Investigating Fire Collapse Early Warning Systems for Portal Frames

Abstract

In recent years, firefighter accidents and people injured by the collapse of steel structures during a fire have occurred frequently, which has attracted the attention of the National Emergency Management Department and the Fire and Rescue Bureau. It is urgent to carry out research on early warning systems for building collapse during a fire. Existing early warning methods mainly use characteristic parameters such as temperature, vibration, and structural deformation. Due to the complexity of an actual fire, it is difficult to accurately predict the critical temperature of fire−induced instability in columns and the failure mode after the instability, and there are deviations in the collapse warnings. In this study, changes in ultrasonic transverse and longitudinal wave velocities at high temperatures are used to monitor the stiffness degradation of columns in fire in real time and improve the accuracy of early warning systems. In this study, four common collapse modes of portal frames are obtained by using the results of parametric numerical analysis. According to key displacements and the displacement rates of simple key measuring points, the elastic modulus threshold of a three−level early warning for portal frame collapse with different collapse modes is obtained. Combined with an ultrasonic experiment, the theoretical relationships between the transverse and longitudinal wave velocities and the elastic modulus of steel at high temperatures are verified, and the relationship between the transverse and longitudinal wave velocities and the overall damage of the portal frame is further constructed; then, a new early warning method for portal frame stability during a fire is proposed. Based on the change in wave velocity, a three-level early warning index for predicting portal frame stability during a fire is determined. When the collapse mode of a portal frame is an overall inward collapse, transverse and longitudinal wave velocities are reduced to 2635 m/s and 5308 m/s, respectively. At a second-level warning, they are reduced to 2035 m/s and 4176 m/s, respectively. At 1504 m/s and 3030 m/s, respectively, third-level warnings are issued. This research shows that the real−time monitoring of wave velocities provides an effective way for early warning systems to identify structural collapse. The proposed early warning method can be used as a quick and efficient early warning system for the collapse of portal frames during a fire, and its accuracy and applicability are verified by experiments.

1. Introduction

Due to the serious degradation of the performance of steel structures in fire, buildings often collapse, which seriously threatens the personal safety of firefighters [1]. In the 2000−2024 period, fire rescue teams in China were dispatched 17.492 million times, the number of people saved was 93.569 million, the number of vehicles saved was 32.599 million, and the number of rescue personnel totaled 2.513 million. A total of 354 fire rescue personnel were killed, and 2688 fire rescue personnel were injured. According to fire accident statistics from 27 building collapse cases during a fire [2], in 16 cases, a steel portal frame structure collapsed; in 4 cases, a reinforced concrete structure collapsed; in 3 cases, a brick structure collapsed; and in 4 cases, a wood structure collapsed. In the early warning systems for building collapse during a fire [3], there were 18 cases of steel portal frame in stability and 8 cases of steel frame structure instability, identified by combining temperature and vibration parameters, and the early warning accuracy was 70%. The warning cases for portal frame steel structures, steel frame structures, and steel−concrete structures monitored using computer image recognition combined with digital camera real-time monitoring numbered 29, 14, and 3, respectively, and the early warning system accuracy was 74%. Using ultrasonic tests, microwave radar, temperature, and other aspects of monitoring, there were 35 and 16 early warnings for portal frame steel structure and steel frame structures, respectively, with an early warning accuracy of 80%. Buildings with steel portal frames are the largest type of buildings to collapse during a fire, so it is urgently necessary to carry out research on the early warning method for portal frame collapse during fire.

O’Meaggher et al. [4] proposed two failure modes for portal frames under seven typical fire scenarios, namely inward collapse and outward collapse. This research provides a basis for fire collapse warning systems but does not provide real−time monitoring methods. Song [5] studied the influences of portal frame foundation stiffness, the load ratio, and beam−column section size on collapse mode. This study emphasizes the importance of structural parameters to fire response and is limited in practical applications. Moss et al. [6] studied the collapse mode of a portal frame by simulating different fire scenarios and column bottom constraints. The results showed that a rigid connection at a column’s foot can effectively prevent the structure from collapsing outward; however, the applicability of internal fire scenarios needs to be further studied. Bai et al. [7] studied the influence of different levels of fire power and structure size on the collapse mode of a portal frame and outlined the influence of secondary components on the performance of the structure during a fire. That work further expanded the understanding of structural responses to fire, but there are deficiencies in real−time early warning systems. Deng et al. [8] explored the influence of different fire source layouts on the vertical displacements of portal frames. Although the influence of fire source location on structural response is provided, there is a lack of a comprehensive evaluation of the overall stability of the structure. Li et al. [9] extensively studied the failure mode of a single−span portal frame during a fire and identified four main collapse mechanisms: the lateral collapse mode of columns, the column yield collapse mode, the overall inward collapse of the structure, and the overall outward collapse of the structure. Examining a single−span portal frame, Li [10] further studied the six collapse forms of double−span portal frames and verified the early warning systems for different collapse mechanisms. Lou et al. [11,12] studied the collapse mode of portal frames in real fire situations. Pyl et al. [13] analyzed the fire safety of industrial buildings and three−dimensional rigid frame structures; however, their research mainly focused on fire simulation, which has limitations for the development of real−time early warning systems.

In order to achieve effective early warning for building collapses, early warning methods and technologies are also very important. Dong et al. [14] invented a building structure collapse vibration monitoring system for reinforced concrete frames in fire scenarios. Through the monitoring of the vibration parameters of the points with large structural deformations, the structural collapse warning is carried out. Although this technology is innovative in theory, it may face challenges when applied in the complex environment of the fire scene. Wang et al. [15] monitored the deformations of reinforced concrete columns based on computer image recognition so as to predict the collapse time of buildings in a fire. This method has potential in improving the accuracy of early warning, and its application in actual fires needs to be further verified. Qu and Wang [16] monitored the vertical deformation of a rigid frame column in real time using a digital camera and determined the early warning value and warning time of the rigid frame structure. This work provides a practical method for structural fire warning, but the applicability in different fire scenarios needs further study. Lyu [17] studied the ultrasonic phenomenon of a three−story full−scale steel frame structure under fire and judged the state of structural members through the change in ultrasonic signals so as to realize the real-time early warning of the structure. That study provides a new idea for structural health monitoring in fire, which may be affected by environmental noise in practical applications. Ji et al. [18] used microwave radar and an inclinometer to synchronously obtain the displacement and rotation of the portal frame for collapse warning. This method has advantages in providing structural dynamic information and may require higher costs and technical requirements. Based on the displacement and displacement rate of the key easy measuring points of a portal frame as the early warning index, Li et al. [19] carried out a three−level early warning for different collapse modes. The early warning thresholds under different collapse modes need to be verified. The fire collapse detection and early warning method based on computer vision by Yin [20] is the research goal. The scene picture returned by the monitoring system is used for fire identification so that the traditional independent fire detection equipment can be separated from the steel structure building and more space can be released, which provides a meaningful reference for the early warning of steel structure fire collapse. Yang [21] tested the mechanical properties of aircraft parts based on the principle of ultrasonic late echo and verified the relationship between the elastic modulus and transverse and longitudinal wave velocities of metal materials. Men et al. [22] used the pulse reflection echo method to measure the wave velocities of 45 steel specimens at high temperatures and established a mapping relationship between material hardness, microstructure, and ultrasonic longitudinal wave velocity [22].

The research status shows that the existing early warning methods mainly use structural deformation, temperature, vibration, and other characteristic parameters for collapse monitoring and early warning, but they are still in the stage of theoretical research. Because it is difficult to determine the fire source parameters, actual load size and distribution, and actual material mechanical properties in actual fires, it is difficult to accurately predict the critical temperature of the fire column instability and the failure mode after instability. In addition, there is a lack of real−time monitoring and early warning systems, and there is a deviation in conventional collapse warning. Therefore, in this study, an ultrasonic monitor is used to monitor the stiffness degradation of the fire column in real time through the changes in the transverse and longitudinal wave velocities of the steel during the heating process, and the three−level early warning of collapse is carried out, which improves the early warning accuracy. This early warning method can also meet the actual needs of fire rescue, as it is convenient, easy to use, accurate, and effective.

2. Numerical Simulation

2.1. Basic Finite Element Model

The ABAQUS (v2016) coupled temperature−displacement analysis module is used to simulate and verify the collapse process of the portal frame structure. In the coupled temperature−displacement analysis, the temperatures are integrated using a backward difference scheme, and the nonlinear coupled system is solved using the Newton method. The test frame has a span of 24 m and a height of 6 m. The geometric size is shown in Figure 1. The basic dimensions of the main and secondary components are shown in

Table 1. Information of steel member sections.

Member Type	Section Type and Size/mm	Material
Column	100 × 50 × 10 × 12	Q235
Beam	(100–150) × 60 × 10 × 12	Q235
Tie beam	Φ80 × 5	Q235
Purlin	90 × 60 × 3.2 × 4.5	Q235
Diagonal bridging	Φ10	Q235

.

The steel density is 7850 kg/m³, and Poisson’s ratio is 0.3. The Eurocode 3 high−temperature stress−strain constitutive mode is used [23]. The unit type is C3D8T, and the sequential coupling analysis step is used for simulation. The beam−column members, the main members, and the secondary members are connected into a whole by tie constraints. The column foot considers two kinds of constraints. The rigid constraint has degrees of freedom U₁−U₃ and rotational degrees of freedom U_R1−U_R3, while the hinged constraint has U₁−U₃. The vertical uniform load acting on the beam is 1.2 kN/m. The thermal parameters of the steel are unified using EN 1993−1−1 [24], which can better represent a real fire scene.

The European standard EN 1993−1−2 [25] gives the thermal conductivity of steel as [25]

K_S = 54 − 3.33 × 10⁻² T     20 °C ≤ T ≤ 800 °C

(1)

where K_S is the thermal conductivity and T is the component temperature.

EN 1993−1−2 [25] also gives the specific heat capacity of steel as

C_S = 425 + 0.773T − 1.69 × 10⁻³ + 2.22 × 10⁻⁶    20 °C ≤ T ≤ 600 °C

(2)

where C_S is the specific heat capacity and T is the component temperature.

The coefficient of thermal expansion αs = 1.4 × 10⁻⁵ of steel is given by EN 1993−1−2 [25]. The changes in the thermal parameters of steel with temperature are shown in

Table 2. Steel thermal parameter properties.

Temperature/°C	Thermal Conductivity W/(m·K)	Specific Heat Capacity J/(kg·°C)	Coefficient of Thermal Expansion
20	3200.5	440.1	1.4 × 10−5
100	3040.2	492.6	1.4 × 10−5
200	2840.4	549.76	1.4 × 10−5
300	2640.6	609.74	1.4 × 10−5
400	2440.8	685.88	1.4 × 10−5
500	2241	791.5	1.4 × 10−5
600	2041.2	939.92	1.4 × 10−5

.

2.2. Simulation of Different Fire Conditions

In the temperature field simulation stage, this study comprehensively considers the heat conduction, convection, and radiation mechanisms of the material. The thermal convection coefficient of the fire surface of the steel is 1500 J/(m²·min·°C), the thermal convection coefficient of the non-fire surface is 540 J/(m²·min·°C), and the thermal radiation coefficient of the steel is 3.402 × 10⁻⁶. The initial temperature is 20 °C and the initial CO₂ concentration is 0. This fire model can more accurately simulate the heat transfer process in a fire and can provide a more realistic fire scene simulation. The GB 51249-17 standard fire model mainly focuses on heat conduction but ignores the influence of heat convection and heat radiation [26]. The temperature field distribution is not accurate. The comprehensive fire model can better simulate the complex heat transfer process in a fire, which is helpful in formulating more accurate collapse warning. Condition 1 is an overall fire, where the fire components are mainly columns and beams, and the fire surface of the component is more. The fire areas are ①–⑧. Condition 2 is a local fire, where the fire component is mainly the column, and the fire surface of the component is mainly the inner side. The fire areas are ①–② and ⑦–⑧. The fire simulation software FDS is used to generate the dynamic ambient temperature field data of the fire. The temperature rise curve is shown in

Table 3. Temperature rise curve of different fire exposure forms.

Time/min	Condition 1/°C	Condition 2/°C
0	20	20
2	482	415
4	594	517
6	712	604
8	780	640
10	845	662
12	886	700
15	902	730

.

After the ambient temperature field data obtained from Table 3 are loaded into ABAQUS in the form of amplitude, the coupled temperature−displacement analysis step is established to obtain the temperature fields of the two fire modes. The temperature rise curves of the two fire−exposed components are shown in Figure 2.

From Figure 2, it can be seen that the temperature rise curve of the column under working condition 1 is significantly higher than that of the column under working condition 2 due to the uniform heating, showing a more rapid heating process. Although the column heating rate under condition 1 is faster, the overall heating trend is still consistent with the standard heating curve. At the same time, whether it is working condition 1 or working condition 2, the heating curve of the beam shows a similar shape, which is slightly lower than the standard heating curve, which reflects the consistent performance of the beam in heat conduction and heat convection.

Huang et al. [27] conducted experiments to derive the relationship between the temperature and the decay of the elastic modulus of Q235 steel, as shown in

Table 4. Dampings of elastic modulus at different temperatures.

Temperature/°C	Elastic Modulus Reduction Factor
20	1
100	1
200	0.9
300	0.8
400	0.7
500	0.6
600	0.31
700	0.22

.

Under fire conditions, the temperatures of steel columns and steel beams increase with time, resulting in gradual decreases in their elastic moduli, which in turn leads to a decrease in the overall structural stiffness. The overall displacement increases with time. The purpose of this section is to focus on the quantitative relationship between the elastic modulus attenuation coefficient of steel columns and the displacement of key points and to find the elastic modulus threshold for fire warning through key displacement and the displacement rate. The deformation at the typical position of the portal frame is shown in Figure 3.

The connection mode of the column base has a great influence on the key displacement. Considering the two connection modes of the column base rigid connection and hinge connection, the rigid connection lateral constraint is strong, and the vertical displacement of the frame is mainly studied. Because of the symmetry of the fire source, U₃, U₄, U₅, and U₆ are also symmetrical, so U₁, U₃, and U₄ are selected as the key displacements of the overall inward collapse. The key displacement and elastic modulus attenuation coefficient of the column base rigid connection under working condition 1 under fire are shown in Figure 4.

When the steel column connection is rigid, the overall inward collapse mode occurs. The collapse mode shows that the lateral displacement of the column is small, and the vertical displacement of the beam span is the largest. In the early stage of the fire, due to thermal expansion, the top of the steel frame will move upward, and the eaves will move outward. As the temperature increases, the material properties of the steel decrease significantly. The vertex of the steel frame begins to move downward after reaching the maximum displacement. If the column base and secondary members can provide sufficient lateral constraints, the outward expansion of the heated column will be limited, and the steel frame bends downward to form a catenary effect. The catenary effect pulls the adjacent columns inward and eventually causes the entire frame to collapse inward, as shown in Figure 5. The OA section is the Security phase. The volume of the fire column and the beam expands during the heating process. The first−level early warning point A is U₁, U₄ begins to decline, and U₃ begins to expand inward; that is, the deformation rate is 0. At the end of the outward expansion stage, the temperature of the fire column is about 400 °C, and the risk of collapse increases. The second−level warning point B is the stage where the deformation rates of U₁, U₃, and U₄ increase continuously. When the deformation rate of point B of the maximum deformation displacement U₁ reaches three times the average deformation rate of the OA stage, a second-level warning is issued, and the temperature of the fire column is about 600 °C. When the deformation rate of point C reaches 3 times the average deformation rate of stage AB, the temperature of the fire column is about 800 °C, and a three−level warning is issued. Fire rescue personnel must evacuate the fire scene.

The hinged connection lateral restraint of the column base is weak, focusing on the lateral displacement and vertical displacement of the frame, and the eaves of the column top should be paid attention to. Because the displacement difference between U₄ and U₅ is small, U₁, U₃, U₄, and U₆ are selected as the key displacements of the overall outward collapse. The key displacement and elastic modulus attenuation coefficient of the hinged column base are shown in Figure 6.

When the connection mode of the steel column is hinged, the overall outward collapse mode occurs. The collapse mode shows that the lateral displacement of the column is large and the vertical displacement is relatively small. In the early stage of the fire, due to thermal expansion, the vertex of the steel frame will move upward, while the eaves will move outward. With the increase in temperature, the material properties of the steel will decrease significantly. The vertex of the steel frame begins to move downward after reaching the maximum displacement, while the eaves continue to expand outward. If the lateral constraint of the column is weak, the heated column will continue to expand outward, eventually leading to the collapse of the frame in one direction, as shown in Figure 7. Due to the lack of lateral constraints, the lateral displacements of beams and columns increase significantly, and the vertical displacements decrease. The OA section is the safety stage. The first−level warning point A is the end stage of U₁, U₃, and U₄ displacement outward expansion. Point A is the point where the deformation rate is 0. The temperature of the fire column is about 400 °C. The second−level early warning point B is the stage where the maximum deformation displacement U₆ deformation rate increases continuously. When the deformation rate of point B reaches 3 times the average deformation rate of the OA stage, a second−level early warning is issued. The temperature of the fire column is about 580 °C. When the deformation rate of point C reaches 3 times the average deformation rate of stage AB, a three−level warning is issued. The temperature of the fire column is about 740 °C, and fire rescue personnel must evacuate the fire scene.

The elastic moduli of the three−level early warning of two different collapse modes under fire in condition 1 are shown in

Table 5. The elastic moduli of two different collapse modes in three−level early warning under working condition 1.

Collapse Mode	Elastic Modulus Attenuation Coefficient in Early Warning	Elastic Modulus in Early Warning/GPa	Warning Temperature/°C
Overall inward collapse	0.30	140.70	400
	0.58	84.42	600
	0.78	44.22	800
Overall outward collapse	0.30	140.70	400
	0.50	100.50	570
	0.72	56.28	740

.

From Table 5, it can be seen that the connection mode of the portal frame in the fire significantly affects the collapse warning, especially the secondary and tertiary warnings. With the increase in temperature, the lateral stiffness of the frame decreases, and it is more likely to collapse. Therefore, the second and third−warning elastic moduli of outward collapse (100.5 GPa and 56.28 GPa) are higher than those of inward collapse (84.42 GPa and 44.22 GPa). In the first warning, the elastic modulus is similar in the two collapse modes, and the influence is small. It shows that outward collapse should be prevented first.

Under condition 2, the fire component is mainly a column. When the column base is hinged, the column will roll and destroy, and the outward expansion of the heated column will continue to increase. Finally, the heated column is destroyed under the combined action of bending moment and axial force, which is manifested as the lateral collapse mode of the column. The key displacements and elastic modulus attenuation coefficients of the column lateral collapse are shown in Figure 8:

Under fire condition 2, the lateral collapse mode is mainly reflected in the increase in the lateral displacement of the column and the decrease in the vertical displacement. When the time of the safety stage increases, the time of the second−level early warning stage is shortened, the early warning point A is the end stage of the outward expansion of the steel, the deformation rate is 0, and a first−level early warning is issued. The temperature of the fire column is about 510 °C. When the deformation rate of point B of the maximum lateral displacement U₃ is 3 times the average deformation rate of the OA section, a second−level warning is issued. The temperature of the fire column is about 780 °C. When the deformation rate of point C is 3 times the average deformation rate of section AB, a three−level warning is issued. The temperature of the fire column is about 920 °C.

Under fire condition 2, when the column base connection is rigid, the column will yield failure. When the axial pressure reaches the critical value, the column will suddenly lose stability. Finally, the column will buckle under the action of axial force, bending deformation occurs, and the column yield collapse mode occurs. The key displacements and elastic modulus attenuation coefficients of the column yield collapse are shown in Figure 9. The warning point A is the first−level warning when the maximum displacement U₂ reaches 1/5 of the ultimate displacement. The temperature of the fire column is about 450 °C. When the deformation rate of point B is 3 times the average deformation rate of the OA segment, a secondary warning is issued. The temperature of the fire column is about 700 °C. When the deformation rate of point C is 3 times the average deformation rate of section AB, a three−level warning is issued. The temperature of the fire column is about 920 °C.

The elastic moduli of the two different collapse modes under condition 2 of the third−level early warning are shown in

Table 6. The elastic moduli of two different collapse modes in three−level early warning under working condition 2.

Collapse Mode	Elastic Modulus Attenuation Coefficient in Early Warning	Elastic Modulus in Early Warning/GPa	Warning Temperature/°C
Lateral collapse mode of column	0.50	100.50	510
	0.75	50.25	780
	0.85	30.15	920
Column yield collapse mode	0.45	110.55	450
	0.65	70.35	700
	0.85	30.15	920

.

Four common collapse modes of portal frames are summarized in Figure 10.

2.3. Fire Simulation of Different Span–Depth Ratios

This section is focused on the influence of different span-to-height ratios on the prediction of structural collapse. This section selects three typical spans, namely 12 m, 18 m, and 24 m. They represent working conditions with span−to−height ratios of 2, 3, and 4, respectively. The fire condition is working condition 1, and the column base connection is rigid. Through the vertical displacement of the ridge and the horizontal displacement of the eaves at the top of the column under different span conditions, the degree of degradation of the stiffness of the steel frame can be evaluated. The mid−span deflection curves under different span conditions are shown in Figure 11.

For structures with different spans, the collapse mode is the overall inward collapse mode, but the displacement response is different. The larger the span, the larger the vertical displacement of the ridge, and the smaller the upward expansion. The horizontal displacement of the eaves decreases with the increase in the span.

According to the simulated working conditions of different spans, the relationship between different spans, the fire time, and the overall stiffness damage coefficient is shown in Figure 12.

It can be seen from Figure 12 that with the extension of fire time and the increase in span, the stiffness damage coefficient of the structure shows a gradual upward trend. For the structure with a span of 12 m, the growth of the damage coefficient shows a linear acceleration in the first 6 min. Then, between 6 min and 15 min, the growth rate increases significantly and eventually stabilizes. For the structure with a span of 24 m, the damage coefficient increases rapidly in the first 9 min. In the period of 9 min to 15 min, the growth rate slows down and then reaches a steady state.

This shows that the influence of span on structural performance degradation is significant. The elastic moduli of three−stage early warning under different spans are shown in

Table 7. Elastic moduli of three−level early warning under different spans.

Span/m	Elastic Modulus Attenuation Coefficient in Early Warning	Elastic Modulus in Early Warning/GPa
12	0.50	100.50
	0.65	70.35
	0.85	30.15
18	0.42	116.58
	0.60	80.40
	0.81	38.19
24	0.30	140.70
	0.58	84.42
	0.78	44.22

.

3. Experimental Verification

3.1. Principle of Real-Time Monitoring of Acoustic Emission

The following two factors are the main foundation for the real-time monitoring of longitudinal and transverse wave velocities in acoustic emission for the stiffness concept of a single-layer portal frame. The principle of acoustic emission monitoring is shown in Figure 13.

• Acoustic emission phenomenon: small fractures or defects may form within a single-layer portal frame as a result of external loads or changes in internal tension. These changes will cause acoustic emission signals. A structure’s stiffness is correlated with the speed of elastic waves, such as longitudinal and transverse waves, which are emitted by acoustic emission.
• Real-time monitoring: by installing acoustic emission sensors, the corresponding wave speed may be determined by recording the acoustic emission signals inside the structure in real time.

3.2. Experimental Equipment

The Q235 steel has a length of 1 m, a cross−section size of 80 mm × 50 mm × 4 mm × 10 mm, a steel density of 7850 kg/m⁻³, and an elastic modulus of 201 GPa at room temperature and was placed horizontally on a non–vibration support frame. The model of the ultrasonic detector is USN80, (Xi Jing University, Xi’an, China) the sound speed range is 300−10,000 m/s, the ultrasonic probe adopts DL5C6L, (Xi Jing University, Xi’an, China) the probe frequency is 5 MHz, the probe was symmetrically arranged around the sample, and the ultrasonic probe was placed along the length of the beam at 250 mm intervals. The central sensor is located in the middle of the span, and the acquisition reduces the error. The ultrasonic probe is aligned vertically with the surface of the steel beam. To ensure the best wave transmission and reception, the position of the ultrasonic probe is shown in Figure 14. Before the start of the test, the steel beam sample was washed with isopropanol to remove surface contaminants, and a water−based gel was used as a coupling agent to evenly apply the ultrasonic probe to the area of contact with the steel beam. The ambient temperature was maintained at 22 ± 2 °C, and the relative humidity was kept below 50% to minimize the environmental factors and eliminate the influence on the ultrasonic wave velocity. This system consists of a data analysis platform, signal processing software, an acoustic emission sensor, and a data gathering device. The data acquisition equipment transforms the acoustic emission signals into digital signals, the signal processing program calculates wave speed and waveform analysis, and the sensor records the signals.

In Figure 15, the experimental apparatus is displayed.

The ultrasonic testing system excites the propagation paths of transverse and longitudinal waves, as shown in Figure 16. The thickness of the steel is 4 mm.

The high-temperature furnace MF−1200−1000 (Xi Jing University, Xi’an, China) was used to uniformly heat the steel beam. The furnace is operated on a controllable electric heating element. The maximum temperature was set to 1200 °C. The temperature in the furnace was monitored and adjusted by thermocouples connected to the PID controller (Xi Jing University, Xi’an, China) to ensure a stable and accurate heating curve. The heating rate was set to 50 °C/min until the desired temperature is reached. The average temperature of 5 probe points was monitored by the high-temperature equipment, as shown in Figure 17.

3.3. Test Results

The acquisition frequency of the ultrasonic testing device is 100 Hz, the sampling time is 80 μs, and the gain is 30 dB. The ultrasonic signals received from the steel at room temperature are shown in Figure 18.

In Figure 18, the first echo time of P−wave and S−wave velocities at room temperature can be observed. In order to ensure the accuracy of the experimental data, the ultrasonic signal was amplified, averaged, and enveloped. “T” represents transverse waves, “L” represents longitudinal waves, and “W” denotes mode conversion echoes. Because the common collapse type of a portal frame is overall inward collapse, the temperature ranges of the three−stage warning are shown in Table 5, which are 400 °C, 600 °C, and 800 °C, respectively. The acoustic signals of steel at 400 °C, 600 °C, and 800 °C are shown in Figure 19.

Interpolation on the above envelope signal was performed, and the echo time corresponding to the maximum amplitude was analyzed. The data are shown in

Table 8. The maximum amplitudes and the corresponding times of shear wave, longitudinal wave, and converted echo at 400 °C.

Temperature/°C	Parameter	Maximal Amplitude/mV	Echo Time/ns	Wave Velocity/m/s	E/GPa
400	T1	200	14,124	2635	145.2
	T2	140	29,660
	T3	145	45,196
	L1	176	7054	5308
	W1	132	10,590
	W2	146	21,780

,

Table 9. The maximum amplitudes and the corresponding times of shear wave, longitudinal wave, and converted echo at 600 °C.

Temperature/°C	Parameter	Maximal Amplitude/mV	Echo Time/ns	Wave Velocity/m/s	E/GPa
600	T1	301	17,073	2035	88.54
	T2	182	35,490
	T3	145	51,080
	L1	206	9033	4176
	L2	178	18,100
	W1	144	13,052

and

Table 10. The maximum amplitudes and the corresponding times of shear wave, longitudinal wave, and converted echo at 800 °C.

Temperature/°C	Parameter	Maximal Amplitude/mV	Echo Time/ns	Wave Velocity/m/s	E/GPa
800	W1	160	19,145	1504	47.6
	T1	350	25,090
	T2	210	50,150
	L1	230	13,200	3030
	L2	196	27,400
	L3	175	40,100

. Let the one−way propagation time for the transverse wave be t_T, and the one−way propagation time for the longitudinal wave be t_L, then t_T1 = Δt + 2t_T, t_T2 = Δt + 4t_T, t_T3 = Δt + 6t_T, t_L1 = Δt + 2t_L, t_L2 = Δt + 4t_L, t_W1 = Δt + t_T + t_L, t_W2 = Δt + 2t_T + 2t_L. The ultrasonic testing system was calibrated, with the default Δt = 0. The elastic modulus was obtained according to the transverse and longitudinal wave velocities of Equation (3) [21].

$$E={\displaystyle \frac{\rho C_{\mathrm{T}}^2\left(3M^2-4\right)}{M^2-1}}$$

(3)

where E stands for the elastic modulus, ρ stands for density, C_T stands for transverse wave velocity, and M stands for the ratio of longitudinal wave velocity to transverse wave velocity.

In the overall inward collapse mode, the temperatures of the three−stage early warning are 400 °C, 600 °C, and 800 °C, respectively. The elastic moduli of the three−stage early warning based on the displacement and rate of the key easy measuring points are 140.7 GPa, 84.42 GPa, and 44.22 GPa, respectively. Based on Table 8, Table 9 and Table 10, the elastic moduli calculated by the ultrasonic transverse and longitudinal wave velocities at the three−stage early warning temperatures are slightly different from the finite element analysis, so the ultrasonic transverse and longitudinal wave velocities are verified. The feasibility of early warning of steel structure fire collapse can be verified.

4. Conclusions

Because it is difficult to determine fire source parameters, the actual load size and distribution, and the actual material mechanical properties in an actual fire, it is difficult to accurately predict the critical temperature of the fire column instability and the failure mode after instability. In addition, there is a lack of real−time monitoring and early warning systems, and there is a deviation in conventional collapse warning. Based on the ultrasonic experimental data and numerical simulation results, this study summarizes the wave velocity threshold of three−stage early warning under four common collapse modes of portal frame, monitors the stiffness degradation in real time, and puts forward the collapse judgment index, which improves the accuracy of early warning. The main conclusions are drawn as follows:

• Different fire modes and column base connection modes affect the collapse mode of the portal frame, and the influence of span–depth ratio is small.
• In this study, the thermal–mechanical coupling simulation method is used to obtain the elastic modulus threshold of the three-level early warning of the portal frame according to the key displacements and displacement rates of the key easy measuring points. Combined with the ultrasonic experiment, the quantitative relationship between the transverse and longitudinal wave velocities and the elastic modulus is established, and the relationship between the sound velocity and the overall damage of the portal frame is further constructed.
• When the portal frame collapses inward as a whole, the first-level warning A is the end of the outward volume expansion of steel; that is, when the deformation rate is 0, the corresponding transverse and longitudinal wave velocities are 2635 m/s and 5308 m/s, respectively. When the deformation rate of the second-level early warning point B reaches three times the average deformation rate of the OA stage, the second-level early warning is issued, and the corresponding transverse and longitudinal wave velocities are 2035 m/s and 4176 m/s, respectively. When the deformation rate of the third-level early warning point C reaches three times the average deformation rate of the AB stage, the third-level early warning is issued, and the corresponding transverse and longitudinal wave velocities are 1504 m/s and 3030 m/s, respectively.
• There are also some limitations in the use of ultrasonic transverse and longitudinal wave velocities for fire collapse warning. The fire scene is usually accompanied by complex environmental factors such as high temperature, smoke, and noise. Smoke may affect the transmission of signals, while noise may be mixed with ultrasonic signals, increasing the difficulty of signal processing. Further research can be combined with a variety of early warning technologies to provide more comprehensive early warning information and use this early warning method to provide warnings for other steel frame structures.