In recent years, the global push for renewable energy has led to widespread adoption of solar power systems, particularly photovoltaic panels installed on building roofs. As a researcher in structural engineering, I have focused on the integration of these photovoltaic systems into lightweight steel structures, such as industrial buildings. The addition of solar panels increases the permanent roof load, which can cause excessive deformation in simply supported purlins, often exceeding code limits. To address this, we propose using a down-stayed purlin structure for reinforcement, enhancing stiffness and load-bearing capacity. However, since purlins in lightweight steel buildings are typically not protected against fire, it is crucial to investigate their mechanical performance under fire conditions. This study employs finite element analysis to evaluate the behavior of down-stayed purlin structures with photovoltaic panels during fires, providing insights for safe design practices.
The finite element model was developed using ANSYS Workbench, with the down-stayed purlin structure comprising C-shaped steel purlins, struts, and tie rods. The purlin span was set to 6 m, with a building height of 20 m and purlin spacing of 2 m, representing a typical large-space structure. The strut height was 0.5 m, and the strut spacing was one-third of the purlin span, i.e., 2 m. The components were modeled using Beam elements, with rigid connections and hinged supports at the purlin ends. The photovoltaic panels, specifically the JAM60 285-PR model, have dimensions of 1650 mm × 991 mm × 40 mm and a weight of 0.13 kN/m². According to load standards, the dead load was 0.5 kN/m² and the live load was 0.5 kN/m², resulting in an equivalent uniform line load of 2.26 kN/m applied to the purlins. The mesh was generated using a general division scheme to ensure accuracy.
For the fire scenario, we considered a large-space building fire, as standard ISO834 curves do not apply due to the absence of flashover. The fire power was set to 5 MW with a medium growth rate, and the air temperature rise was calculated using an empirical formula for large-space fires. The temperature at any point is given by:
$$ T(m,h,t) – T_S(0) = T_h(1 – 0.8e^{-\delta t} – 0.2e^{-0.1\delta t})[\phi + (1 – \phi)e^{(v – x)/\lambda}] $$
where \( T(m,h,t) \) is the air temperature at time \( t \), horizontal distance \( m \), and vertical height \( h \); \( T_S(0) \) is the initial temperature (20°C); \( T_h \) is the maximum air temperature; \( \delta \) is a coefficient based on fire power and growth rate; \( \phi \) is a temperature attenuation factor; and \( v \) and \( \lambda \) are distance parameters. The fire source was located at ground level, centered under the purlin. After 60 minutes of heating, the temperature distribution showed gradients across the structure, with peak temperatures affecting the purlin areas.
The material properties for the steel components were defined based on high-temperature behavior. The purlins and struts used Q235 steel, while the tie rods used HRB400 reinforcement bars. At room temperature, Q235 has a yield strength of 235 MPa and an elastic modulus of 206,000 MPa; HRB400 has a yield strength of 360 MPa. The thermal expansion coefficient for steel is \( 1.2 \times 10^{-5} \), density is 7,850 kg/m³, and Poisson’s ratio is 0.3. The constitutive model assumed ideal elastoplastic behavior. The temperature-dependent mechanical properties are summarized in Table 1, which includes yield strength, elastic modulus, thermal conductivity, and specific heat capacity at various temperatures.
| Temperature (°C) | Yield Strength (MPa) | Elastic Modulus (MPa) | Thermal Conductivity (W/m·°C) | Specific Heat Capacity (J/kg·°C) |
|---|---|---|---|---|
| 20 | 235 | 206,340 | 53.3 | 439.8 |
| 50 | 235 | 206,143 | 52.3 | 459.7 |
| 100 | 235 | 204,245 | 50.7 | 487.6 |
| 150 | 235 | 201,333 | 49.0 | 510.4 |
| 200 | 235 | 197,900 | 47.3 | 529.8 |
| 250 | 235 | 193,910 | 45.7 | 547.3 |
| 300 | 235 | 188,795 | 44.0 | 564.7 |
The temperature rise in steel members was computed considering heat transfer via radiation and convection, along with internal conduction. The incremental temperature change is given by:
$$ T_s(t + \Delta t) = \frac{Q S h_1 (T_a(t) – T_s(t)) \Delta t}{\rho_s c_s} + T_s(t) $$
where \( Q \) is a correction factor (1.0), \( S \) is the surface-to-volume ratio, \( h_1 \) is the net heat flux, \( T_a(t) \) is the ambient air temperature, \( T_s(t) \) is the steel temperature, \( \rho_s \) is density, \( c_s \) is specific heat, and \( \Delta t \) is the time increment (≤5 s). The net heat flux incorporates both convective and radiative components:
$$ h_1 = \mu_c h_c + \mu_r h_r $$
with \( \mu_c = 1.0 \) and \( \mu_r = 0.15 \) as safety factors. The convective heat flux is \( h_c = b_c (T_a – T_s) \), where \( b_c = 25 \, \text{W/(m}^2\cdot\text{°C)} \). The radiative heat flux is calculated as:
$$ h_r = \chi \sigma_m \sigma_f \epsilon [(T_g + 273)^4 – (T_s + 273)^4] $$
where \( \chi = 1.0 \), \( \sigma_m = 0.3 \), \( \sigma_f = 0.8 \), and \( \epsilon = 5.67 \times 10^{-8} \, \text{W·m}^{-2}\cdot\text{K}^{-4} \). These equations were implemented in the finite element analysis to simulate the thermal response.
Under normal temperature conditions, the simply supported purlin with added photovoltaic panels exhibited significant deformation. The maximum displacement at mid-span was 48.59 mm, exceeding the allowable limit of 40 mm (L/150 for a 6 m span). However, the stress remained below the yield strength, with a peak of 119.03 MPa at the supports. This indicates that deformation, not strength, is the critical issue for simply supported purlins with solar panels. In contrast, the down-stayed purlin structure reduced the maximum displacement to 37.12 mm at the tie rods and 14.50 mm at the purlin mid-span, within the allowable limit. The stress also decreased to a maximum of 98.27 MPa, demonstrating improved stiffness and load-bearing capacity. The component specifications for the model are listed in Table 2.
| Component | Cross-Section Dimensions (mm) |
|---|---|
| Purlin | 160 × 70 × 20 × 3 |
| Strut | 25 × 1.5 |
| Tie Rod | 8 |
Under fire conditions, the simply supported purlin showed a rapid increase in displacement, reaching 53.61 mm at 1,800 s, which surpasses the allowable deformation. The stress exceeded the yield strength at 1,300 s, peaking at 248.02 MPa, leading to failure. For the down-stayed purlin, the displacement growth was slower; the purlin displacement reached 37.70 mm at 1,800 s, still within limits, but the tie rods experienced a large displacement of 122.94 mm. The stress in the purlin reached yield at 1,500 s, with a maximum of 242.76 MPa, indicating that the down-stayed configuration enhances stiffness but offers limited improvement in fire resistance for load-bearing capacity. This underscores the importance of passive fire protection, such as fire-resistant coatings, for down-stayed purlins in buildings with photovoltaic systems.
In conclusion, the integration of photovoltaic panels into lightweight steel structures necessitates reinforcement using down-stayed purlin systems to control deformation under normal conditions. However, in fire scenarios, while the down-stayed purlin maintains stiffness, its ability to enhance load-bearing capacity is constrained. Therefore, for roofs reinforced with down-stayed purlins, implementing passive fire protection measures is essential to ensure structural integrity. This research highlights the critical role of comprehensive design considerations for solar panel installations in industrial buildings, contributing to safer and more sustainable energy solutions.