A prismatic cantilever prestressed concrete beam of span length, \( L = 1.5 \, \text{m} \), has one straight tendon placed in the cross-section as shown in the following figure (not to scale). The total prestressing force of 50 kN in the tendon is applied at \( d_c = 50 \, \text{mm} \) from the top in the cross-section of width, \( b = 200 \, \text{mm} \) and depth, \( d = 300 \, \text{mm.}\)
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In a prestressed concrete beam with a concentrated load, the resultant stress at a point can be zero if the prestressing force is balanced by the applied load.
The resultant stress at point \( Q \) due to the applied concentrated load \( P = 5 \, \text{kN} \) and the prestressing force is calculated as follows. The prestressing force is applied at a distance of \( d_c \) from the top. The force \( P \) and the prestressing force create a combined effect on the section.
The bending stress at point \( Q \) can be calculated using the formula for stress in a concrete beam:
\[
\sigma = \frac{M}{S}
\]
where \( M \) is the moment at point \( Q \), and \( S \) is the section modulus of the beam. Since the beam is subjected to both a concentrated load \( P \) and a prestressing force, the combined effect results in no stress at point \( Q \). Hence,
\[
\sigma = 0 \, \text{MPa}.
\]
Thus, the resultant stress experienced at point \( Q \) is \( \boxed{0} \, \text{MPa} \).
