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Structural Failure due to Fire 1. Steel-reinforced concrete pillars are used in the construction of large buildings. Structural failure can occur at high temperatures due to fire because of softening of the metal core. Consider a 200-mm- diameter composite pillar consisting of a central steel core of 100 mm diameter surrounded by 50 mm thick concrete. Assume a thermal contact resistance of R =0.20 m² K/W at the concrete-steel interface. The pillar is at a uniform initial temperature of Ti = 300 K and is suddenly exposed to combustion products at T. = 2000 K, h = 100 W/m². K on the concrete outer surface. The surroundings temperature is also at 2000 K. Steel properties are ks = 50 W/m.K, P. = 8000 kg/m³, C, = 500 J/kg. K.; Concrete properties are: ke = 0.75 W/m.K, Pc = 2300 kg/m³, C = 650 J/kg.K. and E = 0.9 With Ar = 5 mm and At = 100s, write a Matlab program to solve the temperatures at the cell center using Implicit finite-volume method. Express your finite-volume equations in terms Fourier number a.At h.Ar ( Fo= ) and Biot's number Bi ) whenever possible. Ax' k Your report must contain the following items: a. Write an executive summary containing following topies: a brief statement of the problem; summary of your findings; Any suggestion to improve the structural safety of a building during a fire. b. Derive the equations for the implicit FV method for the following cells: (1) A general concrete cell, say cell 15. (2) Cell that faces convective and radiative ht transfer from the surroundings (cell 20) (3) Cell that has a face coincides with the concrete-steel interface (cell 10, cell 11) c. Plot the temperature of the steel at cell 10 with R" -0 and R" -0.20 for0< t 10,000 seconds. d. Plot the temperature of the steel at cell 10 for g=0 and E -0.9 for OS t 10,000 seconds e. your actual MATLAB program (as an attachment to your email)

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