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# Earthquakes and buildings

Paper discusses some fundamental questions about the propagation of earthquake disturbances and the origin of additional loads on buildings due to seismic soil movements. Equations for the propagation of di-sequilibrated tangential and normal strains in an infinite elastic body can be immediately deduced from Navier’s equations, which in their turn are based on such general mechanical principles as the momentum theorem and Hooke’s law. The passing of a plane longitudinal wave across a plane boundary from one elastic medium to an another is dealt with quantitatively for the case of normal incidence and it is shown that the amplitude of the passing wave is greater than that of the arriving wave if the second medium is »softer« than the first one. Rayleigh and Love waves are briefly described and their importance for the amount of soil movements in distant places from the epicenter is stressed. It is pointed out that many theoretical assumptions are not fulfilled for earthquake motions and so the above conclusions give only an approximate picture of the process. Attention is drawn to the distinction between the magnitude of the earth-
quake shoch energy and the intensity of soil motion and a comparative table of soil accelerations during earthquakes of different intensities according to some seismic scales is given.
As regards the determination of additional loads on buildings during earthquakes it is stated that the most suitable reference system is that which moves with the earth as a whole. A very simple form of the main seismic displacement of soil is assumed and the differential equation for the movement of a building is derived in the case that it can be replaced by a mass point on a cantilever beam. General solution of the equation is established, but the expression for the amplitude of additional loads is deduced only in the case that the transient component of bending motion can be neglected. General conclusions for the amount of additional loads can be deduced from the above simple considerations. Finally the influence of some factors is discussed, which were not taken into account in theoretical considerations, and some ways are indicated which would yield better approximations for additional loads of buildings during earthquakes.

Paper discusses some fundamental questions about the propagation of earthquake disturbances and the origin of additional loads on buildings due to seismic soil movements. Equations for the propagation of di-sequilibrated tangential and normal strains in an infinite elastic body can be immediately deduced from Navier’s equations, which in their turn are based on such general mechanical principles as the momentum theorem and Hooke’s law. The passing of a plane longitudinal wave across a plane boundary from one elastic medium to an another is dealt with quantitatively for the case of normal incidence and it is shown that the amplitude of the passing wave is greater than that of the arriving wave if the second medium is »softer« than the first one. Rayleigh and Love waves are briefly described and their importance for the amount of soil movements in distant places from the epicenter is stressed. It is pointed out that many theoretical assumptions are not fulfilled for earthquake motions and so the above conclusions give only an approximate picture of the process. Attention is drawn to the distinction between the magnitude of the earth-

quake shoch energy and the intensity of soil motion and a comparative table of soil accelerations during earthquakes of different intensities according to some seismic scales is given.

As regards the determination of additional loads on buildings during earthquakes it is stated that the most suitable reference system is that which moves with the earth as a whole. A very simple form of the main seismic displacement of soil is assumed and the differential equation for the movement of a building is derived in the case that it can be replaced by a mass point on a cantilever beam. General solution of the equation is established, but the expression for the amplitude of additional loads is deduced only in the case that the transient component of bending motion can be neglected. General conclusions for the amount of additional loads can be deduced from the above simple considerations. Finally the influence of some factors is discussed, which were not taken into account in theoretical considerations, and some ways are indicated which would yield better approximations for additional loads of buildings during earthquakes.

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