Prestressing for statically determinate beams - The Design of Prestressed Concrete Bridges - page 93

5.7 Centre of pressure
In order to calculate the prestress force required to resist the bending moments
tabulated above, it is necessary to understand the concept of centre of pressure. The
centre of pressure is the point at which a normal force effectively acts on the section.
Consider the column shown in Figure 5.4 (a), where it is shown loaded only by an
axial force P . In the absence of any external bending moment, the centre of pressure
is coincident with the point of application of this force, and the stress on the column
is P / A , where A is the cross-sectional area of the column. If a bending moment M is
now applied to the column, Figure 5.4 (b), the centre of pressure is displaced by a
distance e = M / P . The bending moment has added stresses to the column, which at
the extreme fi bres are ± M / z , where z is the section modulus. The total stresses on the
extreme fi bres of the column are now P / A ± M / z . The column is in exactly the same
state of stress as if the load P had been applied at an eccentricity e in the fi rst place,
Figure 5.4 (c).
Thus, if a prestressing force is applied to a beam, in the absence of any external
bending moments, the centre of pressure will be coincident with the centroid of the
prestress force. If the prestress is applied at a distance e from the neutral axis, it applies
a bending moment to the section equal to Pe . The stresses caused by the prestress are
the sum of the axial compressive stress and the stresses due to this internal bending
moment, or P / A ± Pe / z . If the section is not symmetrical and consequently the moduli
of the extreme fi bres are different, the stress on the fi bre remote from the prestress will
be P / A - Pe / z remote , and that closer to the prestress will be P / A + Pe / z close .
Figure 5.4 Centre of pressure