Question 1. (25 points) A steel I-beam with the cross-section shown in Figure 1 is suddenly exposed to a fire during a c

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Question 1 25 Points A Steel I Beam With The Cross Section Shown In Figure 1 Is Suddenly Exposed To A Fire During A C 1 (352.74 KiB) Viewed 24 times

Question 1. (25 points) A steel I-beam with the cross-section shown in Figure 1 is suddenly exposed to a fire during a compartment fire in a building. The top flange of the beam is not exposed to fire (see Figure 1). The fire engineer estimates that the I-beam is mainly exposed to radiant heat from the fire, at a heat flux of 55 kW/m² on all surfaces exposed sides. Cooling of the I-beam is assumed to occur due to convection and radiation losses. Convective cooling can be assumed to happen with a convective heat transfer coefficient hc = 15 W/m²K and radiative cooling can be assumed to happen with a linearised radiation coefficient of hR= 20 W/m²K. The steel has a density of p = 9,000 kg/m³, a thermal conductivity of k = 42 W/mK and a specific heat capacity of cp = 1,000 J/kg.K. The ambient temperature (and also initial temperature of the steel) is approximately To = 20°C, and the critical temperature for the steel is approximately Tc = 500°C. a) Demonstrate that the assumption of no temperature gradients (5 points) within the steel in the I-beam is valid. (10 points) b) Present the full expression for the energy equation that applies to the heating process of the steel l-beam. c) (10 points) Calculate the time to reach the critical temperature (tc) of the steel. You must solve the equation presented in part (b) and present each step of the solution process. h = 250 mm b = 250 mm t = 9.6 mm t = 9.6 mm t 13: = 9.6 mm Figure 1. (left) section of the steel "I-beam" and (right) characteristic geometric dimensions of the steel "l-beam" section. hrt The Biot number is given by Bi = k