A pre-stressed rectangular beam which carries two concentrated loads W at $$\frac{{\text{L}}}{3}$$ from either end, is provided with a bent tendon with tension P such that central one-third portion of the tendon remains parallel to the longitudinal axis, the maximum dip h is
A. $$\frac{{{\text{WL}}}}{{\text{P}}}$$
B. $$\frac{{{\text{WL}}}}{{2{\text{P}}}}$$
C. $$\frac{{{\text{WL}}}}{{3{\text{P}}}}$$
D. $$\frac{{{\text{WL}}}}{{4{\text{P}}}}$$
Answer: Option C
Reaction Ra = W.
Reaction Rb = W.
Bending Moment at Center of the Beam = [W * (L/3 + L/6) ]-[W* (L/6) ].
= WL/3.
Now Moment due to prestressing force = P*h (h= maximum dip).
Dip required => P*h = WL/3.
Therefore h = WL/3P.
2