The global push for sustainable energy has made the integration of solar panels onto existing building structures a widespread practice. For expansive industrial buildings like light steel workshops, the rooftop offers a vast, often underutilized area for photovoltaic (PV) installations. However, this integration introduces significant and permanent new structural loads. The addition of these solar panel arrays can push the existing structural members, particularly roof purlins designed with minimal reserve strength, beyond their intended service limits. The primary failure mode for such cold-formed thin-walled C-section purlins, when adequately laterally restrained by the roof sheeting, is bending failure. The increased permanent load from the solar panel system frequently leads to excessive deflections that violate code serviceability limits, even if the ultimate bending capacity is not immediately exceeded.
To address this, a structural retrofit solution known as the down-stayed purlin system has been proposed and implemented. This system enhances the flexural stiffness and load-bearing capacity of a simply supported purlin by introducing a tension system beneath it. Typically, this involves one or more horizontal struts (or spreader bars) suspended below the purlin at strategic points, which are in turn supported by diagonal and sometimes horizontal tie rods connected back to the purlin’s supports. This creates a truss-like action, allowing the purlin to act as the top chord of a shallow truss, significantly reducing its effective bending span.
While the ambient temperature performance of such retrofitted systems has been studied, their behavior under fire conditions remains largely unexplored. In typical light steel construction, structural fire protection (e.g., intumescent coatings) is seldom applied to secondary members like purlins due to economic considerations. Therefore, understanding how a down-stayed purlin system, installed to support the weight of solar panels, performs when exposed to fire is a critical safety concern. This article investigates the thermo-mechanical response of such systems through finite element analysis, comparing the performance of simply supported and down-stayed purlins under both ambient and fire conditions.
Theoretical Model and Finite Element Setup
The analysis focuses on a typical 6-meter span purlin within a large, high-bay industrial building. The building geometry influences the fire development and subsequent thermal exposure. A down-stayed system with a strut depth of 0.5 m and struts placed at the third-points of the span (2 m spacing) is modeled. All members are modeled using beam elements. The connections between the purlin, struts, and tie rods are idealized as rigid connections, while the purlin end supports are modeled as pinned. The self-weight of all members is included.
Structural Loads from Solar Panels
The added load from the photovoltaic system is a key driver for the retrofit. A typical crystalline silicon solar panel and mounting system can add a significant dead load. For this study, the equivalent uniformly distributed line load on the purlin is calculated based on the following assumptions and code prescriptions. The load combination for the ultimate limit state at ambient temperature is considered.
| Load Type | Value (kN/m²) | Description |
|---|---|---|
| Original Roof Dead Load (G₁) | 0.50 | Sheeting, insulation, etc. |
| Solar Panel & Mounting Dead Load (G₂) | 0.13 | Estimated weight of PV system |
| Roof Live Load (Q) | 0.50 | As per loading code |
The total factored design load (w) on the purlin, with a purlin spacing of 2 meters, is calculated as:
$$w = s \times (1.2 \times (G_1 + G_2) + 1.4 \times Q)$$
$$w = 2.0 \, \text{m} \times (1.2 \times (0.50 + 0.13) \, \text{kN/m}^2 + 1.4 \times 0.50 \, \text{kN/m}^2)$$
$$w = 2.0 \times (0.756 + 0.70) = 2.912 \, \text{kN/m}$$
A slightly lower design value of 2.26 kN/m was used in the referenced analysis, but the principle remains: the solar panel addition substantially increases the permanent load demand.
Fire Model and Thermal Analysis
Standard fire curves like ISO 834 are not applicable to large, high-bay industrial buildings where “flashover” does not occur and a localized fire is more likely. For this analysis, an empirical temperature-time curve for large space fires developed by Li Guoqiang is adopted. The air temperature \(T(m,h,t)\) at time \(t\), horizontal distance \(m\) from fire center, and height \(h\) above ground 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 \(T_s(0)\) is the initial ambient temperature (20°C), \(T_h\) is the maximum air temperature at height \(h\), \(\delta\) is a coefficient dependent on fire growth rate and power, and \(\phi\), \(v\), \(\lambda\) are parameters related to temperature decay with horizontal distance. The fire is assumed to be located centrally below the purlin span with a power of 5 MW and medium growth rate.
The temperature rise in the steel members is calculated based on heat transfer from the hot gases via convection and radiation, neglecting thermal gradients within the cross-section (lumped mass approach). The incremental temperature rise \(\Delta T_s\) in a time step \(\Delta t\) is given by the Eurocode-style formulation:
$$\Delta T_s = \frac{\dot{h}_{net}}{c_s \rho_s} \cdot \frac{A_m}{V} \cdot \Delta t$$
Where \(\dot{h}_{net}\) is the net heat flux per unit area, \(c_s\) and \(\rho_s\) are the specific heat and density of steel, and \(A_m/V\) is the section factor (surface area per unit volume). The net heat flux is:
$$\dot{h}_{net} = \alpha_c (T_g – T_s) + \Phi \cdot \epsilon_m \cdot \epsilon_f \cdot \sigma \cdot [(T_g + 273)^4 – (T_s + 273)^4]$$
Here, \(\alpha_c\) is the convection coefficient (25 W/m²K), \(T_g\) and \(T_s\) are gas and steel temperatures, \(\Phi\) is a configuration factor, \(\epsilon_m\) and \(\epsilon_f\) are emissivities of the member and flames, and \(\sigma\) is the Stefan-Boltzmann constant.
High-Temperature Material Properties
The degradation of steel’s mechanical properties with temperature is crucial. The model uses Q235 steel for the purlin and strut, and HRB400 steel for the tie rods. A simplified ideal elastoplastic model is assumed. Key properties degrade as follows:
| Temperature, T (°C) | Yield Strength, f_y(T) (MPa) | Young’s Modulus, E(T) (GPa) | Thermal Conductivity, k (W/m·K) | Specific Heat, c (J/kg·K) |
|---|---|---|---|---|
| 20 | 235 | 206 | 53.3 | 440 |
| 100 | 235 | 204 | 50.7 | 488 |
| 200 | 235 | 198 | 47.3 | 530 |
| 300 | 235 | 189 | 44.0 | 565 |
| 400 | 216 | 179 | 40.7 | 610 |
| 500 | 145 | 168 | 37.4 | 690 |
The reduction factors for yield strength (\(k_y(T) = f_y(T)/f_y(20°C)\)) and modulus of elasticity (\(k_E(T) = E(T)/E(20°C)\)) can be approximated by piecewise linear or non-linear functions from codes. A common approximation for carbon steel up to 400°C is a linear reduction. The thermal expansion coefficient is taken as \(1.2 \times 10^{-5} \, /°C\).
Performance Analysis Under Ambient Temperature
Simply Supported Purlin
Under the increased load from the solar panel system, the simply supported purlin’s performance is governed by serviceability. The maximum mid-span deflection (\( \delta_{max} \)) for a uniformly loaded simply supported beam is:
$$\delta_{max} = \frac{5 w L^4}{384 E I}$$
Where \(w\) is the service load (unfactored), \(L\) is the span (6m), \(E\) is Young’s modulus, and \(I\) is the second moment of area of the C-section. The permissible deflection limit per many design codes is \(L/150 = 40 \, mm\).
The finite element results confirm the problem: the calculated maximum deflection under service loads significantly exceeds this limit, reaching approximately 48.6 mm. While the maximum bending stress (around 119 MPa) remains below the yield strength of 235 MPa, the excessive deformation itself renders the structure unfit for service. This clearly demonstrates that for a purlin retrofitted to carry solar panels, deflection control is the primary design driver at ambient temperature, not strength.
Down-Stayed Purlin System
The introduction of the down-stay system fundamentally alters the structural system. The purlin now acts as the top chord of a statically indeterminate truss. The vertical load is carried partly by direct bending of the purlin and partly by developing axial forces in the purlin (compression) and the tie system (tension). The mid-span deflection is dramatically reduced. The system’s stiffness can be conceptually understood by analyzing a simply supported beam with a central elastic spring support (representing the stiffness of the down-stay system). The deflection is given by a more complex interaction but will always be less than that of a simple span.
The analysis shows the maximum purlin deflection is reduced to about 14.5 mm, well within the allowable limit. The stress distribution also changes, with the maximum bending stress in the purlin reducing to around 98 MPa. This confirms the dual efficacy of the down-stayed system in the context of solar panel retrofits: it simultaneously improves stiffness (controlling deflection) and reduces working stresses (increasing load-bearing capacity), all necessitated by the permanent load of the solar panel array.
Performance Analysis Under Fire Exposure
Simply Supported Purlin in Fire
Under fire exposure, the performance degrades rapidly due to material softening and thermal bowing. The time-dependent deflection \(\delta(t)\) increases non-linearly because both the load-carrying capacity (via \(E(T)\) and \(f_y(T)\) reduction) and the thermal strains are time- and temperature-dependent. The critical time to failure is reached when the reduced section modulus \(S\) and yield strength \(f_y(T)\) can no longer resist the applied moment \(M\):
$$M \geq S \cdot f_y(T(t))$$
Alternatively, failure is assumed when the deflection becomes excessive or when the calculated stress reaches the temperature-degraded yield strength.
In the simulation, for the simply supported purlin carrying the solar panel load, the stress reaches the degraded yield point at approximately 1300 seconds (21.7 minutes) into the fire. The deflection at this time is about 53.6 mm and continues to grow. The member rapidly progresses to failure as the temperature increases beyond this point, with stresses locally exceeding the yield strength. This underscores the vulnerability of an unprotected purlin, especially one already loaded to a higher level due to solar panels, under fire conditions.
Down-Stayed Purlin System in Fire
The fire performance of the down-stayed system is more complex. All components—purlin, strut, and tie rods—are exposed to heating and lose strength and stiffness. However, the tie rods, typically made of smaller diameter steel, heat up faster due to a higher section factor \((A_m/V)\). This leads to a rapid loss of tensile stiffness and strength in the tie system. As the ties soften, the effectiveness of the down-stay system diminishes, causing the structural system to regress towards a simply supported condition but at elevated temperature.
The analysis reveals two key findings:
1. Stiffness Benefit Persists (Initially): The deflection of the purlin itself remains relatively controlled for a longer period compared to the simply supported case. While the tie system deteriorates, it still provides some restraint, slowing the growth of purlin deflection. The purlin deflection at 1800 seconds was about 37.7 mm, still below the 40 mm ambient limit, though this comparison is not directly meaningful in a fire scenario where stability is the goal.
2. Limited Gain in Load-Bearing Capacity: The time for the purlin stress to reach the degraded yield strength is only delayed marginally to about 1500 seconds (25 minutes), a mere 200-second improvement over the simply supported case. The eventual failure mode and time are thus not substantially altered by the unprotected down-stay system.
The reason is that the failure becomes governed by the strength loss in the critical tension elements (the ties) and the subsequent overloading of the heated purlin. The system’s enhanced capacity at ambient temperature is predicated on the integrity of all its components. In a fire, without protection, the weak link—the rapidly heating tie rods—fails first, nullifying the retrofit’s benefit for ultimate strength under fire conditions. Therefore, while the solar panel retrofit necessitates the down-stay system for serviceability, this same system requires protection to maintain its benefit in a fire.
Parametric Studies and Further Considerations
To generalize the findings, several parameters merit discussion. The performance is sensitive to the system’s geometry and the fire scenario.
Effect of Strut Depth and Location
The depth of the down-stay system (distance between purlin and strut) directly influences its mechanical advantage. A deeper system provides greater leverage, reducing forces in the ties and purlin for the same level of support. The optimal location of struts (e.g., third-points vs. quarter-points) can be analyzed to minimize maximum bending moment. For a purlin under uniform load from solar panels, third-point struts are often near-optimal. The relationship between strut reaction \(R_s\) and mid-span purlin moment \(M_{mid}\) can be expressed for an idealized truss model.
Importance of Tie Rod Material and Size
Since the tie rods are critical and vulnerable in fire, their design is paramount. Using a higher-grade steel (e.g., HRB400) provides more ambient capacity but does not improve high-temperature performance significantly, as all carbon steels degrade similarly. Increasing the diameter reduces the section factor \((A_m/V)\), slowing the temperature rise. This can be evaluated using the heat transfer equations. The time for a tie rod to reach a critical temperature \(T_{crit}\) (e.g., 500°C) can be approximated by solving the heat balance equation. A larger diameter \(d\) increases the thermal mass proportionally to \(d^2\) while increasing surface area only proportionally to \(d\), thus reducing the heating rate.
Fire Scenario Sensitivity
The rate of strength loss is highly dependent on the fire’s severity (heat release rate) and the resulting gas temperatures \(T_g(t)\) near the roof. A slower-growing or less intense fire would extend all failure times. The large-space fire model used here produces slower temperature rises than a standard cellulosic fire, which is more representative of an industrial setting where the fuel is not the building contents but perhaps stored materials. The placement of the solar panel array itself could influence fire spread or provide an additional fuel source in some cases, a factor not considered in this purely mechanical analysis.
Economic and Safety Implication of Fire Protection
The core conclusion points toward the need for passive fire protection (PFP) for the down-stay system if it is intended to provide any fire resistance. Applying an intumescent coating to the tie rods and struts would dramatically slow their temperature rise. The effect of PFP can be modeled by adding a thermal resistance term to the heat transfer equation for the steel member. The modified temperature rise is governed by:
$$\Delta T_s = \frac{(T_g – T_s)}{d_p / k_p + 1 / \alpha} \cdot \frac{A_m}{V} \cdot \frac{\Delta t}{c_s \rho_s}$$
Where \(d_p\) and \(k_p\) are the thickness and thermal conductivity of the protective layer. Even a thin layer can increase the time for the tie rods to reach critical temperature from minutes to potentially over an hour, allowing the down-stay system to maintain its integrity and support the purlin carrying the solar panel load for a meaningful period during a fire.
Conclusion
The integration of solar panel systems onto existing light steel structures presents a clear structural challenge, primarily in the form of increased permanent loads leading to excessive purlin deflections. The down-stayed purlin system is an effective and proven retrofit solution to restore serviceability and increase load-bearing capacity under ambient conditions.
However, this research highlights a significant vulnerability when considering fire safety, a scenario often neglected for secondary structural members. The finite element analysis of a system loaded by a solar panel array demonstrates that while the down-stayed configuration maintains an advantage in controlling purlin deflection for a longer duration during a fire, it offers only a marginal improvement in the time to reach structural failure if its components are unprotected. The system’s efficacy relies on the integrity of the tension elements (tie rods), which, due to their high surface-to-volume ratio, heat up rapidly and lose strength, precipitating a collapse of the enhanced structural action.
Therefore, a critical design implication emerges: for light steel workshop roofs retrofitted with solar panel arrays and subsequently strengthened using down-stayed purlin systems, the fire safety of the retrofit itself must be considered. To ensure the down-stayed system can perform its intended function for a reasonable duration under fire exposure, passive fire protection, such as intumescent coatings, should be applied specifically to the tie rods and struts. This measure would decelerate their temperature rise, preserving the system’s load-redistribution capacity and ultimately contributing to the overall structural stability of the building supporting the solar panel installation during a fire event. This integrated approach to design—considering both the static loads from sustainable technology and the dynamic threat of fire—is essential for safe and resilient infrastructure.