Rods AC and BD are fixed at ends A and B respectively and free at ends C and D respectively. There is a $0\mathrm{.}5$ mm gap between the free ends of the two rods at an ambient temperature of $30$ deg $*$ C as shown in Fig. $1.$ The allowable compressive stress in the rods AC and BD are $120$ MPa and $360$ MPa respectively. If the ambient temperature of the rods is increased, calculate the maximum value of the ambient temperature of the rods $($T max $)$ at which the following conditions are satisfied:$($i$)$ The normal stresses in the two rods are zero.$($ii$)$ The normal stresses in the two rods are within their respective limits of allowable compressive stresses.