Problem # 1

A simply supported beam 30 ft long is prestressed by a straight tendon that carries an effective force of 233 kips. The rectangular beam is 10 in. wide and 20 in. deep and the eccentricity of the prestressing force is 4 in.

A. Calculate the maximum mid-span service moment the beam can support for the allowable stresses listed in the table below:

Compressive Stress (psi)

Tensile Stress (psi)

2,700

0

3,600

0

2,700

580

3,600

580

B. Draw a neat sketch to indicate the location of the center of the compression force and its distance from the tensile force. What conclusions can you draw?

C. Repeat parts A and B but for the maximum service moment but at a location distant 25 in. from the support.