temperature

Problem 265
A bronze bar 3 m long with a cross sectional area of 320 mm² is placed between two rigid walls as shown in Fig. P-265. At a temperature of -20°C, the gap Δ = 2.5 mm. Find the temperature at which the compressive stress in the bar will be 35 MPa. Use α = 18.0 × 10^-6 m/(m·°C) and E = 80 GPa.
 

Temperature changes cause the body to expand or contract. The amount δ_T, is given by
 

where α is the coefficient of thermal expansion in m/m°C, L is the length in meter, T_i and T_f are the initial and final temperatures, respectively in °C. For steel, α = 11.25 × 10^-6 m/m°C.
 

If temperature deformation is permitted to occur freely, no load or stress will be induced in the structure. In some cases where temperature deformation is not permitted, an internal stress is created. The internal stress created is termed as thermal stress.