Fire experiment and fire design method of U-shaped steel-concrete composite beams

Abstract

Four U-shaped steel-concrete composite beams (USCB) were designed and tested under the ISO-834 standard fire curve and distributed vertical load. The research parameters were the load ratio and shear connector form. The temperature distribution, fire resistance, and failure modes of the USCB specimen were investigated. The fire tests showed that the failure mode of the specimen is flexural damage and the connection interface between the flange and web of the composite beam remains intact. The temperature of the fire-resistance reinforcements is below 500°C when the specimens reached the fire resistance, which is in the early stage of material degradation and has high residual strength. The fire resistance increased (improve by 51%) with the decrease of load ratio (0.7 to 0.4) and was not affected by the shear connector form. Then a numerical simulation was applied to establish the temperature field model and fire resistance model of USCB, and the simulation results of the temperature field and fire resistance were in good agreement with the test results. The parameter analysis indicated that the load ratio, the diameter of fire-resistance reinforcement and fire protection layer have an obvious impact on the fire performance. Based on the heat transfer mechanism analysis, the temperature calculation methods for U-shaped steel, fire-resistant reinforcement and concrete were proposed. Moreover, a flexural bearing capacity calculation method for the USCB under the standard temperature rise curve is proposed, which can be applied to calculate fire resistance.

Keywords

U-shaped steel-concrete composite beam fire protection layer fire test high-temperature bearing capacity fire resistance

Highlights

• Fire tests were conducted on U-shaped steel-concrete composite beams (USCBs).

• The finite element model for USCBs was developed and parametric analysis was conducted.

• The temperature calculation methods for different part of USCB were proposed.

• The high-temperature flexural bearing capacity calculation method for USCB is proposed.

Introduction

For the I-shaped steel-concrete composite beam, the steel beam is directly softened by fire and is prone to local buckling under the fire condition, resulting in poor fire resistance and often requiring the addition of fire protection layer. The U-shaped steel-concrete composite beam (USCB) has the advantages of high bearing capacity, high stiffness, easy construction and good fire resistance. The USCB can postpone the local steel buckling under negative bending moment and strengthens the composite action between the U-shaped steel and the concrete. In addition, the thermal conductivity of the concrete under fire is relatively small, which can slow down the heating rate of the U-shaped steel; and as such the steel can prevent the concrete from bursting and the bottom reinforcement in the U-shaped steel can directly carry the load. Last but not least, the shear connectors of channels, web-embedded connectors and reinforced truss system adopted in the USCB can improve the integrity of the specimen and resist the sliding and lifting of the concrete slab. Since the bottom fire-resistance reinforcement inside the beam is protected by concrete and can carry the load directly, the USCB has higher fire resistance than traditional composite beam. The USCB has been applied to actual projects such as Beijing Yintai Center, Shanghai Pudong Yangnan District residential building, and Crystal Tower in Korea.

The research on the fire behavior of steel-concrete composite beams started in 1995 at the BRE Fire Research Laboratory in Cardington, UK (Gillie et al., 2001). After that, scholars have conducted an in-depth analysis of the fire resistance of composite beams through experimental research and theoretical analysis, and have achieved abundant results. The fire performance of restrained composite beam (Selden et al., 2016), partial embedded composite beam (Ahn and Lee, 2017) were researched by standard fire tests and numerical simulation. And the corresponding fire design methods were proposed (Albero et al., 2019; Martinez and Jeffers, 2020). The research results of the fire performance of I-shaped composite beams are summarized in the Chinese standard (MOHURD, 2017) and the European standards (CEN, 2005).

Up to now, few studies on the fire resistance of U-shaped steel-concrete composite beams have been conducted. In 2012, Gao (Gao and Huang, 2012) conducted fire tests on five USCBs with stud connectors, and the results indicated that the fire resistance of the composite beam filled with concrete was 10 min∼20 min higher than that of the box-shaped composite beam without concrete. In 2017, Kim (Kim et al., 2017) conduct the fire test of light steel-concrete composite beams with through bolts. The results showed that the concrete in U-shaped steel can reduce the steel temperature and a reduction factor of bearing capacity calculation method was proposed. In 2018, Wu (Wu and Ji, 2018) studied the fire resistance of five USCBs with stud connectors, and the results showed that the small load ratio, fire protection layer and appropriate bottom fire-resistance reinforcement configurations can improve the fire resistance. In 2020, Liu (Liu, 2020) conducted fire performance tests on four full-scale USCB with angle steel connectors. The result indicated that the fire resistance of USCB without fire protection is only about 23 mins when the load ratio is 0.7. The fire resistance could be respectively improved to 41 mins and 75 mins when applying the bottom fire-resistant reinforcements and fire protection layer. There are problems with the above configuration, such as the residual stress issues with stud connectors, inability of angle steel connectors to improve the torsional stability of U-shaped steel and lifting of concrete slabs, inability to form closed sections and complex construction due to the application of arch. steel bars, and slip phenomenon of through bolts.

At present, the Code for Fire Safety of Steel Structures in Buildings (MOHURD, 2017) only presents the fire design methods for I-shaped steel-concrete composite beams. For the USCB, the steel temperature cannot be calculated directly by the code formula for the existence of in-filled concrete. On the other hand, the temperature distribution between the USCB and the ordinary composite beam is different. Therefore, the fire resistance design of USCB cannot utilize the fire design method of I-shaped composite beam directly. Although the concrete in U-shaped steel can delay the temperature rise of the steel and improve the fire resistance, the USCB usually require certain fire protection measures to meet the fire resistance requirements similar with all exposed steel components. However, the required thickness of the fire protection layer can be significantly reduced compared to ordinary steel beams. So, the fire performance of USCB should be conduct to gain the fire design method.

Regarding the study of fire performance of USCB, fewer experiment was conducted. At the same time, the applicability of the temperature calculation formula and the bearing capacity calculation method is also debatable. The room-temperature tests of USCB under bending (Yang et al., 2021), shear (Zhao et al., 2019), and torsion (Zhao et al., 2020) conducted by our research group proved that this type of composite beam has good mechanical behavior, and the design methods of USCB under room temperature which can be used as a reference for fire design methods have been put forward by our research group. Based on the above studies, the author in this paper carries out the study on the fire resistance of four full-scale USCB, in which the effects of load ratio and form of connectors on the fire resistance are investigated. Then the ABAQUS software is used to establish the fire resistance model, and the temperature calculation formula of the composite beam is proposed. Finally, a calculation method of the high-temperature flexural bearing capacity of the composite beam is proposed.

Experimental program

Specimen design of the fire test

Four full-size U-shaped steel-concrete composite beams (USCB) were designed for fire test, with the cross-sectional dimensions and connector arrangement shown in Figure 1: the beam length = 3800 mm; the clear span = 3600 mm; the overall sectional height = 570 mm, in which the height of U-shaped steel was 450 mm and the thickness of concrete slab was 120 mm; the lower flange width = 200 mm; the upper varus flange width = 65 mm; the U-shaped steel thickness = 6 mm; and the concrete slab width = 1400 mm. The concrete slab is reinforced with two layers of 10mm-diameter rebars in two directions with the rebars spaced at 200 mm. The diameter of the fire-resistance reinforcements placed at the beam bottom is 20 mm and the thickness of reinforcement protective layer is 20 mm. The channel steel is used as the shear connector, which is 65 mm (height) × 40 mm (width) × 4 mm (thickness). The channels are placed at a spacing of 200 mm longitudinally and welded on the varus flanges of U-shaped steel. The number of channel connectors was determined based on the calculation of full composite action. Material strengths are Q355 for the U-shaped steel and channel connectors, HRB400 for the bottom reinforcement and the rebar, and C30 for the concrete. The details of the specimens are listed in Table 1. Besides, another two USCB specimens respectively with web-embedded connectors and reinforced truss system are designed with same sectional dimensions as the composite beam with channel steel connectors, as shown in Figure 1 and schematically in Figure 2.

Figure 1.

Cross-section of U-shape steel-concrete composite beam (unit: mm). (a) The cross section of USCB with channel connectors. (b) The front view of USCB with channel connectors. (c) The cross section of USCB with web-embedded connectors. (d) The front view of U-shaped steel in USCB with web-embedded connectors. (e) The cross section of USCB with reinforced truss system.

Table 1.

The parameters of specimens.

Specimen no.	Thickness of fire protection layer d (mm)	Fire-resistance reinforcement (mm)	Test load ratio n	Test load N (kN)	Fire resistance t_R (min)	Simulated fire resistance t_RFE (min)
CB-0.4-10	10.0	2Φ20	0.4	537	100	110
CB-0.7-10	10.0	2Φ20	0.7	940	66	72
WB-0.7-10	10.0	2Φ20	0.7	940	66	72
RB-0.7-10	10.0	2Φ20	0.7	940	68	74

Figure 2.

Schematic diagram of USCB. (a) The USCB with channel connector. (b) The USCB with web-embedded connector. (c) The USCB with reinforced truss system.

The details of the specimens are listed in Table 1. The test load ratio n is defined as the ratio of the mid-span bending moment induced by the external load to the plastic flexural capacity of the USCB; and the load was applied to the composite beam by the three-point method. The plastic flexural capacity of the composite beam under room temperature was calculated by the finite element software ABAQUS. Specimen CUSCB (shortened as CB) stands for USCB with channel connector, in which prefix W stands for web-embedded connector and prefix R stands for reinforced truss system. Second symbol 0.4 and 0.7 stand for the test load ratio, and the third symbol 10 stands for the thickness of fire protection layer. Besides, the fire protection layer has the thermal conductivity λ = 0.116 W/m·K.

Table 2 summarizes the room-temperature mechanical properties of U-shaped steel and reinforcements as measured according to China’s national standard GB/T 228.1-2010 (MOHURD, 2010). The yield strength f_y and ultimate strength f_u of U-shaped steel are 340.9 MPa and 488.1 MPa respectively. The yield strength f_y and ultimate strength f_u of Channel steel connector are 380.6 MPa and 201.2 MPa respectively. The yield strength f_y and ultimate strength f_u of Fire-resistance reinforcement are 412.5 MPa and 510.6 MPa respectively. According to the China national standard GB/T 50,081-2002 (MOHURD, 2002), the mean value of the compressive strength f_cu for cube specimen (150 mm × 150 mm × 150 mm) is 47.5 MPa.

Table 2.

The relative error of key parameters between numerical and experimental results.

Temperature data	Root mean square (RMS) (°C)	Mid-span displacement	Root mean square (RMS) (mm)	Fire resistance t_R (min)	Simulated fire resistance t_RFE (min)	Relative error (%)
CS1∼CS5 (CB-0.4-10)	4.3, 6.3, 3.7, 2.5, 6.3	CB-0.4-10	3.3	100	110	10
CW1∼CW5 (CB-0.4-10)	3.4, 5.9, 1.5, 7.3, 10.6	CB-0.7-10	2.2	66	72	9.1
A1∼A3 (CB-0.4-10)	5.6, 3.8	WB-0.7-10	5.9	66	72	9.1
B1 (CB-0.4-10)	2.1	RB-0.7-10	3.5	68	74	8.8

Measurement programs

The location of the thermocouples is shown in Figure 3(a). CS1∼CS5 thermocouples are fixed to the rebars to measure slab concrete temperatures; CW1∼CW5 thermocouples are used to measure the concrete temperature distribution in the U-shaped steel; and A1∼A3 thermocouples are used to measure the temperature change in the shear connectors. Two thermocouples B1 and B2 are added to monitor the temperatures of bottom reinforcements. The vertical deformation of the specimen is measured by the displacement meter arranged at the top concrete slab, as shown in Figure 3(b). The white arrow of P/2 is the position of hinged support of distribution beam and the distance between the two loading point is 1200 mm.

Figure 3.

Location of the thermocouples and displacement meters. (a) Location of the thermocouples. (b) Location of the displacement meters.

The fire test was conducted following the requirements of “Fire Resistance Test Methods for Building Elements Part 1: General Requirements” (GB/T 9978.1-2008) (MOHURD, 2008). The test device is shown in Figure 4, in which the two-point loading is realized on the specimen employing jacks and distribution beams, and the ISO-834 standard fire temperature load is applied through the horizontal furnace. The 3000 mm-long middle part of the composite beam is the fire area, and the U-shaped steel and the concrete slab lower surface are directly subjected to fire.

Figure 4.

Test device.

During the fire resistance test, the predetermined load is applied to the specimen in a graded manner, after which the combustion furnace is turned on for specimens’ ambient heating. The specimen is considered to reach the fire resistance when the mid-span deformation reaches D = L²/400d or the deformation rate reaches dD/dt = L²/900d (MOHURD, 2008). In this paper, the mid-span deformation of 56 mm is taken as the limit deformation for the fire resistance.

Test results and discussion

Experimental phenomena and failure modes

Under the ISO-834 standard fire curve, the specimens CB-0.7-10 and WB-0.7-10 and RB-0.7-10 (those with different shear connectors) under the same load ratio have similar experimental phenomena, therefore only specimens CB-0.4-10 and CB-0.7-10 are described in details.

For specimen CB-0.4-10, after 16 min of heating (the corresponding furnace temperature is 748°C), the water seepage phenomenon happened on the slab top surface. The reason is that the crack appeared due to vertical loading on the concrete slab. And the wet mark of the fire protection layer appeared at the beam end (Figure 5(a)). As the heating progressed, the water seepage became more intense (Figure 5(b)) at the heating time of 25 min. The slab top surface was covered with water accumulation area and the heat dissipated when 35 min (864°C, Figure 5(c)). After 58 min (940°C) of heating, the water evaporated from the cracks on the slab top surface, and the fork-shaped water marks appeared on the slab top surface (Figure 5(d)) at the time of 100 min (1021°C). The reason is that the strength of materials and the flexural stiffness of specimen decreased under the action of fire and force loading. The specimen reached the fire resistance when the mid-span deformation reached 56 mm. The fork-shaped cracks and transverse cracks were observed on the slab top surface near the end supports and longitudinal cracks also appeared at the mid-span location (Figure 5(e)). Meanwhile, an oxidation layer formed and its spalling phenomenon were observed on the U-shaped steel surface (Figure 5(f)). And the cracking and spalling phenomena happened on the fire protection layer, which will influence the ultimate fire resistance to a certain extent. By removing the U-shaped steel after the test, web concrete cracks were unevenly distributed with vertical cracks prevailing.

Figure 5.

Test phenomenon of specimen CB-0.4-10. (a) Water seepage phenomenon. (b) Increased water seepage. (c) Water accumulation. (d) Fork-shaped water marks. (e) Cracks on slab top surface. (f) U-shaped steel and the inner concrete.

For specimen CB-0.7-10, after 15 min of heating (738°C), the water seepage phenomenon happened on the slab top surface, and the wet mark of fire protection layer appeared (Figure 6(a)). As the heating progressed, the water seepage became more intense (Figure 6(b)) at the heating time of 20 min and the slab surface was covered with water accumulation area the heat dissipated when 30 min (Figure 6(c)). After 66 min (959°C) of heating, the water evaporated from the cracks on the slab top surface and left with fork-shaped water marks (Figure 6(d)). The specimen reached the fire resistance when the mid-span deformation reached 56 mm. Fork-shaped cracks were observed on the slab top surface near the end supports and longitudinal cracks also appeared at the mid-span (Figure 6(e)). Observing the U-shaped beam, the spalling phenomenon happened on the fire protection layer (Figure 6(f)). By removing the U-shaped steel after the test, the web concrete cracks were unevenly distributed with vertical cracks prevailing.

Figure 6.

Test phenomena of specimen CB-0.7-10. (a) Water seepage phenomenon. (b) Increased water seepage. (c) Water accumulation. (d) Fork-shaped water marks. (e) Cracks on slab top surface. (f) U-shaped steel and the inner concrete.

The specimens successively went through the test phenomena of concrete slab top surface cracking, water seepage, water accumulation at the slab top surface, and water vapor evaporation. The damage mode of the specimens under fire was flexural damage and fork-shaped cracks appeared on the concrete slab surface, while the U-shaped steel at the flange-web interface was intact. The cracking and spalling phenomena happened on the fire protection layer, which will influence the ultimate fire resistance to a certain extent.

Temperature field of the specimens

The temperature-time curves of the four specimens in the furnace and the ISO-834 standard fire are shown in Figure 7. As showed, the test results agreed well with the standard temperature rise curve.

Figure 7.

Comparison of temperatures between the furnace and the ISO834 standard fire curve.

Specimens CB-0.4-10 were taken as examples, and the temperature distributions were shown in Figures 8 and 9, respectively. The temperature increases with the increasing heating time, but with different increase rates at different locations. CS1∼CS5 (Figure 3(a)) are the thermocouples in the slab concrete, which are vertically distant from the top concrete slab surface by 20 mm (CS1 and CS3), 60 mm (CS4), 100 mm (CS2 and CS5), respectively. The temperature decreases in the order of CS5, CS4 and CS3 (Figure 8(a)) with the increasing distance from the bottom fire surface. CS2 and CS5 are at the same distance from the bottom concrete slab surface, but the temperature of CS2 is higher than CS5, as CS2 is closer to the direct fire surface.

Figure 8.

Measured temperature of specimen CB-0.4-10. (a) CS1∼CS5. (b) CW1∼CW5. (c) A1∼A3, B1.

Figure 9.

Comparison of midspan deformation-time curves of specimens.

Thermocouples CW1∼CW5 are embedded in the web concrete (Figure 3(a)), and the measured temperature at CW2 is higher than that at CW5 and CW1 (Figure 8(b)). The reason is that CW2 is a double-sided thermocouple and receives more heat than the single-sided CW1 and CW5. The temperatures of CW5, CW4, and CW3 decrease gradually with the increasing distance from the bottom fire surface. The same temperature distribution pattern is also observed in thermocouples A1∼A3, but the temperature gradient among A1∼A3 is smaller than that among CW5 ∼ CW3. For the bottom fire-resistance reinforcement, the temperature of B1 (142°C) is between CW5 (132°C) and CW2 (200°C) in the concrete (Figure 8(c)), the reason is that the concrete protective cover postpones the temperature rise of bottom reinforcement.

Fire resistance and mid-span deformation curves

The fire resistances of specimens were indicated in Table 1 and the mid-span deformation curves were shown in Figure 9. The mid-span deformations are steadily developed in the early stage, and the flexural stiffness and flexural capacity under high temperatures decrease gradually due to the decreasing material elastic modulus and strength, which finally accelerates the development of mid-span deflections in late stage.

The fire resistance of specimens CB-0.4-10 are higher than specimen CB-0.7-10 (improve by 51%), indicating the fire resistance obviously increased with the decrease of load ratio. The fire resistance of specimens CB-0.7-10, WB-0.7-10 and RB-0.7-10 are relatively close, and the development of curves is also relatively similar, indicating that the fire resistance of USCB is not affected by the shear connectors form under the premise of meeting the shear connection requirement.

Finite element analysis

Temperature field model

The temperature field model of the USCB is established by the finite element software ABAQUS. A four-node thermal shell elements DS4 is used to simulate the U-shaped steel and channel connectors; a three-dimensional eight-node linear thermal solid elements DC3D8 is employed to represent the concrete and fire protection layer; and a two-node thermal truss elements DC1D2 is used to model the reinforcement. The mesh size is 25 mm for the concrete and 50 mm for the U-shaped steel and reinforcement (Figure 10). The contact type between the fire protection layer and the U-shaped steel and between the U-shaped steel and the concrete is “surface-to-surface contact property,” in which the heat loss is considered by specifying the value of contact thermal resistance as 0.01 m²·°C/W. A “Tie” property is used to simulate the interaction between reinforcement and concrete and that between channel connector and concrete.

Figure 10.

Mesh division and boundary condition in the temperature model. (a) CUSCU specimen. (b) WUSCU specimen. (c) RUSCU specimen.

In the fire condition, the heat transfers to the outer surface of the U-shaped steel or the fire protection layer through thermal convection and thermal radiation. Concrete slab side and upper surface are modeled as the non-fire surface. The heat transfer coefficient (Environment to specimen) α_c is 25 W/(m²·°C), and the heat transfer coefficient (Specimen to environment) of the non-fire surface is 9 W/(m²·°C). The value of the Stefan-Boltzmann constant σ is 5.67 × 10⁻⁸ W/(m²·K⁴) and the radiation coefficient ε_r is 0.7. The absolute zero temperature is −273.15°C and the environment temperature is 20°C. The thermal properties of steel and concrete, including the thermal conductivity coefficient, specific heat and density, are adopted in the temperature field model, based on the suggested values in EC code (CEN, 2005).

The temperature comparisons of simulation results and test results are shown in Figure 11. The simulation results agree well with the test results in temperature development trend, platform stage and overall distribution. The temperature A2 appears damaged due to the elevated temperature or specimen installation or concrete vibration. And the temperature of A2 in specimen WB-0.7-10 and RB-0.7-10 can refer to the temperature of A2 in specimen CB-0.7-1.0 or the FE simulation results.

Figure 11.

Comparison of temperature between test and FEA. (a) CS1∼CS5 (specimen CB-0.4-10). (b) CW1∼CW5 (specimen CB-0.4-10). (c) A1∼A3, B1 (specimen CB-0.4-10). (d) CS1∼CS5 (specimen CB-0.7-10). (e) CW1∼CW5 (specimen CB-0.7-10). (f) A1∼A3, B1 (specimen CB-0.7-10). (g) CS1∼CS5 (specimen WB-0.7-10). (h) CW1∼CW5 (specimen WB-0.7-10). (i) A1∼A3, B1 (specimen WB-0.7-10). (j) CS1∼CS5 (specimen RB-0.7-10). (k) CW1∼CW5 (specimen RB-0.7-10). (l) A1∼A3, B1 (specimen RB-0.7-10).

Fire resistance model

The results of the temperature field model are integrated into the fire resistance model through the node temperature file. A three-dimensional reduction integration solid element with eight nodes C3D8R is utilized to model the concrete; the four-node shell element S4R is used to model the U-shaped steel and channel connector; and the one-dimensional linear truss element with two nodes T3D2 is employed to model the reinforcement. The contact relationship between U-shaped steel and internal concrete is the same as that in the temperature field model. The interaction relationship between the bottom fire-resistance rebars and concrete, between the distributed rebars and concrete, and between the channel connector and concrete is represented by “Embedded region”; and the “Merge” relationship is used between channel connector and U-shaped steel. The boundary condition is consistent with that in the test. The stress-strain relationships in high-temperature are adopted according to the EC code (CEN, 2005) for the steel and Lie (Lie and Stringer, 1994) for the concrete. The coefficients of thermal expansion of steel and concrete are adopted according to the EC code (CEN, 2005).

Figure 12 shows the mid-span deformation-time curve comparison between the finite element model and the test (S is the error variance, S² is the standard deviation, and RMS is the root mean square). The comparison results indicated that the finite element simulation is in good agreement with the test in terms of slow deformation stage and sudden deformation increase stage.

Figure 12.

Comparison of the mid-span deformation-time curve between test and FEA. (a) Specimen CB-0.4-10. (b) Specimen CB-0.7-10. (c) Specimen WB-0.7-10. (d) Specimen RB-0.7-10.

The fire resistance value comparison between the simulation and test results is shown in Table 1, in which the relative calculation errors are not more than 10%. Table 2 list the relative error for all the specimen between numerical and experimental results, including key temperatures and mid-span displacement.

Comparisons of failure modes between the test and the finite element results are shown in Figure 13. As seen, the finite element model can simulate the overall bending and crack development of the composite beam accurately, as well as the fire performance of USCBs.

Figure 13.

Comparisons of the failure modes between test and FEA. (a) Comparison of the cracks in concrete slab. (b) Comparison of bending deformations.

Parametric analysis of fire resistance

The main parameters that affect the fire behavior of USCB are the thickness of fire protection layer, configuration of bottom fire-resistance reinforcement, load ratio, size of U-shaped steel section, and material strength. The influences of the parameters on fire resistance of USCB are shown in Figure 14. The fire resistance of USCB decreases with the increasing load ratio (Figure 14(a)). Similarly, the fire resistance of USCBs increases with the increasing diameter of fire-resistance reinforcements (Figure 14(c)). However, the sectional dimensions of USCBs (including the height of U-shaped steel Figure 14(b)) and the strength of materials virtually do not affect the fire resistance (Figure 14(d)∼(e)). The fire resistance of USCBs can be improved significantly by applying the fire protection layer (Figure 14(f)). For examples that, the fire resistance can reach 120 min under the load ratio of 0.3 with 3 mm fire protection layer and under the load ratio of 0.7 can be ensured with 7 mm fire protection layer.

Figure 14.

Influence of different parameters on fire resistance of components. (a) Load ratio n. (b) Height of U-shaped steel h_w. (c) Diameter of fire-resistance reinforcement Ф_r. (d) Concrete compressive strength f_ck. (e) Steel yield strength f_y. (f) Thickness of fire protection layer D_b.

Fire-resistant design methods

Temperature calculation

The temperature calculation of the USCB under fire is the base of the fire resistance calculation. The U-shaped steel and concrete slab bottom are subjected to fire directly, the temperature calculation formula for U-shaped steel is obtained by regression fit as seen in equation (1a).

T_{s} = A (1 - \frac{1}{1 + {(\frac{t}{B \cdot D})}^{C \cdot E}}) + 20

(1a)

A = 1200

B = 0.337 + 11 d_{s}

C = 0.96 + 19.6 d_{s}

D = 1.36 + 730 t_{p}

E = 1.08 - 2.4 t_{p}

In which, T_s—The temperature of the U-shaped steel, °C; t—The heating time, h;

d_s—The thickness of the U-shaped steel, m;

t_p—The thickness of the fire protection layer, m.

The U-shaped steel temperature comparison between the calculation formula results and the finite element results for the steel thickness in the range of 0∼24 mm and the fire protection layer thickness in the range of 0∼20 mm is given in Figure 15, which shows that the formula can predict the U-shaped steel temperature accurately.

Figure 15.

Comparison of steel surface temperatures between FE analysis and formula calculation. (a) The temperature of U-shaped steel under the change of the thickness of the steel. (b) The temperature of U-shaped steel under the change of thickness of the fire protection layer.

In this paper, the USCB is divided into heat transfer regions as shown in Figure 16. The concrete slab directly subjected to fire is a one-dimensional heat transfer region, and the middle part of the concrete slab within the area of the U-shaped steel is a two-dimensional heat transfer region. The lower half of the concrete in the U-shaped steel is two-dimensional heat transfer region and the upper half is one-dimensional heat transfer region.

Figure 16.

Divisions of heat transfer region.

Based on the results of the temperature field parameters analysis, the temperature calculation formula for one-dimensional heat transfer region (the slab concrete and the upper part of the concrete inside the U-shaped steel) is obtained as shown in equations (1b) ∼ (1d):

T_{z} = T_{s} η_{z / y}

(1b)

The slab concrete:

η_{z} = 0.143 \ln (t / z^{1.5}) - 0.706 z^{0.5} - 0.190

(1c)

The concrete in U-shaped steel;

η_{y} = 0.175 \ln (t / y^{1.5}) - 0.030 y^{0.5} - 0.490

(1d)

The concrete temperature comparison of the flange plate and the upper part inside the U-shaped steel between the results calculated by equations (1b) ∼ (1d) and the simulated results are shown in Figure 17. The calculated results are in good agreement with the simulation results.

Figure 17.

Comparison of one-dimensional heat transfer area concrete temperatures between FE analysis and formula calculation. (a) Concrete temperature comparison of the flange plate between calculated and simulated results. (b) Concrete temperature comparison of the upper part inside the U-shaped steel between calculated and simulated results.

In addition, the middle part of the concrete slab is a two-dimensional heat transfer region. The temperature is still below 450°C after 2 h of heating, so the temperature effect of this concrete is not considered. For the lower part of the concrete within the U-shaped steel, the temperature calculation formula is obtained as equations (1e) ∼ (1g). Because the bottom fire-resistance reinforcement is in the two-dimensional heat transfer region, its temperature is the same as the nearby concrete and the temperature can be calculated according to equation (1g).

T_{z} = T_{s} η_{xy}

(1e)

The concrete in U-shaped steel:

η_{xy} = 0.985 (η_{x} + η_{y}) - 1.03 η_{x} η_{y}

(1f)

Bottom fire-resistance reinforcement:

T_{xy, R} = T_{xy} (1 - 0.01 d_{R})

(1g)

The temperature comparison of the concrete in the lower part of the U-shaped steel and bottom fire-resistance reinforcement between the calculated results according to equations (1e) ∼ (1g) and the simulated results are given in Figure 18, which shows that the temperature equation of the two-dimensional heat transfer region can predict the temperature of the two-dimensional heat transfer concrete and bottom fire-resistance reinforcement at the corresponding locations to some extent.

Figure 18.

Comparison of two-dimensional heat transfer area concrete temperatures between FE analysis and formula calculation. (a) Concrete temperature comparison of the lower part of the U-shaped steel between calculated and simulated results. (b) Bottom fire-resistance reinforcement temperature comparison in the U-shaped steel between calculated and simulated results.

High-temperature flexural bearing capacity

When the high-temperature bearing capacity of the USCB decreases to the same as the applied load, the heating time is the fire resistance under the corresponding load. In the calculation of the high-temperature flexural capacity of the USCB, the effects of U-shaped steel, fire-resistance reinforcement in the U-shaped steel and concrete in the pressure zone of the concrete slab are considered.

The temperature of U-shaped steel and bottom fire-resistance reinforcement can be respectively calculated by equations (1a) and (1g), and the yield strength of steel at different temperature is calculated according to strength reduction calculation equation (1h).

k_{yT} = {\begin{cases} 1.0 & 20 ℃ \leq T \leq 300 ℃ \\ 1.24 \times 10^{- 8} T^{3} - 2.069 \times 10^{- 5} T^{3} + 9.228 \times 10^{- 3} T - 0.2168 & 300 ℃ < T < 800 ℃ \\ 0 & 800 ℃ \leq T \leq 1000 ℃ \end{cases}

(1h)

For the temperature of concrete at high temperature, the concrete isotherms calculation method of 500°C is proposed in the EC code, in which that the concrete strength contribution is ignored when the temperature is higher than 500°C, and the concrete strength is not discounted when the temperature is lower than 500°C. In this paper, the calculation method of 500°C isotherm for concrete is used to calculate the actual 500°C position of concrete slab, and the force of the concrete slab can be calculated conservatively. And the expression of 500°C isotherm position can be fitted according to the finite element model, as presented in equation (1i).

h_{dwx} = 0.42 t - 5.8

(1i)

In which: h_dwx—The position of 500°C isotherm of the concrete slab (Distance relative to the top concrete slab), mm;

t—The heating time, min.

The high-temperature flexural bearing capacity of the USCB can be calculated according to the plasticity theory. The calculation model is shown in Figure 19.

Figure 19.

Calculation model of high-temperature positive bending capacity. (a) The neutral axis in the concrete slab. (b) The neutral axis in the U-shaped steel.

The meanings of the letters in the graph and calculation formulas are shown below.

F_{c, \max} = B h_{b} f_{c, k} (T)

(1j)

F_{t, \max} = 2 h_{w} t_{w} f_{ys} (T) + b t_{w} f_{ys} (T) + A_{rb} f_{yr} (T)

(1k)

In which: F_c,max—Maximum compressive force provided by concrete in the compression zone, N;

F_t,max—Maximum tension provided by U-shaped steel and bottom fire-resistance reinforcement, N;

B—The width of concrete slab, mm; h_b—The thickness of the concrete slab, mm;

h_w—The height of U-shaped steel, mm;

t_w—The thickness of U-shaped steel, mm;

b—The width of U-shaped steel, mm;

A_rb—The area of bottom fire-resistance reinforcement, mm²:

f_c,k (T)—The concrete compressive strength at different temperature, MPa;

f_ys (T)—The steel yield strength at different temperature, MPa;

f_yr (T)—The yield strength of bottom fire-resistance reinforcement at different temperatures, MPa.

In the Figure 19, F_cc is the combined force in the compression zone provided by the concrete, and F_tt is the combined force in the tension zone provided by the U-shaped steel and the bottom fire-resistance reinforcement. When F_c,max > F_t,max, it means that the neutral axis is located in the concrete slab, as showed in Figure 19(a). According to the equilibrium of combined forces in the tension and compression zones, it can be obtained that:

F_{tt} = F_{cc} = F_{t, \max} = 2 h_{w} t_{w} f_{ys} (T) + b t_{w} f_{ys} (T) + A_{rb} f_{yr} (T)

(1l)

The height of the compressive zone is calculated as:

d_{n} = F_{cc} / B f_{c, k} (T)

(1m)

Then the distance d_ct between the combined forces points of the tension and compressive zones can be obtained as follows.

d_{ct} = \frac{2 h_{w} t_{w} (\frac{h_{w}}{2} + h_{b} - \frac{d_{n}}{2}) + b t_{w} (H - \frac{t_{w}}{2} - \frac{d_{n}}{2}) + A_{rb} (H - t_{w} - a - \frac{Φ_{rb}}{2} - \frac{d_{n}}{2})}{2 h_{w} t_{w} + b t_{w} + A_{rb}}

(1n)

The high-temperature flexural capacity M_u (T) of the U-shaped steel-concrete composite beam can be calculated as:

M_{u} (T) = F_{cc} d_{ct}

(1o)

When F_c,max < F_t,max, it means that the neutral axis is located inside the U-shaped steel, as shown in Figure 19(b). In favor of safety calculation, the U-shaped steel compressive zone and the concrete compressive zone inside the beam are ignored. According to the equilibrium of combined forces in the tension and compression zones, it can be obtained that:

F_{tt} = F_{cc} = F_{c, \max} = B h_{b} f_{c, k} (T)

(1p)

Then the height of the U-shaped steel tension zone h_wt is calculated by:

h_{wt} = (F_{cc} - b t_{w} f_{ys} (T) - A_{rb} f_{yr} (T)) / 2 t_{w}

(1q)

Then the distance between the combined forces points of the tension and compressive zones can be obtained as follows:

d_{ct} = \frac{2 h_{wt} t_{w} (H - \frac{h_{wt}}{2} - \frac{h_{b}}{2}) + b t_{w} (H - \frac{t_{w}}{2} - \frac{h_{b}}{2}) + A_{rb} (H - t_{w} - a - \frac{Φ_{rb}}{2} - \frac{h_{b}}{2})}{2 h_{wt} t_{w} + b t_{w} + A_{rb}}

(1r)

According to equation (1o), the M_u(T) of USCB at high temperature is calculated. When compared to the existing flexural bearing capacity method, firstly, the temperature calculation method can consider the temperature delay function of the filling concrete to the U-shaped steel. Secondly, the proposed method can be used to calculate the concrete temperature at any position. Thirdly, the proposed method can be used to calculate the flexural bearing capacity of USCB with fire protection layer and the calculated results is in good agreement with the finite element simulation.

The high-temperature flexural bearing capacity of the composite beam is calculated by ABAQUS, in which the corresponding temperature field is introduced into the calculation model, then the high-temperature capacity is obtained by displacement loading. The high-temperature flexural bearing capacity comparison between finite element calculated results and the formula results are shown in Figure 20, in which the high-temperature capacity of the composite beam calculated by the equation (1o) is in good agreement with the finite element simulation.

Figure 20.

Flexural bearing capacity comparison between formula (1r) and simulated results.

The basic parameters and application range of the proposed design method of USCB are the default values presented in Figure 14. And the applicable object is the U-shaped steel-concrete composite beam with simply supported boundary condition subjected to three-side fire exposure. For a U-shaped steel-concrete composite beam with fixed boundary condition, the fire resistance design can be partial to safety to reference consult the design method of composite beam under simply supported (hinge support at one end and roller support at the other end).

Conclusions

(1) The failure mode of the U-shaped steel-concrete composite beam under fire is flexural damage, in which the fork-shaped cracks appeared in slab top surface. The flange-web section remains intact and no fracture phenomenon appeared on U-shaped steel. And the cracks or even spalling phenomena happened on fire protection layer.

(2) The temperature on the outer surface of U-shaped steel and the bottom concrete slab surface is the highest. And the temperature of fire-resistance reinforcement is lower than the U-shaped steel and can retain high strength and bear the load directly. The fire resistance of specimen increased with the decrease of load ratio (improve by 51%). And the fire resistance was not affected by the shear connectors form.

(3) The temperature field model and fire resistance model can predict the temperature distribution, deformation curve and fire resistance of the USCB accurately. The simplified calculation formula for the temperature of the USCB under ISO-834 standard fire curve is proposed, and the calculation method of high-temperature flexural bearing capacity is put forward.

Footnotes

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 authors are very grateful for the support provided by the National Natural Science Foundation of China (Grant Nos. 52178112, 51878098, and 51208241) and the National Key Research and Development Program of China (Grant No. 2021YFF0500903). The authors are thankful for funding supported by the Yujian Building Industry Technology Group Co., Ltd.

ORCID iD

Yuanlong Yang

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