The seismic response of multistory building and other structural systems is affected by the existence of self strains which may be induced by temperature gradients, mechanical actions, or prestraining. The fundamental dynamic properties such as natural frequencies and mode shapes are influenced by the presence of these strains. As a consequence, the response of the structure changes to the extent that the self strains change its dynamic characteristics and to the extent that these characteristics are relevant in the interaction of a particular structure with a given ground motion.
This paper presents a detailed study of some simple structures such as beams and frames whose members are subjected to initial strains. The homogeneous differential equations of motion are expressed in terms of the stiffness, mass, and geometry matrices and a parameter accounting for the self-strain effect. The solution of the resulting eigenvalue problem is used to write the modal equations into which the desired ground motion is applied.
The final response is obtained from the appropriate shock spectrum and the application of root-mean-square superposition technique. The disturbing action produced by the ground motion of the well known El Centro earthquake of 1940 is applied to several structures in which the amount of self-strain is varied as a parameter.