A metallic bar of diameter 20 mm is shown in figure-Modulus of elasticity of bar is 2 - 105 MPa- coefficient of thermal expansions is 12 - 10-6- C- The temperature of metallic bar is increased by 100- C- then what is the reaction generated at right support if the right supports yields by 0-1 mm is kN

Increase in length due to temperature increment = L αΔ T = 200× 12× 10^ 6× 100 = 0.24 mm Deformation prevented = 0.24 gap length yielding =0.24 0.1 0.1 = ...

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A metallic bar of diameter 20 mm is shown in figure.

Modulus of elasticity of bar is $2 \times 10^{5} M P a$ , coefficient of thermal expansions is $12 \times 10^{- 6} /^{\circ} C$ . The temperature of metallic bar is increased by $100^{\circ} C$ , then what is the reaction generated at right support if the right supports yields by 0.1 mm is ___ kN
12.56

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Solution

The correct option is A 12.56
Increase in length due to temperature increment = $L α Δ T$
$= 200 \times 12 \times 10^{- 6} \times 100 = 0.24 m m$ Deformation prevented = 0.24 - gap length - yielding
$= 0.24 - 0.1 - 0.1$ $= 0.04 m m$
Let R be the reaction generated at right support.
$\frac{R L}{A E} = 0.04$
$R = \frac{0.04 \times \frac{π}{4} \times (20)^{2} \times 2 \times 10^{5}}{200} = 12566.3 N$
$R = 12.56 k N$

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