temperature

Solution to Problem 265 Thermal Stress

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.
 

Figure P-265

 

Thermal Stress

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

$\delta_T = \alpha L \, (T_f \, - \, T_i) = \alpha L \, \Delta T$

where α is the coefficient of thermal expansion in m/m°C, L is the length in meter, Ti and Tf 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.
 

 
 
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