3	4.5	0.5
Tf65	Exp (°C)	25.0	304.5	503.4	653.8	770.9
	Num (°C)	25.0	334.8	580.2	690.8	770.0
	Δ (%)	0.0	9.1	13.2	5.3	1.1

in Appendix A).

The test results in Figure 8b show a clear discontinuity when the temperature reaches a plateau of around 100 °C. The phase change in the water causes the temperature increase to slow down during 20–60 min, with almost constant temperatures within this range. Even a year after the specimen was built, considering the related capacity to dry out, it is clear that the thicker section contains more moisture than the thinner. It is also to be considered that the slab prototype was left outside the lab without any environmental protection. In the FE model, the moisture content and migration were not taken into account explicitly, following the standard mapping method described in EN 1992-1.2. Indeed, the effect of moisture content was considered implicitly by acting on the specific heat non-linear curve. Considering the heterogeneity of the concrete (construction procedure, cracking, etc.), the testing procedure, and the limitations of the FE approach used, the curves are deemed to satisfactorily compare, validating the soundness of the modeling strategy.

3.2. Parametric Investigation

3.2.1. The Influence of Slab Ribs

A parametric investigation was carried out on the basis of the cross-section of Figure 5b. Figure 9 shows the temperature profile of the reinforcement for some cross sections proposed in this research. The average “av” between “e” and “i” is also given (in addition, see also

Table A2. Temperatures of the external (e) and intermediate (i) rebars in the ribs and the respective percentage differences (Δ) assuming different concrete thicknesses (C).

60 min Exposure Curve ISO 834
Slab	Rebar	Thickness C (mm)
		10	20	30	40	50	60	70	80	90
80 × 300 × 100	e (°C)	893.3	796.6	707.3	-	-	-	-	-	-
	i (°C)	829.7	750.9	-	-	-	-	-	-	-
	Δ (%)	7.6	6.1	-	-	-	-	-	-	-
100 × 300 × 100	e (°C)	883.4	766.6	649.2	557.7	503.0	-	-	-	-
	i (°C)	786.0	680.1	601.6	-	-	-	-	-	-
	Δ (%)	12.4	12.7	7.9	-	-	-	-	-	-
120 × 300 × 100	e (°C)	879.0	752.0	619.3	507.5	426.8	379.6	-	-	-
	i (°C)	752.9	627.2	533.9	465.4	-	-	-	-	-
	Δ (%)	16.7	19.9	16.0	9.0	-	-	-	-	-
160 × 300 × 100	e (°C)	876.2	742.7	599.1	470.9	366.8	287.1	229.7	193.6	-
	i (°C)	710.5	560.5	449.0	366.2	304.3	257.5	-	-	-
	Δ (%)	23.4	32.5	33.4	28.6	20.5	11.5	-	-	-
190 × 300 × 100	e (°C)	875.8	741.5	596.3	465.4	356.9	270.3	202.3	151.9	125.2
	i (°C)	693.6	534.0	415.3	326.5	259.3	207.5	167.3	-	-
	Δ (%)	26.3	38.9	43.6	42.5	37.7	30.3	20.9	-	-
220 × 300 × 100	e (°C)	875.1	740.3	594.7	463.1	353.5	265.2	194.6	142.1	113.8
	i (°C)	683.5	518.8	396.0	304.0	234.2	180.5	141.9	118.7	106.4
	Δ (%)	28.0	42.7	50.1	52.4	50.9	46.9	37.1	19.7	6.9
250 × 300 × 100	e (°C)	875.1	740.3	594.7	462.9	353.0	264.3	192.9	139.6	110.1
	i (°C)	678.9	511.5	386.7	293.0	221.9	167.7	130.2	108.3	93.2
	Δ (%)	28.9	44.7	53.8	57.9	59.1	57.6	48.1	28.9	18.1
260 × 300 × 100	e (°C)	874.9	740.0	594.3	462.5	352.7	263.9	192.4	139.0	109.4
	i (°C)	677.7	509.7	384.5	290.5	219.1	168.9	127.7	105.6	89.9
	Δ (%)	29.1	45.2	56.6	59.2	60.1	56.2	50.7	31.6	21.7
300 × 300 × 100	e (°C)	874.9	740.0	594.3	462.5	352.7	263.8	192.2	138.6	108.6
	i (°C)	675.6	506.4	380.2	285.4	213.3	158.8	121.7	98.7	81.3
	Δ (%)	29.5	46.1	56.3	62.0	65.3	66.1	57.9	40.4	33.6
350 × 300 × 100	e (°C)	874.9	740.0	594.3	462.5	352.7	263.8	192.2	138.6	108.4
	i (°C)	674.8	505.1	378.5	283.3	210.9	156.1	118.8	95.1	76.9
	Δ (%)	29.6	46.5	53.4	63.3	30.1	69.0	61.8	45.8	41.0
410 × 300 × 100	e (°C)	874.9	740.0	594.3	462.6	352.7	263.8	192.2	138.6	108.5
	i (°C)	674.6	504.7	378.0	282.6	210.2	155.3	117.8	93.8	75.4
	Δ (%)	29.7	46.7	57.2	63.7	67.8	69.9	63.1	47.8	43.9
500 × 300 × 100	e (°C)	874.9	740.1	594.4	462.6	352.7	263.9	192.2	138.6	108.5
	i (°C)	674.6	504.7	377.9	282.6	210.0	155.2	117.7	93.6	75.0
	Δ (%)	29.7	46.7	57.3	63.7	69.7	70.0	63.3	48.1	44.7

in Appendix B).

The rebars placed at the corners of the ribs are more thermally affected and, thus, are more mechanically damaged than the central ones. Rebars in the corners “e” have an almost identical temperature profile (i.e., approximately 900, 800, 600, 500, 400, 300, 200, 150, and 100 °C for concrete cover C = 10, 20, 30, 40, 50, 60, 70, 80, and 90 mm). Thus, the width of the ribs has little effect on the temperature rise in the corner rib rebars. On the contrary, the width of the ribs becomes an important parameter for the limitation of the temperature rise in the intermediate rebar.

In the maximum situation measured in the 500 mm wide rib, the “i” rebar had a 70% lower temperature than “e”. The wider the rib, the greater the temperature difference between “i” and “e”. These differences are small when the “C” thickness is small (10–20 mm) and especially when the rib widths are small (80–100 mm).

The greater the thickness “C”, the smaller the effect on the temperature difference between “e” and “i”. There is an optimum range for the use of “i” reinforcement in these slabs: ribs with a width of more than 100 mm and a thickness C = 20–70 mm. This analysis was based only on the cross-sectional temperature field, and it is proposed to validate this conclusion by a thermomechanical method in the future.

With regard to the temperature field of the “e” rebars, the thickness of the concrete cover proved to be more important than the width of the rib, which is consistent with similar studies on reinforced concrete slabs, as carried out by Wang et al. [49].

Based on only two concrete cover thicknesses, 20 and 50 mm, Figure 10 shows that increasing the rib width has little effect on the temperature of the rebars. Increasing the rib width has an effect on the temperatures measured in the rebars, but the critical factor for these results is the thickness of the “C”.

However, it is important to emphasize that the moisture content of the slab and the type of coarse aggregate can alter the results and must be taken into account in future studies, as described by Coz-Díaz et al. [28] and Zhao et al. [50]. The moisture content delays heating in the cross section, while the nature of the coarse aggregate alters thermal parameters such as thermal conductivity and specific heat, which need to be investigated in future research.

3.2.2. The Influence of the Slab Flange

Assuming various concrete cover thicknesses (C′), Figure 11 shows the temperature history of the reinforcement for the flange thickness range investigated in this research.

Due to their one-sided heating (from the bottom), these rebars are less affected by the temperatures than the rebars of the ribs. The crucial design parameter, therefore, becomes the concrete cover thickness C′. Increasing the thickness C′ by 5 mm can reduce the temperature by more than 100 °C. In fact, in line with similar research such as Das et al. [51], Bolina et al. [52] and Manica et al. [53]. it was found that the rebars placed in the corners can heat up more and reduce their bond capacity more compared to the rebars that are not located in the corners.

Moreover, the dimension of the rib has an influence on the thermal field of the flange, with a strong limitation of the temperature rise for the rebars positioned right above the rib and a positive temperature limitation for the rebars placed in adjacency, progressively vanishing with the distance, asymptotically tending towards the behavior of uni-directional solid slabs.

3.2.3. Thermal Insulation Results

Figure 12 shows the temperature profile at the unexposed surface of the slab. It is referred to as the thermal insulation (Ti) requirement proposed by EN 1992-1.2 [37]. Please see Appendix C.

The thinner the thickness of the slab flange, the shorter the time in which the Ti requirement is met. In the event of fire, it is important to note that this is not primarily a structural thickness. According to EN 1992-1.2 [37], this thickness is required to ensure that the adjacent floor does not reach a critical temperature for users when it exits. In the worst case, reducing the flange thickness by 10 mm resulted in a temperature increase of more than 100 °C, as shown by the comparison between 80 and 90 mm flange thickness in a time of 240 min.

Figure 13 shows the temperature field (isotherms) of a slab with dimensions of 100 mm width and 300 mm height for different ISO 834 time temperatures. Figure 14 shows the isotherms at 120 min of the ISO 834 time–temperature curves for different slab cross sections.

3.3. EN 1992-1.2 Validation

Table 3. Comparison between the tabulated fire resistance parameters.

FRR (min)	Reference	Alternative #1	Alternative #2	Alternative #3
30	EN 1992-1.2 [37]	${\mathrm{b}}_{\mathrm{m}\mathrm{i}\mathrm{n}}=80$	X	X
		$\mathrm{a}=15$	X	X
	Research data	$\mathrm{a}=25$	X	X
60	EN 1992-1.2	${\mathrm{b}}_{\mathrm{m}\mathrm{i}\mathrm{n}}=100$	${\mathrm{b}}_{\mathrm{m}\mathrm{i}\mathrm{n}}=120$	${\mathrm{b}}_{\mathrm{m}\mathrm{i}\mathrm{n}}\ge 200$
		$\mathrm{a}=35$	$\mathrm{a}=25$	$\mathrm{a}=15$
	Research data	$\mathrm{a}=50$	$\mathrm{a}=40$	$\mathrm{a}=35$
90	EN 1992-1.2	${\mathrm{b}}_{\mathrm{m}\mathrm{i}\mathrm{n}}=120$	${\mathrm{b}}_{\mathrm{m}\mathrm{i}\mathrm{n}}=160$	${\mathrm{b}}_{\mathrm{m}\mathrm{i}\mathrm{n}}\ge 250$
		$\mathrm{a}=45$	$\mathrm{a}=40$	$\mathrm{a}=30$
	Research data	$\mathrm{a}=65$	$\mathrm{a}=55$	$\mathrm{a}=50$
120	EN 1992-1.2	${\mathrm{b}}_{\mathrm{m}\mathrm{i}\mathrm{n}}=160$	${\mathrm{b}}_{\mathrm{m}\mathrm{i}\mathrm{n}}=190$	${\mathrm{b}}_{\mathrm{m}\mathrm{i}\mathrm{n}}\ge 300$
		$\mathrm{a}=60$	$\mathrm{a}=55$	$\mathrm{a}=40$
	Research data	$\mathrm{a}=75$	$\mathrm{a}=65$	$\mathrm{a}=60$
180	EN 1992-1.2	${\mathrm{b}}_{\mathrm{m}\mathrm{i}\mathrm{n}}=220$	${\mathrm{b}}_{\mathrm{m}\mathrm{i}\mathrm{n}}=260$	${\mathrm{b}}_{\mathrm{m}\mathrm{i}\mathrm{n}}\ge 410$
		$\mathrm{a}=75$	$\mathrm{a}=70$	$\mathrm{a}=60$
	Research data	$\mathrm{a}=85$	$\mathrm{a}=80$	$\mathrm{a}=75$
240	EN 1992-1.2	${\mathrm{b}}_{\mathrm{m}\mathrm{i}\mathrm{n}}=280$	${\mathrm{b}}_{\mathrm{m}\mathrm{i}\mathrm{n}}=350$	${\mathrm{b}}_{\mathrm{m}\mathrm{i}\mathrm{n}}\ge 500$
		$\mathrm{a}=90$	$\mathrm{a}=75$	$\mathrm{a}=70$
	Research data	$\mathrm{a}=105$	$\mathrm{a}=95$	$\mathrm{a}=90$

compares the results with the tabular method proposed in EN 1992-1.2 for simply-supported slab members. The same applies to the thermal insulation requirements in

Table 4. Comparison between thermal insulation data.

FRR min	Flange h/a mm/mm
	EN 1992	Research data
30	80/10	80/10
60	80/10	80/20
90	100/15	100/30
120	120/20	110/35
180	150/30	140/45
240	170/40	160/55

.

The experimental and numerical results show that the “a” thickness proposed by EN 1992-1.2 is in line, although it differs from the values of this research. The required “a” thickness resulted from the numerical study in all cases (i.e., 100% of cases) greater than suggested in the standard, indicating an unsafe combination. The divergence between the EN values and the values proposed in this study is between 15 and 50%. Analyzing the data, “a” should be 15 mm larger than what is specified in the standard. The discrepancy could possibly be related to the methodology used to produce the standardized tabulated data (see the research carried out by the authors related to composite slabs [54]). It is recalled that the current TM in EN 1992-1.2 [37] is based on experimental studies carried out decades ago, for which the authors could not find references in the literature. The analyses were based on the same rib width (bmin) proposed in the standard.

While maintaining the flange thicknesses (h) suggested in the standard, inconsistent results were obtained for the thermal insulation (Ti) requirements. This analysis also suggested that the “a” thickness should be increased by 15 mm. On the contrary, the minimum requirements for “h” thicknesses could be decreased in some cases. The tabular procedures for thermal insulation proposed in EN 1992-1.2 [37] must be corrected in 83.3% of cases.

It is important to note that the proposed tabulated values must be compared with EN 1992-1.1 [41] in terms of structural design at room temperature. For example, the spacing between the reinforcements, the minimum thickness of the concrete cover to meet the durability criteria, the minimum diameter of the steel reinforcement, etc., must be taken into account in order to apply the proposed tabulated values.

3.4. Proposed Update of Tables

This section proposes design tables that may serve as an update of the current method implemented in EN 1992-1.2. The tables include a novel design principle: in addition to corner reinforcement, intermediate reinforcement (between corners) is assumed. When only two longitudinal reinforcements are considered (at the corners of the rib), a tabulated procedure is proposed in

Table 5. A new tabular method for RC ribbed slabs. (case 1: ribs with only two longitudinal rebars).

FRR	${\mathbf{b}}_{\mathbf{m}\mathbf{i}\mathbf{n}}$ (mm)
	80	100	120	160	190	220	250	300	350	410	500
	C (mm)
30	25	25	20	20	20	20	20	20	20	20	20
60	-	50	40	40	40	40	40	40	40	40	40
90	-	-	-	55	50	50	50	50	50	50	50
120	-	-	-	75	65	65	60	60	60	60	60
150	-	-	-	-	80	75	70	70	70	70	70
180	-	-	-	-	-	85	80	80	80	80	80
210	-	-	-	-	-	95	90	85	85	85	85
240	-	-	-	-	-	-	105	95	95	95	95

and

Table 6. A new tabular method for RC ribbed slabs. (case 2: ribs with three longitudinal rebars).

FRR	${\mathbf{b}}_{\mathbf{m}\mathbf{i}\mathbf{n}}$ (mm)
	80	100	120	160	190	220	250	300	350	410	500
	C (mm)
30	20	20	15	15	15	15	15	15	15	15	15
60	-	-	40	35	35	35	35	35	35	35	35
90	-	-	-	50	45	45	45	45	45	45	45
120	-	-	-	-	60	55	55	55	55	55	55
150	-	-	-	-	-	70	65	65	65	65	65
180	-	-	-	-	-	85	80	75	75	75	75
210	-	-	-	-	-	-	90	85	80	80	80
240	-	-	-	-	-	-	100	90	85	85	85

when additional intermediate reinforcements (in addition to the corner rebars) are provided.

Table 7. A new tabular method for RC ribbed slabs. (case 3: thermal insulation criterion).

Ribbed Slab	FRR (min)
	30	60	90	120	150	180	210	240
h (mm)	80	80	100	110	130	140	150	160
C′ (mm)	10	20	30	35	40	45	50	55

suggests a technique for calculating the thermal insulation.

The proposed tables also suggest fire design parameters for the exposure durations of the ISO 834 curve that are not contained in EN 1992 (as 150 and 210 min), as well as novel combinations of the widths and thicknesses of flanges and ribs, respectively. Moreover, the current standard provides only three combinations of ribs and concrete cover for each FRR intended, while the proposed tables suggest a total of eleven options for each required FRR, widening and further specifying the application field of the method. In some cases, it was not possible to find a solution, especially for thin ribs with required high FRR. This is due to the fact that high concrete cover thicknesses are required, making it impossible to place reinforcement in the thin rib sections. In such cases, a symbol “X” is displayed.

The width of the rib affects the reinforcement temperatures up to a certain temperature. Table 5 shows that for ribs larger than 100 mm with an FRR of 30 min, a minimum concrete cover thickness of 20 mm is required if only two longitudinal reinforcements are used. This thickness increases to 35 mm for ribs greater than 120 mm in length when 60 min is required. For ribs longer than 160 mm, the thickness increases to 50 mm at 90 min. For ribs longer than 220 mm, the thickness is 60 mm when the FRR is 120 min. For ribs wider than 220 mm, the thickness is 70 mm at 150 min, and for ribs wider than 220 mm, the thickness should be 80 mm at 180 min. For ribs wider than 250 mm, it is 85 mm at 210 min. In this sense, it is necessary to increase the width of the ribs to increase the thickness of the concrete cover and, thus, improve the thermal protection of the reinforcement.

When at least three rebars are used, Table 6 shows that for an FRR of 30 min and a width greater than 120 mm, the required concrete cover is 20 mm in all cases. For an FRR of 60 min and a rib thickness greater than 120 mm, the required concrete cover is 40 mm in all cases; for an FRR of 90 min, a concrete cover of 50 mm is used for all rib thicknesses greater than 190 mm. For an FRR of 120, 150, 180, 210, and 240 min and a rib width greater than 190, 250, 250, 300, and 300 mm, the concrete cover required in all cases is 60, 70, 80, 85, and 95 mm, respectively.

Regarding the thermal insulation criterion proposed in Table 7 and the thickness of the concrete cover of the flange, it can be seen that with the intended increase in the FRR, the thickness of the flange and the concrete cover also increase. As a general conclusion, an increase in FRR by 30 min requires an increase in flange and concrete cover thickness of 10 mm. This suggested concrete cover thickness refers to the bottom side of the slab, as the fire heats the bottom side and not the top side. It is the same criterion proposed in EN 1992-1.2 [37]

The proposed tabular procedures provide a simple option for the structural engineer. Only the minimum thicknesses of concrete cover, rib width, and flange thickness are required for the fire design of these slabs at any FRR times. The proposed tables (Table 4, Table 5 and Table 6) were defined only on the basis of a critical average temperature, assuming reinforcement, concrete, and thermal insulation. For the reinforcement, 500 °C was defined as the critical temperature. The same applies to the average concrete cross section. A critical temperature of 140 °C was assumed for the thermal insulation.

4. Conclusions

The general conclusions of this paper are as follows:

• The reinforcement at the rib corners is most affected by the fire. The installation of a third rebar in the central position (between the corner rebars) proved to be an interesting solution to mitigate the loss of mechanical strength in the slab. The temperature of the intermediate rebar can be up to 70% lower than the corner rebar;
• The thickness of the concrete cover has proven to be a key parameter for improving the fire resistance of ribbed slabs, as this variable has the greatest influence on the temperature of the reinforcement, which decreases by 300 °C when the concrete cover is increased by 30 mm, for example;
• When thin ribs are exposed to high temperatures for an extended period of time (ISO 834), their average temperature may rise to 1000 °C. This explains the limitations of the rib narrowness typically adopted by standards;
• The flange thickness was the key parameter concerning the thermal insulation capacity of the slab. The fire resistance rate can be improved to 170 min when the flange thickness improves to 90 mm;
• The tabulated values proposed in the standard for simply supported slabs were found to be unsafe with respect to some of the thermal simulations carried out. As a result, an increase in the concrete cover thickness proposed in EN 1992-1.2 of 15 mm is proposed;
• A similar outcome can also be derived for the thickness of the flange, where, in some cases, this study shows that the thickness of the concrete cover should be increased by 10 to 15 mm. However, in some cases, the flange thickness proposed by EN 1992-1.2 can be reduced by 15 mm;
• The suggested tabulated method is an alternative to the one suggested by EN 1992-1.2;
• The new tabular method also expands the rib width and flange thickness options suggested by EN 1992-1.2, as well as the FRR, providing engineers with new geometry combinations for the fire design of these slabs;
• As a suggestion for future research, the proposed tabulated procedures should be reviewed by other authors; e.g., considering variations in the concrete mix to understand the extent of variation in the proposed results with respect to concrete composition.