thermal stress

Problem 266
Calculate the increase in stress for each segment of the compound bar shown in Fig. P-266 if the temperature increases by 100°F. Assume that the supports are unyielding and that the bar is suitably braced against buckling.
 

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.
 

Problem 264
A steel rod 3 feet long with a cross-sectional area of 0.25 in.² is stretched between two fixed points. The tensile force is 1200 lb at 40°F. Using E = 29 × 10⁶ psi and α = 6.5 × 10^-6 in./(in.·°F), calculate (a) the temperature at which the stress in the bar will be 10 ksi; and (b) the temperature at which the stress will be zero.
 

Problem 263
Steel railroad reels 10 m long are laid with a clearance of 3 mm at a temperature of 15°C. At what temperature will the rails just touch? What stress would be induced in the rails at that temperature if there were no initial clearance? Assume α = 11.7 µm/(m·°C) and E = 200 GPa.
 

Problem 262
A steel rod is stretched between two rigid walls and carries a tensile load of 5000 N at 20°C. If the allowable stress is not to exceed 130 MPa at -20°C, what is the minimum diameter of the rod? Assume α = 11.7 µm/(m·°C) and E = 200 GPa.
 

Problem 261
A steel rod with a cross-sectional area of 0.25 in² is stretched between two fixed points. The tensile load at 70°F is 1200 lb. What will be the stress at 0°F? At what temperature will the stress be zero? Assume α = 6.5 × 10^-6 in/(in·°F) and E = 29 × 10⁶ psi.
 

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.