Base shear of the N storied buildings that first mode of vibration are straight can be calculated by the formula(1)[numerical formula]・・・・・・(1) where W: actual weight of each story, h: mean height of a story, T_N: period of building, θ: deflection angle of building. Base shear coefficient of the equivalent one mass system can be calculated by the formula (2)[numerical formula]・・・・・・(2) The period T_N of the N storied building in relation to the period T_1 of the one storied building are shown by the formula (3)[numerical formula]・・・・・・(3) m is the number that values take from 0 to 1 corresponding to the ratio of the rigidity of upper and lower story of the buildings. To determine the value of m the author takes the condition that the deflection angle θ of the N storied building are equal to θ of the one storied building at the same base shear coefficient. Then the value of m is determined equal to 0.5 and the formula of period are shown by the formula (4)[numerical formula]・・・・・・(4) The formula of base shear coefficient are by the formula (5)[numerical formula]・・・・・・(5)If the buildings have frictions and the damping ratio C/C_C is shown by ν・ν is equal to ξ/E (2π)/T_N and (πν)/2 is equal to ξ/E π^2/T_N that is the energy loss at the quarter cycle of one vibration then the base shear formula must be corrected as formula (6)[numerical formula]・・・・・・(6) To show the actual value of C_N the author assumed that h are from 360cm to 410cm and [numerical formula] are equl to 15. The value of ξ/E where ξ is viscosity coefficient of reinforced concrete are assumed to from 2×10^<-8> to 4×10^<-8> by the measurements in the author's expriments of the reinforced concrete frames builded in the ground. The Fig. 1 shows the relation of C_N, θ and T_1 in the formula (6). The point A in the Fig. 1 (3) shows the [relation θ=2×10^<-4>, T=0.12 and C_N=0.3 and the author had recognized in the several experiments of reinforced concrete wall that the first crack will occur when the deflection angle is equal to 2×10^<-4> and also had proved in the author's paper at the 2nd WCEE that the period of reinforced concrete frames with wall that openning 75% is about 0.12sec. C_N is equal to 0.3 that is nearly equal to the maximun acceration of EL Centre earthquake. The point c in the Fig. 1 (4) shows the relation of θ=2×10^<-8>, T_1=0.4sec and C_N=0.2. The author had recognized that the yielding of reinforced concrete beam and column will begin when deflection angle θ is equal to 2×10^<-8>. By the two limit cases above descrived we can say that [numerical formula] is the upper limit and [numerical formula] is lower limit of period of the N storied buildings. Fig. 2 shows the relation of distributions of observed period of the actual builings in Japan and USA and line a is the lower limit of period and C_N is 0.3, and the line c is the upper limit of period and in the case C_N=0.2. The line b is the average period of N storied building and in the case C_N=0.25. The differences of author's formula in the code in USA are only the determination of value of m in the author's general formula (7) and (8)[numerical formula]・・・・・・(7) [numerical formula]・・・・・・(8) If we take the value of m is equal to 1, [numerical formula]. This formula is inversly proportional to T_N as like as the formula C=0.02/T_N that is San Francisco City Code and if we take the value of m is equal to 0.6 [numerical formula] that is inversly proportional to T_N^<1/3> as like as [numerical formula] that is the Code of Structural Engineers Association of California.
