ABSTRACT
Consider a simply supported beam prestressed by a tendon through its neutral axis and loaded by external loads, as shown in Figure 12.2a. Due to the pretension force F, a uniform compressive stress, σc, occurs across the section of an area A and this is
σc
F
A =
(12.1)
The stress distribution is shown in Figure 12.2c. If M is the maximum moment at the centre of the beam induced by the external load, the normal stress at any point y across the section is
σb
My
I =
(12.2)
where: y is the distance from the neutral axis I is the second moment of area of the section about its neutral axis
The stress distribution defined in Equation 12.2 is illustrated in Figure 12.2d. Thus, the resulting normal stress distribution on the section is:
σ = +
F
A
My
I (12.3)
which is shown in Figure 12.2e. If there is no tensile stress in any section for the given prestress and load conditions, a beam comprising separate blocks and a tendon shown in Figure 12.2b is similar to the beam in Figure 12.2a. The prestress provides compressive stress on the sections of the beam which removes or reduces the tensile stress induced by external loads.
