GATE 2020 CE (CE2) – Question 51
The shown concrete beam has span 15 m, width 150 mm and depth 350 mm. Its parabolic prestressing cable has friction coefficient 0.35 and wave-effect coefficient 0.0015 per metre. If tensioned from one end only, find far-end force percentage loss due to friction, to one decimal.
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Correct answer: 3.8 to 4.7
Explanation
Sag relative to the end chord is 120 mm. Each end slope is approximately $4e/L=0.032$, so total angular change is 0.064 rad. Friction exponent is $\mu\theta+kL=0.35(0.064)+0.0015(15)=0.0449$. Force loss is $100(1-e^{-0.0449})=\mathbf{4.4\%}$.