Innovative Design of Fire Doors: Computational Modeling and Experimental Validation

Abstract

Usually the design of fire doors is carried out to fulfil thermal requirements only, whereas also thermal distortion could significantly affect the safety behavior of the door. Indeed, the door tends to bend away from its supporting frame due to a non-uniform temperature distribution, which could lead to flame and smoke propagation. In this work an innovative design scheme is proposed, where the mechanical response of the door is enhanced without affecting its insulating properties. This improvement is achieved by changing the disposition of the constitutive elements (insulating material and structural plates). The behavior of a conventional and of an innovative door during a fire test was simulated with three-dimensional (3D) finite element models. A non-linear thermo-mechanical transient analysis was performed as well. The numerical results were validated with an experimental campaign made on true scale specimens, where the doors were heated by a furnace reaching a maximum temperature of 950°C. The temperature distribution was measured with several thermocouples and an infrared camera, whereas displacements were monitored with a laser sensor. It was observed that, while temperatures on the unexposed surface were around 120°C in both cases, the maximum out-of-plane displacement measured in the innovative door was 3 times smaller than that of the conventional configuration.

Appendix: Simplified Thermo-Mechanical Model

In order to gain insights into the thermo-mechanical behavior of the fire door, a simplified model is developed considering the steady-state behavior at high temperature. Referring to Fig. 12, a conventional fire door can be considered as a sequence of slices connected one to each other. Neglecting the edges, a single slice can be described by two external steel layers and an internal portion made of insulating material. According to the well-known electrical analogy, where the analogue of current is the heat flux $\dot{q}$ and the analogue of the voltage difference is the temperature difference from hot to cold side (T _hot − T _cold), it follows that:

$$ \dot{q} = \frac{{T_{\text{hot}} - T_{\infty } }}{{\varSigma_{\text{i}} R_{\text{i}} }} = \frac{{T_{\text{hot}} - T_{\text{cold}} }}{{R_{1} + R_{2} + R_{3} }} $$

(3)

The thermal resistance of each layer R _i is, in turn, related to the thickness t and the conductivity k:

$$ R_{1} = R_{3} = \frac{{t_{\text{s}} }}{{k_{\text{s}} }},\quad R_{2} = \frac{{t_{\text{r}} }}{{k_{\text{r}} }} $$

(4)

where the subscripts s and r refers to steel and insulating material, respectively. If the room temperature on the unexposed surface T _∞ is known (a temperature of 20°C is assumed in this work), it is possible to evaluate the temperature on the cold steel plate T _cold, by considering an additional thermal resistance R ₀ = 1/h, where h is the convective heat coefficient, that can be calibrated to account also for radiative heat exchange.

Figure 12

Simplified thermo-mechanical model of a fire door

A value of 10 W/m²K is here considered. Equation (3) then becomes:

$$ \dot{q} = \frac{{T_{\text{hot}} - T_{\infty } }}{{\varSigma_{\text{i}} R_{\text{i}} }} = \frac{{T_{\text{hot}} - T_{\infty } }}{{R_{0} + 2 \cdot R_{1} + R_{2} }} $$

(5)

And:

$$ T_{\text{cold}} = T_{\infty } + \frac{{\dot{q}}}{h} $$

(6)

This strategy is valid under the assumption that also T _hot is a known value. In [2], it has been found that the steel temperature on the hot side reaches the furnace temperature after few minutes from the beginning of the heating process. For this reason, T _hot can be assumed equal to the temperature corresponding to a heating time of 60 min without losing in accuracy. Averaged material properties are reported in Table 2 [3]. According to these data, it is possible to obtain a value of T _cold = 140°C. Although the model is quite simplified, this value is very close to that measured during standard fire tests in the central area of the door.

Table 2 Material Properties and Parameters Considered for Simplified Models

Figure 12 is also representative of a possible interpretative model for the mechanical behavior of the fire door: the temperature distribution across the slice thickness has a linear variation from T _hot to T _cold, which, in turn, gives rise to thermal expansion. The thermal expansion is partially restrained for the presence of the hinges and the lock. The most critical part in terms of amount of thermal distortion is located on the lock side, near the edge of the door. In fact, this slice can be considered as a cantilever beam where the clamped end is constituted by the lock and the other end is free to bend under thermal load. The maximum displacement of the free end can be evaluated as:

$$ u_{\hbox{max} } = \frac{{L^{2} }}{2}\frac{\alpha \Delta T}{{2t_{s} + t_{r} }} = \frac{{L^{2} }}{2}\frac{{\alpha \left( {T_{\text{hot}} - T_{\text{cold}} } \right)}}{{2t_{\text{s}} + t_{\text{r}} }} $$

(7)

where α is the thermal expansion of the steel, and L is the total length of the cantilever. Values reported in Table 2 yield to u _max = 74 mm. Although the model is simplified, this result is in good agreement with that measured at the corner of the door at the end of a fire tests [2].