The method of inertia relief can provide a very inexpensive way of calculating dynamic forces in a structure. In order to perform an inertia relief analysis, an analyst must first select single values to represent the force time histories which are applied to the structure. These forces are then applied to a partially or totally unrestrained structure (i.e., free-free), and the resulting rigid body accelerations are calculated. From these accelerations and the mass of the structure, the inertia forces can be calculated at all points in the structure and then applied along with the original forces. Finally, the structure is restrained from rigid body motion, and a conventional static analysis is performed.
If the periods of the applied loads are much greater than the periods of those modes that would be excited in the structure, this approximate technique is exact. However, should the periods of the loads be close to those of interest in the structure, then the results are not nearly as good.
Several examples are examined to determine the accuracy of the inertia relief method. The dynamic responses of simple series- and parallel-connected spring-mass systems are analyzed and compared with inertia relief calculations. An important conclusion is that for masses connected in series, the error in the inertia relief results increases as one gets farther from the applied load. The final example is a space frame structure composed of welded tubular elements and representing a subcompact vehicle geometry. It is subjected to a load which is similar to that resulting from the 8 km/h (5 mph) bumper impact safety standard.