“…The trilinear-plastic system is defined by 2 normalized yield displacements u 1 and u 2 , corresponding to 2 ductility parameters μ 1 = 1/u 1 and μ = 1/u 2 as shown in Figure 1B. 8,[18][19][20] In most practical applications, the quantity of interest is not R s , max , but rather the maximum residual ratio, R sp , max , that occurs in a random sample, which is affected by the post-peak response of the structure. The first post-yield branch has post-yield stiffness ratio p, while the second post-yield branch has zero stiffness.…”