A "retrofit" solution for Force-Based Design: eliminating the need for iteration and initial period

The limitations and inconsistencies of current force based design procedures, as used worldwide by most practicing engineers, have been recently highlighted and acknowledged. Some of the most significant drawbacks recognized include the uncertainty in the determination of the structure's initial period and the incorrect assumption that such initial period/stiffness remains regardless of the structure's design strength, not known at the beginning of design. As noted in displacement based design methodology, a structure's strength and stiffness are proportional for a given geometric arrangement and such compatibility must be accounted for to obtain a feasible design solution. The actual secant-to-yielding period of the equivalent elasto-plastic system (behind any equal displacement or equal velocity rule in elastic spectra-based design approaches) may differ considerably from the initial design assumption, leading to weak control of the design. The current force-based design methodology may be corrected following an iterative procedure to guarantee that the initial period is equal to the secant-to-yielding period of the elasto-plastic equivalent system. In this paper a closed-form 'retrofit' solution to the iterative procedure is proposed to allow a force- based design to be conducted respecting the aforementioned strength-stiffness compatibility. The closed-form design method provides a set of feasible design solutions, composed of multiple pairs of design base shears and structural ductilities, which may be obtained without the need of an initial period estimation and following iterations. A design example is provided with reference to a single-degree-of-freedom bridge pier, designed following the common-practice force-based design (no iteration), the proposed corrected force-based design (iterative or closed-form), and a direct displacement based design methodology. The designs from the different methodologies are then verified and compared using non-linear time history analysis.