The following equation is important in understanding the difference between Balance and Hyperstatic Loading:
Balance = Primary + Hyperstatic
The balance loading considers all the loads that the tendon puts on the concrete. These include the force results (axial, shear, and moments) in the slab and the restraint (reactions) of the supports.
The primary forces and moments are those that would be expected to be in the concrete due to the post-tensioning if the concrete deformation associated with the post-tensioning was totally unrestrained. This can be calculated at any cross section based purely on the cross section geometry and the tendon location.
The hyperstatic forces and moments are the difference between the unrestrained (primary) and the restrained (balance) results.
Balance: due to tendons and restraint
Primary: due to tendons
Hyperstatic: due to restraint
The effects of both tendons and restraint must be considered for each design rule: service, strength, etc. Typically, the effects are considered differently in service and strength design.
In service design, the concrete stresses based on the applied forces and moments are calculated. This is a simple M/S + P/A calculation. This calculation must include both the effect of the tendon and the restraint. As a result, the balance loading is traditionally used for service design.
In strength and ductility design, the capacity is based on a cross section analysis using the tendons that intersect the section. In this case, the primary tendon force is used as part of the internal moment resisting arm. It would not be appropriate to use the balance loading in this calculation, because it already includes the primary force. If it was used, then the primary force would be included twice in the equilibrium solution. By including the hyperstatic forces in the cross section design and the primary tendon force as an internal cross section force, the entire post-tensioning effect is included in the solution.
Since the strength and ductility designs use a cross section analysis with the intersecting tendon force, it is important that a tendon intersects each left, right, and center strip in the model. Problems can occur in models with banded tendons, if a tendon does not intersect the left or right strips. In these cases, the middle strip will receive significant hyperstatic axial compression and, as a result, will have significant bending strength from that alone. Also, if there is no resultant tension reinforcement in the cross section, the effective depth cannot be calculated, which can lead to both shear design and ductility design problems. For PT slabs designed per ACI, it is common to use full-width design strips, which should ensure that each cross section is intersected by a tendon. In PT slabs designed using other design codes, there may be a requirement to design the slab with column and middle strips. However, these codes should also require some distribution of tendons in both column and middle strips. In these cases, each cross section (left, right, and center) should be intersected by a tendon based on the code required tendon distribution.
Complete Secondary Hyperstatic Effects (PTI Journal Technical Paper by Allan Bommer)
RAM Concept Tendons FAQ
RAM Concept Tendon Parameters