The upper and lower points of a beam cross-section provide information on the effect of adding a strand to a pattern. While they do not predict the magnitudes of the effects, they are, nevertheless, helpful when inputting a strand pattern manually.

Typical Kern Point Locations

If a strand is added below the lower kern point, additional compressive stress is induced in the bottom of the beam and additional tensile stress is induced in the top of the beam. If a strand is added between the two-kern points, compression is induced in both the top and bottom of the beam. Adding a strand above the upper kern point has the opposite effect as that of adding a strand under the lower kern point.

If a strand were to be placed at the lower kern point, the stress in the top of the beam would be exactly zero. Knowing this, the location of the lower kern point can be determined by setting the two components of prestress equal to each other, as follows:

where:

P = Strand force

e = Eccentricity of strand

A = Gross area of precast section

St = Section modulus of top of precast section

Solving for e, the eccentricity of the strand, yields:

Normally, the kern points are specified with respect to the bottom of the beam. Therefore, the distance from the bottom of the beam to the lower kern point is:

The upper kern point can be calculated in a similar manner, as follows: