Frontiers in Geotechnical Engineering (FGE) Volume 1 Issue 1, December 2012 www.seipub.org/fge/ 1 Evaluation of the Seismic Demand Chord Rotations of Structural Reinforced Concrete Members Triantafyllos Makarios *1 Earthquake Engineering Division, Institute of Engineering Seismology & Earthquake Engineering (I.T.S.A.K.) / Earthquake Planning and Protection Organization 5 Ag. Georgiou Str., Patriarchika Pylaia, Thessaloniki, GR-55535, Greece , *1 makarios@itsak.gr; Abstract In the present article, the calculation of seismic demand chord rotations (elastic and plastic) of structural reinforced concrete (r/c) members, without using various inelastic springs at their ends, is analytically developed. Particularly, in order to calculate, in the nonlinear area, the seismic demand chord rotations of structural r/c members, the following three cases must be examined separately: (1) Exterior roof joint of single-storey frame, (2) interior roof joint of single-storey frame and (3) exterior & interior floor joint of multi-storey frame. The above-mentioned three cases consist the theoretical base for the calculation of the seismic demand chord rotations of r/c members of each other case. This presentation is very useful for the develop of suitable software about the seismic nonlinear (static/dynamic) structural analysis without using nonlinear springs. Keywords Seismic Demand Chord Rotations; Seismic Nonlinear Static Analysis; Seismic Nonlinear Response History Analysis Introduction The point of calculating the seismic demand chord rotations (elastic ones and plastic ones) of the structural r/c members, without using springs at their ends, is always addressed in timelines. In the past, many techniques have been presented about the simulation of r/c structures in nonlinear seismic analysis, i.e. see Banon et al (1981) and their references, but in this case, we are going to focus on the contemporary Eurocode EN 1998-3 (2005). This Seismic Code proposes a flexural nonlinear law of Moment- Chord Rotation at each critical end-section of each r/c member of the structure. On an equivalent note, we can say that each structural r/c member is based on the seismic behavior of a cantilever for each critical end- section. In the past, many papers have been published, of varying accuracy as regards their methodology, with reference to the calculation of seismic demand plastic rotations of r/c structural members (Kanaan and Powell, 1975; Litton, 1975; Gupta and Krawinkler, 1999; Goel and Chopra 2004; Eom et al, 2012). However, in the present article we are going to look at the same issue from a different point of view, without the use of inelastic springs. In order to estimate the seismic demand chord rotations of structural r/c members at yielding and ultimate state, without inelastic springs, the geometrical base combined with the Mechanic Principles are used and this is the main target of this article. Additional theoretical bases (Makarios, 2012; Makarios, 2013) and numerical results of examples took place in the past in other works for verification reasons (Makarios, 2005; Makarios, 2009; Makarios, 2010; Makarios & Asteris, 2012;). Theoretical Background The available yielding chord rotation of a structural r/c member (in real of an r/c cantilever) can be estimated by the following semi-empirical equation that is proposed by Eq.(A.10a)/sect.Α.3.2.4 of Eurocode ΕΝ 1998-3, and is based on work by Panagiotakos and Fardis (1999, 2001), where all possible sources that contribute to the yielding rotations of the end-section, such as the action of bending moment and the shear force and the extraction or lap-splice slip of longitudinal steel bars from the fixed-base (or the joint) of the cantilever, taking into account. ( ) ( ) ( ) y b ym y s v y s 1 cm CF 1.50 0.00135 1 3 6 CF ε d f L a z h θ L d d f ϕ ⋅ ⋅ ⋅ + ⋅   ⋅ = + ⋅ + +   ⋅ −   (1) where v a is zero, when the flexural failure precedes the shear failure, and v a is one, when the shear failure precedes the flexural one; z is the length of the internal lever arm, considered equal to 2 d d − in beams and