A stepped steel shaft is subjected to a clockwise torque of 10 Nm at its free end. Shear modulus of steel is 80 GPa. The strain energy stored in the shaft is

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ESE Civil 2017 Official Paper

Option 1 : 1.73 Nmm

CT 3: Building Materials

2962

10 Questions
20 Marks
12 Mins

Total strain energy stored in any shaft is given by, \(u = \frac{{{T^2}L}}{{2GI}}\)

\({u_{Total}} = {u_{AB}} + {u_{BC}}\)

\(= {\left( {\frac{{{T^2}L}}{{2GJ}}} \right)_{AB}} + {\left( {\frac{{{T^2}L}}{{2GJ}}} \right)_{BC}}\)

\(= \frac{{{T^2}L}}{{2G}}\left[ {\frac{1}{{{J_{AB}}}} + \frac{1}{{{I_{BC}}}}} \right]\)

\(= \left( {\frac{{{{\left( {10} \right)}^2} \times 100 \times {{10}^{ - 3}}}}{{2 \times 80 \times {{10}^3} \times {{10}^8}}}} \right)\left[ {\frac{{32}}{{11 \times {{25}^4}}} + \frac{{32}}{{\pi \times {{50}^4}}}} \right] \times {10^{12}}\)

\({u_{Total}} = \left( {\frac{{10}}{{16 \times {{10}^{10}}}}} \right)\left( {2.77 \times {{10}^{ - 5}}} \right) \times {10^{12}}\)

u_{Total} = 1.73 × 10^{-3} N.m or 1.73 N.mm