Issue 74

E. Sharaf et alii, Fracture and Structural Integrity, 74 (2025) 262-293; DOI: 10.3221/IGF-ESIS.74.17

upper floors have a negligible impact on determining the lateral stiffness, allowing for a simplified analysis focused primarily on the lower floors. This assumption helps streamline calculations while maintaining reasonable accuracy for structural behavior under lateral loads. It becomes clear that the previous equation for K eq , expressed in terms of the properties and behaviors of the first two stories, can be generalized for multi-story structures with high accuracy.

Figure 4: The simplification of a multi-storey frame into an SDOF.

Equivalent seismic mass of the multi-storey buildings Equivalent seismic mass is a simplified representation of how each floor's weight contributes to the building's overall seismic response. It considers the distribution of mass and how it affects the structure's dynamic behavior during an earthquake. The sequence of the method is as illustrated in Fig. 5, where the following building consists of three floors. Two iterations are performed to obtain an equivalent mass concentrated at the level of the first floor. The first iteration involves shifting the mass of the third floor to the level of the second floor to obtain m eq1 . Then, the mass obtained from the previous iteration, m eq1 , is shifted to the level of the first floor to calculate m eq2 , resulting in a single equivalent mass at the first-floor level.

Figure 5: Procedures for obtaining equivalent seismic mass.

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