The design deformation for an SDOF system can be determined for inelastic design spectrum given the parameters Tn, ρ and µ.
Application of inelastic design spectrum
The design deformation for an SDOF system can be determined
for inelastic design spectrum given the parameters T_{n}, ρ and µ and design yield
where A_{y} is the
pseudo-acceleration of the inelastic response spectrum. Consider an SDOF system
with T_{n} = 1 s, ρ = 5% peak ground acceleration 0.5g. Table 17.7 gives
strength and deflection demands.
There are two properties that
must be considered while designing a structure, strength and ductility. One can
design a very strong structure or a very ductile one or economic combination of
both the properties. If the combination of strength and ductility is inadequate
repairing such a structure is uneconomical or the structure will collapse.
Inelastic deformation
Assume we want to draw a curve
relating S_{a}/g to D for a peak ground
acceleration of 0.5g. The graph shown in Fig. 17.37 is converted to A_{y}
versus D format, resulting in data pairs (A_{y}, D).
Such a diagram is called demand diagram as shown in Fig. 17.38 for
inelastic systems. Along the radial lines the period is constant. Superimposing
on the demand curve, the load
deformation curve i.e. capacity curve for an elasto-plastic SDOF system,
the ductility factor can be obtained from the intersection point of demand and
capacity curves. This point provides the deformation demand.