46
2 Single Degree of Freedom (SDOF) Systems
Fig. 2.17 El Centro response spectrum for ζ = 0, 2, 5, and 10%. Note that the bottom and top
spectral values are for ζ = 10% and ζ = 0%
Example 2.17 Consider a portal frame with span and height l = 24 ft and h = 12 ft,
square columns and beam with sides 10 in, and weight w = 10 kips. The frame is
modeled as a SDOF system with stiffness k = 96 E I/
7 h 3 = 11.48 kips/in and
natural period T = 2 π
√
m/k = 0.3 s, where E = 3 × 10 3 ksi is the modulus of
elasticity, I denotes the moment of inertia of the beam and columns, and m = w/g
is the mass. Suppose the frame damping ratio is ζ = 5%.
The frame is subjected to the El Centro seismic ground acceleration. The
maximum displacement of the frame and the maximum seismic force acting on
it result directly from the response spectrum developed for this seismic event
which is shown in Fig. 2.17. The maximum deformation of the frame during this
seismic event can be read directly from this response spectrum; it is approximately
0.67 in. The maximum pseudo-acceleration can also be read from this figure; it
is approximately 0.76 g. The corresponding seismic force can be obtained by
multiplication with the frame mass. Note that the bottom and top spectral values
are for ζ = 10% and ζ = 0%.
2 Single Degree of Freedom (SDOF) Systems
Fig. 2.17 El Centro response spectrum for ζ = 0, 2, 5, and 10%. Note that the bottom and top
spectral values are for ζ = 10% and ζ = 0%
Example 2.17 Consider a portal frame with span and height l = 24 ft and h = 12 ft,
square columns and beam with sides 10 in, and weight w = 10 kips. The frame is
modeled as a SDOF system with stiffness k = 96 E I/
7 h 3 = 11.48 kips/in and
natural period T = 2 π
√
m/k = 0.3 s, where E = 3 × 10 3 ksi is the modulus of
elasticity, I denotes the moment of inertia of the beam and columns, and m = w/g
is the mass. Suppose the frame damping ratio is ζ = 5%.
The frame is subjected to the El Centro seismic ground acceleration. The
maximum displacement of the frame and the maximum seismic force acting on
it result directly from the response spectrum developed for this seismic event
which is shown in Fig. 2.17. The maximum deformation of the frame during this
seismic event can be read directly from this response spectrum; it is approximately
0.67 in. The maximum pseudo-acceleration can also be read from this figure; it
is approximately 0.76 g. The corresponding seismic force can be obtained by
multiplication with the frame mass. Note that the bottom and top spectral values
are for ζ = 10% and ζ = 0%.