A steel rod of length 3 m and diameter 20 mm is fixed between two rigid supports as shown in Fig. Y = 2 x 10⁶N/cm², $α$ = 6 x 10^-6/^oC and change in temperature is 80^oC.

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Stress in the rod is 960 N/cm² when the ends do not yield.

Stress in the rod is 293.33 N/cm² when the ends yield is 1 mm.

Stress in the rod is 1587 N/cm² when the ends do not yield.

Stress in the rod is 1800 N/cm² when the ends do not yield.

answer is A, D.

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Detailed Solution

$\begin{array}{l} F = YAαΔT \\ Δl = \frac{F \cdot l}{AY} = l \cdot αΔT \end{array}$
Stress $= YαΔT$
$F = YαΔθ$ when the walls do not yield
= 2 x 10⁶ x 6 x 10^-6 x 80 = 960 N/cm²
and
$\begin{array}{l} Δl = l αΔt = 3 \times 6 \times 10^{- 6} \times 80 \\ = 1440 \times 10^{- 6} m = 1.44 mm \\ ∴ \frac{F}{A} = \frac{{Ye}^{1}}{l} = \frac{2 \times 10^{6} \times (1.44 - 1) \times 10^{- 3}}{3} = 293.33 N / c m^{2} . \end{array}$