Scaling Design Values of Combined Response per ASCE 7-16 with ideCAD

How does ideCAD calculate total equivalent base shear according to ASCE 7-16?

If V<V_t for any earthquake direction, all reduced internal force obtained by the modal analysis applied according to 12.9.1, the equivalent base shear force given by Eq. 12.8-1, is automatically increased by multiplying it by V/V_t.

If the combined response for the modal base shear (V_t) is less than C_sW, drifts are multiplied by C_sW∕V_t automatically.

SYMBOLS

V_t = Total equivalent lateral force (base shear force) acting on the entire building at one of earthquake direction
V = Maximum total earthquake load obtained in the x direction with the modal combination method

From a mathematical point of view, Modal analysis is considered a more precise method than Equivalent Lateral Force Method. However, considering the stiffness of the elements of the structural system, uncertainties in their behavior, and the assumptions made in determining the spectrum curve, this method includes approximation. For this reason, the regulation demands that the results determined in the modal superposition method are compared with the results determined in the Equivalent lateral force method and increased where necessary.

According to the logic of the equivalent lateral force method, this coefficient may be higher than 1 in regular and low-rise buildings that can be represented with the first mode, while it is calculated as less than 1, especially in high-rise buildings. This situation comes from the philosophy of modal analysis method in determining dynamic effects by using single degree of freedom equations of motion for multiple modes. Briefly, it is because of the large number of modes taken into account in determining the earthquake behavior of the building. According to the regulation, the magnification factor should be at least 1.

Calculation of Total Equivalent Base Shear

The equivalent base shear Equivalent Lateral Force Method (ELF) per ASCE 7-16 §12.8, is determined according to Eq. 12.8-1.

In this equation, W corresponds to the total mass of the building calculated considering the live load participation ratio.

In the earthquake parameters table of the dynamic analysis report, the values used in the calculation for the relevant direction and the magnification coefficient obtained as a result of the calculation are given. In the Modal Base Shear Forces section of the earthquake regulation report, the base shear forces combined with the base shear force of each mode determined as a result of the modal analysis for each direction are given.

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