Multiple choice

A simply supported beam of uniform rectangular cross section of width b and depth h is subjected to linear temperature gradient, 0o at the top and To at the bottom, as shown in the figure. The coefficient of linear expansion of the beam material is α. The resulting vertical deflection at the midspan of the beam is

  1. $\frac{\alpha Th^2}{8L}$upwards
  2. $\frac{\alpha TL^2}{8h}$upwards
  3. $\frac{\alpha Th^2}{8L}$downwards
  4. $\frac{\alpha TL^2}{8h}$downwards
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D Correct answer