Intensity-based demand and capacity factor design: A visual format for safety checking

Quantitative safety checking is an essential part of performance-based design and retrofit of new and existing construction. The intensity-based demand and capacity factor design (DCFD) is a practical closed-form safety-checking format that lends itself quite well to visual interpretation. Adopting the critical demand to capacity ratio as a global damage measure directly, skipping the engineering demand parameter, helps in identifying the onset of the prescribed performance levels. For each intensity level, the contribution to the error in the DCFD format in logarithmic domain is visualized as the distance between the hazard curve and its tangent at median intensity at the onset of the performance level weighted by the probability density of the intensity-based capacity. The latter reaches its maximum value at the median intensity at the onset of the performance level, where the error in hazard is zero, and decays with a rate that depends on the logarithmic standard deviation of fragility. The proposed intensity-based DCFD provides accurate safety-checking estimates that are always on the safe side for concave mono-curvature hazard curves in the logarithmic scale.