Numerical Analysis Study on Membrane Action Focusing on Differences in the Direction of Unprotected Secondary Beams in a Composite Flooring System Exposed to Fire

Kisei Shimono; Haruka Kanada; Moe Horie; Takeo Hirashima; Kei Kimura; Yusuke Shintani

doi:10.7731/KIFSE.3ac9997e

Int J Fire Sci Eng > Volume 39(2); 2025 > Article

Shimono, Kanada, Horie, Hirashima, Kimura, and Shintani: Numerical Analysis Study on Membrane Action Focusing on Differences in the Direction of Unprotected Secondary Beams in a Composite Flooring System Exposed to Fire

Research Paper

International Journal of Fire Science and Engineering 2025;39(2):135-147.

Published online: June 24, 2025

DOI: https://doi.org/10.7731/KIFSE.3ac9997e

Numerical Analysis Study on Membrane Action Focusing on Differences in the Direction of Unprotected Secondary Beams in a Composite Flooring System Exposed to Fire

Kisei Shimono¹, Haruka Kanada¹, Moe Horie¹, Takeo Hirashima^1,^†, Kei Kimura², Yusuke Shintani³

¹Chiba University, 1-33 Inage yayoi,Chiba-shi, Chiba, Japan

²Nippon Steel Corporation, 20-1 Shintomi, Futtsu-shi, Chiba, Japan

³Takenaka Corporation, 1-5-1 Ohtsuka, Inzai-shi, Chiba, Japan

^†Corresponding Author, TEL: +81-43-290-3138, FAX: +81-43-290-3138, E-Mail: hirashima@faculity.chiba-u.jp

Presented at the 13th Asia-Oceania Symposium on Fire Science and Technology (Oct. 21-25, 2024, Daegu, Korea) & published in the Special Issue of the IJFSE.

Received February 27, 2025 Revised April 19, 2025 Accepted April 21, 2025

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The purpose of this study was to investigate the membrane action in a fire of a flooring system consisting of a deck composite slab and an unprotected secondary beam. Thermal stress analysis was carried out for two different cases where an unprotected secondary beam was placed in the direction of the long span (long direction) and in the direction of the short span (short direction). The influence of the direction of the unprotected secondary beam on the deflection behavior of the flooring system and the stresses in the welded wire mesh were analyzed. The analysis was carried out on a previous large-scale fire test. The results indicated that when an unprotected secondary beam was placed in long direction, the deflection was larger at an early stage, and the membrane action developed earlier. From the middle of the heating process, the deflection behavior was almost identical when the unprotected secondary beam was placed in the long and short direction. During this period, the stresses in the welded wire mesh in the long direction were larger than in the short direction. In the ultimate state, the stresses in the welded wire mesh in the long direction were smaller when an unprotected secondary beam were placed in the long direction compared to that in the short direction.

Keywords: Composite flooring system; Fire resistance; Membrane action; Direction of unprotected secondary beams; Numerical analysis

1. Introduction

Membrane action increases load-bearing capacity in two-way supported slabs due to increased deflection. Composite slabs are generally designed as one-way support slabs. In the case of fire, it behaves as a two-way supported slab because the welded wire mesh transmits the tensile stresses instead of the steel deck. Previous tests, such as those at Cardington[1] and at FRACOF[2], have demonstrated increased load-bearing capacity in flooring systems with deck composite slabs due to the membrane action. In both tests, it was also demonstrated that the load-bearing capacity was maintained even when the secondary beams were unprotected for fire heating. In the analysis study of the membrane action of composite slabs, Huang et al. performed predictive calculations for the Cardington using a three-dimensional nonlinear finite element method to predict the fire behavior of a steel-structured composite building[3]. Then, Huang et al. proposed a nonlinear layered finite element method based on the Mindlin/ Reissner (thick plate) theory of slabs, which takes into account geometric and material nonlinearities[4,5]. The membrane action during fire in RC slabs was properly modeled in this study, showing a characteristic distribution of the principal membrane forces under membrane action, with tensile membrane forces in the center of the slab and compressive membrane forces at the periphery of the slab. Vassart et al. performed the analysis for the FRACOF test using the SAFIR analysis software. The effective thickness model was used to simulate temperature and slab behavior, and the simplification of the slab with an uneven underside to a flat model was validated[6]. Furthermore, several experimental studies have been carried out on the membrane action of composite floor slabs exposed to fire and a great deal of knowledge has been accumulated based on these results[7]. On the other hand, few reports have discussed the effect of the direction of unprotected secondary beams placed inside the composite flooring system on its behavior during fire.

In general, when deck composite slabs were subjected to loading and heating, large cracks parallel to the direction of the short span (hereafter short direction) expand in the center of the slab, causing large stresses in the welded wire mesh at those locations. Yoshida et al. conducted a load-heating test on a flooring system with an unprotected secondary beam in the direction of the long span[8]. In their test, a large crack along the direction of the long span (hereafter long direction) was observed on the top surface of the slab. At the location of the crack, the welding point of the welded wire mesh in the long direction failed in tension.

Therefore, it is possible that the placement of the unprotected secondary beams in the long direction could prevent large cracks parallel to the direction of the short span, thereby extending the fire resistance time.

The present study investigated the membrane action in a fire of a flooring system consisting of a deck composite slab and an unprotected secondary beam. The analysis was based on the test specimen described by Horie et al.[9]. In the room temperature design of steel structures, the case in which the secondary beams are placed in either the short or long direction can be considered. The reason for this is that the cross section of the secondary beam can be reduced when the secondary beam is placed in the short direction, and the cross section of the primary beam in the long direction can be reduced when the secondary beam is placed in the long direction. The direction of the secondary beams may be also determined to avoid openings or staircases. The purpose of the present study is to investigate the effect of direction of an unprotected secondary beam on the fire resistance of a composite flooring system. Thermal stress analysis was carried out using the numerical analysis software SAFIR[10] for the case of an unprotected secondary beam (USB) in the long direction (USB-long) and the short direction (USB-short). In this analysis, the fire resistance of the flooring system under the membrane action was evaluated in terms of the deflection behavior and stresses in the welded wire mesh.

2. Analysis Method

2.1 Thermal analysis model

In the SAFIR analysis software, thermal analysis uses linear isoparametric finite elements to calculate temperatures based on a pre-determined node. The amount of heat transferred is calculated based on the temperature at each integration point in the heat transfer analysis of a slab with eight integration points.

Figure 1 shows thermal analysis models of the slab and an unprotected secondary beam (USB) and protected primary beam (PPB). These thermal analysis models were identical for USB-long and USB-short.

In specimen, the top and bottom flange of the steel deck was located 80 mm and 130 mm, respectively, from the top of the slab[9]. The thermal analysis model of the slab was simplified as a flat model with an effective thickness of 105 mm from the middle of the top and bottom flanges of the steel deck to the top surface of the slab, referring to EUROCODE4[11]. The ISO 834 standard fire was assigned from the bottom of the slab as the thermal condition and ambient temperature of 20 ℃ was assigned from the top of the slab. The mesh was divided into 10 sections in the direction of thickness, making it a 1D analysis model. For the thermal analysis model of the slab, only concrete was used as material. The effective depth of the welded wire mesh was 36 mm, and the temperature of the welded wire mesh was input to the thermal stress analysis as the temperature of the concrete at the same location.

For the thermal analysis models of USB and PPB, the concrete slab on the top surface is the same as the thermal analysis model of the slab. The thermal conditions were three-sided heating from the bottom and sides. The mesh was divided into rectangular mesh and a 2D analysis model was created. Insulation was placed only on the PPB to reproduce the test.

Table 1 shows the thermal properties of concrete, steel beams and insulation. The specific mass and moisture content of concrete were set to 2,237 kg/m3 and 6.28%, respectively, from material tests. The specific heat of concrete was in accordance with EUROCODE2[12]. The specific heat and thermal conductivity of the steel beams was in accordance with EUROCODE3[13]. Material properties of the insulation were given based on product information. The emissivity and thermal conductivity of the concrete and the convection heat transfer coefficient of the unheated surface of the concrete were determined to simulate the temperature of the test. This is because the temperature difference between the top and bottom surfaces of the slab affects thermal deflection, while the temperature of the welded wire mesh affects mechanical deflection. The mechanical deflection increases due to the reduction in the strength and stiffness of the welded wire mesh and has a larger effect on the ultimate bearing capacity of the slab. The emissivity of USB was determined to simulate the temperature of the test. This is because the temperature of USB affects the deflection behavior in the early stages of heating. Therefore, four thermal properties were considered, and the temperature of each part was simulated.

First, the emissivity of the concrete was determined as 0.20 to track the temperature because of the low emissivity of the steel deck and the air layer between the steel decks and the concrete.

Second, the thermal conductivity of the concrete was used with the upper limit of EUROCODE2 to simulate the temperature of the welded wire mesh in the slab. In the test, the welded wire mesh located above the top flange of the steel deck with a slab thickness of 80 mm had a higher temperature. To track the higher temperatures due to this effect in the flat model, the thermal conductivity was made larger.

Third, the convection heat transfer coefficient at the unheated surface of the concrete slab was larger, 23 W/(m²⋅K) to simulate the temperature there.

Fourth, the emissivity of the USB was set at 0.50 to simulate the temperature difference between the top and bottom flanges. The emissivity of USB was determined to be smaller than the actual emissivity to account for shadow effects due to its shape.

2.2 Thermal stress analysis model

After performing the thermal analysis, the temperature results were input into the thermal stress analysis using SHELL elements for the slab and BEAM elements for the beams. Figure 2(a) shows the thermal stress analysis model of the flooring system with USB in the short direction (USB-short), and Figure 2(b) shows the thermal stress analysis model of the flooring system with USB in the long direction (USB-long). Therefore, the lengths of USBs were 4.6 m for USB-short and 6.9 m for USB-long. The information for the thermal stress analysis model, except for the direction of USB and their boundaries, was the same for both. The size of the flooring system was 4.6 m × 6.9 m. USB were connected to the center of the span of the primary beam. The end of USB was modeled as a pin connection. The vertical displacement was constrained at the corners of the flooring system, and the horizontal displacement and the rotation around the vertical axis were constrained at the center of the flooring system. The live loads were 10.142 kN/m² based on the test applied loads. The dead loads of the slab were assumed to be 2.52 kN/m².

Figure 2(c) shows the slab cross section of the model. The ribs of the steel deck were present in the specimen but were simplified as a flat model in the analysis. The steel deck was eliminated because its bearing capacity rapidly decreases in the early stage of heating. The cross-sectional area of welded wire mesh was 283 mm²/m. The welded wire mesh was assigned with an effective depth of 36 mm as a plane and given axial stiffness. Referring to EUROCODE4[14], the thickness of the analytical model was 105 mm. The temperature of the welded wire mesh was input as the temperature at the same depth of the slab obtained from the thermal analysis.

Table 2 shows the mechanical properties of the steel beams and the welded wire mesh. The yield strength at ambient temperature was determined to be 344.5 N/mm² for USB and 338.0 N/mm² for PPB based on the inspection certificates. The reduction factors of strength and modulus of elasticity and Stress-strain curve of steel beams at high temperature were in accordance with EUROCODE3.

Table 3 shows the mechanical properties of the concrete slab. The aggregate type of concrete was Calcareous and the compressive strength at ambient temperature was 38.86 N/mm². The tensile ductility was 2500 N/mm², which was approximately 4 times the theoretical value, considering the constraining effect of the steel decks. The reduction factors of strength and modulus of elasticity, and thermal expansion coefficient and ss-curve of the concrete at high temperature were in accordance with EUROCODE2.

Figure 3 shows the yield strength at high temperature of the welded wire mesh. The yield strength at ambient temperature of the welded wire mesh in the analytical model was determined to agree with the result of the high temperature coupon test at 500 °C. Figure 4 shows the Stress - strain curve of the welded wire mesh at high temperature. The type of material and ductility class of the welded wire mesh was based on the high temperature coupon test result and was cold formed and ductility class A in accordance with EUROCODE2. The reduction factor of the yield strength of the welded wire mesh was according to EUROCODE2.

Figure 5 shows the yield strength at high temperature of the USB and PPB. The yield strength of these beams at ambient temperature was based on inspection certificates. The reduction factor of the yield strength at high temperature for the beams was in accordance with EUROCODE3. Figure 6 shows the compressive strength of the concrete at high temperature. The compressive strength of the concrete at ambient temperature was given from material tests, and the reduction factor of the strength for finite element analysis was in accordance with EUROCODE2.

3. Analysis Result

3.1 Results of analysis on the temperature

Figure 7 shows the results of the temperatures in the slab. In the test, the slab was heated until 216 minutes, but in the analysis, the heating continued until 240 min. For the temperatures of the slab in the test were averaged for the concave and convex portions of the deck composite slab. The temperatures at the top and bottom of the slab and the temperature difference between the top and bottom of the slab could be simulated. The temperatures of the welded wire mesh were almost identical for test and analysis. Figure 8 shows the results of the beam temperature. PPB remained below 350 °C until the end of heating, and yield strength almost did not decrease. The temperature difference between the top and bottom flanges of USB and the temperature of the top and bottom flanges of USB could be simulated. At the end of heating, the temperature of the USB was about 1100 °C and the yield strength was much decreased.

3.2 Results of the deflection behavior

Figure 9(a) shows the deflection-heating time relationship at the center of the slab for the test and the analysis. Kanada et al. indicated that the deflection behavior could be roughly traced although there were slight differences between the analysis and the test from 20 to 90 min due to differences in the thermal expansion coefficient of the concrete[14]. Figure 9(b) shows the deflection-heating time relationship in the center of the slab for the two analytical models. The deflection for USB-long was larger than that for USB-short up to 90 min of heating. This is because the influence of thermal deflection of USB was larger for USB-long. Thermal deflection was proportional to the temperature difference between the top and bottom flange of USB and the length of the member and was the main cause of the deflection in the early stages of heating. It is considered that USB-long, which has a larger deflection, may have had a larger effect on the membrane action than USB-short. After 90 min, the temperature difference between the top and bottom flanges of the USB becomes below 50 °C, so the deflection behavior was almost identical for both models. The fire resistance time was 205 minutes for USB-short compared to 236 minutes for USB-long. This showed that the fire resistance time probably increased when secondary beams were placed in the long direction.

Figure 10 shows the deflection curves of the slab for the short and long spans. The deflection curves for both models were parabolic. This was agreed with the assumptions of the bearing capacity calculations of Li et al.[15]. Up to 90 min, the deflection curve for USB-long was larger than that for USB-short for all distributions. However, for the long span deflection distribution, USB-short was slightly larger than for USB-long after 120 min. This confirms that the catenary effect of USB was larger for USB-long. For USB-long, the deflection increased up to 236 min at the ultimate state of the flooring system, indicating that the effect of the membrane action was larger. This indicates that for USB-long, the fire resistance time was longer due to the effect of the membrane action.

3.3 Results of stress in unprotected secondary beam

Figure 11 shows the bending moment in the center of slab - time relationship for the USBs. Figure 12 shows the axial force-heating time relationship of the USBs. In the early stage of heating, thermal stress in the USBs caused compressive axial forces. For bending moment, small sagging moment developed for USB-short and hogging moment developed for USB-long. USB-long had a larger thermal stress than USB-short due to the longer beam span. The bending moment and axial force converged to a constant value as the heating time passed until the ultimate state. For USB-long, a tensile axial force of 8.3 kN was developed at the ultimate state. Therefore, the USB slightly transmitted the tensile force and helped the slab to support the load.

3.4 Results of principal membrane force in slab

Figure 13 shows the distribution of principal membrane forces in the slab. The red lines represent the tensile membrane forces, and the blue lines represent the compressive membrane forces. At 15 min of heating, tensile membrane forces around the center of the slab occurred only in the short direction for USB-short, whereas tensile membrane forces around the center of the slab occurred in the short and long direction for USB-long due to the larger deflection. This indicates that the membrane action developed earlier in USB-long. At 60 min of heating, the range of compressive and tensile membrane forces in the long direction expanded for both models. From 120 min to end of heating, both models showed similar principal membrane force distributions with an expanded range of tensile membrane forces.

3.5 Results of stress in the welded wire meshes

Figure 14 shows the stress distribution in the welded wire mesh at 15 min of heating. Stress distributions were nearly symmetrical on the left and right, so each of the half ranges is shown in one figure. For USB-long, stresses in the short and long directions of the welded wire mesh were larger around the center of the slab than for USB-short because of the larger deflection of USB-long. The stresses occurring in USB-long at 15 min of heating were similar in shape to the yield line theory. On the other hand, the stresses for USB-short were widely distributed around the short span in the center of the slab because the deflection was not larger. At this moment, USB-short still behaves due to bending. These results correspond to the principal membrane force distribution, indicating that the welded wire mesh was bearing most of the stresses. Figure 15 shows the stress distribution in the welded wire mesh at 205 min of heating. There was no significant difference between the two models in the stress of the weld wire mesh in the short direction. However, the stresses in the weld wire mesh in the long direction were larger for USB-short than USB-long around the center of the slab.

Figure 16 shows the stresses in the welded wire mesh along the center of the slab span at 205 min. In the short direction, no significant difference was observed for both models, and both did not reach the proportional limit. Near the center in the long direction, USB-short showed an upward convex distribution, whereas USB-long showed a flat distribution. At the center of the slab, the stress on the welded wire mesh was about 350 N/mm² for USB-long and about 400 N/mm² for USB-short. When USB was placed in the long direction, the stresses in the welded wire mesh were reduced.

Figure 17 shows the relationship between stress and heating time at the center of the slab. At up to 30 min of heating, at the early stage of heating and with USB-long, the stresses in the welded wire mesh in the short direction were larger compared to later times due to thermal deflection of the USB. Subsequently, as the heating time progressed, the stress in the mesh in the long direction became larger than that in the short direction. This indicates that the effect of membrane action increases with heating. In the short direction, the stress did not reach the proportional limit for either model. In the long direction, the stress reached the proportional limit after 236 min of heating for USB-long and after 145 min of heating for USB-short. For USB-short, the welded wire mesh supported the load while maintaining its proportional limit of strength. For both models, the stress did not reach the yield strength until the end of heating, and the load-bearing capacity was maintained. From section 3.3, it is considered that USB- long may have reduced the stress in the welded wire mesh at the ultimate state, which may have contributed to the membrane action. This indicates that the time to reach the ultimate state would be longer for USB-long than for USB-short if heated for a longer period. The longer fire resistance time in an unprotected secondary beam in the long direction was due to the reduced stress in the welded wire mesh.

4. Conclusion

In the present study, a thermal stress analysis was carried out for a flooring system consisting of an unprotected secondary beam and a deck composite slab with different directions of the unprotected secondary beam. The membrane action was analyzed from its deflection behavior and the stresses in the welded wire mesh and unprotected secondary beam. The results are shown below.

1. In the early stage of heating, the thermal deflection caused a larger deflection in the case where an unprotected secondary beam was placed in the long direction, and the stresses in the welded wire mesh were also larger. The unprotected secondary beam placed in the long direction developed the membrane action earlier.

2. After 120 minutes of heating, the deflection and principal membrane force distributions were nearly identical for both models. In both models, as the flooring system heated, the stresses in the welded wire mesh were larger in the long direction than in the short direction.

3. In the model with an unprotected secondary beam in the short direction, the stress in the welded wire mesh in the long direction reached the proportional limit at 145 min. When an unprotected secondary beam was placed in the short direction, the stress in the welded wire mesh in the long direction was 400 N/mm² at the ultimate state. Meanwhile, when an unprotected secondary beam was placed in the long direction, the stress was 350 N/mm². It is considered that placing an unprotected secondary beam in the long direction reduces the stress in the welded wire mesh. As a result, the fire resistance time was longer when an unprotected secondary beam was placed in the long direction than in the short direction. It indicates that the time to reach the ultimate state is longer when unprotected secondary beams are placed in the long direction.

However, the results obtained from this study are only findings from one example of a floor system. In actual steel structures, various cases can be assumed, such as multiple secondary beams being placed in the flooring system. In the future, it will be nec-essary to conduct numerical analyses for more realistic cases to accumulate further knowledge.

Notes

Author Contributions

Conceptualization, K.S. and T.H.; validation, T.H., K.K. and Y.S.; formal analysis, K.S.; investigation, K.S.; resources, T.H.; data curation, K.S. and H.K.; writing-original draft preparation, K.S.; writing-review and editing, T.H., K.K. and Y.S.; visualization, K.S.; supervision, T.H.; project administration, T.H.; funding acquisition, T.H. All authors have read and agreed to the published version of the manuscript.

Conflicts of Interest

The authors declare no conflict of interest.

Acknowledgments

This research was funded under the Structural Research and Education Grant Programme by the Japan Iron and Steel Federation.

Figure 1.

Thermal analysis model.

Figure 2.

Structural analysis model.

Figure 3.

Yield strength of the welded wire mesh at high temperatures.

Figure 4.

Stress - Strain relationship of the welded wire mesh at high temperatures.

Figure 5.

Yield strength of the beams.

Figure 6.

Compressive strength of the concrete.

Figure 7.

Result of the temperatures in the slab.

Figure 8.

Result of the temperatures of the steel beams.

Figure 9.

Deflection - heating time relationship at the center of the slabs.

Figure 10.

Deflection curve of the slabs.

Figure 11.

Bending moment - time relationship in USB.

Figure 12.

Axial force - time relationship in USB.

Figure 13.

Principal membrane force in the slabs (- - - : USB direction).

Figure 14.

Stress distribution in welded wire mesh (15 min).

Figure 15.

Stress distribution in welded wire mesh (205 min).

Figure 16.

Stresses in welded wire mesh at 205 min.

Figure 17.

Stress - heating time relationship at the center of the slabs in welded wire mesh.

Table 1

Thermal Properties

Thermal property	Concrete (Normal weight)	Steel beams	Insulation
Specific mass [kg/m³]	2237	7850	128
Moisture content [%]	6.28	-	0.0
Specific heat	EUROCODE2[8]	EUROCODE3[9]	800 J/(kg·K)
Thermal conductivity	EUROCODE2 (top limit)	EUROCODE3	0.060 W/(m·K)
Convection Coeff. under fire heating [W/(m²·K)]	23	23	23
Convection Coeff. under ambient condition [W/(m²·K)]	23	4	4
Relative emissivity [−]	0.20	0.50	0.70

Table 2

Mechanical Properties of the Steel Beams and the Welded Wire Mesh at Ambient Temperature

Type	PPB	USB	Welded wire mesh
Yield strength at ambient temperature [N/mm²]	344.5	338.0	633.3
Young’s modulus at ambient temperature [N/mm²]	2.05 × 10⁵	2.05 × 10⁵	2.05 × 10⁵
Poisson ratio [−]	0.30	0.30	0.30
Reduction factor	EUROCODE3	EUROCODE3	EUROCODE2
SS - curve	EUROCODE3	EUROCODE3	EUROCODE2

Table 3

Mechanical Properties of the Concrete

Aggregate type	Calcareous
Compressive strength at the ambient temperature [N/mm²]	38.86
Tensile strength [N/mm²]	4.12
Poisson ratio [−]	0.20
Tension ductility [N/mm²]	2500
Reduction factor	EUROCODE2
SS - curve	EUROCODE2

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