# Failure Analysis of a Concrete Anchor under Severe Seismic Action
## 2 Response Modification and Overstrength Factors  
The earthquake responses of structures tend to be greatly reduced by attenuation caused by plastic behavior and/or friction. For modeling, a response correction factor (\(R\)) is used. If structural manipulation is expected to significantly reduce any effect of interest, the seismic force can be lowered using that factor. In line with [PERSON]'s law, the maximum inertial force is obtained by multiplying the maximum acceleration by the mass. In Equation (1), \(A\) is the acceleration [usually expressed as the effective peak acceleration (EPA, \(S\)) during design] divided by the gravitational acceleration \(g\). The earthquake hazard map of Korea shows the maximum ground acceleration equivalent to 10% of the excess probability over 100, 250, and 500 years as equidistant lines. These periods and overprobabilities reflect return periods of 1000, 2400, and 4800 years, respectively. DS-0050 [1] determines the zonal factors for earthquakes with return periods of approximately 2400 or 4800 years, applicable to existing and new 765-kV power transmission and distribution facilities; the goal is to prevent collapse. It is often assumed that the PGA expected in the zone is the zonal factor, but this is incorrect. The zonal factor \(z\) is usually determined by the EPA; the acceleration responses of short-cycle (\(S_{DS}\)) structures affected by earthquakes are divided by 2.5 (Equation (1)). \[F_{E}=\frac{A\cdot W}{R}=\left(\frac{\alpha_{p}\alpha_{h}zI/R}{g}\right)\cdot W= \left(\frac{\alpha_{p}\alpha_{h}\left(0.4S_{DS}=\frac{S_{DS}}{2.5}\right)I}{g} \right)\cdot\frac{W}{R}=\left(\frac{\alpha_{p}\alpha_{h}S}{g}\right)\cdot\frac {W}{R} \tag{1}\]  
where \(\alpha_{p}\) and \(\alpha_{h}\) are the component and height amplification factors, respectively and \(S\) is the effective ground acceleration in the form of \(0.4S_{DS}I\). Flexible or high-rise structures with long oscillation cycles are likely to undergo large displacements and be greatly affected by the \(P-\Delta\) effect. The base shear force is the total seismic load acting on the bottom part of the structure when that load is converted into an equivalent static load; it is calculated using Equation (2), where \(F_{E}(=V)\) is the base shear force and \(C_{s}\) is a dynamic factor as illustrated in Figure 1.  
\[F_{E}=\alpha C_{s}\cdot W \tag{2}\]  
If a structure is elastic and subjected to a very large earthquake load, there will be no structural damage. If a structure is inelastic (achieved by lowering the yield strength), the seismic load will also be low because significant plastic deformation will occur; this is likely to cause structural damage. If the yield strength of the structure induces inelastic behavior and the plastic performance prevents major structural damage, the structure can resist earthquakes and the economic burden is minimized. Against this background, the seismic design of structures aims to reduce the yield strength and thus render the structure resistant to earthquakes using structural elements that can withstand plastic deformation. The inelastic energy absorption coefficient \(R_{\mu}\) (ASCE 43-05 [7]) and ductility \(\mu\) are widely used to represent the inelastic response of a structure with elastic behavior (Equation (3)). \(F_{E}\) and \(F_{y}\) are the elastic and yield forces, and \(u_{m}\) and \(u_{y}\) the maximum and yield displacements of the structure, respectively. \[R_{\mu}=\frac{F_{E}}{F_{y}}\,,\ \mu=\frac{u_{m}}{u_{y}} \tag{3}\]  
A reduction of the structural yield strength \(F_{y}\) to a value lower than the elastic seismic load \(F_{E}\) allows the structure to engage in plastic behavior, although this behavior is not as expected because the structure exhibits overstrength. Therefore, to induce the expected behavior, the design strength \(F_{d}\) must be further reduced by imparting structural overstrength. The base shear force that a structure can resist is usually greater than the design base shear force (the yield base shear force \(F_{y}\)).