Hyperstatic forces

The hyperstatic resultant for a design cross section in a structure is the net resultant of all the cross sectional component resultants due to the post-tensioning of the structure (Bommer 2004). There are four critical parts to this definition:

1. It is based on a design cross sections. A design cross section is a portion of a structure that is considered to act as a unit in resisting applied forces. For structural elements such as beams and columns, design cross sections cut entirely through the member (and are almost always perpendicular to the member axis). In more complex structural elements, such as plates and shells, the engineer has some discretion on what is considered a design cross section.
2. All forces and moments on design cross sections are considered. There is no arbitrary exclusion on any cross sectional force or moment.
3. It considers the net force of all components that are part of the design cross section. This includes the forces in the concrete, prestressed and non-prestressed reinforcement. In general, these resultants largely cancel out, so the net resultant is usually much smaller than individual component resultants.
4. The definition applies equally to design cross sections with or without post-tensioning tendons.

External References

• Alan Bommer: Complete Secondary (Hyperstatic) Effects, PTI Journal, January 2004