Structural Concrete - Hassoun

806 Chapter 20 Seismic Design of Reinforced Concrete Structures
For structures for which the 1-s spectral response acceleration, S 1 , is equal to or greater than 0.6 g,
the value of the seismic coefficient, C s , should not be taken less than
C s,min = 0.5S 1
R∕I e
(20.14)
The response modification factor, R, is a function of several factors. Some of them are ductility
capacity and inelastic performance of structural materials and systems during past earthquakes.
Values of R for concrete structures are given in Table 20.7, and are selected by defining the type of
basic seismic force-resisting system for structures (Table 12.2-1 of ASCE 7-10).
Fundamental Period. Elastic fundamental period, T, is a function of the mass and the stiffness of
the structure. If the building is not designed, the period T cannot be precisely determined. On the
other hand, to design a building, the period of vibration should be known, and included in equations
for design. That is why building codes provide equations for calculation of approximate periods of
vibrations, T a . Calculated approximate periods are shorter than the real periods of structure, which
leads to higher base shear values, and as a result safe design.
An approximate period of vibration, T, can be determined using the following equation:
T a = C t h x n (20.15)
where h n is the height in feet above the base to the highest level of the structure, and the coefficients
C t and x are determined from Table 20.8.
For the concrete moment-resisting frame buildings that do not exceed 12 stories in height
and have an average minimum story height of 10 ft, the approximate period of vibration, T, can be
determined using the following equation:
where N is the number of stories in the building above the base.
T a = 0.1N (20.16)
Lateral Seismic Force Calculation. Vertical distribution of the base shear force produces seismic
lateral forces, F x , at any floor level. Seismic lateral forces act at the floor levels because masses of
the structure are concentrated at the floor levels. It is known that the force is a product of mass and
acceleration. Earthquake motions produce accelerations of the structure and induce forces at the
places of mass concentrations (i.e., floor levels).
Table 20.8
Values of Approximate Period Parameters C t
and x(Non-Metric)
Structure Type C t
X
Moment-resisting frame systems in which the frames resist 100% of the
required seismic force and are not enclosed or adjoined by components that
are more rigid and will prevent the frames from deflecting where subjected to
seismic forces:
Steel moment-resisting frames 0.028 0.8
Concrete moment-resisting frames 0.016 0.9
Steel eccentrically braced frames 0.03 0.75
Steel buckling-restrained braced frames 0.03 0.75
All other structural systems 0.02 0.75
Source: ASCE 7-10 Minimum Design Loads for Buildings and Other Structures, 2010. With permission from ASCE.