CE Problem of the Day: Elastic Analysis of Prestressed Concrete Beams

 

1 Problem

A simply supported prestressed concrete beam with a span of 15 m is designed to carry a superimposed dead load of 2.0 kN/m and a service live load of 5.0 kN/m. The beam is made of normal-weight concrete with a density of 24 kN/m³. The concrete strength at transfer and service are \(f'_{ci}\) = 28 MPa and \(f'_c\) = 35 MPa. The beam is post-tensioned with a draped tendon. The eccentricity of the tendon is 250 mm below the concrete centroid at midspan, and it linearly drapes to an eccentricity of 0 mm at the supports (anchored exactly at the neutral axis). The initial prestress force immediately after transfer is \(P_i\) = 850 kN. Time-dependent losses total 18% of the initial prestress force. The gross concrete properties are as follows.

• Concrete area \(A_c\): \(120\times10^3\) mm²
• Moment of inertia \(I_c\): \(5\times10^9\) mm⁴
• Distance to extreme fibers (\(c_t=c_b\)): 400 mm
• Section modulus (\(S_t=S_b\)): \(12.5\times 10^3\) mm³
• Radius of gyration squared \(r^2\): \(41.67\times 10^3\) mm²

Answer the following problems.

1. Calculate the top and bottom stresses at midspan at immediate transfer (in MPa).
2. Calculate the top and bottom stresses at supports at immediate transfer (in MPa).
3. Calculate the top and bottom stresses at midspan at service level (in MPa).
4. Calculate the top and bottom stresses at supports at service level (in MPa).
5. From your answers in #1 to #4, check whether each stress is within allowable stress values per NSCP 2015 provisions (in MPa).

You may want to try to solve the problems first before looking at the solution below.

2 Solution