A shaft is fixed at one end and free at another end. It carries uniformly distributed torque (t kN - m/m) as shown in the figure. The shaft is prismatic and have constant GJ. The angle of twist at the free end is:
A
tL28GJ
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B
tL22GJ
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C
3tL28GJ
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D
None of these
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Solution
The correct option is C3tL28GJ We know, TJ=GθL∫dθ=∫TxdxGJ
Now, Tx=⎧⎪
⎪⎨⎪
⎪⎩tx0<x<L2tL2L2<x<L θ=∫L/20txdxGJ+∫LL/2(tL2)dxGJ =tGJ(x22)L/20+(tL2)1GJ(L−L2) =t2GJ(L24)+tL2GJ×L2 =tL28GJ+tL24GJ=3tL28GJ