The friction dampers are designed not to slip during wind. During a major earthquake, they slip prior to yielding of structural members. In general, the lower bound is about 130% of wind shear and the upper bound is 75% of the shear at which the members will yield. As seen in the diagram for Response versus Slip Load, if the slip load is very low or very high, the response is very high.

Several parametric studies have shown that the slip load of the friction damper is the principal variable with the appropriate selection of which it is possible to tune the response of structure to an optimum value. Optimum slip load gives minimum response. Selection of slip load should also ensure that after an earthquake, the building returns to its near original alignment under the spring action of an elastic structure. Studies have also shown that variations up to ±25% of the optimum slip load do not affect the response significantly. Therefore, small variations in slip load (8-10%) over life of the building do not warrant any adjustments or replacement of friction damper.

The quasi-static design procedure given in most building codes are ductility based and do not explicitly apply to buildings with supplemental damping. In the past few years, several guidelines on the analysis and design procedure of passive energy dissipation devices have been developed in the U.S. The latest and most comprehensive document is the "NEHRP Guidelines for the Seismic Rehabilitation of Buildings, FEMA 356 / 357, issued in 2000".

The Guidelines require that the structure be evaluated for response to two levels of ground shaking - a design basis earthquake (DBE) and a maximum considered earthquake (MCE). The DBE is an event with 10% probability of exceedance in 50 years, while the MCE represents a severe ground motion of probability of 2% in 50 years. Under the DBE, the structure is evaluated to ensure that the strength demands on structural elements do not exceed their capacities and that the drift in the structure is within the acceptable limits. For the MCE, the structure is evaluated to determine the maximum displacement and overstress. It is presumed that if proper ductile detailing has been followed, the structure will have sufficient reserve to avoid collapse during MCE.

Since different earthquake records, even of the same intensity, give widely varying structural responses, results obtained using a single record may not be conclusive. Therefore, three time-history records, suitable for the region should be used, one of which should be preferably site specific. The maximum response is used for the design.

NEHRP guidelines require that friction dampers are designed for 130% MCE displacements and all bracing and connections are designed for 130% of damper slip load. Variation in slip load from design value should not be more that ± 15%.

Non-linear Time- History Dynamic Analysis

The movement of damper in an elastic brace constitutes non-linearity. Also, the amount of energy dissipation or equivalent structural damping is proportional to the displacement. Therefore, non-linear time-history dynamic analysis is a more accurate procedure for the design of buildings with damping devices. With these analyses, the time-history response of the structure during and after an earthquake can be accurately understood.

The modeling of friction dampers is very simple. Since the hysteresis loop of the damper is similar to the rectangular loop of an ideal elasto-plastic material, the slip load of the friction damper can be considered as a fictitious yield force.