A prestressed concrete beam of section 120 mm × 300 mm is used over an effective span of 6000 mm to support a uniformly distributed load of 4 kN/m including the self-weight of the beam. The beam is prestressed by a straight cable carrying a force of 180 kN located at an eccentricity of 50 mm. What is the stress due to prestressing force?

Concept:

Stresses in prestressing beam;

Direct stress due to prestressing force = \(+{P\over A}=+{P\over bd}\)

Extreme stress due to eccentricity of the prestressing force = \(\pm{P\times e\over Z}\)

Extreme stress due to bending moment = \(\pm {M\over Z}\)

Where P = prestressing force, e = eccentricity, b = width of beam, d = depth of beam, and Z = section modulus.

Calculation:

Given

Width of beam (b) = 120 mm

Depth of beam (d) = 300 mm

Effective span (L) = 6000 mm or 6 m

Uniformly distributed load (w) = 4 kN/m

Prestressing force (P) = 180 kN or 180 × 10³ N

Eccentricity (e) = 50 mm

Stress due to prestressing force (σ_p) = \(P\over bd\) = \(180× 10^3\over 120× 300\) = 5 N/mm²

Stress due to prestressing force is 5 N/mm². Hence option (3) is correct.