Ultimate Interaction Diagram
- Tim Kostka
The ultimate interaction diagram is the axial/moment diagram where points defined in the input are placed. The diagram shows a phi factored line (solid line) which is the capacity of the pile. The demand points entered in applied loads will show up in this diagram. Any points within the slenderness line (dashed line) are considered to be passing and will be shown as green dots. Failing points will be colored red.
Secant Method
The Secant Method is an application of slenderness to the moment capacity of a given interaction diagram. This method was first described in ACI Journal, Arthur R. Anderson and Saad E. MOUSTAFA, “Ultimate Strength of Prestressed Concrete Piles and Columns”. The method is derived from classical elastic buckling theory for a prismatic member.
A basis for the selection of the applicable value for EI is determined from the curvature at a given section. Using a strain-curvature relationship the accompanying EI can be found using Mu. Using this, EI can be used in the classical theory of elastic buckling to solve for Mu. Once Mu is found the points are plotted on the interaction diagram as the slenderness line.
ACI Moment Magnification
The ACI Moment Magnification Method is used as an alternative method to calculate the effects of slenderness on the interaction diagram. The moment magnification method is outlined in AASHTO LRFD 4.5.3.2.2b in which a factor is found from AASHTO LRFD Eq. 4.5.3.2.2b-3 and used to modify the moment.