Effect of Local Instability on Fire Response of Steel Beams

In current practice, failure in beams under fire conditions is evaluated based on flexural limit state without any consideration to shear or instability effects. However in certain loading scenarios and sectional configurations, fire exposed steel beams and girders can experience temperature induced instability due to shear rather than flexural effects. This paper presents the development of a three-dimensional nonlinear finite element model that can be used to evaluate behavior of fire exposed steel girders. This model, is capable of predicting fire response of steel girders taking into consideration flexural, shear and deflection limit states. The validated model is utilized to study different conditions under which shear parameters dominate the response of fire exposed steel beams. Results obtained from numerical studies show that shear capacity can degrade at a higher pace than flexural capacity under certain loading scenarios and hence, failure can result from shear effects prior to attaining failure in flexural mode.


INTRODUCTION
Structural members, when exposed to fire, experience loss of capacity and stiffness due to temperature induced degradation in strength and modulus properties of constituent materials.
When the capacity (typically moment capacity) at the critical section of the member drops below the applied moment due to loading, failure occurs. The time to reach this failure is referred to as force. The model was validated against test data on beams and then the model was applied to examine the influence of shear on fire response of steel girders under different loading configurations and web slenderness.

NUMERICAL MODEL
The three dimensional finite element model of the beam has geometry of a typical hotrolled steel W-section commonly used in flexural members. This model was developed in ANSYS and accounts for several parameters including geometric and material nonlinearities, temperature dependent material properties and various failure limit states. For undertaking fire resistance analysis, the beam is discretized with different thermal and structural element, available in ANSYS. SOLID70 and SURF152 elements are used as thermal elements to simulate heat transfer to the beam under fire exposure. SOLID185 is also used for modeling the structural response of three-dimensional solid structure (ANSYS, 2011). Figure 1 shows typical steel beam and associated finite element model. properties of structural steel are assumed to vary with temperature as per Eurocode 3 recommended relations (CEN, 2005). In order to simulate the response of fire exposed steel girders, two stages of analysis are to be carried out at each time step. The first stage examines heat transfer between fire source and steel girder. Then, cross-sectional temperatures are input to the second stage of simulation to carry out structural analysis. In the structural analysis, both temperature and loading is applied simultaneously and the mechanical behavior is evaluated. Sectional capacity can be obtained as well as shown in an earlier study (Kodur and Naser 2013).
Flexural and shear failure occur once the bending moment (or shear force) due to applied loading exceed the moment (or shear) capacity at a critical section. Also to check failure, mid-span deflection is compared against deflection limit state used in BS 476 (BS, 1987). The beam is said to fail, when the beam attains a deflection of (L/20) or rate of deflection reaches (L2/9000d); where L and d are the span and depth of the beam, respectively.

VALIDATION OF NUMERICAL MODEL
The above finite element model was validated using data from tests on conventional steel beams. Kodur and Fike (2009) reported detailed results from fire resistance test on a W12×16 A992 steel beam exposed to ASTM E119 standard fire. The beam was insulated with 50 mm thick spray applied vermiculite based fire insulation to achieve a 2-hr fire resistance rating. The beam was loaded with two symmetrical point loads 1.5 m away from end supports. This loading represents 31 and 5% of its room temperature flexural and shear capacity, respectively as per AISC provisions (2011).
The tested beam is analyzed using the above developed model. The various output parameters generated in the analysis i.e., cross-sectional temperature profile, mid-span deflection and failure mode are compared against measured data from fire test. Figure 2a shows a comparison of measured and predicted temperature (average of both flanges and web) in the steel beam as a function of fire exposure time. As can be seen, there is a good agreement between predicted and measured temperatures up to the first 45 minutes. At 45 minutes, average temperature in steel section was around 350˚C. Beyond 45 minutes, the predicted steel temperatures (from model) tend to be slightly higher than the measured ones in temperature range of 350-600˚C. This can be attributed to differences in assumed and actual thermal properties of fire insulation at elevated temperatures.
A comparison of predicted and measured mid-span deflection response of the tested steel beam is shown in Fig. 2b

CASE STUDIES
The above validated finite element model was applied to study the effect of shear parameters on the fire response in steel beams. The effect of loading pattern and web slenderness on shear capacity and fire response of beams is studied herein.

Effect of loading pattern
For numerical analysis, a simply supported beam of 9 m span and made of W21×44 section noted that the loading on "Beam 2" was chosen to simulate a pure shearing state and this load setup is similar to the one used by Basler et al. (1960) to study shear response of steel beams at room temperature.
The above two beams were analyzed using the above developed model by subjecting them to combined loading and ASTM E119 standard fire exposure. Figure 3a shows temperature progression in the two beams with fire exposure time. Since these steel beams have same geometric and material properties and subjected to same ASTM E119 fire exposure, temperature rise in these beams is identical. It can be seen from Fig. 3a Figs. 3b and c). It is clear that "Beam 1" has much higher reserve shear capacity than that of "Beam 2", hence these beams experience failure in different modes as explained below. shows the predicted mid-span deflection in these three beams as a function of fire exposure time.
The mid-span deflections remain small for about 10 and 6 min in Beams 1 and 2, respectively.
Then, deflections increase at a rapid pace leading to runaway failure in these two beams. and 2 due to significant degradation of stiffness resulting from temperatures in steel exceeding 550 ˚C. While "Beams 1" fails in flexural (moment) mode, "Beam 2" fails in shear limit state earlier to reaching deflection or flexural capacity limit states. Although the applied loading on these two beams resulted in similar bending moment, different loading pattern led to different shear response and failure modes. Thus, loading pattern can significantly affect the fire response of steel beams. Table 1 summarizes failure time in these beams. Additional studies based on different loading pattern can be found else were (Kodur and Naser 2013;Naser and Kodur 2017;Naser, 2016). This is a preprint draft. The published article can be found at: https://doi.org/10.1108/PRR-05-2017-0025

Effect of web slenderness
Generally slenderness of web has significant influence on shear capacity of the beam. For optimum design, slenderness of web is much higher than that of flanges and hence web slenderness is a critical factor in determining shear capacity in a steel beam. The effect of web slenderness on shear capacity is studied by analyzing two fire exposed beams with varying web slenderness.
"Beam 3" is a replicate of "Beam 2" shown above, but with thinner web thickness. These two beams (Beams 2 and 3) were subjected to ASTM E119 fire as well as gravity loading and were analyzed with the above developed model.
Both beams have similar flange slenderness ratio of 7.22, while web slenderness ratio for "Beam 2"and "Beam 3" are 59 and 100, respectively. To illustrate the effect of web slenderness on temperature rise, predicted temperature in the web of "Beam 2"and "Beam 3"are plotted in Fig.   4a as a function of fire exposure time. It can be seen that overall thermal response in "Beam 3" follows similar trend to that of "Beam 2" but temperature in web of "Beams 3" increases at a much faster pace due to slender web. Thus, faster degradation of strength and stiffness properties of web (and thus of beam) occurs in "Beam 3" as compared to that in "Beam 2". Since both Beams 2 and 3 were subjected to applied shear loading of 40-50% of the capacity with minimum bending moment effects, these beams are likely to fail in shear. Thus, Fig.   4b only shows degradation of shear capacity as a function of fire exposure time. Since shear capacity is mainly governed by the size of the web, shear capacity at ambient conditions of "Beam 3" is much lower than that of "Beam 2" due to higher web slenderness (reduced web thickness).
When exposed to fire, moment and shear capacity of Beams 2 and 3 start to degrade after about 8.5 and 4 min of fire exposure time, respectively. At this point, internal stress (due to applied loading) reaches reduced yield strength of steel, sectional instability occurs and also plastic deformation starts to accumulate. These deformations initiate sectional instability. Figure 4c compares predicted mid-span deflection in Beams 2 and 3. In general, mid-span deflections are small in the initial stage of fire exposure and then increase gradually with fire exposure time. The deflections increase at a rapid pace towards final stage of exposure due to very high temperature in steel, and this lead to failure of beams. As expected "Beam 3", with higher web slenderness, undergo larger initial deflections as compared to that of "Beam 2".  respectively as compared to 14 and 13 min in Beam 2. Table 2 summarizes failure modes in these two beams analyzed with different web slenderness. These results clearly infer that web slenderness influences failure mode in fire exposed steel beams and can lead to shear failure prior to reaching flexural or deflection limit states. It should be noted that effect of different failure modes and corresponding failure times can be more apparent in fire insulated beams as discussed in Kodur and Naser (2013) and Naser and Kodur (2016) which have illustrated that a steel girder insulated with 1 hr fire rated insulation system will fail in 65 and 55 min due to flexural and shear effects, respectively. Therefore, accounting for shear effects can significantly alter failure times of girders in certain situations.

CONCLUSIONS
Based on the results of the analysis presented herein, the following conclusions can be drawn 1. The developed finite element model is capable of predicting fire response of steel beams where flexural or shear effects dominate the behavior of steel beams.
2. In a fire exposed steel beam, sectional instabilities can occur in web due to shear parameters prior to that in flange due to flexural parameters under certain loading and sectional configurations.
3. In fire exposed steel beams with higher slender webs, shear capacity can degrade at a higher pace than that of moment capacity. In such beams, failure can occur in shear limit state rather than flexural or deflection limit states.

ACKNOWLEDGMENT
This material is based upon the work supported by the National Science Foundation under Grant number CMMI-1068621 to Michigan State University. Any opinions, findings, and conclusions or recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of the sponsors.