Civil Engineering Reference
In-Depth Information
30
600
20
400
Tension
10
200
0
0
-0.015
-0.010
-0.005
0
00
0.005
0.010
0.015
-0.014
-0.010
-0.006
-0.002
0.002
0.006
0.010
0.014
-200
-1
Compression
-20
-4
-600
-30
Strain
Strain
Figure 4.44
Time history and hysteretic response of normal strains within RC sections discretized through fi bre
elements in the model frame of Figure 4.2: confi ned concrete (
left
) and steel rebars (
right
)
response history of
ε
depicted in Figure 4.44 for both confi ned concrete and steel rebars can be used
to monitor member yielding and column crushing in RC frames. Similarly, when performing inelastic
static analyses, e.g. pushovers discussed in Section 4.6.2.2, the evaluation of axial strains in reinforcing
steel (
ε
y
) and core concrete fi bres (
ε
cu
) can be utilized to detect the occurrence of yielding and crushing.
In Figure 4.44, member yielding is the LS corresponding to the onset of yielding strain
ε
y
= 0.002 in
reinforcement steel fi bres, while column crushing is attained if the extreme fi bre of core concrete reaches
its crushing strain
ε
cu
= 0.003.
On the other hand, global response deformational parameters, such as inter-storey drifts, may be used
to determine the occurrence of different damage states as discussed in Section 4.7. Widely used values
of inter-storey drifts for the seismic performance assessment of framed structures are given in Table
4.12 . Excessive inter -storey drifts are indicators of structural failure, such as weak storeys. Figure 4.45
shows inter-storey drift response histories computed by Jeong and Elnashai (2005) using inelastic
dynamic analyses for the irregular RC full-scale frame in Figure 4.2 .
The sample structure fails under the September 1986 Kalamata earthquake, for a value of PGA equal
to 0.20 g. The deformed shape of the building, which is also included in the fi gure, confi rms the occur-
rence of the failure by weak storey, at the fi rst fl oor. The latter can also be predicted from the results
of the pushover curves in Figure 4.43 and from the distribution of plastic hinge formation at peak base
shear for the sample frame shown in Figure 4.46. At maximum base shear, all the columns of the fi rst
storey exhibit plastic hinging at both ends.
For ductile multi-storey frames, e.g. with weak-beam strong-column, storey drifts are proportional
to beam rotations, as also discussed in Sections 2.3.3 and 4.7. Shear deformations of beam- to - column
connections signifi cantly contribute to horizontal drifts. Moreover, ductility demand-to-capacity ratios
at member levels should also be checked to prevent brittle failure modes. Therefore, beam, column and
connection rotations should always be monitored, as should axial deformations in diagonal braces.
Flexural curvatures and rotations do not account for shear effects in conventional frame analysis.
When assessing bridges with squat piers, shear effects can be monitored through global response
indicators, such as displacement at the top of piers, which account for the contribution of both shear
and fl exure.
Final Project
The RC building shown in Figure 4.47 (Fardis, 1994) is to be constructed close to an active fault. Table
4.14 provides the dimension of the cross sections of the structural members. The characteristic concrete
strength is 30 N/mm
2
and the characteristic yield strength is 420 N/mm
2
for both longitudinal and
transverse steel.
