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Resultant force at a section
We can determine stresses at top and bottom fibres, at a section of a beam, due to pre-stressing force and external loads. Using them, we can draw a distribution of stresses at that section, assuming a linear variation between top and bottom fiber stresses across the depth of section. A resultant force can be determined which, if applied at that section, shall produce the same distribution of stresses at that section. As only the pre-stressing force is applied axially on to the beam element, the magnitude of this resultant force is equal to the pre-stressing force considering the horizontal equilibrium of forces.
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