Question

A prestressed concrete rectangular beam of size 300 × 900 mm is prestressed with an initial prestressing force of 700 kN at an eccentricity of 350 mm at midspan, stress at top fibre at midspan due to prestress alone is :
1. 3.46 MPa (tension)
2. 8.64 MPa (compression)
3. 2.59 MPa (compression)
4. Zero

Answer 1

Correct Answer - Option 1 : 3.46 MPa (tension)

Concept:

Stress at top fibre at midspan due to prestress in compression = \(\frac{{\bf{P}}}{{\bf{A}}} - \frac{{{\bf{P}}.{\bf{e}}}}{{\bf{Z}}}\)

Calculation:

Given,

b= 300 mm, d = 900 mm, e = 350 mm, P = 700 kN 

Where, Z = \(\frac{{\bf{I}}}{{\bf{y}}}\) = \(\frac{{\frac{{{\bf{b}}{{\bf{d}}^3}}}{{12}}}}{{\frac{{\bf{d}}}{2}}} = \frac{{{\bf{b}}{{\bf{d}}^2}}}{6} = \frac{{300 \times {{900}^2}}}{6} = 40.5 \times {10^6}{\bf{m}}{{\bf{m}}^3}\)

Stress at top fibre at midspan due to prestress = \(\frac{{\bf{P}}}{{\bf{A}}} - \frac{{{\bf{P}}.{\bf{e}}}}{{\bf{Z}}}\)

= \(\frac{{700 \times {{10}^3}}}{{300 \times 900}}- \frac{{700 \times {{10}^3} \times 350}}{{40.5 \times {{10}^6}}}\)

= 2.593 - 6.049

= 3.456 MPa (tensile)