3.19 Techniques for Analysing Earthquake Response
119
Therefore, the undamped angular frequency of the system is given by
p =
5.30625 × 10 6
20,663.27
= 16.02 rad/s
Time period is given by
T =
2π
p
=
2π
16.02
= 0.392 s
Based on T = 0.392, ζ = 0.02 and coefficient of seismicity given as 0.4, the
ground acceleration is given by [from Fig. 3.38]
¨
x max = S a = 270 × 0.4 = 108 cm/s
2
From Eq. (3.153), the maximum relative displacement is given by
z max =
S a
p 2 =
108
16.02 × 16.02
= 0.421 cm
Base shear in column (1) = Base shear in column (4)
=
12E I 0
L 3 × z max
=
12 × 2 × 10
11
× 2.7 × 10
− 5
3 3
× 0.421 × 10
−2
= 10,104 N
Base shear in column (2) = Base shear in column (3)
=
3E I 0
L 3 × z max
=
3 × 2 × 10
11
× 2.7 × 10
−5
4 3
× 0.421 × 10
−2
= 1065.66 N
Base moment for column (1) or (4) is
M =
6 × 2 × 10
11
× 2.7 × 10
− 5
9
× 0.421 × 10
− 2
= 15,156 Nm