Post-Fire Stiffness

Pre-Fire, Fire Exposure, and Post-Fire Stiffness... 

On the basis of the thermal and mechanical response models presented in Chapters 6 and 7 and the information gained on F-modulus recovery from DMA, a new model for the prediction of post-fire stiffness is proposed in the following [12]. 

Figure 8.1 and Table 8.1 reveal that a significant recovery occurs in the post-fire stiffness (that is, the post-fire stiffness is higher than the stiffness during fire exposure). Furthermore, based on the two DMA tests performed on the same specimen, it was found that, if cooled down from temperatures between glass transition and decomposition, the E-modulus can recover almost to its initial value (see Figure 8.2). In the modeling of the post-fire stiffness, the decomposed material (with the content a j) has no stiffness, while the material after glass transition but before decomposition (with the content a ) experiences a recovery. Thereby, for the modeling of the post-fire stiffness, the E-modulus model (Eq. (5.6)) can be transformed to [12] ...

The post-fire stifFness thereby is still much higher than the stiffness during the fire exposure, because in Eq. 8.2 is much higher than in Eq. (5.6) (see Chapter 5). 

Figure 8.5 Post-fire stiffness of water-cooled and noncooled specimens after different fire exposure times [12]. (With permission from Elsevier.)...

As shown in Figure 8.5, the post-fire stiffness calculated from the model deceased over the fire exposure time. After a short fire exposure time (about 10min), for both slabs, water-cooled and noncooled, the post-fire stiffness decreased much faster. While the post-fire stiffness of the water-cooled specimen stabilized after the first 10 min, the post-fire stiffness of the noncooled specimen continued to decrease at almost the same rate. The post-fire stiffness at 90 and 120 min can be extracted from the curve of the water-cooling scenario and compared with SLCOl and SLC02, respectively, see Table 8.2. It was found that the experimental post-fire stiffness based on basic beam theory was overestimated by 15.2% for SLCOl and 20.1% for SLC02. 

It should be noted that the post-fire stiffness was estimated with only the inputs of the initial material properties (the values at room temperature), the thermal and mechanical boundary conditions, and the fire exposure time. This imphes... 

The bending stiffness of the specimens was estimated from the second-order lateral deformations. The values at the end of fire exposure (WCl/2, obtained from Chapter 7) and after cooling (post-fire, P-WCl/2) are summarized and compared to the reference value (P-REF) in Table 8.6 [14]. A decrease to 42% and 36% of initial stiffness resulted at the end of fire exposure (for the stiU-hot specimens), while after cooling the post-fire values significantly increased to 76% and 70% of the initial values (values close to the compressive post-fire stiffness given in Table 8.4). 

These results can be compared to the same set of results obtained from the study on beam specimens (SLCOl and SLC02) in Section 8.2, which were subjected to four-point bending during 60 and 120 min fire exposure from the underside, see Table 8.6. In the former study, six-cell specimens were used in contrast to the four-cell specimens used here. The bending stiffnesses obtained from Section 8.2 were therefore corrected by a factor of 4/6 in order to make them comparable. At the end of fire exposure, the bending stiffness of the still-hot specimens (SLCOl/02) dropped to 46% and 43% of the initial value, which almost matched the values obtained for the column specimens. The post-fire stiffnesses (64% and 60%), however, were slightly lower than those of the column specimens (76% and 70%). 

The recently developed models to predict time and temperature-dependent material properties and post-fire properties showed good agreement with the experimental results. On the basis of the proposed models, the post-fire stiffness of FRP composite materials can be predicted before fire exposure. As a result, the post-fire behavior can be predesigned based on the functionality and importance of the stmcture. 

Bai, Y. and Keller, T. (2007) Modeling of post-fire stiffness of E-glass fiber-reinforced polyester composites. Composites Part A, 38 (10), 2142-2153. 

In view of the large lateral deflection responses of the fire-exposed specimens, shown in Figure 8.12, second-order deformations had to be taken into account in the modeling, and for their quantification, the post-fire Euler budding load had first to be determined. The latter was estimated by Eq. (7.12), where EI t) is the effective bending stiffness of the specimen after a fire-exposure duration of t, and L is the height of the specimens (2825 mm). 

To determine the effective bending stiffness, the position of the neutral axis of the post-fire specimens after different fire exposure durations was first determined by beam theory, based on the post-fire elastic modulus distribution shown in Figure 8.19. The resulting distances from the previous hot face were 114.5 mm for P-WCl,... 

Table 8.6 Comparison of bending stiffness of column and slab specimens pre-fire, at the end of fire exposure, post-fire [14]. (With permission from ASCE.)...

---