GATE 2018 CE (CE2) – Question 51
A 6 m simply supported beam is prestressed with the straight cable shown. It carries a 6 kN/m UDL. Effective $EI=2\times10^4$ kN m² and prestressing force is 200 kN. The net increase in cable length, to two decimals, is ______ mm.
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Correct answer: 0.10 to 0.12
Explanation
The cable eccentricity is e = 0.05 m. Integrate its bending strain: $$\Delta l=\frac e{EI}\left[\int_0^L M_{\mathrm{load}}\,dx-PeL\right].$$ For the UDL, the integral is $wL^3/12=108$ kN m², and $PeL=60$ kN m². Thus $\Delta l=0.05(108-60)/20000=0.00012$ m = 0.12 mm. This is the keyed bending-strain result; uniform axial shortening cannot be computed from EI alone.