Civil Engineering Reference
In-Depth Information
500
500
1st level
2nd level
3rd level
1st level
2nd level
3rd level
400
400
300
300
200
200
100
100
0
0
0
50
100
150
200
0
50
100
150
200
Top Lateral Displacement (mm)
Top Lateral Displacement (mm)
Figure 4.43
Storey pushover curves: positive X - direction (
left
) and Y - direction (
right
) of the sample frame in
Figure 4.2 (top displacement at the centre column C3)
stresses
τ
or their combination (equivalent stresses,
σ
eq
) can be determined depending on the system
geometry, discretization adopted and type of applied load. Equivalent stresses can be computed from
3D elasticity (e.g. Chen and Saleeb, 1982). On the other hand, global indicators correspond to internal
actions, e.g. axial forces, bending moments, shear forces and torque, if any. Two bending moments
M
x
and
M
y
, e.g. about principal axes (
x
and
y
) of the member cross sections, and the shear forces,
V
y
and
V
x
, respectively, should be taken into account when performing three-dimensional analyses. In planar
systems, output internal forces include only axial forces
N
, moment (
M
x
or
M
y
) and shear force (
V
y
or
V
x
). In framed structures, bending moments and shears are frequently monitored at each storey level
(referred to as storey moments and shear forces) and at the base (known as base moment and base
shear). These actions result from the contributions of all members at the storey level. Base and storey
shear forces and moments may also be used to detect the occurrence of both local and global LSs pre-
sented in Section 4.7. For example, in the response curve of Figure 4.41, the seismic base shear is
employed to characterize the global yield and the 10% drop in lateral strength. Similarly, the plots of
the storey shear versus top lateral displacement (storey response curves) in Figure 4.43 show that the
formation of a weak storey can be assessed by observing the change of storey shear during the pushover
analysis.
Assuming that lateral force does not increase as the displacement increases, weak storey behaviour
occurs when the capacity curve shows a descending branch as displayed in Figure 4.43 . The ground
storey loses its strength ahead of the second or third storey failure. Therefore, the failure occurs at
ground fl oor. Because failure of ground storey indicates total loss of strength for the whole structure,
monitoring that storey behaviour is, for the sample frame, a critically important measure of limit state
attainment for the entire building.
4.8.2 Deformations
Deformation parameters provide a better indicator of damage of structures subjected to earthquakes
than actions do. Local and global indicators may be used to assess system performance. Normal and
shear strains,
ε
and
γ
respectively, can be obtained only from detailed geometric discretizations of the
structure based on fi bre models, described in Sections 4.5.2 and 4.5.3. Strain values are used to ascertain
the likelihood of local buckling in steel or composite sections and buckling of reinforcement bars in
RC members. For metal plates, it is necessary to determine shear strains
γ
to establish the occurrence
of shear yielding and buckling. Evaluations of normal strains
ε
for section fi bres are essential to monitor
the curvatures in RC, steel and composite framed structures. Normal strains are frequently employed
to determine also the occurrence of LSs, such as steel yield and concrete crushing. For example, the
