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Seismic Design Aids for Nonlinear Analysis
5.3.1 Subdomains 1 to 2(2) b : Collapse Caused by Yielding of Steel In the subdomains from 1 to 2(b2) , strain in tensile steel reaches its ultimate limit, and the corresponding stress reaches the design ultimate stress; strain in compressive steel is given by xc - d e sc = e su D - xc - d
(5.1)
Strain in any generic compression fiber of concrete located at a distance y measure from the extreme compression fiber of concrete is given by
e c ( y) =
e su (x c - y) e su x c , e c ,max = D - xc - d D - xc - d
(5.2)
where e c,max is the maximum strain in concrete. In subdomain 1, neglecting the tensile stress in concrete in the equilibrium equa) 0) tions, the position of the neutral axis lies in the range ] - ∞ , x (c0,lim ]. x (c,lim is the limit ( 1 ) position of neutral axis between two subdomains 1 and 2a for strain in compression steel reaching its elastic limit (refer to Figure 5.2, subdomain 1). It is important to note that the neutral axis positions are chosen only for detecting the characteristics of the P-M boundary; please note that the succeeding states do not belong to the same loading path for the chosen cross-section. This limit position is given by
) x (c0,lim =
d (e su + e s 0 ) - De s 0 (e su - e s 0 )
(5.3)
In subdomain 1, for strain conditions e s 0 < e sc > e su and s sc = s s 0 ,ultimate axial force and bending moment are given by
Pu = s s 0 b (D - d)(pc - p t ) ) ∀x c ∈] - ∞, x (c0,lim ] D M u = Pu b - d 2 pc =
A st A sc , pt = b(D - d) b(D - d)
(5.4)
(5.5)
where pt, pc are percentage of tensile and compression reinforcements, respectively. It may be noted from the above equations that the ultimate axial force and bending